A Case Study of Two Groups of Elementary Prospective Teachers' Experiences in Distinct Mathematics Content Courses

ERIC Educational Resources Information Center

Auslander, Susan Swars; Smith, Stephanie Z.; Smith, Marvin E.; Hart, Lynn C.; Carothers, Jody

2016-01-01

This multiple case study examined two groups of elementary prospective teachers (n=12) completing distinct mathematics content courses. Data were collected via two belief surveys, one content knowledge assessment, and individual interviews. The findings revealed differences in specialized content knowledge and mathematical beliefs between the two…

Examining Prospective Mathematics Teachers' Pedagogical Content Knowledge on Fractions in Terms of Students' Mistakes

ERIC Educational Resources Information Center

Sahin, Ömer; Gökkurt, Burçin; Soylu, Yasin

2016-01-01

The aim of the study is to examine prospective mathematics teachers' pedagogical content knowledge in terms of knowledge of understanding students and knowledge of instructional strategies which are the subcomponents of pedagogical content knowledge. The participants of this research consist of 98 prospective teachers who are studying in two…

Elementary Teachers' Mathematical Knowledge for Teaching Prerequisite Algebra Concepts

ERIC Educational Resources Information Center

Welder, Rachael M.; Simonsen, Linda M.

2011-01-01

The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

Characterizing the Development of Specialized Mathematical Content Knowledge for Teaching in Algebraic Reasoning and Number Theory

ERIC Educational Resources Information Center

Bair, Sherry L.; Rich, Beverly S.

2011-01-01

This article characterizes the development of a deep and connected body of mathematical knowledge categorized by Ball and Bass' (2003b) model of Mathematical Knowledge for Teaching (MKT), as Specialized Content Knowledge for Teaching (SCK) in algebraic reasoning and number sense. The research employed multiple cases across three years from two…

About the Complexities of Video-Based Assessments: Theoretical and Methodological Approaches to Overcoming Shortcomings of Research on Teachers' Competence

ERIC Educational Resources Information Center

Kaiser, Gabriele; Busse, Andreas; Hoth, Jessica; König, Johannes; Blömeke, Sigrid

2015-01-01

Research on the evaluation of the professional knowledge of mathematics teachers (comprising for example mathematical content knowledge, mathematics pedagogical content knowledge and general pedagogical knowledge) has become prominent in the last decade; however, the development of video-based assessment approaches is a more recent topic. This…

Assessing Strengths and Weaknesses of Teacher Knowledge in Asia, Eastern Europe, and Western Countries: Differential Item Functioning in TEDS-M

ERIC Educational Resources Information Center

Blömeke, Sigrid; Suhl, Ute; Döhrmann, Martina

2013-01-01

The "Teacher Education and Development Study in Mathematics" assessed the knowledge of primary and lower-secondary teachers at the end of their training. The large-scale assessment represented the common denominator of what constitutes mathematics content knowledge and mathematics pedagogical content knowledge in the 16 participating…

The Acquisition of Mathematics Pedagogical Content Knowledge in University Mathematics Education Courses: Results of a Mixed Methods Study on the Effectiveness of Teacher Education in Germany

ERIC Educational Resources Information Center

Buchholtz, Nils Frederik

2017-01-01

This paper reports on a longitudinal mixed methods evaluation study on the acquisition and development of mathematical pedagogical content knowledge (MPCK) of future teachers at several German universities. The study is a German supplementary study to the international comparative TEDS-M 2008 study. Besides the pedagogical content knowledge that…

An Exploration of the Common Content Knowledge of High School Mathematics Teachers

ERIC Educational Resources Information Center

Bansilal, Sarah; Brijlall, Deonarain; Mkhwanazi, Thokozani

2014-01-01

Many studies point to the problem of poor mathematics content knowledge of mathematics teachers in South Africa. The purpose of this study was to investigate teachers' knowledge of the mathematics they are themselves teaching. Data was generated from the teachers' (n = 253) written responses to test that was a shortened form of a previous Grade 12…

Examining Mathematics Teacher Content Knowledge: Policy and Practice

ERIC Educational Resources Information Center

Esprivalo Harrell, Pamela; Eddy, Colleen McLean

2012-01-01

This study examines mathematics teacher content knowledge in terms of state and national policymaker recommendations, college coursework and the Mathematics Texas Examination of Educator Standards (TExES) score. Results indicate differences between state and national policy recommendations and college degrees in mathematics. A statistically…

Secondary Teachers’ Mathematics-related Beliefs and Knowledge about Mathematical Problem-solving

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E Siswono, T. Y.; Kohar, A. W.; Hartono, S.

2017-02-01

This study investigates secondary teachers’ belief about the three mathematics-related beliefs, i.e. nature of mathematics, teaching mathematics, learning mathematics, and knowledge about mathematical problem solving. Data were gathered through a set of task-based semi-structured interviews of three selected teachers with different philosophical views of teaching mathematics, i.e. instrumental, platonist, and problem solving. Those teachers were selected from an interview using a belief-related task from purposively selected teachers in Surabaya and Sidoarjo. While the interviews about knowledge examine teachers’ problem solving content and pedagogical knowledge, the interviews about beliefs examine their views on several cases extracted from each of such mathematics-related beliefs. Analysis included the categorization and comparison on each of beliefs and knowledge as well as their interaction. Results indicate that all the teachers did not show a high consistency in responding views of their mathematics-related beliefs, while they showed weaknesses primarily on problem solving content knowledge. Findings also point out that teachers’ beliefs have a strong relationship with teachers’ knowledge about problem solving. In particular, the instrumental teacher’s beliefs were consistent with his insufficient knowledge about problem-solving, while both platonist and problem-solving teacher’s beliefs were consistent with their sufficient knowledge of either content or pedagogical problem solving.

Technological Pedagogical Content Knowledge of Secondary Mathematics Teachers

ERIC Educational Resources Information Center

Handal, Boris; Campbell, Chris; Cavanagh, Michael; Petocz, Peter; Kelly, Nick

2013-01-01

The integration of technology, pedagogy, and content in the teaching of secondary mathematics was explored among 280 secondary mathematics teachers in the State of New South Wales, Australia. The study adopted the technological pedagogical content knowledge (TPCK) model through the administration of a 30-item instrument called TPCK-M. The…

Comparing the Major Definitions of Mathematics Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Johnson, Jeffrey

2017-01-01

The purpose of this research was to compare two definitions and assessments of Mathematics Pedagogical Content Knowledge (PCK). As part of a larger study, nine current and future teachers took an online version of the Measures of Knowledge for Teaching (MKT)--Mathematics assessment and the Cognitively Activating Instruction in Mathematics…

The Relationship Between Teachers' Mathematical Content and Pedagogical Knowledge, Teachers' Perceptions, and Student Achievement

ERIC Educational Resources Information Center

Campbell, Patricia F.; Nishio, Masako; Smith, Toni M.; Clark, Lawrence M.; Conant, Darcy L.; Rust, Amber H.; DePiper, Jill Neumayer; Frank, Toya Jones; Griffin, Matthew J.; Choi, Youyoung

2014-01-01

This study of early-career teachers identified a significant relationship between upper-elementary teachers' mathematical content knowledge and their students' mathematics achievement, after controlling for student- and teacher-level characteristics. Findings provide evidence of the relevance of teacher knowledge and perceptions for teacher…

Secondary Pre-Service Teachers' Content Knowledge for State Assessments: Implications for Mathematics Education Programs

ERIC Educational Resources Information Center

Wilburne, Jane M.; Long, Michael

2010-01-01

Seventy secondary mathematics pre-service teachers from two universities were assessed on their content knowledge, vocabulary knowledge, and their perceived confidence in teaching the content addressed on the eleventh grade state assessment. The results indicate the pre-service teachers had significant content weakness in data analysis, algebra,…

Examination of Lower Secondary Mathematics Teachers' Content Knowledge and Its Connection to Students' Performance

ERIC Educational Resources Information Center

Tchoshanov, Mourat; Cruz, Maria D.; Huereca, Karla; Shakirova, Kadriya; Shakirova, Liliana; Ibragimova, Elena N.

2017-01-01

This mixed methods study examined an association between cognitive types of teachers' mathematical content knowledge and students' performance in lower secondary schools (grades 5 through 9). Teachers (N = 90) completed the Teacher Content Knowledge Survey (TCKS), which consisted of items measuring different cognitive types of teacher knowledge.…

On Singapore Prospective Secondary School Teachers' Mathematical Content Knowledge

ERIC Educational Resources Information Center

Toh, Tin Lam

2017-01-01

This paper reports the performance of one entire cohort of Singapore prospective secondary school mathematics teachers in a mathematics proficiency test. The prospective teachers were admitted to the teacher education program specializing in teaching secondary school mathematics. The strengths of the prospective teachers' content knowledge, their…

Adapting Technological Pedagogical Content Knowledge Framework to Teach Mathematics

ERIC Educational Resources Information Center

Getenet, Seyum Tekeher

2017-01-01

The technological pedagogical content knowledge framework is increasingly in use by educational technology researcher as a generic description of the knowledge requirements for teachers using technology in all subjects. This study describes the development of a mathematics specific variety of the technological pedagogical content knowledge…

Primary Mathematics Teacher Education Encountering Difficult Terrain: A Personal Perspective

ERIC Educational Resources Information Center

Norton, Stephen

2016-01-01

This paper is a case study in preparing prospective primary teachers to teach mathematics at one Australian university. The paper describes the content knowledge of prospective teachers, pre and post a final mathematics curriculum subject. The teaching approach which attempts to account for both content and pedagogical content knowledge is…

An Investigation of Relationships between Students' Mathematical Problem-Posing Abilities and Their Mathematical Content Knowledge

ERIC Educational Resources Information Center

Van Harpen, Xianwei Y.; Presmeg, Norma C.

2013-01-01

The importance of students' problem-posing abilities in mathematics has been emphasized in the K-12 curricula in the USA and China. There are claims that problem-posing activities are helpful in developing creative approaches to mathematics. At the same time, there are also claims that students' mathematical content knowledge could be highly…

First Year Pre-Service Teachers' Mathematical Content Knowledge: Methods of Solution for a Ratio Question

ERIC Educational Resources Information Center

Livy, Sharyn; Vale, Colleen

2011-01-01

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

On the Content-Dependence of Prospective Teachers' Knowledge: A Case of Exemplifying Definitions

ERIC Educational Resources Information Center

Leikin, Roza; Zazkis, Rina

2010-01-01

In this article, we demonstrate that prospective teachers' content knowledge related to defining mathematical concepts is dependent on content area. We use the example of generation (a research tool we developed in a previous study) to investigate prospective teachers' knowledge. We asked prospective secondary mathematics teachers to provide…

Improving Instructional Leadership through the Development of Leadership Content Knowledge: The Case of Principal Learning in Algebra

ERIC Educational Resources Information Center

Steele, Michael D.; Johnson, Kate R.; Otten, Samuel; Herbel-Eisenmann, Beth A.; Carver, Cynthia L.

2015-01-01

Instructional leadership is integral to improving mathematics teaching in secondary schools. However, administrators often lack sufficient content knowledge in mathematics to be effective in this role. This study examined the impact of professional development focused on developing leadership content knowledge in algebra. Data included written…

Theorising about Mathematics Teachers' Professional Knowledge: The Content, Form, Nature, and Course of Teachers' Knowledge

ERIC Educational Resources Information Center

Scheiner, Thorsten

2015-01-01

The guiding philosophy of this theoretical work lays in the argument that mathematics teachers' professional knowledge is the integration of various knowledge facets derived from different sources including teaching experience and research. This paper goes beyond past trends identifying what the teachers' knowledge is about (content) by providing…

Singapore Pre-Service Secondary Mathematics Teachers' Content Knowledge: Findings from an International Comparative Study

ERIC Educational Resources Information Center

Toh, Tin Lam; Kaur, Berinderjeet; Koay, Phong Lee

2013-01-01

In this article, we explore the mathematical content knowledge of one entire cohort of pre-service teachers (N = 107) through analysing their performance in a Secondary Mathematics Audit that was developed for the International Comparative Studies in Mathematics Teacher Training that was initiated by the University of Plymouth. We study how their…

Processes and Pathways: How Do Mathematics and Science Partnerships Measure and Promote Growth in Teacher Content Knowledge?

ERIC Educational Resources Information Center

Moyer-Packenham, Patricia S.; Westenskow, Arla

2012-01-01

Intense focus on student achievement results in mathematics and science has brought about claims that K-12 teachers should be better prepared to teach basic concepts in these disciplines. The focus on teachers' mathematics and science content knowledge has been met by efforts to increase teacher knowledge through funded national initiatives…

Behavioural Intention and Pre-Service Mathematics Teachers' Technological Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Gonzalez, Maria Jose; González-Ruiz, Ignacio

2017-01-01

Teachers' beliefs, together with sound technological pedagogical content knowledge (TPACK), are directly related to the effective integration of technology in mathematics teaching. This study explored the relationship between pre-service teachers' behavioural intention to use technology to teach mathematics and their TPACK. A case-study analysis…

Foundation Content Knowledge: Pre-Service Teachers as Half-Empty or Becoming Fluent?

ERIC Educational Resources Information Center

Anakin, Megan; Linsell, Chris

2014-01-01

The concept of a growth-oriented disposition framed the analysis of theoretical and practical dimensions of pre-service teachers' mathematics content knowledge. We identify historical hangovers, tacit habits, and pedagogical strangleholds that present challenges to the way mathematics education researchers interact with the mathematics content…

Opportunities to Promote Mathematical Content Knowledge for Primary Teaching

ERIC Educational Resources Information Center

Livy, Sharyn; Herbert, Sandra

2014-01-01

Understanding the development of pre-service teachers' mathematical content knowledge (MCK) is important for improving primary mathematics' teacher education. This paper reports on a case study, Rose and her opportunities to develop MCK during the four years of her program. Program opportunities to promote MCK when planning and practicing primary…

Content Knowledge, Attitudes, and Self-Efficacy in the Mathematics New York City Teaching Fellows (NYCTF) Program

ERIC Educational Resources Information Center

Evans, Brian R.

2011-01-01

The purpose of this study was to understand the mathematical content knowledge new teachers have both before and after taking a mathematics methods course in the NYCTF program. Further, the purpose was to understand the attitudes toward mathematics and concepts of self-efficacy that Teaching Fellows had over the course of the semester. The sample…

Pre-Service Elementary Teachers' Mathematics Content Knowledge: A Predictor of Sixth Graders' Mathematics Performance

ERIC Educational Resources Information Center

Shirvani, Hosin

2015-01-01

This study examined the knowledge of mathematics content of elementary pre-service teachers at a sixth grade level. The researcher administered a mathematics test for sixth graders mandated by the Texas Education Agency to pre-service teachers; the same test was given to sixth graders in Texas. The study found that pre-service teachers performed…

Gender Difference in Teachers' Mathematical Knowledge for Teaching in the Context of Single-Sex Classrooms

ERIC Educational Resources Information Center

Haroun, Ramzi F.; Ng, Dicky; Abdelfattah, Faisal A.; AlSalouli, Misfer S.

2016-01-01

This study examines gender differences of teachers on their mathematical knowledge for teaching in the context of single-sex classrooms in Saudi Arabia. A translated version of the Mathematical Knowledge for Teaching (MKT) instrument (Learning Mathematics for Teaching [LMT], 2008) in Number and Operation Content Knowledge (CK) and Knowledge of…

Can Pedagogical Concerns Eclipse Mathematical Knowledge?

ERIC Educational Resources Information Center

Creager, Mark A.; Jacobson, Erik; Aydeniz, Fetiye

2016-01-01

Mathematical knowledge for teaching (MKT) is often thought of as a transformed, mutually-influencing mixture of content and pedagogy. However when individuals' MKT does not integrate content and pedagogy, one type of knowledge can supersede the other, sometimes unconsciously. We exemplify this with Emma, a prospective elementary teacher, whose…

Teachers' Understanding of Mathematical Cognition in Childhood: Towards a Shift in Pedagogical Content Knowledge?

ERIC Educational Resources Information Center

Henning, Elizabeth

2013-01-01

This article about the discourse of pedagogy as related to child cognition in mathematics addresses the issue of what constitutes the main disciplinary content and the pedagogical content knowledge (PCK) of foundation-phase teachers. I argue that, unless child cognition itself is the primary disciplinary content of foundation-phase teacher's…

Early Predictors of High School Mathematics Achievement

ERIC Educational Resources Information Center

Siegler, Robert S.; Duncan, Greg J.; Davis-Kean, Pamela E.; Duckworth, Kathryn; Claessens, Amy; Engel, Mimi; Susperreguy, Maria Ines; Meichu, Chen

2012-01-01

Identifying the types of mathematics content knowledge that are most predictive of students' long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students' knowledge of algebra and overall mathematics…

Measuring Mathematics Teacher Educators' Knowledge of Technology Integrated Teaching: Instrument Development

ERIC Educational Resources Information Center

Getenet, Seyum Tekeher; Beswick, Kim

2013-01-01

This study describes the construction of a questionnaire instrument to measure mathematics teacher educators' knowledge for technology integrated mathematics teaching. The study was founded on a reconceptualisation of the generic Technological Pedagogical Content Knowledge framework in the specific context of mathematics teaching. Steps in the…

Epistemological Beliefs of Prospective Preschool Teachers and Their Relation to Knowledge, Perception, and Planning Abilities in the Field of Mathematics: A Process Model

ERIC Educational Resources Information Center

Dunekacke, Simone; Jenßen, Lars; Eilerts, Katja; Blömeke, Sigrid

2016-01-01

Teacher competence is a multi-dimensional construct that includes beliefs as well as knowledge. The present study investigated the structure of prospective preschool teachers' mathematics-related beliefs and their relation to content knowledge and pedagogical content knowledge. In addition, prospective preschool teachers' perception and planning…

Preservice Mathematics Teachers' Views on Distance Education and Their Web Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Cagirgan Gulten, Dilek

2013-01-01

This research aims to investigate primary preservice mathematics teachers' views on distance education and web pedagogical content knowledge in terms of the subscales of general web, communicative web, pedagogical web, web pedagogical content and attitude towards web based instruction. The research was conducted with 46 senior students in the…

Middle School Mathematics Teachers' Pedagogical Content Knowledge Regarding Teaching Strategies on Quadrilaterals

ERIC Educational Resources Information Center

Akkas, Elif Nur; Türnüklü, Elif

2014-01-01

Pedagogical content knowledge is consisted of two components: student knowledge and teaching strategies. Teaching strategies was defined under two sub-headings as strategies for specific topics and specific strategies for any topic. The purpose of this study was to examine the method with which quadrilaterals were taught by mathematics teachers…

Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop (March 19-21, 1999).

ERIC Educational Resources Information Center

National Academy of Sciences - National Research Council, Washington, DC. Mathematical Sciences Education Board.

The Mathematics Teacher Preparation Content Workshop, held March 19-21, 1999, focused on two questions: (1) What is the mathematical knowledge teachers need to know in order to teach well? and (2) How can teachers develop the mathematical knowledge they need to teach well? Chapters include: (1) "Knowledge of Fundamental Mathematics for Teaching"…

The Effect of Teacher Education Programs on Future Elementary Mathematics Teachers' Knowledge: A Five-Country Analysis Using TEDS-M Data

ERIC Educational Resources Information Center

Qian, Hong; Youngs, Peter

2016-01-01

This article addresses the problem of how opportunities to learn in teacher education programs influence future elementary mathematics teachers' knowledge. This study used data collected for the Teacher Education and Development Study in Mathematics (TEDS-M). TEDS-M measured the mathematics content knowledge (MCK) and the mathematics pedagogical…

Measuring and factors influencing mathematics teachers' technological pedagogical and content knowledge (TPACK) in three southernmost provinces, Thailand

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Adulyasas, Lilla

2017-08-01

Technology becomes an important role in teaching and learning mathematics nowadays. Integrating technology in the classroom helps students have better understanding in many of mathematics concepts. One of the major framework for assessing the knowledge of integrating technology with the pedagogy and content in the classroom is Technological Pedagogical and Content Knowledge (TPACK) framework. This study aimed to measure mathematics teachers' TPACK in three southernmost provinces, Thailand and to study on factors influencing their TPACK. A quantitative study was carried out with 210 secondary level mathematics teachers in the three southernmost provinces, Thailand which were random by two stage sampling technique. Data were collected by using a questionnaire to identify the level of mathematics teachers' TPACK and the factors influencing their TPACK. Descriptive statistics, Pearson product moment correlation and multiple regression analysis were used for analysing data. Findings reveal that the mean score of mathematics teachers' TPACK is 3.33 which is in the medium level and the three factors which have positive correlation at .05 level of significant with the level of TPACK are teaching experience factor, individual specialization factor and personal & organization factor. However, there are only two factors influencing mathematics teachers' TPACK. The two factors are individual specialization factor and personal & organization factors. These give better understanding on mathematics teachers' knowledge in integrating technology with the pedagogy and content which will be the important information for improving mathematics teachers' TPACK.

Tell Me Why! Content Knowledge Predicts Process-Orientation of Math Researchers' and Math Teachers' Explanations

ERIC Educational Resources Information Center

Lachner, Andreas; Nückles, Matthias

2016-01-01

In two studies, we investigated the impact of instructors' different knowledge bases on the quality of their instructional explanations. In Study 1, we asked 20 mathematics teachers (with high pedagogical content knowledge, but lower content knowledge) and 15 mathematicians (with lower pedagogical content knowledge, but high content knowledge) to…

Teacher Self-Efficacy, Content and Pedagogical Knowledge, and Their Relationship to Student Achievement in Algebra I

ERIC Educational Resources Information Center

Fox, Antonia M.

2014-01-01

The purpose of this quantitative study was to explore the relationship between teacher self-efficacy beliefs and the level of student achievement their students obtain as evidenced by the Algebra I Virginia Standards of Learning (SOL) assessment. This study also explored teachers' mathematics content knowledge, mathematics pedagogical knowledge,…

Provoking Contingent Moments: Knowledge for "Powerful Teaching" at the Horizon

ERIC Educational Resources Information Center

Hurst, Chris

2017-01-01

Background: Teacher knowledge continues to be a topic of debate in Australasia and in other parts of the world. There have been many attempts by mathematics educators and researchers to define the knowledge needed by teachers to teach mathematics effectively. A plethora of terms, such as mathematical content knowledge, pedagogical content…

Increasing Your Mathematics and Science Content Knowledge.

ERIC Educational Resources Information Center

Thorson, Annette, Ed.

2002-01-01

This journal is intended for classroom teachers and provides a collection of essays and instructional materials organized around the theme of mathematics and science content knowledge. Articles include: (1) "Watching Ourselves Learn" (Annette Thorson); (2) "Search Smarter!" (Kimberly S. Roempler); (3) "Teacher Education Materials Project" (Joan…

Exploring Mathematics Teachers' Pedagogical Content Knowledge in the Context of Knowledge of Students

ERIC Educational Resources Information Center

Aksu, Zeki; Kul, Ümit

2016-01-01

Functions are one of the basic topics taught in mathematics curriculum at Secondary school level requiring knowledge from the students' past, and uniting mathematical topics. Mathematics teachers have both their own learning experience of functions, as well as their own teaching experience, leading to the question of what level of student…

Deepening Pre-Service Teachers' Knowledge of Technology, Pedagogy, and Content (TPACK) in an Elementary School Mathematics Methods Course

ERIC Educational Resources Information Center

Polly, Drew

2014-01-01

This paper presents the findings of a study that examined pre-service teachers' development of knowledge about technology, pedagogy and content (TPACK) during a mathematics pedagogy course focused on elementary school mathematics in the United States. Data sources included work samples from pre-service teachers as well as an open-ended survey…

An Exploration of the Relevance of the Pedagogy and Academic Content Knowledge That Are Offered to Prospective Science and Mathematics Teachers in Tanzania Teachers' Colleges

ERIC Educational Resources Information Center

Mungure, Daudi Mika

2016-01-01

This paper explored the Relevance of the Pedagogy and Academic Content Knowledge that are offered to Prospective Science and Mathematics Teachers in Tanzania Teachers' colleges. Morogoro Teachers' College and Kleruu Teachers' college were used as a case study. The performance in science and mathematics subjects in form four National examinations…

Pedagogical Content Knowledge: Teacher’s Knowledge of Students in Learning Mathematics on Limit of Function Subject

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Ma'rufi; Ketut Budayasa, I.; Juniati, Dwi

2018-01-01

This research aims at describing the profile of high school teacher’s Pedagogical Content Knowledge in learning mathematics from the perspective of teaching experience. Pedagogical Content Knowledge (PCK) covers teacher’s knowledge of subject matter, knowledge of pedagogy, and knowledge of students. The subject of this research was two high school mathematics teachers who have different teaching experience. The data were obtained through interview and observation then analyzed qualitatively. The focus of this research is the novice teacher’s PCK deals with knowledge of students. Knowledge of Student is defined as teacher’s knowledge about the students’ conception and misconception on limit of function material and teacher’s ability to cope with students’ difficulty, mistake, and misconception. The result of this research shows that novice teacher’s ability in analyzing the cause of students’ difficulty, mistake, and misconception was limited. Novice teacher tended to overcome the students’ difficulty, mistake, and misconception by re-explaining the procedure of question completion which is not understood by the students.

Deepening Pre-Service Secondary Teachers' Mathematical Content Knowledge through Engaging with Peers' Mathematical Contributions

ERIC Educational Resources Information Center

Pournara, C.

2016-01-01

Depth and rigour in mathematical knowledge for pre-service secondary school mathematics teachers may be found in particular experiences of learning and doing school-level mathematics. Drawing on two cases from a course on financial mathematics for secondary school teachers, I illustrate opportunities for exploring compound and exponential growth.…

Investigating the Relevance and Importance of Mathematical Content Knowledge Areas for Beginning Elementary School Teachers. Research Memorandum No. RM-16-10

ERIC Educational Resources Information Center

Martin-Raugh, Michelle P.; Reese, Clyde M.; Howell, Heather; Tannenbaum, Richard J.; Steinberg, Jonathan H.; Xu, Jun

2016-01-01

The purpose of this report is to explore the content-related validity evidence supporting the mathematics components of the "ETS"® National Observational Teaching Exam (NOTE) assessment series, a kindergarten through 6th grade teacher licensure assessment. To establish the content knowledge required for the effective teaching of…

International Comparisons of Foundation Phase Number Domain Mathematics Knowledge and Practice Standards

ERIC Educational Resources Information Center

Human, Anja; van der Walt, Marthie; Posthuma, Barbara

2015-01-01

Poor mathematics performance in schools is both a national and an international concern. Teachers ought to be equipped with relevant subject matter knowledge and pedagogical content knowledge as one way to address this problem. However, no mathematics knowledge and practice standards have as yet been defined for the preparation of Foundation Phase…

The Preparation Experiences of Elementary Mathematics Specialists: Examining Influences on Beliefs, Content Knowledge, and Teaching Practices

ERIC Educational Resources Information Center

Swars, Susan L.; Smith, Stephanie Z.; Smith, Marvin E.; Carothers, Jody; Myers, Kayla

2018-01-01

Many in the field of mathematics education call for elementary schools to have elementary mathematics specialists (EMSs) who provide needed mathematical expertise and support for children and teachers. EMSs serve as a reasonable, immediate alternative to the challenges generated by elementary teachers needing improved mathematical knowledge for…

Advancing K-8 Teachers' STEM Education for Teaching Interdisciplinary Science and Mathematics with Technologies

ERIC Educational Resources Information Center

Niess, Margaret; Gillow-Wiles, Henry

2013-01-01

This primarily online Master's degree program focused on advancing K-8 teachers' interdisciplinary mathematical and science content knowledge while integrating appropriate digital technologies as learning and teaching tools. The mixed-method, interpretive study examined in-service teachers' technological, pedagogical, and content knowledge (TPACK)…

Rethinking about the Pedagogy for Pedagogical Content Knowledge in the Context of Mathematics Teaching

ERIC Educational Resources Information Center

Ozmantar, Mehmet Fatih

2011-01-01

This study reconsiders the notion of pedagogy for pedagogical content knowledge (PCK) in the context of teaching mathematics. The perspectives of critical pedagogy are employed for this reconsideration, stressing the operation of historical, social, ideological, political, institutional and cultural forces in the production of pedagogical…

Pedagogical Content Knowledge in Mathematical Modelling Instruction

ERIC Educational Resources Information Center

Tan, Liang Soon; Ang, Keng Cheng

2012-01-01

This paper posits that teachers' pedagogical content knowledge in mathematical modelling instruction can be demonstrated in the crafting of action plans and expected teaching and learning moves via their lesson images (Schoenfeld, 1998). It can also be developed when teachers shape appropriate teaching moves in response to students' learning…

Examining Change in K-3 Teachers' Mathematical Knowledge, Attitudes, and Beliefs: The Case of Primarily Math

ERIC Educational Resources Information Center

Kutaka, T. S.; Ren, L.; Smith, W. M.; Beattie, H. L.; Edwards, C. P.; Green, J. L.; Chernyavskiy, P.; Stroup, W.; Heaton, R. M.; Lewis, W. J.

2018-01-01

This study examines the impact of the Primarily Math Elementary Mathematics Specialist program on K-3 teachers' mathematical content knowledge for teaching, attitudes toward learning mathematics, and beliefs about mathematics teaching and learning. Three cohorts of teachers participating in the program were compared to a similar group of…

Technological pedagogical content knowledge and teaching practice of mathematics trainee teachers

NASA Astrophysics Data System (ADS)

Tajudin, Nor'ain Mohd.; Kadir, Noor Zarinawaty Abd.

2014-07-01

This study aims to identify the level of technological pedagogical content knowledge (TPCK) of mathematics trainee teachers at Universiti Pendidikan Sultan Idris (UPSI) and explore their teaching practices during practical training at school. The study was conducted in two phases using a mix-method research. In the first phase, a survey method using a questionnaire was carried out on 156 trainee teachers of Bachelor of Mathematics Education (AT14) and Bachelor of Science (Mathematics) with Education (AT48). The instrument used was a questionnaire that measures the level of content knowledge, pedagogy, technology and TPCK of mathematics. Data were analyzed using descriptive statistics, namely the mean. While in the second phase, the interview method involved four trainee teachers were performed. The instrument used was the semi-structured interview protocol to assess the trainee teacher's TPCK integration in their teaching practice. Data were analyzed using the content analysis. The findings showed that the level of knowledge of TPCK among trainee teachers was moderate with overall mean score of 3.60. This level did not show significant differences between the two programs with mean scores of 3.601 for the AT14 group and 3.603 for the AT48 group. However, there was a difference for gender classification such that the female trainees had mean score of 3.58 and male trainees with mean score of 3.72. Although students' TPCK level was moderate, the level of content knowledge (CK), technological knowledge (TK) and pedagogical knowledge (PK), showed a higher level with overall mean scores of 3.75, 3.87 and 3.84 respectively. The findings also showed that in terms of content knowledge, trainee teacher's learning mathematics background was good, but the knowledge of mathematics was limited in the curriculum, philosophy and application aspect. In terms of pedagogical content knowledge, all respondents tend to use lecture and discussion methods in teaching Trigonometry topic in almost the entire teaching and learning sessions. In terms of using technology in teaching and learning process, all respondents were more likely to use PowerPoint presentation as well as assisted by the use of a scientific calculator. The use of PowerPoint was limited in explaining the title and its content and the calculators were used during practice sessions. The four trainee teachers were still at the recognizing and acceptance levels of TPCK integration during their teaching practice. This study indicates that UPSI trainee teachers should be given exposure in the use of information and communication technology and trained to provide alternative teaching strategies in more creative ways if there are obstacles when integrating technology in teaching and learning process.

Concept Maps Provide a Window onto Preservice Elementary Teachers' Knowledge in the Teaching and Learning of Mathematics

ERIC Educational Resources Information Center

Chichekian, Tanya; Shore, Bruce M.

2013-01-01

This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers' visual representations of their mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers' concept maps and analyzed them by…

Developing Mathematical Content Knowledge for Teaching: One Preservice Teacher and Her Planning

ERIC Educational Resources Information Center

Wilson, Susanna

2016-01-01

This paper describes how a new pre-service teacher engaged with mathematical content in order to learn it for teaching, during practicum. The results show that the PST learned mathematical content by initiating and carrying out a preparation phase prior to planning. This phase involved searching through internet sites and making notes that were…

Teaching Efficacy: Exploring Relationships between Mathematics and Science Self-Efficacy Beliefs, PCK and Domain Knowledge among Preservice Teachers from the United States

ERIC Educational Resources Information Center

Thomson, Margareta Maria; DiFrancesca, Daniell; Carrier, Sarah; Lee, Carrie

2017-01-01

This mixed-methods study investigated the relationships among preservice teachers' efficacy beliefs, pedagogical content knowledge (PCK) and their domain knowledge (DK) as related to mathematics and science teaching. Quantitative results revealed that participants' PCK was significantly correlated with their mathematics and science efficacy…

South Dakota Middle School Mathematics Teachers' Perceptions of Teaching Competencies

ERIC Educational Resources Information Center

Bleecker, Heather A.

2017-01-01

This quantitative research study investigates South Dakota middle school (grades 5-8) mathematics teachers' perceptions of teaching competencies including general pedagogical knowledge (GPK) and mathematical pedagogical content knowledge (MPCK). The study also considered how teacher characteristics relate to teacher competencies. The study…

Studying Challenges in Integrating Technology in Secondary Mathematics with Technological Pedagogical and Content Knowledge (TPACK)

ERIC Educational Resources Information Center

Stoilescu, Dorian

2014-01-01

This paper describes challenges encountered by two secondary mathematics teachers when they try to integrate ICT devices in their classes. These findings are based on using the Technological Pedagogical and Content Knowledge (TPACK) context, the four dimension framework developed by Niess: 1) overarching conceptions of integrating ICT, 2)…

Implementation of Pedagogical Content Knowledge (PCK) of Mathematics Teachers in Teaching Practice: A Case Study

ERIC Educational Resources Information Center

Maryono; Sutawidjaja, Akbar; Subanji; Irawati, Santi

2017-01-01

This study aims to describe the implementation of pedagogical content knowledge (PCK) of mathematics teachers in the teaching practice of the material system of linear equations of two variables (SLETV). The approach used is a qualitative case study. The main instrument is the researchers themselves and the supporting instruments is a vignette…

Developing Technological Pedagogical Content Knowledge in Pre-Service Mathematics Teachers through Collaborative Design

ERIC Educational Resources Information Center

Agyei, Douglas D.; Voogt, Joke

2012-01-01

Although many studies have shown the need to pay attention to teachers' preparation for the integration of technology in classroom practice, most teachers in Ghana have not had any preparation that develops their technological pedagogical content knowledge (TPCK). This paper presents a case study of four pre-service mathematics teachers from the…

Developing Pre-Service Teachers' Technological Pedagogical Content Knowledge for Teaching Mathematics with the Geometer's Sketchpad through Lesson Study

ERIC Educational Resources Information Center

Meng, Chew Cheng; Sam, Lim Chap

2013-01-01

The purpose of this study was to develop pre-service secondary teachers' technological pedagogical content knowledge (TPACK) for teaching mathematics with The Geometer's Sketchpad (GSP) through Lesson Study (LS). Specifically, a single-group pretest-posttest design was employed to examine whether there was a significant difference in the…

A Critical Examination of the Technological Pedagogical Content Knowledge Framework: Secondary School Mathematics Teachers Integrating Technology

ERIC Educational Resources Information Center

Stoilescu, Dorian

2015-01-01

This study explores the Technological Pedagogical Content Knowledge (TPACK) for three experienced mathematics secondary teachers from a Toronto public school. By using a multiple case study, teachers' attitudes, skills, and approaches toward the use of Information and Communications Technology (ICT) in classrooms are described. By being aware of…

The Mathematical Content Knowledge of Prospective Teachers in Iceland

ERIC Educational Resources Information Center

Johannsdottir, Bjorg

2013-01-01

This study focused on the mathematical content knowledge of prospective teachers in Iceland. The sample was 38 students in the School of Education at the University of Iceland, both graduate and undergraduate students. All of the participants in the study completed a questionnaire survey and 10 were interviewed. The choice of ways to measure the…

Emergences and Affordances as Opportunities to Develop Teachers' Mathematical Content Knowledge

ERIC Educational Resources Information Center

Julie, Cyril

2014-01-01

Teachers' mathematical content knowledge has been under scrutiny for some time. This development is in the wake of learners' unsatisfactory performance in national examinations and international achievement tests. A widely held belief is that one, if not the most important, of the efforts to improve and enhance the performance and…

Looking at practice: revealing the knowledge demands of teaching data handling in the primary classroom

NASA Astrophysics Data System (ADS)

Leavy, Aisling

2015-09-01

In the evolving field of mathematics education, there is the need to maintain the relationship between what is presented in college level preparation courses and the skills required to teach mathematics in classrooms. This research examines the knowledge demands placed on 73 pre-service primary teachers as they use lesson study to plan and teach data handling in primary classrooms. Pre-service teachers are observed as they plan, teach and re-teach data lessons in classrooms. Problems of practice are identified and categorized using the Ball, Thames and Phelps (2008) subdomains of common content knowledge (CCK), specialized content knowledge (SCK), knowledge of content and students (KCS) and knowledge of content and teaching (KCT). The results provide insights into the specific knowledge demands placed on early career teachers when teaching data and statistics and identifies foci area that can be addressed in teacher preparation programs. The results illustrate that development of understandings in one knowledge subdomain can motivate and impact learning in another subdomain. These interrelationships were found to exist both within and between the domains of content and pedagogical content knowledge.

Open-Ended (Extended/Constructed) Response Questions as Predictors of Success on Subsequent State Mathematics Examination: The Influence of Mathematical Awareness and Conceptual Knowledge

ERIC Educational Resources Information Center

Gullie, Kathy A.

2011-01-01

This study investigated the predictive ability of students' responses to open-ended, constructed/extended questions in third and fourth grade mathematics content subcategories on subsequent fifth grade mathematics achievement proficiency levels. Open-ended, extended/constructed response questions reflected content as outlined by the National…

The Effects of Different Undergraduate Mathematics Courses on the Content Knowledge and Attitude towards Mathematics of Preservice Elementary Teachers

ERIC Educational Resources Information Center

Matthews, Michael E.; Seaman, Walter I.

2007-01-01

Preservice elementary teachers have been shown to generally possess poor mathematical knowledge (e.g. Goulding, Rowland, & Barber, 2002) and also strong negative attitudes toward mathematics (e.g. MacNab & Payne, 2004). Recently, national organizations have proposed interventions to address these issues (Conference Board of the…

Does content knowledge matter for new teachers?

NASA Astrophysics Data System (ADS)

Reeves, Todd D.

There is considerable evidence that new teachers are ill prepared for classroom practice, including self-reported evidence collected from teachers (e.g., Levine, 2006), and statistical evidence for differences in the achievement of students with new versus more experienced teachers (Rivkin, Hanushek, & Kain, 2005). In light of the challenges encountered by new teachers (e.g., Levine, 2006), this study examined the value of different forms of teacher knowledge for teachers with different levels of experience. In particular, this study investigated the interactive relationship between teaching experience and teacher content knowledge, and student achievement in mathematics and science. In New York City, Boyd et al. (2009) linked practice-focused teacher preparation to student mathematics achievement in the first year of teaching and teacher content preparation to achievement in the second. However, other studies demonstrated interactions between teaching experience and content knowledge with different interpretations (e.g., Kukla-Acevedo, 2009; Monk, 1994). At the same time, this study examined the interactive relationship between teaching experience and teachers' pedagogical content knowledge, and student achievement. Extant models of teacher career development (Huberman, 1989; National Research Council, 2010) and how teacher education affects student achievement (e.g., Desimone, 2009) offered theoretical grounding for the study. With nationally representative samples of fourth and eighth grade U.S. students--participants in the 2011 Trends in International Mathematics and Science Study--this study employed hierarchical linear modeling to address its research questions among an array of student achievement outcomes in the domains of mathematics and science. This study attempted to account for salient student, teacher, and contextual factors, and the probabilities of teachers' receipt of various teacher education "treatments" (i.e., propensity score analysis) to reduce the plausibility of selection threats to internal validity. The study found no evidence for relationships between teacher content knowledge or pedagogical content knowledge and student mathematics and science achievement in fourth and eighth grade. Furthermore, the results indicated no interactive relationships between forms of teacher knowledge and teaching experience, and student achievement in these grades/subjects. The limitations of cross-sectional, observational studies using large-scale data and directions for further research are discussed.

Designing Tasks to Examine Mathematical Knowledge for Teaching Statistics for Primary Teachers

NASA Astrophysics Data System (ADS)

Siswono, T. Y. E.; Kohar, A. W.; Hartono, S.

2018-01-01

Mathematical knowledge for teaching (MKT) is viewed as fuel resources for conducting an orchestra in a teaching and learning process. By understanding MKT, especially for primary teachers, it can predict the success of a goal of an instruction and analyze the weaknesses and improvements of it. To explore what teachers think about subject matters, pedagogical terms, and appropriate curriculum, it needs a task which can be identified the teachers’ MKT including the subject matter knowledge (SMK) and pedagogical content knowledge (PCK). This study aims to design an appropriate task for exploring primary teachers’ MKT for statistics in primary school. We designed six tasks to examine 40 primary teachers’ MKT, of which each respectively represents the categories of SMK (common content knowledge (CCK) and specialised content knowledge (SCK)) and PCK (knowledge of content and students (KCS), knowledge of content and teaching (KCT), and knowledge of content and curriculum (KCC)). While MKT has much attention of numbers of scholars, we consider knowledge of content and culture (KCCl) to be hypothesized in the domains of MKT. Thus, we added one more task examining how the primary teachers used their knowledge of content (KC) regarding to MKT in statistics. Some examples of the teachers’ responses on the tasks are discussed and some refinements of MKT task in statistics for primary teachers are suggested.

Teacher Subject Matter Knowledge of Number Sense

ERIC Educational Resources Information Center

Briand-Newman, Hannah; Wong, Monica; Evans, David

2012-01-01

Pedagogical content knowledge has been widely acknowledged by researchers and practitioners as a significant factor for improving student knowledge, understanding and achievement. Recently, the knowledge teachers need for teaching has expanded to include teacher horizon content knowledge, "an awareness of how mathematical topics are related…

MATHEMATICS CLUSTERS IN SELECTED AREAS OF VOCATIONAL EDUCATION, REPORT NUMBER 8.

ERIC Educational Resources Information Center

RAHMLOW, HAROLD F.; WINCHELL, LEONARD

IDENTIFICATIONS WERE MADE OF THE MATHEMATICAL KNOWLEDGES COMMONLY USED IN OCCUPATIONS MOST READILY SUITABLE FOR NONCOLLEGE-BOUND YOUTH. TASK ITEMS FROM QUESTIONNAIRES USED IN OFFICE OCCUPATIONS, GENERAL MERCHANDISING, BUILDING TRADES, ELECTRONICS, FOOD SERVICE, CHILD CARE, AND AGRICULTURE STUDIES WERE EXAMINED FOR MATHEMATICAL KNOWLEDGE CONTENT.…

Development of a Performance Assessment Task and Rubric to Measure Prospective Secondary School Mathematics Teachers' Pedagogical Content Knowledge and Skills

ERIC Educational Resources Information Center

Koirala, Hari P.; Davis, Marsha; Johnson, Peter

2008-01-01

The purpose of this paper is to share a performance assessment task and rubric designed to assess secondary school mathematics preservice teachers' pedagogical content knowledge and skills. The assessment task and rubric were developed in collaboration with five education faculty, four arts and sciences faculty, and four high school teachers over…

Developing an Instrument for Measuring Teachers' Mathematics Content Knowledge on Ratio and Proportion: A Case of Indonesian Primary Teachers

ERIC Educational Resources Information Center

Ekawati, Rooselyna; Lin, Fou-Lai; Yang, Kai-Lin

2015-01-01

In this study, we developed an instrument for assessing teachers' mathematics content knowledge (MCK) on ratio and proportion and examined the profile of Indonesian primary teacher's MCK on this topic. The MCK items were administered to 271 Indonesian in-service primary teachers with a variety of educational backgrounds and teaching experiences.…

Examining the Relationship between Thinking Styles and Technological Pedagogical Content Knowledge of the Candidate Mathematics Teachers

ERIC Educational Resources Information Center

Canbolat, Nuran; Erdogan, Ahmet; Yazlik, Derya Ozlem

2016-01-01

The aim of this research is measuring the technological pedagogical content knowledge of the candidate elementary mathematics teachers, identifying the thinking styles of the same candidates and finding out that whether there is a correlation or not. The research has the characteristics of a basic research to add new information to the scientific…

The Influence of the Pedagogical Content Knowledge Framework on Research in Mathematics Education: A Review across Grade Bands

ERIC Educational Resources Information Center

Matthews, Mary Elizabeth

2013-01-01

This literature review examines the models, theories, and research in mathematics education that are informed by Lee S. Shulman's construct, Pedagogical Content Knowledge. The application of the concept differs in nature and volume across levels of schooling. The research includes substantial work at the elementary level, fewer studies at the…

Mathematical Knowledge and Skills Expected by Higher Education in Engineering and the Social Sciences: Implications for High School Mathematics Curriculum

ERIC Educational Resources Information Center

Basaran, Mehmet; Özalp, Gülümser; Kalender, Ilker; Alacaci, Cengiz

2015-01-01

One important function of school mathematics curriculum is to prepare high school students with the knowledge and skills needed for university education. Identifying them empirically will help making sound decisions about the contents of high school mathematics curriculum. It will also help students to make informed choices in course selection at…

Classroom Stress Promotes Motivated Forgetting of Mathematics Knowledge

ERIC Educational Resources Information Center

Ramirez, Gerardo; McDonough, Ian M.; Jin, Ling

2017-01-01

The ability to retain educationally relevant content in a readily accessible state in memory is critical for students at all stages in schooling. We hypothesized that a high degree of stress in mathematics courses can threaten students' mathematics self-concept and lead to a motivation to forget course content. We tested the aforementioned…

An Examination of the Questioning Interactions of Prospective Teachers during Mathematical Discussions

ERIC Educational Resources Information Center

Darke, Kelly Marie

2010-01-01

Questioning is an essential and generative studying practice for prospective teachers (PTs) as they develop their mathematical content knowledge needed for teaching. This study examines PTs' questioning interactions by describing the types of questions they ask during small group discussions in a required mathematics content course and how their…

Investigating the Effects of a Math-Enhanced Agricultural Teaching Methods Course

ERIC Educational Resources Information Center

Stripling, Christopher T.; Roberts, T. Grady

2013-01-01

Numerous calls have been made for agricultural education to support core academic subject matter including mathematics. Previous research has shown that the incorporation of mathematics content into a teaching methods course had a positive effect on preservice teachers' mathematics content knowledge. The purpose of this study was to investigate…

The Impact of Sustained, Standards-Based Professional Learning on Second and Third Grade Teachers' Content and Pedagogical Knowledge in Integrated Mathematics

ERIC Educational Resources Information Center

Bailey, Lora B.

2010-01-01

This 3 year longitudinal study reports the feasibility of an "Improving Teacher Quality: No Child Left Behind" project for impacting teachers' content and pedagogical knowledge in mathematics in nine Title I elementary schools in the southeastern United States. Data were collected for 3 years to determine the impact of standards and…

Relationship between Pedagogical Strategies and Teachers' Content Knowledge of Mathematics

ERIC Educational Resources Information Center

Kanyongo, Gibbs Y.; Brown, Launcelot I.

2013-01-01

This study employed regression analysis to investigate the relationship between primary school teachers' pedagogical practices and their knowledge of mathematics. The sample composed of 606 Grade 6 mathematics teachers in Namibia, i.e. 304 (50.2%) males and 302 (49.8%) females. The study utilized existing questionnaire data collected by the…

Relationship between mathematics teacher subject matter knowledge, pedagogical content knowledge and professional development needs

NASA Astrophysics Data System (ADS)

Tajudin, Nor'ain Mohd; Chinnappan, Mohan; Saad, Noor Shah

2017-05-01

Two key variables emerged from the literature review is that Specific Matter Knowledge [SMK] and Pedagogical Content Knowledge [PCK] can influence the mathematics teachers' Professional Development [PD] needs. However, the key variables of SMK and PCK that were being investigated were not defined clearly. Empirical evidence that support relationship between SMK and PD and PCK and PD were not verified. In addition, how does PCK mediate SMK and PD is not clear and somewhat lacking. Therefore, the purpose of this paper was to examine the relationship between primary mathematics teacher's SMK, PCK and PD needs. Results of path analysis with SmartPLS indicated that the direct effect of SMK on PD was mediated via PCK. This data provide support for the claim that PD programs for future teachers of primary mathematics should be driven by a more nuanced understanding of the link between SMK and PCK.

The Integration of technology in teaching mathematics

NASA Astrophysics Data System (ADS)

Muhtadi, D.; Wahyudin; Kartasasmita, B. G.; Prahmana, R. C. I.

2017-12-01

This paper presents the Transformation of Technological Pedagogical and Content Knowledge (TPACK) of three pre-service math teacher. They participate in technology-based learning modules aligned with teaching practice taught school and became characteristic of teaching method by using the mathematical software. ICT-based learning environment has been the demands in practice learning to build a more effective approach to the learning process of students. Also, this paper presents the results of research on learning mathematics in middle school that shows the influence of design teaching on knowledge of math content specifically.

The Nation's Report Card: A First Look--2013 Mathematics and Reading. National Assessment of Educational Progress at Grades 4 and 8. NCES 2014-451

ERIC Educational Resources Information Center

National Center for Education Statistics, 2013

2013-01-01

The National Assessment of Educational Progress (NAEP) mathematics assessment measures students' knowledge and skills in mathematics and students' ability to apply their knowledge in problem-solving situations. At each grade, students responded to questions designed to measure what they know and can do across five mathematics content areas: number…

A Study of Strengthening Secondary Mathematics Teachers' Knowledge of Statistics and Probability via Professional Development

ERIC Educational Resources Information Center

DeVaul, Lina

2017-01-01

A professional development program (PSPD) was implemented to improve in-service secondary mathematics teachers' content knowledge, pedagogical knowledge, and self-efficacy in teaching secondary school statistics and probability. Participants generated a teaching resource website at the conclusion of the PSPD program. Participants' content…

Specialised Content Knowledge: Evidence of Pre-Service Teachers' Appraisal of Student Errors in Proportional Reasoning

ERIC Educational Resources Information Center

Chinnappan, Mohan; White, Bruce

2015-01-01

That the quality of teachers' knowledge has direct impact on students' engagement and learning outcomes in mathematics is now well established. But questions about the nature of this knowledge and how to characterise that knowledge are important for mathematics educators. In the present study, we examine a strand of "Specialised Content…

Developing a Scale to Measure Content Knowledge and Pedagogy Content Knowledge of In-Service Elementary Teachers on Fractions

ERIC Educational Resources Information Center

Kazemi, Farhad; Rafiepour, Abolfazl

2018-01-01

The main purpose of this study was to develop a scale for measuring content knowledge (CK) and pedagogy content knowledge (PCK) of in-service elementary teachers on mathematical fractions. Another aim of this study was to consider whether CK and PCK are separate from each other, or are in a single body. Therefore, a scale containing 22 items about…

Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics

PubMed Central

Harr, Nora; Eichler, Andreas; Renkl, Alexander

2014-01-01

In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions (“integrated” vs. “separated”), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education. PMID:25191300

Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics.

PubMed

Harr, Nora; Eichler, Andreas; Renkl, Alexander

2014-01-01

In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions ("integrated" vs. "separated"), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education.

Developing a Questionnaire to Assess the Probability Content Knowledge of Prospective Primary School Teachers

ERIC Educational Resources Information Center

Gómez-Torres, Emilse; Batanero, Carmen; Díaz, Carmen; Contreras, José Miguel

2016-01-01

In this paper we describe the development of a questionnaire designed to assess the probability content knowledge of prospective primary school teachers. Three components of mathematical knowledge for teaching and three different meanings of probability (classical, frequentist and subjective) are considered. The questionnaire content is based on…

Knowledge Growth in Teaching Mathematics/Science with Spreadsheets: Moving PCK to TPACK through Online Professional Development

ERIC Educational Resources Information Center

Niess, Margaret L.; van Zee, Emily H.; Gillow-Wiles, Henry

2011-01-01

Inservice teachers need ways to gain an integrated knowledge of content, pedagogy, and technologies that reflects new ways of teaching and learning in the 21st century. This interpretive study examined inservice K-8 teachers' growth in their pedagogical content knowledge (PCK) toward technology, pedagogy, and content knowledge (TPACK) in an online…

A Case Study on Specialised Content Knowledge Development with Dynamic Geometry Software: The Analysis of Influential Factors and Technology Beliefs of Three Pre-Service Middle Grades Mathematics Teachers

ERIC Educational Resources Information Center

Zambak, Vecihi S.; Tyminski, Andrew M.

2017-01-01

This study characterises the development of Specialised Content Knowledge (SCK) with dynamic geometry software (DGS) throughout a semester. The research employed a single-case study with the embedded units of three pre-service middle grades mathematics teachers. Qualitative data were collected, and factors affecting these three teachers' SCK…

Understanding and Supporting Teacher Horizon Knowledge around Limits: A Framework for Evaluating Textbooks for Teachers

ERIC Educational Resources Information Center

Kajander, Ann; Lovric, Miroslav

2017-01-01

As part of recent scrutiny of teacher capacity, the question of teachers' content knowledge of higher level mathematics emerges as important to the field of mathematics education. Elementary teachers in North America and some other countries tend to be subject generalists, yet it appears that some higher level mathematics background may be…

Teaching 5- and 6-Year-Olds to Count: Knowledge of South African Educators

ERIC Educational Resources Information Center

Feza, Nosisi N.

2016-01-01

Mathematics learning and teaching continues to be a challenge in the South African education system. This challenge is observed in the poor performance of students in national and international assessments. Research suggests that teachers' content knowledge and knowledge of teaching mathematics contribute significantly to students' performance. In…

Connection between Topic-Specific Teacher Knowledge and Student Performance in Lower Secondary School Mathematics

ERIC Educational Resources Information Center

Tchoshanov, Mourat; Quinones, Maria Cruz; Shakirova, Kadriya B.; Ibragimova, Elena N.; Shakirova, Liliana R.

2017-01-01

The interpretive cross-case study focused on the examination of connections between teacher and student topic-specific knowledge of lower secondary mathematics. Two teachers were selected for the study using non-probability purposive sampling technique. Teachers completed the Teacher Content Knowledge Survey before teaching a topic on division of…

Preservice Secondary Mathematics Teachers' Knowledge of Students

ERIC Educational Resources Information Center

Kilic, Hulya

2011-01-01

The aim of this paper is to present the nature of preservice secondary mathematics teachers' knowledge of students as emerged from a study investigating the development of their pedagogical content knowledge in a methods course and its associated field experience. Six preservice teachers participated in the study and the data were collected in the…

Pre-K Mathematics. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2007

2007-01-01

"Pre-K Mathematics" is a supplemental curriculum designed to develop informal mathematical knowledge and skills in preschool children. Mathematical content is organized into seven units. Specific mathematical concepts and skills from each unit are taught in the classroom through teacher-guided, small-group activities with concrete…

Pedagogical content knowledge: Knowledge of pedagogy novice teachers in mathematics learning on limit algebraic function

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-02-01

Teacher is one of the key aspects of student's achievement. Teachers should master content material taught, how to teach it, and can interpret the students' thinking so that students easily understand the subject matter. This research was a qualitative research that aimed at describing profile of PCK's teachers in mathematics on limit algebraic functions in terms of the differences of teaching experience. Pedagogical Content Knowledge (PCK) and understanding of teachers is defined as involving the relationship between knowledge of teaching materials, how to transfer the subject matter, and the knowledge of students in mathematics on limit algebraic functions that the subject matter may be understood by students. The PCK components in this research were knowledge of subject matter, knowledge of pedagogy, and knowledge of students. Knowledge of pedagogy defines as knowledge and understanding of teachers about the planning and organization of the learning and teaching strategy of limit algebraic function. The subjects were two mathematics high school teachers who teach in class XI IPS. Data were collected through observation of learning during five meetings and interviews before and after the lesson continued with qualitative data analysis. Focus of this article was to describe novice teacher's knowledge of student in mathematics learning on limit algebraic function. Based on the results of the analysis of qualitative data the data concluded that novice teacher's knowledge of pedagogy in mathematics on limit algebraic function showed: 1) in teaching the definitions tend to identify prior knowledge of the student experience with the material to be studied, but not in the form of a problem, 2) in posing the questions tend to be monotonous non lead and dig, 3) in response to student questions preservice teachers do not take advantage of the characteristics or the potential of other students, 4) in addressing the problem of students, tend to use the drill approach and did not give illustrations easily to understand by students, 5) in teaching application concepts, tend to explain procedurally, without explaining the reasons why these steps are carried out, 6) less varied in the use of learning strategies.

Preparing Special Education Teachers for Teaching Mathematics and Science with Technology by Integrating the TPACK Framework into the Curriculum: A Study of Teachers' Perceptions

ERIC Educational Resources Information Center

Tournaki, Nelly; Lyublinskaya, Irina

2014-01-01

This study examined the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers via one course. The course focused on the three domains of knowledge related specifically to integrating instructional technology into mathematics and science teaching and learning…

Developing Distinct Mathematical and Scientific Pedagogical Content Knowledge in an Early Childhood Dual-Content Methods Course: An Alternative to Integration

ERIC Educational Resources Information Center

Kalchman, Mindy; Kozoll, Richard H.

2017-01-01

Methods for teaching early childhood mathematics and science are often addressed in a single, dual-content course. Approaches to teaching this type of course include integrating the content and the pedagogy of both subjects, or keeping the subject areas distinct. In this article, the authors discuss and illustrate their approach to such a combined…

Does an Observer's Content Knowledge Influence the Feedback Offered about Mathematics Lessons?

ERIC Educational Resources Information Center

Peck, Duane C.

2016-01-01

The purpose of this study was two-fold. First, feedback from 3 different groups of observers: math content specialists, content specialists in areas other than mathematics, and building principals, was analyzed using an inductive approach to identify themes within the feedback. Second, differences in the feedback offered by participants of the 3…

Knowing and Teaching Fractions: A Cross-Cultural Study of American and Chinese Mathematics Teachers

ERIC Educational Resources Information Center

Zhou, Zheng; Peverly, Stephen T.; Xin, Tao

2006-01-01

Guided by Shulman, 1986 and Shulman, 1987 tripartate model of teacher expertise [subject matter knowledge (SMK), pedagogical content knowledge (PCK), and general pedagogical knowledge (GPK)], the present study examined 162 U.S. and Chinese 3rd grade mathematics teachers' expertise in teaching fractions. Results show that U.S. teachers lag…

The Concept of Slope: Comparing Teachers' Concept Images and Instructional Content

ERIC Educational Resources Information Center

Nagle, Courtney; Moore-Russo, Deborah

2013-01-01

In the field of mathematics education, understanding teachers' content knowledge (Grossman, 1995; Hill, Sleep, Lewis, & Ball, 2007; Munby, Russell, & Martin, 2001) and studying the relationship between content knowledge and instructional decisions (Fennema & Franke, 1992; Raymond, 1997) are both crucial. Teachers need a robust…

Developing Multimedia Enhanced Content to Upgrade Subject Content Knowledge of Secondary School Teachers in Tanzania

ERIC Educational Resources Information Center

Mtebe, Joel S.; Kibga, Elia Y.; Mwambela, Alfred A.; Kissaka, Mussa M.

2015-01-01

The failure rates and lack of interest amongst students in science and mathematics in secondary schools in Tanzania is a serious problem. The Ministry of Education and Vocational Training (MoEVT) implemented a project to enhance and upgrade the pedagogical knowledge and subject content knowledge of teachers in selected difficult topics in science…

The Language Used to Articulate Content as an Aspect of Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Chick, Helen

2015-01-01

Mathematical knowledge in classrooms is mediated through the use of both technical and informal language. This paper is a report of a study of the language use of teachers as they examine students' work and discuss teaching for the topic of fraction operations. This provides a window on their pedagogical content knowledge and also on the way in…

Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication

ERIC Educational Resources Information Center

Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.

2014-01-01

This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…

Using Delphi Methodology to Design Assessments of Teachers' Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Manizade, Agida Gabil; Mason, Marguerite M.

2011-01-01

Descriptions of methodologies that can be used to create items for assessing teachers' "professionally situated" knowledge are lacking in mathematics education research literature. In this study, researchers described and used the Delphi method to design an instrument to measure teachers' pedagogical content knowledge. The instrument focused on a…

A Study of Mathematics Infusion in Middle School Technology Education Classes

ERIC Educational Resources Information Center

Burghardt, M. David; Hecht, Deborah; Russo, Maria; Lauckhardt, James; Hacker, Michael

2010-01-01

The present study examined the impact of introducing a mathematics infused engineering/technology education (ETE) curriculum on students' mathematics content knowledge and attitudes toward mathematics. The purpose of the present study was to: (a) compare the effects of a mathematics infused ETE curriculum and a control curriculum on student…

The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts.

ERIC Educational Resources Information Center

Kaplan, Rochelle G.

This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…

Pre-Service Teacher Training on Game-Enhanced Mathematics Teaching and Learning

ERIC Educational Resources Information Center

Meletiou-Mavrotheris, Maria; Prodromou, Theodosia

2016-01-01

The paper reports the main insights from a study aimed at equipping a group of pre-service teachers with the knowledge, skills, and practical experience required to effectively integrate educational games within the mathematics curriculum. An instructional intervention based on the Technological Pedagogical and Content Knowledge framework was…

Building a Knowledge Base: Understanding Prospective Elementary Teachers' Mathematical Content Knowledge

ERIC Educational Resources Information Center

Thanheiser, Eva; Browning, Christine; Edson, Alden J.; Kastberg, Signe; Lo, Jane-Jane

2013-01-01

This survey of the literature summarizes and reflects on research findings regarding elementary preservice teachers' (PSTs') mathematics conceptions and the development thereof. Despite the current focus on teacher education, peer-reviewed journals offer a surprisingly sparse insight in these areas. The limited research that exists…

Minimalism as a Guiding Principle: Linking Mathematical Learning to Everyday Knowledge

ERIC Educational Resources Information Center

Inoue, Noriyuki

2008-01-01

Studies report that students often fail to consider familiar aspects of reality in solving mathematical word problems. This study explored how different features of mathematical problems influence the way that undergraduate students employ realistic considerations in mathematical problem solving. Incorporating familiar contents in the word…

Utah's New Mathematics Core

ERIC Educational Resources Information Center

Utah State Office of Education, 2011

2011-01-01

Utah has adopted more rigorous mathematics standards known as the Utah Mathematics Core Standards. They are the foundation of the mathematics curriculum for the State of Utah. The standards include the skills and understanding students need to succeed in college and careers. They include rigorous content and application of knowledge and reflect…

Teaching Statistics with Technology

ERIC Educational Resources Information Center

Prodromou, Theodosia

2015-01-01

The Technological Pedagogical Content Knowledge (TPACK) conceptual framework for teaching mathematics, developed by Mishra and Koehler (2006), emphasises the importance of developing integrated and interdependent understanding of three primary forms of knowledge: technology, pedagogy, and content. The TPACK conceptual framework is based upon the…

Bird Boxes Build Content Area Knowledge

ERIC Educational Resources Information Center

Cianca, Sherri Ann

2013-01-01

This article describes a preservice teacher training in line with meeting the Common Core State Standards for Mathematics (CCSSM) using geometric reasoning, spatial sense, measurement, representation, communication, and problem solving. The author infers that when preservice teachers lack pedagogical content knowledge they cannot successfully…

Quality Assurance in Teacher Education and Outcomes: A Study of 17 Countries

ERIC Educational Resources Information Center

Ingvarson, Lawrence; Rowley, Glenn

2017-01-01

This study investigated the relationship between policies related to the recruitment, selection, preparation, and certification of new teachers and (a) the quality of future teachers as measured by their mathematics content and pedagogy content knowledge and (b) student achievement in mathematics at the national level. The study used data…

"Prime Online": Developing Grades 3-5 Teachers' Content Knowledge for Teaching Mathematics in an Online Professional Development Program

ERIC Educational Resources Information Center

Pape, Stephen J.; Prosser, Sherri K.; Griffin, Cynthia C.; Dana, Nancy Fichtman; Algina, James; Bae, Jungah

2015-01-01

This study sought to identify components of an asynchronous online teacher professional development program, "Prime Online," that potentially affected participants' mathematical knowledge for teaching (MKT). Twenty-three third- through fifth-grade general education and special education teachers completed a yearlong online teacher…

How to build a course in mathematical-biological modeling: content and processes for knowledge and skill.

PubMed

Hoskinson, Anne-Marie

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical-biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments.

Activities for Students: Connecting Spatial Reasoning Ideas in Mathematics and Chemistry

ERIC Educational Resources Information Center

Raje, Sonali; Krach, Michael; Kaplan, Gail

2013-01-01

Concepts in mathematics are often universally applicable to other fields. A critical aspect for success in high school or college is the ability to transfer content knowledge from one discipline to another. This is especially true for material learned in the sciences and mathematics. Several studies have suggested that strong mathematical skills…

Focusing on Mathematical Knowledge: The Impact of Content-Intensive Teacher Professional Development. NCEE 2016-4010

ERIC Educational Resources Information Center

Garet, Michael S.; Heppen, Jessica B.; Walters, Kirk; Parkinson, Julia; Smith, Toni M.; Song, Mengli; Garrett, Rachel; Yang, Rui; Borman, Geoffrey D.

2016-01-01

This report examines the impact of content-intensive Professional Development (PD) on teachers' math content knowledge, their instructional practice, and their students' achievement. The study's PD had three components, totaling 93 hours. The core of the PD was "Intel Math," an intensive 80-hour workshop delivered in summer 2013 that…

An Investigation of Technological Pedagogical Content Knowledge, Self-Confidence, and Perception of Pre-Service Middle School Mathematics Teachers towards Instructional Technologies

ERIC Educational Resources Information Center

Karatas, Ilhan; Tunc, Mutlu Piskin; Yilmaz, Nurbanu; Karaci, Gulzade

2017-01-01

Technology provides new methods and approaches for educational activities. Therefore, teachers should improve their ability and knowledge to integrate technology into instruction. The use of technology-based learning environment which is effectively used to improve the technological pedagogical content knowledge of pre-service teachers has a…

Relationship between Teacher Knowledge of Concepts and Connections, Teaching Practice, and Student Achievement in Middle Grades Mathematics

ERIC Educational Resources Information Center

Tchoshanov, Mourat A.

2011-01-01

The mixed method sequential nested study examines whether and how the cognitive type of teachers' content knowledge is associated with student achievement, and correlated with teaching practice. In the context of this study, the "cognitive type" refers to the kind of teacher content knowledge and thinking processes required to accomplish…

Adapting Math Instruction to Support Prospective Elementary Teachers

ERIC Educational Resources Information Center

LeSage, Ann

2012-01-01

Purpose: Elementary teachers' understanding of mathematics is a significant contributor to student success with mathematics. Consequently, teacher educators are frequently charged with the responsibility of supporting the development of prospective elementary teachers' mathematics content knowledge as they re-learn concepts in ways they are…

Developing Mathematical Knowledge for Teaching in a Methods Course: The Case of Function

ERIC Educational Resources Information Center

Steele, Michael D.; Hillen, Amy F.; Smith, Margaret S.

2013-01-01

This study describes teacher learning in a teaching experiment consisting of a content-focused methods course involving the mathematical knowledge for teaching function. Prospective and practicing teachers in the course showed growth in their ability to define function, to provide examples of functions and link them to the definition, in the…

The Role of the Mathematics Supervisor in K-12 Education

ERIC Educational Resources Information Center

Greenes, Carole

2013-01-01

The implementation of "the Common Core Standards for Mathematics" and the assessments of those concepts, skills, reasoning methods, and mathematical practices that are in development necessitate the updating of teachers' knowledge of content, pedagogical techniques to enhance engagement and persistence, and strategies for responding to…

Developing a Pedagogically Useful Content Knowledge in Elementary Mathematics.

ERIC Educational Resources Information Center

Peck, Donald M.; Connell, Michael L.

Elementary school teacher candidates typically enter their professional training with deficiencies in their conceptual understanding of the topics of elementary school mathematics and with a reliance upon procedural (algorithmic) approaches to the solutions of mathematical problems. If elementary school teacher candidates are expected to teach…

Licensure tests for special education teachers: how well they assess knowledge of reading instruction and mathematics.

PubMed

Stotsky, Sandra

2009-01-01

To determine the extent to which knowledge of evidence-based reading instruction and mathematics is assessed on licensure tests for prospective special education teachers, this study drew on information provided by Educational Testing Service (ETS), the American Board for Certification of Teacher Excellence, and National Evaluation Systems (now Evaluation Systems group of Pearson). It estimated the percentage of test items on phonemic awareness, phonics, and vocabulary knowledge and on mathematics content. It also analyzed descriptions of ETS's tests of "principles of teaching and learning." Findings imply that prospective special education teachers should be required to take both a dedicated test of evidence-based reading instructional knowledge, as in California, Massachusetts, and Virginia, and a test of mathematical knowledge, as in Massachusetts. States must design their own tests of teaching principles to assess knowledge of evidence-based educational theories.

A Framework for Proofs and Refutations in School Mathematics: Increasing Content by Deductive Guessing

ERIC Educational Resources Information Center

Komatsu, Kotaro

2016-01-01

The process of proofs and refutations described by Lakatos is essential in school mathematics to provide students with an opportunity to experience how mathematical knowledge develops dynamically within the discipline of mathematics. In this paper, a framework for describing student processes of proofs and refutations is constructed using a set of…

Effects of Teacher Preparation Courses: Do Graduates Use What They Learned to Plan Mathematics Lessons?

ERIC Educational Resources Information Center

Morris, Anne K.; Hiebert, James

2017-01-01

We investigated whether the content pre-service teachers studied in elementary teacher preparation mathematics courses was related to their performance on a mathematics lesson planning task 2 and 3 years after graduation. The relevant mathematics knowledge was studied when the teachers were freshmen, 5 to 6 years earlier. Results showed that when…

Professional Communities in the Context of Teachers' Professional lives: A Case of Mathematics Specialists

ERIC Educational Resources Information Center

Nickerson, Susan D.; Moriarty, Gail

2005-01-01

We describe an urban school initiative aimed at teachers' professional development with the goal of increasing their mathematics content knowledge and helping them improve their practice. In the lowest performing schools, mathematics specialists were employed to teach only mathematics in upper-elementary grades (ages 9-12). One aspect of this…

Unpacking Teachers' Moves in the Classroom: Navigating Micro- and Macro-Levels of Mathematical Complexity

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2015-01-01

The work that mathematics teachers do is frequently mathematical in nature and different from other professions. Understanding and describing common ways that teachers draw upon their content knowledge in the practice of teaching is important. Building on the descriptions by McCrory et al. ("Journal for Research in Mathematics Education"…

"It's Hard Getting Kids to Talk about Math": Helping New Teachers Improve Mathematical Discourse

ERIC Educational Resources Information Center

Bennett, Cory A.

2010-01-01

This article examines how two new teachers, with varied content knowledge and preparation as teachers in mathematics education, improved their use of whole-class discourse in their mathematics classes with a mentor's assistance. Discourse has long been shown to be influential in supporting students' learning of mathematics, but the implementation…

Connecting Biology and Mathematics: First Prepare the Teachers

PubMed Central

2010-01-01

Developing the connection between biology and mathematics is one of the most important ways to shift the paradigms of both established science disciplines. However, adding some mathematic content to biology or biology content to mathematics is not enough but must be accompanied by development of suitable pedagogical models. I propose a model of pedagogical mathematical biological content knowledge as a feasible starting point for connecting biology and mathematics in schools and universities. The process of connecting these disciplines should start as early as possible in the educational process, in order to produce prepared minds that will be able to combine both disciplines at graduate and postgraduate levels of study. Because teachers are a crucial factor in introducing innovations in education, the first step toward such a goal should be the education of prospective and practicing elementary and secondary school teachers. PMID:20810951

Math Intervention Teachers' Pedagogical Content Knowledge and Student Achievement

ERIC Educational Resources Information Center

Waller, Lisa Ivey

2012-01-01

This research investigated the relationship of math intervention teachers' (MITs) pedagogical content knowledge (PCK) and students' math achievement gains in primary math interventions. The Kentucky Center for Mathematics gathered data on the MITs and primary math intervention students included in this study. Longitudinal data were analyzed for a…

Mathematical Ability Relies on Knowledge, Too

ERIC Educational Resources Information Center

Sweller, John; Clark, Richard E.; Kirschner, Paul A.

2011-01-01

Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…

A School-Based Professional Development Programme for Teachers of Mathematical Modelling in Singapore

ERIC Educational Resources Information Center

Tan, Liang Soon; Ang, Keng Cheng

2016-01-01

A school-based professional development programme (SBPD) aimed at developing secondary school mathematics teachers' competencies to teach mathematical modelling in Singapore is presented and evaluated in this article. The SBPD is characterized by two key features--content elements to develop teachers' knowledge and skills, and transformative…

Professional Vision: Elementary School Principals' Perceptions of Mathematics Instruction

ERIC Educational Resources Information Center

Schoen, Robert C.

2010-01-01

This study explored 78 elementary school principals' perceptions of classroom mathematics instruction in an effort to build understanding of the professional vision (Goodwin, 1994) of elementary school principals as it relates to mathematics instruction. This study also tested the theory of Leadership Content Knowledge (Stein & Nelson, 2003)…

An Intelligent Tutor-Assisted Mathematics Intervention Program for Students with Learning Difficulties

ERIC Educational Resources Information Center

Xin, Yan Ping; Tzur, Ron; Hord, Casey; Liu, Jia; Park, Joo Young; Si, Luo

2017-01-01

The Common Core Mathematics Standards have raised expectations for schools and students in the United States. These standards demand much deeper content knowledge from teachers of mathematics and their students. Given the increasingly diverse student population in today's classrooms and shortage of qualified special education teachers,…

Elementary Administrators' Mathematics Supervision and Self-Efficacy Development

ERIC Educational Resources Information Center

Johnson, Kelly M. Gomez

2017-01-01

Mathematics curriculum reform is changing the content and resources in today's elementary classrooms as well as the culture of mathematics teaching and learning. Administrators face the challenge of leading large-scale curricular change efforts with limited prior knowledge or experiences with reform curricula structures. Administrators, as the…

Mathematics Academies: Cohort 1 Evaluation Study, 2011-2013

ERIC Educational Resources Information Center

Stohr, Amber D.

2014-01-01

Commencing in 2011, the Mathematics Academies Initiative is a series of professional development academies (lasting 1 to 2 years, depending on cohort) with the primary objectives of (a) providing educators with a high quality professional development experience that enhances their mathematical content knowledge and pedagogical skills, and (b)…

The Development of Beginning Mathematics Teacher Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Lannin, John K.; Webb, Matthew; Chval, Kathryn; Arbaugh, Fran; Hicks, Sarah; Taylor, Cynthia; Bruton, Rebecca

2013-01-01

Recent research efforts (Schmidt et al. in "The preparation gap: teacher education for middle school mathematics in six countries," MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical…

Reflective Field Experiences for Success in Teaching Elementary Mathematics

ERIC Educational Resources Information Center

Robards, Shirley N.

2009-01-01

In this paper, the author discusses the major components of a junior level pedagogy course for elementary education majors learning to teach mathematics. The course reviews content and knowledge of the teacher candidates and introduces methods and materials for teaching elementary mathematics using the Standards or benchmarks from the National…

Big Challenges and Big Opportunities: The Power of "Big Ideas" to Change Curriculum and the Culture of Teacher Planning

ERIC Educational Resources Information Center

Hurst, Chris

2014-01-01

Mathematical knowledge of pre-service teachers is currently "under the microscope" and the subject of research. This paper proposes a different approach to teacher content knowledge based on the "big ideas" of mathematics and the connections that exist within and between them. It is suggested that these "big ideas"…

TPACK and Pre-Service Teacher Mathematics Education: Defining a Signature Pedagogy for Mathematics Education Using ICT and Based on the Metaphor "Mathematics Is a Language"

ERIC Educational Resources Information Center

Larkin, Kevin; Jamieson-Proctor, Romina; Finger, Glenn

2012-01-01

National professional standards for teachers in Australia (AITSL, 2011) expect teacher education graduates to demonstrate technological, pedagogical and content knowledge (TPACK). Those standards have emerged concurrently with the development of a new Australian mathematics curriculum. Thus, the expectation is that graduates can demonstrate the…

Investigating Pedagogical Content Knowledge-in-Action

ERIC Educational Resources Information Center

Taylan, Rukiye Didem; da Ponte, João Pedro

2016-01-01

This article investigates the pedagogical content knowledge (PCK) of a teacher educator who teaches 5th-grade mathematics in a school in the context of a university-school partnership project. PCK is analyzed in a qualitative way through video-taped classroom episodes with focus on interactions between the teacher and the students as well as the…

ICT Use in Science and Mathematics Teacher Education in Tanzania: Developing Technological Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Kafyulilo, Ayoub; Fisser, Petra; Pieters, Jules; Voogt, Joke

2015-01-01

Currently, teacher education colleges in Tanzania are being equipped with computers to prepare teachers who can integrate technology in teaching. Despite these efforts, teachers are not embracing the use of technology in their teaching. This study adopted Technological Pedagogical Content Knowledge (TPACK) as a framework for describing the…

The Development Process of a Mathematic Teacher's Technological Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Yildiz, Hilal; Gokcek, Tuba

2018-01-01

Technology is an indispensable part of the educational curriculum, and large budgets have been allocated to provide technological infrastructure in secondary education institutions in Turkey. It is important that teachers have the technological pedagogical content knowledge (TPCK) to successfully integrate technology into their courses. The aim of…

Connecting Pre-Service Teachers with Contemporary Mathematics Practices: Selecting and Sequencing Students' Work Samples

ERIC Educational Resources Information Center

Livy, Sharyn; Muir, Tracey; Downton, Ann

2017-01-01

One of the challenges facing teacher educators is providing our pre-service teachers (PSTs) with authentic experiences that cross the boundaries between Initial Teacher Education (ITE) and the classroom. An additional challenge facing the mathematics teacher educator, is addressing and deepening PSTs' mathematical content knowledge (MCK), which…

Students' Perception of Teachers' Characteristics and Their Attitude towards Mathematics in Oron Education Zone, Nigeria

ERIC Educational Resources Information Center

Etuk, Etuk N.; Afangideh, Maria E.; Uya, Asukwo O.

2013-01-01

The study sought to find out the relationship between how students perceive their teachers' in respect of knowledge of Mathematics content, communication ability, use of appropriate teaching strategies and teachers' classroom management skills and students' attitude towards mathematics. The population of the study comprised all the second year…

Elementary Teachers' Understanding and Use of Cognition Based Assessment Learning Progression Materials for Multiplication and Division

ERIC Educational Resources Information Center

Harrison, Ryan Matthew

2012-01-01

Teachers' knowledge of mathematical content and children's mathematical thinking have been identified as critical elements related to teachers' ability to effectively teach mathematics (Fennema & Franke, 1992; Kazemi & Franke, 2001; Ma, 1999; Peterson, Carpenter, & Fennema, 1989). Literature on teachers' knowledge…

Problem Posing as a Pedagogical Strategy: A Teacher's Perspective

ERIC Educational Resources Information Center

Staebler-Wiseman, Heidi A.

2011-01-01

Student problem posing has been advocated for mathematics instruction, and it has been suggested that problem posing can be used to develop students' mathematical content knowledge. But, problem posing has rarely been utilized in university-level mathematics courses. The goal of this teacher-as-researcher study was to develop and investigate…

Mathematics Teachers' Take-Aways from Morning Math Problems in a Long-Term Professional Development Project

ERIC Educational Resources Information Center

Sevis, Serife; Cross, Dionne; Hudson, Rick

2017-01-01

Considering the role of mathematics-focused professional development programs in improving teachers' content knowledge and quality of teaching, we provided teachers opportunities for dealing with mathematics problems and positioning themselves as students in a large-scale long-term professional development (PD) project. In this proposal, we aimed…

Exploring Turkish Mathematics Teachers' Content Knowledge of Quadrilaterals

ERIC Educational Resources Information Center

Butuner, Suphi Onder; Filiz, Mehmet

2017-01-01

The aim of this research was to examine mathematics teachers' performances in defining special types of quadrilaterals, identifying their family and hierarchically classifying them. In this vein, 33 of 58 primary school mathematics teachers working in the province of Yozgat, Turkey were voluntarily recruited for this survey, and they were asked to…

Dynamic and Interactive Mathematics Learning Environments: The Case of Teaching the Limit Concept

ERIC Educational Resources Information Center

Martinovic, Dragana; Karadag, Zekeriya

2012-01-01

This theoretical study is an attempt to explore the potential of the dynamic and interactive mathematics learning environments (DIMLE) in relation to the technological pedagogical content knowledge (TPACK) framework. DIMLE are developed with intent to support learning mathematics through free exploration in a less constrained environment. A…

Practical Use of ICT in Science and Mathematics Teachers' Training at Dar es Salaam University College of Education: An Analysis of Prospective Teachers' Technological Pedagogical Content Knowledge

ERIC Educational Resources Information Center

Kafyulilo, Ayoub C.

2010-01-01

This study investigated the ways through which pre-service science and mathematics teachers at Dar es Salaam University College of Education (DUCE) can acquire competencies for integrating technology pedagogy and content in teaching. Specifically the study investigated the preservice teachers' ICT integration competencies; practices that can be…

"I Believe the Most Helpful Thing Was Him Skipping over the Proof": Examining PCK in a Senior Secondary Mathematics Lesson

ERIC Educational Resources Information Center

Maher, Nicole; Chick, Helen; Muir, Tracey

2016-01-01

Pedagogical content knowledge is widely considered an essential and complex facet of mathematics teacher knowledge, but little research has focused on PCK at the senior secondary level. This study explores some of the complexities of PCK in a teacher's lesson for senior secondary students by analysing data from lesson observation, the teacher's…

Effects on the Technological Pedagogical Content Knowledge of Early Childhood Teacher Candidates Using Digital Storytelling to Teach Mathematics

ERIC Educational Resources Information Center

Kildan, Abdullah Oguzhan; Incikabi, Lutfi

2015-01-01

This study aimed to present early childhood teacher candidates' experiences preparing digital stories and to reveal the resulting changes, if any, in self-reported technological pedagogical content knowledge (TPACK). This study was quasi-experimental and indicated that teacher candidates' evaluations of digital storytelling were affected by their…

Development of Pre-Service Physics Teachers' Pedagogical Content Knowledge (PCK) throughout Their Initial Training

ERIC Educational Resources Information Center

Karal, Isik Saliha; Alev, Nedim

2016-01-01

The purpose of this study was to investigate the development of pre-service physics teachers' pedagogical content knowledge (PCK) on the subject of electricity and magnetism after their completion of physics and mathematics courses. A descriptive longitudinal development research was carried out with 13 pre-service teachers (PTs) who completed…

Repairing Leaks in the Chemistry Teacher Pipeline: A Longitudinal Analysis of Praxis Chemistry Subject Assessment Examinees and Scores

ERIC Educational Resources Information Center

Shah, Lisa; Hao, Jie; Schneider, Jeremy; Fallin, Rebekah; Cortes, Kimberly Linenberger; Ray, Herman E.; Rushton, Gregory T.

2018-01-01

Teachers play a critical role in the preparation of future science, technology, engineering, and mathematics majors and professionals. What teachers know about their discipline (i.e., content knowledge) has been identified as an important aspect of instructional effectiveness; however, studies have not yet assessed the content knowledge of…

Secondary School Teachers' Pedagogical Content Knowledge of Some Common Student Errors and Misconceptions in Sets

ERIC Educational Resources Information Center

Kolitsoe Moru, Eunice; Qhobela, Makomosela

2013-01-01

The study investigated teachers' pedagogical content knowledge of common students' errors and misconceptions in sets. Five mathematics teachers from one Lesotho secondary school were the sample of the study. Questionnaires and interviews were used for data collection. The results show that teachers were able to identify the following students'…

Mentoring to Alleviate Anxiety in Pre-Service Primary Mathematics Teachers: An Orientation towards Improvement Rather than Evaluation

ERIC Educational Resources Information Center

Perkins, Timothy

2015-01-01

Increasing numbers of primary pre-service teachers (PSTs) enrolled in Education degrees in Australia enter university with insufficient mathematical content knowledge (Livy & Vale, 2011) and low confidence levels about their ability to teach and do the mathematics required for their intended role as classroom teachers (Wilson, 2009). Mentoring…

Developing Mathematical Knowledge through Social Justice Pedagogy with Young Adult Arab Women

ERIC Educational Resources Information Center

Tanko, Mohammed Goma; Atweh, Bill

2012-01-01

The study involved a group of Middle Eastern Muslim women learning mathematics through social justice pedagogy. The findings suggest that the involvement of students in social justice issues has not lead into a decline in their opportunity to learn mathematical content as set in the course. However, this approach has helped them to develop…

Teaching Mathematics to Secondary Students with Emotional and Behavioral Disorders: Challenges and Practical Suggestions for Teachers

ERIC Educational Resources Information Center

Mulcahy, Candace A.; Krezmien, Michael; Maccini, Paula

2014-01-01

While the Common Core State Standards and state learning standards guide teachers in what mathematical content knowledge should be addressed as well as the processes and proficiencies necessary for developing mathematical competence, several student- and teacher-related factors may hinder student access to the general education curriculum for…

A Study of Special Education Teachers' TPACK Development in Mathematics and Science through Assessment of Lesson Plans

ERIC Educational Resources Information Center

Lyublinskaya, Irina; Tournaki, Nelly

2014-01-01

Invited as a paper from SITE 2013. This study focuses on the development of Technological Pedagogical And Content Knowledge (TPACK) in mathematics and science of pre-service special education teachers for teaching mathematics and science via one course. This course introduces a variety of strategies and techniques for using instructional…

Perspectives on Pre-Service Teacher Knowledge for Teaching Early Algebra

ERIC Educational Resources Information Center

McAuliffe, Sharon; Lubben, Fred

2013-01-01

This paper examines a pre-service teacher's content knowledge for teaching early algebra from two perspectives, i.e. using "Rowland's Knowledge Quartet" theory and "Ball's framework for Mathematical Knowledge for Testing" (MKfT). The study intends to examine the differences between the influences using each framework and to…

How to Build a Course in Mathematical–Biological Modeling: Content and Processes for Knowledge and Skill

PubMed Central

2010-01-01

Biological problems in the twenty-first century are complex and require mathematical insight, often resulting in mathematical models of biological systems. Building mathematical–biological models requires cooperation among biologists and mathematicians, and mastery of building models. A new course in mathematical modeling presented the opportunity to build both content and process learning of mathematical models, the modeling process, and the cooperative process. There was little guidance from the literature on how to build such a course. Here, I describe the iterative process of developing such a course, beginning with objectives and choosing content and process competencies to fulfill the objectives. I include some inductive heuristics for instructors seeking guidance in planning and developing their own courses, and I illustrate with a description of one instructional model cycle. Students completing this class reported gains in learning of modeling content, the modeling process, and cooperative skills. Student content and process mastery increased, as assessed on several objective-driven metrics in many types of assessments. PMID:20810966

Learning Together

ERIC Educational Resources Information Center

Knapp, Andrea K.; Jefferson, Vetrece M.; Landers, Racheal

2013-01-01

The old adage goes, "Parents are their children's first and most important teachers." Yet when it comes to mathematics, parents often feel inadequate to help their children with homework tasks, let alone teach them important content. Compounding the problem of low parental knowledge of mathematics, parents' "perceived" inadequacies or indifference…

Teaching for Understanding: The Complex Nature of Pedagogical Content Knowledge in Pre-Service Education

ERIC Educational Resources Information Center

Nilsson, Pernilla

2008-01-01

This paper explores the development of student-teachers' pedagogical content knowledge (PCK) during pre-service education. Four student-teachers in mathematics and science participated in a project teaching physics to students aged 9-11 years once a week over a 12-month period. One-third of the lessons were videotaped and the student-teachers were…

"People Can Go against the Government": Risk-Based Decision Making and High School Students' Concepts of Society

ERIC Educational Resources Information Center

Radakovic, Nenad

2015-01-01

Research in mathematics education stresses the importance of content knowledge in solving authentic tasks in statistics and in risk-based decision making. Existing research supports the claim that students rely on content knowledge and context expertise to make sense of data. In this article, however, I present evidence that the relationship…

The Relationship between Agriculture Knowledge Bases for Teaching and Sources of Knowledge

ERIC Educational Resources Information Center

Rice, Amber H.; Kitchel, Tracy

2015-01-01

The purpose of this study was to describe the agriculture knowledge bases for teaching of agriculture teachers and to see if a relationship existed between years of teaching experience, sources of knowledge, and development of pedagogical content knowledge (PCK), using quantitative methods. A model of PCK from mathematics was utilized as a…

In Pursuit of a Connected Way of Knowing: The Case of One Mathematics Teacher

ERIC Educational Resources Information Center

Agudelo-Valderrama, Cecilia; Martínez, Diana

2016-01-01

In this paper, we offer illustrations of a mathematics teacher's difficulties with content knowledge when trying to find connections between school mathematics and science; we do so by describing the development of this teacher's thinking and learning in her pursuit of connections between the concepts of slope of a line and density of matter. The…

Predicting the Quality of Elementary Mathematics Teachers Utilizing Pre-Graduation Data Collected from Teacher Preparation Programs

ERIC Educational Resources Information Center

Robertson, Mary Amos

2016-01-01

In order to change the direction of mathematics education, the training of elementary teachers in the United States needs to be of equal or higher quality than top preforming countries. However, pre-service elementary teachers in the United States fall behind their peers in other countries in mathematical content knowledge and mathematical…

Research on the Development of Middle School Mathematics Pre-Service Teachers' Perceptions Regarding the Use of Technology in Teaching Mathematics

ERIC Educational Resources Information Center

Akkaya, Recai

2016-01-01

This study aimed to investigate the changes in teacher perceptions regarding the use of technology subsequent to the training about technology integration in mathematics teaching. A training program that included combined technology, pedagogy and content knowledge was prepared and implemented on pre-service teachers with this aim. Exploratory…

Developing Elementary Teachers' Knowledge about Functions and Rate of Change through Modeling

ERIC Educational Resources Information Center

Weber, Eric; Tallman, Michael A.; Middleton, James A.

2015-01-01

The purpose of this article is to describe the development of elementary school teachers' mathematical knowledge for teaching as they participated in a Modeling Instruction environment that placed heavy emphasis on improving their subject-matter knowledge as a basis for affecting the development of their pedagogical content knowledge. We…

Construction of teacher knowledge in context: Preparing elementary teachers to teach mathematics and science

NASA Astrophysics Data System (ADS)

Lowery, Maye Norene Vail

1998-12-01

The purposes of this study were to further the understanding of how preservice teacher construct teacher knowledge and pedagogical content knowledge of elementary mathematics and science and to determine the extent of that knowledge in a school-based setting. Preservice teachers, university instructors, inservice teachers, and other school personnel were involved in this context-specific study. Evidence of the preservice teachers' knowledge construction (its acquisition, its dimensions, and the social context) was collected through the use of a qualitative methodology. Collected data included individual and group interviews, course documents, artifacts, and preservice teaching portfolios. Innovative aspects of this integrated mathematics and science elementary methods course included standards-based instruction with immediate access to field experiences. Grade-level teams of preservice and inservice teachers planned and implemented lessons in mathematics and science for elementary students. An on-site, portable classroom building served as a mathematics and science teaching and learning laboratory. A four-stage analysis was performed, revealing significant patterns of learning. An ecosystem of learning within a constructivist learning environment was identified to contain three systems: the university system; the school system; and the cohort of learners system. A mega system for the construction of teacher knowledge was revealed in the final analysis. Learning venues were discovered to be the conduits of learning in a situated learning context. Analysis and synthesis of data revealed an extensive acquisition of teacher knowledge and pedagogical content knowledge through identified learning components. Patience, flexibility, and communication were identified as necessities for successful teaching. Learning components included: collaboration with inservice teachers; implementation of discovery learning and hands-on/minds-on learning; small groupwork; lesson planning; classroom management; and application of standards-based instruction. Prolonged, extensive classroom involvement provided familiarity with the ability levels of elementary students. Gains in positive attitudes and confidence in teaching mathematics and science were identified as direct results of this experience. This may be attributed to the immersion in the school-based setting (hands-on) and the standards-based approach (minds-on) methods course. The results are written in case study form using thick description with an emphasis on preservice teachers.

Content Knowledge in Teaching, an Investigation into an Adequate "Milieu" for Teaching Dance: The Case of Indian Dance in France

ERIC Educational Resources Information Center

Monique, Loquet; Malini, Ranganathan

2010-01-01

Since the 1970s, scientific researchers have shown that the nature and practice of the knowledge being taught plays an important role in the organization of teaching. Teaching content, first in mathematics, then in physical education, has become the object of scientific research in didactics in France. This research questions the commonplace…

Impact of a Required Pharmaceutical Calculations Course on Mathematics Ability and Knowledge Retention

PubMed Central

Buring, Shauna M.; Papas, Elizabeth

2013-01-01

Objective. To assess doctor of pharmacy (PharmD) students’ mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. Methods. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Results. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. Conclusions. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students’ overall ability to perform fundamental and application-based calculations. PMID:23966727

Impact of a required pharmaceutical calculations course on mathematics ability and knowledge retention.

PubMed

Hegener, Michael A; Buring, Shauna M; Papas, Elizabeth

2013-08-12

To assess doctor of pharmacy (PharmD) students' mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students' overall ability to perform fundamental and application-based calculations.

The Correlation between Prospective Teachers' Knowledge of Algebraic Inverse Operations and Teaching Competency--Using the Square Root as an Example

ERIC Educational Resources Information Center

Leung, Issic Kui Chiu; Ding, Lin; Leung, Allen Yuk Lun; Wong, Ngai Ying

2016-01-01

This study is part of a larger study investigating the subject matter knowledge and pedagogical content knowledge of Hong Kong prospective mathematics teachers, the relationship between the knowledge of algebraic operation and its inverse, and their teaching competency. In this paper, we address the subject matter knowledge and pedagogical content…

Toward Technology Integration in Mathematics Education: A Technology-Integration Course Planning Assignment

ERIC Educational Resources Information Center

Kersaint, Gladis

2007-01-01

This article describes a technology integration course planning assignment that was developed to enhance preservice teachers' technological pedagogical content knowledge (TPCK). This assignment required preservice teachers work with peers to integrate various technological tools (e.g., graphing calculators, web-based mathematics applets, etc) in a…

Characterising the Perceived Value of Mathematics Educational Apps in Preservice Teachers

ERIC Educational Resources Information Center

Handal, Boris; Campbell, Chris; Cavanagh, Michael; Petocz, Peter

2016-01-01

This study validated the semantic items of three related scales aimed at characterising the perceived worth of mathematics-education-related mobile applications (apps). The technological pedagogical content knowledge (TPACK) model was used as the conceptual framework for the analysis. Three hundred and seventy-three preservice students studying…

Establishing a Professional Learning Community among Middle School Mathematics Teachers

ERIC Educational Resources Information Center

Koellner-Clark, Karen; Borko, Hilda

2004-01-01

The paper examines how community was established in a professional development institute that focused on algebra content knowledge for middle school mathematics teachers. This qualitative study was framed within a situative perspective. We analyzed multiple data sources to identify the ways in which community was established. Results indicate…

Analyzing Mathematical Tasks: A Catalyst for Change?

ERIC Educational Resources Information Center

Arbaugh, Fran; Brown, Catherine A.

2005-01-01

In this study we investigate a strategy for engaging high school mathematics teachers in an "initial" examination of their teaching in a way that is nonthreatening and at the same time effectively supports the development of teachers' pedagogical content knowledge [Shulman (1986). "Educational Researcher," 15(2), 4-14]. Based on the work…

Traditional vs. Innovative Uses of Computers among Mathematics Pre-Service Teachers in Serbia

ERIC Educational Resources Information Center

Teo, Timothy; Milutinovic, Verica; Zhou, Mingming; Bankovic, Dragic

2017-01-01

This study examined pre-service teachers' intentions to use computers in traditional and innovative teaching practices in primary mathematics classrooms. It extended the technology acceptance model (TAM) by adding as external variables pre-service teachers' experience with computers and their technological pedagogical content knowledge (TPCK).…

Meeting the Demands of the Knowledge Based Economy: Strengthening Undergraduate Science, Mathematics and Engineering Education. Hearing Before the Subcommittee on Research, Committee on Science, House of Representatives, 107th Congress, First Session (March 7, 2002).

ERIC Educational Resources Information Center

Congress of the U.S., Washington, DC. House.

This hearing was held to examine the current state of mathematics, science, and engineering education at the undergraduate level by focusing on the demands of a knowledge-based economy. Contents include opening statements by Representative Nick Smith, Chairman, Subcommittee on Research, Committee in Science, U.S. House of Representatives;…

Informing Estimates of Program Effects for Studies of Mathematics Professional Development Using Teacher Content Knowledge Outcomes.

PubMed

Phelps, Geoffrey; Kelcey, Benjamin; Jones, Nathan; Liu, Shuangshuang

2016-10-03

Mathematics professional development is widely offered, typically with the goal of improving teachers' content knowledge, the quality of teaching, and ultimately students' achievement. Recently, new assessments focused on mathematical knowledge for teaching (MKT) have been developed to assist in the evaluation and improvement of mathematics professional development. This study presents empirical estimates of average program change in MKT and its variation with the goal of supporting the design of experimental trials that are adequately powered to detect a specified program effect. The study drew on a large database representing five different assessments of MKT and collectively 326 professional development programs and 9,365 teachers. Results from cross-classified hierarchical growth models found that standardized average change estimates across the five assessments ranged from a low of 0.16 standard deviations (SDs) to a high of 0.26 SDs. Power analyses using the estimated pre- and posttest change estimates indicated that hundreds of teachers are needed to detect changes in knowledge at the lower end of the distribution. Even studies powered to detect effects at the higher end of the distribution will require substantial resources to conduct rigorous experimental trials. Empirical benchmarks that describe average program change and its variation provide a useful preliminary resource for interpreting the relative magnitude of effect sizes associated with professional development programs and for designing adequately powered trials. © The Author(s) 2016.

Teaching Place Value Concepts to First Grade Romanian Students: Teacher Knowledge and its Influence on Student Learning

ERIC Educational Resources Information Center

Tanase, Madalina

2011-01-01

Researchers (Ball, 2003; Ma, 1999; Schulman, 1986) have long investigated how a teacher's subject matter and pedagogical content knowledge impact on students' learning of mathematics. In an attempt to account for the relationship between teacher knowledge and student learning, this study examined four Romanian first grade teachers' knowledge about…

The Effects of a STEM Intervention on Elementary Students' Science Knowledge and Skills

ERIC Educational Resources Information Center

Cotabish, Alicia; Dailey, Debbie; Robinson, Ann; Hughes, Gail

2013-01-01

The purpose of the study was to assess elementary students' science process skills, content knowledge, and concept knowledge after one year of participation in an elementary Science, Technology, Engineering, and Mathematics (STEM) program. This study documented the effects of the combination of intensive professional development and the use of…

Process Mediates Structure: The Relation between Preschool Teacher Education and Preschool Teachers' Knowledge

ERIC Educational Resources Information Center

Blömeke, Sigrid; Jenßen, Lars; Grassmann, Marianne; Dunekacke, Simone; Wedekind, Hartmut

2017-01-01

Data about processes and outcomes of preschool teacher education is scarce. This paper examines the opportunities to learn (OTL) of prospective preschool teachers (N = 1,851) at different types and stages of preschool teacher education and their relation to general pedagogical knowledge (GPK), mathematics pedagogical content knowledge (MPCK), and…

Virtually the Same: A Comparison of STEM Students' Content Knowledge, Course Performance, and Motivation to Learn in Virtual and Face-to-Face Introductory Biology Laboratories. Research and Teaching

ERIC Educational Resources Information Center

Reece, Amber J.; Butler, Malcolm B.

2017-01-01

Biology I is a required course for many science, technology, engineering, and mathematics (STEM) majors and is often their first college-level laboratory experience. The replacement of the traditional face-to-face laboratory experience with virtual laboratories could influence students' content knowledge, motivation to learn biology, and overall…

The Role of "Local Theories": Teacher Knowledge and Its Impact on Engaging Students with Challenging Tasks

ERIC Educational Resources Information Center

Choppin, Jeffrey

2011-01-01

This study explores the extent to which a teacher elicited students' mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher's knowledge in terms of a "local theory" of instruction, a form of pedagogical content knowledge that involves an empirically tested set of…

A Case Study of Dilemmas Encountered When Connecting Middle School Mathematics Instruction to Relevant Real World Examples

ERIC Educational Resources Information Center

Sugimoto, Amanda T.; Turner, Erin E.; Stoehr, Kathleen J.

2017-01-01

The pedagogical practice of connecting mathematical content to real world contexts, particularly contexts relevant to students' knowledge and experiences, can positively impact student motivation as well as promote conceptual understanding. However, little is known about how middle school teachers actually make relevant world connections, and more…

The Development of a Cognitively-Diagnostic Formative Assessment of the Early Concept of Angle

ERIC Educational Resources Information Center

Khasanova, Elvira

2016-01-01

Students' development of conceptual understandings is a central goal of mathematics education (CCSS-Mathematics, 2010). Such a challenging, yet ambiguous, goal cannot be achieved without empowering teachers with the knowledge and tools critical for their ability to adequately convey the content, and assess and interpret students' performance. This…

Supporting Kindergarten Teachers' Mathematics Instruction and Student Achievement through a Curriculum-Based Professional Development Program

ERIC Educational Resources Information Center

Polly, Drew; Wang, Chuang; Lambert, Richard; Martin, Christie; McGee, Jennifer Richardson; Pugalee, David; Lehew, Amy

2017-01-01

This study investigates the impacts of a year-long professional development program on Kindergarten teachers' beliefs and practices and the association of these changes with student achievement in mathematics measured by curriculum-based instruments. Although teacher content knowledge was not statistically significantly different before and after…

Musical Palindromes for Liberal Arts Students

ERIC Educational Resources Information Center

von Renesse, Christine

2012-01-01

This paper shows how to teach a mathematics for liberal arts class in an inquiry-based way using ideas from music to launch the mathematical activities. No musical knowledge is required to understand and teach the material. The main activity is analyzing the differences between two kinds of rhythmic palindromes. The content is mathematically…

Procedural versus Content-Related Hints for Word Problem Solving: An Exploratory Study

ERIC Educational Resources Information Center

Kock, W. D.; Harskamp, E. G.

2016-01-01

For primary school students, mathematical word problems are often more difficult to solve than straightforward number problems. Word problems require reading and analysis skills, and in order to explain their situational contexts, the proper mathematical knowledge and number operations have to be selected. To improve students' ability in solving…

Pre-Service Teachers' Beliefs about Knowledge, Mathematics, and Science

ERIC Educational Resources Information Center

Cady, Jo Ann; Rearden, Kristin

2007-01-01

This study examines the beliefs of K-8 preservice teachers during a content methods course. The goals of this course included exposing the preservice teachers to student-centered instructional methods for math and science and encouraging the development of lessons that would integrate mathematics and science. Prior research suggested that one must…

Maple (Computer Algebra System) in Teaching Pre-Calculus: Example of Absolute Value Function

ERIC Educational Resources Information Center

Tuluk, Güler

2014-01-01

Modules in Computer Algebra Systems (CAS) make Mathematics interesting and easy to understand. The present study focused on the implementation of the algebraic, tabular (numerical), and graphical approaches used for the construction of the concept of absolute value function in teaching mathematical content knowledge along with Maple 9. The study…

Making Culturally Responsive Mathematics Teaching Explicit: A Lesson Analysis Tool

ERIC Educational Resources Information Center

Aguirre, Julia M.; Zavala, Maria del Rosario

2013-01-01

In the United States, there is a need for pedagogical tools that help teachers develop essential pedagogical content knowledge and practices to meet the mathematical education needs of a growing culturally and linguistically diverse student population. In this article, we introduce an innovative lesson analysis tool that focuses on integrating…

A Mathematics Teacher's Practice in a Technological Environment: A Case Study Analysis Using Two Complementary Theories

ERIC Educational Resources Information Center

Tabach, Michal

2011-01-01

Integrating technology in school mathematics has become more and more common. The teacher is a key person in integrating technology into everyday practice. To understand teacher practice in a technological environment, this study proposes using two theoretical perspectives: the theory of technological pedagogical content knowledge to analyze…

Modeling evolution of the mind and cultures: emotional Sapir-Whorf hypothesis

NASA Astrophysics Data System (ADS)

Perlovsky, Leonid I.

2009-05-01

Evolution of cultures is ultimately determined by mechanisms of the human mind. The paper discusses the mechanisms of evolution of language from primordial undifferentiated animal cries to contemporary conceptual contents. In parallel with differentiation of conceptual contents, the conceptual contents were differentiated from emotional contents of languages. The paper suggests the neural brain mechanisms involved in these processes. Experimental evidence and theoretical arguments are discussed, including mathematical approaches to cognition and language: modeling fields theory, the knowledge instinct, and the dual model connecting language and cognition. Mathematical results are related to cognitive science, linguistics, and psychology. The paper gives an initial mathematical formulation and mean-field equations for the hierarchical dynamics of both the human mind and culture. In the mind heterarchy operation of the knowledge instinct manifests through mechanisms of differentiation and synthesis. The emotional contents of language are related to language grammar. The conclusion is an emotional version of Sapir-Whorf hypothesis. Cultural advantages of "conceptual" pragmatic cultures, in which emotionality of language is diminished and differentiation overtakes synthesis resulting in fast evolution at the price of self doubts and internal crises are compared to those of traditional cultures where differentiation lags behind synthesis, resulting in cultural stability at the price of stagnation. Multi-language, multi-ethnic society might combine the benefits of stability and fast differentiation. Unsolved problems and future theoretical and experimental directions are discussed.

Prospective Teacher Learning: Recognizing Evidence of Conceptual Understanding

ERIC Educational Resources Information Center

Bartell, Tonya Gau; Webel, Corey; Bowen, Brian; Dyson, Nancy

2013-01-01

This study examined prospective teachers' (PSTs) ability to recognize evidence of children's conceptual understanding of mathematics in three content areas before and after an instructional intervention designed to support this ability. It also investigates the role PSTs' content knowledge plays in their ability to recognize children's…

Early Childhood Teachers' Professional Learning in Early Algebraic Thinking: A Model that Supports New Knowledge and Pedagogy

ERIC Educational Resources Information Center

Warren, Elizabeth

2009-01-01

The implementation of a new mathematics syllabus in the elementary context is problematic, especially if it contains a new content area. A professional development model, Transformative Teaching in the Early Years Mathematics (TTEYM) was specifically developed to support the implementation of the new Patterns and Algebra strand. The model was…

Semiotic Structure and Meaning Making: The Performance of English Language Learners on Mathematics Tests

ERIC Educational Resources Information Center

Solano-Flores, Guillermo; Barnett-Clarke, Carne; Kachchaf, Rachel R.

2013-01-01

We examined the performance of English language learners (ELLs) and non-ELLs on Grade 4 and Grade 5 mathematics content knowledge (CK) and academic language (AL) tests. CK and AL items had different semiotic loads (numbers of different types of semiotic features) and different semiotic structures (relative frequencies of different semiotic…

A model of professional competences in mathematics to update mathematical and didactic knowledge of teachers

NASA Astrophysics Data System (ADS)

Díaz, Verónica; Poblete, Alvaro

2017-07-01

This paper describes part of a research and development project carried out in public elementary schools. Its objective was to update the mathematical and didactic knowledge of teachers in two consecutive levels in urban and rural public schools of Region de Los Lagos and Region de Los Rios of southern Chile. To that effect, and by means of an advanced training project based on a professional competences model, didactic interventions based on types of problems and types of mathematical competences with analysis of contents and learning assessment were designed. The teachers' competence regarding the didactic strategy used and its results, as well as the students' learning achievements are specified. The project made possible to validate a strategy of lifelong improvement in mathematics, based on the professional competences of teachers and their didactic transposition in the classroom, as an alternative to consolidate learning in areas considered vulnerable in two regions of the country.

Educating the Next Generation: Improving Teacher Quality in Cambodia. Directions in Development

ERIC Educational Resources Information Center

Tandon, Prateek; Fukao, Tsuyoshi

2015-01-01

This book diagnoses Cambodian teaching quality and presents policy options for reform. Through classroom observation, assessments of mathematics and pedagogical content knowledge, and surveys of teachers and school directors, it sheds light on content and instruction, interactions with school directors, instructional support systems, and the…

Web-Based Instruction on Preservice Teachers' Knowledge of Fraction Operations

ERIC Educational Resources Information Center

Lin, Cheng-Yao

2010-01-01

This study determines whether web-based instruction (WBI) represents an improved method for helping preservice teachers learn procedural and conceptual knowledge of fractions.. The purpose was to compare the effectiveness of web-based instruction (WBI) with the traditional lecture in mathematics content and methods for the elementary school…

The written mathematical communication profile of prospective math teacher in mathematical proving

NASA Astrophysics Data System (ADS)

Pantaleon, K. V.; Juniati, D.; Lukito, A.; Mandur, K.

2018-01-01

Written mathematical communication is the process of expressing mathematical ideas and understanding in writing. It is one of the important aspects that must be mastered by the prospective math teacher as tool of knowledge transfer. This research was a qualitative research that aimed to describe the mathematical communication profile of the prospective mathematics teacher in mathematical proving. This research involved 48 students of Mathematics Education Study Program; one of them with moderate math skills was chosen as the main subject. Data were collected through tests, assignments, and task-based interviews. The results of this study point out that in the proof of geometry, the subject explains what is understood, presents the idea in the form of drawing and symbols, and explains the content/meaning of a representation accurately and clearly, but the subject can not convey the argument systematically and logically. Whereas in the proof of algebra, the subject describes what is understood, explains the method used, and describes the content/meaning of a symbolic representation accurately, systematically, logically, but the argument presented is not clear because it is insufficient detailed and complete.

Integrated learning: ways of fostering the applicability of teachers’ pedagogical and psychological knowledge

PubMed Central

Harr, Nora; Eichler, Andreas; Renkl, Alexander

2015-01-01

In teacher education, general pedagogical and psychological knowledge (PPK) is often taught separately from the teaching subject itself, potentially leading to inert knowledge. In an experimental study with 69 mathematics student teachers, we tested the benefits of fostering the integration of pedagogical content knowledge (PCK) and general PPK with respect to knowledge application. Integration was fostered either by integrating the contents or by prompting the learners to integrate separately taught knowledge. Fostering integration, as compared to a separate presentation without integration help, led to more applicable PPK and greater simultaneous application of PPK and PCK. The advantages of fostering knowledge integration were not moderated by the student teachers’ prior knowledge or working memory capacity. A disadvantage of integrating different knowledge types referred to increased learning times. PMID:26082740

Secondary Math Instructional Practices, Academic Optimism, Instructional Leadership, and Receptivity to Curricular Change in Schools with High and Low Mathematics Mastery and Poverty

ERIC Educational Resources Information Center

Kennedy, Scott J.

2014-01-01

The purpose of this study was to investigate how high school mathematics teachers' descriptions of academic optimism, responsive teaching, technological pedagogical content knowledge, formative assessment, reflective practice, supervisor instructional leadership, and receptivity to change are related to student mastery on a NYS Regents exam in…

The Nature of Argumentation in School Mathematics and Physics Texts: The Case of Periodicity

ERIC Educational Resources Information Center

Triantafillou, Chrissavgi; Spiliotopoulou, Vasiliki; Potari, Despina

2016-01-01

The present study explores reasoning and argumentation in Greek mathematics and physics texts in specific topics related to the notion of periodicity. In our study, argumentation is taken as the sequence of the modes of reasoning (MsoR) that an author develops in a text when organizing and presenting new knowledge. Inductive content analysis was…

Summer Teacher Enhancement Institute for Science, Mathematics, and Technology Using the Problem-Based Learning Model

NASA Technical Reports Server (NTRS)

Petersen, Richard H.

1997-01-01

The objectives of the Institute were: (a) increase participants' content knowledge about aeronautics, science, mathematics, and technology, (b) model and promote the use of scientific inquiry through problem-based learning, (c) investigate the use of instructional technologies and their applications to curricula, and (d) encourage the dissemination of TEI experiences to colleagues, students, and parents.

Exploring the Mathematical Knowledge for Teaching Geometry and Measurement through the Design and Use of Rich Assessment Tasks

ERIC Educational Resources Information Center

Steele, Michael D.

2013-01-01

While recent national and international assessments have shown mathematical progress being made by US students, little to no gains are evident in the areas of geometry and measurement. These reports also suggest that practicing teachers have traditionally had few opportunities to engage in content learning around topics in geometry and…

Pre-service science teachers' perceptions of mathematics courses in a science teacher education programme

NASA Astrophysics Data System (ADS)

Incikabi, Lutfi; Serin, Mehmet Koray

2017-08-01

Most science departments offer compulsory mathematics courses to their students with the expectation that students can apply their experience from the mathematics courses to other fields of study, including science. The current study first aims to investigate the views of pre-service science teachers of science-teaching preparation degrees and their expectations regarding the difficulty level of mathematics courses in science-teaching education programmes. Second, the study investigates changes and the reasons behind the changes in their interest regarding mathematics after completing these courses. Third, the current study seeks to reveal undergraduate science teachers' opinions regarding the contribution of undergraduate mathematics courses to their professional development. Being qualitative in nature, this study was a case study. According to the results, almost all of the students considered that undergraduate mathematics courses were 'difficult' because of the complex and intensive content of the courses and their poor background mathematical knowledge. Moreover, the majority of science undergraduates mentioned that mathematics would contribute to their professional development as a science teacher. On the other hand, they declared a negative change in their attitude towards mathematics after completing the mathematics courses due to continuous failure at mathematics and their teachers' lack of knowledge in terms of teaching mathematics.

Measuring Technological and Content Knowledge of Undergraduate Primary Teachers in Mathematics

NASA Astrophysics Data System (ADS)

Doukakis, Spyros; Chionidou-Moskofoglou, Maria; Mangina-Phelan, Eleni; Roussos, Petros

Twenty-five final-year undergraduate students of primary education who were attending a course on mathematics education participated in a research project during the 2009 spring semester. A repeated measures experimental design was used. Quantitative data on students' computer attitudes, self-efficacy in ICT, attitudes toward educational software, and self-efficacy in maths were collected. Data analysis showed a statistically non-significant improvement on participants' computer attitudes and self-efficacy in ICT and ES, but a significant improvement of self-efficacy in mathematics.

Spaced Retrieval Practice Increases College Students' Short- and Long-Term Retention of Mathematics Knowledge

ERIC Educational Resources Information Center

Hopkins, Robin F.; Lyle, Keith B.; Hieb, Jeff L.; Ralston, Patricia A. S.

2016-01-01

A major challenge college students face is retaining the knowledge they acquire in their classes, especially in cumulative disciplines such as engineering, where ultimate success depends on long-term retention of foundational content. Cognitive psychologists have recently recommended various techniques educators might use to increase retention.…

Examining PCK in a Senior Secondary Mathematics Lesson

ERIC Educational Resources Information Center

Maher, Nicole; Muir, Tracey; Chick, Helen

2015-01-01

Teacher knowledge, including Pedagogical Content Knowledge (PCK), continues to be the focus of research, with the general consensus being that PCK impacts upon teaching and learning. Much of the current research has focused on pre-service teachers and practicing primary teachers, with few studies focused on studying senior secondary teachers' PCK.…

Elementary Education Pre-Service Teachers' Development of Mathematics Technology Integration Skills in a Technology Integration Course

ERIC Educational Resources Information Center

Polly, Drew

2015-01-01

Preparing pre-service teachers to effectively integrate technology in the classroom requires rich experiences that deepen their knowledge of technology, pedagogy, and content and the intersection of these aspects. This study examined elementary education pre-service teachers' development of skills and knowledge in a technology integration course…

Are College Rankings an Indicator of Quality Education?

ERIC Educational Resources Information Center

Schmidt, William; Burroughs, Nathan; Cogan, Lee; Houang, Richard

2011-01-01

Educators need a way of determining how much additional knowledge has been gained by students in a given educational program in comparison with other programs. From the U.S. Teacher Education Study in Mathematics (TEDS), they now have such information. The TEDS yields empirical data on the educational experiences and content knowledge gains of a…

Strategies and Resources for Contextualising the Curriculum Based on the Funds of Knowledge Approach: A Literature Review

ERIC Educational Resources Information Center

Llopart, Mariona; Esteban-Guitart, Moisès

2017-01-01

This article aims to describe and illustrate how the curriculum can be contextualised through different educational experiences based on the funds of knowledge approach. Educational contextualisation is understood to be the linking of curricular content (literacy, science, mathematics, social sciences) with students' lives, including prior…

Topology of Innovation Spaces in the Knowledge Networks Emerging through Questions-And-Answers

PubMed Central

Andjelković, Miroslav; Tadić, Bosiljka; Mitrović Dankulov, Marija; Rajković, Milan; Melnik, Roderick

2016-01-01

The communication processes of knowledge creation represent a particular class of human dynamics where the expertise of individuals plays a substantial role, thus offering a unique possibility to study the structure of knowledge networks from online data. Here, we use the empirical evidence from questions-and-answers in mathematics to analyse the emergence of the network of knowledge contents (or tags) as the individual experts use them in the process. After removing extra edges from the network-associated graph, we apply the methods of algebraic topology of graphs to examine the structure of higher-order combinatorial spaces in networks for four consecutive time intervals. We find that the ranking distributions of the suitably scaled topological dimensions of nodes fall into a unique curve for all time intervals and filtering levels, suggesting a robust architecture of knowledge networks. Moreover, these networks preserve the logical structure of knowledge within emergent communities of nodes, labeled according to a standard mathematical classification scheme. Further, we investigate the appearance of new contents over time and their innovative combinations, which expand the knowledge network. In each network, we identify an innovation channel as a subgraph of triangles and larger simplices to which new tags attach. Our results show that the increasing topological complexity of the innovation channels contributes to network’s architecture over different time periods, and is consistent with temporal correlations of the occurrence of new tags. The methodology applies to a wide class of data with the suitable temporal resolution and clearly identified knowledge-content units. PMID:27171149

Exploring the Reasons for Using Electric Books and Technologic Pedagogical and Content Knowledge of Taiwanese Elementary Mathematics and Science Teachers

ERIC Educational Resources Information Center

Chen, Ho-Yuan; Jang, Syh-Jong

2013-01-01

This study highlights trends and features of E-books and their versatility of this tool in elementary educational settings. There has been little quantitative research employed to examine teachers' reasons for using or not using E-books. The purpose of this study was to examine elementary school mathematics and science teachers' reasons for using…

Making mathematics and science integration happen: key aspects of practice

NASA Astrophysics Data System (ADS)

Ríordáin, Máire Ní; Johnston, Jennifer; Walshe, Gráinne

2016-02-01

The integration of mathematics and science teaching and learning facilitates student learning, engagement, motivation, problem-solving, criticality and real-life application. However, the actual implementation of an integrative approach to the teaching and learning of both subjects at classroom level, with in-service teachers working collaboratively, at second-level education, is under-researched due to the complexities of school-based research. This study reports on a year-long case study on the implementation of an integrated unit of learning on distance, speed and time, within three second-level schools in Ireland. This study employed a qualitative approach and examined the key aspects of practice that impact on the integration of mathematics and science teaching and learning. We argue that teacher perspective, teacher knowledge of the 'other subject' and of technological pedagogical content knowledge (TPACK), and teacher collaboration and support all impact on the implementation of an integrative approach to mathematics and science education.

Technological pedagogical content knowledge of junior high school mathematics teachers in teaching linear equation

NASA Astrophysics Data System (ADS)

Wati, S.; Fitriana, L.; Mardiyana

2018-04-01

Linear equation is one of the topics in mathematics that are considered difficult. Student difficulties of understanding linear equation can be caused by lack of understanding this concept and the way of teachers teach. TPACK is a way to understand the complex relationships between teaching and content taught through the use of specific teaching approaches and supported by the right technology tools. This study aims to identify TPACK of junior high school mathematics teachers in teaching linear equation. The method used in the study was descriptive. In the first phase, a survey using a questionnaire was carried out on 45 junior high school mathematics teachers in teaching linear equation. While in the second phase, the interview involved three teachers. The analysis of data used were quantitative and qualitative technique. The result PCK revealed teachers emphasized developing procedural and conceptual knowledge through reliance on traditional in teaching linear equation. The result of TPK revealed teachers’ lower capacity to deal with the general information and communications technologies goals across the curriculum in teaching linear equation. The result indicated that PowerPoint constitutes TCK modal technological capability in teaching linear equation. The result of TPACK seems to suggest a low standard in teachers’ technological skills across a variety of mathematics education goals in teaching linear equation. This means that the ability of teachers’ TPACK in teaching linear equation still needs to be improved.

Learning Trajectory for Transforming Teachers' Knowledge for Teaching Mathematics and Science with Digital Image and Video Technologies in an Online Learning Experience

ERIC Educational Resources Information Center

Niess, Margaret L.; Gillow-Wiles, Henry

2014-01-01

This qualitative cross-case study explores the influence of a designed learning trajectory on transforming teachers' technological pedagogical content knowledge (TPACK) for teaching with digital image and video technologies. The TPACK Learning Trajectory embeds tasks with specific instructional strategies within a social metacognitive…

Exploring How Understandings from Abstract Algebra Can Influence the Teaching of Structure in Early Algebra

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2017-01-01

Empirical work that connects content knowledge to teaching practice has become increasingly important in discussions around a professional knowledge base for teaching. This paper aims to continue that work, reporting a single exploratory case study of one elementary mathematics teacher. The purpose of the study was to investigate how introducing…

Physics of Non-Newtonian Fluids and Interdisciplinary Relations (Biology and Criminology)

ERIC Educational Resources Information Center

Holubova, R.

2018-01-01

The aim of the paper is the presentation of an interdisciplinary topic that allows applying content knowledge in physics, mathematics and biology in real life environment. Students use to play games and view crime scenes but in common they have little knowledge about the science used during crime scene investigation. In this paper the science…

The analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference

NASA Astrophysics Data System (ADS)

Ma'rufi, Budayasa, I. Ketut; Juniati, Dwi

2017-08-01

The aim of this study was to describe the analysis of mathematics teachers' learning on algebra function limit material based on teaching experience difference. The purpose of this study is to describe the analysis of mathematics teacher's learning on limit algebraic functions in terms of the differences of teaching experience. Learning analysis focused on Pedagogical Content Knowledge (PCK) of teachers in mathematics on limit algebraic functions related to the knowledge of pedagogy. PCK of teachers on limit algebraic function is a type of specialized knowledge for teachers on how to teach limit algebraic function that can be understood by students. Subjects are two high school mathematics teacher who has difference of teaching experience they are one Novice Teacher (NP) and one Experienced Teacher (ET). Data are collected through observation of learning in the class, videos of learning, and then analyzed using qualitative analysis. Teacher's knowledge of Pedagogic defined as a knowledge and understanding of teacher about planning and organizing of learning, and application of learning strategy. The research results showed that the Knowledge of Pedagogy on subject NT in mathematics learning on the material of limit function algebra showed that the subject NT tended to describe procedurally, without explaining the reasons why such steps were used, asking questions which tended to be monotonous not be guiding and digging deeper, and less varied in the use of learning strategies while subject ET gave limited guidance and opportunities to the students to find their own answers, exploit the potential of students to answer questions, provide an opportunity for students to interact and work in groups, and subject ET tended to combine conceptual and procedural explanation.

The influence of test mode and visuospatial ability on mathematics assessment performance

NASA Astrophysics Data System (ADS)

Logan, Tracy

2015-12-01

Mathematics assessment and testing are increasingly situated within digital environments with international tests moving to computer-based testing in the near future. This paper reports on a secondary data analysis which explored the influence the mode of assessment—computer-based (CBT) and pencil-and-paper based (PPT)—and visuospatial ability had on students' mathematics test performance. Data from 804 grade 6 Singaporean students were analysed using the knowledge discovery in data design. The results revealed statistically significant differences between performance on CBT and PPT test modes across content areas concerning whole number algebraic patterns and data and chance. However, there were no performance differences for content areas related to spatial arrangements geometric measurement or other number. There were also statistically significant differences in performance between those students who possess higher levels of visuospatial ability compared to those with lower levels across all six content areas. Implications include careful consideration for the comparability of CBT and PPT testing and the need for increased attention to the role of visuospatial reasoning in student's mathematics reasoning.

Blooms' separation of the final exam of Engineering Mathematics II: Item reliability using Rasch measurement model

NASA Astrophysics Data System (ADS)

Fuaad, Norain Farhana Ahmad; Nopiah, Zulkifli Mohd; Tawil, Norgainy Mohd; Othman, Haliza; Asshaari, Izamarlina; Osman, Mohd Hanif; Ismail, Nur Arzilah

2014-06-01

In engineering studies and researches, Mathematics is one of the main elements which express physical, chemical and engineering laws. Therefore, it is essential for engineering students to have a strong knowledge in the fundamental of mathematics in order to apply the knowledge to real life issues. However, based on the previous results of Mathematics Pre-Test, it shows that the engineering students lack the fundamental knowledge in certain topics in mathematics. Due to this, apart from making improvements in the methods of teaching and learning, studies on the construction of questions (items) should also be emphasized. The purpose of this study is to assist lecturers in the process of item development and to monitor the separation of items based on Blooms' Taxonomy and to measure the reliability of the items itself usingRasch Measurement Model as a tool. By using Rasch Measurement Model, the final exam questions of Engineering Mathematics II (Linear Algebra) for semester 2 sessions 2012/2013 were analysed and the results will provide the details onthe extent to which the content of the item providesuseful information about students' ability. This study reveals that the items used in Engineering Mathematics II (Linear Algebra) final exam are well constructed but the separation of the items raises concern as it is argued that it needs further attention, as there is abig gap between items at several levels of Blooms' cognitive skill.

Validity issues in the evaluation of a measure of science and mathematics teacher knowledge

NASA Astrophysics Data System (ADS)

Talbot, Robert M., III

2011-12-01

This study investigates the reliability and validity of an instrument designed to measure science and mathematics teachers' strategic knowledge . Strategic knowledge is conceptualized as a construct that is related to pedagogical knowledge and is comprised of two dimensions: Flexible Application (FA) and Student Centered Instruction (SCI). The FA dimension describes how a science teacher invokes, applies and modifies her instructional repertoire in a given teaching context. The SCI dimension describes how a science teacher conceives of a given situation as an opportunity for active engagement with the students. The Flexible Application of Student-Centered Instruction (FASCI) survey instrument was designed to measure science teachers' strategic knowledge by eliciting open-ended responses to scenario-based items. This study addresses the following overarching question: What are some potential issues pertaining to the validity of measures of science and mathematics teacher knowledge? Using a validity argument framework, different sources of evidence are identified, collected, and evaluated to examine support for a set or propositions related to the intended score interpretation and instrument use: FASCI scores can be used to compare and distinguish the strategic knowledge of novice science and mathematics teachers in the evaluation of teacher education programs. Three separate but related studies are presented and discussed. These studies focus on the reliability of FASCI scores, the effect of adding specific science content to the scenario-based items, and the observation of strategic knowledge in teaching practice. Serious issues were found with the reliability of scores from the FASCI instrument. It was also found that adding science content to the scenario-based items has an effect on FASCI scores, but not for the reason hypothesized. Finally, it was found that more evidence is needed to make stronger claims about the relationship between FASCI scores and novice teachers' practice. In concluding this work, a set of four recommendations are presented for others who are engaged in similar measure development efforts. These recommendations focus on the areas of construct definition, item design and development, rater recruitment and training, and the validation process.

The transformation of science and mathematics content knowledge into teaching content by university faculty

NASA Astrophysics Data System (ADS)

Flynn, Natalie P.

This study developed a survey from the existing literature in an attempt to illuminate the processes, tools, insights, and events that allow university science and mathematics content experts (Ph.D.'s) unpack their expertise in order to teach develop and teach undergraduate students. A pilot study was conducted at an urban university in order to refine the survey. The study consisted of 72 science or mathematics Ph.D. faculty members that teach at a research-based urban university. Follow-up interviews were conducted with 21 volunteer faculty to further explore their methods and tools for developing and implementing teaching within their discipline. Statistical analysis of the data revealed: faculty that taught while obtaining their Ph.D. were less confident in their ability to teach successful and faculty that received training in teaching believed that students have difficult to change misconceptions and do not commit enough time to their course. Student centered textbooks ranked the highest among tools used to gain teaching strategies followed by grading of exams and assignments for gaining insights into student knowledge and difficulties. Science and mathematics education literature and university provided education session ranked the lowest in rating scale for providing strategies for teaching. The open-ended survey questions were sub-divided and analyzed by the number of years of experience to identify the development of teaching knowledge over time and revealed that teaching became more interactive, less lecture based, and more engaging. As faculty matured and gained experience they became more aware of student misconceptions and difficulties often changing their teaching to eliminate such issues. As confidence levels increase their teaching included more technology-based tools, became more interactive, incorporated problem based activities, and became more flexible. This change occurred when and if faculty members altered their thinking about their knowledge from an expert centered perspective to a student centric view. Follow-up interviews of twenty faculty yielded a wide variety of insights into the complicated method of deconstructing expert science and mathematics content. The interviews revealed a major disconnect between education research and researchers and the science and mathematics content experts who teach. There is a pervasive disregard for science and mathematics education and training. Faculty members find little to no support for teaching. Though 81% obtained their Ph.D. with the intent to enter an academic setting, pedagogical training was non-existent or limited, both prior to and after obtaining faculty positions. Experience alone did not account for confidence or ability to successfully teach. Faculty that were able to 'think like a student' and view their material from a student's perspective' seemed to be the most confident and flexible in their teaching methods. Grading and having an open and interactive teaching style, being on the 'side of the students' also seemed to allow faculty to connect more deeply with the students and learn about common misconceptions and difficulties. Though most faculty claimed to not teach as they were taught and not recall having specific content difficulties, this essential interaction with many students facilitated a shift in thinking about their content. This shift allowed for a reversal from teacher centered classrooms to student centered. Multiple issues arise when teaching at a traditional larger lecture style found in the majority of universities science and mathematics courses that constrain and provide unique teaching challenges. Many faculty have developed unique tools to incorporate successful teaching strategies, such as daily pre-quizzes and smart-phone questioning as well as small group work, computer posted guides, strategic class breaks, and limiting lecture style in favor of a more active engaged classroom. (Abstract shortened by UMI.).

Design of capability measurement instruments pedagogic content knowledge (PCK) for prospective mathematics teachers

NASA Astrophysics Data System (ADS)

Aminah, N.; Wahyuni, I.

2018-05-01

The purpose of this study is to find out how the process of designing a tool of measurement Pedagogical Content Knowledge (PCK) capabilities, especially for prospective mathematics teachers are valid and practical. The design study of this measurement appliance uses modified Plomp development step, which consists of (1) initial assessment stage, (2) design stage at this stage, the researcher designs the measuring grille of PCK capability, (3) realization stage that is making measurement tool ability of PCK, (4) test phase, evaluation, and revision that is testing validation of measurement tools conducted by experts. Based on the results obtained that the design of PCK capability measurement tool is valid as indicated by the assessment of expert validator, and the design of PCK capability measurement tool, shown based on the assessment of teachers and lecturers as users of states strongly agree the design of PCK measurement tools can be used.

Teacher spatial skills are linked to differences in geometry instruction.

PubMed

Otumfuor, Beryl Ann; Carr, Martha

2017-12-01

Spatial skills have been linked to better performance in mathematics. The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Fifty-six middle school teachers participated in the study. The teachers were administered spatial measures of mental rotations and spatial visualization. Next, a single geometry class was videotaped. Correlational analyses revealed that spatial skills significantly correlate with teacher's use of representational gestures and content and pedagogical knowledge during instruction of geometry. Spatial skills did not independently correlate with the use of pointing gestures or the use of pictorial representations. However, an interaction term between spatial skills and content and pedagogical knowledge did correlate significantly with the use of pictorial representations. Teacher experience as measured by the number of years of teaching and highest degree did not appear to affect the relationships among the variables with the exception of the relationship between spatial skills and teacher content and pedagogical knowledge. Teachers with better spatial skills are also likely to use representational gestures and to show better content and pedagogical knowledge during instruction. Spatial skills predict pictorial representation use only as a function of content and pedagogical knowledge. © 2017 The British Psychological Society.

Assessing Quality in the Teaching of Content to English Language Learners. Research Report. ETS RR-12-10

ERIC Educational Resources Information Center

Turkan, Sultan; Croft, Andrew; Bicknell, Jerome; Barnes, Andwatta

2012-01-01

This paper offers a chain of evidence collected to identify and verify the domain of teacher knowledge and skills required to teach ELLs content effectively in mathematics, science, reading/English language arts, and social studies. We initially assessed this domain through a review of literature and state standards for nonspecialized teacher…

ICT integration in mathematics initial teacher training and its impact on visualization: the case of GeoGebra

NASA Astrophysics Data System (ADS)

Dockendorff, Monika; Solar, Horacio

2018-01-01

This case study investigates the impact of the integration of information and communications technology (ICT) in mathematics visualization skills and initial teacher education programmes. It reports on the influence GeoGebra dynamic software use has on promoting mathematical learning at secondary school and on its impact on teachers' conceptions about teaching and learning mathematics. This paper describes how GeoGebra-based dynamic applets - designed and used in an exploratory manner - promote mathematical processes such as conjectures. It also refers to the changes prospective teachers experience regarding the relevance visual dynamic representations acquire in teaching mathematics. This study observes a shift in school routines when incorporating technology into the mathematics classroom. Visualization appears as a basic competence associated to key mathematical processes. Implications of an early integration of ICT in mathematics initial teacher training and its impact on developing technological pedagogical content knowledge (TPCK) are drawn.

What Teachers Need to Know to Teach Mathematics: An Argument for a Reconceptualised Model

ERIC Educational Resources Information Center

Hurrell, Derek P.

2013-01-01

Since Shulman's (1986) seminal work on Pedagogical Content Knowledge (PCK) was released, it has created opportunities for the creation of constructs to scaffold the knowledge and understandings that teachers need in order to be effective. Adapting this work from being a heuristic to an operational structure has seen the development of many models.…

Wikis: Developing Pre-Service Teachers' Leadership Skills and Knowledge of Content Standards

ERIC Educational Resources Information Center

Reid-Griffin, Angelia; Slaten, Kelli M.

2016-01-01

In this initial phase of our multi-year research study we set out to explore the development of leadership skills in our pre-service secondary teachers after using an online wiki, Wikispaces. This paper presents our methods for preparing a group of 13 mathematics and 3 science secondary pre-service teachers to demonstrate the essential knowledge,…

The Nature of Middle School Mathematics Teachers' Pedagogical Content Knowledge: The Case of The Volume of Prisms

ERIC Educational Resources Information Center

Tekin-Sitrava, Reyhan; Isiksal-Bostan, Mine

2018-01-01

This study investigated middle school teachers' knowledge of students' misconceptions and the sources of these misconceptions related to the volume of prisms. This case study investigated four middle school teachers who taught 8th grade students in Ankara (Turkey). Based on the analysis of the data, two misconceptions related to the volume of…

Through Fairy-Tales to Math in the Lessons

ERIC Educational Resources Information Center

Andersone, Rudite

2009-01-01

Every person in his lifetime has many times experienced the miraculous impact of the fairy-tale on his imagination, mind and feelings. But we seldom reflect upon the content not only in the ethical aspect of fairy-tales but also as a source of different kinds of knowledge, among them the knowledge of mathematics. The use of fairy-tales in lessons…

Bunny hops: using multiplicities of zeroes in calculus for graphing

NASA Astrophysics Data System (ADS)

Miller, David; Deshler, Jessica M.; Hansen, Ryan

2016-07-01

Students learn a lot of material in each mathematics course they take. However, they are not always able to make meaningful connections between content in successive mathematics courses. This paper reports on a technique to address a common topic in calculus I courses (intervals of increase/decrease and concave up/down) while also making use of students' pre-existing knowledge about the behaviour of functions around zeroes based on multiplicities.

Student perceptions of writing projects in a university differential-equations course

NASA Astrophysics Data System (ADS)

Latulippe, Christine; Latulippe, Joe

2014-01-01

This qualitative study surveyed 102 differential-equations students in order to investigate how students participating in writing projects in university-level mathematics courses perceive the benefits of writing in the mathematics classroom. Based on previous literature on writing in mathematics, students were asked specifically about the benefits of writing projects as a means to explore practical uses of mathematics, deepen content knowledge, and strengthen communication. Student responses indicated an awareness of these benefits, supporting justifications commonly cited by instructors assigning writing projects. Open-ended survey responses highlighted additional themes which students associated with writing in mathematics, including using software programs and technology, working in groups, and stimulating interest in mathematics. This study provides student feedback to support the use of writing projects in mathematics, as well as student input, which can be utilized to strengthen the impact of writing projects in mathematics.

Examining a math-science professional development program for teachers in grades 7-12 in an urban school district in New York State

NASA Astrophysics Data System (ADS)

Kaszczak, Lesia

With the adoption of the Common Core State Standards in New York State and the Next Generation Science Standards, it is more important than ever for school districts to develop professional development programs to provide teachers with the resources that will assist them in incorporating the new standards into their classroom instruction. This study focused on a mathematics and science professional development program known as STEMtastic STEM. The two purposes of the study were: to determine if there is an increase in STEM content knowledge of the participants involved in year two of a three year professional development program and to examine the teachers' perceptions of the impact of the professional development program on classroom instruction. The sample included teachers of grades 7-12 from an urban school district in New York State. The scores of a content knowledge pre-test and post-test were analyzed using a paired sample t-test to determine any significant differences in scores. In order to determine mathematics and science teachers' perceptions of the impact of the professional development program, responses from a 22 item Likert-style survey were analyzed to establish patterns of responses and to determine positive and negative perceptions of participants of the professional development program. A single sample t-test was used to determine if the responses were significantly positive. The results of this study indicated that there was no significant increase in content knowledge as a result of participation in the STEMtastic STEM professional development program. Both mathematics and science teachers exhibited significant positive perceptions of items dealing with hands-on participation during the professional development; support provided by STEMtastic STEM specialists; and the support provided by the administration. It was concluded that both mathematics and science teachers responded positively to the training they received during the professional development sessions, but that their classroom practices did not change as a result of the professional development program.

The role of mathematics for physics teaching and understanding

NASA Astrophysics Data System (ADS)

Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette

2016-05-01

-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.

Contextual Teaching and Learning Approach of Mathematics in Primary Schools

NASA Astrophysics Data System (ADS)

Selvianiresa, D.; Prabawanto, S.

2017-09-01

The Contextual Teaching and Learning (CTL) approach is an approach involving active students in the learning process to discover the concepts learned through to knowledge and experience of the students. Similar to Piaget’s opinion that learning gives students an actives trying to do new things by relating their experiences and building their own minds. When students to connecting mathematics with real life, then students can looking between a conceptual to be learned with a concept that has been studied. So that, students can developing of mathematical connection ability. This research is quasi experiment with a primary school in the city of Kuningan. The result showed that CTL learning can be successful, when learning used a collaborative interaction with students, a high level of activity in the lesson, a connection to real-world contexts, and an integration of science content with other content and skill areas. Therefore, CTL learning can be applied by techer to mathematics learning in primary schools.

Implementation and outcomes of inquiry-based learning in mathematics content courses for pre-service teachers

NASA Astrophysics Data System (ADS)

Laursen, Sandra L.; Hassi, Marja-Liisa; Hough, Sarah

2016-02-01

This mixed-methods study describes classroom characteristics and student outcomes from university mathematics courses that are based in mathematics departments, targeted to future pre-tertiary teachers, and taught with inquiry-based learning (IBL) approaches. The study focused on three two-term sequences taught at two research universities, separately targeting elementary and secondary pre-service teachers. Classroom observation established that the courses were taught with student-centred methods that were comparable to those used in IBL courses for students in mathematics-intensive fields at the same institutions. To measure pre-service teachers' gains in mathematical knowledge for teaching, we administered the Learning Mathematics for Teaching (LMT) instrument developed by Hill, Ball and Schilling for in-service teacher professional development. Results from the LMT show that pre-service teachers made significant score gains from beginning to end of their course, while data from interviews and from surveys of learning gains show that pre-service teachers viewed their gains as relevant to their future teaching work. Measured changes on pre-/post-surveys of attitudes and beliefs were generally supportive of learning mathematics but modest in magnitude. The study is distinctive in applying the LMT to document pre-service teachers' growth in mathematical knowledge for teaching. The study also suggests IBL is an approach well suited to mathematics departments seeking to strengthen their pre-service teacher preparation offerings in ways consistent with research-based recommendations.

Fadeout in an early mathematics intervention: Constraining content or preexisting differences?

PubMed

Bailey, Drew H; Nguyen, Tutrang; Jenkins, Jade Marcus; Domina, Thurston; Clements, Douglas H; Sarama, Julie S

2016-09-01

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children's long-term mathematical development result more from relatively stable preexisting differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these 2 hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of posttreatment achievement and preexisting differences between these 2 groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to preexisting differences between children in treatment and control groups with the same level of achievement at posttest. These differences were fully statistically attenuated by children's prior academic achievement. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

Fadeout in an Early Mathematics Intervention: Constraining Content or Pre-existing Differences?

PubMed Central

Bailey, Drew H.; Nguyen, Tutrang; Jenkins, Jade Marcus; Domina, Thurston; Clements, Douglas H.; Sarama, Julie S.

2016-01-01

A robust finding across research on early childhood educational interventions is that the treatment effect diminishes over time, with children not receiving the intervention eventually catching up to children who did. One popular explanation for fadeout of early mathematics interventions is that elementary school teachers may not teach the kind of advanced content that children are prepared for after receiving the intervention, so lower-achieving children in the control groups of early mathematics interventions catch up to the higher-achieving children in the treatment groups. An alternative explanation is that persistent individual differences in children’s long-term mathematical development result more from relatively stable pre-existing differences in their skills and environments than from the direct effects of previous knowledge on later knowledge. We tested these two hypotheses using data from an effective preschool mathematics intervention previously known to show a diminishing treatment effect over time. We compared the intervention group to a matched subset of the control group with a similar mean and variance of scores at the end of treatment. We then tested the relative contributions of factors that similarly constrain learning in children from treatment and control groups with the same level of post-treatment achievement and pre-existing differences between these two groups to the fadeout of the treatment effect over time. We found approximately 72% of the fadeout effect to be attributable to pre-existing differences between children in treatment and control groups with the same level of achievement at post-test. These differences were fully statistically attenuated by children’s prior academic achievement. PMID:27505700

NASA/DoD Aerospace Knowledge Diffusion Research Project. Report Number 20. The Use of Selected Information Products and Services by U.S. Aerospace Engineers and Scientists: Results of Two Surveys.

DTIC Science & Technology

1994-02-01

within and between organizations. The technical report has been defined etymologically , according to report content and method (U.S. Department of...number) I AERONAUTICS 6 MATHEMATICAL & COMPUTER SCIENCES 2 ASTRONAUTICS 7 MATERIALS & CHEMISTRY 3 ENGINEERING 8 PHYSICS 4 GEOSCIENCES 9 SPACE SCIENCES 5...the application of your work? (Circle ONLY one number) 1 AERONAUTICS 6 MATHEMATICAL & COMPUTER SCIENCES 2 ASTRONAUTICS 7 MATERIALS & CHEMISTRY 3

Collegiality and Better Science Teaching

ERIC Educational Resources Information Center

Weiser, Brenda

2012-01-01

For the past five years, teachers from four Houston-area school districts have joined together in a professional learning community (PLC) to improve their science teaching. Through the University of Houston-Clear Lake (UHCL) Regional Collaborative for Excellence in Science and Mathematics Teaching, the teachers strengthen content knowledge and…

Construct Relevant and Irrelevant Variables in Math Problem Solving Assessment

ERIC Educational Resources Information Center

Birk, Lisa E.

2013-01-01

In this study, I examined the relation between various construct relevant and irrelevant variables and a math problem solving assessment. I used independent performance measures representing the variables of mathematics content knowledge, general ability, and reading fluency. Non-performance variables included gender, socioeconomic status,…

Teaching Strategies to Improve Algebra Learning

ERIC Educational Resources Information Center

Zbiek, Rose Mary; Larson, Matthew R.

2015-01-01

Improving student learning is the primary goal of every teacher of algebra. Teachers seek strategies to help all students learn important algebra content and develop mathematical practices. The new Institute of Education Sciences[IES] practice guide, "Teaching Strategies for Improving Algebra Knowledge in Middle and High School Students"…

Abstract Algebra for Teachers: An Evaluative Case Study

ERIC Educational Resources Information Center

Hoffman, Andrew Joseph

2017-01-01

This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…

Culture in the Classroom.

ERIC Educational Resources Information Center

Le, Thuong Van; Le, Nancylee

New methods are proposed for teachers to increase the cultural knowledge of their students. Rather than emphasizing food, festivals, and famous faces from other lands, there should be an attempt to use culture in the classroom as content in the regular instruction of speaking, listening, writing, mathematics, reading, and science. Teaching…

76 FR 12263 - Read Across America Day, 2011

Federal Register 2010, 2011, 2012, 2013, 2014

2011-03-04

..., discussing the story, and encouraging children to ask questions on words or content they do not understand... areas of knowledge, including the subjects of science, technology, engineering, and mathematics. The... to the world as Dr. Seuss. Through amusing wordplay and engaging tales, his stories have helped...

Characterising the perceived value of mathematics educational apps in preservice teachers

NASA Astrophysics Data System (ADS)

Handal, Boris; Campbell, Chris; Cavanagh, Michael; Petocz, Peter

2016-03-01

This study validated the semantic items of three related scales aimed at characterising the perceived worth of mathematics-education-related mobile applications (apps). The technological pedagogical content knowledge (TPACK) model was used as the conceptual framework for the analysis. Three hundred and seventy-three preservice students studying primary school education from two public and one private Australian universities participated in the study. The respondents examined three different apps using a purposively designed instrument in regard to either their explorative, productive or instructive instructional role. While construct validity could not be established due to a broad range of variability in responses implying a high degree of subjectivity in respondents' judgments, the qualitative analysis was effective in establishing content validity.

The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks

NASA Astrophysics Data System (ADS)

Choppin, Jeffrey

2011-03-01

This study explores the extent to which a teacher elicited students' mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher's knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher's reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students' ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.

Representations in Simulated Workplaces

ERIC Educational Resources Information Center

van Schaik, Martijn; Terwel, Jan; van Oers, Bert

2014-01-01

In vocational education students are to be prepared to participate in communities of practice. Hence they need technical skills as well as content knowledge e.g. science and mathematics. Research has shown that the instructional strategy of guided co-construction may lead to deeper understandings within a practice. The research questions in this…

Explaining Student Achievement: The Influence of Teachers' Pedagogical Content Knowledge in Statistics

ERIC Educational Resources Information Center

Callingham, Rosemary; Carmichael, Colin; Watson, Jane M.

2016-01-01

Statistics is an increasingly important component of the mathematics curriculum. "StatSmart" was a project intended to influence middle-years students' learning outcomes in statistics through the provision of appropriate professional learning opportunities and technology to teachers. Participating students in grade 5/6 to grade 9…

Choosing the Right Tool

ERIC Educational Resources Information Center

Boote, Stacy K.

2016-01-01

Students' success with fourth-grade content standards builds on mathematical knowledge learned in third grade and creates a conceptual foundation for division standards in subsequent grades that focus on the division algorithm. The division standards in fourth and fifth grade are similar; but in fourth grade, division problem divisors are only one…

A Hermeneutic Phenomenological Study of the Experience of Teacher-Learners

ERIC Educational Resources Information Center

Bechtel, Patricia L.

2011-01-01

Teachers who choose to participate in professional development to acquire new instructional methods or enhance their content knowledge are teacher-learners. For this study, data consisted of the reflective writings of 19 secondary mathematics and science teacher-learners in an 11-month professional development project. These writings provided a…

Teacher Spatial Skills Are Linked to Differences in Geometry Instruction

ERIC Educational Resources Information Center

Otumfuor, Beryl Ann; Carr, Martha

2017-01-01

Background: Spatial skills have been linked to better performance in mathematics. Aim The purpose of this study was to examine the relationship between teacher spatial skills and their instruction, including teacher content and pedagogical knowledge, use of pictorial representations, and use of gestures during geometry instruction. Sample:…

Conditions for the Effectiveness of Multiple Visual Representations in Enhancing STEM Learning

ERIC Educational Resources Information Center

Rau, Martina A.

2017-01-01

Visual representations play a critical role in enhancing science, technology, engineering, and mathematics (STEM) learning. Educational psychology research shows that adding visual representations to text can enhance students' learning of content knowledge, compared to text-only. But should students learn with a single type of visual…

Levels of line graph question interpretation with intermediate elementary students of varying scientific and mathematical knowledge and ability: A think aloud study

NASA Astrophysics Data System (ADS)

Keller, Stacy Kathryn

This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems, science data to be analyzed, or they were confused and had to guess. A second set of findings corroborated how science background knowledge affected graph interpretation: correct science knowledge supported students' reasoning, but it was not necessary to answer any question correctly; correct science knowledge could not compensate for incomplete mathematics knowledge; and incorrect science knowledge often distracted students when they tried to use it while answering a question. Finally, using Roth and Bowen's (2001) two-stage semiotic model of reading graphs, representative vignettes showed emerging patterns from the study. This study added to our understanding of the role of science content knowledge during line graph interpretation, highlighted the importance of heuristics and mathematics procedural knowledge, and documented the importance of perception attentions, motivation, and students' self-generated questions. Recommendations were made for future research in line graph interpretation in mathematics and science education and for improving instruction in this area.

Mathematics/Arithmetic Knowledge-Based Way of Thinking and Its Maintenance Needed for Engineers

NASA Astrophysics Data System (ADS)

Harada, Shoji

Examining curriculum among universities revealed that no significant difference in math class or related subjects can be seen. However, amount and depth of those studies, in general, differed depending on content of curriculum and the level of achievement at entrance to individual university. Universalization of higher education shows that students have many problems in learning higher level of traditional math and that the memory of math they learned quickly fades away after passing in exam. It means that further development of higher math knowledgebased engineer after graduation from universities. Under these circumstances, the present author, as one of fun of math, propose how to maintain way of thinking generated by math knowledge. What necessary for engineer is to pay attention to common books, dealing with elementary mathematics or arithmetic- related matters. This surely leads engineer to nourish math/arithmetic knowledge-based way of thinking.

Teacher leadership in mathematics and science: Subject content knowledge and the improvement of instruction

NASA Astrophysics Data System (ADS)

Manno, Christopher M.

This study explores the role of teacher leader subject content knowledge in the promotion of professional development and instructional reform. Consistent with a distributed leadership perspective, many have asserted that the promotion of school effectiveness can be enhanced through the application of teacher leadership (Frost & Durrant, 2003; Harris, 2002a; Sherrill, 1999; Silva, Gimbert, & Nolan, 2000; York-Barr & Duke, 2004). There has been much discussion in the research about the significance of teachers' subject content knowledge in teaching and learning which has generally asserted a positive relationship with instructional practice and student achievement (Darling-Hammond, 2000; Newton & Newton, 2001; Parker & Heywood, 2000). The role of content knowledge in teacher leader work has been less researched. This study focused on deepening understanding of perceptions regarding teacher leaders' roles in improving instructional practice. Based on a framework of common teacher leader tasks, qualitative methods were used to investigate the relationship between teacher leader subject content knowledge and perceptions of effectiveness in promoting professional development and instructional reform. The study indicates that content experts behave differently than their non-expert counterparts. Content experts recognize deficiencies in colleagues' content knowledge as a primary problem in the implementation of math or science reform. Content experts view their work as advocacy for improved curriculum and instruction for all children, and work within a small set of task categories to promote discussions about teaching, learning, and content. Content experts develop trust and rapport with colleagues by demonstrating expertise, and are respected for their deep knowledge and efforts to help teachers learn the content. They also differ from non-content experts in the professional growth experiences in which they engage. The consideration of content expertise as an influence to teacher leader work helps to refine our conception of teacher leadership. A task-focused model of content expert teacher leadership is presented, and provides guidance for recruitment, selection, and development of future teacher leaders. Content expertise is presented as a form of human capital that promotes task-focused distributed leadership. Practical recommendations for future teacher leadership initiatives and suggestions for future research are presented.

An Investigation of Secondary Teachers’ Understanding and Belief on Mathematical Problem Solving

NASA Astrophysics Data System (ADS)

Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani

2016-02-01

Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.

Teachers' Pedagogical Content Knowledge and Mathematics Achievement of Students in Peru

ERIC Educational Resources Information Center

Cueto, Santiago; León, Juan; Sorto, M. Alejandra; Miranda, Alejandra

2017-01-01

After improving enrolment rates significantly, many developing countries such as Peru are facing the challenge to increase learning levels among students. Over the past few years, many researchers have turned to teacher-related variables as a way to better understand classroom processes that may help increase learning levels among students. In…

Teaching Math and Science: Improving Instruction through Local Systemic Change Initiatives

ERIC Educational Resources Information Center

Weiss, Iris R.; Pasley, Joan D.

2007-01-01

Local Systemic Change projects, funded by the National Science Foundation, were designed to help teachers of mathematics and science deepen their content knowledge and improve their instructional practices. Ms. Weiss and Ms. Pasley describe how these aims were accomplished through a combination of intensive professional development and follow-up…

Integrating Literacy and Math: Strategies for K-6 Teachers

ERIC Educational Resources Information Center

Fogelberg, Ellen; Skalinder, Carole; Satz, Patti; Hiller, Barbara; Bernstein, Lisa; Vitantonio, Sandra

2008-01-01

Many K-6 teachers and students still think of mathematics as a totally separate subject from literacy. Yet incorporating math content into the language arts block helps students gain skills for reading many kinds of texts. Bringing reading, writing, and talking into the math classroom supports the development of conceptual knowledge and problem…

Developing Second Grade Teachers' Pedagogical Content Knowledge of Place Value

ERIC Educational Resources Information Center

Kulhanek, Stefani Michelle

2013-01-01

An understanding of whole number place value is a critical component of second-grade mathematics. This understanding of place value provides the foundational concept for operations with whole numbers. The ability to understand the concept of place value and transfer that understanding to teaching addition and subtraction are often problems…

The Common Core Learning Standards and Elementary Teachers' Math Instructional Practices, Receptivity to Change, Instructional Leadership and Academic Optimism

ERIC Educational Resources Information Center

Sullivan, Dennis D.

2016-01-01

This study sought to identify the relationships among elementary teachers instructional practices in mathematics pre- and post-CCLS implementation in relation to technological and pedagogical content knowledge (TPACK), formative assessment, reflective practice, receptivity to change, academic optimism, and instructional leadership across age,…

Co-Teaching Math Content and Math Pedagogy for Elementary Pre-Service Teachers: A Pilot Study

ERIC Educational Resources Information Center

Ford, Pari; Strawhecker, Jane

2011-01-01

With a national need to improve Science, Technology, Engineering and Mathematics Education (STEM), elementary pre-service teachers must be provided with ample opportunities to increase their own knowledge and confidence in STEM disciplines. This article describes a Math Block experience developed for a special population of non-traditional…

Supporting Teachers' Technological Pedagogical Content Knowledge of Fractions through Co-Designing a Virtual Manipulative

ERIC Educational Resources Information Center

Hansen, Alice; Mavrikis, Manolis; Geraniou, Eirini

2016-01-01

This study explores the impact that co-designing a virtual manipulative, Fractions Lab, had on teachers' professional development. Tapping into an existing community of practice of mathematics specialist teachers, the study identifies how a cooperative enquiry approach utilising workshops and school-based visits challenged 23 competent primary…

Improving Middle Grades STEM Teacher Content Knowledge and Pedagogical Practices through a School-University Partnership

ERIC Educational Resources Information Center

McCollough, Cherie; Jeffery, Tonya; Moore, Kim; Champion, Joe

2016-01-01

This paper outlines a University-School District partnership with the intent to increase the number of middle grades mathematics and science teachers. This externally funded initiative includes onsite, authentically situated professional development for pre- and in-service teachers at three different urban, low-socioeconomic schools with a…

An Ecologist Is Born: An Integrated Experiential Learning Activity

ERIC Educational Resources Information Center

Behrendt, Marc; Behrendt, Barbara

2012-01-01

Language arts and mathematics are high priority content areas in early grades. Science is often a secondary concern, even though students appear to have minimal knowledge or interest in their local ecology. This article describes a year-long project integrating science and technology with language arts. Students researched and wrote about local…

Assessing Teacher and Student Effects of the Research Goes to School Project

ERIC Educational Resources Information Center

Kararo, Alex T.

2017-01-01

There have been calls by the Federal government and policymakers for improvements in science, technology, engineering and mathematics (STEM) education through the development of excellent teachers with the content knowledge and skills to teach and motivate students. A shared goal among teacher professional development (PD) programs is to improve…

Teachers' Construction of Meanings of Signed Quantities and Integer Operation

ERIC Educational Resources Information Center

Kumar, Ruchi S.; Subramaniam, K.; Naik, Shweta Shripad

2017-01-01

Understanding signed quantities and its arithmetic is one of the challenging topics of middle school mathematics. The "specialized content knowledge" (SCK) for teaching integers includes understanding of a variety of representations that may be used while teaching. In this study, we argue that meanings of integers and integer operations…

Improving Conceptual and Procedural Knowledge: The Impact of Instructional Content within a Mathematics Lesson

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Loehr, Abbey M.

2016-01-01

Background: Students, parents, teachers, and theorists often advocate for direct instruction on both concepts and procedures, but some theorists suggest that including instruction on procedures in combination with concepts may limit learning opportunities and student understanding. Aims: This study evaluated the effect of instruction on a math…

Pre-Service Teachers' TPACK Development and Conceptions through a TPACK-Based Course

ERIC Educational Resources Information Center

Durdu, Levent; Dag, Funda

2017-01-01

This study examines pre-service teachers' Technological Pedagogical Content Knowledge (TPACK) development and analyses their conceptions of learning and teaching with technology. With this aim in mind, researchers designed and implemented a computer-based mathematics course based on a TPACK framework. As a research methodology, a parallel mixed…

Preservice Secondary Teachers Perceptions of College-Level Mathematics Content Connections with the Common Core State Standards for Mathematics

ERIC Educational Resources Information Center

Olson, Travis A.

2016-01-01

Preservice Secondary Mathematics Teachers (PSMTs) were surveyed to identify if they could connect early-secondary mathematics content (Grades 7-9) in the Common Core State Standards for Mathematics (CCSSM) with mathematics content studied in content courses for certification in secondary teacher preparation programs. Respondents were asked to…

Initial Characterization of Colombian High School Physics Teachers' Pedagogical Content Knowledge on Electric Fields

NASA Astrophysics Data System (ADS)

Melo-Niño, Lina Viviana; Cañada, Florentina; Mellado, Vicente

2017-02-01

We explore the initial characterization of the pedagogical content knowledge of four, in-service, Colombian pre-university secondary education physics teachers on the concept of electric field. Two of them teach the content in English as a second language. The aim of the study was to obtain an image of the participants' teaching of electric field and the inherent complexities that go with that. The results revealed that factors which involved their personal educational models, such as, how they interpret their school's curriculum, the relationship they see between physics and mathematics, the most effective strategies for teaching physics, and the time they have available to develop the topic played a significant role. The teachers considered it essential to establish new strategies that would motivate the pupils by helping them visualize the electric field.

Technology Focus: Enhancing Conceptual Knowledge of Linear Programming with a Flash Tool

ERIC Educational Resources Information Center

Garofalo, Joe; Cory, Beth

2007-01-01

Mathematical knowledge can be categorized in different ways. One commonly used way is to distinguish between procedural mathematical knowledge and conceptual mathematical knowledge. Procedural knowledge of mathematics refers to formal language, symbols, algorithms, and rules. Conceptual knowledge is essential for meaningful understanding of…

Comparing the development of the multiplication of fractions in Turkish and American textbooks

NASA Astrophysics Data System (ADS)

Kar, Tuğrul; Güler, Gürsel; Şen, Ceylan; Özdemir, Ercan

2018-02-01

This study analyzed the methods used to teach the multiplication of fractions in Turkish and American textbooks. Two Turkish textbooks and two American textbooks, Everyday Mathematics (EM) and Connected Mathematics 3 (CM), were analyzed. The analyses focused on the content and the nature of the mathematical problems presented in the textbooks. The findings of the study showed that the American textbooks aimed at developing conceptual understanding first and then procedural fluency, whereas the Turkish textbooks aimed at developing both concurrently. The American textbooks provided more opportunities for different computational strategies. The solutions to most problems in all textbooks required a single computational step, a numerical answer, and procedural knowledge. Furthermore, compared with the Turkish textbooks, the American textbooks contained a greater number of problems that required high-level cognitive skills such as mathematical reasoning.

The mathematics textbook at tertiary level as curriculum material - exploring the teacher's decision-making process

NASA Astrophysics Data System (ADS)

Randahl, Mira

2016-08-01

This paper reports on a study about how the mathematics textbook was perceived and used by the teacher in the context of a calculus part of a basic mathematics course for first-year engineering students. The focus was on the teacher's choices and the use of definitions, examples and exercises in a sequence of lectures introducing the derivative concept. Data were collected during observations of lectures and an interview, and informal talks with the teacher. The introduction and the treatment of the derivative as proposed by the teacher during the lectures were analysed in relation to the results of the content text analysis of the textbook. The teacher's decisions were explored through the lens of intended learning goals for engineering students taking the mathematics course. The results showed that the sequence of concepts and the formal introduction of the derivative as proposed by the textbook were closely followed during the lectures. The examples and tasks offered to the students focused strongly on procedural knowledge. Although the textbook proposes both examples and exercises that promote conceptual knowledge, these opportunities were not fully utilized during the observed lectures. Possible reasons for the teacher's choices and decisions are discussed.

Knowledge of Curriculum Embedded Mathematics: Exploring a Critical Domain of Teaching

ERIC Educational Resources Information Center

Remillard, Janine; Kim, Ok-Kyeong

2017-01-01

This paper proposes a framework for identifying the mathematical knowledge teachers activate when using curriculum resources. We use the term "knowledge of curriculum embedded mathematics" (KCEM) to refer to the mathematics knowledge activated by teachers when reading and interpreting mathematical tasks, instructional designs, and…

The transformation of primary school science and mathematics: A cross-national analysis, 1900-1995

NASA Astrophysics Data System (ADS)

McEneaney, Elizabeth H.

1998-12-01

The global rise of the liberal individualist polity produces several broad cultural changes that influence the content of mass educational curricula, and that do so on a worldwide basis. First, there is a dramatic broadening of the range of persons constituted as actors, so that subjects such as science are seen as relevant for everyone. Second, the cultural domain of science and mathematics expands so that they are understood to provide solutions to personal and societal problems of all kinds. A critical tension arises, however, since science also becomes increasingly differentiated, such that expertise becomes defined in ever-narrower fields. I argue that these global cultural changes transform the content and style of primary science and mathematics textbooks. World-polity theory guides the interpretation of a content analysis of upper elementary level textbooks from over 50 nations, published between 1900 and 1995. Science textbooks become much more participatory in their orientations over the course of the century, fully incorporating individual actors (with large increases, for example, in the inclusion of girls and women) and hands-on activities. School science also becomes more culturally accessible through an emphasis on personal relevance and humor or fun. Thus, science is portrayed as a truly human endeavor rather than as a body of knowledge unsullied by human experience. The trends are similar, though somewhat more muted, for mathematics. At the same time, the study shows that school science and mathematics retain a significant emphasis on disciplinary expertise, reflecting the increasingly specialized and technocratic nature of science. Multivariate statistical analyses support the claim that the construction of modern curricular materials such as textbooks is highly sensitive to various kinds of organizational, cultural, and professional linkages to world society. This helps explain why the data show that changes tend to be worldwide. In contrast, characteristics of individual nation-states tend to be relatively weak correlates of textbook content. I argue that the trends shown in science and mathematics are most accurately seen as part of a wider shift in curricular content, cutting across all subject areas and extending through university-level curricula.

Professionalizing In-Service Teachers' Focus on Technological Pedagogical and Content Knowledge

ERIC Educational Resources Information Center

Getenet, Seyum Tekeher; Beswick, Kim; Callingham, Rosemary

2016-01-01

In Ethiopia, primary school teachers of science and mathematics are encouraged to integrate Information and Communication Technology (ICT) into their teaching as a means to improve the quality of education. However, there has not been the same emphasis placed on providing professional learning opportunities for teachers on how to use ICT in their…

Experiences of Teaching the Heat Energy Topic in English as a Second Language

ERIC Educational Resources Information Center

Halim, Lilia; Dahlan, Fathiyah; Treagust, David F.; Chandrasegaran, A. L.

2012-01-01

In view of the current debate in Malaysia about the teaching of science and mathematics in English, a qualitative study was undertaken involving a purposeful sampling of three non-physics teachers to ascertain how well equipped they were with the necessary pedagogical content knowledge relating to the teaching of the topic of "heat…

Turning the Table on Professional Development in Mathematics by Setting the Stage for Teacher-Led Inquiry: An Action Research Study

ERIC Educational Resources Information Center

McCullough, Sabrina D.

2016-01-01

This action research study investigated the change in professional development model in the acquisition of content knowledge for fourth-grade math teachers. The current professional development atmosphere is a traditional "sit and get" opportunity. However, research offers that teachers should be active participants in their learning.…

Comparing Eighth-Grade Diagnostic Test Results for Korean, Czech, and American Students.

ERIC Educational Resources Information Center

Um, Eunkyoung; Dogan, Enis; Im, Seongah; Tatsuoka, Kimumi; Corter, James E.

Diagnostic analyses were conducted on data from the Third International Mathematics and Science Study second population (TIMSS-R; 1999) from the United States, Korea, and the Czech Republic in terms of test item attributes (i.e., content, processing skills, and item format) and inferred students' knowledge. The Rule Space model (K. Tatsuoka, 1998)…

Preschool Teachers' Sensitivity to Mathematics in Children's Play: The Influence of Math-Related School Experiences, Emotional Attitudes, and Pedagogical Beliefs

ERIC Educational Resources Information Center

Anders, Yvonne; Rossbach, Hans-Günther

2015-01-01

Without a doubt, math-related pedagogical content knowledge (PCK), pedagogical beliefs, and emotional attitudes are considered important dimensions of preschool teachers' professional competence. This research, however, documents that they are still understudied. This study focuses on certain aspects of the described dimensions: the sensitivity…

Variations of In-Service Training for Primary Mathematics Teachers: An Empirical Study

ERIC Educational Resources Information Center

Selter, Christoph; Gräsel, Cornelia; Reinold, Martin; Trempler, Kati

2015-01-01

Previous findings indicate that the effectiveness of in-service teacher training can be increased by a (pedagogical) content knowledge orientation on the one hand and the stimulation of cooperation among teachers on the other. In this paper, three versions of a multi-phase training program were compared in a quasi-experimental field study with a…

Improving Access to Elementary School Social Studies Instruction: Strategies to Support Students with Learning Disabilities

ERIC Educational Resources Information Center

Ciullo, Stephen

2015-01-01

Social studies instruction in upper elementary school (Grades 3-5) is important for building foundational content knowledge to equip students for the secondary school curriculum. Due to numerous school initiatives and demands on the time of teachers, social studies instruction can play second fiddle to reading and mathematics instruction, which…

Introducing Algebraic Structures through Solving Equations: Vertical Content Knowledge for K-12 Mathematics Teachers

ERIC Educational Resources Information Center

Wasserman, Nicholas H.

2014-01-01

Algebraic structures are a necessary aspect of algebraic thinking for K-12 students and teachers. An approach for introducing the algebraic structure of groups and fields through the arithmetic properties required for solving simple equations is summarized; the collective (not individual) importance of these axioms as a foundation for algebraic…

The Achievement Progress of English Learner Students in Nevada. REL 2016-154

ERIC Educational Resources Information Center

Haas, Eric; Huang, Min; Tran, Loan; Yu, Airong

2016-01-01

The purpose of this study was to examine the cumulative progress of English learner students in Nevada in English language proficiency (ELP) and in academic content knowledge in both reading and mathematics. This study identified students in grades kindergarten, 3, and 6 who were designated as English learner students in 2006/07 and examined their…

Responses to Different Types of Inquiry Prompts: College Students' Discourse, Performance, and Perceptions of Group Work in an Engineering Class

ERIC Educational Resources Information Center

Balgopal, Meena M.; Casper, Anne Marie A.; Atadero, Rebecca A.; Rambo-Hernandez, Karen E.

2017-01-01

Working in small groups to solve problems is an instructional strategy that allows university students in science, technology, engineering, and mathematics disciplines the opportunity to practice interpersonal and professional skills while gaining and applying discipline-specific content knowledge. Previous research indicates that not all group…

TPACK Development in a Three-Year Online Masters Program: How Do Teacher Perceptions Align with Classroom Practice?

ERIC Educational Resources Information Center

Staus, Nancy; Gillow-Wiles, Henry; Niess, Margaret

2014-01-01

A new primarily distance education Master's degree program was focused on the development of technological pedagogical content knowledge (TPACK) for integrating appropriate digital technologies in mathematics and science classes. In this mixed-method multiple case study, we documented in-service K-8 teachers' perceptions of their TPACK…

Defining the Relationship of Student Achievement Between STEM Subjects Through Canonical Correlation Analysis of 2011 Trends in International Mathematics and Science Study (TIMSS) Data

NASA Astrophysics Data System (ADS)

O'Neal, Melissa Jean

Canonical correlation analysis was used to analyze data from Trends in International Mathematics and Science Study (TIMSS) 2011 achievement databases encompassing information from fourth/eighth grades. Student achievement in life science/biology was correlated with achievement in mathematics and other sciences across three analytical areas: mathematics and science student performance, achievement in cognitive domains, and achievement in content domains. Strong correlations between student achievement in life science/biology with achievement in mathematics and overall science occurred for both high- and low-performing education systems. Hence, partial emphases on the inter-subject connections did not always lead to a better student learning outcome in STEM education. In addition, student achievement in life science/biology was positively correlated with achievement in mathematics and science cognitive domains; these patterns held true for correlations of life science/biology with mathematics as well as other sciences. The importance of linking student learning experiences between and within STEM domains to support high performance on TIMSS assessments was indicated by correlations of moderate strength (57 TIMSS assessments was indicated by correlations of moderate strength (57 < r < 85) stronger correlations (73 < r < 97) between life science/biology and other science domains. Results demonstrated the foundational nature of STEM knowledge at the fourth grade level, and established the importance of strong interconnections among life science/biology, mathematics, and other sciences. At the eighth grade level, students who built increasing levels of cognitive complexity upon firm foundations were prepared for successful learning throughout their educational careers. The results from this investigation promote a holistic design of school learning opportunities to improve student achievement in life science/biology and other science, technology, engineering, and mathematics (STEM) subjects at the elementary and middle school levels. While the curriculum can vary from combined STEM subjects to separated mathematics or science courses, both professional learning communities (PLC) for teachers and problem-based learning (PBL) for learners can be strengthened through new knowledge construction beyond the traditional boundaries of each subject. It is the knowledge transfer across subjects that breaks barriers of future STEM discoveries to improve STEM education outcomes.

Valid and Reliable Science Content Assessments for Science Teachers

NASA Astrophysics Data System (ADS)

Tretter, Thomas R.; Brown, Sherri L.; Bush, William S.; Saderholm, Jon C.; Holmes, Vicki-Lynn

2013-03-01

Science teachers' content knowledge is an important influence on student learning, highlighting an ongoing need for programs, and assessments of those programs, designed to support teacher learning of science. Valid and reliable assessments of teacher science knowledge are needed for direct measurement of this crucial variable. This paper describes multiple sources of validity and reliability (Cronbach's alpha greater than 0.8) evidence for physical, life, and earth/space science assessments—part of the Diagnostic Teacher Assessments of Mathematics and Science (DTAMS) project. Validity was strengthened by systematic synthesis of relevant documents, extensive use of external reviewers, and field tests with 900 teachers during assessment development process. Subsequent results from 4,400 teachers, analyzed with Rasch IRT modeling techniques, offer construct and concurrent validity evidence.

Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

ERIC Educational Resources Information Center

Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

2017-01-01

Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…

Preservice Secondary Mathematics Teachers' Development of Mathematical Knowledge for Teaching and Their Use of Knowledge in Their Instruction

ERIC Educational Resources Information Center

Moon, Kyunghee

2013-01-01

This study examined how preservice secondary mathematics teachers developed mathematical knowledge for teaching (MKT) around representations and big ideas through mathematics and mathematics education courses. The importance of big ideas and representations in mathematics has been emphasized in national standards as well as in literature. Yet,…

The effects of an intervention to increase liberal arts mathematics and science majors' knowledge of and attitudinal favorability toward the teaching profession

NASA Astrophysics Data System (ADS)

Klemballa, Carolyn

In light of the persistent shortage of qualified mathematics and science teachers and the new teacher qualification provisions of the recently passed No Child Left Behind Act, This study tested the impact of an educational intervention designed to enhance interest in public school teaching careers among undergraduate students who were declared/intended majors in mathematics and/or natural science. Besides salary, research reveals content fear as the biggest roadblock to attracting mathematics and science teachers. Because of this, liberal arts majors in mathematics and science are a target pool of individuals to recruit into teaching. The researcher hypothesized that knowledge and attitudinal favorability would both increase after an intervention about teaching careers and that an increase in one variable would be associated with the other. Also, knowledge and attitudinal favorability would have a greater increase after a more intensive intervention than a less intensive intervention or no intervention. The researcher also hypothesized that if undergraduates were less decided in their career, lower classmen, and female, their attitudes toward the teaching profession would increase the most. One hundred eighty-nine college students, 73 males and 116 females, including 85 freshmen, 67 sophomores, 18 juniors and 19 seniors, at University A and University B were randomly assigned to a workshop, reading, or control group. The workshop group attended a workshop about the teaching profession. The reading group read articles with the same information presented in the workshop. The control group read unrelated articles. The findings from this study indicate that an intervention about teaching does significantly increase both knowledge and attitudinal favorability toward teaching (p < .01). A low significant correlation was found between knowledge and attitudinal favorability (p < .05). Findings also suggested that a more intensive intervention yields a higher increase in both knowledge and attitudinal favorability than a less intensive intervention (p < .01). Lastly, the level of career indecision, undergraduate class, and gender did not have a significant relationship with attitudinal favorability towards teaching. Based on these findings, the researcher made recommendations for future research and policy, in particular urging more communication between schools of education and liberal arts.

Validation of an instrument for mathematics enhancement teaching efficacy of Pacific Northwest agricultural educators

NASA Astrophysics Data System (ADS)

Jansen, Daniel J.

Teacher efficacy continues to be an important area of study in educational research. This study tested an instrument designed to assess the perceived efficacy of agricultural education teachers when engaged in lessons involving mathematics instruction. The study population of Oregon and Washington agricultural educators utilized in the validation of the instrument revealed important demographic findings and specific results related to teacher efficacy for the study population. An instrument was developed from the assimilation of three scales previously used and validated in efficacy research. Participants' mathematics teaching efficacy was assessed using a portion of the Mathematics Teaching Efficacy Beliefs Instrument (MTEBI), and personal mathematics efficacy was evaluated by the mathematics self-belief instrument which was derived from the Betz and Hackett's Mathematics Self-Efficacy Scale. The final scale, the Teachers' Sense of Efficacy Scale (TSES) created by Tschannen-Moran and Woolfolk Hoy, examined perceived personal teaching efficacy. Structural equation modeling was used as the statistical analyses tool to validate the instrument and examine correlations between efficacy constructs used to determine potential professional development needs of the survey population. As part of the data required for validation of the Mathematics Enhancement Teaching Efficacy instrument, demographic information defining the population of Oregon and Washington agricultural educators was obtained and reported. A hypothetical model derived from teacher efficacy literature was found to be an acceptable model to verify construct validity and determine strength of correlations between the scales that defined the instrument. The instrument produced an alpha coefficient of .905 for reliability. Both exploratory and confirmatory factor analyses were used to verify construct and discriminate validity. Specifics results related to the survey population of agricultural educators concluded that personal mathematics efficacy has a stronger correlation with mathematics teaching efficacy than personal teaching efficacy of teachers for this population. The implications of such findings suggest that professional development and pre-service preparation should be more focused on mathematics content knowledge rather than pedagogical knowledge when the objective is to enhance mathematics in interdisciplinary lessons.

Pre-service Mathematics Teachers' Knowledge of History of Mathematics and Their Attitudes and Beliefs Towards Using History of Mathematics in Mathematics Education

NASA Astrophysics Data System (ADS)

Alpaslan, Mustafa; Işıksal, Mine; Haser, Çiğdem

2014-01-01

This study examined pre-service mathematics teachers' knowledge of history of mathematics and their attitudes and beliefs towards using history of mathematics in mathematics education based on year level in teacher education program and gender. The sample included 1,593 freshman, sophomore, junior, and senior pre-service middle school (grades 4-8) mathematics teachers from nine universities in Turkey. Data were collected through Knowledge of History of Mathematics Test and Attitudes and Beliefs towards the Use of History of Mathematics in Mathematics Education Questionnaire. Results indicate that pre-service teachers have moderate knowledge of history of mathematics and positive attitudes and beliefs towards using history of mathematics. Their knowledge scores increase as the year level in teacher education program advanced. Males' knowledge scores are significantly higher than females' scores in the first 2 years. This situation reverses in the last 2 years, but it is not statistically significant. Pre-service teachers have more positive attitudes and availing beliefs towards using history of mathematics as they progress in their teacher education program. Females have greater attitudes and beliefs mean scores than males in each of the years. The results indicate that the teacher education program may have enhanced the pre-service teachers' knowledge of history of mathematics by related courses. However, the moderate knowledge scores indicate that there is a need for revision of these courses. The pre-service teachers' positive attitudes and beliefs towards using history of mathematics stress the importance of teacher education program in order to prepare them for implementing this alternative strategy in the future.

Prospective Teachers' Initial Conceptions about Pupils' Difficulties in Science and Mathematics: A Potential Resource in Teacher Education

ERIC Educational Resources Information Center

Kellner, Eva; Gullberg, Annica; Attorps, Iiris; Thoren, Ingvar; Tarneberg, Roy

2011-01-01

A crucial issue for prospective teachers (PTs) in their education is to develop pedagogical content knowledge (PCK; i.e. how to make a topic comprehensible to pupils). However, research has shown that PTs may have tacit ideas about teaching that act as filters preventing consideration of unfamiliar and discrepant ideas. These ideas must be…

Spontaneous Focusing on Quantitative Relations as a Predictor of the Development of Rational Number Conceptual Knowledge

ERIC Educational Resources Information Center

McMullen, Jake; Hannula-Sormunen, Minna M.; Laakkonen, Eero; Lehtinen, Erno

2016-01-01

Many people have serious difficulties in understanding rational numbers, limiting their ability to interpret and make use of them in modern daily life. This also leads to later difficulties in learning more advanced mathematical content. In this study, novel tasks are used to measure 263 late primary school students' spontaneous focusing on…

Pearson-Praxis Assessments Review Teacher Certification Assessment Technology Education: A Report for the Council on Technology and Engineering Teacher Education

ERIC Educational Resources Information Center

Mahoney, Mark P.

2015-01-01

The Praxis Series, developed by Educational Testing Services (ETS), has been the long standing assessment for teacher licensure. It is comprised of three separate skills examinations: (1) Praxis Core Academic Skills for Educators (Core) (attempts to measure academic skills in reading, writing, and mathematics; content knowledge of candidates…

The Achievement Progress of English Learner Students in Utah. REL 2016-155

ERIC Educational Resources Information Center

Haas, Eric; Huang, Min; Tran, Loan; Yu, Airong

2016-01-01

The purpose of this study was to examine the cumulative progress of English learner students in Utah in English language proficiency (ELP) and in academic content knowledge in both English language arts (ELA) and mathematics. This study identified students in grades kindergarten, 3, and 6 who were designated as English learner students in 2006/07…

Using Productive Disposition to Differentiate between Students' Level of Precision When Critiquing a Peer's Work

ERIC Educational Resources Information Center

Gilbert, Melissa C.

2014-01-01

This study examined the productive disposition of pre-algebra students who demonstrated similar knowledge of the focal content but varied in other academic behaviors expected in the Common Core State Standards for Mathematics (CCSSM). Specifically, the study considered students' attention to precision when critiquing a peer's work. The…

Focusing on Mathematical Knowledge: The Impact of Content-Intensive Teacher Professional Development. Executive Summary. NCEE 2016-4009

ERIC Educational Resources Information Center

Garet, Michael S.; Heppen, Jessica B.; Walters, Kirk; Parkinson, Julia; Smith, Toni M.; Song, Mengli; Garrett, Rachel; Yang, Rui; Borman, Geoffrey D.

2016-01-01

Improving math achievement among U.S. students remains a high priority as results from recent math assessments continue to show room for improvement. For example, 60 percent of fourth-graders scored below the proficient level on the 2015 National Assessment of Educational Progress. On the most recent Program for International Student Assessment's…

Development and Evaluation of the "Tigriopus" Course-Based Undergraduate Research Experience: Impacts on Students' Content Knowledge, Attitudes, and Motivation in a Majors Introductory Biology Course

ERIC Educational Resources Information Center

Olimpo, Jeffrey T.; Fisher, Ginger R.; DeChenne-Peters, Sue Ellen

2016-01-01

Within the past decade, course-based undergraduate research experiences (CUREs) have emerged as a viable mechanism to enhance novices' development of scientific reasoning and process skills in the science, technology, engineering, and mathematics disciplines. Recent evidence within the bioeducation literature suggests that student engagement in…

Knowledge Concerning the Mathematical Horizon: A Close View

ERIC Educational Resources Information Center

Guberman, Raisa; Gorev, Dvora

2015-01-01

The main objective of this study is to identify components of teachers' mathematical knowledge for teaching, associated with the knowledge of mathematical horizon (KMH) in order to describe this type of knowledge from the viewpoint of elementary school mathematics teachers. The research population of this study consisted of 118 elementary school…

Embedded Mathematics in Chemistry: A Case Study of Students' Attitudes and Mastery

NASA Astrophysics Data System (ADS)

Preininger, Anita M.

2017-02-01

There are many factors that shape students' attitudes toward science, technology, engineering and mathematics. This exploratory study of high school students examined the effect of enriching chemistry with math on chemistry students' attitudes toward math and careers involving math. To measure student attitudes, a survey was administered before and after the 18-week chemistry class; results from the chemistry class were compared to survey results from students in an elective science class that did not emphasize mathematics. At the end of the 18-week period, only the chemistry students exhibited more positive views toward their abilities in mathematics and careers that involve mathematics, as compared to their views at the outset of the course. To ensure that chemistry mastery was not hindered by the additional emphasis on math, and that mastery on state end-of-course examinations reflected knowledge acquired during the math-intensive chemistry class, a chemistry progress test was administered at the start and end of the term. This exploratory study suggests that emphasizing mathematical approaches in chemistry may positively influence attitudes toward math in general, as well as foster mastery of chemistry content.

The Impact of STEM Outreach Programs in Addressing Teacher Efficacy and Broader Issues in STEM Education

NASA Astrophysics Data System (ADS)

Myszkal, Philip Ian

This study explores the potential of the Outreach Workshops in STEM (OWS) to affect Science, Technology, Engineering, and Mathematics (STEM) teachers' content knowledge, self-efficacy, and pedagogical approaches, as well as its viability as a potential form of professional development (PD). The data for the thesis is taken from a larger longitudinal study looking at the potential of OWS to influence middle school students' and teachers' attitudes and beliefs around STEM. The study employs a mixed-methods design, utilizing surveys, open-ended questions, interviews, and observations. The findings show that there were no significant changes in teachers' content knowledge, confidence, or pedagogical approaches. However, the majority of participants reported that they learned new teaching ideas and considered the workshops to be an effective PD opportunity.

Mathematical Knowledge: Its Growth through Teaching. Mathematics Education Library, Volume 10.

ERIC Educational Resources Information Center

Bishop, Alan J., Ed.; And Others

This book presents issues concerning relationships between mathematical knowledge and the teaching and learning processes, focusing especially on the genesis of mathematical knowledge in the classroom. The chapter titles are: (1) The Fragility of Knowledge (Guy Brousseau and Michael Otte); (2) The Double Bind as a Didactical Trap (Stieg…

Dissociations in mathematical knowledge: case studies in Down's syndrome and Williams syndrome.

PubMed

Robinson, Sally J; Temple, Christine M

2013-02-01

A study is reported of mathematical vocabulary and factual mathematical knowledge in PQ, a 22 year old with Down's syndrome (DS) who has a verbal mental age (MA) of 9 years 2 months and ST, a 15 year old with Williams syndrome (WS) who has a verbal MA of 9 years 6 months, matched to typically developing controls. The number of mathematical words contained within PQ's lexical stores was significantly reduced as reflected by performance on lexical decision. PQ was also impaired at both naming from descriptions and describing mathematical words. These results contrast with normal lexical decision and item descriptions for concrete words reported recently for PQ (Robinson and Temple, 2010). PQ's recall of mathematical facts was also impaired, whilst his recall of general knowledge facts was normal. This performance in DS indicates a deficit in both lexical representation and semantic knowledge for mathematical words and mathematical facts. In contrast, ST, the teenager with WS had good accuracy on lexical decision, naming and generating definitions for mathematical words. This contrasted with the atypical performance with concrete words recently reported for ST (Robinson and Temple, 2009). Knowledge of addition facts and general knowledge facts was also unimpaired for ST, though knowledge of multiplication facts was weak. Together the cases form a double dissociation and provide support for the distinct representation of mathematical and concrete items within the lexical-semantic system during development. The dissociations between mathematical and general factual knowledge also indicate that different types of factual knowledge may be selectively impaired during development. There is further support for a modular structure within which mathematical vocabulary and mathematical knowledge have distinct representations. This supports the case for the independent representation of factual and language-based knowledge within the semantic system during development. Copyright © 2011 Elsevier Ltd. All rights reserved.

Primary school teachers' use of digital technology in mathematics: the complexities

NASA Astrophysics Data System (ADS)

Loong, Esther Yook-Kin; Herbert, Sandra

2018-02-01

This paper seeks to theorise primary teachers' degree of integration of digital technology in the mathematics classroom. In an age where digital technology use is ubiquitous, the issues surrounding teachers' choice, and ultimately their uptake of digital technologies in the classroom, is an area that need to be further unpacked. Cross-case analysis of the two teachers' uptake of digital technologies in their classroom, their pedagogical approaches and the reason for their choices provide insight into teachers' technological, pedagogical and content knowledge (TPACK). Differences in the way the teachers use digital technology in their classroom seem to be connected to their TPACK developmental stage.

Finnish Mentor Mathematics Teachers' Views of the Teacher Knowledge Required for Teaching Mathematics

ERIC Educational Resources Information Center

Asikainen, Mervi A.; Pehkonen, Erkki; Hirvonen, Pekka E.

2013-01-01

Seven Finnish mentor mathematics teachers were interviewed about their views regarding the teacher knowledge required for teaching mathematics. The results of the interviews revealed not only the teachers' spontaneous views of the knowledge base needed for effective mathematics teaching but also their views of the particular types of teacher…

Mathematical knowledge for teaching: Making the tacit more explicit in mathematics teacher education

NASA Astrophysics Data System (ADS)

Abdullah, Mohd Faizal Nizam Lee; Vimalanandan, Lena

2017-05-01

Teaching practice during school based experiences, afford an opportunity for pre service teachers to put into practice their knowledge for teaching mathematics. Like all knowledge, Mathematical Knowledge for Teaching (MKT) is held in both tacit and explicit form, making it especially difficult to study and map during instruction. This study investigates the tacit and explicit nature of MKT held by pre service teachers in a Malaysian Teacher Education Program and how it impacts the Mathematical Quality of their instruction (MQI). This study of three mathematics pre-service teachers (PSTs), utilised videos of mathematics lessons, reflective debriefs and interviews. The findings suggest that factors such as reflecting, peer-sharing, conferencing with mentors and observing support in making tacit knowledge more explicit during planning and instruction. Implications for preparation of mathematics teachers capable of high Mathematical Quality of Instruction are also discussed.

Mathematics Content Coverage and Student Learning in Kindergarten

PubMed Central

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2017-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998–99 and 2010–11 school years, they continued to place more emphasis on basic content. We find that time on advanced content is positively associated with student learning, whereas time on basic content has a negative association with learning. We argue that increased exposure to more advanced mathematics content could benefit the vast majority of kindergartners. PMID:29353913

Designing Adaptive-Content trough E-learning on Electromagnetic Concept

NASA Astrophysics Data System (ADS)

Hakim, L.; Setiawan, A.; Sinaga, P.

2017-02-01

Teacher competence development is a national education agenda. Although teachers have adequate learning experience, based on UKA (Academic Competence Test) 2013 results, the content mastery of teachers is still low. In order to reach the maximum development of teacher, it is a must to consider the knowledge level of teachers and the difficulty of content given. This study used a questionnaire given to 40 teachers but only 25 teachers who returned the questionnaire. According to the research, 82% of teachers stated that the electromagnetic is a difficult content. There are several factors why electro magnetic content is considered to be difficult by teachers such as it is abstract, uses a lot of mathematical equations, and correlation with other concepts and content material. From these results, adaptive e-learning design for teacher to learn electromagneticis created.

A neotropical Miocene pollen database employing image-based search and semantic modeling.

PubMed

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W; Jaramillo, Carlos; Shyu, Chi-Ren

2014-08-01

Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery.

Developing Pre-Service Teacher Capacity to Make Appropriate Choices of Tasks and Resources through Diagnostic Assessment of Children's Work

ERIC Educational Resources Information Center

Hurst, Chris

2014-01-01

This paper reports on one phase of a long-term project investigating mathematical content knowledge of pre-service teachers. A cohort of second year PSTs conducted a diagnostic assessment and a series of associated tutoring sessions with a primary aged child. The focus here is on the PSTs' ability to make appropriate task choices following the…

Using Lesson Study to Support the Teaching of Early Number Concepts: Examining the Development of Prospective Teachers' Specialized Content Knowledge

ERIC Educational Resources Information Center

Leavy, Aisling; Hourigan, Mairead

2018-01-01

Growing awareness of the importance of education in the early years has led professional organizations and policy makers to consider the effectiveness of mathematics education for young children. Factors such as educational environments, early years curricula and teacher education are some of the many aspects that have been examined. This paper…

Beyond the Professional Development Academy: Teachers' Retention of Discipline-Specific Science Content Knowledge throughout a 3-Year Mathematics and Science Partnership

ERIC Educational Resources Information Center

Clary, Renee M.; Elder, Anastasia; Dunne, James; Saebo, Svein; Beard, Debbie; Wax, Charles; Tucker, Deborah L.

2018-01-01

The Teacher Academy in the Natural Sciences (TANS) provided middle school (U.S. Grades 6-8) teachers (N = 81) with intensive professional development (PD) in chemistry, geosciences, and physics, with teachers enrolled in one scientific discipline per year. Because some teachers were retained and rotated into different disciplines, the TANS program…

"Highly Qualified" to Do What? The Relationship between NCLB Teacher Quality Mandates and the Use of Reform-Oriented Instruction in Middle School Mathematics

ERIC Educational Resources Information Center

Smith, Thomas M.; Desimone, Laura M.; Ueno, Koji

2005-01-01

The federal No Child Left Behind Act of 2001 (NCLB) calls for a highly qualified teacher in every classroom. According to the legislation, "highly qualified" is defined as full certification, a bachelor's degree, and demonstrated content knowledge in all core subjects taught. States, district, and schools are spending considerable…

Why Understanding 1-3/4 divided by 1/2 Matters to Math Reform: ABE Teachers Learn the Math They Teach.

ERIC Educational Resources Information Center

Brover, Charles; Deagan, Denise; Farina, Solange

This paper explains the investigative attempts of The New York City Math Exchange Group (MEG) on elementary mathematics teachers' content knowledge in Adult Basic Education (ABE). The study is comparative in nature and took place in a workshop at the Adults Learning Maths Conference in Boston. The new members of the MEG professional development…

Evolution of Mathematics Teachers' Pedagogical Knowledge When They Are Teaching through Modeling

ERIC Educational Resources Information Center

Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat; Alacaci, Cengiz; Cakiroglu, Erdinc; Cetinkaya, Bulent

2017-01-01

Use of mathematical modeling in mathematics education has been receiving significant attention as a way to develop students' mathematical knowledge and skills. As effective use of modeling in classes depends on the competencies of teachers we need to know more about the nature of teachers' knowledge to use modeling in mathematics education and how…

The Relationship of Mathematics Anxiety and Mathematical Knowledge to the Learning of Mathematical Pedagogy by Preservice Elementary Teachers.

ERIC Educational Resources Information Center

Battista, Michael T.

1986-01-01

Examined how preservice elementary teachers' (N=38) mathematical knowledge and mathematics anxiety affect their success in a mathematics methods course. Also examined the hypothesis that a mathematics methods course can reduce the mathematics anxiety of these teachers. One finding is that mathematics anxiety does not inhibit their learning of…

The extent to which Latina/o preservice teachers demonstrate culturally responsive teaching practices during science and mathematics instruction

NASA Astrophysics Data System (ADS)

Hernandez, Cecilia M.

2011-12-01

Complex social, racial, economic, and political issues involved in the practice of teaching today require beginning teachers to be informed, skilled, and culturally responsive when entering the classroom. Teacher educators must educate future teachers in ways that will help them teach all children regardless of language, cultural background, or prior knowledge. The purpose of this study was to explore the extent to which culturally and linguistically diverse (CLD) novice teachers described and demonstrated culturally responsive teaching strategies using their students' cultural and academic profiles to inform practice in science and mathematics instruction. This qualitative exploratory case study considered the culturally responsive teaching practices of 12, non-traditional, Latina/o students as they progressed through a distance-based collaborative teacher education program. Qualitative techniques used throughout this exploratory case study investigated cultural responsiveness of these student teachers as they demonstrated their abilities to: a) integrate content and facilitate knowledge construction; b) illustrate social justice and prejudice reduction; and c) develop students academically. In conclusion, student teachers participating in this study demonstrated their ability to integrate content by: (1) including content from other cultures, (2) building positive teacher-student relationships, and (3) holding high expectations for all students. They also demonstrated their ability to facilitate knowledge construction by building on what students knew. Since there is not sufficient data to support the student teachers' abilities to assist students in learning to be critical, independent thinkers who are open to other ways of knowing, no conclusions regarding this subcategory could be drawn. Student teachers in this study illustrated prejudice reduction by: (1) using native language support to assist students in learning and understanding science and math content, (2) fostering positive student-student interactions, and (3) creating a safe learning environment. Results also indicated that these student teachers demonstrated their ability to develop students academically by creating opportunities for learning in the classroom through their knowledge of students and by the use of research-based instructional strategies. However, based on the data collected as part of this study, the student teachers' abilities to illustrate or model social justice during science and math instruction were not demonstrated.

Interactive basic mathematics web using Wordpress

NASA Astrophysics Data System (ADS)

Septia, Tika; Husna; Cesaria, Anna

2017-12-01

Wordpress is a popular open source tool that can be used for developing learning media. Basic Mathematics is the difficult subject for a physics student. The students need an interactive learning to improve their knowledge. The aims of this study were to develop the interactive media using Wordpress and to know the effectiveness of web as a learning media to improve the ICT Literacy students. This study used ADDIE models. The effectiveness of interactive web can be described as the students’ equipness of ICT literacy. The population is physics students. The findings show that the interactive web is valid for the content, presentation, linguistic, and graphic aspects. The results concluded that basic mathematic interactive web is effective to equip the learners ICT literacy of categories of high, medium, and low with the observations and questionnaires are in very good criteria.

Mathematics Content Coverage and Student Learning in Kindergarten

ERIC Educational Resources Information Center

Engel, Mimi; Claessens, Amy; Watts, Tyler; Farkas, George

2016-01-01

Analyzing data from two nationally representative kindergarten cohorts, we examine the mathematics content teachers cover in kindergarten. We expand upon prior research, finding that kindergarten teachers report emphasizing basic mathematics content. Although teachers reported increased coverage of advanced content between the 1998-1999 and…

Mathematics understanding and anxiety in collaborative teaching

NASA Astrophysics Data System (ADS)

Ansari, B. I.; Wahyu, N.

2017-12-01

This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.

On the Relationships between (Relatively) Advanced Mathematical Knowledge and (Relatively) Advanced Problem-Solving Behaviours

ERIC Educational Resources Information Center

Koichu, Boris

2010-01-01

This article discusses an issue of inserting mathematical knowledge within the problem-solving processes. Relatively advanced mathematical knowledge is defined in terms of "three mathematical worlds"; relatively advanced problem-solving behaviours are defined in terms of taxonomies of "proof schemes" and "heuristic behaviours". The relationships…

Re-"Conceptualizing" Procedural Knowledge in Mathematics.

ERIC Educational Resources Information Center

Star, Jon R.

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is…

Mathematical Language Skills of Mathematics Prospective Teachers

ERIC Educational Resources Information Center

Gürefe, Nejla

2018-01-01

Effective mathematics teaching can be actualized only with correct use of the mathematical content language which comprises mathematical rules, concepts, symbols and terms. In this research, it was aimed to examine the mathematics prospective teachers' content language skills in some basic geometric concepts which are ray, angle, polygon,…

Content Area Literacy in the Mathematics Classroom

ERIC Educational Resources Information Center

Armstrong, Abbigail; Ming, Kavin; Helf, Shawnna

2018-01-01

Content area literacy has an important role in helping students understand content in specific disciplines, such as mathematics. Although the strategies are not unique to each individual content area, they are often adapted for use in a specific discipline. For example, mathematicians use mathematical language to make sense of new ideas and…

Language and emotions: emotional Sapir-Whorf hypothesis.

PubMed

Perlovsky, Leonid

2009-01-01

An emotional version of Sapir-Whorf hypothesis suggests that differences in language emotionalities influence differences among cultures no less than conceptual differences. Conceptual contents of languages and cultures to significant extent are determined by words and their semantic differences; these could be borrowed among languages and exchanged among cultures. Emotional differences, as suggested in the paper, are related to grammar and mostly cannot be borrowed. The paper considers conceptual and emotional mechanisms of language along with their role in the mind and cultural evolution. Language evolution from primordial undifferentiated animal cries is discussed: while conceptual contents increase, emotional reduced. Neural mechanisms of these processes are suggested as well as their mathematical models: the knowledge instinct, the dual model connecting language and cognition, neural modeling fields. Mathematical results are related to cognitive science, linguistics, and psychology. Experimental evidence and theoretical arguments are discussed. Dynamics of the hierarchy-heterarchy of human minds and cultures is formulated using mean-field approach and approximate equations are obtained. The knowledge instinct operating in the mind heterarchy leads to mechanisms of differentiation and synthesis determining ontological development and cultural evolution. These mathematical models identify three types of cultures: "conceptual" pragmatic cultures in which emotionality of language is reduced and differentiation overtakes synthesis resulting in fast evolution at the price of uncertainty of values, self doubts, and internal crises; "traditional-emotional" cultures where differentiation lags behind synthesis, resulting in cultural stability at the price of stagnation; and "multi-cultural" societies combining fast cultural evolution and stability. Unsolved problems and future theoretical and experimental directions are discussed.

Developmental Change in the Influence of Domain-General Abilities and Domain-Specific Knowledge on Mathematics Achievement: An Eight-Year Longitudinal Study

PubMed Central

Geary, David C.; Nicholas, Alan; Li, Yaoran; Sun, Jianguo

2016-01-01

The contributions of domain-general abilities and domain-specific knowledge to subsequent mathematics achievement were longitudinally assessed (n = 167) through 8th grade. First grade intelligence and working memory and prior grade reading achievement indexed domain-general effects and domain-specific effects were indexed by prior grade mathematics achievement and mathematical cognition measures of prior grade number knowledge, addition skills, and fraction knowledge. Use of functional data analysis enabled grade-by-grade estimation of overall domain-general and domain-specific effects on subsequent mathematics achievement, the relative importance of individual domain-general and domain-specific variables on this achievement, and linear and non-linear across-grade estimates of these effects. The overall importance of domain-general abilities for subsequent achievement was stable across grades, with working memory emerging as the most important domain-general ability in later grades. The importance of prior mathematical competencies on subsequent mathematics achievement increased across grades, with number knowledge and arithmetic skills critical in all grades and fraction knowledge in later grades. Overall, domain-general abilities were more important than domain-specific knowledge for mathematics learning in early grades but general abilities and domain-specific knowledge were equally important in later grades. PMID:28781382

Causal Connections between Mathematical Language and Mathematical Knowledge: A Dialogic Reading Intervention

ERIC Educational Resources Information Center

Purpura, David J.; Napoli, Amy R.; Wehrspann, Elizabeth A.; Gold, Zachary S.

2017-01-01

The acquisition of early mathematical knowledge is critical for successful long-term academic development. Mathematical language is one of the strongest predictors of children's early mathematical success. Findings from previous studies have provided correlational evidence supporting the importance of mathematical language to the development of…

Cortical circuits for mathematical knowledge: evidence for a major subdivision within the brain's semantic networks.

PubMed

Amalric, Marie; Dehaene, Stanislas

2017-02-19

Is mathematical language similar to natural language? Are language areas used by mathematicians when they do mathematics? And does the brain comprise a generic semantic system that stores mathematical knowledge alongside knowledge of history, geography or famous people? Here, we refute those views by reviewing three functional MRI studies of the representation and manipulation of high-level mathematical knowledge in professional mathematicians. The results reveal that brain activity during professional mathematical reflection spares perisylvian language-related brain regions as well as temporal lobe areas classically involved in general semantic knowledge. Instead, mathematical reflection recycles bilateral intraparietal and ventral temporal regions involved in elementary number sense. Even simple fact retrieval, such as remembering that 'the sine function is periodical' or that 'London buses are red', activates dissociated areas for math versus non-math knowledge. Together with other fMRI and recent intracranial studies, our results indicated a major separation between two brain networks for mathematical and non-mathematical semantics, which goes a long way to explain a variety of facts in neuroimaging, neuropsychology and developmental disorders.This article is part of a discussion meeting issue 'The origins of numerical abilities'. © 2017 The Author(s).

A multi-disciplinary curriculum for 11- to 13-year-olds: immunization, plus!

PubMed

Glik, D C; Stone, K M; McNeil, J D; Berkanovic, E; Jones, M C; Richardes, D A; Mirocha, J M

1997-09-01

A sixth grade curriculum entitled "Immunization, Plus!" Was developed to promote adolescent immunization. This targeted immunization curriculum utilized contemporary learning theory and innovative teaching approaches and styles to maximize acceptability among educators. Because instructional time in school was limited, a thematic curriculum was created to embed immunization and communicable disease content within mathematics, science/health, and language arts units. The curriculum, which reflected the theory of multiple intelligences among students, offered an array of different learning formats, including linguistic, logical-mathematical, spatial, and bodily-kinesthetic. The curriculum was made available free of charge to school districts in California, and its evaluation was planned to track distribution, utilization, and changes in students' knowledge, attitude, and behavior.

Learning To Teach: Constructing Meaningful Understanding of Mathematical Content. Craft Paper 89-3.

ERIC Educational Resources Information Center

Lappan, Glenda; Even, Ruhama

This paper discusses the development of the mathematical experiences which make up the three-term sequence of mathematics courses taken by participants in the Elementary Mathematics Project (EMP), a longitudinal study of change in preservice teachers' perceptions and beliefs about mathematics. For the mathematics courses, both content and teaching…

What Math Knowledge Does Teaching Require?

ERIC Educational Resources Information Center

Thames, Mark Hoover; Ball, Deborah Loewenberg

2010-01-01

No one would argue with the claim that teaching mathematics requires mathematics knowledge. However, a clear description of such knowledge needed for teaching has been surprisingly elusive. To differentiate teachers' levels of mathematical knowledge, numerous studies have examined whether a teacher has a certification in math or a degree as well…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge From Ages 4 to 11.

PubMed

Rittle-Johnson, Bethany; Fyfe, Emily R; Hofer, Kerry G; Farran, Dale C

2017-09-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math topics, as well as potential pathways from preschool to middle grades mathematics achievement. In preschool, nonsymbolic quantity, counting, and patterning knowledge predicted fifth-grade mathematics achievement. By the end of first grade, symbolic mapping, calculation, and patterning knowledge were the important predictors. Furthermore, the first-grade predictors mediated the relation between preschool math knowledge and fifth-grade mathematics achievement. Findings support the early math trajectories model among low-income children. © 2016 The Authors. Child Development © 2016 Society for Research in Child Development, Inc.

Effects of professional development on the knowledge and classroom practices of elementary school science teachers

NASA Astrophysics Data System (ADS)

Minuskin, Sondra

The purpose of this study was to determine the effects of professional development on the knowledge and classroom practices of teachers of science in kindergarten through Grade 5. These teachers, trained to be generalists in the content areas, were strongly prepared in pedagogical practices, reading skills, basic language arts, and mathematics content areas. Science reform has led to more content-specific science standards that were difficult for these unprepared teachers to address without professional development. The researcher implemented a professional development program that used a collaborative model involving 8 teachers in Grade 4. The researcher conducted the professional development, assisted at times by personnel from the New Jersey State Department of Education. The new standards were learned, reinforced, and adopted. The data that were analyzed to determine the effects of the professional development came from a comparison of student achievement of the classes of 2 sets of teachers in Grade 4, one of which was the control set ( n = 8). The other was the experimental set (n = 8). The researcher administered pre- and postintervention content tests to both groups to measure teacher knowledge. In addition, the researcher reviewed lesson plans, conducted observations, and administered surveys to determine whether professional development in science impacted teacher practices in the classroom. This limited study suggested that teacher instruction did not significantly differ after professional development intervention. It also suggested that teacher content knowledge did not significantly increase due to the intervention. The researcher believes that local factors influenced the outcome and recommends a more systemic program that includes the involvement of all stakeholders.

Mitigating the Mathematical Knowledge Gap between High School and First Year University Chemical Engineering Mathematics Course

ERIC Educational Resources Information Center

Basitere, Moses; Ivala, Eunice

2015-01-01

This paper reports on a study carried out at a University of Technology, South Africa, aimed at identifying the existence of the mathematical knowledge gap and evaluating the intervention designed to bridge the knowledge gap amongst students studying first year mathematics at the Chemical Engineering Extended Curriculum Program (ECP). In this…

Elementary Preservice Teachers' and Elementary Inservice Teachers' Knowledge of Mathematical Modeling

ERIC Educational Resources Information Center

Schwerdtfeger, Sara

2017-01-01

This study examined the differences in knowledge of mathematical modeling between a group of elementary preservice teachers and a group of elementary inservice teachers. Mathematical modeling has recently come to the forefront of elementary mathematics classrooms because of the call to add mathematical modeling tasks in mathematics classes through…

The Nature of Mathematics: A Heuristic Inquiry

ERIC Educational Resources Information Center

Pair, Jeffrey David

2017-01-01

What is mathematics? What does it mean to be a mathematician? What should students understand about the nature of mathematical knowledge and inquiry? Research in the field of mathematics education has found that students often have naive views about the nature of mathematics. Some believe that mathematics is a body of unchanging knowledge, a…

Knowledge and Knowing in Mathematics and Pedagogy: A Case Study of Mathematics Student Teachers' Epistemological Beliefs

ERIC Educational Resources Information Center

Löfström, Erika; Pursiainen, Tuomas

2015-01-01

This study focuses on mathematics student teachers' epistemological beliefs in mathematics and education. The study aimed at gaining insight into the challenges that students experience in the consolidation of knowledge in the two disciplines. The case study with three mathematics pre-service teachers utilised mathematical and pedagogical…

Investigating students' view on STEM in learning about electrical current through STS approach

NASA Astrophysics Data System (ADS)

Tupsai, Jiraporn; Yuenyong, Chokchai

2018-01-01

This study aims to investigate Grade 11 students' views on Science Technology Engineering Mathematics (STEM) with the integration of learning about electrical current based on Science Technology Society (STS) approach [8]. The participants were 60 Grade 11 students in Demonstration Secondary School, Khon Kaen University, Khon Kaen Province, Thailand. The methodology is in the respect of interpretive paradigm. The teaching and learning about Electrical Current through STS approach carried out over 6 weeks. The Electrical Current unit through STS approach was developed based on framework[8] that consists of five stages including (1) identification of social issues, (2) identification of potential solutions, (3) need for knowledge, (4) decision making, and (5) socialization stage. To start with, the question "what if this world is lack of electricity" was challenged in the class in order to move students to find the problem of how to design Electricity Generation from Clean Energy. Students were expected to apply scientific and other knowledge to design of Electricity Generation. Students' views on STEM were collected during their learning by participant' observation and students' tasks. Their views on STEM were categorized when they applied their knowledge for designing the Electricity Generation. The findings indicated that students cooperatively work to solve the problem when applying knowledge about the content of Science and Mathematics and processing skill of Technology and Engineering. It showed that students held the integration of science, technology, engineering and mathematics to design their possible solutions in learning about Electrical Current. The paper also discusses implications for science teaching and learning through STS in Thailand.

The Language of Mathematics: The Importance of Teaching and Learning Mathematical Vocabulary

ERIC Educational Resources Information Center

Riccomini, Paul J.; Smith, Gregory W.; Hughes, Elizabeth M.; Fries, Karen M.

2015-01-01

Vocabulary understanding is a major contributor to overall comprehension in many content areas, including mathematics. Effective methods for teaching vocabulary in all content areas are diverse and long standing. Teaching and learning the language of mathematics is vital for the development of mathematical proficiency. Students' mathematical…

The Challenges and Success of Implementing Climate Studies Lessons for Pre-Professional Teachers at a Small Historically Black College to Engage Student Teaching of Science Pedagogy and Content Skill Based Learning.

NASA Astrophysics Data System (ADS)

Arnold, J.; Wider-Lewis, F.; Miller-Jenkins, A.

2017-12-01

This poster is a description of the challenges and success of implementing climate studies lessons for pre-service teachers to engage student teaching pedagogy and content skill based learning. Edward Waters College is a historical black college with an elementary education teacher program focused on urban elementary school teaching and learning. Pre-Service Elementary Educator Students often have difficulty with science and mathematics content and pedagogy. This poster will highlight the barriers and successes of using climate studies lessons to develop and enhance pre-service teachers' knowledge of elementary science principles particularly related to climate studies, physical and earth space science.

Status of Teachers' Proficiency in Mathematical Knowledge for Teaching at Secondary School Level in Kenya

ERIC Educational Resources Information Center

Miheso-O'Connor Khakasa, Marguerite; Berger, Margot

2016-01-01

Mathematical knowledge for teaching (MKT), defined by Ball ("Elementary Journal," 93, 373-397, 1993) as knowledge that is needed to teach mathematics, has been used as a framework by researchers to interrogate various aspects of teaching and learning mathematics. In this article, which draws from a larger study, we show how an in-depth…

Secondary School Mathematics Teachers' Knowledge Levels and Use of History of Mathematics

ERIC Educational Resources Information Center

Bütüner, Suphi Önder

2018-01-01

This study describes secondary school mathematics teachers' use of history of mathematics in their classes and their knowledge levels in this field. The study population included a total of 58 secondary school mathematics teachers working at the secondary schools located in Yozgat city center, and the sample included 32 mathematics teachers from…

Mathematical Knowledge for Teaching, Standards-Based Mathematics Teaching Practices, and Student Achievement in the Context of the "Responsive Classroom Approach"

ERIC Educational Resources Information Center

Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross A.; Berry, Robert Q.

2015-01-01

This study investigates the effectiveness of the Responsive Classroom (RC) approach, a social and emotional learning intervention, on changing the relations between mathematics teacher and classroom inputs (mathematical knowledge for teaching [MKT] and standards-based mathematics teaching practices) and student mathematics achievement. Work was…

A neotropical Miocene pollen database employing image-based search and semantic modeling1

PubMed Central

Han, Jing Ginger; Cao, Hongfei; Barb, Adrian; Punyasena, Surangi W.; Jaramillo, Carlos; Shyu, Chi-Ren

2014-01-01

• Premise of the study: Digital microscopic pollen images are being generated with increasing speed and volume, producing opportunities to develop new computational methods that increase the consistency and efficiency of pollen analysis and provide the palynological community a computational framework for information sharing and knowledge transfer. • Methods: Mathematical methods were used to assign trait semantics (abstract morphological representations) of the images of neotropical Miocene pollen and spores. Advanced database-indexing structures were built to compare and retrieve similar images based on their visual content. A Web-based system was developed to provide novel tools for automatic trait semantic annotation and image retrieval by trait semantics and visual content. • Results: Mathematical models that map visual features to trait semantics can be used to annotate images with morphology semantics and to search image databases with improved reliability and productivity. Images can also be searched by visual content, providing users with customized emphases on traits such as color, shape, and texture. • Discussion: Content- and semantic-based image searches provide a powerful computational platform for pollen and spore identification. The infrastructure outlined provides a framework for building a community-wide palynological resource, streamlining the process of manual identification, analysis, and species discovery. PMID:25202648

Exploring the Associations Among Nutrition, Science, and Mathematics Knowledge for an Integrative, Food-Based Curriculum.

PubMed

Stage, Virginia C; Kolasa, Kathryn M; Díaz, Sebastián R; Duffrin, Melani W

2018-01-01

Explore associations between nutrition, science, and mathematics knowledge to provide evidence that integrating food/nutrition education in the fourth-grade curriculum may support gains in academic knowledge. Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across North Carolina and Ohio; mean age 10 years old; gender (I = 53.2% female; C = 51.6% female). Dependent variable = post-test-nutrition knowledge; independent variables = baseline-nutrition knowledge, and post-test science and mathematics knowledge. Analyses included descriptive statistics and multiple linear regression. The hypothesized model predicted post-nutrition knowledge (F(437) = 149.4, p < .001; Adjusted R = .51). All independent variables were significant predictors with positive association. Science and mathematics knowledge were predictive of nutrition knowledge indicating use of an integrative science and mathematics curriculum to improve academic knowledge may also simultaneously improve nutrition knowledge among fourth-grade students. Teachers can benefit from integration by meeting multiple academic standards, efficiently using limited classroom time, and increasing nutrition education provided in the classroom. © 2018, American School Health Association.

The development of a model of culturally responsive science and mathematics teaching

NASA Astrophysics Data System (ADS)

Hernandez, Cecilia M.; Morales, Amanda R.; Shroyer, M. Gail

2013-12-01

This qualitative theoretical study was conducted in response to the current need for an inclusive and comprehensive model to guide the preparation and assessment of teacher candidates for culturally responsive teaching. The process of developing a model of culturally responsive teaching involved three steps: a comprehensive review of the literature; a synthesis of the literature into thematic categories to capture the dispositions and behaviors of culturally responsive teaching; and the piloting of these thematic categories with teacher candidates to validate the usefulness of the categories and to generate specific exemplars of behavior to represent each category. The model of culturally responsive teaching contains five thematic categories: (1) content integration, (2) facilitating knowledge construction, (3) prejudice reduction, (4) social justice, and (5) academic development. The current model is a promising tool for comprehensively defining culturally responsive teaching in the context of teacher education as well as to guide curriculum and assessment changes aimed to increase candidates' culturally responsive knowledge and skills in science and mathematics teaching.

Building Knowledge Structures by Testing Helps Children with Mathematical Learning Difficulty

ERIC Educational Resources Information Center

Zhang, Yiyun; Zhou, Xinlin

2016-01-01

Mathematical learning difficulty (MLD) is prevalent in the development of mathematical abilities. Previous interventions for children with MLD have focused on number sense or basic mathematical skills. This study investigated whether mathematical performance of fifth grade children with MLD could be improved by developing knowledge structures by…

Indonesian Primary Teachers' Mathematical Knowledge for Teaching Geometry: Implications for Educational Policy and Teacher Preparation Programs

ERIC Educational Resources Information Center

Ng, Dicky

2011-01-01

This study examines Indonesian primary teachers' mathematical knowledge for teaching geometry and what factors contribute to this knowledge. A translated and adapted version of the Learning Mathematics for Teaching measures and the Indonesian Educational Survey were used to gather information on teachers' knowledge for teaching geometry and their…

Life skills, mathematical reasoning and critical thinking: a curriculum for the prevention of problem gambling.

PubMed

Turner, Nigel E; Macdonald, John; Somerset, Matthew

2008-09-01

Previous studies have shown that youth are two to three times more likely than adults to report gambling related problems. This paper reports on the development and pilot evaluation of a school-based problem gambling prevention curriculum. The prevention program focused on problem gambling awareness and self-monitoring skills, coping skills, and knowledge of the nature of random events. The results of a controlled experiment evaluating the students learning from the program are reported. We found significant improvement in the students' knowledge of random events, knowledge of problem gambling awareness and self-monitoring, and knowledge of coping skills. The results suggest that knowledge based material on random events, problem gambling awareness and self-monitoring skills, and coping skills can be taught. Future development of the curriculum will focus on content to expand the students' coping skill options.

Preschool children's mathematical knowledge: The effect of teacher "math talk.".

PubMed

Klibanoff, Raquel S; Levine, Susan C; Huttenlocher, Janellen; Vasilyeva, Marina; Hedges, Larry V

2006-01-01

This study examined the relation between the amount of mathematical input in the speech of preschool or day-care teachers and the growth of children's conventional mathematical knowledge over the school year. Three main findings emerged. First, there were marked individual differences in children's conventional mathematical knowledge by 4 years of age that were associated with socioeconomic status. Second, there were dramatic differences in the amount of math-related talk teachers provided. Third, and most important, the amount of teachers' math-related talk was significantly related to the growth of preschoolers' conventional mathematical knowledge over the school year but was unrelated to their math knowledge at the start of the school year. Copyright 2006 APA, all rights reserved.

Mathematical Methods of Subjective Modeling in Scientific Research: I. The Mathematical and Empirical Basis

NASA Astrophysics Data System (ADS)

Pyt'ev, Yu. P.

2018-01-01

mathematical formalism for subjective modeling, based on modelling of uncertainty, reflecting unreliability of subjective information and fuzziness that is common for its content. The model of subjective judgments on values of an unknown parameter x ∈ X of the model M( x) of a research object is defined by the researcher-modeler as a space1 ( X, p( X), P{I^{\\bar x}}, Be{l^{\\bar x}}) with plausibility P{I^{\\bar x}} and believability Be{l^{\\bar x}} measures, where x is an uncertain element taking values in X that models researcher—modeler's uncertain propositions about an unknown x ∈ X, measures P{I^{\\bar x}}, Be{l^{\\bar x}} model modalities of a researcher-modeler's subjective judgments on the validity of each x ∈ X: the value of P{I^{\\bar x}}(\\tilde x = x) determines how relatively plausible, in his opinion, the equality (\\tilde x = x) is, while the value of Be{l^{\\bar x}}(\\tilde x = x) determines how the inequality (\\tilde x = x) should be relatively believed in. Versions of plausibility Pl and believability Bel measures and pl- and bel-integrals that inherit some traits of probabilities, psychophysics and take into account interests of researcher-modeler groups are considered. It is shown that the mathematical formalism of subjective modeling, unlike "standard" mathematical modeling, •enables a researcher-modeler to model both precise formalized knowledge and non-formalized unreliable knowledge, from complete ignorance to precise knowledge of the model of a research object, to calculate relative plausibilities and believabilities of any features of a research object that are specified by its subjective model M(\\tilde x), and if the data on observations of a research object is available, then it: •enables him to estimate the adequacy of subjective model to the research objective, to correct it by combining subjective ideas and the observation data after testing their consistency, and, finally, to empirically recover the model of a research object.

The Mathematics Education of Elementary Teachers: Issues and Strategies for Content Courses

ERIC Educational Resources Information Center

Hart, Lynn C., Ed.; Oesterle, Susan, Ed.; Auslander, Susan Swars, Ed.; Kajander, Ann, Ed.

2016-01-01

This book is an edited volume addressing specific issues of significance for individuals involved with the undergraduate mathematics content preparation of prospective elementary teachers (PSTs). Teaching mathematics content courses to this group of students presents unique challenges. While some PSTs enter their teacher preparation with weak…

The Transition from Informal to Formal Mathematical Knowledge: Mediation by Numeral Knowledge

ERIC Educational Resources Information Center

Purpura, David J.; Baroody, Arthur J.; Lonigan, Christopher J.

2013-01-01

The purpose of the present study was to determine if numeral knowledge--the ability to identify Arabic numerals and connect Arabic numerals to their respective quantities--mediates the relation between informal and formal mathematical knowledge. A total of 206 3- to 5-year-old preschool children were assessed on 6 informal mathematics tasks and 2…

Construction of knowledge about teaching practice and educating students from diverse cultures in an online induction program

NASA Astrophysics Data System (ADS)

Bice, Lawrence Raymond

2005-11-01

Beginning teachers in both urban areas and geographically isolated rural areas often do not have access to a mentor teacher of the same content area or grade level in their school or district. This project is a study of learning in the on-line e-Mentoring for Student Success (eMSS) program, which provides induction for science and mathematics teachers in Montana and California. The study centered on a particular segment of eMSS called the Diversity Module. Two examinations were conducted: (1) Analysis of discourse by all participants in the Diversity Module, and (2) case study of five beginning teachers with diverse student populations. Analysis of learning by cases was conducted by examining discourse in the Diversity Module, private on-line discussions with their assigned mentors during a two-year period, and pre and post Diversity Module interviews and interviews of their mentors. Three frameworks were developed to aid understanding of findings: (1) discourse analysis, (2) competencies of multicultural teachers, and, (3) competencies of pedagogical and pedagogical content knowledge. Cases developed their knowledge of teaching along a continuum of needs over two years of participation in the eMSS program. Initial needs expressed by mentees were in areas such as classroom management and general methods of instruction. Cases increased their knowledge in virtually all aspects of pedagogical knowledge, changing their expressed needs to pedagogical content knowledge concerns such as adapting and differentiating instruction for particular content and individual students, and building their repertoire of instructional representations. Through on-line discussion, teachers developed or advanced awareness of student culture and learning characteristics, and adapted their practice to foster a climate of student respect. Findings provided little evidence of adapting instruction for diverse student learning. Teachers who had a strong awareness of their own and their students' cultures advanced their understanding of multicultural teaching competencies further than those who did not. Interview results indicated that learning sometimes takes place in a non-visible manner. Growth in multicultural teaching knowledge, as well as several aspects of pedagogical and pedagogical content knowledge, was clearly evident for participants who posted few messages, but read and actively reflected on thoughts of others.

Initial Teacher Training Science Nature and Mathematics and the Teaching of Astronomy

NASA Astrophysics Data System (ADS)

Macedo, Josué Antunes de

2014-11-01

Although Astronomy is part of the National Curriculum Parameters, it is rarely taught adequately in basic education. In this regard, this research has been developed aiming to investigate contributions to the use of traditional resources combined with digital technologies, in order to create autonomy for future teachers of Natural Sciences and Mathematics in relation to themes in Astronomy. The following steps were taken: i) analysis of educational pedagogical projects (EPP) from licentiate courses at the Federal Institution of Education, Science and Technology in the North of Minas Gerais (FINMG); ii) analysis of students' preconceptions on Astronomy and digital technologies; iii) elaboration of the course and application, developed under the education modality of blended learning, using the teaching proposal of methological pluralism; iv) application and analysis of the final questionnaire. The research subjects were constituted by thirty-two students of Physics, Mathematics and Biological Sciences courses. A mixed methodology with a pre-experimental delineation, combined with content analysis, has been used. The results showed the following: at the IFNMG, only the licentiate course in physics includes Astronomy content in several curriculum subjects; students´ rates of previous knowledge of Astronomy are low, and there are indications of meaningful learning of concepts related to Astronomy. This research sought to contribute to initial teacher training, particularly in relation to Astronomy teaching, proposing new alternatives to promote the teaching of this knowledge area. Furthermore, the intention was to respond to requests of institutions for implementation of blended learning or distance courses, since during the survey it was verified that, although discussions in forums are important, there is a need for such courses to promote on-site meetings conducting practical and manipulative activities.

Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

NASA Astrophysics Data System (ADS)

Misu, La; Ketut Budayasa, I.; Lukito, Agung

2018-03-01

This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

Informal Content and Student Note-Taking in Advanced Mathematics Classes

ERIC Educational Resources Information Center

Fukawa-Connelly, Timothy; Weber, Keith; Mejía-Ramos, Juan Pablo

2017-01-01

This study investigates 3 hypotheses about proof-based mathematics instruction: (a) that lectures include informal content (ways of thinking and reasoning about advanced mathematics that are not captured by formal symbolic statements), (b) that informal content is usually presented orally but not written on the board, and (c) that students do not…

Mathematical Content of Curricula and Beginning Salaries of Graduating Students

ERIC Educational Resources Information Center

Lee, B. Brian; Lee, Jungsun

2009-01-01

The authors examined an association between mathematical content in college-level curricula and beginning salaries of graduating students on the basis of data collected from a public university in the southern region of the United States. The authors classified the mathematical content requirements of the curricula into the following 5 groups…

Assessing Understanding through Reading and Writing in Mathematics

ERIC Educational Resources Information Center

Adu-Gyamfi, Kwaku; Bosse, Michael J.; Faulconer, Johna

2010-01-01

The mathematics education community recognizes the integrality of reading and writing in learning and communicating mathematics knowledge. Unfortunately, many students have yet to significantly experience this integrality in their mathematics classrooms despite the power these tools offer teachers for assessing student knowledge. This paper…

The Effect of an Integrated Science and Mathematics Content-Based Course on Science and Mathematics Teaching Efficacy of Preservice Elementary Teachers

ERIC Educational Resources Information Center

Moseley, Christine; Utley, Juliana

2006-01-01

The purpose of this study was to determine the effect of an earth systems science course (integrated mathematics and science content) on preservice elementary teachers' mathematics and science teaching efficacy. Paired t-tests revealed that the personal mathematics and science teaching efficacy and science teaching outcome expectancy significantly…

Financial Mathematical Tasks in a Middle School Mathematics Textbook Series: A Content Analysis

ERIC Educational Resources Information Center

Hamburg, Maryanna P.

2009-01-01

This content analysis examined the distribution of financial mathematical tasks (FMTs), mathematical tasks that contain financial terminology and require financially related solutions, across the National Standards in K-12 Personal Finance Education categories (JumpStart Coalition, 2007), the thinking skills as identified by "A Taxonomy for…

Mathematical foundations of biomechanics.

PubMed

Niederer, Peter F

2010-01-01

The aim of biomechanics is the analysis of the structure and function of humans, animals, and plants by means of the methods of mechanics. Its foundations are in particular embedded in mathematics, physics, and informatics. Due to the inherent multidisciplinary character deriving from its aim, biomechanics has numerous connections and overlapping areas with biology, biochemistry, physiology, and pathophysiology, along with clinical medicine, so its range is enormously wide. This treatise is mainly meant to serve as an introduction and overview for readers and students who intend to acquire a basic understanding of the mathematical principles and mechanics that constitute the foundation of biomechanics; accordingly, its contents are limited to basic theoretical principles of general validity and long-range significance. Selected examples are included that are representative for the problems treated in biomechanics. Although ultimate mathematical generality is not in the foreground, an attempt is made to derive the theory from basic principles. A concise and systematic formulation is thereby intended with the aim that the reader is provided with a working knowledge. It is assumed that he or she is familiar with the principles of calculus, vector analysis, and linear algebra.

Examining the impact of the Guided Constructivist teaching method on students' misconceptions about concepts of Newtonian physics

NASA Astrophysics Data System (ADS)

Ibrahim, Hyatt Abdelhaleem

The effect of Guided Constructivism (Interactivity-Based Learning Environment) and Traditional Expository instructional methods on students' misconceptions about concepts of Newtonian Physics was investigated. Four groups of 79 of University of Central Florida students enrolled in Physics 2048 participated in the study. A quasi-experimental design of nonrandomized, nonequivalent control and experimental groups was employed. The experimental group was exposed to the Guided Constructivist teaching method, while the control group was taught using the Traditional Expository teaching approach. The data collection instruments included the Force Concept Inventory Test (FCI), the Mechanics Baseline Test (MBT), and the Maryland Physics Expectation Survey (MPEX). The Guided Constructivist group had significantly higher means than the Traditional Expository group on the criterion variables of: (1) conceptions of Newtonian Physics, (2) achievement in Newtonian Physics, and (3) beliefs about the content of Physics knowledge, beliefs about the role of Mathematics in learning Physics, and overall beliefs about learning/teaching/appropriate roles of learners and teachers/nature of Physics. Further, significant relationships were found between (1) achievement, conceptual structures, beliefs about the content of Physics knowledge, and beliefs about the role of Mathematics in learning Physics; (2) changes in misconceptions about the physical phenomena, and changes in beliefs about the content of Physics knowledge. No statistically significant difference was found between the two teaching methods on achievement of males and females. These findings suggest that differences in conceptual learning due to the nature of the teaching method used exist. Furthermore, greater conceptual learning is fostered when teachers use interactivity-based teaching strategies to train students to link everyday experience in the real physical world to formal school concepts. The moderate effect size and power of the study suggest that the effect may not be subtle, but reliable. Physics teachers can use these results to inform their decisions about structuring learning environment when conceptual learning is important.

A Case Study of Four Latina/o Pre-Service Teachers in Learning to Teach Mathematics for Understanding and Integrate a Child's Out-of-School Mathematical Knowledge and Experiences

ERIC Educational Resources Information Center

Kalinec-Craig, Crystal

2012-01-01

This dissertation study examines the experiences of four Latina/o pre-service teachers (PSTs) as they learn about teaching mathematics for understanding (TM4U) and integrating a child's out-of-school mathematical knowledge and experiences during instruction. Studying the knowledge and experiences of Latina/o PSTs is necessary because PSTs…

Applying mathematical concepts with hands-on, food-based science curriculum.

PubMed

Roseno, Ashley T; Carraway-Stage, Virginia G; Hoerdeman, Callan; Díaz, Sebastián R; Eugene, Geist; Duffrin, Melani W

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student's mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.

Applying mathematical concepts with hands-on, food-based science curriculum

PubMed Central

Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Eugene, Geist; Duffrin, Melani W.

2015-01-01

This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the impact of the FoodMASTER Intermediate curriculum on fourth-grade student’s mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students’ mathematics knowledge while building a foundation for becoming quantitatively literate adults. PMID:26494927

Strengthening Mathematics And Science Education (SMASE) For Improving The Quality Of Teachers in Nigeria

NASA Astrophysics Data System (ADS)

Shuaibu, Zainab Muhammad

2016-04-01

The education system in Nigeria, especially at the basic education level, teachers who teach mathematics and science need to be confident with what they are teaching, they need to have appropriate techniques and strategies of motivating the pupils. If these subjects are not taught well at the basic education level its extraordinarily hard to get them (pupils/students) back to track, no matter what will be done in the secondary and tertiary level. Teachers as the driving force behind improvements in the education system are in the best position to understand and propose solutions to problems faced by students. Teachers must have access to sustainable, high quality professional development in order to improve teaching and student learning. Teachers' professional development in Nigeria, however, has long been criticized for its lack of sustainability and ability to produce effective change in teaching and students achievement. Education theorists today believe that a critical component of educational reform lies in providing teachers with various opportunities and supports structures that encourage ongoing improvement in teachers' pedagogy and discipline-specific content knowledge. However, the ongoing reforms in education sector and the need to refocus the Nigeria education system towards the goal of the National Economical Empowerment and Development Strategies (NEEDS) demand that the existing In-service and Education Training (INSET) in Nigeria be refocused. It is against this premise that an INSET programme aimed at Strengthening Mathematics And Science Education (SMASE) for primary and secondary school teachers was conceived. The relevance of the SMASE INSET according to the Project Design Matrix (PDM) was derived from an In-service aimed at enhancing the quality of teachers in terms of positive attitude, teaching methodology, mastery of content, resource mobilization and utilization of locally available teaching and learning materials. The intervention of Strengthening Mathematics And Science Education (SMASE) in training and re-training of teachers at enhancing quality classroom activities in Mathematics and Science subjects through Activity, Student-centre, Experiments, Improvisation (ASEI)-Plan, Do, See, Improve (PDSI) instructional strategy. This instructional strategy has cultivates learner's mathematical and scientific thinking ability and have provided one of the best regular INSET for primary and secondary Mathematics and Science teachers as observed during the SMASE impact survey in the three piloted states in Nigeria. To build a common ground for teaching method irrespective of teacher and teaching style School-Based Training (SBT) is now advocated in SMASE, SBT is aimed at improving teaching and learning activities in the classroom through Lesson Study model. Lesson Study is a teaching improvement and knowledge building process that has its origin in the Japanese elementary education it involves a comprehensive process of planning, observation, analysis and identifying the best approaches in a classroom. This an inquiry approach to professional development that requires teachers to identify an area of instructional interest, collect data to analyses and make instructional changes based on the data. This kind of professional development make teachers acquires current and up to date knowledge in the field of mathematics and science.

The Microevolution of Mathematical Knowledge: The Case of Randomness.

ERIC Educational Resources Information Center

Pratt, Dave; Noss, Richard

2002-01-01

Explores the growth of mathematical knowledge and the relationship between abstraction and context. Builds on work to construct a viable model of the micro-evolution of mathematical knowledge in context whose central feature is the visibility of its mechanisms. Illustrates a case study of 10-11-year-old children's construction of meanings for…

The Role of Teachers in Facilitating Mathematics Learning Opportunities in Agriculture, Food, and Natural Resources

ERIC Educational Resources Information Center

McKim, Aaron J.; Velez, Jonathan J.; Everett, Michael W.; Sorensen, Tyson J.

2017-01-01

Strengthening knowledge and skills in mathematics is critically important to preparing the next generation of innovators, problem solvers, and interdisciplinary thinkers. School-based agricultural education offers a valuable context to co-develop mathematics knowledge and skills alongside knowledge and skills in agriculture, food, and natural…

Didactics and History of Mathematics: Knowledge and Self-Knowledge

ERIC Educational Resources Information Center

Fried, Michael N.

2007-01-01

The basic assumption of this paper is that mathematics and history of mathematics are both forms of knowledge and, therefore, represent different ways of knowing. This was also the basic assumption of Fried (2001) who maintained that these ways of knowing imply different conceptual and methodological commitments, which, in turn, lead to a conflict…

Elementary School Quality: The Mathematics Curriculum and the Role of Local Knowledge.

ERIC Educational Resources Information Center

Balfanz, Robert

This report considers how the mathematical knowledge children develop on their own outside of formal school instruction can be used to increase the distribution and level of mathematical knowledge attained by students in grades K-3. Included are preliminary results of an investigation of the counting and calculating abilities brought to…

The Framing Discussion: Connecting Student Experience with Mathematical Knowledge

ERIC Educational Resources Information Center

Henning, John E.; Balong, Megan

2011-01-01

This article introduces the framing discussion, an informal discussion of a mathematical problem that takes place at the beginning of a lesson or unit. The purpose of the framing discussion is to assess student knowledge, motivate student interest, and to serve as a basis for guiding students to more formal mathematical knowledge. The article…

Mathematics Teachers' Knowledge of Student Thinking and Its Evidences in Their Instruction

ERIC Educational Resources Information Center

Çelik, Aytug Özaltun; Güzel, Esra Bukova

2017-01-01

The aim of this case study is to examine mathematics teachers' knowledge of students' thinking and its evidences in their teaching. The participants were three secondary mathematics teachers. Data were gathered from interviews and observations. While analyzing the data, the framework about teachers' knowledge of students' thinking was used. The…

Prospective Middle Grade Mathematics Teachers' Knowledge of Algebra for Teaching

ERIC Educational Resources Information Center

Huang, Rongjin; Kulm, Gerald

2012-01-01

This study examined prospective middle grade mathematics teachers' knowledge of algebra for teaching with a focus on knowledge for teaching the concept of function. 115 prospective teachers from an interdisciplinary program for mathematics and science middle teacher preparation at a large public university in the USA participated in a survey. It…

The Predominance of Procedural Knowledge in Fractions

ERIC Educational Resources Information Center

Forrester, Tricia; Chinnappan, Mohan

2010-01-01

Teachers play a crucial role in the mathematical learning outcomes of their students. The quality of teachers' mathematical knowledge has been of interest to key stakeholders and several lines of inquiry have been running in an effort to better understand the kinds of knowledge that mathematics teachers need to acquire and use to drive their…

Making Connections in Practice: How Prospective Elementary Teachers Connect to Children's Mathematical Thinking and Community Funds of Knowledge in Mathematics Instruction

ERIC Educational Resources Information Center

Aguirre, Julia M.; Turner, Erin E.; Bartell, Tonya Gau; Kalinec-Craig, Crystal; Foote, Mary Q.; Roth McDuffie, Amy; Drake, Corey

2013-01-01

This study examines the ways prospective elementary teachers (PSTs) made connections to children's mathematical thinking and children's community funds of knowledge in mathematics lesson plans. We analyzed the work of 70 PSTs from across three university sites associated with an instructional module for elementary mathematics methods courses that…

Developing a Leveling Framework of Mathematical Belief and Mathematical Knowledge for Teaching of Indonesian Pre-Service Teachers

ERIC Educational Resources Information Center

Novikasari, Ifada; Darhim, Didi Suryadi

2015-01-01

This study explored the characteristics of pre-service primary teachers (PSTs) influenced by mathematical belief and mathematical knowledge for teaching (MKT) PSTs'. A qualitative approach was used to investigate the levels of PSTs on mathematical belief and MKT. The two research instruments used in this study were an interview-based task and a…

Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy

ERIC Educational Resources Information Center

Schmidt, William H.; Cogan, Leland S.; Houang, Richard T.; McKnight, Curtis C.

2011-01-01

This article utilizes the 1999 TIMSS-R data from U.S. states and districts to explore the consequences of variation in opportunities to learn specific mathematics content. Analyses explore the relationship between classroom mathematics content coverage and student achievement as measured by the TIMSS-R international mathematics scaled score.…

Depth of Teachers' Knowledge: Frameworks for Teachers' Knowledge of Mathematics

ERIC Educational Resources Information Center

Holmes, Vicki-Lynn

2012-01-01

This article describes seven teacher knowledge frameworks and relates these frameworks to the teaching and assessment of elementary teacher's mathematics knowledge. The frameworks classify teachers' knowledge and provide a vocabulary and common language through which knowledge can be discussed and assessed. These frameworks are categorized into…

Freedom Quilts: Mathematics on the Underground Railroad

ERIC Educational Resources Information Center

Neumann, Maureen D.

2005-01-01

A mathematics activity is presented which is a lesson frequently taught to upper elementary school students. It helps the students to see the connection of mathematics with a real-world activity, appreciate the mathematical knowledge required of quilt makers, reinforce their knowledge of the geometrical properties of different shapes and bring…

Using Analogies to Facilitate Conceptual Change in Mathematics Learning

ERIC Educational Resources Information Center

Vamvakoussi, Xenia

2017-01-01

The problem of adverse effects of prior knowledge in mathematics learning has been amply documented and theorized by mathematics educators as well as cognitive/developmental psychologists. This problem emerges when students' prior knowledge about a mathematical notion comes in contrast with new information coming from instruction, giving rise to…

Prospective Secondary Mathematics Teachers' Perspectives and Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Karagöz-Akar, Gülseren

2016-01-01

This study investigated the relationship between prospective secondary mathematics teachers' perspectives and their mathematical knowledge for teaching in action. Data from two prospective teachers' practice-teachings, one in geometry and one in algebra, their lesson plans and self-reflections were analyzed with Teacher Perspectives and Knowledge…

Contrasting Knowledge for Elementary and Secondary Mathematics Teaching

ERIC Educational Resources Information Center

Rowland, Tim

2012-01-01

This paper describes and analyses two mathematics lessons, one with very young pupils, about subtraction, the other for lower secondary school pupils, about gradients [slopes] and graphs. The focus of the analysis is on teacher knowledge, and on the fundamental mathematical and mathematics-pedagogical prerequisites that underpin teaching these…

Reflective Awareness in Mathematics Teachers' Learning and Teaching

ERIC Educational Resources Information Center

Chapman, Olive

2015-01-01

The nature of mathematics teachers' knowledge specific to teaching mathematics [MTK] is of ongoing concern in mathematics education research. This article contributes to our under-standing of this knowledge with particular focus on reflective awareness. It discusses MTK based on ways it has been used in research. It highlights reflective awareness…

Influences on Mathematical Preparation of Secondary School Teachers of Mathematics.

ERIC Educational Resources Information Center

Johnson, Carl S.; Byars, Jackson A.

The results of a survey related to the impact of various recommendations on preservice content programs for teachers of mathematics are reported. The content of current programs is compared to the recommendations of the Committee on Undergraduate Programs in Mathematics (CUPM). The acceptance of CUPM and the Cambridge Conference on School…

An instrument measuring prospective mathematics teacher self-regulated learning: validity and reliability

NASA Astrophysics Data System (ADS)

Nugroho, A. A.; Juniati, D.; Siswono, T. Y. E.

2018-03-01

Self Regulated Learning (SRL) is an individual's ability to achieve academic goals by controlling behavior, motivate yourself and use cognitive in learning, so it is important for a teacher especially teachers of mathematics related to the ability of management, design, implementation of learning and evaluation of learning outcomes. The purpose of the research is to develop an instrument to describe the SRL of a prospective mathematics teacher. Data were collected by (1) the study of the theory of SRL produced the indicator SRL used to design the questionnaire SRL; (2) analysis of the questionnaire SRL obtained from several References; and (3) development stage of the SRL questionnaire through validity test of content and empirical validation. The study involved 2 content experts in mathematics, 1 linguist, and 92 prospective mathematics teachers. The results of the research on content validity test based on Indonesian expert and 2 content experts indicate that the content can assess the indicator of the SRL and feasible to be used, in the test of legibility of two prospective mathematics teacher concluded that the instrument has a language that can be understood by the prospective teacher of mathematics and on empirical validation involving 92 prospective mathematics teacher generate data that of 65 statements there are 3 invalid statements. Reliability calculation shows high category that values 0,93. The conclusion is the SRL instrument developed for the prospective mathematics teacher.

A Case Study of Pedagogy of Mathematics Support Tutors without a Background in Mathematics Education

ERIC Educational Resources Information Center

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to…

Understanding Understanding Mathematics. Artificial Intelligence Memo No. 488.

ERIC Educational Resources Information Center

Michener, Edwina Rissland

This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…

Provocative Mathematics Questions: Drawing Attention to a Lack of Attention

ERIC Educational Resources Information Center

Klymchuk, Sergiy

2015-01-01

The article investigates the role of attention in the reflective thinking of school mathematics teachers. It analyses teachers' ability to pay attention to detail and "use" their mathematical knowledge. The vast majority of teachers can be expected to have an excellent knowledge of mathematical techniques. The question examined here is…

The Effects of Teacher Collaboration in Grade 9 Applied Mathematics

ERIC Educational Resources Information Center

Egodawatte, Gunawardena; McDougall, Douglas; Stoilescu, Dorian

2011-01-01

The current emphasis of many mathematics education reform documents is on the need to change the environment of mathematics classrooms from the transmission of knowledge by the teacher to the transaction of knowledge between the teacher and the students which promotes mathematical investigation and exploration. In this article, we discuss the…

Rethinking Teacher Preparation: Conceptualizing Skills and Knowledge of Novice Teachers of Secondary Mathematics

ERIC Educational Resources Information Center

Cummings, Margarita Borelli

2010-01-01

This dissertation examines the extent to which novice secondary mathematics teachers (licensed and currently teaching in Utah) perceive they are prepared to do the work of teaching secondary mathematics. It first examined if novice secondary mathematics teachers' perceptions of their knowledge and skills of doing their work fell into four…

First-Year Students' Beliefs about Context Problems in Mathematics in University Science Programmes

ERIC Educational Resources Information Center

Drobnic Vidic, Andreja

2015-01-01

Mathematics-related beliefs play an important role in the willingness to engage in academic activities in mathematics education. Such beliefs might not be consistent with the beliefs students hold about context problems that require sufficient mathematical knowledge and the application of such knowledge to various real-life situations. This study…

Hybrid Task Design: Connecting Learning Opportunities Related to Critical Thinking and Statistical Thinking

ERIC Educational Resources Information Center

Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David

2017-01-01

Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…

Results of a Comprehension Test in Mathematics

ERIC Educational Resources Information Center

Debrenti, Edith

2013-01-01

In higher education the main subjects build on the knowledge acquired in high school. Research shows that students entering universities have acquired basic knowledge to different extents. It is very important to be able to apply mathematical knowledge directly. Students often treat practical knowledge separately from theoretical knowledge. They…

Effects of Prior Knowledge in Mathematics on Learner-Interface Interactions in a Learning-by-Teaching Intelligent Tutoring System

ERIC Educational Resources Information Center

Bringula, Rex P.; Basa, Roselle S.; Dela Cruz, Cecilio; Rodrigo, Ma. Mercedes T.

2016-01-01

This study attempted to determine the influence of prior knowledge in mathematics of students on learner-interface interactions in a learning-by-teaching intelligent tutoring system. One hundred thirty-nine high school students answered a pretest (i.e., the prior knowledge in mathematics) and a posttest. In between the pretest and posttest, they…

Assessing Key Epistemic Features of Didactic-Mathematical Knowledge of Prospective Teachers: The Case of The Derivative

ERIC Educational Resources Information Center

Pino-Fan, Luis R.; Godino, Juan D.; Font, Vicenç

2018-01-01

In recent years, there has been a growing interest in studying the knowledge that mathematics teachers require in order for their teaching to be effective. However, only a few studies have focused on the design and application of instruments that are capable of exploring different aspects of teachers' didactic-mathematical knowledge about specific…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Ages 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2017-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An early math trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from ages 4 to 11. This model includes a broad range of math…

Early Math Trajectories: Low-Income Children's Mathematics Knowledge from Age 4 to 11

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Fyfe, Emily R.; Hofer, Kerry G.; Farran, Dale C.

2016-01-01

Early mathematics knowledge is a strong predictor of later academic achievement, but children from low-income families enter school with weak mathematics knowledge. An Early Math Trajectories model is proposed and evaluated within a longitudinal study of 517 low-income American children from age 4 to 11. This model includes a broad range of math…

Stereotype Threat Effects on Learning From a Cognitively Demanding Mathematics Lesson.

PubMed

Lyons, Emily McLaughlin; Simms, Nina; Begolli, Kreshnik N; Richland, Lindsey E

2018-03-01

Stereotype threat-a situational context in which individuals are concerned about confirming a negative stereotype-is often shown to impact test performance, with one hypothesized mechanism being that cognitive resources are temporarily co-opted by intrusive thoughts and worries, leading individuals to underperform despite high content knowledge and ability (see Schmader & Beilock, ). We test here whether stereotype threat may also impact initial student learning and knowledge formation when experienced prior to instruction. Predominantly African American fifth-grade students provided either their race or the date before a videotaped, conceptually demanding mathematics lesson. Students who gave their race retained less learning over time, enjoyed the lesson less, reported a diminished desire to learn more, and were less likely to choose to engage in an optional math activity. The detrimental impact was greatest among students with high baseline cognitive resources. While stereotype threat has been well documented to harm test performance, the finding that effects extend to initial learning suggests that stereotype threat's contribution to achievement gaps may be greatly underestimated. Copyright © 2017 Cognitive Science Society, Inc.

Connecting Mathematics and Literature: An Analysis of Pre-Service Elementary School Teachers' Changing Beliefs and Knowledge

ERIC Educational Resources Information Center

Wilburne, Jane M.; Napoli, Mary

2008-01-01

The National Council of Teachers of Mathematics calls for students to see relationships and connections with mathematics (2000). This study examined the influences on eight pre-service elementary school teachers' beliefs and knowledge of teaching mathematics through literature. The semester long project involved both the language arts and…

The Relationship between Mathematical Knowledge of Numbers and Operations and Mathematics Beliefs of Prospective Teachers

ERIC Educational Resources Information Center

Stiegelmeyer, Cindy

2012-01-01

This study surveyed 82 preservice elementary teachers using items from an instrument designed to predict student achievement based on a teacher's mathematics knowledge for teaching (MKT) in numbers and operations concepts. Additional mathematics beliefs items asked participants to rate their level of agreement with math myths and math anxiety…

The Influence of University Courses and Field Experiences on Chinese Elementary Candidates' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Youngs, Peter; Qian, Hong

2013-01-01

In this article, we draw on survey data to investigate associations between Chinese elementary teaching candidates’ mathematical knowledge for teaching (MKT) and their experiences in mathematics courses, mathematics methods courses, and student teaching. In our study, we found that (a) Chinese teaching candidates' completion of courses in number…

The Development of Mathematical Knowledge for Teaching of Mathematics Teachers in Lesson Analysis Process

ERIC Educational Resources Information Center

Baki, Mujgan

2015-01-01

This study aims to explore the role of lesson analysis in the development of mathematical knowledge for teaching. For this purpose, a graduate course based on lesson analysis was designed for novice mathematics teachers. Throughout the course the teachers watched videos of group-mates and discussed the issues they identified in terms of…

Mathematics as an Im/Pure Knowledge System: Symbiosis, (W)Holism and Synergy in Mathematics Education

ERIC Educational Resources Information Center

Luitel, Bal Chandra

2013-01-01

The problem of culturally decontextualised mathematics education faced by Nepali students, teachers and teacher educators has often been oriented by the view of the nature of "mathematics as a body of pure knowledge," which gives rise to an exclusive emphasis on an ideology of singularity, epistemology of objectivism, language of…

Using Video as a Stimulus to Reveal Elementary Teachers' Mathematical Knowledge for Teaching

ERIC Educational Resources Information Center

Barlow, Angela T.; Gaddy, Angeline K.; Baxter, Wesley A.

2017-01-01

The purpose of this article is to explore the usefulness of a video-based tool for measuring teachers' mathematical knowledge for teaching. Unique to this tool is the use of a video featuring a mathematical disagreement that occurred in an elementary classroom. The authors define mathematical disagreements as instances in which students challenge…

What Math Matters? Types of Mathematics Knowledge and Relationships to Methods Course Performance

ERIC Educational Resources Information Center

Kajander, Ann; Holm, Jennifer

2016-01-01

This study investigated the effect of a departmental focus on enhanced mathematics knowledge for teaching on overall performance in upper elementary mathematics methods courses. The study examined the effect of performance on a new course in mathematics for teaching on performance at the methods course level. In addition, the effect of performance…

Deaf college students' mathematical skills relative to morphological knowledge, reading level, and language proficiency.

PubMed

Kelly, Ronald R; Gaustad, Martha G

2007-01-01

This study of deaf college students examined specific relationships between their mathematics performance and their assessed skills in reading, language, and English morphology. Simple regression analyses showed that deaf college students' language proficiency scores, reading grade level, and morphological knowledge regarding word segmentation and meaning were all significantly correlated with both the ACT Mathematics Subtest and National Technical Institute for the Deaf (NTID) Mathematics Placement Test scores. Multiple regression analyses identified the best combination from among these potential independent predictors of students' performance on both the ACT and NTID mathematics tests. Additionally, the participating deaf students' grades in their college mathematics courses were significantly and positively associated with their reading grade level and their knowledge of morphological components of words.

Mapping Mathematics in Classroom Discourse

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth A.; Otten, Samuel

2011-01-01

This article offers a particular analytic method from systemic functional linguistics, "thematic analysis," which reveals the mathematical meaning potentials construed in discourse. Addressing concerns that discourse analysis is too often content-free, thematic analysis provides a way to represent semantic structures of mathematical content,…

Separating Cognitive and Content Domains in Mathematical Competence

ERIC Educational Resources Information Center

Harks, Birgit; Klieme, Eckhard; Hartig, Johannes; Leiss, Dominik

2014-01-01

The present study investigates the empirical separability of mathematical (a) content domains, (b) cognitive domains, and (c) content-specific cognitive domains. There were 122 items representing two content domains (linear equations vs. theorem of Pythagoras) combined with two cognitive domains (modeling competence vs. technical competence)…

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2014 CFR

2014-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2012 CFR

2012-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

20 CFR 901.12 - Eligibility for enrollment.

Code of Federal Regulations, 2013 CFR

2013-04-01

...) Basic actuarial knowledge. The applicant shall demonstrate knowledge of basic actuarial mathematics and... mathematics and methodology including compound interest, principles of life contingencies, commutation... concentration was actuarial mathematics, or (ii) Which included at least as many semester hours or quarter hours...

How Education Affects Mathematics Teachers' Knowledge: Unpacking Selected Aspects of Teacher Knowledge

ERIC Educational Resources Information Center

Koponen, Mika; Asikainen, Mervi A.; Viholainen, Antti; Hirvonen, Pekka E.

2017-01-01

It is no surprise that all mathematics teacher education programs attempt to increase future teachers' knowledge, since teachers' knowledge has an effect not only on their teaching but also on their students' achievements. However, measuring the relationship between teachers' knowledge and their education is overly demanding. In this study we…

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities

PubMed Central

Chu, Felicia W.; vanMarle, Kristy; Geary, David C.

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement. PMID:27252675

Predicting Children's Reading and Mathematics Achievement from Early Quantitative Knowledge and Domain-General Cognitive Abilities.

PubMed

Chu, Felicia W; vanMarle, Kristy; Geary, David C

2016-01-01

One hundred children (44 boys) participated in a 3-year longitudinal study of the development of basic quantitative competencies and the relation between these competencies and later mathematics and reading achievement. The children's preliteracy knowledge, intelligence, executive functions, and parental educational background were also assessed. The quantitative tasks assessed a broad range of symbolic and nonsymbolic knowledge and were administered four times across 2 years of preschool. Mathematics achievement was assessed at the end of each of 2 years of preschool, and mathematics and word reading achievement were assessed at the end of kindergarten. Our goals were to determine how domain-general abilities contribute to growth in children's quantitative knowledge and to determine how domain-general and domain-specific abilities contribute to children's preschool mathematics achievement and kindergarten mathematics and reading achievement. We first identified four core quantitative competencies (e.g., knowledge of the cardinal value of number words) that predict later mathematics achievement. The domain-general abilities were then used to predict growth in these competencies across 2 years of preschool, and the combination of domain-general abilities, preliteracy skills, and core quantitative competencies were used to predict mathematics achievement across preschool and mathematics and word reading achievement at the end of kindergarten. Both intelligence and executive functions predicted growth in the four quantitative competencies, especially across the first year of preschool. A combination of domain-general and domain-specific competencies predicted preschoolers' mathematics achievement, with a trend for domain-specific skills to be more strongly related to achievement at the beginning of preschool than at the end of preschool. Preschool preliteracy skills, sensitivity to the relative quantities of collections of objects, and cardinal knowledge predicted reading and mathematics achievement at the end of kindergarten. Preliteracy skills were more strongly related to word reading, whereas sensitivity to relative quantity was more strongly related to mathematics achievement. The overall results indicate that a combination of domain-general and domain-specific abilities contribute to development of children's early mathematics and reading achievement.

The impact of focused, long-term, and collaborative professional development in math and science participants' self-efficacy, classroom practice, and student achievement

NASA Astrophysics Data System (ADS)

Nottingham, Mary E.

The purpose of this study was to investigate the impact of a 2-year professional development model in math and science on the self-efficacy of the teacher and its effects on teacher practice and student outcomes. Further, this study sought to incorporate the instructional use of Inquiry-Based Learning methods of Problem-Based Learning, Japanese Lesson Study, and Action Research. Additionally, this study examined the impacts of these interventions on teacher efficacy and student outcomes. Thirty-eight collaborating participants were purposefully selected by the Math and Science Teacher Academy (MASTA) project grant co-directors because of their content-focused classrooms of mathematics and science. This quasi-experimental study included mathematics and science in-service teachers working on their masters in education. The 2-year, bi-monthly professional development model included collaborating Inquiry-Based Learning communities with in-depth focus on Japanese Lesson Study, Problem-Based Learning instruction, and Action Research. A chi-square analysis was conducted by grade on the difference in passing rate from the Texas Assessment of Knowledge and Skills mathematics and science tests between the MASTA participants and the state passing average. In mathematics there were significant v differences only at grades 3 and 7 where the state passing average was significantly higher than the MASTA students' passing rate. Only at grade 5 was the MASTA students' passing rate higher than the state, but the difference was not significantly different. The science passing rate received from three grade 5 MASTA participants was compared to the state average and a chi-squared was conducted. Although the passing rate for the grade 5 science test was 6% higher for MASTA student that the state, the difference was not statistically significant. However, after analyzing the qualitative participant responses from data gathered during the 2-year MASTA grant the data clearly reflected that teachers participating in the MASTA grant felt the professional development helped to improve their own teacher-efficacy and knowledge in their content areas.

Secondary School Advanced Mathematics, Chapter 1, Organizing Geometric Knowledge, Chapter 2, Concepts and Skills in Algebra. Student's Text.

ERIC Educational Resources Information Center

Stanford Univ., CA. School Mathematics Study Group.

This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…

Teaching Early Knowledge of Whole Number Concepts through Technology: Findings from a Feasibility Study of an iPad Delivered Kindergarten Mathematics Intervention

ERIC Educational Resources Information Center

Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy

2013-01-01

Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…

Characteristics and Impact of the Further Mathematics Knowledge Networks: Analysis of an English Professional Development Initiative on the Teaching of Advanced Mathematics

ERIC Educational Resources Information Center

Ruthven, Kenneth

2014-01-01

Reports from 13 Further Mathematics Knowledge Networks supported by the National Centre for Excellence in the Teaching of Mathematics [NCETM] are analysed. After summarizing basic characteristics of the networks regarding leadership, composition and pattern of activity, each of the following aspects is examined in greater depth: Developmental aims…

A Study of Students' Conceptual, Procedural Knowledge, Logical Thinking and Creativity during the First Year of Tertiary Mathematics

ERIC Educational Resources Information Center

Tularam, Gurudeo Anand; Hulsman, Kees

2015-01-01

This study focuses on students in first year environmental science degree programs, where traditionally mathematical emphasis has been much less than within the strict science or math majors. The importance now placed on applied mathematics, however, means that students need to gain more conceptual and quantitative knowledge of mathematics in not…

Exploring the Impact of a Standards-Based Mathematics and Pedagogy Class on Preservice Teachers' Beliefs and Subject Matter Knowledge

ERIC Educational Resources Information Center

Stohlmann, Micah Stephen

2012-01-01

This case study explored the impact of a standards-based mathematics and pedagogy class on preservice elementary teachers' beliefs and conceptual subject matter knowledge of linear functions. The framework for the standards-based mathematics and pedagogy class in this study involved the National Council of Teachers of Mathematics Standards,…

What do Mathematics Teachers and Teacher Trainees Know about the History of Mathematics?

ERIC Educational Resources Information Center

Gazit, Avikam

2013-01-01

The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants…

Mathematical knowledge in teaching of fraction concepts using diagrammatical approach

NASA Astrophysics Data System (ADS)

Veloo, Palanisamy Kathir; Puteh, Marzita

2017-05-01

Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.

The Nation's Report Card[TM]: Mathematics 2005: Performance in Puerto Rico. Focus on the Content Areas. NCES 2007-460

ERIC Educational Resources Information Center

Dion, Gloria S.; Haberstroh, Jeff G.; Dresher, Amy R.

2007-01-01

This report focuses on the performance of fourth-and eighth-grade students in Puerto Rico in various mathematics content areas on the 2005 National Assessment of Educational Progress (NAEP) in mathematics. The NAEP mathematics assessment was administered to public school students in Puerto Rico for the first time in 2003. Although NAEP had…

Alignment Content Analysis of TIMSS and PISA Mathematics and Science Assessments Using the Surveys of Enacted Curriculum Methodology

ERIC Educational Resources Information Center

Council of Chief State School Officers, 2009

2009-01-01

In Fall 2008, the Council of Chief State School Officers (CCSSO) conducted an alignment content analysis of the 2007 TIMSS Mathematics and Science education assessments for students at grades 4 and 8 and the 2006 PISA Mathematics and Science Literacy assessments for students at age 15 (i.e., TIMSS--Trends in Mathematics and Science Study,…

Considering Indigenous Knowledges and Mathematics Curriculum

ERIC Educational Resources Information Center

Sterenberg, Gladys

2013-01-01

Across Canada, significant program changes in school mathematics have been made that encourage teachers to consider Aboriginal perspectives. In this article, I investigate one Aboriginal teacher's approaches to integrating Indigenous knowledges and the mandated mathematics curriculum in a Blackfoot First Nation school. Using a framework that…

Food-based science curriculum yields gains in nutrition knowledge.

PubMed

Carraway-Stage, Virginia; Hovland, Jana; Showers, Carissa; Díaz, Sebastián; Duffrin, Melani W

2015-04-01

Students may be receiving less than an average of 4 hours of nutrition instruction per year. Integrating nutrition with other subject areas such as science may increase exposure to nutrition education, while supporting existing academics. During the 2009-2010 school year, researchers implemented the Food, Math, and Science Teaching Enhancement Resource (FoodMASTER) Intermediate (FMI) curriculum in 18 fourth-grade classrooms, whereas 16 classrooms served as comparison. FMI is a hands-on, integrative curriculum for children in grades 3-5 that uses food as a tool to teach mathematics and science. Researchers developed a 28-item multiple-choice questionnaire to assess students' nutrition knowledge in 6 content areas. Students were evaluated at baseline and post-intervention. Data were analyzed using independent t tests. Analysis of covariance was employed to control for differences at baseline when assessing the effectiveness of the FMI curriculum to increase nutrition knowledge. A significant improvement was observed in total nutrition knowledge at post-intervention (adjusting for baseline) between groups (F [1] = 128.95; p < .01) and in all content areas post-intervention. Findings from this study suggest teachers were successfully able to integrate science and nutrition to meet multiple academic standards. More specifically, results showed implementation of the integrative FMI curriculum effectively improved fourth-graders' nutrition knowledge compared with students not exposed to FMI. © 2015, American School Health Association.

Theoretical Framework of Researcher Knowledge Development in Mathematics Education

ERIC Educational Resources Information Center

Kontorovich, Igor'

2016-01-01

The goal of this paper is to present a framework of researcher knowledge development in conducting a study in mathematics education. The key components of the framework are: knowledge germane to conducting a particular study, processes of knowledge accumulation, and catalyzing filters that influence a researcher's decision making. The components…

Assessing Knowledge of Mathematical Equivalence: A Construct-Modeling Approach

ERIC Educational Resources Information Center

Rittle-Johnson, Bethany; Matthews, Percival G.; Taylor, Roger S.; McEldoon, Katherine L.

2011-01-01

Knowledge of mathematical equivalence, the principle that 2 sides of an equation represent the same value, is a foundational concept in algebra, and this knowledge develops throughout elementary and middle school. Using a construct-modeling approach, we developed an assessment of equivalence knowledge. Second through sixth graders (N = 175)…

Maths Games: A Universal Design Approach to Mathematical Reasoning

ERIC Educational Resources Information Center

Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia E.

2017-01-01

Providing students with an opportunity to explore mathematical content through games allows teachers to include tasks that: (1) present alternative representations of the content; (2) welcome various expressions of mathematical reasoning; and (3) incorporate variations that empower all students to engage in the problem solving process. Games not…

A Cognitive Theory Driven New Orientation of Indonesian Lessons

ERIC Educational Resources Information Center

Nowinska, Edyta

2014-01-01

The main focus of this design research was on students' mathematical thinking and skills and on their understanding of mathematical concepts and methods. The mathematical content our project starts with is the introduction of integers. For this content new learning environments have been developed, implemented and evaluated. An important question…

The Relationship between Scores of Mathematics Knowledge and Teaching Practice of Diploma Mathematics Students: A Quest for Quality Assurance

ERIC Educational Resources Information Center

Adamu, L. E.

2015-01-01

The purpose of the study was to determine the relationship between scores in mathematics knowledge and teaching practice of Diploma mathematics students. A sample of 39 students was used. Two research questions and two hypotheses were asked and formulated respectively. An ex-post facto correlation design was used. The data were analyzed using…

Mathematical Knowledge for Teaching Fraction Multiplication

ERIC Educational Resources Information Center

Izsak, Andrew

2008-01-01

The present study contrasts mathematical knowledge that two sixth-grade teachers apparently used when teaching fraction multiplication with the Connected Mathematics Project materials. The analysis concentrated on those tasks from the materials that use drawings to represent fractions as length or area quantities. Examining the two teachers'…

Digital fabrication as an instructional technology for supporting upper elementary and middle school science and mathematics education

NASA Astrophysics Data System (ADS)

Tillman, Daniel

The purpose of this three-paper manuscript dissertation was to study digital fabrication as an instructional technology for supporting elementary and middle school science and mathematics education. Article one analyzed the effects of digital fabrication activities that were designed to contextualize mathematics education at a summer mathematics enrichment program for upper elementary and middle school students. The primary dependent variables studied were the participants' knowledge of mathematics and science content, attitudes towards STEM (science, technology, engineering, and mathematics) and STEM-related careers. Based upon the data collected, three results were presented as having justifiable supporting empirical evidence: (1) The digital fabrication activities, combined with the other mathematics activities at the enrichment program, resulted in non-significant overall gains in students' mathematics test scores and attitudes towards STEM. (2) The digital fabrication activities, combined with the other mathematics activities at the enrichment program, resulted in noteworthy gains on the "Probability & Statistics" questions. (3) Some students who did poorly on the scored paper test on mathematics and science content were nonetheless nominated by their teachers as demonstrating meritorious distinction during the digital fabrication activities (termed "Great Thinkers" by the 5th-grade teachers). Article two focused on how an instructional technology course featuring digital fabrication activities impacted (1) preservice elementary teachers' efficacy beliefs about teaching science, and (2) their attitudes and understanding of how to include instructional technology and digital fabrication activities into teaching science. The research design compared two sections of a teaching with technology course featuring digital fabrication activities to another section of the same course that utilized a media cycle framework (Bull & Bell, 2005) that did not feature digital fabrication activities. Based upon analysis of the data collected, two main results were determined to have justifiable supporting empirical evidence: (1) After the instructional technology course featuring digital fabrication activities, the participants reported statistically significant overall gains in science teaching efficacy beliefs. (2) When asked to describe their future plans for using three instructional technologies in their teaching, the top five most mentioned instructional technologies were: interactive whiteboards, video, class website, interactive online timeline, and digital fabrication. Of the participants that mentioned digital fabrication, the specific content areas mentioned were: history (four out of eight students mentioned), social studies (two out of eight), and science, math, engineering, and technology were each mentioned once. Article three assessed the impact of a series of lessons incorporating a NASA-themed transmedia book featuring digital fabrication activities on 5th-grade students who had been recognized as advanced in mathematics. The main dependent variables studied were the students' knowledge of science content from the Virginia Standards of Learning, attitude towards science, and student reported likes and dislikes about the project. Based upon analysis of the data collected, three main results were presented: (1) Students demonstrated significant positive gains in correct answers to questions on the topic of "Force, Matter, Energy, & Motion" from pretest to posttest. (2) There were nonsignificant gains reported by students on the attitude survey questions about attitude towards science, but this was chiefly because of one question that was significantly impacted in a negative direction. (3) Students articulated five main categories of likes and six main categories of dislikes of the experience, thereby providing insight into their own perception of some of the affordances and constraints of the educational activities. The five topics mentioned most often by students as self-reported likes about the experience included: hands-on activities including building, making, or designing (18 of 29 students mentioned; 62.1%), experimenting (9 of 29; 31.0%), presenting (9 of 29; 31.0%), drawing (6 of 29; 20.7%), and working in groups (6 of 29; 20.7%). The six topics most mentioned by students as self-reported dislikes about the experience included: taking tests (13 of 29 students mentioned; 44.8%), drawing (7 of 29; 24.1%), confusing / too fast (4 of 29; 13.8%), class discussions (4 of 29; 13.8%), reviewing (4 of 29; 13.8%), and attitude surveys (4 of 29; 13.8%). Cumulatively these three articles aim to contribute to the body of research studying the impact of digital fabrication as an instructional technology for supporting upper elementary and middle school science and mathematics education. This goal is described in greater detail in the "Manuscript Theme" section that begins on the next page. Keywords: STEM, digital fabrication, upper elementary science education, contextual mathematics, modeling-based science instruction, transmedia books, performance assessment, preservice elementary teacher education, science teaching efficacy beliefs

A case study of pedagogy of mathematics support tutors without a background in mathematics education

NASA Astrophysics Data System (ADS)

Walsh, Richard

2017-01-01

This study investigates the pedagogical skills and knowledge of three tertiary-level mathematics support tutors in a large group classroom setting. This is achieved through the use of video analysis and a theoretical framework comprising Rowland's Knowledge Quartet and general pedagogical knowledge. The study reports on the findings in relation to these tutors' provision of mathematics support to first and second year undergraduate engineering students and second year undergraduate science students. It was found that tutors are lacking in various pedagogical skills which are needed for high-quality learning amongst service mathematics students (e.g. engineering/science/technology students), a demographic which have low levels of mathematics upon entering university. Tutors teach their support classes in a very fast didactic way with minimal opportunities for students to ask questions or to attempt problems. It was also found that this teaching method is even more so exaggerated in mandatory departmental mathematics tutorials that students take as part of their mathematics studies at tertiary level. The implications of the findings on mathematics tutor training at tertiary level are also discussed.

Multilingualism in indigenous mathematics education: an epistemic matter

NASA Astrophysics Data System (ADS)

Parra, Aldo; Trinick, Tony

2017-12-01

An investigation into an aspect of indigenous education provides the opportunity to forefront an epistemological discussion about mathematical knowledge. This paper analyses indigenous peoples' educational experiences in Colombia and Aotearoa/New Zealand of mathematics education, focusing on, among other things, sociolinguistic issues such as language planning. In these experiences, researchers, teachers and local communities, working together, elaborated their respective languages to create a corpus of lexicon that has enabled the teaching of Western mathematics. An analysis using decolonial theory is made, showing how this corpus development works to enable the teaching of [Western] mathematics resulted in investigations into culture, language and mathematics that revealed an interplay among knowledge and power. Such analysis raises issues about the epistemology of mathematics and the politics of knowledge, analogous with current discussions on multilingualism in mathematics education and in ethnomathematics. The paper concludes that mathematics educators can explore and take advantage of the sociolinguistic and epistemological issues that arise when an indigenous language is elaborated in a short period of time in comparison to other languages which have been developed incrementally over hundreds of years and thus much more difficult to critique.

Primary Trait Analysis to Assess a Learner-Centered, Upper-Level Mathematics Course

ERIC Educational Resources Information Center

Alsardary, Salar; Pontiggia, Laura; Hamid, Mohammed; Blumberg, Phyllis

2011-01-01

This study presents a primary trait analysis of a learner-centered, discrete mathematics course based on student-to-student instruction. The authors developed a scoring rubric for the primary traits: conceptual knowledge, procedural knowledge, application of understanding, and mathematical communication skills. Eleven students took an exam…

Guide to Mathematics Released Items: Understanding Scoring

ERIC Educational Resources Information Center

Partnership for Assessment of Readiness for College and Careers, 2017

2017-01-01

The Partnership for Assessment of Readiness for College and Careers (PARCC) mathematics items measure critical thinking, mathematical reasoning, and the ability to apply skills and knowledge to real-world problems. Students are asked to solve problems involving the key knowledge and skills for their grade level as identified by the Common Core…

Is There a Role for Executive Functions in the Development of Mathematics Ability?

ERIC Educational Resources Information Center

Blair, Clancy; Knipe, Hilary; Gamson, David

2008-01-01

This article examines the role of working memory, attention shifting, and inhibitory control executive cognitive functions in the development of mathematics knowledge and ability in children. It suggests that an examination of the executive cognitive demand of mathematical thinking can complement procedural and conceptual knowledge-based…

Integrating the Use of Interdisciplinary Learning Activity Task in Creating Students' Mathematical Knowledge

ERIC Educational Resources Information Center

Mahanin, Hajah Umisuzimah Haji; Shahrill, Masitah; Tan, Abby; Mahadi, Mar Aswandi

2017-01-01

This study investigated the use of interdisciplinary learning activity task to construct students' knowledge in Mathematics, specifically on the topic of scale drawing application. The learning activity task involved more than one academic discipline, which is Mathematics, English Language, Art, Geography and integrating the Brunei Darussalam…

Children's Mathematical Knowledge Prior to Starting School

ERIC Educational Resources Information Center

Gervasoni, Ann; Perry, Bob

2013-01-01

The introduction of the "Early Years Learning Framework and the Australian Curriculum-Mathematics" in Australian preschools and primary schools has caused early childhood educators to reconsider what may be appropriate levels of mathematics knowledge to expect from children as they start school. This paper reports on initial data from an…

Field Experience and Prospective Teachers' Mathematical Knowledge and Beliefs

ERIC Educational Resources Information Center

Jacobson, Erik D.

2017-01-01

This study (n = 1,044) used data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between field experience focus (instruction- or exploration-focused), duration, and timing (early or not) and prospective elementary teachers' intertwined knowledge and beliefs about mathematics and mathematics…

Eleventh-Grade High School Students' Accounts of Mathematical Metacognitive Knowledge: Explicitness and Systematicity

ERIC Educational Resources Information Center

van Velzen, Joke H.

2016-01-01

Theoretically, it has been argued that a conscious understanding of metacognitive knowledge requires that this knowledge is explicit and systematic. The purpose of this descriptive study was to obtain a better understanding of explicitness and systematicity in knowledge of the mathematical problem-solving process. Eighteen 11th-grade…

Indigenous teachers' experiences of the implementation of culture-based mathematics activities in Sámi school

NASA Astrophysics Data System (ADS)

Nutti, Ylva Jannok

2013-03-01

The goal of Indigenous education is that it should be approached on the basis of the Indigenous language and culture; this is also the case with Sámi education. The Sámi School Board has stated that all teaching in Sámi schools should be culturally based, despite the fact that Sámi culture-based teaching is not specifically defined. Therefore, teachers themselves must adapt the teaching and as a result, usually no Sámi culture-based mathematics teaching takes place. The aim of this article is to discuss Indigenous teachers' experiences with designing and implementing culture-based mathematics activities in Sámi preschool and primary school. The teachers' work with culture-based mathematics activities took the form of Sámi cultural thematic work with ethnomathematical content, Multicultural school mathematics with Sámi cultural elements, and Sámi intercultural mathematics teaching. Culture-based mathematics activities took place within an action research study in the Swedish part of Sápmi. Sápmi comprises northern Norway, Sweden, and Finland, as well as the Kola Peninsula in Russia. In the action research study, six teachers conducted culture-based mathematics activities in preschool and primary school on the basis of the action research loop "plan-act-observe-reflect." During the study the teachers changed from a problem-focused perspective to a possibility-focused culture-based teaching perspective characterised by a self-empowered Indigenous teacher role, as a result of which they started to act as agents for Indigenous school change. The concept of "decolonisation" was visible in the teachers' narratives. The teachers' newly developed knowledge about the ethnomathematical research field seemed to enhance their work with Indigenous culture-based mathematics teaching.

A Study of the Correlation between STEM Career Knowledge, Mathematics Self-Efficacy, Career Interests, and Career Activities on the Likelihood of Pursuing a STEM Career among Middle School Students

ERIC Educational Resources Information Center

Blotnicky, Karen A.; Franz-Odendaal, Tamara; French, Frederick; Joy, Phillip

2018-01-01

Background: A sample of 1448 students in grades 7 and 9 was drawn from public schools in Atlantic Canada to explore students' knowledge of science and mathematics requirements for science, technology, engineering, and mathematics (STEM) careers. Also explored were their mathematics self-efficacy (MSE), their future career interests, their…

The Dependence on Mathematical Theory in TIMSS, PISA and TIMSS Advanced Test Items and Its Relation to Student Achievement

ERIC Educational Resources Information Center

Hole, Arne; Grønmo, Liv Sissel; Onstad, Torgeir

2018-01-01

Background: This paper discusses a framework for analyzing the dependence on mathematical theory in test items, that is, a framework for discussing to what extent knowledge of mathematical theory is helpful for the student in solving the item. The framework can be applied to any test in which some knowledge of mathematical theory may be useful,…

Identifying Mathematics Content and Integrating It into Science Instruction

ERIC Educational Resources Information Center

Schwols, Amitra; Miller, Kirsten Brush

2012-01-01

Science teachers know that the mathematics concepts taught in the Common Core are critical for students' understanding of science. But what can a teacher do when his/her students lack the necessary mathematics skills to master science content? There may be other reasons besides students not paying attention in their math courses. Maybe the…

Mathematical Modelling Research in Turkey: A Content Analysis Study

ERIC Educational Resources Information Center

Çelik, H. Coskun

2017-01-01

The aim of the present study was to examine the mathematical modelling studies done between 2004 and 2015 in Turkey and to reveal their tendencies. Forty-nine studies were selected using purposeful sampling based on the term, "mathematical modelling" with Higher Education Academic Search Engine. They were analyzed with content analysis.…

A Comparison between Mathematics Textbook Content and a Statewide Mathematics Proficiency Test.

ERIC Educational Resources Information Center

Chandler, Donald G.; Brosnan, Patricia A.

1995-01-01

Percentages of mathematics content for 7 text series, grades 1-8, were compared with percentages on the Ohio Ninth Grade Proficiency Test. Ratios of text:test percentages were arithmetic (63:30), measurement (10:25), geometry (12:15), data analysis (11:15), and algebra (4:15). Implications are discussed. (MSD)

Didactic Transposition in Mathematics Textbooks.

ERIC Educational Resources Information Center

Kang, Wan; Kilpatrick, Jeremy

1992-01-01

Didactic transposition theory asserts that bodies of knowledge are designed not to be taught but to be used. Discusses didactic transposition, the transposition of knowledge regarded as a tool to be used to knowledge as something to be learned in mathematics textbooks. (14 references) (MDH)

The COPD Knowledge Base: enabling data analysis and computational simulation in translational COPD research.

PubMed

Cano, Isaac; Tényi, Ákos; Schueller, Christine; Wolff, Martin; Huertas Migueláñez, M Mercedes; Gomez-Cabrero, David; Antczak, Philipp; Roca, Josep; Cascante, Marta; Falciani, Francesco; Maier, Dieter

2014-11-28

Previously we generated a chronic obstructive pulmonary disease (COPD) specific knowledge base (http://www.copdknowledgebase.eu) from clinical and experimental data, text-mining results and public databases. This knowledge base allowed the retrieval of specific molecular networks together with integrated clinical and experimental data. The COPDKB has now been extended to integrate over 40 public data sources on functional interaction (e.g. signal transduction, transcriptional regulation, protein-protein interaction, gene-disease association). In addition we integrated COPD-specific expression and co-morbidity networks connecting over 6 000 genes/proteins with physiological parameters and disease states. Three mathematical models describing different aspects of systemic effects of COPD were connected to clinical and experimental data. We have completely redesigned the technical architecture of the user interface and now provide html and web browser-based access and form-based searches. A network search enables the use of interconnecting information and the generation of disease-specific sub-networks from general knowledge. Integration with the Synergy-COPD Simulation Environment enables multi-scale integrated simulation of individual computational models while integration with a Clinical Decision Support System allows delivery into clinical practice. The COPD Knowledge Base is the only publicly available knowledge resource dedicated to COPD and combining genetic information with molecular, physiological and clinical data as well as mathematical modelling. Its integrated analysis functions provide overviews about clinical trends and connections while its semantically mapped content enables complex analysis approaches. We plan to further extend the COPDKB by offering it as a repository to publish and semantically integrate data from relevant clinical trials. The COPDKB is freely available after registration at http://www.copdknowledgebase.eu.

NASA/DoD Aerospace Knowledge Diffusion Research Project. Report Number 19. The U. S. Government Technical Report and the Transfer of Federally Funded Aerospace R&D: An Analysis of Five Studies

DTIC Science & Technology

1994-01-01

defined etymologically , according to report content and method (U.S. Department of Defense, 1964); behaviorally, according to the influence on the reader...SCIENCES 2 ASTRONAUTICS 7 MATERIALS & CHEMISTRY 3 ENGINEERING 8 PHYSICS 4 GEOSCIENCES 9 SPACE SCIENCES 5 LIFE SCIENCES 10 OTHER (specify) 63. IsANYof...YOUR work? (Circle ONLY one number) I AERONAUTICS 6 MATHEMATICAL & COMPUTER SCIENCES 2 ASTRONAUTICS 7 MATERIALS & CHEMISTRY 3 ENGINEERING 8 PHYSICS 4

Pre-service teachers' experiences teaching secondary mathematics in English-medium schools in Tanzania

NASA Astrophysics Data System (ADS)

Kasmer, Lisa

2013-09-01

In order to promote mathematical understanding among English Language Learners (ELLs), it is necessary to modify instructional strategies to effectively communicate mathematical content. This paper discusses the instructional strategies used by four pre-service teachers to teach mathematics to secondary students in English-medium schools in Arusha, Tanzania as a result of the tensions they faced and reflections on their teaching. Strategies such as code switching, attending to sentence structure, non-linguistic representations, and placing the content within a familiar context proved to be beneficial strategies for conveying mathematical ideas.

Science and Mathematics Teacher Candidates' Environmental Knowledge, Awareness, Behavior and Attitudes

ERIC Educational Resources Information Center

Yumusak, Ahmet; Sargin, Seyid Ahmet; Baltaci, Furkan; Kelani, Raphael R.

2016-01-01

The purpose of this study was to measure science and mathematics teacher candidates' environmental knowledge level, awareness, behavior and environmental attitudes. Four instruments comprising Environmental Sensitivity Scale, environmental Behavior Scale, Environmental Attitudes Scale and Environmental Knowledge Test were administered to a total…

Mathematics and Structural Learning. Final Report.

ERIC Educational Resources Information Center

Scandura, Joseph M.

This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

A Case Study on the Impact of Teacher Mathematical Knowledge on Pedagogical Practices

ERIC Educational Resources Information Center

Hughes, Sally

2016-01-01

This study explores the implications for mathematical knowledge and pedagogical practices of primary teachers in Papua New Guinea making a shift from a transmission approach to a connectionist approach to teaching mathematics. The research participants were engaged in a professional development program designed to support the teaching and learning…

Investigating Mathematics Teachers Candidates' Knowledge about Problem Solving Strategies through Problem Posing

ERIC Educational Resources Information Center

Ünlü, Melihan

2017-01-01

The aim of the study was to determine mathematics teacher candidates' knowledge about problem solving strategies through problem posing. This qualitative research was conducted with 95 mathematics teacher candidates studying at education faculty of a public university during the first term of the 2015-2016 academic year in Turkey. Problem Posing…

Investigating First Year Elementary Mathematics Teacher Education Students' Knowledge of Prism

ERIC Educational Resources Information Center

Bozkurt, Ali; Koc, Yusuf

2012-01-01

The purpose of this study was to investigate first year elementary mathematics teacher education students' knowledge of prism. For this goal, the participants were asked to define the geometric concept of prism. The participants were 158 first year elementary mathematics teacher education students from a public university in Southern Turkey. The…

The Development of Mathematical Knowledge for Teaching for Quantitative Reasoning Using Video-Based Instruction

ERIC Educational Resources Information Center

Walters, Charles David

2017-01-01

Quantitative reasoning (P. W. Thompson, 1990, 1994) is a powerful mathematical tool that enables students to engage in rich problem solving across the curriculum. One way to support students' quantitative reasoning is to develop prospective secondary teachers' (PSTs) mathematical knowledge for teaching (MKT; Ball, Thames, & Phelps, 2008)…

Why Use Multiple Representations in the Mathematics Classroom? Views of English and German Preservice Teachers

ERIC Educational Resources Information Center

Dreher, Anika; Kuntze, Sebastian; Lerman, Stephen

2016-01-01

Dealing with multiple representations and their connections plays a key role for learners to build up conceptual knowledge in the mathematics classroom. Hence, professional knowledge and views of mathematics teachers regarding the use of multiple representations certainly merit attention. In particular, investigating such views of preservice…

Investigating Lebanese Grade Seven Biology Teachers Mathematical Knowledge and Skills: A Case Study

ERIC Educational Resources Information Center

Raad, Nawal Abou; Chatila, Hanadi

2016-01-01

This paper investigates Lebanese grade 7 biology teachers' mathematical knowledge and skills, by exploring how they explain a visual representation in an activity depending on the mathematical concept "Function". Twenty Lebanese in-service biology teachers participated in the study, and were interviewed about their explanation for the…