Sample records for mathematical knowledge increases

  1. 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…

  2. 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…

  3. 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…

  4. 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.

  5. 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.

  6. 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

  7. Noticing numeracy now! Examining changes in preservice teachers' noticing, knowledge, and attitudes

    NASA Astrophysics Data System (ADS)

    Fisher, Molly H.; Thomas, Jonathan; Schack, Edna O.; Jong, Cindy; Tassell, Janet

    2018-06-01

    This study examined the impact of an intervention, focused on professional noticing of children's conceptual development in whole number and arithmetic reasoning, on preservice elementary teachers' (PSETs') professional noticing skills, attitudes toward mathematics, and mathematical knowledge for teaching mathematics. A video-based professional noticing module, situated in the pedagogies of practice framework, was used with 224 PSETs from five universities. Comparison data was also collected with similar groups not participating in the instructional module. Through pre- and post-assessments, findings indicated that PSETs can develop sound professional noticing skills as a result of participation in a video-based module. The impact on attitudes toward mathematics was less convincing as significant changes were revealed in intervention as well as comparison groups. We hypothesized the potential for professional noticing of children's mathematical thinking to serve as a mechanism for increasing the capabilities of PSETs to negotiate the complexities of mathematics teaching and learning; however, mathematics knowledge for teaching showed no significant increase for either group.

  8. 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.

  9. 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…

  10. Developing Mathematical Thinking: Changing Teachers' Knowledge and Instruction

    ERIC Educational Resources Information Center

    Brendefur, Jonathan L.; Thiede, Keith; Strother, Sam; Bunning, Kim; Peck, Duane

    2013-01-01

    In the present research, we evaluated the effectiveness of a multi-year professional development program in mathematics for elementary teachers. Each year the program focused on a different domain of mathematics. We found the program increased teachers' knowledge of (a) number and operations, (b) measurement and geometry, and (c) probability and…

  11. Hands-On Mathematics: Two Cases from Ancient Chinese Mathematics

    ERIC Educational Resources Information Center

    Wang, Youjun

    2009-01-01

    In modern mathematical teaching, it has become increasingly emphasized that mathematical knowledge should be taught by problem-solving, hands-on activities, and interactive learning experiences. Comparing the ideas of modern mathematical education with the development of ancient Chinese mathematics, we find that the history of mathematics in…

  12. Middle School Students' Mathematics Knowledge Retention: Online or Face-To-Face Environments

    ERIC Educational Resources Information Center

    Edwards, Clayton M.; Rule, Audrey C.; Boody, Robert M.

    2017-01-01

    Educators seek to develop students' mathematical knowledge retention to increase student efficacy in follow-on classwork, improvement of test scores, attainment of standards, and preparation for careers. Interactive visuals, feedback during problem solving, and incorporation of higher-order thinking skills are known to increase retention, but a…

  13. The Development of Logico-Mathematical Knowledge in a Block-Building Activity at Ages 1-4

    ERIC Educational Resources Information Center

    Kamii, Constance; Miyakawa, Yoko; Kato, Yasuhiko

    2004-01-01

    To study the developmental interrelationships among various aspects of logico-mathematical knowledge, 80 one- to 4-year-olds were individually asked to build "something tall" with 20 blocks. Percentages of new and significant behaviors increased with age and were analyzed in terms of the development of logico-mathematical relationships. It was…

  14. 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.

  15. 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

  16. What is the Role of Mathematics Education in the Computer Age?

    ERIC Educational Resources Information Center

    Popp, Jerome A.

    1986-01-01

    Proposes that the role of mathematics education be re-examined in terms of an increased emphasis on mathematical knowledge rather than attainment of calculational speed. Offers perspectives on the reform movement in mathematics education and advocates the teaching of the history, logic, and method of mathematical thinking. (ML)

  17. Secondary-Level Student Teachers' Conceptions of Mathematical Proof

    ERIC Educational Resources Information Center

    Varghese, Thomas

    2009-01-01

    Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers' knowledge and beliefs play in shaping students' understanding of mathematics, their confidence in and outlook on mathematics…

  18. 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…

  19. Professional Development for Mathematics Teachers: Using Task Design and Analysis

    ERIC Educational Resources Information Center

    Lee, Hea-Jin; Özgün-Koca, S. Asli

    2016-01-01

    This study is based on a Task Design and Analysis activity from a year-long professional development program. The activity was designed to increase teacher growth in several areas, including knowledge of mathematics, understanding of students' cognitive activity, knowledge of good questions, and ability to develop and improve high quality tasks.…

  20. 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.

  1. 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…

  2. 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…

  3. 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

  4. 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.

  5. Learning to teach upper primary school algebra: changes to teachers' mathematical knowledge for teaching functional thinking

    NASA Astrophysics Data System (ADS)

    Wilkie, Karina J.

    2016-06-01

    A key aspect of learning algebra in the middle years of schooling is exploring the functional relationship between two variables: noticing and generalising the relationship, and expressing it mathematically. This article describes research on the professional learning of upper primary school teachers for developing their students' functional thinking through pattern generalisation. This aspect of algebra learning has been explicitly brought to the attention of upper primary teachers in the recently introduced Australian curriculum. Ten practising teachers participated over 1 year in a design-based research project involving a sequence of geometric pattern generalisation lessons with their classes. Initial and final survey responses and teachers' interactions in regular meetings and lessons were analysed from cognitive and situated perspectives on professional learning, using a theoretical model for the different types of knowledge needed for teaching mathematics. The teachers demonstrated an increase in certain aspects of their mathematical knowledge for teaching algebra as well as some residual issues. Implications for the professional learning of practising and pre-service teachers to develop their mathematics knowledge for teaching functional thinking, and challenges with operationalising knowledge categories for field-based research are presented.

  6. Assessing Mathematical Problem Solving Using Comparative Judgement

    ERIC Educational Resources Information Center

    Jones, Ian; Swan, Malcolm; Pollitt, Alastair

    2015-01-01

    There is an increasing demand from employers and universities for school leavers to be able to apply their mathematical knowledge to problem solving in varied and unfamiliar contexts. These aspects are however neglected in most examinations of mathematics and, consequentially, in classroom teaching. One barrier to the inclusion of mathematical…

  7. 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,…

  8. Understanding Mathematics and Science Matters. Studies in Mathematical Thinking and Learning Series

    ERIC Educational Resources Information Center

    Romberg, Thomas A., Ed.; Carpenter, Thomas P., Ed.; Dremock, Fae, Ed.

    2005-01-01

    The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics…

  9. Promoting Social Change through Writing: A Quantitative Study of Research-Based Best Practices in Eighth-Grade Mathematics

    ERIC Educational Resources Information Center

    Bettencourt, Connie Lynn

    2009-01-01

    Studies report that U.S. students rank among the lowest in the area of mathematical knowledge of all industrialized countries. Schools in the United States are producing graduates ill-prepared to be successful at jobs which require mathematical competency. To increase mathematical understanding, this study examined the inclusion of writing in…

  10. Comparing Mathematics Achievement Scores: Face-To-Face versus Online Delivery

    ERIC Educational Resources Information Center

    Lenderman, Ami

    2017-01-01

    The purpose of this quantitative study was to explore the relationship between the use of online courseware at Georgia Virtual School as an instructional delivery method and student achievement of 9th and 10th grade mathematics students as measured by Mathematics I and Mathematics II End of Course Test (EOCT) scores. The knowledge of an increase,…

  11. Iterating between Lessons on Concepts and Procedures Can Improve Mathematics Knowledge

    ERIC Educational Resources Information Center

    Rittle-Johnson, Bethany; Koedinger, Kenneth

    2009-01-01

    Background: Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. Aims: The purpose of the current study was to evaluate the…

  12. 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…

  13. Teaching Mathematics That Addresses Learners' Multiple Intelligences

    ERIC Educational Resources Information Center

    Gouws, E.; Dicker, A-M.

    2011-01-01

    To meet the demands of our highly technological and globally competitive society, it is becoming increasingly important for all learners in South Africa to obtain skills and knowledge in mathematics. However, South Africa performed the worst of all the countries who participated in the Trends in International Mathematics and Science Study (TIMMS).…

  14. Perceptions of Challenging Tasks and Achievement by New Zealand Students

    ERIC Educational Resources Information Center

    Linsell, Chris; Holmes, Marilyn; Sullivan, Peter

    2016-01-01

    This paper examines the learning by students who were participating in a project designed to promote persistence while working on mathematical tasks. We examined their learning of mathematics concepts and learning about the processes of engaging in mathematical tasks. There were substantial increases in students' knowledge of angles and also…

  15. Evaluating the Effects of Mastery Learning in Postsecondary Developmental Mathematics

    ERIC Educational Resources Information Center

    Bradley, Kirk

    2016-01-01

    The purpose of this study was to determine which academic and affective student factors were significant to student success in a mastery learning program in developmental mathematics and to determine if the mastery learning program led to increased mathematical knowledge retention and success in the subsequent math course. The first phase of the…

  16. 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…

  17. An appraisal of an online tutorial system for the teaching and learning of engineering physics in conjunction with contextual physics and mathematics, and relevant mathematics

    NASA Astrophysics Data System (ADS)

    Bhathal, Ragbir

    2016-09-01

    The number of students entering engineering schools in Australian universities has increased tremendously over the last few years because of the Australian Federal Government's policy of increasing the participation rates of Higher School Certificate students and students from low social economic status backgrounds in the tertiary sector. They now come with a diverse background of skills, motivations and prior knowledge. It is imperative that new methods of teaching and learning be developed. This paper describes an online tutorial system used in conjunction with contextual physics and mathematics, and the revision of the relevant mathematical knowledge at the appropriate time before a new topic is introduced in the teaching and learning of engineering physics. Taken as a whole, this study shows that students not only improved their final examination results but there was also an increase in the retention rate of first-year engineering students which has financial implications for the university.

  18. 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)…

  19. 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…

  20. Examining Elementary Pre-Service Teachers' Capacity to Use Children's Mathematical Understanding to Select and Pose Mathematical Tasks

    ERIC Educational Resources Information Center

    Gichobi, Mary N.

    2013-01-01

    The need to design teacher preparation programs to ensure that pre-service teachers (PSTs) are prepared and equipped with knowledge, skills and practices to increase the chances that they will become effective novice mathematics teachers is of prime importance. Teacher educators are facing lingering challenges, since teacher education is…

  1. Overcoming Challenges of Being an In-Field Mathematics Teacher in Indigenous Secondary School Classrooms

    ERIC Educational Resources Information Center

    Sandhu, Satwant; Kidman, Gillian; Cooper, Tom

    2013-01-01

    Queensland rural and remote schools have difficulty in attracting experienced, in-field mathematics teachers. Thus, when such teachers arrive, much is expected of them to increase the mathematics knowledge of students. This paper looks at one such teacher who, against the high expectations placed upon him as an in-field teacher, experienced…

  2. 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,…

  3. 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…

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

    NASA Astrophysics Data System (ADS)

    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.

  5. Mathematics teaching experiences of elementary preservice teachers with high and low mathematics anxiety during student teaching: A multiple case study

    NASA Astrophysics Data System (ADS)

    Nisbet, Leslie Deanna

    This study investigated the teaching experiences of six elementary preservice teachers (EPTs), three with high mathematics anxiety and three with low mathematics anxiety, during their student teaching semester. The EPTs were selected from an initial pool of 121 EPTs who took the Abbreviated Mathematics Anxiety Scale. The cases were compared in a cross case analysis to highlight mathematics teaching experiences among EPTs. Data sources included EPT and researcher journal entries, interview transcripts, pre-lesson surveys, field notes, lesson plans, and artifacts of observed lessons. Data were coded using Shulman's content knowledge, Graeber's mathematics pedagogical content knowledge, and mathematics anxiety characteristics. Findings revealed both similarities and differences across EPTs as related to four major categories: (a) planning and resources used, (b) role of the cooperating teacher, (c) content knowledge, and (d) pedagogical content knowledge. All EPTs used mostly direct instruction and relied on the course textbook and their respective cooperating teacher as their primary resources for planning. Additionally, across participants, the cooperating teacher influenced EPTs' perceptions of students and teaching. Also, EPTs with high mathematics anxiety were weaker with respect to content knowledge and pedagogical content knowledge. Findings suggest a need to re-design methods courses to address improving the pedagogical content knowledge of EPTs with mathematics anxiety. Findings also suggest a need to develop content specific mathematics courses for EPTs to improve their content knowledge. Future studies could include a longitudinal study to follow highly anxious EPTs who take content specific elementary mathematics courses to observe their content knowledge and mathematics anxiety.

  6. 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…

  7. Mathematics University Teachers' Perception of Pedagogical Content Knowledge (PCK)

    ERIC Educational Resources Information Center

    Khakbaz, Azimehsadat

    2016-01-01

    Teaching mathematics in university levels is one of the most important fields of research in the area of mathematics education. Nevertheless, there is little information about teaching knowledge of mathematics university teachers. Pedagogical content knowledge (PCK) provides a suitable framework to study knowledge of teachers. The purpose of this…

  8. A "Knowledge Quartet" Used to Identify a Second-Year Pre-Service Teacher's Primary Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Livy, Sharyn

    2010-01-01

    This paper draws on observation of a primary mathematics lesson prepared and taught by a second-year pre-service teacher who lacked mathematical content knowledge. A "knowledge quartet" (Rowland, Turner, Thwaites, & Huckstep, 2009) was used to investigate when and how a pre-service teacher drew on their knowledge of mathematics during primary…

  9. Toward Improving the Mathematics Preparation of Elementary Preservice Teachers

    ERIC Educational Resources Information Center

    Cardetti, Fabiana; Truxaw, Mary P.

    2014-01-01

    Research suggests the importance of mathematics knowledge for teaching (MKT) for enabling elementary school teachers to effectively teach mathematics. MKT involves both mathematical content knowledge (M-CK) and mathematical pedagogical content knowledge (M-PCK). However, there is no consensus on how best to prepare elementary preservice teachers…

  10. Pre-Service Teachers' Mathematics Content Knowledge: Implications for How Mathematics Is Taught in Higher Education

    ERIC Educational Resources Information Center

    Lowrie, Tom; Jorgensen, Robyn

    2016-01-01

    This investigation explored pre-service teachers' mathematics content knowledge (MCK) and beliefs associated with mathematics education practices. An Exploratory Factor Analysis, conducted on a beliefs and attitudes questionnaire, produced three common attitude factors associated with (1) inquiry-based teaching; (2) how mathematics knowledge is…

  11. Definitions of Mathematical Knowledge for Teaching: Using These Constructs in Research on Secondary and College Mathematics Teachers

    ERIC Educational Resources Information Center

    Speer, Natasha M.; King, Karen D.; Howell, Heather

    2015-01-01

    The construct "mathematical knowledge for teaching" (MKT) has received considerable attention in the mathematics education community in recent years. The development and refinement of the MKT construct, including the components of common content knowledge (CCK) and specialized content knowledge (SCK), came from research into elementary…

  12. 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…

  13. 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.

  14. Going beyond the lesson: Self-generating new factual knowledge in the classroom

    PubMed Central

    Esposito, Alena G.; Bauer, Patricia J.

    2016-01-01

    For children to build a knowledge base, they must integrate and extend knowledge acquired across separate episodes of new learning. Children’s performance was assessed in a task requiring them to self-generate new factual knowledge from the integration of novel facts presented through separate lessons in the classroom. Whether self-generation performance predicted academic outcomes in reading comprehension and mathematics was also examined. The 278 participating children were in grades K-3 (mean age 7.7 years; range 5.5–10.3 years). Children self-generated new factual knowledge through integration in the classroom; age-related increases were observed. Self-generation performance predicted both reading comprehension and mathematics academic outcomes, even when controlling for caregiver education. PMID:27728784

  15. 14 CFR § 1260.12 - Choice of award instrument.

    Code of Federal Regulations, 2014 CFR

    2014-01-01

    ...) Capturing student interest and/or improving student performance in science, mathematics, technology, or related fields; (ii) Enhancing the skill, knowledge, or ability of teachers or faculty members in science... programs or research to increase participation and/or to enhance performance in science, mathematics, or...

  16. Primary Mathematics Trainee Teacher Confidence and Its Relationship to Mathematical Knowledge

    ERIC Educational Resources Information Center

    Norton, Stephen J.

    2017-01-01

    The purpose of this paper is to examine trainee primary school teachers' confidence in their mathematical content knowledge (MCK) and confidence to teach specific primary mathematics concepts (mathematics pedagogical content knowledge --MPCK) which was correlated to their actual MCK on specific tasks. For this correlational study survey and test…

  17. The Hidden Strand of Mathematical Proficiency: Defining and Assessing for Productive Disposition in Elementary School Teachers' Mathematical Content Knowledge

    ERIC Educational Resources Information Center

    Siegfried, John Zig Michael

    2012-01-01

    Teachers' mathematical content knowledge is one of the most important constructs considered by researchers studying elementary mathematics education (Fennema & Franke, 1992). One component of mathematical content knowledge that is complicated, ill-defined, and oft-ignored is "productive disposition," defined as the…

  18. 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…

  19. The Challenge of Learning Physics Before Mathematics: A Case Study of Curriculum Change in Taiwan

    NASA Astrophysics Data System (ADS)

    Chiu, Mei-Shiu

    2016-12-01

    The aim of this study was to identify challenges in implementing a physics-before- 10 mathematics curriculum. Obviously, students need to learn necessary mathematics skills in order to develop advanced physics knowledge. In the 2010 high school curriculum in Taiwan, however, grade 11 science students study two-dimensional motion in physics without prior learning experiences of trigonometry in mathematics. The perspectives of three curriculum developers, 22 mathematics and physics teachers, two principals, and 45 science students were obtained by interview. The results of qualitative data analysis revealed six challenges and suggested likely solutions. The national level includes political and social challenges, resolved by respecting teachers as professionals; the teacher level includes knowledge and teaching challenges, resolved by increasing teacher trans-literal capacities; and the student level includes learning and justice challenges, resolved by focusing on students' diverse developments in cross-domain learning.

  20. 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.

  1. 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…

  2. Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties

    ERIC Educational Resources Information Center

    Hassinger-Das, Brenna; Jordan, Nancy C.; Dyson, Nancy

    2015-01-01

    The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were…

  3. Past and Future of Astronomy and SETI Cast in Maths

    NASA Astrophysics Data System (ADS)

    Maccone, C.

    Assume that the history of Astronomy and SETI is the leading proof of the evolution of human knowledge on Earth over the last 3000 years. Then, human knowledge has increased a lot, although not at a uniform pace. A mathematical description of how much human knowledge has increased, however, is difficult to achieve. In this paper, we cast a mathematical model of the evolution of human knowledge over the last three thousand years that seems to reflect reasonably well both what is known from the past and might be extrapolated into the future. Our model is based on two seminal books by Sagan and Finney and Jones. Our model is based on the use of two cubic curves, representing the evolution of Astronomy and of SETI, respectively. We conclude by extrapolating these curves into the future and reach the conclusion that the "Star Trek" age of humankind might possibly begin by the end of this century.

  4. 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…

  5. The challenges facing initial teacher education: Irish prospective elementary teachers' mathematics subject matter knowledge

    NASA Astrophysics Data System (ADS)

    Hourigan, Mairéad; O'Donoghue, John

    2013-01-01

    Given the acknowledged relationship between teachers' knowledge, their teaching and pupil learning, teachers' mathematics subject matter knowledge (MSMK) has received increased attention internationally. As children's early mathematics experiences have been recognized as a critical stage, elementary teachers' MSMK has become a focal point among researchers and policy makers alike. International research findings have uncovered that in many cases, there is a mismatch between what is perceived to be an appropriate MSMK for teaching elementary mathematics and that demonstrated by many qualified and prospective elementary teachers. Following repeated incidences of weak MSMK during interactions with prospective elementary teachers in one Irish College of Education (provider of initial teacher education programme for elementary teachers), this study sought to examine and address the issue purposefully through two cycles of action research. This article focuses on the data collected prospective teachers' MSMK in the initial stage (reconnaissance) of these cycles, i.e. pre-test findings. While considerable differences were evident among the pre-test population, the findings suggest that prior to the intervention stage many participating prospective teachers; regardless of previous mathematics achievements or the level of mathematics study; demonstrate weaknesses and gaps in their 'common' MSMK. Particular difficulties were evident in relation to pre-test items requiring knowledge of rational numbers, conceptual understanding or problem solving. These findings highlight the inadequacy of previous mathematics achievements and indeed minimum entry requirements as predictors of MSMK for teaching. As well as its contribution at a local and national level, the findings provide an Irish perspective on this international issue.

  6. 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"…

  7. 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…

  8. 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.…

  9. Impact of Summer Recess on Mathematics Learning Retention

    ERIC Educational Resources Information Center

    Hornack, David

    2016-01-01

    School administrators across the nation are actively searching for solutions to increase student achievement due in part to the significant amount of knowledge that is lost annually each summer. Mathematical computation skills are especially at-risk. This quantitative research study was designed to investigate the impact of summer recess also…

  10. Pathways to Arithmetic Fact Retrieval and Percentage Calculation in Adolescents

    ERIC Educational Resources Information Center

    Träff, Ulf; Skagerlund, Kenny; Olsson, Linda; Östergren, Rickard

    2017-01-01

    Background: Developing sufficient mathematical skills is a prerequisite to function adequately in society today. Given this, an important task is to increase our understanding regarding the cognitive mechanisms underlying young people's acquisition of early number skills and formal mathematical knowledge. Aims: The purpose was to examine whether…

  11. 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…

  12. 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…

  13. 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…

  14. 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…

  15. Connecting mathematics learning through spatial reasoning

    NASA Astrophysics Data System (ADS)

    Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

    2018-03-01

    Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

  16. Does Knowing More Advanced Mathematics Ensure Effectiveness of Working towards Demonstrating Specialised Mathematical Content Knowledge of Second-Year Pre-Service Teachers?

    ERIC Educational Resources Information Center

    Livy, Sharyn

    2012-01-01

    The theoretical understanding that underpins a teacher's foundation knowledge draws on their common content knowledge (CCK) and influences their mathematics' teaching (Rowland, Turner, Thwaites, & Huckstep, 2009). Teachers who have specialised content knowledge (SCK) demonstrate a unique kind of content knowledge which is more than knowing the…

  17. 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…

  18. 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).

  19. 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…

  20. The Science of Living Spaces: Women in the Environment of the 21st Century. An Evaluation and Guide Book.

    ERIC Educational Resources Information Center

    Greenlee, Shelia; Lambert, Lynn

    The Science of Living Spaces program provides girls aged 11-13 increased access to and awareness of the possibilities inherent in pursuing careers in science, engineering, and mathematics. Objectives of the program include expanding career knowledge and opportunities; increasing participants' knowledge of and exposure to science, engineering, and…

  1. Two-Year Community: Increasing Science Knowledge among High-Risk Student Populations through a Community College Honors/Service-Learning Program

    ERIC Educational Resources Information Center

    Ellerton, Sharon; Carmona, Naydu; Tsimounis, Areti

    2016-01-01

    There is an urgent need to increase K-12 science knowledge and STEM (science, technology, engineering, and mathematics) preparedness for college. State and national data suggest a strong correlation between student performance in STEM subjects and student socioeconomic status, race, and ethnicity. Queensborough Community College (QCC) is situated…

  2. 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.

  3. Connecting Adolescent Girls of Color and Math/Science Interventions.

    ERIC Educational Resources Information Center

    Murphy, Diane S.; Sullivan, Kathleen

    This paper describes a study of Project SPLASH!, a program for minority adolescent girls with high potential in mathematics and science. This paper aims to contribute to the knowledge base on characteristics of program interventions which may increase the representation of women and minorities in the fields of mathematics and science. Findings on…

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. 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…

  11. 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…

  12. 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.…

  13. 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…

  14. 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…

  15. Improving of prospective elementary teachers' reasoning: Learning geometry through mathematical investigation

    NASA Astrophysics Data System (ADS)

    Sumarna, Nana; Sentryo, Izlan

    2017-08-01

    This research applies mathematical investigation approach in teaching geometry to improve mathematical reasoning abilities of prospective elementary teachers. Mathematical investigation in this study involved non-routine tasks through a mathematical investigation process, namely through a series of activities as an attribute of mathematical investigation. Developing the ability of mathematical reasoning of research subjects obtained through capability of research subjects in the analysis, generalization, synthesis, justify, and resolve non-routine, which is operationally constructed as an indicator of research and is used as a criterion for measuring the ability of mathematical reasoning. Research design using Quasi-Experimental design. Based on this type, the researchers apply a pre-and posttest design, which is divided into two study groups: control group and the treatment group. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The conclusion of this study stated that (1) Investigation of mathematics as an approach to learning is able to give a positive response to the increasing ability of mathematical reasoning, and (2) There is no interaction effect of the factors of learning and prior knowledge of mathematics to the increased ability of mathematical reasoning.

  16. Iterating between lessons on concepts and procedures can improve mathematics knowledge.

    PubMed

    Rittle-Johnson, Bethany; Koedinger, Kenneth

    2009-09-01

    Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. The purpose of the current study was to evaluate the instructional benefits of an iterative lesson sequence compared to a concepts-before-procedures sequence for students learning decimal place-value concepts and arithmetic procedures. In two classroom experiments, sixth-grade students from two schools participated (N=77 and 26). Students completed six decimal lessons on an intelligent-tutoring systems. In the iterative condition, lessons cycled between concept and procedure lessons. In the concepts-first condition, all concept lessons were presented before introducing the procedure lessons. In both experiments, students in the iterative condition gained more knowledge of arithmetic procedures, including ability to transfer the procedures to problems with novel features. Knowledge of concepts was fairly comparable across conditions. Finally, pre-test knowledge of one type predicted gains in knowledge of the other type across experiments. An iterative sequencing of lessons seems to facilitate learning and transfer, particularly of mathematical procedures. The findings support an iterative perspective for the development of knowledge of concepts and procedures.

  17. 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…

  18. Mathematics Teacher TPACK Standards and Development Model

    ERIC Educational Resources Information Center

    Niess, Margaret L.; Ronau, Robert N.; Shafer, Kathryn G.; Driskell, Shannon O.; Harper, Suzanne R.; Johnston, Christopher; Browning, Christine; Ozgun-Koca, S. Asli; Kersaint, Gladis

    2009-01-01

    What knowledge is needed to teach mathematics with digital technologies? The overarching construct, called technology, pedagogy, and content knowledge (TPACK), has been proposed as the interconnection and intersection of technology, pedagogy, and content knowledge. Mathematics Teacher TPACK Standards offer guidelines for thinking about this…

  19. 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…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. 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.

  5. The Resilience of Overgeneralization of Knowledge about Data Representations.

    ERIC Educational Resources Information Center

    Baker, Ryan Shaun; Corbett, Albert T.; Koedinger, Kenneth R.

    Data analysis has become a topic of increasing emphasis within middle school mathematics in the last few years, especially in the recent recommendations by the National Council of Teachers of Mathematics (NCTM 2000). In order to better inform efforts to expand data analysis's role in middle school curricula, we have begun the development of a…

  6. Characterizing the Use of Mathematical Knowledge in Boundary-Crossing Situations at Work

    ERIC Educational Resources Information Center

    Kent, Phillip; Noss, Richard; Guile, David; Hoyles, Celia; Bakker, Arthur

    2007-01-01

    The first aim of this article is to present a characterization of the techno-mathematical literacies needed for effective practice in modern, technology-rich workplaces that are both highly automated and increasingly focused on flexible response to customer needs. The second aim is to introduce an epistemological dimension to activity theory,…

  7. First-Year Seminar Intervention: Enhancing First-Year Mathematics Performance at the University of Johannesburg

    ERIC Educational Resources Information Center

    Jacobs, Melanie; Pretorius, Estherna

    2016-01-01

    South Africa has opened up access to higher education over the past 20 years. The massive increase in enrolments (with almost 70% first-generation students) substantially affects progress and graduation rates in Science programmes in higher education. First-year students in Science realise that university mathematics requires knowledge and skills…

  8. Fostering Instructor Knowledge of Student Thinking Using the Flipped Classroom

    ERIC Educational Resources Information Center

    Strayer, Jeremy F.; Hart, James B.; Bleiler, Sarah K.

    2015-01-01

    In this article, we share a model of flipped instruction that allowed us to gain a window into our students' mathematical thinking. We depict how that increased awareness of student thinking shaped our mathematics instruction in productive ways. Drawing on our experiences with students in our own classrooms, we show how flipped instruction can be…

  9. 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…

  10. Exploring Connections between Content Knowledge, Pedagogical Content Knowledge, and the Opportunities to Learn Mathematics: Findings from the TEDS-M Dataset

    ERIC Educational Resources Information Center

    Murray, Eileen; Durkin, Kelley; Chao, Theodore; Star, Jon R.; Vig, Rozy

    2018-01-01

    Past work on mathematics teachers' content knowledge (CK) and pedagogical content knowledge (PCK) has resulted in mixed findings about the strength of the relationship between and development of these constructs. The current study uses data from the Teacher Education and Development Study in Mathematics (TEDS-M) to examine the relationship between…

  11. 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…

  12. 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…

  13. 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.

  14. Determining Quality Teachers: Mathematical Content Knowledge, Perceptions of Teaching Self-Efficacy, and Attitudes toward Mathematics among a Teach for America Cohort

    ERIC Educational Resources Information Center

    Evans, Brian R.

    2010-01-01

    The purpose of this study was to understand the relationships between mathematical content knowledge, perceptions of teaching self-efficacy, and attitudes toward mathematics in one cohort of Teach for America teachers who took the New York State Content Special Test in mathematics at the start of their program, and a mathematics attitude…

  15. 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…

  16. Preservice Elementary Teachers' Mathematics Content Knowledge and Teacher Efficacy

    ERIC Educational Resources Information Center

    Newton, Kristie Jones; Leonard, Jacqueline; Evans, Brian R.; Eastburn, Julie A.

    2012-01-01

    The purpose of this study was to examine the relationship between mathematics content knowledge and teacher efficacy during an elementary mathematics methods course. A positive moderate relationship between content knowledge and personal teaching efficacy was found, and this relationship was stable during the course. No relationship was found…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. Increasing Cognitive Inhibition with a Difficult Prior Task: Implications for Mathematical Thinking

    ERIC Educational Resources Information Center

    Attridge, Nina; Inglis, Matthew

    2015-01-01

    Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…

  2. Mathematics from High School to Community College: Using Existing Tools to Increase College-Readiness Now. Policy Brief 14-1

    ERIC Educational Resources Information Center

    Jaffe, Louise

    2014-01-01

    The adoption and implementation of the Common Core State Standards and Smarter Balanced assessments in mathematics are intended to provide all students in California with the knowledge and skills required to transition from high school to college-level coursework. This implementation will take time. Concurrent with these efforts, policymakers and…

  3. 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.

  4. 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…

  5. TEDS-M 2008 User Guide for the International Database. Supplement 4: TEDS-M Released Mathematics and Mathematics Pedagogy Knowledge Assessment Items

    ERIC Educational Resources Information Center

    Brese, Falk, Ed.

    2012-01-01

    The goal for selecting the released set of test items was to have approximately 25% of each of the full item sets for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) that would represent the full range of difficulty, content, and item format used in the TEDS-M study. The initial step in the selection was to…

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. Effects of an Additional Mathematics Content Course on Elementary Teachers' Mathematical Beliefs and Knowledge for Teaching

    ERIC Educational Resources Information Center

    Smith, Marvin E.; Swars, Susan L.; Smith, Stephanie Z.; Hart, Lynn C.; Haardorfer, Regine

    2012-01-01

    This longitudinal study examines the effects of changes in an elementary teacher preparation program on mathematics beliefs and content knowledge for teaching of two groups of prospective teachers (N = 276): (1) those who completed a program with three mathematics content courses and two mathematics methods courses and (2) those who completed a…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. Examination of Mathematics Teachers' Pedagogical Content Knowledge of Probability

    ERIC Educational Resources Information Center

    Danisman, Sahin; Tanisli, Dilek

    2017-01-01

    The aim of this study is to explore the probability-related pedagogical content knowledge (PCK) of secondary school mathematics teachers in terms of content knowledge, curriculum knowledge, student knowledge, and knowledge of teaching methods and strategies. Case study design, a qualitative research model, was used in the study, and the…

  20. 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…

  1. 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…

  2. 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…

  3. Infusing Mathematics Content into a Methods Course: Impacting Content Knowledge for Teaching

    ERIC Educational Resources Information Center

    Burton, Megan; Daane, C. J.; Giesen, Judy

    2008-01-01

    This study compared content knowledge for teaching mathematics differences between elementary pre-service teachers in a traditional versus an experimental mathematics methods course. The experimental course replaced 20 minutes of traditional methods, each class, with an intervention of elementary mathematics content. The difference between groups…

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. 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…

  9. Human Infants' Preference for Left-to-Right Oriented Increasing Numerical Sequences

    PubMed Central

    de Hevia, Maria Dolores; Girelli, Luisa; Addabbo, Margaret; Macchi Cassia, Viola

    2014-01-01

    While associations between number and space, in the form of a spatially oriented numerical representation, have been extensively reported in human adults, the origins of this phenomenon are still poorly understood. The commonly accepted view is that this number-space association is a product of human invention, with accounts proposing that culture, symbolic knowledge, and mathematics education are at the roots of this phenomenon. Here we show that preverbal infants aged 7 months, who lack symbolic knowledge and mathematics education, show a preference for increasing magnitude displayed in a left-to-right spatial orientation. Infants habituated to left-to-right oriented increasing or decreasing numerical sequences showed an overall higher looking time to new left-to-right oriented increasing numerical sequences at test (Experiment 1). This pattern did not hold when infants were presented with the same ordinal numerical information displayed from right to left (Experiment 2). The different pattern of results was congruent with the presence of a malleable, context-dependent baseline preference for increasing, left-to-right oriented, numerosities (Experiment 3). These findings are suggestive of an early predisposition in humans to link numerical order with a left-to-right spatial orientation, which precedes the acquisition of symbolic abilities, mathematics education, and the acquisition of reading and writing skills. PMID:24802083

  10. Magnitude knowledge: the common core of numerical development.

    PubMed

    Siegler, Robert S

    2016-05-01

    The integrated theory of numerical development posits that a central theme of numerical development from infancy to adulthood is progressive broadening of the types and ranges of numbers whose magnitudes are accurately represented. The process includes four overlapping trends: (1) representing increasingly precisely the magnitudes of non-symbolic numbers, (2) connecting small symbolic numbers to their non-symbolic referents, (3) extending understanding from smaller to larger whole numbers, and (4) accurately representing the magnitudes of rational numbers. The present review identifies substantial commonalities, as well as differences, in these four aspects of numerical development. With both whole and rational numbers, numerical magnitude knowledge is concurrently correlated with, longitudinally predictive of, and causally related to multiple aspects of mathematical understanding, including arithmetic and overall math achievement. Moreover, interventions focused on increasing numerical magnitude knowledge often generalize to other aspects of mathematics. The cognitive processes of association and analogy seem to play especially large roles in this development. Thus, acquisition of numerical magnitude knowledge can be seen as the common core of numerical development. © 2016 John Wiley & Sons Ltd.

  11. 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…

  12. 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…

  13. 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…

  14. 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…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. 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…

  2. 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…

  3. 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…

  4. 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…

  5. 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…

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. 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…

  11. 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.

  12. 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...

  13. 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...

  14. 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...

  15. 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…

  16. 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…

  17. Narrative assessment: making mathematics learning visible in early childhood settings

    NASA Astrophysics Data System (ADS)

    Anthony, Glenda; McLachlan, Claire; Lim Fock Poh, Rachel

    2015-09-01

    Narratives that capture children's learning as they go about their day-to-day activities are promoted as a powerful assessment tool within early childhood settings. However, in the New Zealand context, there is increasing concern that learning stories—the preferred form of narrative assessment—currently downplay domain knowledge. In this paper, we draw on data from 13 teacher interviews and samples of 18 children's learning stories to examine how mathematics is made visible within learning stories. Despite appreciating that mathematics is embedded in a range of everyday activities within the centres, we found that the nature of a particular activity appeared to influence `how' and `what' the teachers chose to document as mathematics learning. Many of the teachers expressed a preference to document and analyse mathematics learning that occurred within explicit mathematics activities rather than within play that involves mathematics. Our concern is that this restricted documentation of mathematical activity could potentially limit opportunities for mathematics learning both in the centre and home settings.

  18. 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…

  19. 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

  20. 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.

  1. Climate Change: Creating Conditions Conducive to Quality STEM Undergraduate Education

    ERIC Educational Resources Information Center

    Baldwin, Roger G.

    2009-01-01

    In an era of global competition and a technology-based economy, it is increasingly important that college students graduate with a solid foundation of knowledge and understanding of science and mathematics. They must be able to use their scientific knowledge on their jobs and in their role as citizens of a society where complex policy and resource…

  2. 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…

  3. Aerodynamics and mathematics in National Socialist Germany and Fascist Italy: a comparison of research institutes.

    PubMed

    Epple, Moritz; Karachalios, Andreas; Remmert, Volker R

    2005-01-01

    The article is concerned with the mathematical sciences in National Socialist Germany and Fascist Italy, with special attention to research important to the war effort. It focuses on three institutional developments: the expansion of the Kaiser Wilhelm Institute for Fluid Dynamics in Göttingen, the foundation of the Reich Institute for Mathematics in Oberwolfach (Black Forest), and the work of the Istituto Nazionale per le Applicazioni del Calcolo in Rome. All three developments are embedded in the general political background, thus providing a basis for comparative conclusions about the conditions of the mathematical sciences and military-related research in Germany and Italy. It turns out that in both countries, the increasing demand for mathematical knowledge in modern warfare led to the establishment of "extra-university" national institutions specifically devoted to mathematical research.

  4. Technological Pedagogical Content Knowledge of Prospective Mathematics Teacher in Three Dimensional Material Based on Sex Differences

    NASA Astrophysics Data System (ADS)

    Aqib, M. A.; Budiarto, M. T.; Wijayanti, P.

    2018-01-01

    The effectiveness of learning in this era can be seen from 3 factors such as: technology, content, and pedagogy that covered in Technological Pedagogical Content Knowledge (TPCK). This research was a qualitative research which aimed to describe each domain from TPCK include Content Knowledge, Pedagogical Knowledge, Pedagogical Content Knowledge, Technological Knowledge, Technological Content Knowledge, Technological Pedagogical Knowledge and Technological, Pedagogical, and Content Knowledge. The subjects of this research were male and female mathematics college students at least 5th semester who has almost the same ability for some course like innovative learning, innovative learning II, school mathematics I, school mathematics II, computer applications and instructional media. Research began by spreading the questionnaire of subject then continued with the assignment and interview. The obtained data was validated by time triangulation.This research has result that male and female prospective teacher was relatively same for Content Knowledge and Pedagogical Knowledge domain. While it was difference in the Technological Knowledge domain. The difference in this domain certainly has an impact on other domains that has technology components on it. Although it can be minimized by familiarizing the technology.

  5. 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…

  6. 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…

  7. 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…

  8. 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…

  9. 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…

  10. 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…

  11. 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…

  12. 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,…

  13. 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…

  14. 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.

  15. 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.

  16. 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…

  17. 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…

  18. Understanding Malaysian Pre-Service Teachers Mathematical Content Knowledge and Pedagogical Content Knowledge

    ERIC Educational Resources Information Center

    Leong, Kwan Eu; Meng, Chew Cheng; Rahim, Suzieleez Syrene Abdul

    2015-01-01

    This article seeks to present findings from the analysis of the TEDS-M reports on the mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) of the pre-service teachers in Malaysia. The main objective of this study was to investigate the level of teaching knowledge attained by the Malaysian pre-service primary and secondary…

  19. Foundation Content Knowledge: What Do Pre-Service Teachers Need to Know?

    ERIC Educational Resources Information Center

    Linsell, Chris; Anakin, Megan

    2013-01-01

    The mathematics content knowledge of pre-service teachers is a growing area of inquiry. This topic requires further theoretical development due to the limited applicability of current cognitive and practice-oriented frameworks of mathematics content knowledge to beginning pre-service teachers. Foundation content knowledge is an integrated,…

  20. 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…

  1. 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)…

  2. 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.

  3. 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…

  4. 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…

  5. 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'…

  6. The Increase of Critical Thinking Skills through Mathematical Investigation Approach

    NASA Astrophysics Data System (ADS)

    Sumarna, N.; Wahyudin; Herman, T.

    2017-02-01

    Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.

  7. 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.

  8. 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.

  9. 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.

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. 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.…

  15. 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…

  16. 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…

  17. 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…

  18. 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…

  19. 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…

  20. 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…

  1. 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…

  2. 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.…

  3. The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

    NASA Astrophysics Data System (ADS)

    Priatna, Nanang

    2017-08-01

    The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

  4. 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…

  5. 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,…

  6. 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)

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

    NASA Astrophysics Data System (ADS)

    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.

  8. Translating University Biosensor Research to a High School Laboratory Experience

    ERIC Educational Resources Information Center

    Heldt, Caryn L.; Bank, Alex; Turpeinen, Dylan; King, Julia A.

    2016-01-01

    The need to increase science, technology, engineering, and mathematics (STEM) graduates is great. To interest more students into STEM degrees, we made our graphene biosensor research portable, inexpensive, and safe to demonstrate technology development to high school students. The students increased their knowledge of biosensors and proteins, and…

  9. 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…

  10. 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…

  11. 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…

  12. 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…

  13. 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…

  14. 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)…

  15. 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…

  16. 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…

  17. 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…

  18. Examining Relations between Mathematics Teachers' Instructional Vision and Knowledge and Change in Practice

    ERIC Educational Resources Information Center

    Munter, Charles; Correnti, Richard

    2017-01-01

    This article provides a longitudinal examination of how changes in more than 200 middle-grades mathematics teachers' instructional practices related to their (a) mathematical knowledge for teaching (MKT) and (b) instructional vision. Results of this multilevel regression analysis suggest that MKT and instructional vision are related to instruction…

  19. 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…

  20. The Transformation of Mathematics in On-Line Courses

    ERIC Educational Resources Information Center

    Borba, Marcelo C.

    2005-01-01

    This paper presents some research findings regarding the changes in the mathematics produced by mathematics teachers in on-line distance courses. Predicated on the belief that knowledge is generated by collectives of humans-with-media, and that different technologies modify the nature of the knowledge generated, we have sought to understand how…

  1. 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…

  2. Investigating Level of Mathematics Knowledge for Students Attending Vocational Schools in Turkey

    ERIC Educational Resources Information Center

    Colakoglu, Nurdan

    2013-01-01

    Students attend mathematics courses in Turkey for totally 11 years, throughout education life ranging from primary school to university, including eight years in primary education and three years in secondary education (four years based on new arrangement); however, level of mathematic knowledge of students is upsetting when they reach university…

  3. The Building of Pre-Service Primary Teachers' Knowledge of Mathematics Teaching: Interaction and Online Video Case Studies

    ERIC Educational Resources Information Center

    Llinares, Salvador; Valls, Julia

    2009-01-01

    This study explores how preservice primary teachers became engaged in meaning-making mathematics teaching when participating in online discussions within learning environments integrating video-clips of mathematics teaching. We identified different modes of participation in the online discussions and different levels of knowledge-building. The…

  4. Focusing on the Interactive Development of Secondary School Teachers' Knowledge of Mathematical Statements

    ERIC Educational Resources Information Center

    Levenson, Esther; Tsamir, Pessia; Tirosh, Dina; Dreyfus, Tommy; Barkai, Ruthi; Tabach, Michal

    2012-01-01

    This paper focuses on the first session of a professional development course revolving around the topic of mathematical statements and their appropriate proving methods. It analyzes the interactive development of the teachers' knowledge by focusing on the relation between the mathematical statements, the instructor, and the teachers. Different…

  5. Sociological Tools in the Study of Knowledge and Practice in Mathematics Teacher Education

    ERIC Educational Resources Information Center

    Parker, Diane; Adler, Jill

    2014-01-01

    In this paper, we put Basil Bernstein's theory of pedagogic discourse to work together with additional theoretical resources to interrogate knowledge and practice in mathematics teacher education. We illustrate this methodology through analysis of an instance of mathematics teacher education pedagogic practice. While the methodology itself is…

  6. The Devalued Student: Misalignment of Current Mathematics Knowledge and Level of Instruction

    ERIC Educational Resources Information Center

    LeMire, Steven D.; Melby, Marcella L.; Haskins, Anne M.; Williams, Tony

    2012-01-01

    Within this study, we investigated the association between 10th-grade students' mathematics performance and their feelings of instructional misalignment between their current mathematics knowledge and educator support. Data from the 2002 Education Longitudinal Study, which included a national sample of 750 public and private high schools in the…

  7. Teaching Multidigit Multiplication: Combining Multiple Frameworks to Analyse a Class Episode

    ERIC Educational Resources Information Center

    Clivaz, Stéphane

    2017-01-01

    This paper provides an analysis of a teaching episode of the multidigit algorithm for multiplication, with a focus on the influence of the teacher's mathematical knowledge on their teaching. The theoretical framework uses Mathematical Knowledge for Teaching, mathematical pertinence of the teacher and structuration of the milieu in a descending and…

  8. 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…

  9. What do mathematics teachers and teacher trainees know about the history of mathematics?

    NASA Astrophysics Data System (ADS)

    Gazit, Avikam

    2013-06-01

    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 knew about the origin of our counting system and the only item that reached above 50% was the item relating to the man who edited the book which is the basis for the plane geometry - Euclid (about 83%). Another meaningful finding was that the group with the highest score was that of mathematics teacher trainees in the accelerated track - a unique training scheme for middle school teachers (65.7%). The group with the lowest score was that of the elementary school mathematics student teachers (19.3%). One obvious conclusion is that we need to strengthen the knowledge of the history of mathematics in teacher training and in-service teachers' advanced studies.

  10. Adolescents’ Functional Numeracy Is Predicted by Their School Entry Number System Knowledge

    PubMed Central

    Geary, David C.; Hoard, Mary K.; Nugent, Lara; Bailey, Drew H.

    2013-01-01

    One in five adults in the United States is functionally innumerate; they do not possess the mathematical competencies needed for many modern jobs. We administered functional numeracy measures used in studies of young adults’ employability and wages to 180 thirteen-year-olds. The adolescents began the study in kindergarten and participated in multiple assessments of intelligence, working memory, mathematical cognition, achievement, and in-class attentive behavior. Their number system knowledge at the beginning of first grade was defined by measures that assessed knowledge of the systematic relations among Arabic numerals and skill at using this knowledge to solve arithmetic problems. Early number system knowledge predicted functional numeracy more than six years later (ß = 0.195, p = .0014) controlling for intelligence, working memory, in-class attentive behavior, mathematical achievement, demographic and other factors, but skill at using counting procedures to solve arithmetic problems did not. In all, we identified specific beginning of schooling numerical knowledge that contributes to individual differences in adolescents’ functional numeracy and demonstrated that performance on mathematical achievement tests underestimates the importance of this early knowledge. PMID:23382934

  11. 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…

  12. An analysis of the changes in ability and knowledge of students taking A-level physics and mathematics over a 35 year period

    NASA Astrophysics Data System (ADS)

    Barham, Peter J.

    2012-03-01

    New undergraduate students arriving to study physics at the University of Bristol from 1975 onwards have all taken the same test of their knowledge and understanding of physics and mathematics. Many of the questions test knowledge of material that has been in the A-level syllabus for maths or physics throughout this period. The ability of incoming students to answer these questions declined significantly in the 1990s with average scores falling from around 75% up to 1990 to below 50% after 2000 against a background of increasing A-level grades of the entrants to the programme. It is suggested that changes in teaching and examination methods have caused students to be less able to carry out multi-stage calculations and that the introduction of modular examinations may have encouraged a culture where students tend to forget material learnt in previous modules.

  13. Enhancing Students’ Interest through Mathematics Learning

    NASA Astrophysics Data System (ADS)

    Azmidar, A.; Darhim, D.; Dahlan, J. A.

    2017-09-01

    A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

  14. The Effectiveness of the GeoGebra Software: The Intermediary Role of Procedural Knowledge on Students' Conceptual Knowledge and Their Achievement in Mathematics

    ERIC Educational Resources Information Center

    Zulnaidi, Hutkemri; Zamri, Sharifah Norul Akmar Syed

    2017-01-01

    The aim of this study was to identify the effects of GeoGebra software on students' conceptual and procedural knowledge and the achievement of Form Two students in Mathematics particularly on the topic Function. In addition, this study determined the role of procedural knowledge as a mediator between conceptual knowledge and students' achievement.…

  15. Use of Learning Trajectories to Examine Pre-Service Teachers' Mathematics Knowledge for Teaching Area and Perimeter: Emerging Issues

    ERIC Educational Resources Information Center

    Butterfield, Barbara; Forrester, Tricia; McCallum, Faye; Chinnappan, Mohan

    2013-01-01

    A current concern is student learning outcomes and these are largely a function of teachers' knowledge and their practice. This position paper is premised on the notion that certain knowledge is required for the teaching of mathematics. An exploration of literature demonstrates that such professional knowledge development can be supported by…

  16. 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…

  17. Survey Team On: Conceptualisation of the Role of Competencies, Knowing and Knowledge in Mathematics Education Research

    ERIC Educational Resources Information Center

    Niss, Mogens; Bruder, Regina; Planas, Núria; Turner, Ross; Villa-Ochoa, Jhony Alexander

    2016-01-01

    This paper presents the outcomes of the work of the ICME 13 Survey Team on "Conceptualisation and the role of competencies, knowing and knowledge in mathematics education research". It surveys a variety of historical and contemporary views and conceptualisations of what it means to master mathematics, focusing on notions such as…

  18. Meta Didactic-Mathematical Knowledge of Teachers: Criteria for the Reflection and Assessment on Teaching Practice

    ERIC Educational Resources Information Center

    Breda, Adriana; Pino-Fan, Luis Roberto; Font, Vicenç

    2017-01-01

    The objective of this study is to demonstrate that the criteria of didactical suitability, proposed by the theoretical framework known as the Onto-Semiotic Approach (OSA) of mathematical knowledge and instruction, are powerful tools for organizing the reflection and assessment of instruction processes carried out by mathematics teachers. To this…

  19. Building Connections between Sociomathematical Norms and Cognitive Demand to Improve the Quality of Whole Class Mathematics Conversations

    ERIC Educational Resources Information Center

    Williams, Lori

    2010-01-01

    Mathematical discussions support and promote student learning as an integral part of the contexts in which students learn mathematics. Yet, American school practices often focus on teachers disseminating knowledge to students and students acquiring that knowledge through rote rehearsal rather than higher order thinking. One barrier to change in…

  20. Secondary School Results for the Fourth NAEP Mathematics Assessment: Discrete Mathematics, Data Organization and Interpretation, Measurement, Number and Operations.

    ERIC Educational Resources Information Center

    Brown, Catherine A.; And Others

    1988-01-01

    Suggests that secondary school students seem to have reasonably good procedural knowledge in areas of mathematics as rational numbers, probability, measurement, and data organization and interpretation. It appears, however, that students are lacking the conceptual knowledge enabling them to successfully do the assessment items on applications,…

  1. Improving Geometric and Trigonometric Knowledge and Skill for High School Mathematics Teachers: A Professional Development Partnership

    ERIC Educational Resources Information Center

    Merrill, Chris; Devine, Kevin L.; Brown, Joshua W.; Brown, Ryan A.

    2010-01-01

    In the summer of 2009, a professional development partnership was established between the Peoria Public School District (PPSD), a local education agency (LEA), and Illinois State University (ISU) to improve geometric and trigonometric knowledge and skill for high school mathematics teachers as part of the Illinois Mathematics and Science…

  2. Using the Mixture Rasch Model to Explore Knowledge Resources Students Invoke in Mathematic and Science Assessments

    ERIC Educational Resources Information Center

    Zhang, Danhui; Orrill, Chandra; Campbell, Todd

    2015-01-01

    The purpose of this study was to investigate whether mixture Rasch models followed by qualitative item-by-item analysis of selected Programme for International Student Assessment (PISA) mathematics and science items offered insight into knowledge students invoke in mathematics and science separately and combined. The researchers administered an…

  3. A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

    ERIC Educational Resources Information Center

    Tuna, Abdulkadir

    2013-01-01

    This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

  4. 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…

  5. Mathematics Learning Difficulties in Primary Education: Teachers' Professional Knowledge and the Use of Commercially Available Learning Packages

    ERIC Educational Resources Information Center

    Van Steenbrugge, H.; Valcke, M.; Desoete, A.

    2010-01-01

    The present study builds on teachers' professional knowledge about mathematics learning difficulties. Based on the input of 918 primary school teachers, an attempt is made to develop an overview of difficult curriculum topics in primary school mathematics. The research approach builds on new conceptions about the professional identity of teachers…

  6. An intervention for early mathematical success: outcomes from the hybrid version of the Building Math Readiness Parents as Partners (MRPP) project.

    PubMed

    Kritzer, Karen L; Pagliaro, Claudia M

    2013-01-01

    The Building Math Readiness in Young Deaf/Hard-of- Hearing Children: Parents as Partners (MRPP) Project works with parents to increase the understanding of foundational mathematics concepts in their preschool deaf/hard-of-hearing (d/hh) children in preparation for formal mathematics education. A multiple-case/single-unit case study incorporating descriptive statistics and grounded theory analysis was conducted on the hybrid version of the intervention. Results showed productive changes in parental behaviors indicating a possible positive effect on parent knowledge, recognition, and mediation of early matthematics concepts with their young d/hh children.

  7. 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…

  8. 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.

  9. Physics and Mathematics as Interwoven Disciplines in Science Education

    NASA Astrophysics Data System (ADS)

    Galili, Igal

    2018-03-01

    The relationship between physics and mathematics is reviewed upgrading the common in physics classes' perspective of mathematics as a toolkit for physics. The nature of the physics-mathematics relationship is considered along a certain historical path. The triadic hierarchical structure of discipline-culture helps to identify different ways in which mathematics is used in physics and to appreciate its contribution, to recognize the difference between mathematics and physics as disciplines in approaches, values, methods, and forms. We mentioned certain forms of mathematical knowledge important for physics but often missing in school curricula. The geometrical mode of codification of mathematical knowledge is compared with the analytical one in context of teaching school physics and mathematics; their complementarity is exemplified. Teaching may adopt the examples facilitating the claims of the study to reach science literacy and meaningful learning.

  10. Mathematical skills in 3- and 5-year-olds with spina bifida and their typically developing peers: a longitudinal approach.

    PubMed

    Barnes, Marcia A; Stubbs, Allison; Raghubar, Kimberly P; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M; Smith-Chant, Brenda

    2011-05-01

    Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual-spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual-spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual-spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder.

  11. Mathematical Skills in 3- and 5-Year-Olds with Spina Bifida and Their Typically Developing Peers: A Longitudinal Approach

    PubMed Central

    Barnes, Marcia A.; Stubbs, Allison; Raghubar, Kimberly P.; Agostino, Alba; Taylor, Heather; Landry, Susan; Fletcher, Jack M.; Smith-Chant, Brenda

    2011-01-01

    Preschoolers with spina bifida (SB) were compared to typically developing (TD) children on tasks tapping mathematical knowledge at 36 months (n = 102) and 60 months of age (n = 98). The group with SB had difficulty compared to TD peers on all mathematical tasks except for transformation on quantities in the subitizable range. At 36 months, vocabulary knowledge, visual–spatial, and fine motor abilities predicted achievement on a measure of informal math knowledge in both groups. At 60 months of age, phonological awareness, visual–spatial ability, and fine motor skill were uniquely and differentially related to counting knowledge, oral counting, object-based arithmetic skills, and quantitative concepts. Importantly, the patterns of association between these predictors and mathematical performance were similar across the groups. A novel finding is that fine motor skill uniquely predicted object-based arithmetic abilities in both groups, suggesting developmental continuity in the neurocognitive correlates of early object-based and later symbolic arithmetic problem solving. Models combining 36-month mathematical ability and these language-based, visual–spatial, and fine motor abilities at 60 months accounted for considerable variance on 60-month informal mathematical outcomes. Results are discussed with reference to models of mathematical development and early identification of risk in preschoolers with neurodevelopmental disorder. PMID:21418718

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

    NASA Astrophysics Data System (ADS)

    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.

  13. 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…

  14. Mathematics Funds of Knowledge: "Sotmaute" and "Sermaute" Fish in a Torres Strait Islander Community

    ERIC Educational Resources Information Center

    Ewing, Bronwyn

    2012-01-01

    The purpose of this article is to describe a project with one Torres Strait Islander Community. It provides some insights into parents' funds of knowledge that are mathematical in nature, such as sorting shells and giving fish. The idea of funds of knowledge is based on the premise that people are competent and have knowledge that has been…

  15. Using the "Knowledge Quartet" to Quantify Mathematical Knowledge in Teaching: The Development of a Protocol for Initial Teacher Education

    ERIC Educational Resources Information Center

    Weston, Tracy L.

    2013-01-01

    This study examined trainee teachers' mathematical knowledge in teaching (MKiT) over their final year in a US Initial Teacher Education (ITE) programme. This paper reports on an exploratory methodological approach taken to use the "Knowledge Quartet" to quantify MKiT through the development of a new protocol to code trainees' teaching of…

  16. A Collective Case Study of the Influence of Teachers' Beliefs and Knowledge on Error-Handling Practices during Class Discussion of Mathematics

    ERIC Educational Resources Information Center

    Bray, Wendy S.

    2011-01-01

    This collective case study examines the influence of 4 third-grade teachers' beliefs and knowledge on their error-handling practices during class discussion of mathematics. Study findings suggest that, although teachers' ways of handling student errors during class discussion of mathematics are clearly linked to both teacher beliefs and teacher…

  17. Engaging in Problem Posing Activities in a Dynamic Geometry Setting and the Development of Prospective Teachers' Mathematical Knowledge

    ERIC Educational Resources Information Center

    Lavy, Ilana; Shriki, Atara

    2010-01-01

    In the present study we explore changes in perceptions of our class of prospective mathematics teachers (PTs) regarding their mathematical knowledge. The PTs engaged in problem posing activities in geometry, using the "What If Not?" (WIN) strategy, as part of their work on computerized inquiry-based activities. Data received from the PTs'…

  18. Teacher Knowledge That Supports Student Processes in Learning Mathematics: A Study at All-Female Middle Schools in Saudi Arabia

    ERIC Educational Resources Information Center

    Alsaeed, Maha Saad

    2012-01-01

    Teachers in Saudi Arabia are attempting to advance their teaching in mathematics to address specific reforms by the Ministry of Education. Saudi teachers must improve their students' thinking through engagement in problem solving. This qualitative study investigated how teachers use knowledge of student mathematical learning and how they promote…

  19. The Impact of a Professional Development Program on Teachers' Mathematical Knowledge for Teaching, Instruction, and Student Achievement

    ERIC Educational Resources Information Center

    Jacob, Robin; Hill, Heather; Corey, Doug

    2017-01-01

    In this paper, we describe findings from a three-year evaluation of a well-developed mathematics professional development program that is commercially available on a wide scale. The professional development is designed to improve teachers' mathematical knowledge for teaching and to enable them to elicit more student thinking and reasoning during…

  20. Relations between Mathematical Knowledge for Teaching, Mathematics Instructional Quality, and Student Achievement in the Context of the "Responsive Classroom (RC)" Approach

    ERIC Educational Resources Information Center

    Ottmar, Erin R.; Rimm-Kaufman, Sara E.; Larsen, Ross; Merritt, Eileen G.

    2011-01-01

    Despite over thirty years of theoretically based research investigating "how" teacher mathematical knowledge and instructional practice relate to student learning, it is still largely unclear how these constructs are related, and policy makers and practitioners are still situated in a context with insufficient data to make decisions. Thus, there…

  1. 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…

  2. Visual Representation in Mathematics: Special Education Teachers' Knowledge and Emphasis for Instruction

    ERIC Educational Resources Information Center

    van Garderen, Delinda; Scheuermann, Amy; Poch, Apryl; Murray, Mary M.

    2018-01-01

    The use of visual representations (VRs) in mathematics is a strongly recommended practice in special education. Although recommended, little is known about special educators' knowledge of and instructional emphasis about VRs. Therefore, in this study, the authors examined special educators' own knowledge of and their instructional emphasis with…

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

    ERIC Educational Resources Information Center

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

    2018-01-01

    Background: 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. Methods: Secondary analysis of a quasi-experimental study. Sample included 438 students in 34 fourth-grade classrooms across…

  4. 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…

  5. Preservice Primary Teachers' Geometric Thinking: Is Pre-Tertiary Mathematics Education Building Sufficiently Strong Foundations?

    ERIC Educational Resources Information Center

    Hourigan, Mairéad; Leavy, Aisling M.

    2017-01-01

    Teacher knowledge is a critical focus of educational research in light of the potential impact of teacher knowledge on student learning. The dearth of research exploring entry-level preservice teachers' geometric knowledge poses an onerous challenge for mathematics educators in initial teacher education (ITE) when designing experiences that…

  6. 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…

  7. Towards a Methodology for the Characterization of Teachers' Didactic-Mathematical Knowledge

    ERIC Educational Resources Information Center

    Pino-Fan, Luis R.; Assis, Adriana; Castro, Walter F.

    2015-01-01

    This research study aims at exploring the use of some dimensions and theoretical-methodological tools suggested by the model of Didactic-Mathematical Knowledge (DMK) for the analysis, characterization and development of knowledge that teachers should have in order to efficiently develop within their practice. For this purpose, we analyzed the…

  8. 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…

  9. Investigating the Knowledge Needed for Teaching Mathematics: An Exploratory Validation Study Focusing on Teaching Practices

    ERIC Educational Resources Information Center

    Charalambous, Charalambos Y.

    2016-01-01

    Central in the frameworks proposed to capture the knowledge needed for teaching mathematics is the assumption that teachers need more than pure subject-matter knowledge. Validation studies exploring this assumption by recruiting contrasting populations are relatively scarce. Drawing on a sample of 644 Greek-Cypriots preservice and inservice…

  10. 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,…

  11. 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…

  12. Operationalizing Levels of Academic Mastery Based on Vygotsky's Theory: The Study of Mathematical Knowledge

    ERIC Educational Resources Information Center

    Nezhnov, Peter; Kardanova, Elena; Vasilyeva, Marina; Ludlow, Larry

    2015-01-01

    The present study tested the possibility of operationalizing levels of knowledge acquisition based on Vygotsky's theory of cognitive growth. An assessment tool (SAM-Math) was developed to capture a hypothesized hierarchical structure of mathematical knowledge consisting of procedural, conceptual, and functional levels. In Study 1, SAM-Math was…

  13. 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…

  14. Young Children Use Graphs to Build Mathematical Reasoning

    ERIC Educational Resources Information Center

    Larson, Mark J.; Whitin, David J.

    2010-01-01

    Mathematical, scientific, and technological knowledge is critical for people in a 21st Century world that is dependent upon a global interconnectedness and a knowledge-based economy. This is the kind of knowledge that will power innovations and drive decision making in the years ahead. Schools are therefore being called upon to devise a…

  15. 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…

  16. Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties.

    PubMed

    Hassinger-Das, Brenna; Jordan, Nancy C; Dyson, Nancy

    2015-12-01

    The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as "equal," "more," and "less," and associated number concepts would increase at-risk children's vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were recruited from kindergarten classes in four schools. Participants were randomly assigned to one of three groups: a storybook number competencies (SNC) intervention, a number sense intervention, or a business-as-usual control. Interventions were carried out in groups of four children over 8 weeks (24 thirty-minute sessions). Findings demonstrated that the SNC intervention group outperformed the other groups on measures of mathematics vocabulary, both in terms of words that were closely aligned to the intervention and those that were not. There was no effect of the SNC intervention, however, on general mathematics measures, suggesting a need to provide the mathematics vocabulary work along with more intensive instruction in number concepts.

  17. State and trait effects on individual differences in children's mathematical development.

    PubMed

    Bailey, Drew H; Watts, Tyler W; Littlefield, Andrew K; Geary, David C

    2014-11-01

    Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. © The Author(s) 2014.

  18. State and Trait Effects on Individual Differences in Children's Mathematical Development

    PubMed Central

    Bailey, Drew H.; Watts, Tyler W.; Littlefield, Andrew K.; Geary, David C.

    2015-01-01

    Substantial longitudinal relations between children's early mathematics achievement and their much later mathematics achievement are firmly established. These findings are seemingly at odds with studies showing that early educational interventions have diminishing effects on children's mathematics achievement across time. We hypothesized that individual differences in children's later mathematical knowledge are more an indicator of stable, underlying characteristics related to mathematics learning throughout development than of direct effects of early mathematical competency on later mathematical competency. We tested this hypothesis in two longitudinal data sets, by simultaneously modeling effects of latent traits (stable characteristics that influence learning across time) and states (e.g., prior knowledge) on children's mathematics achievement over time. Latent trait effects on children's mathematical development were substantially larger than state effects. Approximately 60% of the variance in trait mathematics achievement was accounted for by commonly used control variables, such as working memory, but residual trait effects remained larger than state effects. Implications for research and practice are discussed. PMID:25231900

  19. From Preface to Practice: A Narrative Study of Women Learning to Teach Mathematics

    ERIC Educational Resources Information Center

    Stoehr, Kathleen Jablon

    2014-01-01

    My dissertation research explored the experiences of mathematics anxieties in women elementary preservice teachers while learning mathematics as K-12 students and while learning to teach mathematics. Previous studies conducted in mathematics teacher education have emphasized the importance of preservice teachers' mathematical knowledge for…

  20. The effectiveness of a head-heart-hands model for natural and environmental science learning in urban schools.

    PubMed

    Jagannathan, Radha; Camasso, Michael J; Delacalle, Maia

    2018-02-01

    We describe an environmental and natural science program called Nurture thru Nature (NtN) that seeks to improve mathematics and science performance of students in disadvantaged communities, and to increase student interest in Science, Technology, Engineering and Mathematics (STEM) careers. The program draws conceptual guidance from the Head-Heart-Hands model that informs the current educational movement to foster environmental understanding and sustainability. Employing an experimental design and data from seven cohorts of students, we find some promising, albeit preliminary, indications that the program can increase students' science knowledge and grades in mathematics, science and language arts. We discuss the special adaptations that environmental and sustainability education programs need to incorporate if they are to be successful in today's resource depleted urban schools. Copyright © 2017 Elsevier Ltd. All rights reserved.

  1. 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.

  2. 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.

  3. Introducing Seismic Tomography with Computational Modeling

    NASA Astrophysics Data System (ADS)

    Neves, R.; Neves, M. L.; Teodoro, V.

    2011-12-01

    Learning seismic tomography principles and techniques involves advanced physical and computational knowledge. In depth learning of such computational skills is a difficult cognitive process that requires a strong background in physics, mathematics and computer programming. The corresponding learning environments and pedagogic methodologies should then involve sets of computational modelling activities with computer software systems which allow students the possibility to improve their mathematical or programming knowledge and simultaneously focus on the learning of seismic wave propagation and inverse theory. To reduce the level of cognitive opacity associated with mathematical or programming knowledge, several computer modelling systems have already been developed (Neves & Teodoro, 2010). Among such systems, Modellus is particularly well suited to achieve this goal because it is a domain general environment for explorative and expressive modelling with the following main advantages: 1) an easy and intuitive creation of mathematical models using just standard mathematical notation; 2) the simultaneous exploration of images, tables, graphs and object animations; 3) the attribution of mathematical properties expressed in the models to animated objects; and finally 4) the computation and display of mathematical quantities obtained from the analysis of images and graphs. Here we describe virtual simulations and educational exercises which enable students an easy grasp of the fundamental of seismic tomography. The simulations make the lecture more interactive and allow students the possibility to overcome their lack of advanced mathematical or programming knowledge and focus on the learning of seismological concepts and processes taking advantage of basic scientific computation methods and tools.

  4. History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Clark, Kathleen Michelle

    2012-01-01

    The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

  5. Measure for Measure: What Combining Diverse Measures Reveals about Children's Understanding of the Equal Sign as An Indicator of Mathematical Equality

    ERIC Educational Resources Information Center

    Matthews, Percival; Rittle-Johnson, Bethany; McEldoon, Katherine; Taylor, Roger

    2012-01-01

    Knowledge of the equal sign as an indicator of mathematical equality is foundational to children's mathematical development and serves as a key link between arithmetic and algebra. The current findings reaffirmed a past finding that diverse items can be integrated onto a single scale, revealed the wide variability in children's knowledge of the…

  6. Using Video Analysis to Support Prospective K-8 Teachers' Noticing of Students' Multiple Mathematical Knowledge Bases

    ERIC Educational Resources Information Center

    Roth McDuffie, Amy; Foote, Mary Q.; Bolson, Catherine; Turner, Erin E.; Aguirre, Julia M.; Bartell, Tonya Gau; Drake, Corey; Land, Tonia

    2014-01-01

    As part of a larger research project aimed at transforming preK-8 mathematics teacher preparation, the purpose of this study was to examine the extent to which prospective teachers notice children's competencies related to children's mathematical thinking, and children's community, cultural, and linguistic funds of knowledge or what…

  7. 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…

  8. A Model of Professional Competences in Mathematics to Update Mathematical and Didactic Knowledge of Teachers

    ERIC Educational Resources Information Center

    Díaz, Verónica; Poblete, Alvaro

    2017-01-01

    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…

  9. 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…

  10. Construction of the mathematical concept of pseudo thinking students

    NASA Astrophysics Data System (ADS)

    Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

    2018-05-01

    Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

  11. Generating Procedural and Conceptual Knowledge of Fractions by Pre-Service Teachers

    ERIC Educational Resources Information Center

    Chinnappan, Mohan; Forrester, Tricia

    2014-01-01

    Knowledge that teachers bring to the teaching context is of interest to key stakeholders in improving levels of numeracy attained by learners. In this regard, the centrality of, and the need to investigate, the quality of teachers' mathematical knowledge for teaching mathematics has been gaining momentum in recent years. There is a general…

  12. 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,…

  13. 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…

  14. The Effects of Professional Development on the Knowledge, Attitudes, & Anxiety of Intermediate Teachers of Mathematics

    ERIC Educational Resources Information Center

    McCartney, Kathleen Perry

    2013-01-01

    This study examined the effects of a short-term professional development on the mathematical knowledge, anxiety, and attitudes of intermediate teachers. Participants in the control and experimental groups were pre-tested for knowledge using the eighth grade TCAP Item Sampler. Anxiety was measured through the use of Suinn and Winston's (2003)…

  15. Preservice Secondary Mathematics Teachers' Statistical Knowledge: A Snapshot of Strengths and Weaknesses

    ERIC Educational Resources Information Center

    Lovett, Jennifer N.; Lee, Hollylynne S.

    2017-01-01

    Amid the implementation of new curriculum standard regarding statistics and new recommendations for preservice secondary mathematics teachers [PSMTs] to teach statistics, there is a need to examine the current state of PSMTs' common statistical knowledge. This study reports on the statistical knowledge 217 PSMTs from a purposeful sample of 18…

  16. Developmental Foundations of Children's Fraction Magnitude Knowledge.

    PubMed

    Mou, Yi; Li, Yaoran; Hoard, Mary K; Nugent, Lara D; Chu, Felicia W; Rouder, Jeffrey N; Geary, David C

    2016-01-01

    The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children's mathematical development, and the knowledge of fraction magnitudes influences children's later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8 th and 9 th graders' (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9 th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7 th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8 th and 9 th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9 th but not 8 th graders' fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students' understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually.

  17. Early mathematics development and later achievement: Further evidence

    NASA Astrophysics Data System (ADS)

    Aubrey, Carol; Godfrey, Ray; Dahl, Sarah

    2006-05-01

    There is a growing international recognition of the importance of the early years of schooling as well as an interest being shown in the relationship of early education to later achievement. This article focuses on a cohort of English pupils who have been tracked through primary school during the first five years of the new National Numeracy Strategy. It reports a limited longitudinal study of young children's early mathematical development, initially within three testing cycles: at the mid-point and towards the end of their reception year (at five years-of-age) and again at the mid-point of Year 1 (at six years-ofage). These cycles were located within the broader context of progress through to the end of Key Stage 1 (at seven years) and Key Stage 2 (at eleven years) on the basis of national standardised assessment tests (SATs). Results showed that children who bring into school early mathematical knowledge do appear to be advantaged in terms of their mathematical progress through primary school. Numerical attainment increases in importance across the primary years and practical problem solving remains an important element of this. This finding is significant given the current emphasis on numerical calculation in the English curriculum. It is concluded that without active intervention, it is likely that children with little mathematical knowledge at the beginning of formal schooling will remain low achievers throughout their primary years and, probably, beyond.

  18. Constructing Mathematical Knowledge: Epistemology and Mathematics Education. Studies in Mathematics Education Series: 4.

    ERIC Educational Resources Information Center

    Ernest, Paul, Ed.

    This book illustrates the breadth of theoretical and philosophical perspectives that can be brought to bear on mathematics and education. Part 1, "Constructivism and the Learning of Mathematics," contains the following chapters: (1) "A Radical Constructivist View of Basic Mathematical Concepts" (E. von Glasersfeld); (2) "Interaction and Children's…

  19. Summative and Formative Assessments in Mathematics Supporting the Goals of the Common Core Standards

    ERIC Educational Resources Information Center

    Schoenfeld, Alan H.

    2015-01-01

    Being proficient in mathematics involves having rich and connected mathematical knowledge, being a strategic and reflective thinker and problem solver, and having productive mathematical beliefs and dispositions. This broad set of mathematics goals is central to the Common Core State Standards for Mathematics. High-stakes testing often drives…

  20. Spreadsheets as a Transparent Resource for Learning the Mathematics of Annuities

    ERIC Educational Resources Information Center

    Pournara, Craig

    2009-01-01

    The ability of mathematics teachers to decompress mathematics and to move between representations are two key features of mathematical knowledge that is usable for teaching. This article reports on four pre-service secondary mathematics teachers learning the mathematics of annuities. In working with spreadsheets students began to make sense of…

  1. Differences in the Mathematics-Vocabulary Knowledge of Fifth-Grade Students with and without Learning Difficulties

    ERIC Educational Resources Information Center

    Forsyth, Suzanne R.; Powell, Sarah R.

    2017-01-01

    The purpose of this pilot study was to explore the impact of mathematics and reading learning difficulties on the mathematics-vocabulary understanding of fifth-grade students. Students (n = 114) completed three measures: mathematics computation, general vocabulary, and mathematics vocabulary. Based on performance on the mathematics computation and…

  2. Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

    PubMed

    Nguyen, Tutrang; Watts, Tyler W; Duncan, Greg J; Clements, Douglas H; Sarama, Julie S; Wolfe, Christopher; Spitler, Mary Elaine

    In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children's emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement.

  3. 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

  4. Cognitive Correlates of Performance in Advanced Mathematics

    ERIC Educational Resources Information Center

    Wei, Wei; Yuan, Hongbo; Chen, Chuansheng; Zhou, Xinlin

    2012-01-01

    Background: Much research has been devoted to understanding cognitive correlates of elementary mathematics performance, but little such research has been done for advanced mathematics (e.g., modern algebra, statistics, and mathematical logic).Aims: To promote mathematical knowledge among college students, it is necessary to understand what factors…

  5. 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…

  6. 34 CFR 280.40 - What costs are allowable?

    Code of Federal Regulations, 2012 CFR

    2012-07-01

    ... equipment (including computers) and the maintenance and operation of materials, equipment and computers. Any... related to improving student reading skills or knowledge of mathematics, science, history, geography... improving student reading skills or knowledge of mathematics, science, history, geography, English, foreign...

  7. 34 CFR 280.40 - What costs are allowable?

    Code of Federal Regulations, 2014 CFR

    2014-07-01

    ... equipment (including computers) and the maintenance and operation of materials, equipment and computers. Any... related to improving student reading skills or knowledge of mathematics, science, history, geography... improving student reading skills or knowledge of mathematics, science, history, geography, English, foreign...

  8. 34 CFR 280.40 - What costs are allowable?

    Code of Federal Regulations, 2013 CFR

    2013-07-01

    ... equipment (including computers) and the maintenance and operation of materials, equipment and computers. Any... related to improving student reading skills or knowledge of mathematics, science, history, geography... improving student reading skills or knowledge of mathematics, science, history, geography, English, foreign...

  9. Achieving Fluency: Special Education and Mathematics

    ERIC Educational Resources Information Center

    Fennell, Francis

    2011-01-01

    "Achieving Fluency" presents the understandings that all teachers need to play a role in the education of students who struggle: those with disabilities and those who simply lack essential foundational knowledge. This book serves teachers and supervisors by sharing increasingly intensive instructional interventions for struggling students on…

  10. The Role of Teachers' Knowledge of Functions in Their Teaching: A Conceptual Approach with Illustrations from Two Cases

    ERIC Educational Resources Information Center

    Watson, Anne; Harel, Guershon

    2013-01-01

    We investigate whether and how personal mathematical knowledge at an advanced level impacts on teaching at a lower school level. We study this in the context of functions because understanding them permeates secondary and advanced mathematics. Textbook treatment of these can be patchy, implying a need for knowledgeable teachers to rectify…

  11. Knowledge Base of Mathematics Teacher Educators: A Goals-Knowledge-Practice Approach

    ERIC Educational Resources Information Center

    Veselovsky, Aleksandra

    2017-01-01

    Critical analysis of the literature reveals that many questions about the knowledge and practice of mathematics teacher educators (MTEs) remain in need of further research: how do they know what to teach; how do they learn how to teach teachers; how do they prepare to teach their courses; how does the research on teacher education inform their…

  12. Four (Algorithms) in One (Bag): An Integrative Framework of Knowledge for Teaching the Standard Algorithms of the Basic Arithmetic Operations

    ERIC Educational Resources Information Center

    Raveh, Ira; Koichu, Boris; Peled, Irit; Zaslavsky, Orit

    2016-01-01

    In this article we present an integrative framework of knowledge for teaching the standard algorithms of the four basic arithmetic operations. The framework is based on a mathematical analysis of the algorithms, a connectionist perspective on teaching mathematics and an analogy with previous frameworks of knowledge for teaching arithmetic…

  13. Early Career Mathematics Teachers' General Pedagogical Knowledge and Skills: Do Teacher Education, Teaching Experience, and Working Conditions Make a Difference?

    ERIC Educational Resources Information Center

    König, Johannes; Blömeke, Sigrid; Kaiser, Gabriele

    2015-01-01

    We examined several facets of general pedagogical knowledge and skills of early career mathematics teachers, asking how they are associated with characteristics of teacher education, teaching experience, and working conditions. Declarative general pedagogical knowledge (GPK) was assessed via a paper-and-pencil test, while early career teachers'…

  14. Mathematics, Anyone?

    ERIC Educational Resources Information Center

    Reys, Robert; Reys, Rustin

    2011-01-01

    In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…

  15. Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    1999-01-01

    Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

  16. Why Singaporean 8th Grade Students Gain Highest Mathematics Ranking in TIMSS (1999-2011)

    ERIC Educational Resources Information Center

    Lessani, Abdolreza; Yunus, Aida Suraya Md; Tarmiz, Rohani Ahmad; Mahmud, Rosnaini

    2014-01-01

    The international comparison of students' mathematics knowledge and competencies is an effective method of evaluating students' mathematics performance and developing policies to improve their achievements in mathematics. Trends in International Mathematics and Science Study (TIMSS) are among the most well-recognized international comparisons that…

  17. An Investigation of the Mathematics-Vocabulary Knowledge of First-Grade Students

    ERIC Educational Resources Information Center

    Powell, Sarah R.; Nelson, Gena

    2017-01-01

    Competency with mathematics requires use of numerals and symbols as well as an understanding and use of mathematics vocabulary (e.g., "add," "more," "triangle"). Currently, no measures exist in which the primary function is to gauge mathematics-vocabulary understanding. We created a 64-item mathematics-vocabulary…

  18. An Objectivist Critique of Relativism in Mathematics Education

    NASA Astrophysics Data System (ADS)

    Rowlands, Stuart; Graham, Ted; Berry, John

    Many constructivists tag as `absolutist' references to mathematics as an abstract body of knowledge, and stake-out the moral high-ground with the argument that mathematics is not only utilised oppressively but that mathematics is, in-itself, oppressive. With much reference to Ernest's (1991) Philosophy of Mathematics Education this tag has been justified on the grounds that if mathematics is a social-cultural creation that is mutable and fallible then it must be social acceptance that confers the objectivity of mathematics. This paper argues that mathematics, albeit a social-cultural creation that is mutable and fallible, is a body of knowledge the objectivity of which is independent of origin or social acceptance. Recently, Ernest (1998) has attempted to express social constructivism as a philosophy of mathematics and has included the category of logical necessity in his elaboration of the objectivity of mathematics. We argue that this inclusion of logical necessity not only represents a U-turn, but that the way in which Ernest has included this category is an attempt to maintain his earlier position that it is social acceptance that confers the objectivity of mathematics.

  19. Building Knowledge Structures by Testing Helps Children With Mathematical Learning Difficulty.

    PubMed

    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 testing using a web-based curriculum learning system. A total of 142 children with MLD were recruited; half of the children were in the experimental group (using the system), and the other half were in the control group (not using the system). The children were encouraged to use the web-based learning system at home for at least a 15-min session, at least once a week, for one and a half months. The mean accumulated time of testing on the system for children in the experimental group was 56.2 min. Children in the experimental group had significantly higher scores on their final mathematical examination compared to the control group. The results suggest that web-based curriculum learning through testing that promotes the building of knowledge structures for a mathematical course was helpful for children with MLD. © Hammill Institute on Disabilities 2014.

  20. Operationalizing Levels of Academic Mastery Based on Vygotsky’s Theory

    PubMed Central

    Nezhnov, Peter; Kardanova, Elena; Ludlow, Larry

    2014-01-01

    The present study tested the possibility of operationalizing levels of knowledge acquisition based on Vygotsky’s theory of cognitive growth. An assessment tool (SAM-Math) was developed to capture a hypothesized hierarchical structure of mathematical knowledge consisting of procedural, conceptual, and functional levels. In Study 1, SAM-Math was administered to 4th-grade students (N = 2,216). The results of Rasch analysis indicated that the test provided an operational definition for the construct of mathematical competence that included the three levels of mastery corresponding to the theoretically based hierarchy of knowledge. In Study 2, SAM-Math was administered to students in 4th, 6th, 8th, and 10th grades (N = 396) to examine developmental changes in the levels of mathematics knowledge. The results showed that the mastery of mathematical concepts presented in elementary school continued to deepen beyond elementary school, as evidenced by a significant growth in conceptual and functional levels of knowledge. The findings are discussed in terms of their implications for psychological theory, test design, and educational practice. PMID:29795820

  1. How Are the Mathematical Identities of Low Achieving South African Eleventh Graders Related to Their Ability to Solve Mathematical Tasks?

    ERIC Educational Resources Information Center

    Cranfield, Corvell

    2013-01-01

    The construct of mathematical identity has recently been widely used in mathematics education with the intention to understand how students relate to and engage (or disengage) with mathematics. Grootenboer and Zevenbergen (2008) define mathematical identity as the students' knowledge, abilities, skills, beliefs, dispositions, attitudes and…

  2. [The discussion of the infiltrative model of mathematical knowledge to genetics teaching].

    PubMed

    Liu, Jun; Luo, Pei-Gao

    2011-11-01

    Genetics, the core course of biological field, is an importance major-basic course in curriculum of many majors related with biology. Due to strong theoretical and practical as well as abstract of genetics, it is too difficult to study on genetics for many students. At the same time, mathematics is one of the basic courses in curriculum of the major related natural science, which has close relationship with the establishment, development and modification of genetics. In this paper, to establish the intrinsic logistic relationship and construct the integral knowledge network and to help students improving the analytic, comprehensive and logistic abilities, we applied some mathematical infiltrative model genetic knowledge in genetics teaching, which could help students more deeply learn and understand genetic knowledge.

  3. Teaching Mathematics in Geography Degrees

    ERIC Educational Resources Information Center

    Bennett, Robert

    1978-01-01

    Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)

  4. Mathematics in the Early Years.

    ERIC Educational Resources Information Center

    Copley, Juanita V., Ed.

    Noting that young children are capable of surprisingly complex forms of mathematical thinking and learning, this book presents a collection of articles depicting children discovering mathematical ideas, teachers fostering students' informal mathematical knowledge, adults asking questions and listening to answers, and researchers examining…

  5. Developing the STS sound pollution unit for enhancing students' applying knowledge among science technology engineering and mathematics

    NASA Astrophysics Data System (ADS)

    Jumpatong, Sutthaya; Yuenyong, Chokchai

    2018-01-01

    STEM education suggested that students should be enhanced to learn science with integration between Science, Technology, Engineering and Mathematics. To help Thai students make sense of relationship between Science, Technology, Engineering and Mathematics, this paper presents learning activities of STS Sound Pollution. The developing of STS Sound Pollution is a part of research that aimed to enhance students' perception of the relationship between Science Technology Engineering and Mathematics. This paper will discuss how to develop Sound Pollution through STS approach in framework of Yuenyong (2006) where learning activities were provided based on 5 stages. These included (1) identification of social issues, (2) identification of potential solutions, (3) need for knowledge, (4) decisionmaking, and (5) socialization stage. The learning activities could be highlighted as following. First stage, we use video clip of `Problem of people about Sound Pollution'. Second stage, students will need to identification of potential solutions by design Home/Factory without noisy. The need of scientific and other knowledge will be proposed for various alternative solutions. Third stage, students will gain their scientific knowledge through laboratory and demonstration of sound wave. Fourth stage, students have to make decision for the best solution of designing safety Home/Factory based on their scientific knowledge and others (e.g. mathematics, economics, art, value, and so on). Finally, students will present and share their Design Safety Home/Factory in society (e.g. social media or exhibition) in order to validate their ideas and redesigning. The paper, then, will discuss how those activities would allow students' applying knowledge of science technology engineering, mathematics and others (art, culture and value) for their possible solution of the STS issues.

  6. 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.

  7. The Frontiers of the Astronomical Universe

    ERIC Educational Resources Information Center

    Pecker, Jean-Claude

    1977-01-01

    Reviews the current state of knowledge obtained by means of observations using the increasingly powerful or proficient instruments of astrophysics, radio astronomy, and space astronomy by satellite. In conclusion, he refers to certain mathematical entities introduced into the theory of the origins and evolution of the cosmos. (Author/MA)

  8. 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…

  9. 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…

  10. Developing an Understanding of What Constitutes Mathematics Teacher Educator PCK: A Case Study of a Collaboration between Two Teacher Educators

    ERIC Educational Resources Information Center

    Muir, Tracey; Wells, Jill; Chick, Helen

    2017-01-01

    Previous research into the knowledge required for teaching has focused primarily on pre-service and in-service teachers' knowledge. What is less researched, however, is the role of the teacher educator in helping pre-service teachers (PSTs) develop the knowledge needed in order to teach mathematics to students. The focus thus shifts from examining…

  11. The Effect of Syllabus on Mathematical Knowledge

    ERIC Educational Resources Information Center

    Belsom, C. G. H.; Elton, L. R. B.

    1974-01-01

    Item analysis of a mathematics preknowledge test given to physics students revealed that significant differences existed on certain items between groups of students who had followed different mathematics syllabuses. (MLH)

  12. Resilience in mathematics after early brain injury: The roles of parental input and early plasticity.

    PubMed

    Glenn, Dana E; Demir-Lira, Özlem Ece; Gibson, Dominic J; Congdon, Eliza L; Levine, Susan C

    2018-04-01

    Children with early focal unilateral brain injury show remarkable plasticity in language development. However, little is known about how early brain injury influences mathematical learning. Here, we examine early number understanding, comparing cardinal number knowledge of typically developing children (TD) and children with pre- and perinatal lesions (BI) between 42 and 50 months of age. We also examine how this knowledge relates to the number words children hear from their primary caregivers early in life. We find that children with BI, are, on average, slightly behind TD children in both cardinal number knowledge and later mathematical performance, and show slightly slower learning rates than TD children in cardinal number knowledge during the preschool years. We also find that parents' "number talk" to their toddlers predicts later mathematical ability for both TD children and children with BI. These findings suggest a relatively optimistic story in which neural plasticity is at play in children's mathematical development following early brain injury. Further, the effects of early number input suggest that intervening to enrich the number talk that children with BI hear during the preschool years could narrow the math achievement gap. Copyright © 2017 The Authors. Published by Elsevier Ltd.. All rights reserved.

  13. Inquiry based learning: a student centered learning to develop mathematical habits of mind

    NASA Astrophysics Data System (ADS)

    Handayani, A. D.; Herman, T.; Fatimah, S.; Setyowidodo, I.; Katminingsih, Y.

    2018-05-01

    Inquiry based learning is learning that based on understanding constructivist mathematics learning. Learning based on constructivism is the Student centered learning. In constructivism, students are trained and guided to be able to construct their own knowledge on the basis of the initial knowledge that they have before. This paper explained that inquiry based learning can be used to developing student’s Mathematical habits of mind. There are sixteen criteria Mathematical Habits of mind, among which are diligent, able to manage time well, have metacognition ability, meticulous, etc. This research method is qualitative descriptive. The result of this research is that the instruments that have been developed to measure mathematical habits of mind are validated by the expert. The conclusion is the instrument of mathematical habits of mind are valid and it can be used to measure student’s mathematical habits of mind.

  14. Implementing an Effective Mathematics Fact Fluency Practice Activity

    ERIC Educational Resources Information Center

    Riccomini, Paul J.; Stocker, James D., Jr.; Morano, Stephanie

    2017-01-01

    Proficiency in mathematics involves the seamless synchronization of conceptual understanding, procedural knowledge, computational fluency, and problem solving (NMAP, 2008). Clearly, fluency with mathematics facts is one element embedded within mathematical proficiency and important for students with disabilities to develop. As more and more…

  15. Impact of the Course Teaching and Learning of Mathematics on Preservice Grades 7 and 8 Mathematics Teachers in Singapore

    ERIC Educational Resources Information Center

    Kaur, Berinderjeet

    2017-01-01

    This paper explores the impact of the course "Teaching and Learning of Mathematics (Grades 7 and 8)" for the preparation of pre-service secondary mathematics teachers. It examines how pre-service teachers perceived mathematical problem solving and communicating mathematical knowledge before and after the course. The main objective of the…

  16. The Interface between ChE and Mathematics: What Do Students Really Need?

    ERIC Educational Resources Information Center

    Graham, Michael D.; Ganter, Susan L.

    2001-01-01

    Summarizes the report given to the Committee on the Undergraduate Program in Mathematics of the Mathematical Association of America (MAA) who is developing new guidelines for instruction in mathematics with a chemical engineering group at Clemson University in order to list specific knowledge and skills in mathematics needed by engineering…

  17. Vicissitudes of Children's Mathematical Knowledge: Implications of Developmental Research for Early Childhood Mathematics Education

    ERIC Educational Resources Information Center

    Sophian, Catherine

    2013-01-01

    Hachey's (2013) article celebrates a revolution that is taking place in early childhood mathematics education, fueled in part by developmental research demonstrating the mathematical capabilities of young children. At the same time, Hachey notes that the mathematics revolution she describes is not yet complete. In this commentary, the author…

  18. Interesting and Difficult Mathematical Problems: Changing Teachers' Views by Employing Multiple-Solution Tasks

    ERIC Educational Resources Information Center

    Guberman, Raisa; Leikin, Roza

    2013-01-01

    The study considers mathematical problem solving to be at the heart of mathematics teaching and learning, while mathematical challenge is a core element of any educational process. The study design addresses the complexity of teachers' knowledge. It is aimed at exploring the development of teachers' mathematical and pedagogical conceptions…

  19. Preparing Mathematics Teachers for Elementary High-Poverty Schools: Perceptions and Suggestions from Preservice Teachers

    ERIC Educational Resources Information Center

    McKinney, Sueanne E.; Berry, Robert Q., III; Jackson, Joan M.

    2007-01-01

    The National Council of Teachers of Mathematics articulates an ambitious vision of a high-quality mathematics program. Achieving this vision requires competent and knowledgeable teachers who can support all students in learning mathematics concepts with understanding. Effective mathematics teachers are especially needed for high-poverty schools…

  20. Need for Equipping Student Teachers with Language of Mathematics

    ERIC Educational Resources Information Center

    Gafoor, K. Abdul; Sarabi, M. K.

    2015-01-01

    The significance of curriculum in building up language of mathematics which enables learners to construct and communicate knowledge of mathematics has not received due attention even as the pedagogical challenges faced by the students in learning mathematics have been discussed for years. Learning language of mathematics is not only valuable in…

  1. 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…

  2. Task Modification and Knowledge Utilization by Korean Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Lee, Kyeong-Hwa; Lee, Eun-Jung; Park, Min-Sun

    2016-01-01

    It has been asserted that mathematical tasks play a critical role in the teaching and learning of mathematics. Modification of tasks included in intended curriculum materials, such as textbooks, can be an effective activity for prospective teachers to understand the role of mathematical tasks in the teaching and learning of mathematics; designing…

  3. 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.

  4. Developmental Foundations of Children’s Fraction Magnitude Knowledge

    PubMed Central

    Mou, Yi; Li, Yaoran; Hoard, Mary K.; Nugent, Lara D.; Chu, Felicia W.; Rouder, Jeffrey N.; Geary, David C.

    2016-01-01

    The conceptual insight that fractions represent magnitudes is a critical yet daunting step in children’s mathematical development, and the knowledge of fraction magnitudes influences children’s later mathematics learning including algebra. In this study, longitudinal data were analyzed to identify the mathematical knowledge and domain-general competencies that predicted 8th and 9th graders’ (n=122) knowledge of fraction magnitudes and its cross-grade gains. Performance on the fraction magnitude measures predicted 9th grade algebra achievement. Understanding and fluently identifying the numerator-denominator relation in 7th grade emerged as the key predictor of later fraction magnitudes knowledge in both 8th and 9th grades. Competence at using fraction procedures, knowledge of whole number magnitudes, and the central executive contributed to 9th but not 8th graders’ fraction magnitude knowledge, and knowledge of whole number magnitude contributed to cross-grade gains. The key results suggest fluent processing of numerator-denominator relations presages students’ understanding of fractions as magnitudes and that the integration of whole number and fraction magnitudes occurs gradually. PMID:27773965

  5. 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.

  6. Reading Stories to Learn Math: Mathematics Vocabulary Instruction for Children with Early Numeracy Difficulties

    PubMed Central

    Hassinger-Das, Brenna; Jordan, Nancy C.; Dyson, Nancy

    2015-01-01

    The present study involved examining whether a storybook reading intervention targeting mathematics vocabulary, such as “equal,” “more,” and “less,” and associated number concepts would increase at-risk children’s vocabulary knowledge and number competencies. Children with early numeracy difficulties (N = 124) were recruited from kindergarten classes in four schools. Participants were randomly assigned to one of three groups: a storybook number competencies (SNC) intervention, a number sense intervention, or a business-as-usual control. Interventions were carried out in groups of four children over 8 weeks (24 thirty-minute sessions). Findings demonstrated that the SNC intervention group outperformed the other groups on measures of mathematics vocabulary, both in terms of words that were closely aligned to the intervention and those that were not. There was no effect of the SNC intervention, however, on general mathematics measures, suggesting a need to provide the mathematics vocabulary work along with more intensive instruction in number concepts. PMID:26726261

  7. 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.

  8. Mario Bunge's Philosophy of Mathematics: An Appraisal

    ERIC Educational Resources Information Center

    Marquis, Jean-Pierre

    2012-01-01

    In this paper, I present and discuss critically the main elements of Mario Bunge's philosophy of mathematics. In particular, I explore how mathematical knowledge is accounted for in Bunge's systemic emergent materialism.

  9. Connecting Advanced and Secondary Mathematics

    ERIC Educational Resources Information Center

    Murray, Eileen; Baldinger, Erin; Wasserman, Nicholas; Broderick, Shawn; White, Diana

    2017-01-01

    There is an ongoing debate among scholars in understanding what mathematical knowledge secondary teachers should have in order to provide effective instruction. We explore connections between advanced and secondary mathematics as an entry point into this debate. In many cases, advanced mathematics is considered relevant for secondary teachers…

  10. Students' Relationships with Mathematics: Affect and Identity

    ERIC Educational Resources Information Center

    Ingram, Naomi

    2015-01-01

    In this paper, an examination of students' relationships with mathematics is informed by affective research into internal mathematical structures and identity research into students' narratives. By analysing the perceptions of a class of 31 adolescents, five interacting elements emerged: students' views, feelings, mathematical knowledge,…

  11. 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…

  12. Assessment and Learning of Mathematics.

    ERIC Educational Resources Information Center

    Leder, Gilah C., Ed.

    This book addresses the link between student learning of mathematics, the teaching method adopted in the mathematics classroom, and the assessment procedures used to determine and measure student knowledge. Fifteen chapters address issues that include a review of different models of mathematics learning and assessment practices, three contrasting…

  13. Clinical Assessment in Mathematics: Learning the Craft.

    ERIC Educational Resources Information Center

    Hunting, Robert P.; Doig, Brian A.

    1997-01-01

    Discusses a professional development program called Clinical Approaches to Mathematics Assessment. Argues for the advanced training of mathematics teachers who understand knowledge construction processes of students; can use clinical tools for evaluating a student's unique mathematical "fingerprint"; and can create or adapt problems, tasks, or…

  14. Which Preschool Mathematics Competencies Are Most Predictive of Fifth Grade Achievement?

    PubMed Central

    Nguyen, Tutrang; Watts, Tyler W.; Duncan, Greg J.; Clements, Douglas H.; Sarama, Julie S.; Wolfe, Christopher; Spitler, Mary Elaine

    2016-01-01

    In an effort to promote best practices regarding mathematics teaching and learning at the preschool level, national advisory panels and organizations have emphasized the importance of children’s emergent counting and related competencies, such as the ability to verbally count, maintain one-to-one correspondence, count with cardinality, subitize, and count forward or backward from a given number. However, little research has investigated whether the kind of mathematical knowledge promoted by the various standards documents actually predict later mathematics achievement. The present study uses longitudinal data from a primarily low-income and minority sample of children to examine the extent to which preschool mathematical competencies, specifically basic and advanced counting, predict fifth grade mathematics achievement. Using regression analyses, we find early numeracy abilities to be the strongest predictors of later mathematics achievement, with advanced counting competencies more predictive than basic counting competencies. Our results highlight the significance of preschool mathematics knowledge for future academic achievement. PMID:27057084

  15. Competence with Fractions Predicts Gains in Mathematics Achievement

    PubMed Central

    Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

    2012-01-01

    Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

  16. 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…

  17. UCSMP Algebra. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "University of Chicago School Mathematics Project (UCSMP) Algebra," designed to increase students' skills in algebra, is appropriate for students in grades 7-10, depending on the students' incoming knowledge. This one-year course highlights applications, uses statistics and geometry to develop the algebra of linear equations and inequalities, and…

  18. Review of Student Difficulties in Upper-Level Quantum Mechanics

    ERIC Educational Resources Information Center

    Singh, Chandralekha; Marshman, Emily

    2015-01-01

    Learning advanced physics, in general, is challenging not only due to the increased mathematical sophistication but also because one must continue to build on all of the prior knowledge acquired at the introductory and intermediate levels. In addition, learning quantum mechanics can be especially challenging because the paradigms of classical…

  19. Developing a National STEM Workforce Strategy: A Workshop Summary

    ERIC Educational Resources Information Center

    Alper, Joe

    2016-01-01

    The future competitiveness of the United States in an increasingly interconnected global economy depends on the nation fostering a workforce with strong capabilities and skills in science, technology, engineering, and mathematics (STEM). STEM knowledge and skills enable both individual opportunity and national competitiveness, and the nation needs…

  20. Early Predictors of Middle School Fraction Knowledge

    PubMed Central

    Bailey, Drew H.; Siegler, Robert S.; Geary, David C.

    2014-01-01

    Recent findings that earlier fraction knowledge predicts later mathematics achievement raise the question of what predicts later fraction knowledge. Analyses of longitudinal data indicated that whole number magnitude knowledge in first grade predicted knowledge of fraction magnitudes in middle school, controlling for whole number arithmetic proficiency, domain general cognitive abilities, parental income and education, race, and gender. Similarly, knowledge of whole number arithmetic in first grade predicted knowledge of fraction arithmetic in middle school, controlling for whole number magnitude knowledge in first grade and the other control variables. In contrast, neither type of early whole number knowledge uniquely predicted middle school reading achievement. We discuss the implications of these findings for theories of numerical development and for improving mathematics learning. PMID:24576209

  1. How Do Kindergarteners Express Their Mathematics Understanding?

    ERIC Educational Resources Information Center

    Johns, Kyoko

    2015-01-01

    This article describes how kindergarten students represent their understanding of mathematical knowledge. The study examines the students' use of oral expressions, drawings, written language, and gestures when communicating mathematically with their classmates and teacher.

  2. An Analysis of the Changes in Ability and Knowledge of Students Taking A-Level Physics and Mathematics over a 35 Year Period

    ERIC Educational Resources Information Center

    Barham, Peter J.

    2012-01-01

    New undergraduate students arriving to study physics at the University of Bristol from 1975 onwards have all taken the same test of their knowledge and understanding of physics and mathematics. Many of the questions test knowledge of material that has been in the A-level syllabus for maths or physics throughout this period. The ability of incoming…

  3. Measuring Computer Science Knowledge Level of Hungarian Students Specialized in Informatics with Romanian Students Attending a Science Course or a Mathematics-Informatics Course

    ERIC Educational Resources Information Center

    Kiss, Gabor

    2012-01-01

    An analysis of Information Technology knowledge of Hungarian and Romanian students was made with the help of a self developed web based Informatics Test. The goal of this research is an analysis of the Computer Science knowledge level of Hungarian and Romanian students attending a Science course or a Mathematics-Informatics course. Analysed was…

  4. Examining Thai high school students' developing STEM projects

    NASA Astrophysics Data System (ADS)

    Teenoi, Kultida; Siripun, Kulpatsorn; Yuenyong, Chokchai

    2018-01-01

    Like others, Thailand education strongly focused on STEM education. This paper aimed to examine existing Thai high school students' integrated knowledge about science, technology, engineering, and mathematics (STEM) in their developing science project. The participants included 49 high school students were studying the subject of individual study (IS) in Khon Kaen wittayayon school, Khon Kaen, Thailand. The IS was provided to gradually enhance students to know how to do science project starting from getting start to do science projects, They enrolled to study the individual study of science project for three year in roll. Methodology was qualitative research. Views of students' integrated knowledge about STEM were interpreted through participant observation, interview, and students' science projects. The first author as participant observation has taught this group of students for 3 years. It found that 16 science projects were developed. Views of students' integrated knowledge about STEM could be categorized into three categories. These included (1) completely indicated integration of knowledge about science, technology, engineering, and mathematics, (2) partial indicated integration of knowledge about science, technology, engineering, and mathematics, and (3) no integration. The findings revealed that majority of science projects could be categorized as completely indicated integration of knowledge about science, technology, engineering, and mathematics. The paper suggested some ideas of enhancing students to applying STEM for developing science projects.

  5. Enhancing students’ mathematical representation and selfefficacy through situation-based learning assisted by geometer’s sketchpad program

    NASA Astrophysics Data System (ADS)

    Sowanto; Kusumah, Y. S.

    2018-05-01

    This research was conducted based on the problem of a lack of students’ mathematical representation ability as well as self-efficacy in accomplishing mathematical tasks. To overcome this problem, this research used situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP). This research investigated students’ improvement of mathematical representation ability who were taught under situation-based learning (SBL) assisted by geometer’s sketchpad program (GSP) and regular method that viewed from the whole students’ prior knowledge (high, average, and low level). In addition, this research investigated the difference of students’ self-efficacy after learning was given. This research belongs to quasi experiment research using non-equivalent control group design with purposive sampling. The result of this research showed that students’ enhancement in their mathematical representation ability taught under SBL assisted by GSP was better than the regular method. Also, there was no interaction between learning methods and students prior knowledge in student’ enhancement of mathematical representation ability. There was significant difference of students’ enhancement of mathematical representation ability taught under SBL assisted by GSP viewed from students’ prior knowledge. Furthermore, there was no significant difference in terms of self-efficacy between those who were taught by SBL assisted by GSP with the regular method.

  6. Construction of Mathematical Knowledge Using Graphic Calculators (CAS) in the Mathematics Classroom

    ERIC Educational Resources Information Center

    Hitt, Fernando

    2011-01-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics…

  7. An Investigation of Teachers' Noticing, Cognitive Demand, and Mathematical Knowledge for Teaching: Video Reflections in an Elementary Mathematics Context

    ERIC Educational Resources Information Center

    Coddington, Lorelei R.

    2014-01-01

    In the past decade, mathematics performance by all students, especially minority students in low socioeconomic schools, has shown limited improvement nationwide (NCES, 2011). Traditionally in the United States, mathematics has consisted of arithmetic and computational fluency; however, mathematics researchers widely believe that this method of…

  8. Quality of Teaching Mathematics and Learning Achievement Gains: Evidence from Primary Schools in Kenya

    ERIC Educational Resources Information Center

    Ngware, Moses W.; Ciera, James; Musyoka, Peter K.; Oketch, Moses

    2015-01-01

    This paper examines the contribution of quality mathematics teaching to student achievement gains. Quality of mathematics teaching is assessed through teacher demonstration of the five strands of mathematical proficiency, the level of cognitive task demands, and teacher mathematical knowledge. Data is based on 1907 grade 6 students who sat for the…

  9. Enabling Metacognitive Skills for Mathematics Problem Solving: A Collective Case Study of Metacognitive Reflection and Awareness

    ERIC Educational Resources Information Center

    Jagals, Divan; van der Walt, Marthie

    2016-01-01

    Metacognition encompasses knowledge and regulation that, through reflection, sustain problem solving behaviour. How metacognitive awareness is constructed from reflection on metacognitive knowledge and regulation and how these reflections enable metacognitive skills for Mathematics problem solving remain unclear. Three secondary schools…

  10. Argumentative Knowledge Construction in an Online Graduate Mathematics Course: A Case Study

    ERIC Educational Resources Information Center

    Bayazit, Nermin; Clarke, Pier Angeli Junor; Vidakovic, Draga

    2018-01-01

    The authors report on three students' argumentative knowledge construction in an asynchronous online graduate level geometry course designed for in-service secondary mathematics (ISM) teachers. Using Weinberger and Fischer's framework, they analyzed the ISM teachers' (a) geometry autobiography and (b) discussion board posts (both comments and…

  11. The Commerce of Utility: Teaching Mathematical Geography in Early Modern England

    ERIC Educational Resources Information Center

    Cormack, Lesley B.

    2006-01-01

    The teaching and learning of geographical and mathematical knowledge in early modern England was a complex interaction among scholars, practitioners, merchants, and gentry. Each group had different values and goals associated with geographical knowledge and therefore different educational venues and different topics to be investigated. This paper…

  12. Beyond Epistemological Deficits: Dynamic Explanations of Engineering Students' Difficulties with Mathematical Sense-Making

    ERIC Educational Resources Information Center

    Gupta, Ayush; Elby, Andrew

    2011-01-01

    Researchers have argued against deficit-based explanations of students' difficulties with mathematical sense-making, pointing instead to factors such as epistemology. Students' beliefs about knowledge and learning can hinder the activation and integration of productive knowledge they have. Such explanations, however, risk falling into a…

  13. Pretend Play and the Cultural Foundations of Mathematics

    ERIC Educational Resources Information Center

    Worthington, Maulfry; van Oers, Bert

    2016-01-01

    The aim of this study is to uncover the emergence of cultural mathematical understandings and communications in young children's spontaneous pretend play. It is based on Vygotskian cultural-historical perspectives and social-semiotic theory, informed by research into "funds of knowledge" and considers how children's informal knowledge of…

  14. Deaf College Students' Mathematical Skills Relative to Morphological Knowledge, Reading Level, and Language Proficiency

    ERIC Educational Resources Information Center

    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…

  15. Family Child Care Learning Environments: Caregiver Knowledge and Practices Related to Early Literacy and Mathematics

    ERIC Educational Resources Information Center

    Phillips, Beth M.; Morse, Erika E.

    2011-01-01

    This paper presents findings from a stratified-random survey of family child care providers' backgrounds, caregiving environments, practices, attitudes, and knowledge related to language, literacy, and mathematics development for preschool children. Descriptive results are consistent with prior studies suggesting that home-based providers are…

  16. Modelling in Primary School: Constructing Conceptual Models and Making Sense of Fractions

    ERIC Educational Resources Information Center

    Shahbari, Juhaina Awawdeh; Peled, Irit

    2017-01-01

    This article describes sixth-grade students' engagement in two model-eliciting activities offering students the opportunity to construct mathematical models. The findings show that students utilized their knowledge of fractions including conceptual and procedural knowledge in constructing mathematical models for the given situations. Some students…

  17. 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)…

  18. Enhancing Thinking Skills in the Sciences and Mathematics.

    ERIC Educational Resources Information Center

    Halpern, Diane F., Ed.

    The need to provide an improved science and mathematics curriculum is imperative. Over recent years cognitive psychologists and educators have responded to this need by designing instructional programs that are more compatible with our knowledge of how people acquire, use, and retain knowledge. This book contains many of the guiding principles…

  19. 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…

  20. Agency as Inference: Toward a Critical Theory of Knowledge Objectification

    ERIC Educational Resources Information Center

    Gutiérrez, José Francisco

    2013-01-01

    This article evaluates the plausibility of synthesizing theory of knowledge objectification (Radford, 2003) with equity research on mathematics education. I suggest the cognitive phenomenon of mathematical inference as a promising locus for investigating the types of agency that equity-driven scholars often care for. In particular, I conceptualize…

  1. 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…

  2. 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…

  3. 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…

  4. 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.

  5. 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…

  6. The Mathematical Preparation of Prospective Elementary Teachers: Reflections from Solving an "Interesting Problem"

    ERIC Educational Resources Information Center

    Ellis, Mark W.; Contreras, Jose; Martinez-Cruz, Armando M.

    2009-01-01

    Problem solving tasks offer valuable opportunities to strengthen prospective elementary teachers' knowledge of and disposition toward mathematics, providing them with new experiences doing mathematics. Mathematics educators can influence future instruction by modeling effective pedagogical strategies that engage students in making sense of…

  7. Multiple Proof Approaches and Mathematical Connections

    ERIC Educational Resources Information Center

    Jiang, Zhonghong; O'Brien, George E.

    2012-01-01

    One of the most rewarding accomplishments of working with preservice secondary school mathematics teachers is helping them develop conceptually connected knowledge and see mathematics as an integrated whole rather than isolated pieces. To help students see and use the connections among various mathematical topics, the authors have paid close…

  8. Understanding the Chinese Approach to Creative Teaching in Mathematics Classrooms

    ERIC Educational Resources Information Center

    Niu, Weihua; Zhou, Zheng; Zhou, Xinlin

    2017-01-01

    Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…

  9. Cognitive and Neural Correlates of Mathematical Giftedness in Adults and Children: A Review

    PubMed Central

    Myers, Timothy; Carey, Emma; Szűcs, Dénes

    2017-01-01

    Most mathematical cognition research has focused on understanding normal adult function and child development as well as mildly and moderately impaired mathematical skill, often labeled developmental dyscalculia and/or mathematical learning disability. In contrast, much less research is available on cognitive and neural correlates of gifted/excellent mathematical knowledge in adults and children. In order to facilitate further inquiry into this area, here we review 40 available studies, which examine the cognitive and neural basis of gifted mathematics. Studies associated a large number of cognitive factors with gifted mathematics, with spatial processing and working memory being the most frequently identified contributors. However, the current literature suffers from low statistical power, which most probably contributes to variability across findings. Other major shortcomings include failing to establish domain and stimulus specificity of findings, suggesting causation without sufficient evidence and the frequent use of invalid backward inference in neuro-imaging studies. Future studies must increase statistical power and neuro-imaging studies must rely on supporting behavioral data when interpreting findings. Studies should investigate the factors shown to correlate with math giftedness in a more specific manner and determine exactly how individual factors may contribute to gifted math ability. PMID:29118725

  10. 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.

  11. How students learn to coordinate knowledge of physical and mathematical models in cellular physiology

    NASA Astrophysics Data System (ADS)

    Lira, Matthew

    This dissertation explores the Knowledge in Pieces (KiP) theory to account for how students learn to coordinate knowledge of mathematical and physical models in biology education. The KiP approach characterizes student knowledge as a fragmented collection of knowledge elements as opposed to stable and theory-like knowledge. This dissertation sought to use this theoretical lens to account for how students understand and learn with mathematical models and representations, such as equations. Cellular physiology provides a quantified discipline that leverages concepts from mathematics, physics, and chemistry to understand cellular functioning. Therefore, this discipline provides an exemplary context for assessing how biology students think and learn with mathematical models. In particular, the resting membrane potential provides an exemplary concept well defined by models of dynamic equilibrium borrowed from physics and chemistry. In brief, membrane potentials, or voltages, "rest" when the electrical and chemical driving forces for permeable ionic species are equal in magnitude but opposite in direction. To assess students' understandings of this concept, this dissertation employed three studies: the first study employed the cognitive clinical interview to assess student thinking in the absence and presence of equations. The second study employed an intervention to assess student learning and the affordances of an innovative assessment. The third student employed a human-computer-interaction paradigm to assess how students learn with a novel multi-representational technology. Study 1 revealed that students saw only one influence--the chemical gradient--and that students coordinated knowledge of only this gradient with the related equations. Study 2 revealed that students benefited from learning with the multi-representational technology and that the assessment detected performance gains across both calculation and explanation tasks. Last, Study 3 revealed how students shift from recognizing one influence to recognizing both the chemical and the electrical gradients as responsible for a cell's membrane potential reaching dynamic equilibrium. Together, the studies illustrate that to coordinate knowledge, students need opportunities to reflect upon relations between representations of mathematical and physical models as well as distinguish between physical quantities such as molarities for ions and transmembrane voltages.

  12. Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability

    NASA Astrophysics Data System (ADS)

    Juandi, D.; Priatna, N.

    2018-05-01

    The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.

  13. 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…

  14. How Young Students Communicate Their Mathematical Problem Solving in Writing

    ERIC Educational Resources Information Center

    Teledahl, Anna

    2017-01-01

    This study investigates young students' writing in connection to mathematical problem solving. Students' written communication has traditionally been used by mathematics teachers in the assessment of students' mathematical knowledge. This study rests on the notion that this writing represents a particular activity which requires a complex set of…

  15. 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…

  16. Learning over Time: Learning Trajectories in Mathematics Education

    ERIC Educational Resources Information Center

    Maloney, Alan P., Ed.; Confrey, Jere, Ed.; Nguyen, Kenny H., Ed.

    2014-01-01

    The driving forces behind mathematics learning trajectories is the need to understand how children actually learn and make sense of mathematics--how they progress from prior knowledge, through intermediate understandings, to the mathematics target understandings--and how to use these insights to improve instruction and student learning. In this…

  17. Lexicography and Mathematics Learning: A Case Study of "Variable."

    ERIC Educational Resources Information Center

    Frawley, William

    1992-01-01

    Lexicography is shown to offer some useful new tools to researchers in mathematics education. The paper examines the relationship between the sublanguage of mathematics and the acquisition of mathematical knowledge, and also the use of definitions in research and curriculum design. An Explanatory Combinatorial Dictionary is advocated for improving…

  18. Developing Prospective Mathematics Teachers in Mexico: A Lesson on the Relationship between Integration and Differentiation

    ERIC Educational Resources Information Center

    Ponce-Campuzano, Juan Carlos

    2013-01-01

    Mexican authorities and universities are actively working to improve mathematics teaching and learning across the education system. Thus, efforts are underway to raise the historically low performance in mathematics, which include theoretically grounded pedagogy and curriculum development to raise mathematical knowledge in teacher education…

  19. The Microevolution of Mathematical Representations in Children's Activity.

    ERIC Educational Resources Information Center

    Meira, Luciano

    1995-01-01

    Discusses children's design of mathematical representations on paper. Suggests that the design of displays during problem solving shapes one's mathematical activity and sense making in crucial ways, and that knowledge of mathematical representations is not simply recalled and applied to problem solving, but also emerges out of one's interactions…

  20. Preservice Mathematics Teachers' Perceptions of Drama Based Instruction

    ERIC Educational Resources Information Center

    Bulut, Neslihan

    2016-01-01

    The purpose of this study was to determine the perceptions of pre-service mathematics teachers related to drama-based instruction. For this purpose, effects of a drama-based mathematics course on senior class pre-service mathematics teachers' knowledge about drama-based instruction and teacher candidates' competencies for developing and…

  1. Mathematical Problem Solving Ability of Eleventh Standard Students

    ERIC Educational Resources Information Center

    Priya, J. Johnsi

    2017-01-01

    There is a general assertion among mathematics instructors that learners need to acquire problem solving expertise, figure out how to communicate using mathematics knowledge and aptitude, create numerical reasoning and thinking, to see the interconnectedness amongst mathematics and other subjects. Based on this perspective, the present study aims…

  2. Investigating Engineering Practice Is Valuable for Mathematics Learning

    ERIC Educational Resources Information Center

    Goold, Eileen

    2015-01-01

    While engineering mathematics curricula often prescribe a fixed body of mathematical knowledge, this study takes a different approach; second-year engineering students are additionally required to investigate and document an aspect of mathematics used in engineering practice. A qualitative approach is used to evaluate the impact that students'…

  3. Evidence of the Need to Prepare Prospective Teachers to Engage in Mathematics Consultations

    ERIC Educational Resources Information Center

    van Ingen, Sarah; Eskelson, Samuel L.; Allsopp, David

    2016-01-01

    The mathematics consultation represents a powerful opportunity for mathematics teachers to leverage the knowledge base of special education professionals to advance equity for students with special education needs. Yet, most teacher preparation programs do not specifically prepare prospective teachers to engage in mathematics-specific…

  4. Changes in Elementary Mathematics Teachers' Understanding of Cognitive Demand: When Adapting, Creating, and Using Mathematical Performance Tasks

    ERIC Educational Resources Information Center

    Jamieson, Thad Spencer

    2015-01-01

    The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…

  5. The Teaching of Mathematics in Secondary Schools as a Tool for Self-Reliance and Re-Branding Process in Nigeria

    ERIC Educational Resources Information Center

    Jonah, Tali D.; Caleb, Mbwas .L.; Stephen, Abe A.

    2012-01-01

    Mathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching…

  6. A cognitive framework for analyzing and describing introductory students' use and understanding of mathematics in physics

    NASA Astrophysics Data System (ADS)

    Tuminaro, Jonathan

    Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of mathematical use in the context physics, and (2) a detailed understanding, in terms of the proposed theoretical framework, of the errors that students make when using mathematics in the context of physics.

  7. Strengthening Connections between Elementary Classroom Mathematics and Literacy

    ERIC Educational Resources Information Center

    Altieri, Jennifer L.

    2009-01-01

    Enjoyable literacy strategies help elementary teachers reinforce students' mathematics knowledge. This article shares a number of literacy strategies that can easily connect with mathematics. These strategies include word associations, multimeaning word cards, and games. (Contains 7 figures.)

  8. Investigating the School Teacher's Preparation in Mathematics Pedagogy in Ukraine

    ERIC Educational Resources Information Center

    Tarasenkova, N. A.; Akulenko, I. A.

    2015-01-01

    Teacher education has become an area of considerable interest among policymakers in many countries over recent years. Teacher's knowledge and skills in qualified teaching is of great importance. The main purpose was to study the level and depth of the school mathematics and related teaching knowledge attained by prospective Ukrainian secondary…

  9. 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…

  10. Embracing "Nepantla": Rethinking "Knowledge" and Its Use in Mathematics Teaching

    ERIC Educational Resources Information Center

    Gutiérrez, Rochelle

    2012-01-01

    Although educational researchers are moving beyond purely psychological and cognitive models of learning to consider the ways in which mathematics teaching might reach a more diverse student population, this work remains in its infancy, and the concept of "knowledge" is rarely questioned. This paper begins with the idea that mathematics…

  11. Creative Reasoning and Shifts of Knowledge in the Mathematics Classroom

    ERIC Educational Resources Information Center

    Hershkowitz, Rina; Tabach, Michal; Dreyfus, Tommy

    2017-01-01

    In the course of the last few years, we have investigated shifts of knowledge among different settings in inquiry-based mathematics classrooms: the individual, the small group and the whole class community. The different theoretical perspectives we used for analysing group work and for analysing whole class discussions, and the empirical data, led…

  12. Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

    2017-01-01

    This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

  13. Vamos a Jugar Counters! Learning Mathematics through Funds of Knowledge, Play, and the Third Space

    ERIC Educational Resources Information Center

    Razfar, Aria

    2012-01-01

    Drawing on Cultural Historical Activity Theory (CHAT), funds of knowledge, and third space, this article presents a model for practitioners and researchers to think about how Latina/o, bilingual children develop explicit mathematics strategies through multilingual and multigenerational interactions. Using data collected through fieldwork in an…

  14. Mathematical Learning Models that Depend on Prior Knowledge and Instructional Strategies

    ERIC Educational Resources Information Center

    Pritchard, David E.; Lee, Young-Jin; Bao, Lei

    2008-01-01

    We present mathematical learning models--predictions of student's knowledge vs amount of instruction--that are based on assumptions motivated by various theories of learning: tabula rasa, constructivist, and tutoring. These models predict the improvement (on the post-test) as a function of the pretest score due to intervening instruction and also…

  15. Exploring Prospective Secondary Mathematics Teachers' Interpretation of Student Thinking through Analysing Students' Work in Modelling

    ERIC Educational Resources Information Center

    Didis, Makbule Gozde; Erbas, Ayhan Kursat; Cetinkaya, Bulent; Cakiroglu, Erdinc; Alacaci, Cengiz

    2016-01-01

    Researchers point out the importance of teachers' knowledge of student thinking and the role of examining student work in various contexts to develop a knowledge base regarding students' ways of thinking. This study investigated prospective secondary mathematics teachers' interpretations of students' thinking as manifested in students' work that…

  16. "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…

  17. Measurement in the Service of Mathematics Education Research: The Case of Cognitively Guided Instruction

    ERIC Educational Resources Information Center

    Helding, Brandon Alan

    2010-01-01

    The purpose of this dissertation is to demonstrate one iterate of a process for developing a measurement instrument for student knowledge within educational interventions. Student mathematical knowledge is framed within Cognitively Guided Instruction (CGI) and its tenets. That is, the construct underlying the measurement instrument corresponded…

  18. Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

    ERIC Educational Resources Information Center

    Hatisaru, Vesife; Erbas, Ayhan Kursat

    2017-01-01

    The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…

  19. Microteaching Lesson Study: Mentor Interaction Structure and Its Relation to Elementary Preservice Mathematics Teacher Knowledge Development

    ERIC Educational Resources Information Center

    Molina, Roxanne V.

    2012-01-01

    This study investigated Microteaching Lesson Study (MLS) and three possible MLS mentor interaction structures during the debriefing sessions in relation to elementary preservice teacher development of knowledge for teaching. One hundred three elementary preservice teachers enrolled in five different sections of a mathematics methods course at a…

  20. With an Eye on the Mathematical Horizon: Dilemmas of Teaching Elementary School Mathematics. Craft Paper 90-3.

    ERIC Educational Resources Information Center

    Ball, Deborah Loewenberg

    Much educational discourse centers on the importance of teachers' subject matter knowledge. Complementing concerns for subject matter knowledge is interest in developing and studying alternative pedagogies that emphasize active learning and meaningful engagement. Teaching and learning would be improved, so the argument goes, if classrooms were…

  1. A Collaborative Inquiry to Promote Pedagogical Knowledge of Mathematics in Practice

    ERIC Educational Resources Information Center

    Moghaddam, Alireza; Sarkar Arani, Mohammad Reza; Kuno, Hiroyuki

    2015-01-01

    The present study attempts to report a collaborative cycle of professional development in teaching elementary school mathematics through lesson study. It explores a practice of lesson study conducted by teachers aiming to improve their knowledge of pedagogy. The study adopts an ethnographic approach to examine how collaborative teaching within an…

  2. 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.

  3. Modal Representations and Their Role in the Learning Process: A Theoretical and Pragmatic Analysis

    ERIC Educational Resources Information Center

    Gunel, Murat; Yesildag-Hasancebi, Funda

    2016-01-01

    In the construction and sharing of scientific knowledge, modal representations such as text, graphics, pictures, and mathematical expressions are commonly used. Due to the increasing importance of their role in the production and communication of science, modal representations have become a topic of growing interest in science education research…

  4. Psychology of Working Narratives of STEM Career Exploration for Non-Dominant Youth

    ERIC Educational Resources Information Center

    Mark, Sheron L.

    2016-01-01

    Science, technology, engineering, and mathematics (STEM) is a domain of knowledge, skills, and practices that is pervasive and of critical importance in our highly technological, rapidly advancing, and increasingly connected world; however, non-dominant youth, namely from non-White, lower-income, non-English-speaking, and immigrant backgrounds,…

  5. Evaluation of the Effect of a Digital Mathematics Game on Academic Achievement

    ERIC Educational Resources Information Center

    Wale, Christine M.

    2013-01-01

    Digital games are widely popular and interest has increased for their use in education. Digital games are thought to be powerful instructional tools because they promote active learning and feedback, provide meaningful contexts to situate knowledge, create engagement and intrinsic motivation, and have the ability individualize instruction.…

  6. Increasing Middle School Student Interest in STEM Careers with Videos of Scientists

    ERIC Educational Resources Information Center

    Wyss, Vanessa L.; Heulskamp, Diane; Siebert, Cathy J.

    2012-01-01

    Students are making choices in middle school that will impact their desire and ability to pursue STEM careers. Providing middle school students with accurate information about STEM (Science, Technology, Engineering, Mathematics) careers enables them to make more knowledgeable choices about courses of study and career paths. Practical ways of…

  7. 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…

  8. Validation of Scores from a New Measure of Preservice Teachers' Self-Efficacy to Teach Statistics in the Middle Grades

    ERIC Educational Resources Information Center

    Harrell-Williams, Leigh M.; Sorto, M. Alejandra; Pierce, Rebecca L.; Lesser, Lawrence M.; Murphy, Teri J.

    2014-01-01

    The influential "Common Core State Standards for Mathematics" (CCSSM) expect students to start statistics learning during middle grades. Thus teacher education and professional development programs are advised to help preservice and in-service teachers increase their knowledge and confidence to teach statistics. Although existing…

  9. 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…

  10. Using the Principles of "BIO2010" to Develop an Introductory, Interdisciplinary Course for Biology Students

    ERIC Educational Resources Information Center

    Matthews, Kelly E.; Adams, Peter; Goos, Merrilyn

    2010-01-01

    Modern biological sciences require practitioners to have increasing levels of knowledge, competence, and skills in mathematics and programming. A recent review of the science curriculum at the University of Queensland, a large, research-intensive institution in Australia, resulted in the development of a more quantitatively rigorous undergraduate…

  11. Beyond Knowledge and Skills: Rethinking the Development of Professional Identity during the STEM Doctorate

    ERIC Educational Resources Information Center

    Hancock, Sally; Walsh, Elaine

    2016-01-01

    The science, technology, engineering, mathematics (STEM) doctorate is the established entry qualification for a scientific research career. However, contemporary STEM doctoral graduates assume increasingly diverse professional paths, with many forging non-academic careers. Using the UK as an example, the authors suggest that the STEM PhD fails to…

  12. KEMET Academy: A University Outreach Model for Addressing the Wholeness of Learning in a Rural Context

    ERIC Educational Resources Information Center

    Davis, Dannielle Joy; Davis-Maye, Denise; Thomas, Chippewa M.; Seals, Cheryl; Alfred, Dorienna M.; Tripp, Lucretia Octavia; King-Jupiter, Kimberly L.; Lovett, Garnetta Laverne

    2011-01-01

    This work introduces a model of university outreach in rural communities which promotes increasing post-secondary options for rural dwelling African American youth. KEMET (Knowledge and Excellence in Mathematics, Equilibrium, and Technology) Academy is a comprehensive academic enrichment program targeting African American students enrolled in…

  13. Instructor Facilitation of Whole-Class Discussion in Two Mathematics Classes for Preservice Teachers

    ERIC Educational Resources Information Center

    Young, Sarah Helen

    2014-01-01

    This study investigated how instructors engage preservice teachers (PSTs) in whole-class discussion in mathematics classes for PSTs. Participating in discussions of mathematical ideas by explaining mathematical ideas to others and responding to others' ideas and arguments might be beneficial for PSTs both to help them develop deeper knowledge of…

  14. Mathematics Learning Styles of Chinese Immigrant Students. Final Research Report.

    ERIC Educational Resources Information Center

    Tsang, Sau-Lim

    Major revision in the U.S. mathematics curriculum since the 1960s have led to significant differences between the mathematics curriculum of the United States and those of many other countries. This study explored how eight Chinese immigrant students, with different cultural backgrounds, mathematics knowledge, and learning styles, learned in an…

  15. An Ideology Critique of the Use-Value of Mathematics

    ERIC Educational Resources Information Center

    Pais, Alexandre

    2013-01-01

    The idea that mathematics is needed for our mundane everyday activities has raised the question of how people deal with mathematics outside the school walls. Much has been written in mathematics education research about the possibility of transferring knowledge from and into school. Whereas the majority of this literature commends the possibility…

  16. 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…

  17. National Mathematics Advisory Panel Reports of the Task Groups and Subcommittees

    ERIC Educational Resources Information Center

    US Department of Education, 2008

    2008-01-01

    For students to compete in the 21st-century global economy, knowledge of and proficiency in mathematics are critical. Whether headed to college or to the workforce, today's high school graduates need solid mathematics skill. The National Mathematics Advisory Panel was created in 2006 and charged with reviewing the best available scientific…

  18. Understanding Prospective Teachers' Mathematical Modeling Processes in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat

    2017-01-01

    This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…

  19. Reframing Research on Methods Courses to Inform Mathematics Teacher Educators' Practice

    ERIC Educational Resources Information Center

    Kastberg, Signe E.; Tyminski, Andrew M.; Sanchez, Wendy B.

    2017-01-01

    Calls have been made for the creation of a shared knowledge base in mathematics teacher education with the power to inform the design of scholarly inquiry and mathematics teacher educators' (MTEs) scholarly practices. Focusing on mathematics methods courses, we summarize and contribute to literature documenting activities MTEs use in mathematics…

  20. Adolescent Mathematical Problem Solving: The Role of Metacognition, Strategies and Beliefs.

    ERIC Educational Resources Information Center

    Fitzpatrick, Corine

    Mathematical problem solving has been the focus of much concern. This study investigated the relationship of various cognitive factors, attributions, and gender to the solution of mathematics problems by 100 high school seniors. The independent variables examined in this study included: (1) mathematics knowledge as measured by a score on the…

  1. An Interview with the 1985 USA Team to the International Mathematical Olympiad.

    ERIC Educational Resources Information Center

    Page, Warren

    1985-01-01

    This interview with the six members of the 1985 American team to the International Mathematical Olympiad (IMO) focuses on such areas as their evolving mathematical knowledge, mathematical pursuits, accomplishments, and interests. Also included are biographical sketches of the team members and the 1985 IMO problems (with solutions). (JN)

  2. The Effects of STEM PBL on Students' Mathematical and Scientific Vocabulary Knowledge

    ERIC Educational Resources Information Center

    Bilgin, Ali; Boedeker, Peter; Capraro, Robert M.; Capraro, Mary M.

    2015-01-01

    Vocabulary is at the surface level of language usage; thus, students need to develop mathematical and scientific vocabulary to be able to explicitly communicate their mathematical and scientific reasoning with others. The National Council of Teachers of Mathematics (NCTM) and the National Science Teachers Association (NSTA) have both created…

  3. Asking Questions in First-Grade Mathematics Classes: Potential Influences on Mathematical Thought.

    ERIC Educational Resources Information Center

    Perry, Michelle; And Others

    1993-01-01

    Types of questions asked in first-grade mathematics classes in Japan, Taiwan, and the United States were investigated. Observations of 311 lessons by 16 Japanese, 20 Taiwanese, and 33 U.S. teachers suggest that the kinds of questions asked in Taiwan and Japan contribute to more sophisticated mathematical knowledge. (SLD)

  4. An Investigation of Prospective Secondary Mathematics Teachers' Conceptual Knowledge of and Attitudes Towards Statistics

    ERIC Educational Resources Information Center

    Hannigan, Ailish; Gill, Olivia; Leavy, Aisling M.

    2013-01-01

    The development of statistical literacy is fast becoming the focus of a large part of mathematics instruction at primary, secondary and tertiary levels. This broadening of the mathematics curriculum to encompass a focus on statistics makes considerable demands on teachers. Most mathematics teachers acknowledge the practical importance of…

  5. Competence with fractions predicts gains in mathematics achievement.

    PubMed

    Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

    2012-11-01

    Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

  6. Problem based learning - A brief review

    NASA Astrophysics Data System (ADS)

    Nunes, Sandra; Oliveira, Teresa A.; Oliveira, Amílcar

    2017-07-01

    Teaching is a complex mission that requires not only the theoretical knowledge transmission, but furthermore requires to provide the students the necessary skills for solving real problems in their respective professional activities where complex issues and problems must be frequently faced. Over more than twenty years we have been experiencing an increase in scholar failure in the scientific area of mathematics, which means that Teaching Mathematics and related areas can be even a more complex and hard task. Scholar failure is a complex phenomenon that depends on various factors as social factors, scholar factors or biophysical factors. After numerous attempts made in order to reduce scholar failure our goal in this paper is to understand the role of "Problem Based Learning" and how this methodology can contribute to the solution of both: increasing mathematical courses success and increasing skills in the near future professionals in Portugal. Before designing a proposal for applying this technique in our institutions, we decided to conduct a survey to provide us with the necessary information about and the respective advantages and disadvantages of this methodology, so this is the brief review aim.

  7. Estrategias Didácticas y Conocimiento Especializado de Profesores de Matemáticas. Un Caso en Álgebra Escolar = Teaching Strategies and Mathematics Teacher's Specialized Knowledge. A Case in School Algebra

    ERIC Educational Resources Information Center

    Sandoval, Ivonne; Solares Rojas, Armando; García-Campos, Montserrat

    2017-01-01

    We present results of the analysis of knowledge used by a secondary school mathematics teacher in her classroom practice. This knowledge takes shape and is displayed as specific teaching strategies in the management of her class when she incorporates Computer Algebra Systems. Based on observations of regular classes, we find that her knowledge…

  8. 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.

  9. Effects of Experiential Learning Approach on Students' Mathematical Creativity among Secondary School Students of Kericho East Sub-County, Kenya

    ERIC Educational Resources Information Center

    Chesimet, M. C.; Githua, B. N.; Ng'eno, J. K.

    2016-01-01

    Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for…

  10. A Mixed Methods Study of Teach for America Teachers' Mathematical Beliefs, Knowledge, and Classroom Teaching Practices during a Reform-Based University Mathematics Methods Course

    ERIC Educational Resources Information Center

    Swars, Susan Lee

    2015-01-01

    This mixed methods study examined the mathematical preparation of elementary teachers in a Teach for America (TFA) program, focal participants for whom there is scant extant research. Data collection occurred before and after a university mathematics methods course, with a particular focus on the participants' (n = 22) mathematical beliefs,…

  11. The Role of Cognitive Processes, Foundational Math Skill, and Calculation Accuracy and Fluency in Word-Problem Solving versus Pre-Algebraic Knowledge

    PubMed Central

    Fuchs, Lynn S.; Gilbert, Jennifer K.; Powell, Sarah R.; Cirino, Paul T.; Fuchs, Douglas; Hamlett, Carol L.; Seethaler, Pamela M.; Tolar, Tammy D.

    2016-01-01

    The purpose of this study was to examine child-level pathways in development of pre-algebraic knowledge versus word-problem solving, while evaluating the contribution of calculation accuracy and fluency as mediators of foundational skills/processes. Children (n = 962; mean 7.60 years) were assessed on general cognitive processes and early calculation, word-problem, and number knowledge at start of grade 2; calculation accuracy and calculation fluency at end of grade 2; and pre-algebraic knowledge and word-problem solving at end of grade 4. Important similarities in pathways were identified, but path analysis also indicated that language comprehension is more critical for later word-problem solving than pre-algebraic knowledge. We conclude that pathways in development of these forms of 4th-grade mathematics performance are more alike than different, but demonstrate the need to fine-tune instruction for strands of the mathematics curriculum in ways that address individual students’ foundational mathematics skills or cognitive processes. PMID:27786534

  12. 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.

  13. Number sense in the transition from natural to rational numbers.

    PubMed

    Van Hoof, Jo; Verschaffel, Lieven; Van Dooren, Wim

    2017-03-01

    Rational numbers are of critical importance both in mathematics and in other fields of science. However, they form a stumbling block for learners. One widely known source of the difficulty learners have with rational numbers is the natural number bias, that is the tendency to (inappropriately) apply natural number properties in rational number tasks. Still, it has been shown that a good understanding of natural numbers is highly predictive for mathematics achievement in general, and for performance on rational number tasks in particular. In this study, we further investigated the relation between learners' natural and rational number knowledge, specifically in cases where a natural number bias may lead to errors. Participants were 140 sixth graders from six different primary schools. Participants completed a symbolic and a non-symbolic natural number comparison task, a number line estimation task, and a rational number sense test. Learners' natural number knowledge was found to be a good predictor of their rational number knowledge. However, after first controlling for learners' general mathematics achievement, their natural number knowledge only predicted the subaspect of operations with rational numbers. The results of this study suggest that the relation between learners' natural and rational number knowledge can largely be explained by their relation with learners' general mathematics achievement. © 2016 The British Psychological Society.

  14. Upper Primary School Teachers' Mathematical Knowledge for Teaching Functional Thinking in Algebra

    ERIC Educational Resources Information Center

    Wilkie, Karina J.

    2014-01-01

    This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…

  15. 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)…

  16. 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…

  17. Problem-Based Learning--Buginese Cultural Knowledge Model--Case Study: Teaching Mathematics at Junior High School

    ERIC Educational Resources Information Center

    Cheriani, Cheriani; Mahmud, Alimuddin; Tahmir, Suradi; Manda, Darman; Dirawan, Gufran Darma

    2015-01-01

    This study aims to determine the differences in learning output by using Problem Based Model combines with the "Buginese" Local Cultural Knowledge (PBL-Culture). It is also explores the students activities in learning mathematics subject by using PBL-Culture Models. This research is using Mixed Methods approach that combined quantitative…

  18. Secondary Mathematics Teachers' Beliefs, Attitudes, Knowledge Base, and Practices in Meeting the Needs of English Language Learners

    ERIC Educational Resources Information Center

    Gann, Linda

    2013-01-01

    The research centered on secondary mathematics teachers' beliefs, attitudes, knowledge base, and practices in meeting the academic and language needs of English language learners. Using socio-cultural theory and social practice theory to frame the study, the research design employed a mixed methods approach incorporating self-reported surveys,…

  19. SKOPE-IT (Shareable Knowledge Objects as Portable Intelligent Tutors): Overlaying Natural Language Tutoring on an Adaptive Learning System for Mathematics

    ERIC Educational Resources Information Center

    Nye, Benjamin D.; Pavlik, Philip I., Jr.; Windsor, Alistair; Olney, Andrew M.; Hajeer, Mustafa; Hu, Xiangen

    2018-01-01

    Background: This study investigated learning outcomes and user perceptions from interactions with a hybrid intelligent tutoring system created by combining the AutoTutor conversational tutoring system with the Assessment and Learning in Knowledge Spaces (ALEKS) adaptive learning system for mathematics. This hybrid intelligent tutoring system (ITS)…

  20. 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…

  1. 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…

  2. Professional Knowledge Required When Teaching Mathematics for Numeracy in the Multiplicative Domain

    ERIC Educational Resources Information Center

    Mills, Judith

    2015-01-01

    This paper presents findings as part of a wider study that investigated the professional knowledge of teachers when teaching mathematics for numeracy in the primary school classroom. This paper focuses on teachers in action as they taught two lessons on multiplication. It outlines the specific pedagogical categories the teachers used and the…

  3. 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…

  4. Problem Solving as a Professional Development Strategy for Teachers: A Case Study with Fractions

    ERIC Educational Resources Information Center

    Perdomo-Díaz, Josefa; Felmer, Patricio; Randolph, Valeria; González, Guillermo

    2017-01-01

    In this paper we present a professional development course designed to impact on teachers' mathematical knowledge for teaching fractions. The main features of the course are the use of i) problem solving activities related with mathematical knowledge for teaching fractions ii) peer discussions and iii) monitor's interventions focused on answering…

  5. Children's Construction of Mathematical Knowledge in Solving Novel Isomorphic Problems in Concrete and Written Form.

    ERIC Educational Resources Information Center

    English, Lyn D.

    1996-01-01

    Presents case study data of low- and high-achieving nine-year olds focusing on construction and analogical transfer of mathematical knowledge during novel problem solving, as reflected in strategies for dealing with isomorphic combinatorial problems presented in hands-on and written form. Results showed that achievement level does not predict…

  6. The Impact of Assumed Knowledge Entry Standards on Undergraduate Mathematics Teaching in Australia

    ERIC Educational Resources Information Center

    King, Deborah; Cattlin, Joann

    2015-01-01

    Over the last two decades, many Australian universities have relaxed their selection requirements for mathematics-dependent degrees, shifting from hard prerequisites to assumed knowledge standards which provide students with an indication of the prior learning that is expected. This has been regarded by some as a positive move, since students who…

  7. Identification of Prospective Science Teachers' Mathematical-Logical Structures in Reference to Magnetism

    ERIC Educational Resources Information Center

    Yilmaz, Ismail

    2014-01-01

    This paper is a qualitative case study designed to identify prospective science teachers' mathematical-logical structures on the basis of their knowledge and achievement levels in magnetism. The study also made an attempt to reveal the effects of knowledge-level variables and procedural variables, which were considered to be potential…

  8. 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…

  9. Developing Mathematics Teacher Knowledge: The Paradidactic Infrastructure of "Open Lesson" in Japan

    ERIC Educational Resources Information Center

    Miyakawa, Takeshi; Winslow, Carl

    2013-01-01

    In this paper, we first present a theoretical approach to study mathematics teacher knowledge and the conditions for developing it, which is firmly rooted in a systemic approach to didactic phenomena at large, namely the anthropological theory of the didactic. Then, a case of open lesson is presented and analysed, using this theoretical approach,…

  10. Approaches to Teaching in Thematic Work: Early Childhood Teachers' Integration of Mathematics and Art

    ERIC Educational Resources Information Center

    Björklund, Camilla; Ahlskog-Björkman, Eva

    2017-01-01

    Thematic work that integrates different knowledge areas is considered suitable for developing young children's knowledge and skills in early childhood education. This paper reports evidence from a survey of early childhood teachers' work with mathematics and art integrated in thematic work. In this study, we aim to explore how teachers perceive…

  11. STEM Learning Research through a Funds of Knowledge Lens

    ERIC Educational Resources Information Center

    Civil, Marta

    2016-01-01

    This article examines STEM learning as a cultural process with a focus on non-dominant communities. Building on my work in funds of knowledge and mathematics education, I present three vignettes to raise some questions around connections between in-school and out-of-school mathematics. How do we define competence? How do task and environment…

  12. Socioeconomic Status and Preschoolers' Mathematical Knowledge: The Contribution of Home Activities and Parent Beliefs

    ERIC Educational Resources Information Center

    DeFlorio, Lydia; Beliakoff, Amber

    2015-01-01

    Research Findings: Children from families of lower socioeconomic status (SES) enter kindergarten with less developed mathematical knowledge compared to children from middle SES families. This discrepancy is present at age 3 years and likely stems from differences in the home learning environment. This study reports SES-related differences both in…

  13. An Investigation of Pattern Problems Posed by Middle School Mathematics Preservice Teachers Using Multiple Representation

    ERIC Educational Resources Information Center

    Yilmaz, Yasemin; Durmus, Soner; Yaman, Hakan

    2018-01-01

    This study investigated the pattern problems posed by middle school mathematics preservice teachers using multiple representations to determine both their pattern knowledge levels and their abilities to transfer this knowledge to students. The design of the study is the survey method, one of the quantitative research methods. The study group was…

  14. Building Pre-Service Teacher's Mathematical Knowledge for Teaching of High School Geometry

    ERIC Educational Resources Information Center

    Somayajulu, Ravi Bhamidipati

    2012-01-01

    There were two primary goals of the research conducted for this dissertation study. Firstly, to fill a gap in the research literature and begin a discussion around secondary pre-service teachers Mathematical Knowledge for Teaching (MKT) as it pertains to geometry. Although a multitude of studies exist for elementary teachers' MKT, few exist at the…

  15. 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…

  16. 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…

  17. 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…

  18. Developing an Assessment Instrument to Measure Early Elementary Teachers' Mathematical Knowledge for Teaching

    ERIC Educational Resources Information Center

    Schoen, Robert C.; Bray, Wendy; Wolfe, Christopher; Tazaz, Amanda M.; Nielsen, Lynne

    2017-01-01

    This study reports on the development and field study of K-TEEM, a web-based assessment instrument designed to measure mathematical knowledge for teaching (MKT) at the early elementary level. The development process involved alignment with early elementary curriculum standards, expert review of items and scoring criteria, cognitive interviews with…

  19. Inclusivity: An Effective Tool for Achieving Quality Mathematics Classroom Instruction in Nigerian Secondary Schools

    ERIC Educational Resources Information Center

    Bature, Iliya Joseph; Atweh, Bill; Treagust, David

    2016-01-01

    Mathematics classrooms instruction in Nigeria secondary schools has been termed a major problem to both teachers and their students. Most classroom activities are teacher-centred with students as mere listeners and recipients of knowledge rather than being active initiators of their knowledge. This paper seeks to investigate the effects of…

  20. Activating Junior Secondary School Students' Prior Knowledge for the Development of Vocabulary, Concepts and Mathematics through Instructional Strategies

    ERIC Educational Resources Information Center

    Oyinloye, Olu; Popoola, Abiodun A.

    2013-01-01

    This paper investigates the activation of students' prior knowledge for the development of vocabulary, concepts and mathematics. It has been observed that many secondary school students are not performing well in the examination conducted by the West African Examinations Council and National Examinations Council of Nigeria. The situation became…

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