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…
Transfer of Mathematical Knowledge: Series
ERIC Educational Resources Information Center
Akgun, Levent; Isik, Cemalettin; Tatar, Enver; Isleyen, Tevfik; Soylu, Yasin
2012-01-01
The aim of this study is to explain students' ability to transfer their knowledge about mathematical series to the problems that they encounter. The data of the study were obtained by using two different tests, namely "Problem Solving Test (PST)" and "Series Character Identification Test (SCT)" which were developed by the researchers. The study…
Reconceptualizing Knowledge at the Mathematical Horizon
ERIC Educational Resources Information Center
Zazkis, Rina; Mamolo, Ami
2011-01-01
This article extends the notion of "knowledge at the mathematical horizon" or "horizon knowledge" introduced by Ball and colleagues as a part of teachers' subject matter knowledge. Our focus is on teachers' mathematical knowledge beyond the school curriculum, that is, on mathematics learnt during undergraduate college or university studies. We…
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
ERIC Educational Resources Information Center
Zopf, Deborah Ann
2010-01-01
This dissertation investigates the mathematical work and knowledge demands of this work to teach mathematics to teachers. The last 20 years have seen progress in the study of the specialized knowledge of mathematics needed for the work of teaching, as well as much discussion about the importance of strengthening teachers' mathematical preparation.…
Elementary Mathematics Teachers' Knowledge of Equity Pedagogy
ERIC Educational Resources Information Center
Jackson, Christa
2013-01-01
Currently, mathematics instruction in U.S. classrooms is far from achieving equity for African American students. This qualitative study reports the results of eight successful elementary mathematics teachers' knowledge of equity pedagogy, specifically their knowledge of culturally relevant pedagogy, cultural competence, and critical…
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…
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…
Connected Knowledge in Science and Mathematics Education
ERIC Educational Resources Information Center
Zohar, Anat
2006-01-01
While the traditional meaning of connected knowledge is valuable in some school subjects, it does not address the main activities of knowledge acquisition in subjects such as physics and mathematics. The goal of this article is to analyze the relationships between the concepts "learning for understanding" and "connected knowledge", a central theme…
Pedagogical Content Knowledge and Content Knowledge of Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Krauss, Stefan; Brunner, Martin; Kunter, Mareike; Baumert, Jurgen; Neubrand, Michael; Blum, Werner; Jordan, Alexander
2008-01-01
Drawing on the work of L. S. Shulman (1986), the authors present a conceptualization of the pedagogical content knowledge and content knowledge of secondary-level mathematics teachers. They describe the theory-based construction of tests to assess these knowledge categories and the implementation of these tests in a sample of German mathematics…
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'…
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…
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…
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…
Mathematics university teachers' perception of pedagogical content knowledge (PCK)
NASA Astrophysics Data System (ADS)
Khakbaz, Azimehsadat
2016-02-01
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 paper is to make explicit the perception of mathematics university teachers about PCK. For this purpose, a phenomenological study was done. Data resources included semi-structured interviews with 10 mathematics university teachers who were in different places of the mathematics university teaching experience spectrum. Data analysis indicated a model consisting of four cognitive themes which are mathematics syntactic knowledge, knowledge about mathematics curriculum planning, knowledge about students' mathematics learning and knowledge about creating an influential mathematics teaching-learning environment. Besides, it was found out that three contextual themes influenced on PCK for teaching mathematics in university levels which were the nature of mathematics subjects, university teachers' features and terms of learning environment.
Connected Knowledge in Science and Mathematics Education
NASA Astrophysics Data System (ADS)
Zohar, Anat
2006-10-01
While the traditional meaning of connected knowledge is valuable in some school subjects, it does not address the main activities of knowledge acquisition in subjects such as physics and mathematics. The goal of this article is to analyze the relationships between the concepts “learning for understanding” and “connected knowledge”, a central theme in feminist epistemology. In learning for understanding, the learner forms multiple, intricate connections among the concepts she is studying in school, between school concepts and her everyday concepts, and between school concepts and their wider context. Viewing connected knowledge as tightly related to understanding has several important implications. It brings connected knowledge into the central learning activities that take place in school science and mathematics, and gives it a high status. It contributes to our understanding of gender-related patterns in thinking; and it may form a unifying theoretical framework for many studies and projects in the field of gender fair education.
Increase Productivity Through Knowledge Management
NASA Astrophysics Data System (ADS)
Gavrikova, N. A.; Dolgih, I. N.; Dyrina, E. N.
2016-04-01
Increase in competition level requires companies to improve the efficiency of work force use characterized by labor productivity. Professional knowledge of staff and its experience play the key role in it. The results of Extrusion Line operator’s working time analysis are performed in this article. The analysis revealed that the reasons of working time ineffective use connected with inadequate information exchange and knowledge management in the company. Authors suggest the way to solve this problem: the main sources of knowledge in engineering enterprise have been defined, the conditions of success and the stages of knowledge management control have been stated.
Identifying the borders of mathematical knowledge
NASA Astrophysics Data System (ADS)
Nascimento Silva, Filipi; Travençolo, Bruno A. N.; Viana, Matheus P.; da Fontoura Costa, Luciano
2010-08-01
Based on a divide and conquer approach, knowledge about nature has been organized into a set of interrelated facts, allowing a natural representation in terms of graphs: each 'chunk' of knowledge corresponds to a node, while relationships between such chunks are expressed as edges. This organization becomes particularly clear in the case of mathematical theorems, with their intense cross-implications and relationships. We have derived a web of mathematical theorems from Wikipedia and, thanks to the powerful concept of entropy, identified its more central and frontier elements. Our results also suggest that the central nodes are the oldest theorems, while the frontier nodes are those recently added to the network. The network communities have also been identified, allowing further insights about the organization of this network, such as its highly modular structure.
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…
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…
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,…
ERIC Educational Resources Information Center
Burke, Margaret Meg Kathleen
2013-01-01
The research indicated effective mathematics teaching to be more complex than assuming the best predictor of student achievement in mathematics is the mathematical content knowledge of a teacher. This dissertation took a novel approach to addressing the idea of what it means to examine how a teacher's knowledge of mathematics impacts student…
Measuring Teachers' Mathematical Knowledge. CSE Technical Report 696
ERIC Educational Resources Information Center
Heritage, Margaret; Vendlinski, Terry
2006-01-01
Teachers' knowledge of mathematics is pivotal to their capacity to provide effective mathematics instruction and to their ability to assess student learning (Ball, Hill, & Bass, 2005; Ma, 1999; Schifter, 1999). The National Council for the Teaching of Mathematics (NCTM, 2000) makes it clear that teachers need knowledge of the whole domain as well…
Public knowledge about AIDS increasing.
Campbell, M J; Waters, W E
1987-04-01
In response to concern over the perceived limited effectiveness of Department of Health and Social Security (UK) advertising campaigns to inform the public of the basic facts of Acquired Immunodeficiency Syndrome (AIDS), a prospective questionnaire study was undertaken in Southampton, England to test the effectiveness of government education prior to a January, 1987 government television/leaflet advertising campaign. 300 questionnaires about AIDS were mailed in December of 1986 to a sample drawn from electoral rolls. The response rate was 61%. Most of the questions were drawn from material covered in the campaign. The results seemed to indicate a small overall increase in knowledge about AIDS. Some changes from a June survey were noted, e.g.: more people were aware that AIDS is a virus for which there is no cure and that it is not readily transmitted by sharing washing, eating or drinking utensils; more people believed that the statement that women are at greater risk for catching AIDS is false. Respondents were generally favorable to the government's continued use of television, even with explicit language, and to its use of the schools, for AIDS education. Many were not aware of the dangers to intravenous drug users or of the symptoms of AIDS. Other surveys have shown an increasing knowledge of AIDS dangers. It is possible that television coverage of the problem will continue to be necessary, in order that less literate populations be reached. Further AIDS health education in general is needed. PMID:3105789
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…
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…
How Mathematical Knowledge for Teaching May Profit from the Study of History of Mathematics
ERIC Educational Resources Information Center
Mosvold, Reidar; Jakobsen, Arne; Jankvist, Uffe Thomas
2014-01-01
In this theoretical article, we aim at theorizing the old statement that mathematics teachers might profit from studying the history of mathematics. We do this by drawing upon the theoretical framework of mathematical knowledge for teaching (MKT). A selection of international studies on the history and pedagogy of mathematics is used as starting…
Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics.
Harr, Nora; Eichler, Andreas; Renkl, Alexander
2014-01-01
In teacher education at universities, general pedagogical and psychological principles are often treated separately from subject matter knowledge and therefore run the risk of not being applied in the teaching subject. In an experimental study (N = 60 mathematics student teachers) we investigated the effects of providing aspects of general pedagogical/psychological knowledge (PPK) and pedagogical content knowledge (PCK) in an integrated or separated way. In both conditions ("integrated" vs. "separated"), participants individually worked on computer-based learning environments addressing the same topic: use and handling of multiple external representations, a central issue in mathematics. We experimentally varied whether PPK aspects and PCK aspects were treated integrated or apart from one another. As expected, the integrated condition led to greater application of pedagogical/psychological aspects and an increase in applying both knowledge types simultaneously compared to the separated condition. Overall, our findings indicate beneficial effects of an integrated design in teacher education. PMID:25191300
Integrating pedagogical content knowledge and pedagogical/psychological knowledge in mathematics
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
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…
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…
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…
Sean vs. Cantor: Using Mathematical Knowledge in "Experience of Disturbance"
ERIC Educational Resources Information Center
Zazkis, Rina; Mamolo, Ami
2009-01-01
Mathematical knowledge used in teaching has attracted the interest of many researchers, but was mainly explored considering teaching at the elementary school level. This paper attends to mathematical knowledge used in teaching at the University level. We present a story about a student suggesting reconsideration of Cantor's diagonal method and the…
ERIC Educational Resources Information Center
Kwiatkowski-Egizio, Erica
2013-01-01
The two research questions that guided this study were: (1) How do preservice teachers develop mathematical knowledge for teaching during a coordinated math methods course and field experience? and (2) What types of portfolio tasks lend themselves to documenting mathematical knowledge in teaching? Six, female, elementary (K-8) teacher candidates…
Knowledge for teaching secondary school mathematics: what counts?
NASA Astrophysics Data System (ADS)
Goos, Merrilyn
2013-10-01
This article discusses key issues surrounding the nature and development of professional knowledge for effective teaching of mathematics, especially at the secondary school level. In the education research community it is generally accepted that teachers need more than knowledge of the content they will teach; an additional construct, pedagogical content knowledge, has been proposed to describe the knowledge teachers need in order to make the content comprehensible to learners. Studies demonstrate that mathematical content knowledge (MCK) and pedagogical content knowledge (PCK) predict students' mathematics achievement gains, and that PCK has the greater influence on achievement. However, the relationship between these two types of knowledge, and how their development might be influenced by studying university level mathematics, remains unclear. The article reports on an Australian study of the knowledge for teaching mathematics of prospective secondary school teachers, which found that MCK is a statistically significant predictor of PCK, and vice versa, although in each case only a small proportion of the variance in the outcome variable was explained. A higher level of prior mathematical experience was also associated with higher levels of MCK, but not PCK. These results suggest that although university level study of mathematics may be beneficial in developing secondary school MCK, it does not have a significant influence on PCK and is therefore inadequate, on its own, for preparing effective teachers of secondary school mathematics.
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…
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…
Selecting and Sequencing Mathematics Tasks: Seeking Mathematical Knowledge for Teaching
ERIC Educational Resources Information Center
Galant, Jaamia
2013-01-01
In this article, I present an initial analysis of an empirical study that was undertaken in an attempt to elicit what subject-matter knowledge, pedagogic content knowledge and curriculum knowledge teachers bring to bear on decisions for teaching. The analysis is based on interview data with 46 Grade 3 teachers, who were presented with two…
Connecting Mathematical Knowledge: A Dialectical Perspective.
ERIC Educational Resources Information Center
Schmittau, Jean
1993-01-01
Based on the cognitive psychological theories of Vygotsky and Davydov, discusses the establishment of connections between mathematical elements, and the algorithmic rules that govern them, and children's spontaneous mathematical concepts. Presents examples that establish connections involving addition and subtraction, comparing numerical…
Why (Urban) Mathematics Teachers Need Political Knowledge
ERIC Educational Resources Information Center
Gutiérrez, Rochelle
2013-01-01
Rochelle Gutiérrez has spent 15 years researching effective, urban high school mathematics departments that served Black, Latin@ and low-income adolescents (see, e.g., Gutiérrez, 1996, 1999a, 1999b, 2000, 2002). These were schools where students took more mathematics than was required by their district; where English learners, recent immigrants,…
Mathematical Ability Relies on Knowledge, Too
ERIC Educational Resources Information Center
Sweller, John; Clark, Richard E.; Kirschner, Paul A.
2011-01-01
Recent "reform" curricula both ignore the absence of supporting data and completely misunderstand the role of problem solving in cognition. If, the argument goes, teachers are not really teaching people mathematics but rather are teaching them some form of general problem solving, then mathematical content can be reduced in importance. According…
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…
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…
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…
Building Mathematical Knowledge in an Authentic Mobile Phone Environment
ERIC Educational Resources Information Center
Daher, Wajeeh
2010-01-01
Although many researchers have examined knowledge building in traditional settings and distance learning, few have examined middle school students' building of mathematical knowledge using mobile phones. The present study uses two well-known models of knowledge building to carry out the examination: the interactive analysis model of knowledge…
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…
Mathematical Knowledge of Japanese, Chinese, and American Elementary School Children.
ERIC Educational Resources Information Center
Stigler, James W.; And Others
This study compared the results of group tests of computational skills and tests of knowledge and skills in mathematics between three groups of first and fifth grade students from the United States, Japan, and Taiwan. The battery of tests were constructed after reviewing the mathematics textbooks used in each location and discussing the major…
Interconnections of Knowledge and Beliefs in Teaching Mathematics
ERIC Educational Resources Information Center
Holm, Jennifer; Kajander, Ann
2012-01-01
As part of a 5-year project that examined teachers' knowledge and beliefs about mathematics and teaching mathematics, interviews were conducted with preservice elementary teachers during their certification year. The transcripts of five of these sets of pretest/posttest interviews were chosen as illustrative of the significant challenges that…
ERIC Educational Resources Information Center
Alpaslan, Mustafa; Isiksal, Mine; Haser, Çigdem
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…
Preservice Teachers' Subject Matter Knowledge of Mathematics
ERIC Educational Resources Information Center
Menon, Ramakrishnan
2009-01-01
Sixty four preservice teachers taking a mathematics methods class for middle schools were given 3 math problems: multiply a three digit number by a two digit number; divide a whole number by a fraction; and compare the volume of two cylinders made in different ways from the same rectangular sheet. They were to a) solve them, explaining their…
"Concreteness Fading" Promotes Transfer of Mathematical Knowledge
ERIC Educational Resources Information Center
McNeil, Nicole M.; Fyfe, Emily R.
2012-01-01
Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are "faded" into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three…
ERIC Educational Resources Information Center
Platas, Linda Michele
2008-01-01
Two survey instruments were developed and validated to measure early childhood teachers' (1) knowledge of early mathematical development and (2) beliefs about mathematics teaching and learning in the preschool classroom. The Knowledge of Mathematical Development (KMD) Survey was designed to measure teachers' knowledge of mathematical development…
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…
Exploring Kindergarten Teachers' Pedagogical Content Knowledge of Mathematics
ERIC Educational Resources Information Center
Lee, Joohi
2010-01-01
The purpose of this study was to assess 81 kindergarten teachers' pedagogical content knowledge of mathematics on six subcategory areas such as number sense, pattern, ordering, shapes, spatial sense, and comparison. The data showed participants possessed a higher level of pedagogical content knowledge of "number sense" (M = 89.12) compared to…
Knowledge for Teaching Secondary School Mathematics: What Counts?
ERIC Educational Resources Information Center
Goos, Merrilyn
2013-01-01
This article discusses key issues surrounding the nature and development of professional knowledge for effective teaching of mathematics, especially at the secondary school level. In the education research community it is generally accepted that teachers need more than knowledge of the content they will teach; an additional construct, pedagogical…
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…
ERIC Educational Resources Information Center
Stephens, Walter Maxwell
This study considered the meaning that was given to knowing/doing mathematics in classrooms comprising the observational study conducted by the Wisconsin Center for Education Research during 1978-81. The study interprets the work of teachers and students, and considers what constitutes appropriate mathematical knowledge for children to learn. A…
ERIC Educational Resources Information Center
Stephens, W. M.; Romberg, T. A.
This study examined the aspirations of the Developing Mathematical Processes (DMP) program and sought to ascertain the extent to which it has been implemented in observed classrooms. DMP was intended to reshape conceptions of mathematical knowledge and school work and to create a pedagogy in which children would be active in creating and testing…
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…
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…
Advanced Mathematical Knowledge in Teaching Practice: Perceptions of Secondary Mathematics Teachers
ERIC Educational Resources Information Center
Zazkis, Rina; Leikin, Roza
2010-01-01
For the purpose of our research we define Advanced Mathematical Knowledge (AMK) as knowledge of the subject matter acquired during undergraduate studies at colleges or universities. We examine the responses of secondary school teachers about their usage of AMK in teaching. We find that the majority of teachers focus on the purposes and advantages…
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…
What Knowledge Is Shaping Teacher Preparation in Early Childhood Mathematics?
ERIC Educational Resources Information Center
Parks, Amy Noelle; Wager, Anita A.
2015-01-01
This article examines the bodies of knowledge that influence and inform the teaching of mathematics methods courses for preservice early childhood teachers, focusing on the U.S. context. In particular, the article reports on an analysis of scholarship published over the last 20 years in four journals (two focused on early childhood education and…
A Study of Elementary Mathematics Teachers' Knowledge of Equity
ERIC Educational Resources Information Center
Jackson, Christa D.
2010-01-01
Currently, mathematics instruction in U.S. classrooms is far from achieving equity for African American students. Establishing an equitable classroom environment that results in student learning for African Americans requires specialized teacher knowledge, productive dispositions and beliefs, and effective teaching practices. The study reports on…
Mathematical Knowledge for Teaching and Task Unfolding: An Exploratory Study
ERIC Educational Resources Information Center
Charalambous, Charalambos Y.
2010-01-01
Although teachers' knowledge is thought to contribute to the selection and implementation of mathematical tasks, empirical evidence supporting this claim is scarce. To investigate this relationship and understand its nature, this exploratory study examines the unfolding of tasks in a series of lessons led by 2 elementary school teachers who…
Measuring Mathematical Knowledge for Teaching Fractions with Drawn Quantities
ERIC Educational Resources Information Center
Izsak, Andrew; Jacobson, Erik; de Araujo, Zandra; Orrill, Chandra Hawley
2012-01-01
Researchers have recently used traditional item response theory (IRT) models to measure mathematical knowledge for teaching (MKT). Some studies (e.g., Hill, 2007; Izsak, Orrill, Cohen, & Brown, 2010), however, have reported subgroups when measuring middle-grades teachers' MKT, and such groups violate a key assumption of IRT models. This study…
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…
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…
The Development of Diploma in Education Student Teachers' Mathematics Pedagogical Content Knowledge
ERIC Educational Resources Information Center
Lim-Teo, Suat Khoh; Chua, Kwee Gek; Cheang, Wai Kwong; Yeo, Joseph K.
2007-01-01
Mathematics pedagogical content knowledge (MPCK) of teachers cannot be easily defined but is a complex concept integrating generic pedagogical knowledge, mathematics teaching methodology as well as knowledge of the discipline of mathematics. It is the objective of mathematics methodology courses in teacher preparation programmes to begin the…
Mathematical Knowledge and Skills: Selected Results from the Second Assessment of Mathematics.
ERIC Educational Resources Information Center
Kahl, Stuart
This is one of a series of reports summarizing the results of the second mathematics assessment conducted by the National Assessment of Educational Progress (NAEP). Nine, 13- and 17-year-olds were assessed during the 1977-78 school year. The assessment measured achievement in various content areas at four levels of cognitive processes (knowledge,…
Slowing presentation speed increases illusions of knowledge.
Fazio, Lisa K; Marsh, Elizabeth J
2008-02-01
Prior research on false memories has shown that suggestibility is often reduced when the presentation rate is slowed enough to allow monitoring. We examined whether slowing presentation speed would reduce factual errors learned from fictional stories. Would subjects use the extra time to detect the errors in the stories, reducing reproduction of these errors on a later test? Surprisingly, slowing presentation speed increased the production of story errors on a later general knowledge test. Instructing the reader to mark whether each sentence contained an error, however, did decrease suggestibility. Readers appear to passively accept information presented in stories and need a constant reminder to monitor for errors. These results highlight differences between typical episodic false memories and illusions of knowledge (such as learning from fiction). Manipulations that reduce suggestibility for episodic false memories do not always reduce suggestibility for illusions of knowledge. PMID:18605500
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…
Visual Programming: A Programming Tool for Increasing Mathematics Achivement
ERIC Educational Resources Information Center
Swanier, Cheryl A.; Seals, Cheryl D.; Billionniere, Elodie V.
2009-01-01
This paper aims to address the need of increasing student achievement in mathematics using a visual programming language such as Scratch. This visual programming language facilitates creating an environment where students in K-12 education can develop mathematical simulations while learning a visual programming language at the same time.…
What's Past Is Prologue: Relations between Early Mathematics Knowledge and High School Achievement
ERIC Educational Resources Information Center
Watts, Tyler W.; Duncan, Greg J.; Siegler, Robert S.; Davis-Kean, Pamela E.
2014-01-01
Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, and few have investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at…
ERIC Educational Resources Information Center
Subramaniam, Karthigeyan
2014-01-01
Prospective secondary mathematics teachers' pedagogical knowledge for teaching the estimation of length measurements was investigated by examining their personal benchmarks for measurement estimation. Benchmarks for measurement estimation are the meaningful representations of units that serve to increase one's understanding of…
ERIC Educational Resources Information Center
Turner, Erin E.; Drake, Corey; McDuffie, Amy Roth; Aguirre, Julia; Bartell, Tonya Gau; Foote, Mary Q.
2012-01-01
Research repeatedly documents that teachers are underprepared to teach mathematics effectively in diverse classrooms. A critical aspect of learning to be an effective mathematics teacher for diverse learners is developing knowledge, dispositions, and practices that support building on children's mathematical thinking, as well as their cultural,…
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…
Elementary school quality, the mathematics curriculum and the role of local knowledge
NASA Astrophysics Data System (ADS)
Balfanz, Robert
1990-03-01
This article uses data from several elementary school classrooms in Chicago on how students learn to calculate, and reviews similar data from a number of developing countries to examine the strengths and limitations of using the mathematical knowledge which students develop on their own outside of formal schooling to increase the amount, range and power of mathematical knowledge which is acquired through formal schooling. In so doing it attempts to reconcile the views of those who believe that the key to improving elementary school quality lies in improving the technology of instruction and those who believe that it lies in a deeper understanding of the mental life of children. It concludes by arguing that the quality of elementary schooling can be improved through skilled management of the environmentally acquired knowledge which students bring to instruction, if this knowledge is transformed through pedagogic and curricular interventions into a set of portable intellectual skills.
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.
NASA Astrophysics Data System (ADS)
Wilkie, Karina J.
2015-08-01
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.
Increased Knowledge in Geometry and Instructional Practice.
ERIC Educational Resources Information Center
Swafford, Jane O.; And Others
1997-01-01
Examines the effects on instruction of an intervention program designed to enhance teachers' knowledge of geometry and their knowledge of research on student cognition in geometry. Findings indicate significant gains in content knowledge and in van Hiele level, and marked changes in what was taught, how it was taught, and the characteristics…
Generative Adolescent Mathematical Learners: The Fabrication of Knowledge
ERIC Educational Resources Information Center
Lawler, Brian R.
2008-01-01
This dissertation is embedded in a deconstruction of the field of Mathematics Education in order to reconstitute the mathematics student as a generative mathematical learner. The purpose of the dissertation is to understand how generative adolescent mathematical learners (GAMLs) maneuver through their mathematics courses while maintaining such a…
Pre-Service Students' Responses to Being Tested on Their Primary School Mathematical Knowledge
ERIC Educational Resources Information Center
Meaney, Tamsin; Lange, Troels
2010-01-01
The limited mathematical knowledge of pre-service primary teachers is an international concern. The areas of mathematical difficulties have been well documented, which has led to many universities instituting testing regimes to ensure that their pre-service teachers have appropriate knowledge of primary school mathematics. In this study, the…
ERIC Educational Resources Information Center
Zulnaidi, Hutkemri; Zakaria, Effandi
2010-01-01
The purpose of this study was to determine the effect of information mapping strategy on mathematics conceptual knowledge of junior high school students in Rokan Hulu Riau, Indonesia. The study also examined the relationship between mathematics conceptual knowledge and mathematics achievement. Using a quasi-experimental method, the study was…
Comparing Knowledge Bases and Reasoning Structures in Discussions of Mathematics and Pedagogy
ERIC Educational Resources Information Center
Steele, Michael D.
2005-01-01
While teaching, teachers need to access both their knowledge of mathematics and knowledge of pedagogy. Practice-based materials afford teachers opportunities to reason about both mathematics and pedagogy within the context of teaching. Accepted systems exist for explaining and reasoning in the domain of mathematics; logic, procedures, and…
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…
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…
ERIC Educational Resources Information Center
Harrell, Pamela Esprivalo; Eddy, Colleen McLean
2011-01-01
This study examined mathematics teacher content knowledge in terms of policy maker recommendations, college coursework and teacher certification mathematics test scores. Transcript analysis indicated poor alignment of national policy maker recommendations for mathematics teachers and college degrees in mathematics. Teacher certification test…
What’s Past is Prologue: Relations Between Early Mathematics Knowledge and High School Achievement
Watts, Tyler W.; Duncan, Greg J.; Siegler, Robert S.; Davis-Kean, Pamela E.
2015-01-01
Although previous research has established the association between early-grade mathematics knowledge and later mathematics achievement, few studies have measured mathematical skills prior to school entry, nor have they investigated the predictive power of early gains in mathematics ability. The current paper relates mathematical skills measured at 54 months to adolescent mathematics achievement using multi-site longitudinal data. We find that preschool mathematics ability predicts mathematics achievement through age 15, even after accounting for early reading, cognitive skills, and family and child characteristics. Moreover, we find that growth in mathematical ability between age 54 months and first grade is an even stronger predictor of adolescent mathematics achievement. These results demonstrate the importance of pre-kindergarten mathematics knowledge and early math learning for later achievement. PMID:26806961
ERIC Educational Resources Information Center
Copur-Gencturk, Yasemin
2015-01-01
In this study, I examined the relationship between teachers' mathematical knowledge and instruction. Twenty-one K-8 teachers who were enrolled in a master's program were followed for 3 years to study how their mathematical knowledge and teaching changed over time. The results of multilevel growth models indicated that gains in teachers'…
ERIC Educational Resources Information Center
Davis, Brent; Renert, Moshe
2013-01-01
We discuss the teachers' disciplinary knowledge of mathematics in this article, arguing two main points as we report on a 2-year study involving 22 practicing teachers. First we argue that teachers' knowledge of mathematics might be productively construed as a complex evolving form, a significant dimension of which is tacit knowledge. Second,…
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…
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…
The Key to Enhancing Students' Mathematical Vocabulary Knowledge
ERIC Educational Resources Information Center
Riccomini, Paul J.; Sanders, Sharon; Jones, Julie
2008-01-01
The importance of learning mathematical vocabulary is vital for the development of proficiency in mathematics. In an effort to improve students' mathematical performance, educators must use research-validated instructional methods to teach important mathematical vocabulary. Mnemonic instruction is a set of evidenced-based strategies used to…
Increasing Minorities' Mathematics Preparedness: The College Readiness Program.
ERIC Educational Resources Information Center
Duren, Phillip E.; Kelly, Margaret
Black and Hispanic students have historically been underrepresented at state universities in relationship to the percentage of the population of these minorities in the state at large. With the increase of requirements from two to three years of high school mathematics, there is real concern that this underrepresentation will continue to worsen.…
Using Manipulative Materials to Increase Student Achievement in Mathematics
ERIC Educational Resources Information Center
Lett, Steven W.
2007-01-01
This is an action research project to test a null hypothesis, which states that the use of manipulative materials within the context of mathematics instruction will not yield a significant increase in student achievement. Based on the research, using manipulative materials should have a positive impact on student achievement. Allowing students to…
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…
ERIC Educational Resources Information Center
Oleson, Vicki
2010-01-01
This study sought to understand the process of change elementary teachers experienced as they participated in mathematics professional development. This investigation explored the impact of mathematics professional development on teachers' content knowledge for teaching, their ability to implement innovative pedagogical practices, and the…
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…
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 universality and…
ERIC Educational Resources Information Center
Curcio, Frances R.
This study was designed to extend the schema-theoretic perspective of understanding general discourse to include graph comprehension. The sample included 204 fourth-grade and 185 seventh-grade pupils. Data were collected on achievement in reading and mathematics, sex, prior knowledge of topic, mathematical content, graphical form, and graph…
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 Mathematical…
ERIC Educational Resources Information Center
Osana, Helena P.; Lacroix, Guy L.; Tucker, Bradley J.; Desrosiers, Chantal
2006-01-01
The objective of this study was to examine the nature of preservice teachers' evaluations of elementary mathematics problems using the Mathematical Tasks Framework (MTF), a model designed to discriminate among tasks according to their cognitive complexity. We also tested the relationship between mathematics content knowledge and problem length on…
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…
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…
ERIC Educational Resources Information Center
Yüksel, Ismail
2014-01-01
The aim of this paper is to examine the impact of activity-based mathematics instruction on mathematics performance and investigate those factors, which contribute to the mathematics performance of a sample of children aged between 10 and 12 years. The study was designed to consider the impact of prior knowledge, self-regulation, prior attitude,…
Orienteering in knowledge spaces: the hyperbolic geometry of Wikipedia Mathematics.
Leibon, Gregory; Rockmore, Daniel N
2013-01-01
In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or "The MathWiki." The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of "knowledge space" in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017
Orienteering in Knowledge Spaces: The Hyperbolic Geometry of Wikipedia Mathematics
Leibon, Gregory; Rockmore, Daniel N.
2013-01-01
In this paper we show how the coupling of the notion of a network with directions with the adaptation of the four-point probe from materials testing gives rise to a natural geometry on such networks. This four-point probe geometry shares many of the properties of hyperbolic geometry wherein the network directions take the place of the sphere at infinity, enabling a navigation of the network in terms of pairs of directions: the geodesic through a pair of points is oriented from one direction to another direction, the pair of which are uniquely determined. We illustrate this in the interesting example of the pages of Wikipedia devoted to Mathematics, or “The MathWiki.” The applicability of these ideas extends beyond Wikipedia to provide a natural framework for visual search and to prescribe a natural mode of navigation for any kind of “knowledge space” in which higher order concepts aggregate various instances of information. Other examples would include genre or author organization of cultural objects such as books, movies, documents or even merchandise in an online store. PMID:23844017
Statewide Mathematics Professional Development: Teacher Knowledge, Self-Efficacy, and Beliefs
ERIC Educational Resources Information Center
Carney, Michele B.; Brendefur, Jonathan L.; Thiede, Keith; Hughes, Gwyneth; Sutton, John
2016-01-01
We examined the impact of a state-mandated K-12 mathematics professional development course on knowledge, self-efficacy, and beliefs of nearly 4,000 teachers and administrators. Participants completed the Mathematical Thinking for Instruction course, emphasizing student thinking, problem-solving, and content knowledge specific to mathematics…
Mathematical Knowledge for Teaching Teachers: The Case of Multiplication and Division of Fractions
ERIC Educational Resources Information Center
Olanoff, Dana E.
2011-01-01
This study attempts to answer the question, "What is the mathematical knowledge required by teachers of elementary mathematics content courses in the area of multiplication and division of fractions?" Beginning in the mid-1980s, when Shulman (1986) introduced the idea of pedagogical content knowledge, researchers have been looking at the knowledge…
ERIC Educational Resources Information Center
Bonner, Emily P.; Ruiz, Elsa C.; Travis, Betty
2013-01-01
Teacher content knowledge has been repeatedly linked to student achievement. Alternative Mathematics Teacher Education Programs are popular and prevalent, but do they prepare teachers with the content knowledge needed to teach secondary mathematics? This study reports on a quantitative analysis comparing scores between traditionally and…
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…
The Nature and Predictors of Elementary Teachers' Mathematical Knowledge for Teaching
ERIC Educational Resources Information Center
Hill, Heather C.
2010-01-01
This article explores elementary school teachers' mathematical knowledge for teaching and the relationship between such knowledge and teacher characteristics. The Learning Mathematics for Teaching project administered a multiple-choice assessment covering topics in number and operation to a nationally representative sample of teachers (n = 625)…
Primary Teachers' Knowledge for Teaching Ratio and Proportion in Mathematics: The Case of Indonesia
ERIC Educational Resources Information Center
Ekawati, Rooselyna; Lin, Fou-Lai; Yang, Kai-Lin
2015-01-01
In this study, we aimed at examining Indonesian In-Service primary Teachers' Mathematics Content Knowledge (MCK) and Mathematics Pedagogical Content Knowledge (MPCK) for teaching ratio and proportion. The instruments were administered to 271 in-service primary teachers with various education background. There were three underlined factors on MCK…
ERIC Educational Resources Information Center
Davis, Jon D.
2009-01-01
This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers' pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete…
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…
The Development of Beginning Mathematics Teacher Pedagogical Content Knowledge
ERIC Educational Resources Information Center
Lannin, John K.; Webb, Matthew; Chval, Kathryn; Arbaugh, Fran; Hicks, Sarah; Taylor, Cynthia; Bruton, Rebecca
2013-01-01
Recent research efforts (Schmidt et al. in "The preparation gap: teacher education for middle school mathematics in six countries," MSU Center for Research in Mathematics and Science Education, 2007) demonstrate that teacher development programs in high-performing countries offer experiences that are designed to develop both mathematical…
Developmental Mathematics Success: Impact of Students' Knowledge and Attitudes
ERIC Educational Resources Information Center
Benken, Babette M.; Ramirez, Jorge; Li, Xuhui; Wetendorf, Scott
2015-01-01
In order to improve student success within developmental programs, we conducted a study of 1st year students taking required, developmental mathematics courses at a large, urban public university. Findings suggest that merely the number of years of mathematics that students take in high school is not a precise indicator of student readiness and…
Strengthening Pre-Service Teachers' Mathematical Content Knowledge
ERIC Educational Resources Information Center
Hine, Gregory S. C.
2015-01-01
Over the past two decades there has been a growing body of literature concerning the preparation of pre-service mathematics teachers. Research efforts have focused principally on approaches conducted by tertiary educators to adequately prepare pre-service teachers (PST) for the mathematics classroom. Despite the extensive literature there is no…
Distributed Leadership: Key to Improving Primary Students' Mathematical Knowledge
ERIC Educational Resources Information Center
Larson, Matthew R.; Smith, Wendy M.
2013-01-01
The purpose of this article is to present the findings of a quantitative study focused on primary mathematics teachers who participated in an intensive professional development program and then had leadership responsibility for the implementation of a new primary mathematics curriculum in their district. The study examines the effect of the…
Using Problem Solving to Assess Young Children's Mathematics Knowledge
ERIC Educational Resources Information Center
Charlesworth, Rosalind; Leali, Shirley A.
2012-01-01
Mathematics problem solving provides a means for obtaining a view of young children's understanding of mathematics as they move through the early childhood concept development sequence. Assessment information can be obtained through observations and interviews as children develop problem solutions. Examples of preschool, kindergarten, and primary…
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…
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…
ERIC Educational Resources Information Center
Wagner, Joseph F.; Speer, Natasha M.; Rossa, Bernd
2007-01-01
In this research report we examine knowledge other than content knowledge needed by a mathematician in his first use of an inquiry-oriented curriculum for teaching an undergraduate course in differential equations. Collaboratively, the mathematician and two mathematics education researchers identified the challenges faced by the mathematician as…
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…
ERIC Educational Resources Information Center
Faulkner, Valerie N.; Cain, Chris R.
2013-01-01
Student performance in mathematics has been linked to the mathematical knowledge of the teacher. Based on this finding, a 5-day professional development module was created to improve teachers' mathematical knowledge and their understanding of number sense. We found no difference prior to the professional development in mathematical content…
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…
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…
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…
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…
Characterizing Mathematical Knowledge for Secondary Teaching: A Case from High School Algebra
ERIC Educational Resources Information Center
Howell, Heather
2012-01-01
This dissertation study describes the nature of the mathematical knowledge required to teach a unit on exponents at the secondary school level, and further explores the adequacy of extant theoretical models for characterizing that knowledge. Researchers agree that teacher content knowledge contributes to teaching quality, which in turn contributes…
ERIC Educational Resources Information Center
Serafino, Kathleen; Cicchelli, Terry
2003-01-01
Tested the effects of prior knowledge and two instructional models--structured problem solving and guided generation (GG)--on mathematical problem solving and transfer to an analogous task. Data on students with high and low prior knowledge highlighted significant main effects for prior knowledge, significant differences on transfer to analogous…
ERIC Educational Resources Information Center
Silverman, Jason; Clay, Ellen L.
2010-01-01
In this article the authors describe their efforts to support teachers' development of deep, connected understandings of school mathematics and to find ways to make use of the teachers' learning as a context for subsequent mathematical and pedagogical development. The authors detail the evolution of their model for Online Asynchronous…
ERIC Educational Resources Information Center
Bell, Courtney A.; Wilson, Suzanne M.; Higgins, Traci; McCoach, D. Betsy
2010-01-01
This study examines the impact of a nationally disseminated professional development program, Developing Mathematical Ideas (DMI), on teachers' specialized knowledge for teaching mathematics and illustrates how such research could be conducted. Participants completing 2 DMI modules were compared with similar colleagues who had not taken DMI.…
ERIC Educational Resources Information Center
Kulikowich, Jonna M.
2007-01-01
Operating from multiple literature bases in cognitive psychology, mathematics education, and theoretical and applied psychometrics, Schilling, Hill and their colleagues provide a systemic approach to studying the validity of scores of mathematical knowledge for teaching. This system encompasses an array of task formats and methodologies. The…
ERIC Educational Resources Information Center
Roche, Anne; Clarke, Doug M.
2013-01-01
This article reports on a study that was conducted with 378 primary teachers from Catholic schools in Victoria who participated in the first year of a 2-year research and professional learning program in mathematics. One aim of the program was to enhance teacher knowledge in mathematics in its many forms. As part of the larger study, the teachers…
Measuring Mathematical Knowledge for Teaching: A Longitudinal Study Using Two Measures
ERIC Educational Resources Information Center
Copur-Gencturk, Yasemin; Lubienski, Sarah T.
2013-01-01
This longitudinal study examines growth in teacher knowledge as measured by two popular assessments--Learning Mathematics for Teaching (LMT) and Diagnostic Teacher Assessments in Mathematics and Science (DTAMS). Using data collected from 24 teachers, we compare the extent to which each assessment captured teacher learning during a K-8 mathematics…
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…
ERIC Educational Resources Information Center
Hsieh, Feng-Jui
2013-01-01
This paper discusses different conceptual frameworks for measuring mathematics pedagogical content knowledge (MPCK) in international comparison studies. Two large-scale international comparative studies, "Mathematics Teaching in the Twenty-First Century" (MT21; Schmidt et al., 2011) and the "Teacher Education and Development Study…
ERIC Educational Resources Information Center
Speer, Natasha M.; Wagner, Joseph F.
2009-01-01
Using case study analysis and a cognitive theoretical orientation, we examine elements of knowledge for teaching needed by a mathematician to orchestrate whole-class discussions in an undergraduate mathematics classroom. The instructor, an experienced teacher and mathematics researcher, used an inquiry-oriented curriculum to teach a differential…
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…
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…
ERIC Educational Resources Information Center
Usman, Ahmed Ibrahim
2015-01-01
Knowledge and understanding of mathematical operations serves as a pre-reequisite for the successful translation of algebraic word problems. This study explored pre-service teachers' ability to recognize mathematical operations as well as use of those capabilities in constructing algebraic expressions, equations, and their solutions. The outcome…
ERIC Educational Resources Information Center
Barnett, Carne
1991-01-01
Researchers studied how a cognitive flexibility and knowledge transfer theory framed the design of a case-based curriculum for mathematics teacher education. The paper includes a sample mathematics teaching case and analyzes four discussions based on the case. The analysis shows the potential of subject-specific cases for enhancing mathematics…
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…
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…
The use of video analysis and the Knowledge Quartet in mathematics teacher education programmes
NASA Astrophysics Data System (ADS)
Liston, Miriam
2015-01-01
This study investigates the potential of video analysis and a mathematical knowledge for teaching framework, the Knowledge Quartet (KQ), in mathematics teacher education programmes. It reports on the effectiveness of these tools in analysing and supporting secondary level pre-service mathematics teachers' subject matter knowledge and pedagogical content knowledge. This paper describes how a videotaped lesson of one pre-service teacher, teaching a class of mature students, was analysed and makes comparisons between the teacher educators' and the pre-service teacher's observations. Inter-rater reliability was investigated and a Kappa coefficient of .72 indicated substantial agreement between both coders. Findings are presented and implications of the use of video and the KQ for mathematics teacher education are drawn.
The effects of teacher mathematics knowledge and pedagogy on student achievement in rural Guatemala
NASA Astrophysics Data System (ADS)
Marshall, Jeffery H.; Sorto, M. Alejandra
2012-04-01
Why are some teachers more effective than others? The importance of understanding the interplay between teacher preparation, pedagogy and student achievement has motivated a new line of research focusing on teacher knowledge. This study analyses the effects of teacher mathematics knowledge on student achievement using longitudinal data from rural Guatemalan primary schools. After presenting a conceptual framework for linking the work of the teacher with student learning in mathematics together with an overview of the different forms of teacher knowledge, the paper introduces the Guatemalan context and the analytical framework including the sample, data and methods. Overall, the results provide some empirical support for a widely held, if infrequently tested, belief in mathematics education: effective teachers have different kinds of mathematical knowledge. The results also suggest specific mechanisms by which effective teachers can make substantial impacts on student learning, even in extremely poor contexts.
Assessing Pre-Service Teachers' Mathematics Subject Knowledge
ERIC Educational Resources Information Center
Ryan, Julie; McCrae, Barry
2006-01-01
We report the development of an assessment instrument that provides a profile of the attainment and the errors of pre-service primary teachers across the mathematics curriculum. We describe test development, analyses and test validation involving a sample of 426 pre-service teachers in the first year of their training in primary education courses…
Learning Mathematics Does Not (Necessarily) Mean Constructing the Right Knowledge
ERIC Educational Resources Information Center
Dawson, Sandy
2015-01-01
In this article, which was first published in 1991, the late Sandy Dawson, discusses aspects of a Lakatosian approach to mathematics teaching. The ideas are illustrated with examples from three teaching situations: making conjectures about the next number in a sequence; making conjectures about the internal angles in a triangle using Logo; and…
Identity, Knowledge and Departmental Practices: Mathematics of Engineers and Mathematicians
ERIC Educational Resources Information Center
Bingolbali, Erhan; Monaghan, John
2004-01-01
This report explores first year undergraduate mechanical engineering and mathematics students' conceptions of the derivative and the contribution that membership of different departments may have on these conceptions. Quantitative results suggest that mechanical engineering students develop a proclivity for rate of change aspects of the derivative…
How Mathematics Propels the Development of Physical Knowledge
ERIC Educational Resources Information Center
Schwartz, Daniel L.; Martin, Taylor; Pfaffman, Jay
2005-01-01
Three studies examined whether mathematics can propel the development of physical understanding. In Experiment 1, 10-year-olds solved balance scale problems that used easy-to-count discrete quantities or hard-to-count continuous quantities. Discrete quantities led to age typical performances. Continuous quantities caused performances like those of…
Uniquely Precise: Importance of Conceptual Knowledge and Mathematical Language
ERIC Educational Resources Information Center
Shockey, Tod; Pindiprolu, Sekhar
2015-01-01
The importance of mathematical concept development and language is recognized early in children's schooling as they mature through shape and counting experiences. The reader may recall instances of a youngster referring to a "corner" of a shape before the reader has the language of vertex. This language precision needs to continue to…
Increasing mathematical problem-solving performance through relaxation training
NASA Astrophysics Data System (ADS)
Sharp, Conni; Coltharp, Hazel; Hurford, David; Cole, Amykay
2000-04-01
Two intact classes of 30 undergraduate students enrolled in the same general education mathematics course were each administered the IPSP Mathematics Problem Solving Test and the Mathematics Anxiety Rating Scale at the beginning and end of the semester. Both groups experienced the same syllabus, lectures, course requirements, and assessment techniques; however, one group received relaxation training during an initial class meeting and during the first 5 to 7 minutes of each subsequent class. The group which had received relaxation training had significantly lower mathematics anxiety and significantly higher mathematics performance at the end of the course. The results suggest that relaxation training may be a useful tool for treating anxiety in undergraduate general education mathematics students.
Emergences and affordances as opportunities to develop teachers' mathematical content knowledge
NASA Astrophysics Data System (ADS)
Julie, Cyril
2014-04-01
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 achievement in mathematics of learners is addressing teachers' mathematical content and pedagogical content knowledge through continuous professional development initiatives. The focus of this article is on the former. It describes how emergent and affording opportunities are brought to the fore from classroom observations and interactions in workshops and institutes with practising teachers. It concludes that this in situ dealing with mathematical content knowledge holds much promise for buy-in by teachers because it addresses an immediate need related to their practice.
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…
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…
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…
ERIC Educational Resources Information Center
Vierra, Vicki Ann
2011-01-01
This descriptive study compares the entry-level pedagogical content knowledge of single subject mathematics credential candidates based on career status and undergraduate majors. Career changers from science, technology, engineering or math (STEM) fields are compared to first career candidates to see if they bring different skills and knowledge to…
ERIC Educational Resources Information Center
Kersting, Nicole B.; Givvin, Karen B.; Thompson, Belinda J.; Santagata, Rossella; Stigler, James W.
2012-01-01
This study explores the relationships between teacher knowledge, teaching practice, and student learning in mathematics. It extends previous work that developed and evaluated an innovative approach to assessing teacher knowledge based on teachers' analyses of classroom video clips. Teachers watched and commented on 13 fraction clips. These written…
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…
ERIC Educational Resources Information Center
McCray, Jennifer S.; Chen, Jie-Qi
2012-01-01
This study examines the construct validity of a new teacher interview designed to assess teachers' pedagogical content knowledge (PCK) for preschool mathematics. PCK describes the subject matter knowledge a teacher needs for effective teaching. Data from 22 teachers and 113 Head Start children in a large midwestern city in the United States were…
ERIC Educational Resources Information Center
Mabbott, Donald J.; Bisanz, Jeffrey
2008-01-01
Knowledge and skill in multiplication were investigated for late elementary-grade students with mathematics learning disabilities (MLD), typically achieving age-matched peers, low-achieving age-matched peers, and ability-matched peers by examining multiple measures of computational skill, working memory, and conceptual knowledge. Poor…
ERIC Educational Resources Information Center
Schmidt, Peter
A conception of discussing mathematical material in the domain of calculus is outlined. Applications include that university students work at their knowledge and prepare for their oral examinations by utilizing the dialog system. The conception is based upon three pillars. One central pillar is a knowledge base containing the collections of…
Validation of instruments to measure students' mathematical knowledge
NASA Astrophysics Data System (ADS)
Khatimin, Nuraini; Zaharim, Azami; Aziz, Azrilah Abd
2015-02-01
This paper describes instruments' validation process to identify the suitability and accuracy of the final examination questions for engineering mathematics. As a compulsory subject for second year students from 4 departments in Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia, the Differential Equations 1 course (KKKQ2124) was considered in this study. The data used in this study consists of the raw marks for final examination of semester 2, 2012/2013 session. The data then will be run and analyzed using the Rasch measurement model. Rasch model can also examine the ability of students and redundancy of instrument constructs.
NASA Astrophysics Data System (ADS)
Cook, Samuel A.; Fukawa-Connelly, Timothy
2016-02-01
Studies have shown that at the end of an introductory statistics course, students struggle with building block concepts, such as mean and standard deviation, and rely on procedural understandings of the concepts. This study aims to investigate the understandings entering freshman of a department of mathematics and statistics (including mathematics education), students who are presumably better prepared in terms of mathematics and statistics than the average university student, have of introductory statistics. This case study found that these students enter college with common statistical misunderstandings, lack of knowledge, and idiosyncratic collections of correct statistical knowledge. Moreover, they also have a wide range of beliefs about their knowledge with some of the students who believe that they have the strongest knowledge also having significant misconceptions. More attention to these statistical building blocks may be required in a university introduction statistics course.
NASA Astrophysics Data System (ADS)
Flynn, Natalie P.
This study developed a survey from the existing literature in an attempt to illuminate the processes, tools, insights, and events that allow university science and mathematics content experts (Ph.D.'s) unpack their expertise in order to teach develop and teach undergraduate students. A pilot study was conducted at an urban university in order to refine the survey. The study consisted of 72 science or mathematics Ph.D. faculty members that teach at a research-based urban university. Follow-up interviews were conducted with 21 volunteer faculty to further explore their methods and tools for developing and implementing teaching within their discipline. Statistical analysis of the data revealed: faculty that taught while obtaining their Ph.D. were less confident in their ability to teach successful and faculty that received training in teaching believed that students have difficult to change misconceptions and do not commit enough time to their course. Student centered textbooks ranked the highest among tools used to gain teaching strategies followed by grading of exams and assignments for gaining insights into student knowledge and difficulties. Science and mathematics education literature and university provided education session ranked the lowest in rating scale for providing strategies for teaching. The open-ended survey questions were sub-divided and analyzed by the number of years of experience to identify the development of teaching knowledge over time and revealed that teaching became more interactive, less lecture based, and more engaging. As faculty matured and gained experience they became more aware of student misconceptions and difficulties often changing their teaching to eliminate such issues. As confidence levels increase their teaching included more technology-based tools, became more interactive, incorporated problem based activities, and became more flexible. This change occurred when and if faculty members altered their thinking about their
ERIC Educational Resources Information Center
Provost, Lauren E.
2013-01-01
This work investigates middle school teachers' mathematics knowledge for teaching (MKT) as defined by Hill (2007). Within this two-part dissertation, the level of MKT was considered as well as the role of teacher beliefs in actual specialized content knowledge (SCK) use, a specific type of mathematics knowledge for teaching vital in quality…
ERIC Educational Resources Information Center
Aguirre, Julia M.; Zavala, Maria del Rosario; Katanyoutanant, Tiffany
2012-01-01
This study documents and describes efforts to develop robust forms of pre-service teachers' pedagogical content knowledge through a culturally responsive mathematics teaching approach. Embedded in a university K-8 mathematics methods course emphasising the connections among mathematics, children's mathematical thinking, and…
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…
ERIC Educational Resources Information Center
Platas, Linda M.; Ketterlin-Geller, Leanne R.; Sitabkhan, Yasmin
2016-01-01
This paper describes the development and intended uses of the Early Grades Mathematics Assessment (EGMA), which measures essential early mathematical knowledge and skills that are foundational to more sophisticated mathematical abilities, predictive of later achievement, and teachable. Administering the EGMA can provide policy makers,…
The Nature and Development of Middle School Mathematics Teachers' Knowledge
ERIC Educational Resources Information Center
Beswick, Kim; Callingham, Rosemary; Watson, Jane
2012-01-01
In this article, we report on the use of a teacher profiling instrument with 62 middle school teachers at the start of a 3-year professional learning programme. The instrument was designed to assess the aspects of teachers' knowledge identified by Shulman ("1987") refined by Ball et al. ("2008") and extended to include teachers' confidence to use…
Mathematical Connections and Their Relationship to Mathematics Knowledge for Teaching Geometry
ERIC Educational Resources Information Center
Eli, Jennifer A.; Mohr-Schroeder, Margaret J.; Lee, Carl W.
2013-01-01
Effective competition in a rapidly growing global economy places demands on a society to produce individuals capable of higher-order critical thinking, creative problem solving, connection making, and innovation. We must look to our teacher education programs to help prospective middle grades teachers build the mathematical habits of mind that…
Active learning increases student performance in science, engineering, and mathematics.
Freeman, Scott; Eddy, Sarah L; McDonough, Miles; Smith, Michelle K; Okoroafor, Nnadozie; Jordt, Hannah; Wenderoth, Mary Pat
2014-06-10
To test the hypothesis that lecturing maximizes learning and course performance, we metaanalyzed 225 studies that reported data on examination scores or failure rates when comparing student performance in undergraduate science, technology, engineering, and mathematics (STEM) courses under traditional lecturing versus active learning. The effect sizes indicate that on average, student performance on examinations and concept inventories increased by 0.47 SDs under active learning (n = 158 studies), and that the odds ratio for failing was 1.95 under traditional lecturing (n = 67 studies). These results indicate that average examination scores improved by about 6% in active learning sections, and that students in classes with traditional lecturing were 1.5 times more likely to fail than were students in classes with active learning. Heterogeneity analyses indicated that both results hold across the STEM disciplines, that active learning increases scores on concept inventories more than on course examinations, and that active learning appears effective across all class sizes--although the greatest effects are in small (n ≤ 50) classes. Trim and fill analyses and fail-safe n calculations suggest that the results are not due to publication bias. The results also appear robust to variation in the methodological rigor of the included studies, based on the quality of controls over student quality and instructor identity. This is the largest and most comprehensive metaanalysis of undergraduate STEM education published to date. The results raise questions about the continued use of traditional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teaching practice in regular classrooms. PMID:24821756
Active learning increases student performance in science, engineering, and mathematics
Freeman, Scott; Eddy, Sarah L.; McDonough, Miles; Smith, Michelle K.; Okoroafor, Nnadozie; Jordt, Hannah; Wenderoth, Mary Pat
2014-01-01
To test the hypothesis that lecturing maximizes learning and course performance, we metaanalyzed 225 studies that reported data on examination scores or failure rates when comparing student performance in undergraduate science, technology, engineering, and mathematics (STEM) courses under traditional lecturing versus active learning. The effect sizes indicate that on average, student performance on examinations and concept inventories increased by 0.47 SDs under active learning (n = 158 studies), and that the odds ratio for failing was 1.95 under traditional lecturing (n = 67 studies). These results indicate that average examination scores improved by about 6% in active learning sections, and that students in classes with traditional lecturing were 1.5 times more likely to fail than were students in classes with active learning. Heterogeneity analyses indicated that both results hold across the STEM disciplines, that active learning increases scores on concept inventories more than on course examinations, and that active learning appears effective across all class sizes—although the greatest effects are in small (n ≤ 50) classes. Trim and fill analyses and fail-safe n calculations suggest that the results are not due to publication bias. The results also appear robust to variation in the methodological rigor of the included studies, based on the quality of controls over student quality and instructor identity. This is the largest and most comprehensive metaanalysis of undergraduate STEM education published to date. The results raise questions about the continued use of traditional lecturing as a control in research studies, and support active learning as the preferred, empirically validated teaching practice in regular classrooms. PMID:24821756
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
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
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…
Increasing Fourth-Grade Students' Proficiency at Solving Mathematical Word Problems
ERIC Educational Resources Information Center
Norford, Jennifer A.
2012-01-01
The purpose of the study was to identify effective pedagogical strategies to increase 4th grade students' mathematics problem-solving skills. Numerous researchers have looked at mathematics problem solving; however, there is a scarcity of data relating to 4th grade mathematics problem solving proficiency. Fourth grade students at the…
Increasing Students' Involvement in Technology-Supported Mathematics Lesson Sequences
ERIC Educational Resources Information Center
Prodromou, Theodosia; Lavicza, Zsolt; Koren, Balazs
2015-01-01
This article aims to report on a pilot or proof of concept study with experienced Hungarian teachers who introduced mathematical concepts through a sequence of lessons utilising a pedagogical framework (Lavicza, Hohenwarter, Jones, Lu and Dawes, 2009a and Lavicza, Hohenwarter and Lu 2009b) for general technology integration. Our aim was to examine…
Increasing military social work knowledge: an evaluation of learning outcomes.
Forgey, Mary Ann; Young, Sharon L
2014-02-01
Service members and veterans face a myriad of health, mental health, and social challenges stemming from the combat and operational stressors experienced during deployment and the challenges ofreintegration to civilian life. To intervene effectively with this population, social workers must be knowledgeable about these issues and the cultural context within which they occur. Although schools of social work across the country are developing course work in military social work, little is known about the learning outcomes of these courses. This article describes a military social work course that was developed to increase student preparedness to work with a military or veteran population and the learning outcomes achieved. Using a quasi-experimental pre-post design, this study compared the learning outcomes of students enrolled in the course with a group of students who had not taken the course. To measure this knowledge, the authors developed a 50-item Military Social Work Knowledge Scale for the study. Significant differences between pre- and posttest scores were found for the social work students enrolled in the course. Specific areas of knowledge that increased for the class participants included knowledge about cultural sensitivity to military populations and knowledge about service and advocacy frameworks. PMID:24693599
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…
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
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,…
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…
ERIC Educational Resources Information Center
Doerr, Helen M.; Wood, Terry
2004-01-01
This research forum addresses the question: what is the nature of the mathematical knowledge that is needed for secondary teaching? Six international contributors: (1) Australia (Kaye Stacey); (2) Brazil (Marcelo Borba); (3) Israel (Ruhama Even); (4) Norway (Bodil Kleve and Barbara Jaworski); (5) Taiwan (Fou-Lai Lin); and (6) USA (Helen Doerr)…
Does Strategy Knowledge Influence Working Memory in Children with Mathematical Disabilities?
ERIC Educational Resources Information Center
Keeler, Marsha L.; Swanson, H. Lee
2001-01-01
A study investigated the relationship between working memory (WM), declarative strategy knowledge, and math achievement in 111 children with and without mathematical disabilities (MD). Results found verbal and visual-spatial WM, stable verbal strategy choices, and expert strategy choices related to visual-spatial processing all contributed…
Developing Primary Pre-Service Teachers' Mathematical Content Knowledge during Practicum Teaching
ERIC Educational Resources Information Center
Livy, Sharyn L.; Vale, Colleen; Herbert, Sandra
2016-01-01
While it is recognised that a teachers' mathematical content knowledge (MCK) is crucial for teaching, less is known about when different categories of MCK develop during teacher education. This paper reports on two primary pre-service teachers, whose MCK was investigated during their practicum experiences in first, second and fourth years of a…
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…
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…
NASA Astrophysics Data System (ADS)
Bidaibekov, Yessen Y.; Kornilov, Viktor S.; Kamalova, Guldina B.; Akimzhan, Nagima Sh.
2015-09-01
Methodical aspects of teaching students of higher educational institutions of natural science orientations of training of inverse problems for differential equations are considered in the article. A fact that an academic knowledge and competence in the field of applied mathematics is formed during such training is taken into consideration.
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…
Measuring Pre-Service Primary Teachers' Knowledge for Teaching Mathematics
ERIC Educational Resources Information Center
Beswick, Kim; Goos, Merrilyn
2012-01-01
This paper reports on the knowledge for teaching mathematics of 294 pre-service primary teachers from seven Australian universities participating in a project aimed at establishing a culture of evidence-based improvement of teacher education. The project was funded by the Australian Learning and Teaching Council. Rasch measurement techniques were…
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…
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…
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…
ERIC Educational Resources Information Center
van Klinken, Eduarda
2010-01-01
Poor results in Queensland Year Three NAPLAN Numeracy tests have provided a focus to critically review the classroom practices of lower primary mathematics teachers. This paper outlines how pedagogical content knowledge can be strengthened by emphasising conceptual understanding, by utilising dynamic classroom discourse, by an awareness of…
ERIC Educational Resources Information Center
Venville, Grady; Rennie, Leonie; Wallace, John
2004-01-01
This article reports on students' decision making processes and sources of knowledge in an integrated teaching and learning setting. The study was conducted in a Year 9 classroom as students undertook a 10-week solar-powered boat project and were exposed to related concepts from science, technology and mathematics. Data collection involved…
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…
Developing Teachers' Knowledge of Students as Learners of Mathematics through Structured Interviews
ERIC Educational Resources Information Center
Jenkins, Oliver F.
2010-01-01
A structured interview process is proffered as an effective means to advance prospective teachers' understandings of students as learners of mathematics, a key component of pedagogical content knowledge. The interview process is carried out in three phases with the primary objective of developing listening skills for accessing students'…
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…
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…
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…
ERIC Educational Resources Information Center
Santos-Trigo, Manuel; Barrera-Mora, Fernando
2011-01-01
The study documents the extent to which high school teachers reflect on their need to revise and extend their mathematical and practicing knowledge. In this context, teachers worked on a set of tasks as a part of an inquiring community that promoted the use of different computational tools in problem solving approaches. Results indicated that the…
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…
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…
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)…
ERIC Educational Resources Information Center
Turner, Erin E.; Drake, Corey
2016-01-01
Researchers have studied the preparation of elementary teachers to teach mathematics to students from diverse racial, ethnic, and linguistic backgrounds by focusing either on teachers' learning about children's mathematical thinking (CMT) or, less frequently, about children's cultural funds of knowledge (CFoK) related to mathematics. Despite this…
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…
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…
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…
NASA Astrophysics Data System (ADS)
Şahin, Ömer; Gökkurt, Burçin; Soylu, Yasin
2016-05-01
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 universities in Turkey. The participants were selected with the purposive sampling method which is one of the non-random sampling methods. Case study method, which is based on the qualitative research approach, was used. The answers given by secondary school students to fraction-related open-ended questions in the study of Soylu and Soylu were used as the data collection tool. The obtained data were analyzed via the content analysis technique. The analyses showed that the prospective mathematics teachers' pedagogical content knowledge on fractions was not at an adequate level in identifying and correcting students' errors. However, it was observed that the prospective teachers experienced more difficulty in the knowledge of instructional strategies compared to the knowledge of understanding students.
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…
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…
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…
ERIC Educational Resources Information Center
Moss, Joan; Beatty, Ruth
2010-01-01
Three classrooms of Grade 4 students from different schools and diverse backgrounds collaborated in early algebra research to solve a series of linear and quadratic generalizing problems. Results revealed that high- and low-achieving students were able to solve problems of recognized difficulty. We discuss Knowledge Building principles and…
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…
Mazzocco, Michèle M M; Myers, Gwen F; Lewis, Katherine E; Hanich, Laurie B; Murphy, Melissa M
2013-06-01
Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to one-half, fraction pairs with common denominators) differentiates those with mathematics learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics and whether long-term learning trajectories of this knowledge also differentiate these groups. We confirmed that although fourth graders with TA (n=93) were more accurate in evaluating "one-half" fractions than in evaluating "non-half" fractions (until they reached ceiling performance levels on both types of fractions), children with MLD (n=11) did not show a one-half advantage until Grade 7 and did not reach ceiling performance even by Grade 8. Both the MLD and LA groups had early difficulties with fractions, but by Grade 5 the LA group approached performance levels of the TA group and deviated from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short-lived for the TA group (because ceiling level was achieved across formats), whereas it was slightly more persistent for the LA group and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties vary across children with math difficulties (MLD or LA). PMID:23587941
Mazzocco, Michèle M. M.; Myers, Gwen F.; Lewis, Katherine E.; Hanich, Laurie B.; Murphy, Melissa M.
2014-01-01
Fractions pose significant challenges for many children, but for some children those challenges persist into high school. Here we administered a fractions magnitude comparison test to 122 children, from Grades 4 to 8, to test whether their knowledge of fractions typically learned early in the sequence of formal math instruction (e.g., fractions equivalent to “one-half,” and fraction pairs with common denominators) differentiates those with mathematical learning disability (MLD) versus low achievement (LA) or typical achievement (TA) in mathematics, and whether long term learning trajectories of this knowledge also differentiate these groups. We confirmed that although 4th graders with LA (n = 18) or TA (n = 93) are more accurate evaluating one-half vs. non-half fractions (until they reach ceiling performance levels on both types of fractions), children with MLD (n=11) do not show a one-half advantage until Grade 7 and do not reach ceiling performance even by Grade 8. Both the MLD and LA groups have early difficulties with fractions, but by Grade 5 the LA group approaches performance levels of the TA group and deviates from the MLD group. All groups showed a visual model advantage over Arabic number representation of fractions, but this advantage was short lived for the TA group (because ceiling level was achieved across formats), slightly more persistent for the LA group, and persisted through Grade 8 for children with MLD. Thus, difficulties with fractions persist through Grade 8 for many students, but the nature and trajectories of those difficulties varies across children with math difficulties (MLD or LA). PMID:23587941
Knowledge dissemination and use in science and mathematics education: A literature review
NASA Astrophysics Data System (ADS)
Hutchinson, Janet R.; Huberman, Michael
1994-03-01
A synthesis of the literature on knowledge dissemination and use in education, notably in science and mathematics, is presented. Perspectives have changed in the ways in which knowledge and products are seen to reach potential users. From the top-down, linear models, we have come closer to bottom-up approaches and to the crucial role of linking agents. At present, the most influential approach is a "constructivist" one, whereby research and other kinds of specialized knowledge is exchanged between researchers and professionals in a mutually constructed social context. While there is still debate over the best predictors of successful knowledge use, the scope of the field has been considerably enlarged by including users' perspectives. To some extent then, specialists in this field are now working in a new paradigm.
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…
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…
A Guide to Mathematics Coaching: Processes for Increasing Student Achievement
ERIC Educational Resources Information Center
Hull, Ted H.; Balka, Don S.; Miles, Ruth Harbin
2010-01-01
Math coaches play a vital role in strengthening math instruction and learning in schools. However, without a collegial relationship with the teachers they are trying to help, it is difficult to foster productive collaborations that lead to better teaching practice and increased student achievement. This resource helps coaches confidently clarify,…
ERIC Educational Resources Information Center
Yesildere Imre, Sibel; Akkoc, Hatice
2012-01-01
The purpose of this study is to investigate the development of three prospective elementary mathematics teachers' pedagogical content knowledge (PCK) of number patterns with its two components: (1) knowledge of students' understanding and difficulties and (2) knowledge of topic-specific strategies and representations. For our investigation, we use…
A fuzzy mathematics model for radioactive waste characterization by process knowledge
Smith, M.; Stevens, S.; Elam, K.; Vrba, J.
1994-12-31
Fuzzy mathematics and fuzzy logic are means for making decisions that can integrate complicated combinations of hard and soft factors and produce mathematically validated results that can be independently verified. In this particular application, several sources of information regarding the waste stream have been compiled, including facility operating records, other waste generated from the facility in the past, laboratory analysis results, and interviews with facility personnel. A fuzzy mathematics model is used to interrelate these various sources of information and arrive at a defensible estimate of the contaminant concentration in the final waste product. The model accounts for the separate process knowledge-based contaminant concentrations by providing a weighted averaging technique to incorporate information from the various sources. Reliability estimates are provided for each of the component pieces of information and combined using the model into an estimate that provides a near-probabilistic value for contaminant concentration. The speadsheet accounts for the estimated uncertainty in the concentration on the basis of {open_quotes}reliability curves,{close_quotes} which are derived from personal process knowledge as well as limited independent measurements.
NASA Astrophysics Data System (ADS)
Peace, Heather Marie Bjorum
This research focuses on a cohort of pre-service elementary teachers and their perspectives with respect to the knowledge required for teaching science and mathematics at the beginning and end of their first academic year in a teacher preparation program. An activity, designed to emphasize the differences between factual/procedural knowledge and conceptual knowledge in elementary mathematics and science, was analyzed along with classroom discussions in order to gain deeper understandings of the perspectives of knowledge for teaching for the given cohort. Additionally, subject specific efficacy beliefs were compared to teaching confidence ratings related to specific science and mathematics topics. The pre-service teachers' expressed a variety of ideas regarding the role of content knowledge, and the different types of content knowledge (i.e., factual/procedural and conceptual), in teaching mathematics and science. Furthermore, their perceptions of the nature of mathematics and the nature of science were discussed. By utilizing both quantitative and qualitative methods, this project was able to not only note data trends, but also obtain depth and richness regarding conceptions of the knowledge required for teaching mathematics and science provided by the voices of the pre-service teachers.
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…
ERIC Educational Resources Information Center
Polly, Drew; Neale, Henry; Pugalee, David K.
2014-01-01
This study examined how a task-focused, year-long mathematics professional development program influenced elementary school teachers' knowledge, beliefs, and practices. Participants completed 84 h of professional development over 13 months that were focused on exploring, modifying and implementing cognitively-demanding mathematical tasks.…
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…
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…
ERIC Educational Resources Information Center
Bleiler, Sarah K.
2015-01-01
Collaborations between mathematicians and mathematics teacher educators are increasingly being expected, and realized, within the context of mathematics teacher education. Most research related to collaborative efforts between members of the mathematics and mathematics education communities has focused on the products, rather than the process of…
Validity issues in the evaluation of a measure of science and mathematics teacher knowledge
NASA Astrophysics Data System (ADS)
Talbot, Robert M., III
2011-12-01
This study investigates the reliability and validity of an instrument designed to measure science and mathematics teachers' strategic knowledge . Strategic knowledge is conceptualized as a construct that is related to pedagogical knowledge and is comprised of two dimensions: Flexible Application (FA) and Student Centered Instruction (SCI). The FA dimension describes how a science teacher invokes, applies and modifies her instructional repertoire in a given teaching context. The SCI dimension describes how a science teacher conceives of a given situation as an opportunity for active engagement with the students. The Flexible Application of Student-Centered Instruction (FASCI) survey instrument was designed to measure science teachers' strategic knowledge by eliciting open-ended responses to scenario-based items. This study addresses the following overarching question: What are some potential issues pertaining to the validity of measures of science and mathematics teacher knowledge? Using a validity argument framework, different sources of evidence are identified, collected, and evaluated to examine support for a set or propositions related to the intended score interpretation and instrument use: FASCI scores can be used to compare and distinguish the strategic knowledge of novice science and mathematics teachers in the evaluation of teacher education programs. Three separate but related studies are presented and discussed. These studies focus on the reliability of FASCI scores, the effect of adding specific science content to the scenario-based items, and the observation of strategic knowledge in teaching practice. Serious issues were found with the reliability of scores from the FASCI instrument. It was also found that adding science content to the scenario-based items has an effect on FASCI scores, but not for the reason hypothesized. Finally, it was found that more evidence is needed to make stronger claims about the relationship between FASCI scores and novice
Buring, Shauna M.; Papas, Elizabeth
2013-01-01
Objective. To assess doctor of pharmacy (PharmD) students’ mathematics ability by content area before and after completing a required pharmaceutical calculations course and to analyze changes in scores. Methods. A mathematics skills assessment was administered to 2 cohorts of pharmacy students (class of 2013 and 2014) before and after completing a pharmaceutical calculations course. The posttest was administered to the second cohort 6 months after completing the course to assess knowledge retention. Results. Both cohorts performed significantly better on the posttest (cohort 1, 13% higher scores; cohort 2, 15.9% higher scores). Significant improvement on posttest scores was observed in 6 of the 10 content areas for cohorts 1 and 2. Both cohorts scored lower in percentage calculations on the posttest than on the pretest. Conclusions. A required, 1-credit-hour pharmaceutical calculations course improved PharmD students’ overall ability to perform fundamental and application-based calculations. PMID:23966727
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,…
The impact of assumed knowledge entry standards on undergraduate mathematics teaching in Australia
NASA Astrophysics Data System (ADS)
King, Deborah; Cattlin, Joann
2015-10-01
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 may be returning to study, or who are changing career paths but do not have particular prerequisite study, now have more flexible pathways. However, there is mounting evidence to indicate that there are also significant negative impacts associated with assumed knowledge approaches, with large numbers of students enrolling in degrees without the stated assumed knowledge. For students, there are negative impacts on pass rates and retention rates and limitations to pathways within particular degrees. For institutions, the necessity to offer additional mathematics subjects at a lower level than normal and more support services for under-prepared students impacts on workloads and resources. In this paper, we discuss early research from the First Year in Maths project, which begins to shed light on the realities of a system that may in fact be too flexible.
NASA Technical Reports Server (NTRS)
Mahon, Lee
1997-01-01
The purpose of this proposal was to field test and evaluate a Teacher Training program that would prepare teachers to increase the motivation and achievement of culturally diverse students in the areas of science and mathematics. Designed as a three year program, this report covers the first two years of the training program at the Ronald McNair School in the Ravenswood School district, using the resources of the NASA Ames Research Center and the California Framework for Mathematics and Science.
A brief simulation intervention increasing basic science and clinical knowledge
Sheakley, Maria L.; Gilbert, Gregory E.; Leighton, Kim; Hall, Maureen; Callender, Diana; Pederson, David
2016-01-01
Background The United States Medical Licensing Examination (USMLE) is increasing clinical content on the Step 1 exam; thus, inclusion of clinical applications within the basic science curriculum is crucial. Including simulation activities during basic science years bridges the knowledge gap between basic science content and clinical application. Purpose To evaluate the effects of a one-off, 1-hour cardiovascular simulation intervention on a summative assessment after adjusting for relevant demographic and academic predictors. Methods This study was a non-randomized study using historical controls to evaluate curricular change. The control group received lecture (nl=515) and the intervention group received lecture plus a simulation exercise (nl+s=1,066). Assessment included summative exam questions (n=4) that were scored as pass/fail (≥75%). USMLE-style assessment questions were identical for both cohorts. Descriptive statistics for variables are presented and odds of passage calculated using logistic regression. Results Undergraduate grade point ratio, MCAT-BS, MCAT-PS, age, attendance at an academic review program, and gender were significant predictors of summative exam passage. Students receiving the intervention were significantly more likely to pass the summative exam than students receiving lecture only (P=0.0003). Discussion Simulation plus lecture increases short-term understanding as tested by a written exam. A longitudinal study is needed to assess the effect of a brief simulation intervention on long-term retention of clinical concepts in a basic science curriculum. PMID:27060102
Mathematical learning models that depend on prior knowledge and instructional strategies
NASA Astrophysics Data System (ADS)
Pritchard, David E.; Lee, Young-Jin; Bao, Lei
2008-06-01
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 depend on the type of instruction. We introduce a connectedness model whose connectedness parameter measures the degree to which the rate of learning is proportional to prior knowledge. Over a wide range of pretest scores on standard tests of introductory physics concepts, it fits high-quality data nearly within error. We suggest that data from MIT have low connectedness (indicating memory-based learning) because the test used the same context and representation as the instruction and that more connected data from the University of Minnesota resulted from instruction in a different representation from the test.
NASA Astrophysics Data System (ADS)
Gobithaasan, R. U.; Miura, Kenjiro T.; Hassan, Mohamad Nor
2014-07-01
Computer Aided Geometric Design (CAGD) which surpasses the underlying theories of Computer Aided Design (CAD) and Computer Graphics (CG) has been taught in a number of Malaysian universities under the umbrella of Mathematical Sciences' faculty/department. On the other hand, CAD/CG is taught either under the Engineering or Computer Science Faculty. Even though CAGD researchers/educators/students (denoted as contributors) have been enriching this field of study by means of article/journal publication, many fail to convert the idea into constructive innovation due to the gap that occurs between CAGD contributors and practitioners (engineers/product/designers/architects/artists). This paper addresses this issue by advocating a number of technologies that can be used to transform CAGD contributors into innovators where immediate impact in terms of practical application can be experienced by the CAD/CG practitioners. The underlying principle of solving this issue is twofold. First would be to expose the CAGD contributors on ways to turn mathematical ideas into plug-ins and second is to impart relevant CAGD theories to CAD/CG to practitioners. Both cases are discussed in detail and the final section shows examples to illustrate the importance of turning mathematical knowledge into innovations.
Types of Changes That Occur as Declarative Knowledge Increases
ERIC Educational Resources Information Center
Oosterhof, Albert
2012-01-01
Declarative knowledge involves being able to state and explain characteristics, terminologies, properties, phenomena, concepts, principles, and techniques. Chi and Ohlsson (2005) characterize it as the dominant form of knowledge, maintaining that it does not involve isolated units but rather is organized as semantic networks, theories, schemas, or…
ERIC Educational Resources Information Center
Yigit, Melike
2014-01-01
In recent years, researchers have advanced the Technological, Pedagogical, and Content Knowledge (TPACK) framework to describe both in-service and pre-service teachers' knowledge related to effectively integrating technology. This study is a systematic literature review about pre-service mathematics teachers' (PSMTs) development of TPACK, and the…
ERIC Educational Resources Information Center
Yigit, Melike
2014-01-01
In recent years, researchers have advanced the Technological, Pedagogical, and Content Knowledge (TPACK) framework to describe both in-service and pre-service teachers' knowledge related to effectively integrating technology. This study is a systematic literature review about pre-service mathematics teachers' (PSMTs) development of…
ERIC Educational Resources Information Center
Kersting, Nicole B.; Givvin, Karen B.; Sotelo, Francisco L.; Stigler, James W.
2010-01-01
This study explores the relationship between teacher knowledge and student learning in the area of mathematics by developing and evaluating an innovative approach to assessing teacher knowledge. This approach is based on teachers' analyses of classroom video clips. Teachers watched 13 video clips of classroom instruction and then provided written…
NASA Astrophysics Data System (ADS)
Venville, Grady; Rennie, Léonie; Wallace, John
2004-04-01
This article reports on students'' decision making processes and sources of knowledge in an integrated teaching and learning setting. The study was conducted in a Year 9 classroom as students undertook a 10-week solar-powered boat project and were exposed to related concepts from science, technology and mathematics. Data collection involved detailed case studies of three pairs of students, interviews, classroom observation and analysis of the artefacts and portfolios produced by the students. Students were found to access knowledge from a variety of sources, including teacher''s notes from formal instruction, informal interactions with the teacher, observation of and interaction with other students, as well as sources outside the classroom. However, the utility of the knowledge sources was influenced by the nature of the task. When students were performing open-ended tasks, they drew on a wider variety of knowledge sources than when they were performing less open tasks. Moreover, subject discipline-based sources often were not as helpful in solving open tasks. The study leads to several important implications for designing teaching and learning in integrated curriculum settings.
Does strategy knowledge influence working memory in children with mathematical disabilities?
Keeler, M L; Swanson, H L
2001-01-01
This study investigated the relationship between working memory (WM), declarative strategy knowledge, and math achievement in children with and without mathematical disabilities (MD). Experiment 1 examined the relationship between strategy knowledge, verbal WM, and visual-spatial WM in children with MD as a function of initial, gain, and maintenance conditions. The results showed that after partialing the influence of reading, stable strategy choices rather than specific strategy knowledge was related to verbal and visual-spatial WM span in high demand (maintenance) conditions. Experiment 2 compared children with MD to a group of chronological age-matched children and a group of math ability-matched children on the same conditions as Experiment 1. Age-matched children's verbal and visual-spatial WM performance was superior to that of children with MD, whereas WM performance was statistically comparable between children with MD and younger children matched on math ability. The selection of expert strategies was related to high WM span scores in the initial conditions. After controlling for reading achievement in a regression analysis, verbal and visual-spatial WM, stable verbal strategy choices, and expert strategy choices related to visual-spatial processing all contributed independent variance to math achievement. Overall, these results suggest that WM and math achievement are related to strategy knowledge. PMID:15503591
ERIC Educational Resources Information Center
Nasir, Na'ilah Suad; Hand, Victoria; Taylor, Edd V.
2008-01-01
This chapter is about culture and mathematics teaching and learning. The authors' goal is to offer a thoughtful treatment of the role of culture in the teaching and learning of mathematics and to synthesize literature that is relevant to this concern from multiple subdisciplines in education, including math education, educational anthropology,…
Morgan, Paul L; Farkas, George; Wu, Qiong
2011-01-01
The authors used a large sample of children (N ≈ 7,400) participating in the Early Childhood Longitudinal Study--Kindergarten Cohort (ECLS-K) to estimate kindergarten children's academic achievement growth trajectories in reading and mathematics. The authors were particularly interested in whether the growth trajectories of children with learning disabilities (LD) or speech language impairments (SLI)--as well as those of other groups of children--were consistent with a cumulative or compensatory developmental cycle. Both LD and SLI children displayed significantly lower levels of kindergarten reading achievement than nondisabled children. However, and over the subsequent 5 years of elementary school, only children with SLI lagged increasingly behind nondisabled peers in their reading skills growth. The authors observed a different pattern for mathematics achievement. Children with LD, but not SLI, lagged increasingly behind nondisabled children in their mathematics skills growth. The authors also observed some consistency in "poor-get-poorer" effects across reading and mathematic achievement for additional population subgroups. Those kindergarten children who were from lower socioeconomic status families, who were African American, and who more frequently displayed learning-related behavior problems initially had lower levels of reading and mathematics achievement and also lagged increasingly behind in their acquisition of these skills over time. Some groups of children, including those with SLI, experience a cumulative rather than a compensatory cycle of achievement growth. PMID:21856991
ERIC Educational Resources Information Center
Taylor, Cynthia E.
2011-01-01
Prospective mathematics teachers (PTs) need to develop pedagogical content knowledge (PCK) to improve the teaching and learning of mathematics. Therefore, faculty who prepare teachers of mathematics (i.e., mathematics teacher educators [MTEs]), need to help PTs develop PCK in their courses (Marks, 1990; Mason, 2008). Yet, we know very little about…
ERIC Educational Resources Information Center
Zhao, Yan-jun
2011-01-01
Ethnic students will face the problem of "cultural discontinuities" when they learn school mathematics. "Cultural discontinuity" is the main obstacle when they learn school mathematics. Teachers should put up the bridge for introducing ethnic mathematical knowledge into school mathematics teaching. The concrete tactics are: widening ethnic…
Food-based Science Curriculum Increases 4(th) Graders Multidisciplinary Science Knowledge.
Hovland, Jana A; Carraway-Stage, Virginia G; Cela, Artenida; Collins, Caitlin; Díaz, Sebastián R; Collins, Angelo; Duffrin, Melani W
2013-10-01
Health professionals and policymakers are asking educators to place more emphasis on food and nutrition education. Integrating these topics into science curricula using hand-on, food-based activities may strengthen students' understanding of science concepts. The Food, Math, and Science Teaching Enhancement Resource (FoodMASTER) Initiative is a compilation of programs aimed at using food as a tool to teach mathematics and science. Previous studies have shown that students experiencing the FoodMASTER curriculum were very excited about the activities, became increasingly interested in the subject matter of food, and were able to conduct scientific observations. The purpose of this study was to: 1) assess 4(th) graders food-related multidisciplinary science knowledge, and 2) compare gains in food-related science knowledge after implementation of an integrated, food-based curriculum. During the 2009-2010 school year, FoodMASTER researchers implemented a hands-on, food-based intermediate curriculum in eighteen 4(th) grade classrooms in Ohio (n=9) and North Carolina (n=9). Sixteen classrooms in Ohio (n=8) and North Carolina (n=8), following their standard science curricula, served as comparison classrooms. Students completed a researcher-developed science knowledge exam, consisting of 13 multiple-choice questions administered pre- and post-test. Only subjects with pre- and post-test scores were entered into the sample (Intervention n=343; Control n=237). No significant differences were observed between groups at pre-test. At post-test, the intervention group scored (9.95±2.00) significantly higher (p=.000) than the control group (8.84±2.37) on a 13-point scale. These findings suggest the FoodMASTER intermediate curriculum is more effective than a standard science curriculum in increasing students' multidisciplinary science knowledge related to food. PMID:25152539