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1. Professional Standards and Professional Learning: A Position Paper

Author

Mathematics Education Research Group of Australasia and McDaid, Karen

Abstract

The educational discourse in recent years in Australia, and in particular NSW has been on advancing the status of the teaching profession through the development of a framework of standards, and by supporting the nature of teachers' work in addition to improving student-learning outcomes. The close link between student learning outcomes and quality mathematics teaching has resulted in the call for an increase in teacher accountability and quality. This paper is an exploration of the relevant literature that focused on the professionalisation of the teaching profession in Australia and its potential impact on teaching in Australia. [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

Published
2010

2. Annual Proceedings of Selected Research and Development Papers Presented at the Annual Convention of the Association for Educational Communications and Technology (35th, Louisville, Kentucky, 2012). Volume 2

Author

Association for Educational Communications and Technology and Simonson, Michael

Abstract

For the thirty-fifth year, the Research and Theory Division of the Association for Educational Communications and Technology (AECT) is sponsoring the publication of these Proceedings. Papers published in this volume were presented at the national AECT Convention in Louisville, Kentucky. The Proceedings of AECT's Convention are published in two volumes. Volume 1 contains papers dealing primarily with research and development topics. Papers dealing with the practice of instructional technology including instruction and training issues are contained in Volume 2. (Individual papers contain references.) [For Volume 1, see ED546875.]

Published
2012

3. Students''Understanding' of Tasks in the View of Mathematics Teachers. Occasional Paper 58.

Author

Bielefeld Univ. (West Germany). Inst. for Didactics in Mathematics., Bromme, Rainer, and Juhl, Katharina

Abstract

Investigated was the question of whether understanding is explained by means of concepts referring to tasks, being domain-specific for certain subject matter areas, or is it explained by concepts which extend across tasks and are not domain-specific? Also explored were: (1) which explanatory concepts are present, that is, which steps and conditions of understanding are thematized in the explanations? and (2) do explanatory concepts differentiate according to success and failure in understanding or by sex? A two-dimensional table was constructed for coding explanations of 20 male mathematics teachers in grades 5 and 6 of schools in West Germany. Results indicated a marked predominance of explanations referring to domain-specific tasks as compared to explanations extending across tasks. The order of frequency of steps and conditions of understanding are noted, and sex differences in a few categories were found. The discussion focuses on: (1) reference to the task and type of explanation; and (2) obtaining explanations referring to task: problems and opportunities. (MNS)

Published
1984

4. Proceedings of the International Association for Development of the Information Society (IADIS) International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA) (18th, Virtual, October 13-15, 2021)

Author

International Association for Development of the Information Society (IADIS), Sampson, Demetrios G., Ifenthaler, Dirk, and Isaías, Pedro

Abstract

These proceedings contain the papers of the 18th International Conference on Cognition and Exploratory Learning in the Digital Age (CELDA 2021), held virtually, due to an exceptional situation caused by the COVID-19 pandemic, from October 13-15, 2021, and organized by the International Association for Development of the Information Society (IADIS). The CELDA conference aims to address the main issues concerned with evolving learning processes and supporting pedagogies and applications in the digital age. There have been advances in both cognitive psychology and computing that have affected the educational arena. The convergence of these two disciplines is increasing at a fast pace and affecting academia and professional practice in many ways. The CELDA 2021 Conference received 68 submissions from more than 21 countries. Out of the papers submitted, 34 were accepted as full papers for an acceptance rate of 50%; 16 were accepted as short papers, and 2 were accepted as reflection papers. In addition to the presentation of full, short and reflection papers, the conference also includes one keynote presentation from an internationally distinguished researcher: Dr. David Scaradozzi, Department of Information Engineering, Università Politecnica delle Marche, Italy. [Individual papers are indexed in ERIC.]

Published
2021

5. Confident Learning Curves in Additive Factors Modeling

Author

Goutte, Cyril and Durand, Guillaume

Abstract

Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is some uncertainty associated with estimating the model from that sample, and a risk that the inferences made using learning curves derived from the estimated model are over-confident one way or another. Based on previous work modeling the uncertainty on Additive Factors Model parameters, we derive a principled way to quantify the confidence in learning curves associated with each knowledge component. We show that our approach leads to relatively tight bounds on the learning curves, much tighter than a naive approach relying only on parameter uncertainty. This also reveals a disparity across knowledge components regarding how confident one can be in how well these skills are mastered. [For the full proceedings, see ED607784.]

Published
2020

6. Proceedings of the International Conference on Educational Data Mining (EDM) (12th, Montreal, Canada, July 2-5, 2019)

Author

International Educational Data Mining Society, Lynch, Collin F., Merceron, Agathe, Desmarais, Michel, and Nkambou, Roger

Abstract

The 12th iteration of the International Conference on Educational Data Mining (EDM 2019) is organized under the auspices of the International Educational Data Mining Society in Montreal, Canada. The theme of this year's conference is EDM in Open-Ended Domains. As EDM has matured it has increasingly been applied to open-ended and ill-defined tasks such as writing, design, and collaborative problem solving, and it has been used in new informal contexts where student actions are at best semi-structured. This iteration of the conference includes a range of work in these and other areas. This year's conference features three invited talks: Julita Vassileva, Professor at the Department of Computer Science, University of Saskatchewan, Canada; Steve Ritter, Co-Founder and Chief Scientist, Carnegie Learning Inc., Pittsburgh; and Michael Mozer, Professor Department of Computer Science and Institute of Cognitive Science University of Colorado. The number of accepted papers include 22 full papers and 42 short papers. An additional 47 papers were accepted to the poster track. The poster and demo track itself accepted 14 contributions out of 34 submissions. Together with the "Journal of Educational Data Mining" ("JEDM"), the EDM 2019 conference held a "JEDM" Track that provides researchers a venue to deliver more substantial mature work than is possible in a conference proceeding and to present their work to a live audience. The papers submitted to this track followed the "JEDM" peer review process. Two such papers are featured in the conference's program. Additionally this year, papers that were regularly published in the journal in 2018 were invited for presentation at the conference. Two authors accepted this invitation. The main conference invited contributions to an Industry Track in addition to the main track. The EDM 2019 Industry Track received eleven submissions of which six were accepted. The EDM conference continues its tradition of providing opportunities for young researchers to present their work and receive feedback from their peers and senior researchers. The doctoral consortium this year features eight such presentations. This year's conference includes also an invited talk by the authors of the 2018 winner of the EDM Test of Time Award. This year's talk is delivered by Mykola Pechenizkiy. In addition to the main program, there are three workshops: (1) Learning Analytics: Building bridges between the Education and the Computing communities; (2) Reinforcement Learning for Educational Data Mining; and (3) Workshop on EDM & Games: Leveling Up Engaged Learning with Data-Rich Analytics. Three tutorials were presented as well: (1) Sharing and Reusing Data and Analytic Methods with LearnSphere; (2) Causal Discovery with Tetrad in LearnSphere's Tigris and Designing and Developing Open; and (3) Pedagogically-Based Predictive Models using the Moodle Analytics API.

Published
2019

7. Desirable Difficulty and Other Predictors of Effective Item Orderings

Author

International Educational Data Mining Society, Tang, Steven, Gogel, Hannah, and McBride, Elizabeth

Abstract

Online adaptive tutoring systems are increasingly being used in classrooms as a way to provide guided learning for students. Such tutors have the potential to provide tailored feedback based on specific student needs and misunderstandings. Bayesian knowledge tracing (BKT) is used to model student knowledge when knowledge is assumed to be changing throughout a single assessment period. The basic BKT model assumes that the chance a student transitions from "not knowing" to "knowing" after each item is the same, with each item in the tutor considered a learning opportunity. It could be the case, however, that learning is actually context sensitive; context in our analysis is the order in which the items were administered. In this paper, we use BKT models to find such context sensitive transition probabilities in a mathematics tutoring system and offer a methodology to test the significance of our model based findings. We employ cross validation techniques to find models where including item ordering context improves predictive capability compared to the base BKT models. We then use regression testing to try to find features that may predict the effectiveness of an item ordering. [For complete proceedings, see ED560503.]

Published
2015

8. Marzano's New Taxonomy as a Framework for Investigating Student Affect

Author

Irvine, Jeff

Abstract

In 1998 Marzano proposed a taxonomy of learning that integrated three domains or systems: the self system, which involves student motivation; the metacognitive system, involving goal setting and planning; and the cognitive system, required to complete the task at hand. Although extant for 20 years, a paucity of studies have utilized this taxonomy, even though employing Marzano's taxonomy as a framework is particularly appropriate for studies involving student affect. This study provides an exemplar of the use of Marzano's taxonomy as a framework to investigate the impact of a classroom intervention using active and social strategies to enhance student participation. Further, this paper provides suggestions for employing Marzano's taxonomy in other areas for practising teachers, teacher educators, and educational researchers.

Published
2020

9. Research in Mathematics Education through a Keyhole: Task Problematization

Author

Sierpinska, Anna

Abstract

There is a dream, among mathematics educators, for a common direction that would unite teachers, policy makers and researchers, with researchers collaborating to accumulate knowledge and thus contribute to the understanding and improvement of school practice. But this dream becomes less and less realistic in view of the tendency of mathematics education to multiply and diversify its epistemological foundations, theoretical approaches, methodologies and research questions. In response to concerns and challenges, mathematics educators started engaging in "meta-studies" such as attempts at outlining a definition of the domain, more or less comprehensive syntheses of research approaches and theories, comparison of theories, and analyses of articles published in leading journals and conference proceedings over the past 10 or more years. The author decided to take a more empirical approach and have a good look at a more or less "random sample" of papers, in the sense that they were not specially selected to represent this or that issue, theme, theoretical perspective or mathematical topic. In reading the reports, the author had several questions in mind. In this article, the author will initially give an overview of the results from this empirical study, and then elaborate a little more on one particular issue (namely, task problematization). She will give examples of task problematization from the 55 PME papers, but she shall also go beyond the sample and speak more broadly on various approaches to this kind of work, known to her from other publications.

Published
2004

10. School Mathematics: Options for the 1990s. Proceedings of the Conference (Madison, Wisconsin, December 5-8, 1983). [Volume 2].

Author

Wisconsin Center for Education Research, Madison., National Council of Teachers of Mathematics, Inc., Reston, VA., Romberg, Thomas A., and Stewart, Deborah M.

Abstract

Papers presented for a conference on school mathematics are compiled in this document. The purpose of the conference was: (1) to identify new goals and needed change for school mathematics; and (2) to recommend strategies or describe scenarios whereby these goals and changes can be realized. The document summarizes the deliberations in 20 papers plus discussion and summary reports. Following a background paper by Romberg, the status of mathematics instruction was discussed by Senese, Willoughby, Pollak, and Romberg. The mathematics curriculum was then explored, with the focus on new goals by Pollak, computers by Braun, statistics by Hunter, and needed changes by Usiskin. In the third section, focusing on learning and teaching, research on learning was described by Siegler and on teaching by Peterson. In the same section, Case discussed implications of cognitive science, Carpenter explored learning as a critical variable in curriculum reform, and Lappan discussed implications of research to mathematics teachers. Work group reports were then summarized, followed by papers on policy implications and impediments. Williams discussed the preparation of teachers, and then various perspectives were presented: Makhmaltchi, on publishers; Jones, on test developers; Barclay, on materials and producers; Hala, on mathematics supervisors; and Gawronski, on school administrators. Several annotated references are included. (MNS)

Published
1984

11. Semantic Features of Math Problems: Relationships to Student Learning and Engagement

Author

Slater, Stefan, Baker, Ryan, Ocumpaugh, Jaclyn, Inventado, Paul, Scupelli, Peter, and Heffernan, Neil

Abstract

The creation of crowd-sourced content in learning systems is a powerful method for adapting learning systems to the needs of a range of teachers in a range of domains, but the quality of this content can vary. This study explores linguistic differences in teacher-created problem content in ASSISTments using a combination of discovery with models and correlation mining. Specifically, we find correlations between semantic features of mathematics problems and indicators of learning and engagement, suggesting promising areas for future work on problem design. We also discuss limitations of semantic tagging tools within mathematics domains and ways of addressing these limitations.

Published
2016

12. Temporally Coherent Clustering of Student Data

Author

Klingler, Severin, Käser, Tanja, Solenthaler, Barbara, and Gross, Markus

Abstract

The extraction of student behavior is an important task in educational data mining. A common approach to detect similar behavior patterns is to cluster sequential data. Standard approaches identify clusters at each time step separately and typically show low performance for data that inherently suffer from noise, resulting in temporally inconsistent clusters. We propose an evolutionary clustering pipeline that can be applied to learning data, aiming at improving cluster stability over multiple training sessions in the presence of noise. Our model selection is designed such that relevant cluster evolution effects can be captured. The pipeline can be used as a black box for any intelligent tutoring system (ITS). We show that our method outperforms previous work regarding clustering performance and stability on synthetic data. Using log data from two ITS, we demonstrate that the proposed pipeline is able to detect interesting student behavior and properties of learning environments. [For the full proceedings, see ED592609.]

Published
2016

13. Semantic Features of Math Problems: Relationships to Student Learning and Engagement

Author

Slater, Stefan, Baker, Ryan, Ocumpaugh, Jaclyn, Inventado, Paul, Scupelli, Peter, and Heffernan, Neil

Abstract

The creation of crowd-sourced content in learning systems is a powerful method for adapting learning systems to the needs of a range of teachers in a range of domains, but the quality of this content can vary. This study explores linguistic differences in teacher-created problem content in ASSISTments using a combination of discovery with models and correlation mining. Specifically, we find correlations between semantic features of mathematics problems and indicators of learning and engagement, suggesting promising areas for future work on problem design. We also discuss limitations of semantic tagging tools within mathematics domains and ways of addressing these limitations. [For the full proceedings, see ED592609. For the grantee submission see ED571512.]

Published
2016

14. Critical Responses to Enduring Challenges in Mathematics Education. Proceedings of the Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education (37th, East Lansing, Michigan, November 5-8, 2015)

Author

International Group for the Psychology of Mathematics Education, North American Chapter (PME-NA), Bartell, Tonya Gau, Bieda, Kristen N., Putnam, Ralph T., Bradfield, Kenneth, and Dominguez, Higinio

Abstract

The theme of this year's conference is "Critical Responses to Enduring Challenges in Mathematics Education." The theme of this year's conference invites mathematics education scholars to reflect upon and critically respond to enduring challenges in teaching and learning mathematics for all students. To ignite discussion within the field, the organizers of this conference organized the conference around four focal-enduring challenges, each of which is featured in one of four plenary talks: (1) teaching as responsive to various conceptions of mathematics; (2) addressing the needs of marginalized populations in school mathematics; (3) the impact of teacher evaluation and high-stakes assessment in teaching; and (4) the role of assessment in teaching and learning. It is the hope of the organizers that the conference will catalyze collective reflection, collaborative inquiry, and discussion about various means for responding to and addressing these, and other, challenges. Submissions received numbered 528. The overall acceptance rate was 64%. The conference program includes 92 Research Report sessions, 96 sessions, 136 Posters, and 12 Working Groups. Chapters include: (1) Plenary Papers; (2) Special Session; (3) Curriculum and Related Factors; (4) Early Algebra, Algebra, and Number Concepts; (5) Geometry and Measurement; (6) Mathematical Processes; (7) Statistics and Probability; (8) Student Learning and Related Factors; (9) Teacher Education and Knowledge; (10) Teaching and Classroom Practice; (11) Technology; (12) Theory and Research Methods; and (13) Working Groups. [Individual plenary and research papers are available in ERIC. Financial and personnel support was provided by the Michigan State University CREATE for STEM Institute.]

Published
2015

15. Coming to 'Know' Mathematics through 'Acting, Talking and Doing' Mathematics

Author

Mathematics Education Research Group of Australasia and Hunter, Roberta

Abstract

This paper adds to a discussion initiated by Askew (2007) about two contrasting views of scaffolding; as a "tool for results" and a "tool-and-result". The study took place in four primary classrooms within a low socioeconomic setting. Two classroom episodes drawn from one of the teacher's classroom, illustrate the two different perspectives of scaffolding. These are presented and the learning that evolved from each episode is discussed. The paper illustrates that when scaffolding was used as a "tool for results" the learning was restricted but when the students were scaffolded within a tool-and-result perspective the mathematical knowledge and ways of doing and talking mathematics were generative. (Contains 1 footnote.) [For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

Published
2010

16. Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group = Actes De La Rencontre Annuelle 2014 Du Groupe Canadien D'étude en Didactique Des Mathématiques (38th, Edmonton, Alberta, Canada, May 30-June 3, 2014)

Author

Canadian Mathematics Education Study Group (CMESG), Oesterle, Susan, and Allan, Darien

Abstract

This submission contains the Proceedings of the 2014 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at the University of Alberta in Edmonton, Alberta. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, an elder talk memoire, panel discussions, working group reports, topic sessions, new PhD reports, and summaries of ad hoc and poster sessions. Papers include: (1) The Economic Use of Time and Effort in the Teaching and Learning of Mathematics (Dave Hewitt); (2) Mathematics in Industry, Mathematics in the Classroom: Analogy and Metaphor (Nilima Nigam); (3) Inter-action and Mathematics Knowing--An Elder's Memoire (Tom Kieren); (4) Basic Facts about PISA 2012 (Lynn M. McGarvey); (5) What Have We Not Been Hearing About PISA? (David A. Reid); (6) The performance of Québec students on PISA's mathematics assessment: What's going on in Québec? (Annie Savard); (7) PISA Reporting: Not Saying What PISA Is and Does (David Wagner); (8) Mathematical Habits of Mind/Modes de pensée mathématiques (Frédéric Gourdeau, Susan Oesterle, and Mary Stordy); (9) Formative Assessment in Mathematics: Developing Understandings, Sharing Practice, and Confronting Dilemmas (Nadia Hardy and Christine Suurtamm); (10) Texter mathématique/Texting Mathematics (Richard Barwell and Jean-François Maheux); (11) Complex Dynamical Systems (France Caron, David Lidstone, and Miroslav Lovric); (12) Role-Playing and Script-Writing in Mathematics Education: Practice and Research (Caroline Lajoie and Rina Zazkis); (13) Mathematical Problem-solving Proficiency and Knowledge for Teaching (Olive Chapman); (14) Interactions de la classe: tensions entre compréhension et difficultés à apprendre les mathématiques/Interactions in the Classroom: Tensions Between Interpretations and Difficulties Learning Mathematics (Lucie Deblois) [Written in French and English]; (15) Mawkinumasultinej! Let's Learn Together! Developing CulturallyBased Inquiry Projects in Mi'kmaw Communities (Lisa Lunney Borden); (16) Problem Posing as Storyline: Collective Authoring of Mathematics by Small Groups of Middle School Students (Alayne Armstrong); (17) Des manières de faire des mathématiques comme enseignants abordées dans une perspective ethnométhodologique pour explorer la transition secondaire collégial/An Ethnomethodological Perspective on Teachers' Ways of Doing Mathematics to Explore the Transition from Secondary to Postsecondary Level (Claudia Corriveau) [Written in French and English]; (18) Making Sense of Sense Making: Learning, Anxiety, and Education (Lissa M. D'Amour); (19) Listening to Students: A Study of Elementary Students' Engagement in Mathematics Through the Lens of Imaginative Education (Pamela A. Hagen); (20) Societal Views of Mathematics and Mathematicians and Their Influence on Elementary Students (Jennifer Hall); (21) Perceptions, Pedagogies, and Practices: Teacher Perspectives of Student Engagement in Grade 9 Applied Mathematics Classrooms (Limin Jao); (22) From Frustration to Understanding: An Inquiry into Secondary Mathematics Teachers' Experiences with Government Mandated Examinations (Richelle Marynowski); (23) Towards the Pedagogy of Risk: Teaching and Learning Risk in the Context of Secondary Mathematics (Nenad Radakovic); (24) Transitions Between Representational Modes in Calculus (Dov Zazkis); (25) A War Zone: The Framing of Mathematics Education in Public News Reporting (Richard Barwell and Yasmine Abtahi); (26) Rethinking Lesson Planning in Mathematics Classrooms (Martha J. Koch); (27) Unpacking Students' Meaning During Learning of New Concepts and Application to Task (Lydia Oladosu); (28) Mathematical Arts: Change the Name… Change the Lens (…?) … Change the Experience… (?) (Jamie Pyper); (29) Day-to-Day, Moment-to-Moment Teaching: What Does it Mean to Teach Mathematics? (Amanjot Toor); (30) Students' Images of Mathematics (Jennifer Hall, Jo Towers, and Lyndon C. Martin); (31) Unfolding of Diagramming and Gesturing Between Mathematics Graduate Student and Supervisor During Research Meetings (Petra Menz); and (32) Exploring Mathematics Through Narrative/Stories: A Humanistic Approach for Teaching Mathematics (Amanjot Toor). Individual papers contain references. [For the 2013 proceedings, see ED547247.]

Published
2015

17. Learning the Concepts of Limits with Technology.

Author

Rochowicz, John A.

Abstract

An understanding of limits is valuable for learning advanced mathematics. Fundamental to almost all branches of mathematics, studying and applying limits enable students to pursue meanings instead of calculations to many different applications. The idea of nearness to a point instead of exactness is different for many students. Using spreadsheets and other forms of technology provide a variety of ways for the learner to understand and determine limits. This paper describes the use of spreadsheets and spreadsheet macros to calculate limits and visualize output. A variety of examples are shown for differentiation and integration. Through the use of technology, relevant situations become the focus of mathematical study. Concepts are more important than computations. And technology enables the student to be an active participant in the learning of mathematics. (Author)

Published
2001

18. Deconstructing the Walls between Sciences and Humanities.

Author

Hoffman, Lorrie L., Gillette, David, Lindbeck, A. Graeme, and Morton, Bill

Abstract

This paper describes the Learning IN Communities (LINC) integrated curriculum project implemented at the University of Central Florida. The report reviews two programs initiated in the fall of 1998, a Biology-English-Statistics class and a Calculus-English-Humanities class. The paper discusses the rationale for attempting this alternate teaching methodology, the approach to instruction, characteristics of the student body, classroom specifics, and the expected and realized benefits and shortcomings of the classes. The program achieved the goals of enhancing teaching and research experiences for the participating faculty and improving student learning. Prior experience across the nation as reported in journal articles indicated that other programs have had the same outcomes. Sections of the report provide an introduction; background information; discussion of anticipated benefits; development, delivery, and documentation of the project; cohort activity examples; and a discussion of outcomes and realized and unrealized benefits of the project. Appended are questions relating to one of the cited articles and a current lifestyle IQ test. (Contains 15 references.) (JM)

Published
1999

19. Supporting Students in Making Sense of Connections and in Becoming Perceptually Fluent in Making Connections among Multiple Graphical Representations

Author

Rau, Martina A., Aleven, Vincent, and Rummel, Nikol

Abstract

Prior research shows that multiple representations can enhance learning, provided that students make connections among them. We hypothesized that support for connection making is most effective in enhancing learning of domain knowledge if it helps students both in making sense of these connections and in becoming perceptually fluent in making connections. We tested this hypothesis in an experiment with 428 4th- and 5th-grade students who worked with different versions of an intelligent tutoring system for fractions learning. Results did not show main effects for sense-making or fluency-building support but an interaction effect, such that a combination of sense-making and fluency-building support is most effective in enhancing fractions knowledge. Causal path analysis of log data from the system shows that sense-making support enhances students' benefit from fluency-building support, but fluency-building support does not enhance their benefit from sense-making support. Our results suggest that both understanding of connections and perceptual fluency in connection making are critical aspects of learning of domain knowledge with multiple graphical representations. Findings from the causal path analysis lead to the testable prediction that instruction should provide sense-making support and fluency-building support for connection making. [This paper was published in "Journal of Educational Psychology" v109 n3 p355-373 2017 (EJ1136559).]

Published
2017
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20. A Multiple-Case Study of Elementary Prospective Teachers' Experiences in Distinct Mathematics Content Courses

Author

Swars, Susan L., Smith, Stephanie Z., Smith, Marvin E., Hart, Lynn C., and Carothers, Jody

Abstract

This multiple-case study explored the experiences of two groups of elementary prospective teachers (n=12) completing distinct mathematics content courses. Individual interviews revealed perspectives on knowing, learning, and teaching mathematics as experienced by the two groups; the quantitative findings indicated differences in mathematical beliefs. One group characterized mathematics as a record of knowledge, difficult to understand and lacking in relevance; learning occurred through rote memorization and via external expertise, with teaching typified as explaining. The other group portrayed mathematics as process-focused, internally constructed, and relevant; learning took place through a focus on children's thinking, with teaching characterized as guiding and questioning. [For the complete proceedings, see ED585874.]

Published
2011

21. Documenting the Learning of Teacher Communities across Changes in Their Membership

Author

Mathematics Education Research Group of Australasia and Visnovska, Jana

Abstract

Teacher mobility is often viewed as a limitation of longitudinal analyses of teacher learning in communities, in which membership changes. I introduce an analytical tool developed to address the continuation of the learning of such communities across changes in membership. In the case analysis, I examine whether changes in membership should be framed as induction of new members into a single community that evolves across the years, or instead as the emergence of a new community each time the membership changes. (Contains 4 footnotes.) [Funding for this paper was provided by The University of Queensland. For the complete proceedings, "Shaping the Future of Mathematics Education. Proceedings of the Annual Conference of the Mathematics Education Research Group of Australasia (33rd, Freemantle, Western Australia, Australia, July 3-7, 2010)," see ED520764.]

Published
2010

22. Culminating Experience Action Research Projects, Volume 9, Fall 2006

Author

McAllister, Deborah A., Ezell, Benjamin T., McAllister, Deborah A., and Ezell, Benjamin T.

Abstract

As a part of the teacher licensure program at the graduate level at The University of Tennessee at Chattanooga (UTC), the M.Ed. Licensure candidate is required to complete an action research project during a 3-semester-hour course that coincides with the 9-semester-hour student teaching experience. This course, Education 590 Culminating Experience, requires the student to implement an action research plan designed through (a) the Education 500 Introduction to Inquiry course, (b) one of the two learning assessments required during student teaching, or (c) a newly-designed project not used as one of the learning assessments. With funding through a UTC Teaching, Learning, and Technology Faculty Fellows award, the Education 590 course is conducted through the use of an online, course management system (Blackboard Learning System Release 6), allowing for asynchronous discussion and use of the digital drop box feature for submitting required papers. The course syllabus for Education 590 Culminating Experience is presented in the next section, followed by action research projects from fall semester 2006. (Individual papers contain references, figures, and tables.)

Published
2010

23. Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group = Actes de la Rencontre Annuelle 2004 du Groupe Canadien d'Etude en Didactique des Mathematiques (28th, Quebec City, Quebec, Canada, May 28-Jun 1, 2004)

Author

Canadian Mathematics Education Study Group (CMESG), Simmt, Elaine, and Davis, Brent

Abstract

This submission contains the Proceedings of the 2004 Annual Meeting of the Canadian Mathematics Education Study Group (CMESG), held at Universite Laval in Quebec City, Quebec. The CMESG is a group of mathematicians and mathematics educators who meet annually to discuss mathematics education issues at all levels of learning. The aims of the Study Group are: to advance education by organizing and coordinating national conferences and seminars to study and improve the theories of the study of mathematics or any other aspects of mathematics education in Canada at all levels; and to undertake research in mathematics education and to disseminate the results of this research. These proceedings include plenary lectures, working group reports, topic session descriptions, new PhD reports, and summaries of ad hoc and panel sessions. Papers include: (1) La situation du professeur et les connaissances en jeu au cours de l'activite mathematique en classe (Claire Margolinas) [Written in French]; (2) La personnalite d'Evariste Galois: le contexte psychologique d'un gout prononce pour les mathematiques abstraites (Nicolas Bouleau) [Written in French]; (3) Learner-Generated Examples (Nathalie Sinclair, Anne Watson, and Rina Zazkis); (4) Transition to University Mathematics (Tom O'Shea and Peter Taylor); (5) L'integration de l'application et de la modelisation dans les mathematiques au secondaire et au collegial / Integrating Applications and Modelling in Secondary and Postsecondary Mathematics (France Caron and Eric Muller); (6) Elementary Teacher Education: Defining the Crucial Experiences (Ann Kajander and Jean Dionne); (7) La technologie dans l'enseignement des mathematiques: regard critique sur le discours et la pratique / A Critical Look at the Language and Practice of Mathematics Education (Andre Boileau and Geoffrey Roulet; (8) L'enseignment des probabilities dans les ecoles primaires du Quebec (Renee Caron) [Written in French]; (9) Feedback (Dave Hewitt); (10) Body, Tool, and Symbol: Semiotic Reflections on Cognition (Luis Radford); (11) Standards for Excellence in Teaching Mathematics (Steve Thornton); (12) The AHA! Experience: Mathematical Contexts, Pedagogical Implications (Peter Liljedahl); (13) The Issues of Learning the Equals Sign for Grade 1 Students (Laurent Theis); (14) Measuring the Impact of a Mentor Program (A. J. Dawson); (15) Ten Dimensions of Mathematics Education--A Framework for Improving Mathematics (Douglas McDougall); (16) To JUMP or not to JUMP (Tom Steinke and Stewart Craven); (17) Undergraduate Students' Errors That May Be Related to Confusing a Set with Its Elements (Kalifa Traore, Caroline Lajoie, and Roberta Mura); (18) Expressing Mathematical Fluency (David Wagner); (19) What is Canadian about Canadian Mathematics Education? / La didactique des mathematiques au Canada se distingue-t-elle de ce qui se fait ailleurs dans le monde? (David A. Reid) [Presented in both English and French]; (20) What are the Issues and Problems Facing Mathematical Education in Canada? (Eric Muller); and (21) Unique Features of the Body of Mathematics Education in Canada: A Brief Sketch (Thomas E. Kieren). Appended are: (1) Working Groups at Each Annual Meeting; (2) Plenary Lectures at Each Annual Meeting; and (3) Proceedings of Annual Meetings. Individual papers contain references, figures, and tables. [Abstract modified to meet ERIC guidelines. For the 2003 proceedings, see ED529558.]

Published
2005

24. Teachers' Mathematics: Curious Obligations

Author

Simmt, Elaine, Davis, Brent, and Gordon, Lynn

Abstract

We explore the nature and consequences of teachers' problem solving through an example of a teacher's mathematical problem solving as it was occasioned by a student's mathematics. This illustration demonstrates the value of an interpretive framework that points to the mathematics of the classroom as a collective. Arising from this exploration is our core assertion, that the mathematics teacher has an obligation to be curious about mathematics. Our research has significant implications for teacher education as it points to the significance of the teacher's mathematics within the classroom collective and the possibilities for the growth of the teachers' understandings within that collective. (Contains 1 endnote and 3 figures.) [This paper is based on data collected in a year-long teaching experiment funded by the Social Sciences and Humanities Research Council. For complete proceedings, see ED500860.]

Published
2003

25. Results of Using Writing Tasks To Enhance Fourth-Grade Children's Acquisition of Fraction Knowledge.

Author

Sharp, Janet M.

Abstract

Schumacher and Nash (1991) theorize that writing provides an avenue for people to reorganize their knowledge. Kieren (1988) is one of several researchers who theorize that children's school fraction experiences should begin with personal knowledge of fractions. The purpose of this study was to determine whether or not children who engaged in journal writing about fractional situations showed an increase in fraction knowledge. Two groups of fourth-grade children at a large, Southwestern United States, urban elementary school participated in the study. One group completed a four-week intermittent writing experiment. The other group had no such experience. The results of this study indicated a significant difference between pre- and post-test scores for the writing group children. The results add evidence to the theory that writing causes learning and call teachers to provide writing situations associated with children's existing informal knowledge of fractions. (Contains 35 references.) (Author/ASK)

Published
1998

26. Images, Anxieties, and Attitudes toward Mathematics

Author

Belbase, Shashidhar

Abstract

The purpose of this paper is to discuss and analyze images, anxieties, and attitudes towards mathematics in order to foster meaningful teaching and learning of mathematics. Images of mathematics seem to be profoundly shaped by epistemological, philosophical, and pedagogical perspectives of one who views mathematics either as priori or a posteriori, absolute or relative, and concrete or nominal. These images, as perceived by an individual can play a significant role in the development of attitudes towards mathematics in the long run. Images of mathematics can have possible negative and positive impacts on teaching and learning of mathematics with the subsequent development of attitudes toward mathematics as positive or negative and also associated mathematics anxiety. A theoretical model with different combinations of images, anxieties, and attitudes toward mathematics can be a helpful tool to develop an understanding of the different relationships among them. Some pedagogical implications can be drawn from these relationships.

Published
2013

27. The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

Author

Mischo, Christoph and Maaß, Katja

Abstract

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and findings from mathematics education. Teacher beliefs about mathematics, learning and self-efficacy were expected to have a major impact on their classroom practices. We therefore assessed teacher beliefs about the usefulness of mathematics, learning (constructivist and socio-constructivist beliefs) and teacher self-efficacy when teaching modeling (teacher or class level variable). The student level variables assessed were modeling competence and other individual factors, such as basic mathematical skills and cognitive abilities. The effectiveness of the intervention was measured in a pre-post control group design using multilevel structural equation modeling. The results showed no direct effect of the intervention on student modeling competence. However, they did reveal that the intervention had a significant effect on teacher beliefs about learning (constructivist and socio-constructivist view) and an effect of these teacher beliefs about learning on student modeling competence. Further, the results showed that students' gains in modeling competence is not only mediated by teacher beliefs, but also influenced by individual factors. Implications for teaching as well as limitations of the study are discussed.

Published
2013

28. Use of a Survival Analysis Technique in Understanding Game Performance in Instructional Games. CRESST Report 812

Author

National Center for Research on Evaluation, Standards, and Student Testing, Kim, Jinok, and Chung, Gregory K. W. K.

Abstract

In this study we compared the effects of two math game designs on math and game performance, using discrete-time survival analysis (DTSA) to model players' risk of not advancing to the next level in the game. 137 students were randomly assigned to two game conditions. The game covered the concept of a unit and the addition of like-sized fractional pieces. The math content in the baseline version of the game focused on procedures and did not elaborate on the math topics. The experimental version of the game provided more conceptual instruction by emphasizing the underlying concepts in fractional addition. Students played the game for 30 minutes. DTSA was used to examine student game performance, and whether and how game performance relates to students' prior math knowledge and game experience. Students who played the experimental version of the game were less likely to fail in the game relative to students who played the baseline version of the game (odds ratio = 0.64). Students with higher prior knowledge of fractions also were less likely to fail in the game (odds ratio = 0.41), and students with more game experience were less likely to fail (odds ration = 0.58). The use of DTSA provided an analytical method to understand game performance and game process data. DTSA enabled examination of the game play progression of students with various characteristics over sequences of game levels. Goals and Knowledge Specifications in "Save Patch" Game Levels are appended. (Contains 5 figures and 6 tables.) [This paper was supported under the Educational Research and Development Centers Program.]

Published
2012

29. Re-'Conceptualizing' Procedural Knowledge in Mathematics.

Author

Star, Jon R.

Abstract

Many mathematics educators have lost sight of the critical importance of the mathematical understanding which underlies procedural competence, in part because we do not have a language to refer to this kind of understanding. The modal way of categorizing mathematical knowledge--conceptual and procedural knowledge--is limited in that: (a) it is almost exclusively focused on the mathematics of elementary school, and (b) in studies using this framework. Knowledge of procedures and concepts are assessed in very different ways. Three students' solutions to a linear equation are presented and compared. This paper shows that the difference between what these three students know about linear equation solving can be framed in terms of students' planning knowledge of the procedures--in other words, conceptual knowledge about procedures. (Author)

Published
2002

30. Improving Mathematics Education: Resources for Decision Making.

Author

National Academy of Sciences - National Research Council, Washington, DC. Mathematical Sciences Education Board., Leinwand, Steve, and Burrill, Gail

Abstract

This report describes the message of current publications in mathematics education. Eight documents were selected to be reviewed which provides a starting point for readers. Papers include: (1) "Principles and Standards for School Mathematics"; (2) "Adding It Up: Helping Children Learn Mathematics"; (3) "How People Learn: Brain, Mind, Experience, and School"; (4) "Before It's Too Late: A Report to the Nation From the National Commission on Mathematics and Science Teaching for the 21st Century"; (5) "Educating Teachers of Science, Mathematics, and Technology: New Practices for the New Millennium"; (6) "The Mathematical Education of Teachers"; (7) "High Stakes: Testing for Tracking, Promotion, and Graduation"; and (8) "Every Child Mathematically Proficient: An Action Plan of the Learning First Alliance." (Contains 10 references.) (YDS)

Published
2001

31. Learning for Mathematical Insight: A Longitudinal Comparison of Two Dutch Curricula on Fractions.

Author

Keijzer, Ronald and Terwel, Jan

Abstract

Twenty primary school students were randomly assigned by a matching procedure to either an experimental or control group. During the whole school year, both groups were taught mathematics according to the curriculum in the school; however, the groups followed different programs in fractions. Students in the experimental curriculum were provided with opportunities to develop number sense in a program where class discussion and the number line takes a central place as a mental model for formal reasoning in learning fractions. By contrast, in the curriculum of the control group the circle was used as a model to reach formalization. At various time points, the teaching and learning processes and the outcomes of the two curricula were investigated by participant-observations, in-depth interviews and tests for mathematical understanding. This comparison particularly shows qualitative differences in operating with fractions between experimental group and control group. In their mental models, strategies and reflections students from the experimental group demonstrated clearly more insight i.e., aspects of number sense in processing fractions, both relatively when compared to the controls, as absolutely in regard to the national standards. Moreover, we observed differential effects in comparing the experimental with the control group. The outcomes of the study are discussed and some implications for curriculum theory and practice are presented. (Contains 65 references. (Author/CCM)

Published
2000

32. Seeing Culture and Power in Mathematical Learning: Toward a Model of Equitable Instruction

Author

Hand, Victoria

Abstract

This paper is centered on creating equitable opportunities for learners in mathematics education. Through observations of teacher practice, the paper seeks to theorize how teachers enact their dispositions toward mathematics instruction. These observed propensities, in relation to teachers' aims for students to "take up their space" in and beyond the mathematics classroom, then inform a model of equitable mathematics instruction. Teachers' dispositions are considered in relation to Mason's discipline of noticing and Bourdieu's notion of the symbolic violence of dominant discourses.

Published
2012
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33. When Does an Opportunity Become an Opportunity? Unpacking Classroom Practice through the Lens of Ecological Psychology

Author

Gresalfi, Melissa Sommerfeld, Barnes, Jacqueline, and Cross, Dionne

Abstract

Drawing on ecological psychology, this paper considers how student engagement is an accomplishment of the classroom system. Specifically, this paper presents an analysis of two teachers and their students who were using a project-based unit in their mathematics classes. The two teachers used identical curricular materials, but had dramatically different personal histories of teaching and different instructional practices. Our goal is to investigate the role of the teacher in supporting student engagement by considering the kinds of opportunities to learn that were presented by the teacher, and the relationship between those opportunities to learn and the ways their students engaged. Pragmatically, this paper contributes to our understanding of how teachers' framing of activity significantly impacts the ways that students are likely to engage tasks. Theoretically, this paper highlights the interactional nature of learning, with the goal of clarifying why learning is not simply an individual accomplishment.

Published
2012
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34. Identification of Action Units Related to Affective States in a Tutoring System for Mathematics

Author

Padrón-Rivera, Gustavo, Rebolledo-Mendez, Genaro, Parra, Pilar Pozos, and Huerta-Pacheco, N. Sofia

Abstract

Affect is an important element of the learning process both in the classroom and with educational technology. This paper presents analyses in relation to the identification of Action Units (AUs) related to affective states and their impact on learning with a tutoring system. To assess affect, a tool was devised to identify AUs on pictures of human faces. Action Units are combinations of individual facial muscles or groups of muscles that create facial expressions in association with affect. Pictures from a population of students were taken while using an intelligent tutoring system for mathematics in a secondary school in a suburban school in Veracruz, Mexico. The students were asked to interact with the tutoring system for 40 minutes and they were photographed with the tool at a rate of 1 picture every 5 seconds acquiring a dataset consisting of 16,800 photos. To achieve identification, the software analyzes individual pictures using Principal Component Analyses (PCA) and Euclidian distance. The tool developed to classify affective states shows 88.88% accuracy in the identification of AUs when matching the recognized AU to the Cohn-Kanade AU-Coded facial expression database. The analyses also elicited the most common AUs for the population and their association with learning with the intelligent tutoring system. These preliminary results shed light on the issues of affect in relation to learning mathematics with tutoring systems and pave the way for the implementation of coping strategies based on the automatic recognition of facial expressions.

Published
2016

35. Problem-Solving Performance and Memory for Mathematical Problems: Solving Related Problems.

Author

Silver, Edward A.

Abstract

This study, presented at the 1979 meeting of the American Educational Research Association (AERA) in San Francisco, examines the relationship between a student's mathematical problem-solving ability and the nature of the student's recall of information from previously-solved problems. Seventy-seven seventh-grade students completed tasks measuring their initial perceptions of problem relatedness, their ability to solve verbal problems, and their recall of information from previously-solved problems. Results suggested that good and poor problem solvers differed in the nature of their problem recall. Good problem solvers tended to recall information about a problem's structure, whereas poor problem solvers rarely did. Nevertheless, poor problem solvers were sometimes able to recall the details of a problem's statement better than were poor problem solvers. A significant transfer effect was found from the solution and discussion of one problem to the solution of a structurally related problem. (Author/HM)

Published
1979

36. An Investigation of the Learning of Addition and Subtraction.

Author

Wisconsin Univ., Madison. Research and Development Center for Individualized Schooling., Carpenter, Thomas P., and Moser, James M.

Abstract

This paper describes the research program of the Mathematics Work Group of the Wisconsin Research and Development Center for Individualized Schooling. The major interest is in the development of children's abilities to solve verbal addition and subtraction problems and particularly in the processes and strategies used by children. Three factors are considered: (1) problem structure, (2) student characteristics, and (3) the nature of instruction. An analysis of verbal problems is presented. This analysis includes a discussion of various types of problem entities: discrete sets, continuous attributes, and actions or transformations. Problem structure is also analyzed along three dimensions: action vs. static relationships, set inclusion, and order (larger vs. smaller). Examples of various problem types are given. Results from the first year of an ongoing (1978-1981) longitudinal study of primary age students are included. These results are mainly gathered from individual problem-solving interviews with about 150 subjects. Various strategies employed and their change over time are examined. The paper concludes with a discussion of the implications of the research, both present and contemplated, for instruction. (Author/MK)

Published
1979

37. Teaching Mathematics in the Elementary School (A Collection of Essays).

Author

Ediger, Marlow

Abstract

These eleven essays range across a variety of topics. They concern: (1) philosophy and the curriculum, with comments on accountability, humanism, programmed learning, hierarchies, structure, idealism, existentialism, realism, experimentalism, and essentialism; (2) philosophy in the mathematics curriculum, with comments on mathematics laboratories, programmed learning, contracts, management systems, and learning centers; (3) objectives and learning activities in the mathematics curriculum, focusing on objectives and on using various types of materials; (4) providing for individual differences and designing the mathematics curriculum, with sections on slow learners, talented pupils, learning activities, other ways of providing for individual differences, and scope; (5) principles of learning and the mathematics curriculum, with comments on purpose, interest, problem solving, meaningful learning, individual differences, mathematics concepts, decision-making, and evaluation; (6) mathematics and the learner; (7) change in education; (8) inservice education and the computer; (9) innovation, technology, and the mathematics curriculum; (10) knowledge of results, with comments on evaluation procedures, behaviorism, and humanism; and (11) evaluating achievement in mathematics, including the use of observations, checklists, teacher-made tests, standardized tests, work samples, parent-teacher conferences, tape recorders, pupils' responses, and pupil-teacher conferences. Some chapters provide selected references. (MNS)

Published
1984

38. Bibliography of Publications, 1982 Supplement.

Author

Wisconsin Center for Education Research, Madison. and Smith, Marshall

Abstract

This supplementary bibliography of publications produced in 1981 under the auspices of the Wisconsin Center for Education Research is intended to inform the educational community of the latest research and development on the education of individuals and diverse groups of students in elementary and secondary schools. A total of 50 technical reports, theoretical papers, working papers, books, books in preparation, Ph.D. dissertations, and master's theses are listed and annotated in the bibliography. Publications are presented in five sections: (1) books summarizing and synthesizing work in areas related to student diversity; (2) studies of student diversity in learning and development; (3) studies of skill development processes in relation to student diversity; (4) studies of interaction and organization of classroom processes in relation to student diversity; and (5) studies of student diversity and school processes. Also included are an author index, a numerical listing of papers and reports, and information on obtaining publications included in the bibliography. (ESR)

Published
1982

40. Developing Systems of Notation as a Trace of Reasoning

Author

Tillema, Erik and Hackenberg, Amy

Abstract

In this paper, we engage in a thought experiment about how students might notate their reasoning for composing fractions multiplicatively (taking a fraction of a fraction and determining its size in relation to the whole). In the thought experiment we differentiate between two levels of a fraction composition scheme, which have been identified in prior research, and discuss differences in systems of notation that students might produce, depending on the level of their scheme. We situate this discussion within a framework for learning in order to articulate how developing systems of notation with students can contribute to their learning.

Published
2011

41. Educating Americans for the 21st Century: A Plan of Action for Improving Mathematics, Science and Technology Education for All American Elementary and Secondary Students So That Their Achievement Is the Best in the World by 1995. Source Materials.

Author

National Science Foundation, Washington, DC. National Science Board Commission on Precollege Education in Mathematics, Science and Technology.

Abstract

This volume is composed of 11 source documents which report activities sponsored by the National Science Board Commission on Precollege Education in Mathematics, Science and Technology, deliberations of a subgroup of the National Science Foundation Engineering Advisory Committee, and a paper prepared for the Pfizer Corporation. The first four presentations address the teaching/learning of mathematics, science, and technology in grades K-12. Issues of appropriate content and process are discussed. Suggestions for changing some of the content of traditional elementary and secondary education are presented and arguments for the need for all students to study mathematics, science, and technology every year during their elementary/secondary education are made. Section five reports on the uses of technology as a tool in education rather than learning about technology. The last five sections report on: research and cognition and behavior relevant to education in mathematics, science, and technology; results of a 50-state survey of initiatives in science, mathematics, and computer education; magnet schools; an assessment of programs that facilitate increased access and achievement of females and minorities in K-12 mathematics and science education; a case study of Lyons Township (LaGrange, Illinois) high school computer literacy program; and business' role in precollegiate education. (JN)

Published
1983

42. Elementary School Quality: The Mathematics Curriculum and the Role of Local Knowledge.

Author

Balfanz, Robert

Abstract

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 instruction by students in grades K-3 in Chicago (Illinois) and similar research from a number of developing countries. This demonstrates the dangers both of ignoring the knowledge children develop outside of formal school instruction and of becoming too dependent upon it. It is argued that a key means by which elementary school quality can be improved is to begin with the knowledge students develop on their own and transform it though pedagogic and curricular intervention into a set of portable intellectual skills. The point is also made that children around the world bring more knowledge to school with them today than students 50 years ago did, yet curricular materials fail to account for this. This knowledge depends not so much on where they live, what their sex is, or who their parents are, but on the level and complexity of mathematical experience their out-of-school activities provide. (MNS)

Published
1988

43. Teacher Learning in Lesson Study.

Author

Lewis, Jennifer M., Fischman, Davida, Riggs, Iris, and Wasserman, Kelli

Subjects
*TEACHERS, *LEARNING, *CAREER development, *MATHEMATICS education, *LESSON planning
Abstract

This article documents teacher learning through participation in lesson study, a form of professional development that originated in Japan and is currently practiced widely in the US. Specifically, the paper shows how teachers in three different lesson study teams 1) expanded their mathematical content knowledge, 2) grew more skillful at eliciting and analyzing student thinking, 3) became more curious about mathematics and about student thinking, 4) emphasized students' autonomous problem-solving, and 5) increasingly used multiple representations for solving mathematics problems. These outcomes were common across three lesson study teams, despite significant differences among teams composition, and content foci. [ABSTRACT FROM AUTHOR]

Published
2013
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44. Developing fluency in the mathematical register through conversation in a tenth-grade classroom.

Author

Temple, Codruta and Doerr, Helen

Subjects
MATHEMATICS education, DISCOURSE analysis, LEARNING, STUDENTS, TEACHERS
Abstract

The purpose of this study was to identify the interactional strategies that one teacher used in a discourse-rich tenth-grade classroom to develop her students' facility with the mathematical register. Viewing the mathematical register as multi-semiotic and having a specific grammatical patterning, we used discourse analysis () to examine the teacher's initiation and feedback moves that supported students in using symbolic and natural language in mathematical ways during three consecutive lesson episodes. Our findings suggest that, while teacher interactional strategies which focus or probe student thinking are effective for supporting students' learning of the mathematical register, strategies that funnel or lead student contributions towards predetermined answers may also serve that purpose through creating opportunities for meaningful language practice. [ABSTRACT FROM AUTHOR]

Published
2012
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45. Community college students’ views on learning mathematics in terms of their epistemological beliefs: a Q method study.

Author

Wheeler, Denna L. and Montgomery, Diane

Subjects
MATHEMATICS education, COMMUNITY colleges, COLLEGE students, LEARNING, CHI-squared test, ANALYSIS of variance, THEORY of knowledge, EDUCATIONAL psychology
Abstract

The purpose of this study was to explore the views of students enrolled at a small United States Midwestern community college toward learning mathematics, and to examine the relationship between student beliefs about mathematic learning and educational experiences with mathematics using Q methodology and open-ended response prompts. Schommer’s ( Journal of Educational Psychology, 82, 495–504, ) multidimensional theory of personal epistemology provided the structural framework for the development of 36 domain specific Q sort statements. Analysis of the data revealed three distinct but related views of learning mathematic which were labeled Active Learners, Skeptical Learners, and Confident Learners. Chi-square tests of independence revealed no significant differences based on gender. Additionally, there was no evidence for differences based on level of mathematics completed, age, or college hours accumulated. Student’s previous experiences in instructional environments, however, were closely associated with beliefs. Results are discussed in view of the implications for establishing learning environments and considerations in implementing Standards-based curricula in higher education. [ABSTRACT FROM AUTHOR]

Published
2009
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46. Teaching multiplication to low math performers: Guided versus structured instruction.

Author

Kroesbergen, Evelyn H. and van Luit, Johannes E. H.

Subjects
MULTIPLICATION, MATHEMATICS education, STUDENTS, SPECIAL education, LEARNING, EDUCATION
Abstract

The results of an intervention program for students with difficulties learning mathematics are reported. Two kinds of math intervention, guided versus structured instruction, were compared to regular math instruction. A total of 75 students from regular and special education, aged seven to thirteen, participated. Ability and automaticity multiplication tests were administered before and after the four-month training period. The results show that the students in both of the experimental conditions improved more than the students in the control condition. Some additional differences were found between the two experimental interventions. Guided instruction appeared to be more effective for low performing students than structured instruction and especially for those students in regular education. Special education students appear to benefit most from structured instruction for the automaticity of multiplication problems. A three month follow-up test showed the acquired knowledge to be well-established in both groups. [ABSTRACT FROM AUTHOR]

Published
2002
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47. Use of wiris quizzes in an online calculus course

Author

Núria Parés Mariné, Teresa Sancho-Vinuesa, Carme Olivé, Remei Calm, Francesc Pozo, Jordi Ripoll, Ramon Masià, Universitat de Girona, Universitat Rovira i Virgili, Universitat Politècnica de Catalunya, Universitat Oberta de Catalunya. Estudis d'Informàtica, Multimèdia i Telecomunicació, Universitat Politècnica de Catalunya. Departament de Matemàtiques, Universitat Politècnica de Catalunya. LACÀN - Mètodes Numèrics en Ciències Aplicades i Enginyeria, and Universitat Politècnica de Catalunya. CoDAlab - Control, Modelització, Identificació i Aplicacions

Subjects
Computer science, Teaching method, instrumentos de evaluación, instruments d'avaluació, 02 engineering and technology, lcsh:Technology, Continuous assessment, actividad continua, cálculo en linea, Matemàtica -- Ensenyament assistit per ordinador, 0202 electrical engineering, electronic engineering, information engineering, Calculus, ComputingMilieux_COMPUTERSANDEDUCATION, Statistical analysis, Ensenyament assistit per ordinador -- Avaluació, lcsh:LC8-6691, 05 social sciences, Càlcul, 050301 education, Matemàtiques i estadística [Àrees temàtiques de la UPC], Continuous activity, Numerical calculations, Viewpoints, Assessment tools, Learning, Assessment tools, Online calculus, Continuous activity, Avaluació educativa, lcsh:Education, Education, Higher, Càlculs numèrics, Online calculus, Education, Ensenyament i aprenentatge::Metodologies docents [Àrees temàtiques de la UPC], Tools, Cálculos numéricos, 020204 information systems, Mathematics education, Ensenyament i aprenentatge::Ensenyament universitari [Àrees temàtiques de la UPC], Learning, Ensenyament universitari, Mathematics instruction, activitat contínua, lcsh:Special aspects of education, lcsh:T, Ensenyament virtual, E-Learning, Engineering education, lcsh:TA1-2040, càlcul en línia, lcsh:L, lcsh:Engineering (General). Civil engineering (General), 0503 education, Qualitative research
Abstract

Calculus courses often present a large number of difficulties to undergraduate students of scientific studies, especially in engineering degrees. These difficulties are sometimes related to teaching and assessment strategies. In this paper, a teaching innovation experience is presented within the framework of the Universitat Oberta de Catalunya. This teaching experience is focused on a continuous assessment through a systematic use of the so-called WIRIS quizzes. Academic outcomes are very positive from both quantitative and qualitative viewpoints.

Published
2017

48. Revising the Community of Inquiry Framework for the Analysis of One-To-One Online Learning Relationships

Author

Annelie Hulkko, Malin Jansson, and Stefan Stenbom

Subjects
Social Sciences and Humanities, 020205 medical informatics, Computer science, Teaching method, Distance education, 02 engineering and technology, Community of inquiry, Education, Professional learning community, Pedagogy, 0202 electrical engineering, electronic engineering, information engineering, Mathematics education, ComputingMilieux_COMPUTERSANDEDUCATION, Learning, One-to-one, Statistical analysis, Mathematics instruction, LC8-6691, Online learning, 05 social sciences, 050301 education, online coaching, Special aspects of education, Lärande, community of inquiry, Sciences Humaines et Sociales, one-to-one online learning, 0503 education, relationship of inquiry
Abstract

In online learning research, the theoretical community of inquiry framework has been used extensively to analyze processes of inquiry among learners and instructors within a community. This paper examines a special case of community of inquiry consisting of only one learner and one instructor. Together they en­gage in an online coaching discourse to form a relationship of inquiry. Within these relationships, coachees pass through processes of practical inquiry process while a coach supports the process. In this study, a framework and coding scheme were developed for use in a transcript coding procedure including 3,109 messages from an online coaching case in math for K–12 students. It is found that the elements of cognitive, teaching, and social presence, as well as the newly proposed emotional presence, which outlines a community of inquiry, comprise an effective structure for the analysis of one-to-one online coaching environments. The findings of this exploratory study suggest that a relationship of inquiry framework has the potential to support development of one-to-one online learning.

Published
2016

49. Teaching Mathematics Effectively to Primary Students in Developing Countries : Insights from Neuroscience and Psychology of Mathematics

Author

Soendergaard, Bettina Dahl and Cachaper, Cecile

Subjects
MATHEMATICS TEXTBOOKS, NATIONAL ASSESSMENT, TEACHING MATERIALS, UNIVERSITY STUDENTS, LEARNING OUTCOMES, ADVANCED STUDENTS, ADULT STUDENTS, BILINGUALISM, EXAMS, PRIMARY GRADE, CLASSROOM, MATHEMATICS, KNOWLEDGE BASE, YOUNG PEOPLE, SOCIAL STUDIES, LEARNING THEORIES, CURRICULA, ENROLLMENT RATES, SPEECH, UNIVERSITY LEVEL, SKILL DEVELOPMENT, REASONING, LEARNING DISABILITIES, SUBJECT MATTER, METAMEMORY, INTERVENTIONS, LEARNING ENVIRONMENTS, LEARNERS, READING, BASIC SKILLS, WORKBOOKS, TEACHERS, COMPETENCIES, CREATIVITY, STUDENTS LEARNING, SUBJECT AREAS, STUDENT ATTITUDES, LEARNING PROGRAMS, ELEMENTARY SCHOOL STUDENTS, HOMEWORK, COGNITIVE SKILLS, TEACHER, PLAYING, STUDENT PROGRESS, PRIMARY STUDENTS, FORMAL SCHOOLING, LESSON PLANNING, CONCEPTUAL UNDERSTANDING, METACOGNITION, RECOGNITION, PROFESSIONAL GROWTH, SCHOOL CURRICULUM, PRIMARY TEACHING, YOUNG CHILDREN, COGNITIVE PROCESSES, APTITUDE, ANALOGICAL REASONING, INSTRUCTIONAL TECHNOLOGY, INSTRUCTIONAL MATERIALS, LONG TERM MEMORY, GROSS ENROLLMENT, LANGUAGE OF INSTRUCTION, INSTRUCTIONAL STRATEGIES, TEXTBOOKS, BELIEFS, EDUCATIONAL PRACTICE, ComputingMilieux_COMPUTERSANDEDUCATION, CURRICULAR REFORMS, ELEMENTS, PEDAGOGICAL CONTENT KNOWLEDGE, TEACHER EXPECTATIONS, TEACHER EDUCATION PROGRAMS, COGNITIVE PSYCHOLOGY, EDUCATIONAL SYSTEM, STUDENT ACHIEVEMENT, CONFORMITY, TUTORING, MENTAL REPRESENTATION, PROBLEM SOLVING, TEACHER EDUCATION, GER, NUTRITION, RESEARCHERS, TEACHING PROCESS, ACADEMIC ACHIEVEMENT, NORMAL TEACHING, MOTHER TONGUE, INSTRUCTION, PROBLEM-SOLVING SKILLS, GROSS ENROLLMENT RATES, OLD STUDENTS, CLASSROOM SIZE, STUDENT LEARNING, ELEMENTARY SCHOOLS, ENROLLMENT RATIO, MATHEMATICS TEACHERS, COOPERATIVE LEARNING, LEARNING PRACTICES, PERCEPTION, PROFESSIONAL DEVELOPMENT, PRIMARY TEACHERS, ATTENTION, QUALITY OF TEACHING, COGNITIVE DEVELOPMENT, STUDENT OUTCOMES, INSTRUCTIONAL HOURS, MATHEMATICS EDUCATION, EARLY GRADES, NER, LEADERSHIP, GENDER, INTEGRATED LEARNING SYSTEMS, LEARNING ACTIVITIES, TEACHING METHOD, TUTORS, CHILDHOOD, GRADE LEVELS, INFANTS, ARITHMETIC OPERATIONS, EDUCATIONAL OBJECTIVES, EDUCATIONAL RESEARCH, MATH TEXTBOOKS, LEARNING PROCESS, TEST SCORES, RETENTION, EDUCATIONAL PRINCIPLES, LEARNING STYLES, COGNITIVE SCIENCE, LEARNING PROCESSES, COMPUTER TECHNOLOGIES, SUBJECTS, EDUCATORS, CURRICULUM, HOURS OF INSTRUCTION, PRIMARY GRADES, GIRLS, KINDERGARTEN, CONCEPTUAL KNOWLEDGE, ROTE LEARNING, DISSERTATIONS, LEARNING RESULTS, STUDENT PERFORMANCE, CBI, PRIMARY EDUCATION, MINISTRY OF EDUCATION, CRITICAL THINKING, LANGUAGE DEVELOPMENT, SCHOOLS, PRIMARY SCHOOL TEACHERS, ACHIEVEMENT SCORES, ACHIEVEMENT IN SCHOOL, TEACHER TRAINING, MATHEMATICS SKILLS, ABILITY LEVELS, DECISION MAKING, LEARNING GROUPS, ACHIEVEMENT TESTS, CLASSROOMS, PROFICIENCY, COMPETENCE, QUALITY OF LEARNING, STUDENTS WITH LEARNING DIFFICULTIES, CONTROL GROUPS, TEACHING PROGRAMS, LET, ARITHMETIC, COGNITIVE RESEARCH, CLASSROOM TEACHERS, LITERATURE, MATHEMATICS INSTRUCTION, RESEARCH FINDINGS, PEDAGOGY, EARLY INTERVENTION, DIRECT INSTRUCTION, EDUCATIONAL SOFTWARE, FORMAL TEACHING, TEACHING METHODS, WORKING MEMORY, INCIDENTAL LEARNING, BILINGUAL PROGRAMS, MATHEMATICS CURRICULUM, PROBLEM SOLVING SKILLS, EDUCATION PROGRAMS, MATHEMATICS STUDENTS, ComputingMilieux_GENERAL, FORMAL EDUCATION, QUALITY TEACHING, ACHIEVEMENTS, TEACHER KNOWLEDGE, LEARNING DIFFICULTIES, NET ENROLLMENT, TEACHING PRACTICE, TEACHING, LEARNING, PRIMARY SCHOOLS, MATHEMATICAL PROBLEMS, ELEMENTARY SCHOOL TEACHERS, INSTRUCTIONAL TIME, INTUITION, TEACHER QUALIFICATIONS, PRIMARY SCHOOL, EFFECTIVE TEACHING, BILINGUAL EDUCATION, PRE-SCHOOL PROGRAMS, MOTIVATION, RECALL, FIRST GRADE, LEARNING MATHEMATICS, CLASS SIZE, END OF GRADE, LEARNING METHODS, GIFTED STUDENTS, INSTRUCTIONAL EFFICIENCY, NET ENROLLMENT RATIO, MATH ACHIEVEMENT
Abstract

This paper uses research from neuroscience and the psychology of mathematics to arrive at useful recommendations for teaching mathematics at primary level to poor students in developing countries. The enrollment rates of the poorer students have improved tremendously in the last decade. And the global Net Enrollment Ratio (NER) has improved since 2001 from 83.2 percent to 90-95 percent except in Sub-Saharan Africa and South Asia. Making teaching of math and other subjects efficient for the poor in developing countries is a great challenge, particularly in south Asia and Sub-Saharan Africa. Many developing countries have explored new means of teaching math and other subjects. Mongolia changed its mathematics education, aiming to build a new set of priorities and practices, given the abandonment of earlier traditions. Similar to international trends of the time, South Africa in the 1990s extensively applied the constructivist learning philosophy which relied on exploration and discovery, with little emphasis on memorization, drill, In conformity with a belief that teachers could develop their own learning programs, there was virtual absence of a national or provincial syllabus or textbooks. Students were expected to develop their own methods for arithmetic operations, but most found it impossible to progress on their own from counting to actual calculating. This study integrates pertinent research from neuroscience and the psychology of mathematics to arrive at recommendations for curricular and efficient means of mathematics instruction particularly for developing countries and poor students at primary level. Specifically, the latest research in neuroscience, cognitive science, and discussions of national benchmarks for primary school mathematics learning, form the basis of our recommendations. These recommendations have a reasonable chance of working in the situational contexts of developing countries, with their traditions and resources.

Published
2008