Beliefs and Their Influence on Mathematical Performance

1989 ◽  
Vol 82 (7) ◽  
pp. 502-505 ◽  
Author(s):  
Joe Garofalo
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Mathematical Tasks ◽  
Mathematical Task ◽  
Mathematical Content ◽  
Mathematical Performance ◽  
Mathematics Problems ◽  
Course Of Action ◽  
Mathematical Behavior ◽  
Research In Mathematics Education

Recent research in mathematics education has shown that success or failure in solving mathematics problems often depends on much more than the knowledge of requisite mathematical content. Knowing appropriate facts, algorithms, and procedures is not sufficient to guarantee success. Other factors, such as the decisions one makes and the strategies one uses in connect ion with the control and regulation of one's actions (e.g., deciding to analyze the conditions of a problem, planning a course of action, assessing progress), the emotions one fee ls while working on a mathematical task (e.g., anxiety, frustration, enjoyment), and the beliefs one holds relevant to performance on mathematical tasks, influence the direction and outcome of one's performance (Garofalo and Lester 1985; Schoenfe ld 1985; McLeod 1988). These other factors, although not explicitly addressed in typical mathematics instruction, are nonetheless important aspects of mathematical behavior.

scholarly journals Enhancing Number System Knowledge to Promote Number Sense and Adaptive Expertise: A Case Study of a Second-Grade Mathematics Student

2018 ◽  
Vol 15 (3) ◽  
Author(s):  
Cami Player ◽  
Jessica Shumway
Keyword(s):  
Mathematics Education ◽  
Mathematics Instruction ◽  
Number Sense ◽  
Number System ◽  
Second Grade ◽  
Adaptive Expertise ◽  
Instructional Treatment ◽  
Mathematics Problems ◽  
System Knowledge

Instruction for developing students’ number sense is a critical area of research in mathematics education due to the role number sense plays in early mathematics learning. Specifically, number system knowledge—systematic relations among numerals and the use of number relations to solve arithmetic problems—has been identified as a key cognitive mechanism in number sense development. Number system knowledge is a component of number sense, and the researchers of this study hypothesize that it plays a critical role in second-grade students’ understanding of relationships among numbers and adaptive expertise with mathematics problems. The purpose of this exploratory case study was to investigate the variations of an eight-year-old student’s number system knowledge learning as she participated in an instructional treatment over nine weeks. The main research question of this study was: In what ways does a student struggling in mathematics develop number system knowledge during a nine-week period in her second-grade classroom as she engages in a number system knowledge instructional treatment? The case in this study was selected based on her low pretest score combined with her desire for making sense of mathematics. The data sources for this study were a number system knowledge assessment and student interviews. The analysis involved a multiple-cycle coding process that resulted in themes of adaptive expertise and the union of procedural and conceptual knowledge in mathematics instruction. The results suggest that this number system knowledge instructional treatment provided this case-study student to develop more pronounced adaptive expertise in solving mathematics problems. An in-depth analysis of how and why one struggling student develops number system knowledge during a nine-week instructional treatment within the context of her mathematics class provides exploratory evidence to help researchers and teachers develop and implement similar practices in elementary mathematics instruction. KEYWORDS: Number Sense; Number System Knowledge; Mathematics Education; Whole Numbers and Operations; Elementary Education; Teaching and Learning; Case Study Research

scholarly journals Forty Years of Mathematics Education: 1980-2019

2021 ◽  
Vol 9 (3) ◽  
pp. 514-539
Author(s):  
Semirhan Gökçe ◽  
Pınar Guner
Keyword(s):  
Mathematics Education ◽  
Bibliometric Analysis ◽  
Mathematics Instruction ◽  
Web Of Science ◽  
Theoretical Framework ◽  
Related Factors ◽  
Policy Makers ◽  
Mathematics Assessments ◽  
The Third ◽  
Research In Mathematics Education

The purpose of this study is to establish the evolution and expose the trends of research in mathematics education between 1980 and 2019. The bibliometric analysis of the articles in Web of Science database indicated four-clustered structure. The first cluster covers the items related to the theoretical framework of mathematics education whereas the second cluster has the terms defining the methods for effective mathematics instruction. The third cluster includes the concepts interrelated to mathematics education while the fourth cluster encloses the studies about international mathematics assessments. The earlier studies look mathematics education mostly in students’ perspective and investigates generalization, restructuring, interiorization and representation. Between 1995 and 2010, curriculum and teacher-related factors were dominant in mathematics education studies. After 2010, the articles investigated specific topics and carried the traces from all stakeholders in mathematics education. The investigation on the trends of mathematics education would provide gain insight about the areas that need more research, contribute to the researchers, teachers, students and policy makers in this field and light the way ‎for further studies.

scholarly journals Taxonomy of Key Terms for Mathematics Education

2021 ◽  
Vol 9 (4) ◽  
pp. 585-613
Author(s):  
Paola Castro ◽  
Pedro Gómez
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Open Access ◽  
Educational Level ◽  
Web Of Science ◽  
Foundations Of Mathematics ◽  
Mathematical Content ◽  
Frequency Of Use ◽  
Key Terms ◽  
Research In Mathematics Education

We present the process of developing a taxonomy of key terms for Mathematics Education. We build on the existing taxonomy of key terms that has been used in an open access document repository. Additionally, we took into account terms that have been established in encyclopedias of the discipline and the frequency of use of keywords in specialized journals that were indexed in Scopus and Web of Science. We made a review of synonymy between these terms and the terms of the existing taxonomy. We included in our proposal the terms that are relevant given their frequency of use in the journals. We removed from the existing taxonomy the terms that are little used in practice. The new taxonomy is organized in six main categories: approach, educational level, foundations of Mathematics Education, research in Mathematics Education, pedagogical notions and mathematical content. This proposal was validated in three phases by researchers, innovators in Mathematics Education, and editors of specialized journals and experts who lead associations and events in the discipline.

scholarly journals Future themes of mathematics education research: an international survey before and during the pandemic

2021 ◽  
Vol 107 (1) ◽  
pp. 1-24
Author(s):  
Arthur Bakker ◽  
Jinfa Cai ◽  
Linda Zenger
Keyword(s):  
Education Research ◽  
Mathematics Education ◽  
Teacher Professional Development ◽  
Mathematics Education Research ◽  
International Survey ◽  
Teaching Approaches ◽  
Education Teacher ◽  
Development Technology ◽  
Teacher Professional ◽  
Research In Mathematics Education

AbstractBefore the pandemic (2019), we asked: On what themes should research in mathematics education focus in the coming decade? The 229 responses from 44 countries led to eight themes plus considerations about mathematics education research itself. The themes can be summarized as teaching approaches, goals, relations to practices outside mathematics education, teacher professional development, technology, affect, equity, and assessment. During the pandemic (November 2020), we asked respondents: Has the pandemic changed your view on the themes of mathematics education research for the coming decade? If so, how? Many of the 108 respondents saw the importance of their original themes reinforced (45), specified their initial responses (43), and/or added themes (35) (these categories were not mutually exclusive). Overall, they seemed to agree that the pandemic functions as a magnifying glass on issues that were already known, and several respondents pointed to the need to think ahead on how to organize education when it does not need to be online anymore. We end with a list of research challenges that are informed by the themes and respondents’ reflections on mathematics education research.

scholarly journals Mathematical Thinking Styles—The Advantage of Analytic Thinkers When Learning Mathematics

2021 ◽  
Vol 11 (6) ◽  
pp. 289
Author(s):  
Jaime Huincahue ◽  
Rita Borromeo-Ferri ◽  
Pamela Reyes-Santander ◽  
Viviana Garrido-Véliz
Keyword(s):  
Mathematical Thinking ◽  
Quantitative Approach ◽  
Mathematical Tasks ◽  
Thinking Styles ◽  
Mathematical Performance ◽  
Test Instrument ◽  
Analytical Thinking ◽  
Learning Mathematics ◽  
Valid Test ◽  
Insight Into

School is a space where learning mathematics should be accompanied by the student’s preferences; however, its valuation in the classroom is not necessarily the same. From a quantitative approach, we ask from the mathematical thinking styles (MTS) theory about the correlations between preferences of certain MTS and mathematical performance. For this, a valid test instrument and a sample of 275 16-year-old Chilean students were used to gain insight into their preferences, beliefs and emotions when solving mathematical tasks and when learning mathematics. The results show, among other things, a clear positive correlation between mathematical performance and analytical thinking style, and also evidence the correlation between self-efficacy, analytical thinking and grades. It is concluded that students who prefer the analytical style are more advantageous in school, since the evaluation processes have a higher valuation of analytic mathematical thinking.

A Validity Framework for the Design of Comparative International Research in Mathematics Education

2020 ◽  
pp. 33-51
Author(s):  
Maria Teresa Tatto ◽  
Michael C. Rodriguez ◽  
Mark D. Reckase ◽  
Wendy M. Smith ◽  
Kiril Bankov ◽  
...  
Keyword(s):  
Mathematics Education ◽  
International Research ◽  
Research In Mathematics Education
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