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Marios Pittalis – Mathematics Education Research Journal, 2025
A theoretical model describing Grade 7 students' rational number sense was formulated and validated empirically (n = 360), hypothesizing that rational number sense is a general construct consisting of three factors: basic rational number sense, arithmetic sense, and flexibility with rational numbers. Data analysis suggested that rational-number…
Descriptors: Middle School Mathematics, Middle School Students, Grade 7, Numbers
Venenciano, Linda C. H.; Yagi, Seanyelle L.; Zenigami, Fay K.; Dougherty, Barbara J. – Investigations in Mathematics Learning, 2020
First-grade mathematics curriculum has been typically constructed to emphasize the development of whole number and operations. Topics addressed to a lesser extent include algebraic thinking, measurement, and geometry. In this research study, we suggest an alternative to this balance of topics. We compared prior research and learning expectations…
Descriptors: Grade 1, Elementary School Mathematics, Mathematics Curriculum, Algebra
Roberts, Anthea; le Roux, Kate – Pythagoras, 2019
Concerns have been expressed that although learners may solve linear equations correctly they cannot draw on mathematically valid resources to explain their solutions or use their strategies in unfamiliar situations. This article provides a detailed qualitative analysis of the thinking of 15 Grade 8 and Grade 9 learners as they talk about their…
Descriptors: Foreign Countries, Mathematics Instruction, Equations (Mathematics), Grade 8
Herrera, Christine A.; McCabe, Terrance; Strictland, Sharon; White, Alexander – PRIMUS, 2018
In an undergraduate analysis course taught by one of the authors, three prompts are regularly given: (i) What do we know? (ii) What do we need to show? (iii) Let's draw a picture. We focus on the third prompt and its role in helping students develop their confidence in learning how to construct proofs. Specific examples of visual models and their…
Descriptors: Mathematics Instruction, Mathematical Logic, Validity, Mathematics Skills
Gürefe, Nejila; Aktas, Gülfem Sarpkaya – South African Journal of Education, 2020
The teaching of mathematics does not only require the teacher to have knowledge about the subject, but the teacher also needs mathematical knowledge that is useful for the teaching and explaining thereof, as the teacher's knowledge effects the students' knowledge. A teacher should use appropriate mathematical explanation to be understood well by…
Descriptors: Mathematics Instruction, Knowledge Base for Teaching, Pedagogical Content Knowledge, Teacher Competencies
Garcia, Stephan Ramon – PRIMUS, 2017
A second course in linear algebra that goes beyond the traditional lower-level curriculum is increasingly important for students of the mathematical sciences. Although many applications involve only real numbers, a solid understanding of complex arithmetic often sheds significant light. Many instructors are unaware of the opportunities afforded by…
Descriptors: Algebra, Mathematics Instruction, Numbers, College Mathematics
Gürefe, Nejla; Aktas, Gülfem Sarpkaya – International Journal of Progressive Education, 2019
In this study, it was aimed to reveal the explanatory strategies that preservice teachers use in the process of explaining the concept of divisibility by zero. It was investigated how the concept of divisibility by zero, which can be used in expressing the case where the denominator is present in the definition of important concepts of the…
Descriptors: Division, Preservice Teachers, Mathematics Teachers, Algebra
Pollack, Courtney; Leon Guerrero, Sibylla; Star, Jon R. – ZDM: The International Journal on Mathematics Education, 2016
Higher-level mathematics requires a connection between literal symbols (e.g., "x") and their mental representations. The current study probes the nature of mental representations for literal symbols using both the priming distance effect, in which ease of comparing a target number to a fixed standard is a function of prime-target…
Descriptors: Comparative Analysis, Mathematics, Priming, Symbols (Mathematics)
Switzer, J. Matt – Investigations in Mathematics Learning, 2018
Research findings have established common student misconceptions for literal symbolic representations of variables but lack corresponding findings of when or how these misconceptions arise. This article reports findings from an exploratory study of U.S. grade 4-6 students' conception(s) for various representations of unknown addends commonly found…
Descriptors: Grade 4, Grade 5, Grade 6, Numbers
Gleason, Brian – Mathematics Teacher, 2018
In this article, a mathematics teacher educator presents an activity designed to pique the interest of prospective secondary mathematics teachers who may doubt the value of learning abstract algebra for their chosen profession. Herein, he contemplates: what "is" intended by the widespread requirement that high school mathematics teachers…
Descriptors: Mathematics Instruction, Mathematics Teachers, Teacher Educators, Secondary Education
Wheeler, Ann; Champion, Joe – Mathematics Teaching in the Middle School, 2016
Students are faced with many transitions in their middle school mathematics classes. To build knowledge, skills, and confidence in the key areas of algebra and geometry, students often need to practice using numbers and polygons in a variety of contexts. Teachers also want students to explore ideas from probability and statistics. Teachers know…
Descriptors: Probability, Middle School Students, Mathematics, Mathematics Instruction
Hitt, Fernando; Saboya, Mireille; Zavala, Carlos Cortés – Educational Studies in Mathematics, 2017
Part of the research community that has followed the Early Algebra paradigm is currently delimiting the differences between arithmetic thinking and algebraic thinking. This trend could prevent new research approaches to the problem of learning algebra, hiding the importance of considering an arithmetico-algebraic thinking, a new approach which…
Descriptors: Arithmetic, Algebra, Educational Technology, Thinking Skills
Hurrell, Derek – Australian Primary Mathematics Classroom, 2014
In providing a continued focus on tasks and activities that help to illustrate key ideas embedded in the new Australian Curriculum, this issue will focus on Number in the Number and Algebra strand. In this article Derek Hurrell provides a few tried and proven activities to develop place value understanding. These activities are provided for…
Descriptors: National Curriculum, Educational Practices, Performance Factors, Number Systems
Thomas, Amande; Edson, Alden J. – Mathematics Teacher, 2014
Since the introduction of the Common Core State Standards for Mathematics (CCSSM) in 2010, stakeholders in adopting states have engaged in a variety of activities to understand CCSSM standards and transition from previous state standards. These efforts include research, professional development, assessment and modification of curriculum resources,…
Descriptors: State Standards, Mathematics Education, Educational Principles, Educational Practices
Jacobs, Jennifer A. – ProQuest LLC, 2013
Adults are prone to treating percents, one representational format of rational numbers, as novel cases of natural number. This suggests that percent values are not differentiated from natural numbers; a conceptual shift from the natural numbers to the rational numbers has not yet occurred. This is most surprising, considering people are inundated…
Descriptors: Numbers, Statistics, Algebra, Problem Solving