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Showing 1 to 15 of 139 results Save | Export
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Giovanni Vincenzi – International Journal of Mathematical Education in Science and Technology, 2025
Using the basic properties of the base-b representation of rational numbers, we will give an elementary proof of Gauss's lemma: "Every real root of a monic polynomial with integer coefficients is either an integer or irrational." The paper offers a new perspective in understanding the meaning of 'irrational numbers' from a deeper…
Descriptors: Mathematical Logic, Validity, Numbers, Mathematics
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Rani, Narbda; Mishra, Vinod – International Journal of Mathematical Education in Science and Technology, 2022
This paper contains interesting facts regarding the powers of odd ordered special circulant magic squares along with their magic constants. It is shown that we always obtain circulant semi-magic square and special circulant magic square in the case of even and odd positive integer powers of these magic squares respectively. These magic squares…
Descriptors: Numbers, Mathematical Logic, Mathematics Education, Mathematical Concepts
Josephine Relaford-Doyle – ProQuest LLC, 2022
It is widely assumed within developmental psychology that spontaneously-arising conceptualizations of natural number--those that develop without explicit mathematics instruction--match the formal characterization of natural number given in the Dedekind-Peano Axioms (e.g., Carey, 2004; Leslie et al., 2008; Rips et al., 2008). Specifically,…
Descriptors: Mathematical Concepts, Number Concepts, Mathematical Logic, Undergraduate Students
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Roche, Anne; Clarke, Doug; Sexton, Matt – Australian Primary Mathematics Classroom, 2023
The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…
Descriptors: Mathematics Instruction, Grade 5, Grade 6, Elementary School Students
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Karagöz Akar, Gülseren; Saraç, Merve; Belin, Mervenur – Mathematics Teacher Educator, 2023
In this study, we investigated prospective secondary mathematics teachers' development of a meaning for the Cartesian form of complex numbers by examining the roots of quadratic equations through quantitative reasoning. Data included transcripts of the two sessions of classroom teaching experiments prospective teachers participated in, written…
Descriptors: Secondary School Teachers, Mathematics Teachers, Preschool Teachers, Number Concepts
Schifter, Deborah; Bastable, Virginia; Russell, Susan Jo – National Council of Teachers of Mathematics, 2018
The "Reasoning Algebraically about Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The thirty-four cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation into the…
Descriptors: Mathematics Instruction, Elementary Schools, Middle Schools, Teaching Methods
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Ghergu, Marius – International Journal of Mathematical Education in Science and Technology, 2018
We explore the connection between the notion of critical point for a function of one variable and various inequalities for iterated exponentials defined on the positive semiline of real numbers.
Descriptors: Mathematics, Mathematics Instruction, Mathematical Concepts, Numbers
Brown, Ethan C. – ProQuest LLC, 2019
Extensive research has documented students' difficulty understanding and applying the Empirical Law of Large Numbers, the statistical principle that larger random samples result in more precise estimation. However, existing interventions appear to have had limited success, perhaps because they merely demonstrate the Empirical Law of Large Numbers…
Descriptors: Mathematics Instruction, Mathematical Logic, Mathematical Concepts, Numbers
McMillan, Brandon – ProQuest LLC, 2018
Even though algebraic ideas are addressed across a number of grades, algebra continues to serve as a gatekeeper to upper mathematics and degree attainment because of the high percentage of students that fail algebra classes and become halted in their educational progress. One reason for this is students not having the opportunity to build on their…
Descriptors: Mathematics Instruction, Mathematical Concepts, Mathematical Logic, Thinking Skills
Sidney, Pooja; Thompson, Clarissa G.; Opfer, John E. – Grantee Submission, 2019
Children's understanding of fractions, including their symbols, concepts, and arithmetic procedures, is an important facet of both developmental research on mathematics cognition and mathematics education. Research on infants', children's, and adults' fraction and ratio reasoning allows us to test a range of proposals about the development of…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Fractions
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Wong, Terry Tin-Yau – British Journal of Educational Psychology, 2019
Background: While it has been widely demonstrated that children's and adolescents' understanding of rational number plays an important role in their mathematics achievement, we have limited knowledge about the cognitive correlates of this understanding. Aims: The current study aimed at examining whether children's non-symbolic ratio processing and…
Descriptors: Mathematics Skills, Knowledge Level, Mathematical Concepts, Fractions
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Tempier, Frédérick – Journal of Mathematics Teacher Education, 2016
Many studies have shown the difficulties of learning and teaching the decimal number system for whole numbers. In the case of numbers bigger than one hundred, complexity is partly due to the multitude of possible relationships between units. This study was aimed to develop conditions of a resource which can help teachers to enhance their teaching…
Descriptors: Mathematics, Mathematical Concepts, Mathematics Instruction, Mathematical Logic
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Gerstenschlager, Natasha E.; Strayer, Jeremy F. – Mathematics Teaching in the Middle School, 2019
Teachers often use number talks at the beginning of class to hear the ways that students understand mathematical topics so that they can base future instruction on student thinking. Students who engage in number talks become accustomed to thinking about mathematics in multiple ways, sharing their thoughts and critiquing the thoughts of others. The…
Descriptors: Numbers, Statistics, Probability, Mathematics Instruction
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Brickwedde, James – Teaching Children Mathematics, 2018
This article examines the importance of developing the notion of place value as a rate of ten. In exploring how to nurture this concept, the author looks at the role of the language of value, the problem types of multistep multiplication and addition along with measurement division, each with ten as an organizing unit, as well as strategically…
Descriptors: Mathematics Instruction, Mathematical Concepts, Concept Formation, Multiplication
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Reikerås, Elin; Salomonsen, Tone – Early Child Development and Care, 2019
The aim of the study is to examine how toddlers (33 months) with weak mathematical skills differ from their peers, the extent to which those weak skills persist into preschool age (57 months), and how the group with persisting weak skills differs from the group with temporary weak skills. Participants were 692 children (344 girls, 348 boys). The…
Descriptors: Mathematics Skills, Toddlers, Preschool Children, Child Development
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