Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs' attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator…

With a focus on related rates problems, the present study reports on quantitative and covariational reasoning opportunities provided by five widely used calculus textbooks in the United States. There are three major results from this study. First, quantitative reasoning opportunities are plentiful, while covariational reasoning opportunities are…

Functions and graphs are fundamental mathematical concepts in mathematics and are vital to helping students comprehend the relationship between variables and other advanced topics in higher-level mathematics. Research has shown that students continually possess misconceptions and inaccurate thinking about functions and function representations.…

Background/purpose. One of the current problems facing mathematics students, graduates in mathematics, and engineering is the disconnection between the meanings, symbolic representations, and graphics of derivatives when solving problems, which hinders their understanding. This article analyzes engineering students' understanding activated by…

This research memorandum highlights the collaborative efforts of the numeracy panel for the ETS Return on Investment (ROI) Study, Phase 1, comprising David Tout, Kees Hoogland, and Javier Díez-Palomar, in developing their research memorandum, "Improving the Quality of Numeracy Skills: Progressing from Level 2 to Level 4 on the PIAAC Cycle 2…

The recruitment and retention of underrepresented minority students into STEM fields, is a critical goal for educators, particularly in an increasingly tech-oriented world and a diverse society. Research suggests that integrating art into mathematics courses can increase student engagement and broaden participation. Additionally,…

This study examines factors shaping teachers' instructions of mathematical proof in Singapore. Using a qualitative case study, two teachers' conceptions, beliefs, and challenges were analysed. Findings reveal reliance on empirical and axiomatic proof schemes, shaping instruction. Teachers faced challenges such as limited curriculum emphasis and…

Background: Performance in fraction word problems in primary school indicates that learners face challenges when working with fraction word problems, despite their frequent use of textbooks as learning materials. Aim: This article presents a comparative analysis of three commonly used Grade 6 mathematics textbooks, with the objective of evaluating…

'Success' is a frequently cited yet ambiguously defined term in mathematics education, often carrying contradictory meanings and messages. We surveyed 139 Australian teachers of mathematics to determine their conceptions of 'success'. This paper documents teachers' responses to an alternate word or phrase for 'success'. Thematic analysis…

In this article, we investigate the effects of the app "Fingu" on a child's understanding of the part-whole concept. Using the Artifact Centric Activity Theory framework, we initially analyse the internalisation and externalisation processes that appear to occur during one child's use of the app. Based on the learning from this process,…

Problem-based instruction (PBI) is a research-based, student-centered instructional strategy that uses rich mathematical tasks to connect students' previously acquired math knowledge to new mathematical concepts. Unlike traditional teaching and learning strategies, PBI facilitates learning by making connections between mathematical concepts and…

After waiting in a long line for your favourite cup of coffee, you finally sit down with your mug and find that the coffee is still scalding hot! How long do you need to wait before you can enjoy it? Once it cools enough, how much time do you have to enjoy it? Are there ways to speed up the process? These questions motivate the presented modelling…

Teachers' knowledge of the subject matter is considered an important component of their expertise in teaching mathematics. Yet how teachers' understanding of one content area is related to other content areas has not been investigated in depth. We explored this question by investigating teachers' knowledge of two theoretically related areas: (1)…

Rational number proficiency is predictive of later mathematics achievement, especially for rigorous mathematics courses, such as Algebra I. Students with learning disabilities (LD) in mathematics struggle to make adequate progress on rational number concepts and skills that lay the foundation for successfully completing secondary mathematics…

Across multiple age groups and academic disciplines, research has shown that incorporating multimodal signs into instruction can enhance student learning. For instance, gesture might be synchronized with speech or written signs. The present study reports on the semiotic resources used by a teacher-researcher to support kindergarten students'…