Proportional reasoning has been greatly influencing the development of students' mathematical abilities. Along with the area conservation ability, it helps elementary students comprehend area measurement. This exploratory study aimed to produce qualitative-descriptive data on elementary students' proportional reasoning in solving the conservation…

This paper describes a model of mathematics bianshi teaching using one problem with several solutions, changes, and applications in an inquiry-based classroom. Based on the model of mathematics bianshi teaching, the author discusses a class-room experience where one Chinese mathematics teacher takes a simple plane geometry problem to guide…

Most research has focused solely on understanding high school or college students' mathematical creative thinking abilities while understanding younger students' creative thinking in mathematics was ignored. These studies of older students have focused mainly on students' creative products rather than creative processes. The authors of the present…

The aim of this study is to examine the effect of the learning environment designed based on different approaches on the change in pre-service teachers' approach preferences and geometry achievement in geometry problems. Twenty pre-service mathematics teachers were involved in geometry lessons for 10 weeks in a learning environment designed based…

Intelligent Tutoring Systems (ITSs) for Math still use traditional data input methods: computers' keyboard and mouse. However, students usually solve math tasks using paper and pen. Therefore, the gap between the manner the students work and the requirements imposed by these typing-based systems expose students to an extraneous cognitive load,…

Background: With the recent pivot to online instruction and/or to mixed online/face-to-face (i.e., hybrid) models of teaching necessitated by the novel coronavirus pandemic, the uses of technology to support instruction would seem to have great importance. Whereas effective integration of technology in mathematics classrooms requires recognition…

Generalization and proof are a foundation of mathematical practice and as such should be integral to K-12 mathematics instruction. However, if generalizing and proving are to become popular within K-12 mathematics classrooms, we must consider how to effectively enlist pre-service teachers (PSTs) into supporting these activities in their…

A multiple probe across participants design was used to examine the effectiveness of a treatment package to teach students with moderate intellectual disability how to solve simple linear equations. The investigator read realistic scenarios of a problem, used actual items as manipulatives, presented a visual aid of the equation, and used a system…

The purpose of this single case study was to evaluate the effects of a multicomponent motivational intervention that consisted of explicit timing, immediate feedback through self- scoring, goal setting, and positive reinforcement on the arithmetical skills of three third graders with learning disabilities. An ABA reversal multiple-baseline…

The aim of this mixed methods study was to investigate the difficulties prospective elementary mathematics teachers have in solving the Programme for International Student Assessment (PISA) 2012 released items. A mathematics test consisting of 26 PISA items was administered, followed by interviews. Multiple data were utilized to provide rich…

The purpose of this study was to investigate the flow of thought of the pre-service mathematics teachers through the answers of a function limit evaluation by formal definition. This study used a qualitative approach with descriptive method. The research subjects were the students of mathematics education department of Universitas Serang Raya,…

This article focuses mainly on two key mathematical processes (representation, and reasoning and proof). Firstly, we observed how teachers learn these processes and subsequently identify what and how to assess learners on the same processes. Secondly, we reviewed one teacher's attempt to facilitate the learning of the processes in his classroom.…

One of the foundational topics in first-year algebra concerns the concept of factoring. This article discusses an alternative strategy for factoring quadratics of the form ax[superscript 2] + bx + c, known as "factoring for roots." This strategy enables students to extend the knowledge they used when the leading coefficient was 1 and…

Multiplicative thinking is widely accepted as a critically important 'big idea' of mathematics that underpins much mathematical understanding beyond the primary years. It is therefore important to ensure not only that children can think multiplicatively, but that they can do so at a conceptual rather than procedural level. This paper reports on a…

The present study took a reciprocal learning approach to examine Canadian and Chinese elementary school students' (N=40) mathematics problem posing and problem solving. Data included student performance, Skype meeting videos, meeting notes, and interviews transcripts through direct and indirect interactions between a pair of Canadian and Chinese…