Background: The ability to translate concrete manipulatives into abstract mathematical formulas can aid in the solving of mathematical word problems among students, and metacognitive prompts play a significant role in enhancing this process. Aims: Based on the concept of semantic congruence, we explored the effects of metacognitive prompts and…

The transition between arithmetic and algebraic thinking is challenging for students. One notable difficulty for students is understanding algebraic symbols--pronumerals. Researchers are exploring pedagogical approaches in seeking to address this issue. The current paper is contributing to this body of literature by illustrating how an online card…

Influenced by COVID-19, online learning has become one of the most important forms of education in the world. In the era of intelligent education, knowledge tracing (KT) can provide excellent technical support for individualized teaching. For online learning, we come up with a new knowledge tracing method that integrates mathematical exercise…

Online discussion forums provide open workspace allowing learners to share information, exchange ideas, address problems and discuss on specific themes. But the substantial impediment to its promotion as effective e-learning facility lies in the continuously increasing messages but with discrete and incoherent structure as well as the loosely-tied…

Four hundred and three 3rd- and 5th-grade Chinese students took the Multiplication Estimation Test or participated in the interview on it, designed to assess their computational estimation performance on whole-number multiplication. Students perform better when tasks are presented visually than orally. Third graders tend to use rounding based…

Examines how selected U.S. and Asian mathematics curricula are designed to facilitate students' understanding of the arithmetic average. Discusses similarities and differences of learning goals, focuses, and concepts among U.S. commercial, Asian, and U.S. reform curriculum series. (Author/KHR)

Usiskin takes another look at fractions, years after writing the article "The Future of Fractions" for "Arithmetic Teacher".

This document contains the second volume of the proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education. Conference papers are centered around the theme of "Learners and Learning Environments." This volume features 43 research reports by presenters with last names beginning between Adl…