This study examined characteristics of problem posing and its relationship with the teaching experience of elementary school mathematics teachers from ethnic minority areas in the Southwest of China. Eighty-one (N = 81) elementary school mathematics teachers responded to a task-based questionnaire and posed mathematical problems based on given…

In this study we aimed to understand teaching mathematics through problem posing based on an analysis of 22 teaching cases. Teaching mathematics through problem posing starts with problem-posing tasks. This study provides not only specific examples of problem-posing tasks used in classrooms but also related task variables to consider when…

This study investigated 45 undergraduate students' mathematical problem posing based on four problem situations. This study was designed to better understand the kinds of problems they pose, and the kinds of mathematical ideas exhibited when problem posing. The findings of this study support that underprepared college students can pose…

In this study we aimed to inquire into the impact of the use of early arithmetic strategies by a group of fifth-grade students, on their solving of equations involving two representations of unknowns. Pre- and post-tests consisting of equation-solving items involving two representations of unknowns (number sentences containing empty 'brackets', as…

Any effort to integrate problem-posing instruction in school mathematics must attend to teachers' beliefs about the advantages of teaching through problem posing and especially their beliefs about the challenges of teaching in this way. This study investigated teachers who were learning how to teach mathematics through problem posing. The primary…

This study investigated the relationship between three cognitive features of mathematical instruction tasks (high cognitive demand, multiple representations, and multiple solution methods) and student learning outcomes among 1,779 students from 30 Chinese fifth-grade classrooms using a new mathematics curriculum. Measures of mathematics learning…

This study examined 361 Chinese and 345 Singaporean sixth-grade students' performance and problem-solving strategies for solving 14 problems about speed. By focusing on students from two distinct high-performing countries in East Asia, we provide a useful perspective on the differences that exist in the preparation and problem-solving strategies…

This paper reports on 2 studies that examine how mathematical problem posing is integrated in Chinese and US elementary mathematics textbooks. Study 1 involved a historical analysis of the problem-posing (PP) tasks in 3 editions of the most widely used elementary mathematics textbook series published by People's Education Press in China over 3…

This study analyzed the problem-posing tasks in Chinese and U.S. elementary mathematics textbooks. Significant differences were found between the Chinese and U.S. textbooks in the presentation of problem posing activities. By analyzing problem posing in textbooks, we gain insight into how reform ideas are reflected in the mathematics curriculum.…

This study investigates Chinese and U.S. teachers' construction and use of pedagogical representations surrounding implementation of mathematical tasks. It does this by analyzing video-taped lessons from the Learner's Perspective Study, involving 15 Chinese and 10 U.S. consecutive lessons on the topic of linear equations/linear relations. We…

Presents some ideas about how teachers can foster mathematical communication by encouraging students to find multiple solutions to problems. Discusses three problems that help develop communication ability in mathematics. Views communication of multiple solutions as an instructional strategy to help students make sense of mathematics. (KHR)

Often after students solve a problem they believe they have accomplished their mission and stop further exploration. The purpose of this article is to discuss ways to encourage students to "look back" so as to maximise their learning opportunities. According to Polya, by "looking back" at a completed solution, by reconsidering and re-examining the…

Assessed the effectiveness of instruction in promoting sixth-grade students' conceptual understanding of the concept of averages using a leveling model and an open-ended problem-solving approach. Found that students were more capable of using the leveling approach and applying formal averaging algorithm to solve problems than using the open-ended…

This study involved an investigation of the relationship between the kinds of solution representations Chinese and U.S. students use and the sorts of pedagogical representations Chinese and U.S. teachers use during instruction. The findings suggest that the representations teachers use influence the representations their students use and, hence,…