Problem-Posing Research in Mathematics Education: Some Answered and Unanswered Questions

Abstract

This chapter synthesizes the current state of knowledge in problemposing research and suggests questions and directions for future study. We discuss ten questions representing rich areas for problem-posing research: (a) Why is problem posing important in school mathematics? (b) Are teachers and students capable of posing important mathematical problems? (c) Can students and teachers be effectively trained to pose high-quality problems? (d) What do we know about the cognitive processes of problem posing? (e) How are problem-posing skills related to problem-solving skills? (f) Is it feasible to use problem posing as a measure of creativity and mathematical learning outcomes? (g) How are problem-posing activities included in mathematics curricula? (h) What does a classroom look like when students engage in problem-posing activities? (i) How can technology be used in problem-posing activities? (j) What do we know about the impact of engaging in problem-posing activities on student outcomes?

Improving mathematical learning in Scotland's Curriculum for Excellence through problem posing: an integrative review

“…The requirement to consider teachers is grounded on a growing body of research which has acknowledged problem posing as a valuable tool in developing mathematics teaching at all levels (e.g. Pittalis et al, 2004;Cai et al, 2015;Ellerton, 2015). Ticha and Hospesova (2013) found that prospective primary teachers acquired a deeper conceptual understanding of fractions.…”

“…Problem posing is considered by many stakeholders as a pedagogy that can augment the learning and teaching of mathematics (e.g. Cai et al, 2015;Singer et al, 2015).…”

Problem Solving in Mathematics Education

“…It is interesting to realize that some of these questions are among the unanswered questions proposed and analyzed by Cai et al (2015) in Chap. 1 of the book Mathematical Problem Posing (Singer et al 2015).…”

The Effects of Problem Posing Learning Model on Students’ Learning Achievement and Motivation

“…Proposing a problem can be useful in bringing together a number of learning goals, both in group and individual learning setting. Furthermore, Cai, Hwang, Jiang, & Silber (2015) posit that problem-posing activities can improve students' learning achievement, reasoning and communication skills, and capture their motivation.…”