At the start of every school year, teachers typically wonder what their new students know coming into the grade level. Sometimes, though, they place too much emphasis on what children do not know or have forgotten over summer break. After all, those gaps can be glaring. Helping their students grow is like helping an acorn grow; they must watch for…

In "Principles to Actions: Ensuring Mathematical Success for All," NCTM (2014) defines productive struggle as students delving "more deeply into understanding the mathematical structure of problems and relationships among mathematical ideas, instead of simply seeking correct solutions" (p. 48). Hiebert and Grouws (2007, p. 387)…

In its mathematics standards, National Council of Teachers of Mathematics (NCTM) states that problem solving is an integral part of all mathematics learning and exposure to problem solving strategies should be embedded across the curriculum. Furthermore, by high school, students should be able to use, decide and invent a wide range of strategies.…

Several decades ago, V. A. Krutetskii conducted a multiyear study to investigate the various types of thinking that academically advanced, or as he called them, gifted mathematicians used. Following an in-depth look at Krutetskii's nine ways of thinking, a model is proposed that will provide direction for teachers in selecting problems. The model…

For many children, mathematics is an inherently difficult subject to learn. Between 5 and 8 percent of children between the ages of 6 and 14 have a particular type of cognitive deficiency that limits their aptitude to acquire knowledge and understanding of fundamental ideas in numeracy. Increasingly, researchers in the cognitive sciences are…

People spontaneously discover new representations during problem solving. Discovery of a mathematical representation is of special interest, because it shows that the underlying structure of the problem has been extracted. In the current study, participants solved gear-system problems as part of a game. Although none of the participants initially…

This study developed a web-based multimedia whiteboard system to help students learning with mathematical problem solving. The purpose is to promote a new online mathematical learning model that students not only use electronic whiteboard to write down their mathematical problem solving solutions but also use voice recording tool to give oral…

Explores possible reasons for the gender differences in mathematics problem-solving strategies found in primary-grade students in the study by E. Fennema and others and considers implications of the findings for mathematics instruction. (SLD)

Considers implications of the findings of the study by E. Fennema and others that boys in the primary grades use different mathematics problem-solving strategies than girls and suggests that equitable mathematics instruction may require specific attention to gender differences and underachieving groups. (SLD)

Suggests that an explanation for the differences in mathematics problem-solving strategies found in the study by E. Fennema and others may be simply that the girls in the study population are less interested in mathematics than the boys and explores some implications of this explanation. (SLD)

Suggests that the instructional methods used with the subjects in the study by E. Fennema and others may have allowed teachers' gender stereotypes to be activated more than traditional instructional methods do, resulting in differences in primary-grade students' problem-solving strategies. (SLD)

Problem solving is seen to lie at the "heart" of mathematics (Cockcroft, 1982). Problem solving is also of great importance to industry that claims many young people leave school and take up jobs without the skills needed to sort out difficulties and problems (Smith Report, 2004). So is problem solving at the heart of mathematics teaching in…