Examples play a variety of roles in proving and disproving. Buchbinder and Zaslavsky (2019) have produced an a priori mathematical framework for assessing students' understanding of the role of examples when proving and disproving universal and existential statements. In this paper, I highlight three important aspects that suggest an extension of…

Intuitive conceptions in mathematics guide the interpretation of mathematical concepts. We investigated if they bias teachers' conceptions of student arithmetic word problem solving strategies, which should be part of their pedagogical content knowledge (PCK). In individual interviews, teachers and non-teaching adults were asked to describe…

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…

Educational literature indicates that solving open mathematical tasks (OTs) is a powerful creativity-directed activity. However, the use of these tasks with school students on an everyday basis is extremely limited. To promote implementation of OTs in middle school, we manage a large-scale R&D project, Math-Key, which makes open mathematical…

Are students with special educational needs excluded from the reform promise of "mathematics for all"? This paper explores the discursive production of students with special educational needs in the context of professional development (PD) for collaborative problem-solving teaching. We held interviews with Chilean primary school teachers…

Although mathematical practice has traditionally valued two distinct kinds of mathematical work--referred to by Gowers (2000) as theory building and problem solving--activity in classrooms appears to be organized largely around the latter, rather than the former. This study takes up the question of whether there is a customary role for theory…

Not only are the problems teachers pose throughout their teaching of great importance but also the ways in which they use those problems make this a critical component of teaching. A problem-posing episode includes the problem setup, the statement of the problem, and the follow-up questions. Analysis of problem-posing episodes of precalculus…

"From Another Perspective" is a year-long course for teachers of mathematics that is designed to enhance teachers' awareness of the way that their students think when they are experiencing difficulties in geometry. It also aims at equipping teachers with tools needed to analyze and cope with Problematic Learning Situations in geometry (Gal &…

The aim of this study is to investigate the efficiency of cooperative learning on preschoolers' verbal mathematics problem-solving abilities and to present the observational findings of the related processes and the teachers' perspectives about the application of the program. Two experimental groups and one control group participated in the study.…

This study brings together two lines of research on teachers' affective responses toward mathematics curriculum reforms: their concerns and their efficacy beliefs. Using structural equation modeling to analyze data on 151 elementary mathematics teachers' concerns and efficacy beliefs 5 years into a mandated curriculum reform on problem solving,…

How do teachers conceptualize and deal with context of mathematics word problems in their teaching? This question is discussed based on a study of 14 experienced teachers at the elementary, junior high and senior high school levels. Bruner's notions of paradigmatic and narrative modes of knowing formed the basis of analysis of data from sources…

Described is the Educational Leaders in Mathematics (ELM) Project, a four-stage inservice teacher program designed to stimulate teachers' development of a constructivist view of learning. The impact of the intervention was studied, and results indicated that teachers' beliefs were affected, producing changes in teaching strategies. (MDH)

The opinions of 98 Australian educational experts concerning mathematics skills necessary for future numeracy were solicited. The qualitative comments were incorporated into three scenarios reflecting alternative visions for the future: a careful scenario, a futuristic scenario, and a process scenario. (24 references) (MDH)