This qualitative semi-structured interview study investigated how the opportunity to learn with productive struggle emerges in a teacher's beliefs, anticipation, planning, teaching, and response to struggle in learning mathematics. In this study, the experiences of student struggle in the teaching and learning of fractions was investigated through…

Productive struggle is an essential part of mathematics instruction that promotes learning with deep understanding. A video scenario is used to provide a glimpse of productive struggle in action and to showcase its characteristics for both students and teachers. Suggestions for supporting productive struggle are provided.

The aim of this article is to present a scheme for coding and categorizing students' written explanations of mathematical problem-solving activities. The scheme was used successfully within a study project carried out to determine whether student problem-solving behaviour could be positively affected by writing explanatory strategies to…

This study investigated how a teacher in a multilingual classroom attempted to support learners who are struggling to translate written/verbal mathematics into a symbolic form. Thirty-six Grade ten learners in one multilingual classroom in South Africa were given a written test involving one algebraic question and then a discussion on the solution…

"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 &…

Skills in reading, writing, and mathematics are key to academic learning but are conventionally taught separately from the discipline areas to which they must be applied. For example, students may be taught writing skills in the morning in an English course and then be expected to apply them to writing an essay in a history class in the afternoon.…

Problems in mathematics education as a social activity are the major focus of this document. Paragraphs that describe major problems in mathematics education point out at least eleven major issues as seen from the author's perspective. (MP)

Explanations for problems in mathematics are offered, and examples that may lead to a better understanding of problems in mathematics are discussed. Examples include the developmental, dyscalculia, dyspedagogia, behaviorist, medical, psychoanalytic, cultural, curricular, social, transactional, moral, and eclectic models. A case study exemplifies…

Calculus is one of those topics in mathematics where the algorithmic manipulation of symbols is easier than understanding the underlying concepts. Around 1680 Leibniz invented a symbol system for calculus that codifies and simplifies the essential elements of reasoning. The calculus of Leibniz brings within the reach of an ordinary student…

This dissertation seeks to understand how teachers learn through interactions in newly formed workplace communities by examining how mathematics teachers engaged in equity-oriented reforms frame problems of practice. It examines how teachers' framings develop over time, and how teachers' shifting frames connect to their learning in a community of…

Presents a rationale for including applied functions and graphs in developmental mathematics courses, arguing that the ability to construct, interpret, and represent functional relationships is important in every discipline. Discusses student difficulties with abstract and applied functions and curricular and instructional implications. (DMM)

This article describes current goals for K-8 school mathematics and outlines 7 critical areas in which students frequently experience difficulty. Effective mathematics teaching is related to teaching that takes into account the 3 learning principles articulated in the National Research Council (2006) publication, "How Students Learn". Research…