In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…

In this study, we decomposed the broad practice of deciphering multiple solution strategies. We conducted interviews with 11 preservice elementary teachers, in which we asked teachers to decipher students' standard and nonstandard strategies to multiplication and division problems. We examined what teachers said and did--what we refer to as…

This paper discusses some difficulties in teaching introductory courses to programming, paying particular attention to their mathematical nature. We consider some aspects, which have not been commented in detail in textbooks and often neglected by course outlines and schedules. Some of these are constructing complex conditions, exceeding array…

This article describes how teachers address issues and tensions that students meet in learning division of fractions. First, students must make sense of division of fractions on their own by working individually and in small groups, using concrete or pictorial representations, inventing their own processes, and presenting and justifying their…

The teaching and learning of mathematics cannot be understood without considering the resolution of word problems. These kinds of problems not only connect mathematical concepts with language (and therefore with reality) but also promote the learning related to other scientific areas. In primary school, problems are solved by using basic…

What does it look like to "understand" operations with fractions? The Common Core State Standards for Mathematics (CCSSM) uses the term "understand" when describing expectations for students' knowledge related to each of the fraction operations within grades 4 through 6 (CCSSI 2010). Furthermore, CCSSM elaborates that…

This study compared one lesson across four U.S. "traditional" textbook series, two U.S. reform-based textbook series, and one Chinese mathematics textbook series in teaching the connection between multiplication and division. The results showed the differences across U.S. and Chinese lessons in both the teaching and the practice parts of…

This book contains 16 papers on the theory, research, and practice of adult numeracy development. The following papers are included: "The Numeracy Challenge" (Iddo Gal); "Numeracy, Mathematics, and Adult Learning" (Diane Coben); "Building a Problem-Solving Environment for Teaching Mathematics" (Peter Kloosterman, Bin Hassan Mohamad-Ali, Lynda R.…