In a teaching experiment, I examined a theoretical model of mathematics teaching and learning in practice. In this paper I focus on how the model can guide the teacher's thinking about students' understandings and the generation of activities that foster intended transformations in those understandings. As a research-teacher I taught, twice a week…

The case of Lucina must be placed at a level of a partial advance achieved in the development of an exhaustive qualitative research recently conclude in a night elementary school of Mexico City, an institution that provides young people and adults with academic formation. The research problem herein discussed is the enrichment of semantic and…

The teaching and learning in algebra has been much debated. Traditionally early algebra has relied heavily on arithmetic. Recently our focus has changed to teaching algebraic thinking with arithmetic thinking. This paper explores the models that assist young students generalise the patterns of arithmetic compensation. A teaching experiment was…

Arithmetic is the major focus of elementary mathematics instruction. This book offers lessons for developing children's numerical understanding and skills. The lessons help children learn to estimate, understand numerical relationships, develop number sense, compute mentally and with paper and pencil, and use arithmetic as a tool to solve…

We present in this paper five case studies of instrumental genesis of number-theoretic concepts and techniques involving multiples, divisors, and numerical decomposition. The pupils, who were 12 to 15 years old, used the multi-line screen display of the graphing calculator to explore numerical tasks related to the "Five steps to zero"…

If we consider the gap between mathematics at elementary and secondary levels, and the logical nature of the higher level, it is important that aspects of children's logical development in the latter grades in elementary school be clarified. We focused on 5th graders' learning "division with decimals" as it is known to be difficult to…

By studying and practicing metacognition, teachers and parents are instilling positive attitudes toward learning by teaching how-to-learn skills that prepare children for assessing their own thinking about learning as they become more and more developmentally prepared. This book stresses the strategies for thinking in mathematical terms without…

Twenty teacher-made multiple choice items in mathematics are presented. (MM)

Four worksheets showing how number patterns may be used to give extra practice and insight into the decimal numeration system and the basic properties of arithmetic. (MM)

Students who can compute mathematical problems in their heads have learned a skill that is important for estimating and for understanding the number system. Practice activities that can help students master mental computation skills are described. (PP)

Research conducted in several countries has shown consistent patterns of performance on "change,""combine," and "compare" word problems involving addition and subtraction. These findings are interpreted within a theoretical framework which emphasizes development of levels of word problem-solving ability related to…