Although the complexity of children's number learning is recognized, trade books about number have been treated as a simple, undifferentiated set. This analysis of 186 children's books, however, categorized a distinct subset of books about number as "counting books." These counting books were complex with regard to portrayal of counting…

This article shares two activities geared toward students in middle school that engage students in analyzing measures of center, specifically the arithmetic mean, and using transnumerative thinking with the ultimate goal of improving students' statistical literacy. Both activities support the Common Core standard, 6.SP.B.5 "Summarize and…

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…

Introducing the distributivity property of multiplication over addition is a well-known challenge in mathematics education, especially in primary school. As a contribution, this paper presents the results of a cycle of design research that focuses on the design, implementation and evaluation of a modelling activity in which 2nd-grade students are…

We report here on an intervention implementing a structural approach to arithmetic problem-solving in relation to learning outcomes among preschoolers. Using the fundamental principles of the variation theory of learning for developing the intervention and as an analytical framework, we discuss teaching and learning in commensurable terms. The…

Children need support in the early elementary grades to construct a deep, formal understanding of foundational prealgebraic concepts. In this article, the authors share recommendations for teaching one such foundational concept--mathematical equivalence. First, they define mathematical equivalence and discuss research supporting the benefits of…

Ethnomatemics-based mathematics concept implementation can be carried out through constructivism-based learning such as realistic mathematics, problem-based and learning with a scientific approach. This research purpose to explore the form of ethnomatemics on the woven cabbage leaves of the Tutuwaru community and analyze the process of…

The number one plays a special role in mathematics because it is the identity element in multiplication and division. The present findings, however, indicate that many middle school students do not demonstrate mathematical flexibility representing one as a fraction. Despite possessing explicit knowledge of fraction forms of one (e.g., 95% of…

Students often show difficulties in understanding rational numbers. Often, these are related to the natural number bias, that is, the tendency to apply the properties of natural numbers to rational number tasks. Although this phenomenon has received a lot of research interest over the last two decades, research on the existence of qualitatively…

The study and interest of figurate numbers can be observed even in ancient Greece. On the other hand, it becomes very important the historical understanding about an evolutionary process and the particular generalization of such 2D, 3D and m-D figurate numbers and they remain the interest of current scientific investigations. On the other hand, in…

Although basing instruction on a learning trajectory (LT) is often recommended, there is little direct evidence to support the premise of a "LT approach"--that to be maximally meaningful, engaging, and effective, instruction is best presented one LT level beyond a child's present level of thinking. The present report serves to address…

This research aims to explore the use of ethnomathematics in revealing mathematical representations and in the formulation of a calculation system used in the "Marosok" trading tradition by the Minangkabau tribe in West Sumatra. Ethnomathematics studies ideas in various cultural activities practiced by ethnic, social, or professional…

Background & aims: In recent years, there has been an increased interest in analyzing the mathematical performance of students with learning difficulties in order to provide them with teaching methods adapted to their needs. In particular, the importance of studying the type of informal strategy that students use when solving problems has been…

This document includes instructional tips on: (1) Building on students' informal understanding of sharing and proportionality to develop initial fraction concepts; (2) Helping students recognize that fractions are numbers that expand the number system beyond whole numbers, and using number lines to teach this and other fraction concepts; (3)…