After years of noticing the challenge our students have with fraction operations, we decided to implement a scaffold approach that focuses on using benchmarks to better develop both students' understanding of a fraction as a quantity and their ability to think about fraction operations meaningfully. While we found this approach supported students…

This article proposes a practical method of teaching the addition of unit fractions using a series of mirror equation experiments.

In this writing, I report on how two 12-year old children used fraction strips to add 1/2 and 2/5. In their interaction with the tool, I look for the emergence of the tool-mediated Zone of Proximal Development to analyse the knowing that become available to the children. In thinking about this interaction, I ask what is the role of the more…

This paper makes a proposal, from the perspective of a research mathematician interested in mathematics education, for broadening and deepening whole number arithmetic instruction, to make it more relevant for the twenty-first century, in particular, to enable students to deal with large numbers, arguably an essential skill for modern citizenship.…

Mathematics educators and researchers have advocated for the use of manipulatives to teach mathematics for decades. The purpose of this article is to provide illustrative uses of a readily available manipulative rather than a complete list. From an Australian perspective, Pop-it fidget toys can be used across the mathematics curriculum. This paper…

A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…

The "Making Meaning for Operations Casebook" was developed as the key resource for participants' Developing Mathematical Ideas seminar experience. The twenty-nine cases, written by teachers describing real situations and actual student thinking in their classrooms, provide the basis of each session's investigation of specific…

Fractions are troublesome for many children, especially students with learning difficulties and disabilities in mathematics. To address this serious educational concern, this article recommends the use of number lines to build fraction sense. Math activities that center on the number line build fraction concepts as early as third grade. A number…

By the time they reach middle school, all students have been taught to add fractions. However, not all have "learned" to add fractions. The common mistake in adding fractions is to report that a/b + c/d is equal to (a + c)/(b + d). It is certainly necessary to correct this mistake when a student makes it. However, this occasion also…

Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…

When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…

This paper focuses on an implementation a sequence of instructional activities about addition of fractions that has been developed and implemented in grade four of primary school in Surabaya, Indonesia. The theory of Realistic Mathematics Education (RME) has been applied in the sequence, which aims to assist low attaining learners in supporting…

The transition from whole numbers to integers involves challenges for both students and teachers. Leadership in mathematics education calls for an ability to translate depth of understanding into effective teaching methods, and this landscape includes alternative treatments of familiar topics. Noting the multiple meanings associated with the…

This paper describes the Rational Number Project (RNP), teaching experiments concerned with the teaching and learning of fractions among 4th and 5th grade students. Interviews with 4th grade students who used the RNP curriculum and with students who used a traditional curriculum were conducted by RNP staff as well as classroom teachers. This paper…

Provides a bibliography of children's literature exploring mathematical concepts: classification; place value and numeration systems; counting, addition, and subtraction; multiplication and division; fractions; estimation; big numbers; geometry; measurement; and games and puzzles. Highlights one book for each concept, suggests class activities,…