During professional development, the authors learned about strings--a powerful instructional routine used in elementary classrooms to elicit students' mental mathematics strategies and use those strategies to build conceptual understanding. Strings provided the authors with a way to make relatively small changes to guided notes in algebra 1,…

Number talks encourage mathematical discourse and develop students' reasoning about number and operation (Parrish 2011). In a number talk, a teacher presents a purposefully crafted computation problem to solve mentally. Students share their solutions and explain their processes with the teacher facilitating the discussion through strategic…

This article discusses the use of number talks to engage kindergarten children in regular joyful math opportunities in the classroom. As an educator of four- and five-year-old students in a full day kindergarten (FDK) program in Ontario, Canada, I embrace inquiry-based learning to guide children's activities. Inspired by the childcare centres in…

A strong foundation in early number concepts is critical for students' future success in mathematics. Research suggests that visual representations, like a number line, support students' development of number sense by helping them create a mental representation of the order and magnitude of numbers. In addition, explicitly sequencing instruction…

Although the early development of children's number sense is a strong predictor of their later mathematics achievements, it has been overlooked in primary schools in Malaysia. Mainly attributable to underdeveloped number sense of Malaysian primary and secondary school children, their inability to handle simple mathematics tasks, which require the…

This investigation presents students with the challenge of determining the total number of eggs in a photograph of a stack of egg trays. The perspective of the photograph does not allow students to count all the individual eggs in the top tray but does allow them to see the number of eggs in one row and one column of the top tray. During this…

After studying the Common Core State Standards for Mathematics (CCSSM) and brain-based learning research, James Olsen believes mental math instruction in secondary school mathematics (grades 7-12) and in teacher education programs needs increased attention. The purpose of this article is to share some keys for teaching mental math. Olsen also…

In this article James Russo presents the Strategies, Understanding, Reading and Fast Facts Framework (SURF) for mental computation. He explains how this framework can be used to deepen mathematical understanding and build mental flexibility.

This article presents a sequence of learning activities that lead to using the area model of multiplication to understand the distributive property (DP). The connection between area and multiplication is an important one, both for algebraic thinking and for geometry, as indicated in two of the critical areas for the third grade in the Common Core…

Subtraction can be understood by two basic models--taking away (ta) and determining the difference (dd)--and by its inverse relation to addition. Epistemological analyses and empirical examples show that the two models are not relevant only in single-digit arithmetic. As curricula should be developed in a longitudinal perspective on mathematics…

Mrs. Fisher's class was learning about arithmetic functions by pretending to operate real-world "function machines" (Reeves 2006). Functions are a unifying mathematics topic, and a great deal of emphasis is placed on understanding them in prekindergarten through grade 12 (Kilpatrick and Izsák 2008). In its Algebra Content Standard, the…

This author agrees with the sentiments of John Hibbs' article "Was there ever any point to the three-part lesson?" (MT219). In particular the author fully supports a flexible approach to the structure of lessons. There are two interesting questions that arise from Hibbs' article: (1) Are there reasons for the large-scale adherence of teachers to…

Marlene Chesney describes a piece of research where the participants were asked to complete a calculation, 16 + 8, and then asked to describe how they solved it. The diversity of invented strategies will be of interest to teachers along with the recommendations that are made. So "how do 'you' solve 16 + 8?"

Mental computation--that is, calculating in the head--is a relatively new topic in mathematics curricula for primary-age children. It is an important skill because it enables children to learn more deeply how numbers work, make decisions about procedures, and create strategies for calculating, thus promoting number sense--a well-developed…

Exploring number systems of other cultures can be an enjoyable learning experience that enriches students' knowledge of numbers and number systems in important ways. It helps students deepen mental computation fluency, knowledge of place value, and equivalent representations for numbers. This article describes how the author designed her…