Mathematical thinking is a complex, multi-faceted process that has been described as messy and difficult but can also show growth and insights into conceptual understanding and knowing. This paper explores the application of Edward de Bono's practical thinking, in particular, the occurrence of porridge words to examine the mathematical thinking of…

Computational thinking (CT) has been supported as an important skill every young person should possess for the 21st century, with possible implications for problem-solving, self-expression, and creativity. Numerous initiatives, both within and outside classroom settings, have been developed in response to policy mandates aiming at broadening…

This article draws on the simple context of a two animal farm to create an engaging and mathematically meaningful problem solving task for students. It aims to encourage students to think systematically and to present their findings methodically. The task is structured sequentially, making it suitable for primary school students from Year 1 to…

Tangrams are a traditional Chinese puzzle comprising seven pieces that fit together to make a square. The seven pieces include two large right angled isosceles triangles, one medium size right angled isosceles triangle, two small right angled isosceles triangles, a small parallelogram, and a small square. The literature shows tangrams have been…

This article presents a series of open-ended tasks exploring the development of algebraic expressions suitable for exploration with Year 7 students. The tasks use a familiar tool, the hundreds chart, to aid the transition between representational tools and abstract ways of working. The tasks outline a developmental progression of patterns and…

This study investigates students' and adults' performance in judging reasonableness of computational results, namely reflecting on whether these results qualify as acceptable answers to mathematical tasks. Data was gathered via task-based questionnaires from 160 participants, evenly divided between fifth-graders and adults. Their responses to a…

This article describes the two types of reasoning in fraction conceptions that students often use, "gap" and "missing piece," and one that the authors aspire their students to reach, "residual." Each of these types of reasoning are underpinned by a different conception of fractions. Students who use "gap…

In this article, we draw on assemblage theory to investigate how children aged 5 engage with different material surfaces to explore ordinal and relational aspects of number. The children participate in an activity in which they first interact with a strip on the floor, then with a multi-touch iPad application, to work with numbers in expressive…

The authors describe a lesson--"You Decide"--which challenges students but also provides opportunities for success for those who may struggle. They show how this lesson has been helpful for teachers in revealing some misconceptions that often exist in primary students' thinking. In this article, they share data on the apparent relative…

As early as first grade, some children are more likely than others to perform arithmetic using inefficient or other overt counting strategies. To partially address this problem, the primary investigator developed a skill hierarchy with procedures based on applied behavior analysis. The novel early-intervention program included a combination of…

This paper reports on the design, implementation, and evaluation processes of an activity that focused on the comparison meaning of the subtraction of integers and included the number line model as the primary representation. Finding the answer and determining the sign of the answer in the subtraction questions were targeted as the learning…

Understanding and supporting students' development of graph literacy is important. We studied how aspects of graph literacy might be supported (or hindered) in middle school by analyzing the content in textbooks. Specifically, we conducted a content analysis of tasks involving two-dimensional Cartesian graphs presented in grade 6-8 US textbooks.…

Growing evidence suggests that parents' practices contribute to their children's cognitive development and that such practices may reflect SES disparities. This study investigated longitudinal interrelations between home mathematics environment (HME), children's math achievement, and two facets of SES (mother's educational attainment and household…

This study examined the engagement of preservice elementary teachers (PSTs) with mathematics tasks that were open in various ways and to varying extents. In K-12 settings, practitioners who have implemented recently popular open tasks report increased engagement and from a wider variety of students. While these anecdotal reports and related…

The ability to relate mathematics teaching to real life is the common goal of many countries' mathematics curriculum National Society for Experiential Education's (NSEE) [2011] "Eight Principles of Good Practice for All Experiential Learning Activities." (intention, originality, planning, clarity, monitoring and evaluation, reflection,…