Theoretical analysis of whole number-based calculation strategies and digit-based algorithms for multi-digit multiplication and division reveals that strategy use includes two kinds of reasoning: reasoning about the relations between numbers and reasoning about the relations between operations. In contrast, algorithms aim to reduce the necessary…

Many children fail to master fraction arithmetic even after years of instruction. A recent theory of fraction arithmetic (Braithwaite, Pyke, & Siegler, in press) hypothesized that this poor learning of fraction arithmetic procedures reflects poor conceptual understanding of them. To test this hypothesis, we performed three experiments…

Each weighted mean of two values has a counterpart, equidistant from the arithmetic mean, obtained by exchanging roles between the weights or by inversing each weight. These elementary relations are apt for introductory courses.

This paper addresses the continuing need for mathematics teachers to enrich their mathematical knowledge beyond the school curriculum, in order to effectively engage students in creative and imaginative thinking, particularly, but not exclusively, students who show exceptional promise. The author, a retired university professor, works staff and…

A robust understanding of place value is essential. Using a problem-based approach set within meaningful contexts, students' attention may be drawn to the multiplicative structure of place value. By using quotitive division problems through a concrete-representational-abstract lesson structure, this study showed a powerful strengthening of Year 3…

In this study, it was aimed to investigate the primary mathematics teacher candidates' perceptions about the equal sign within the scope of neuroscience studies. To reveal their perceptions about the equal sign, three types of addition operations were asked to the participants: a+b=[], []=a+b, a+b=[]+c. Their brain waves were recorded by EEG…

It is well documented in literature that rational number is an important area of understanding in mathematics. Therefore, it follows that teachers and students need to have an understanding of rational number and related concepts such as fraction multiplication and division. This practitioner reference paper examines models that are important to…

Children who experience difficulties with learning mathematics should be taught by teachers who focus on the child's best way of learning. Analyses of the mathematical difficulties are necessary for fine-tuning mathematics education to the needs of these children. For this reason, an instrument for Observing and Analyzing children's Mathematical…

An understanding of partitive division is foundational for numerous other mathematics topics, including unit rate, slope, and probability. However, research has shown that learners tend to have a limited understanding of partitive division when the divisor is a proper fraction. To extend research on conceptions of partitive division in this study,…

Is it possible that a meeting of mathematicians and primary school teachers will be productive? This question became intriguing when one professor of mathematics initiated a professional development course for practicing primary school teachers, which he taught alongside a group of mathematics Ph.D. students. This report scrutinizes the uncommon…

The current study employed a randomized controlled trial to evaluate the use of peer tutoring and fluency-based instruction to increase mathematics fluency with addition and subtraction computation skills. Forty-one elementary school students between the ages of eight and 12 years participated in the 8-week study using cross-age peer tutoring, Say…

Research has identified various domain-general and domain-specific cognitive abilities as predictors of children's individual differences in mathematics achievement. However, research into the predictors of children's individual growth rates, namely between-person differences in within-person change in mathematics achievement is scarce. We…

This review protocol guides the review of research that informs the What Works Clearinghouse (WWC) "Assisting Students Struggling with Mathematics: Intervention in the Elementary and Middle School Grades" practice guide. The mathematics intervention practice guide will be an update of the original practice guide, "Assisting Students…

There is a call for enabling students to use a range of efficient mental and written strategies when solving addition and subtraction problems. To do so, students should recognise numerical structures and be able to change a problem to an equivalent problem. The purpose of this article is to suggest an activity to facilitate such understanding in…

While Educational Data Mining research has traditionally emphasized the practical aspects of learner modeling, such as predictive modeling, estimating students knowledge, and informing adaptive instruction, in the current study, we argue that Educational Data Mining can also be used to test and improve our fundamental theories of human learning.…