Using mathematical modelling to solve problems appears in all year levels in the Australian Curriculum: Mathematics (v. 9), and is probably the most authentic way of teaching mathematics in context. However, the term mathematical modelling, even if familiar to teachers, may not be well understood or enacted confidently by teachers in their…

Second-order covariation is a form of mathematical reasoning that needs to be characterized both concerning students' cognitive processes and the design of tasks that promote it. This contribution aims to shed light on these two issues by comparing data related to the same learning experiment performed in two different learning environments:…

The low results of learning mathematics from year to year give rise to suggestions for students that mathematics is a difficult lesson. This needs to be researched to find out the relationship between mathematics learning attitudes, anxiety, habits, and additional mathematics learning outcomes. Quantitative research method with a survey approach.…

Some situations are presented with perplexing properties, which become clearer by looking at contingency tables. This in turn leads to problems that can be solved using conditional frequencies and thus leading to the Bayes formula with natural frequencies or probabilities.

Students and teachers often approach math with a single goal in mind: to get the right answer. But teachers must resist the urge to simply teach a procedure, writes educator LauraMarie Coleman. Instead, they should make a conscious decision to facilitate a discussion that leads to deeper student learning.

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook…

It is well-known that a key to promoting students' mathematics learning is to provide opportunities for problem solving and reasoning, but also that maintaining such opportunities in student-teacher interaction is challenging for teachers. In particular, teachers need support for identifying students' specific difficulties, in order to select…

The effectiveness of group problem-solving in mathematics depends on the extent to which meaningful participation is distributed across all group members. One way to explore how participation is distributed within groups is by examining how students are positioned within group interactions. In this study, we explore the social instructional…

Although children learn more when teachers gesture, it is not clear "how" gesture supports learning. Here, we sought to investigate the nature of the memory processes that underlie the observed benefits of gesture on lasting learning. We hypothesized that instruction with gesture might create memory representations that are particularly…

Since its first notable appearance in the "Second Handbook of Research on Mathematics Teaching and Learning," the phrase productive struggle has garnered support from a few, yet very influential, educational researchers. However, since the phrase was popularized by Hiroko Warshauer in 2011, examinations of the productive struggle have…

Learning Transformation Geometry (TG) needs a more informal approach to concern situational problems. This study aims to develop actionable knowledge of TG in the form of design related to context and yet general enough to use digital manipulative activities in new situations. We propose such knowledge in the form of conjectured Local…

This paper explores the specialized knowledge mobilized by a mathematics teacher in the selection and use of examples for teaching sequences. Taking an experimental case study approach, we analyse the examples deployed in a series of third-year secondary level lessons on sequences and identify the different knowledge subdomains activated according…

Students at the elementary level should have opportunities to critique the world through mathematics and to see themselves as capable doers of mathematics. The lesson described in this article prompted students to consider how to use mathematics to organize an emergency evacuation. In this article, the authors show how small changes to a task…

A one-degree angle would certainly be difficult to draw accurately, especially without the aid of other tools like a protractor. However, mentally making a one-degree angle in visualized imagination is not only possible, but it is important for students' emergent understandings of angular measure. When students begin learning about length,…

Considering the negative situations faced by the migrating societies, it is known that the language and culture factors exert a stronger influence on the mathematics course than the other undesirable conditions. From this perspective, it is known that the mathematical performance of individuals is likely to increase by placing the concept of…