Recently, there has been a growing interest in learning approaches that combine two phases: an initial problem-solving phase followed by an instruction phase (PS-I). Two often cited examples of instructional approaches following the PS-I scheme include Productive Failure and Invention. Despite the growing interest in PS-I approaches, to the best…

Using expository text and examples available in 10 college textbooks we identify two conceptions of angles, trigonometric functions, and inverse trigonometric functions that rely on either a static or a dynamic definition of angle. Although the textbooks favor a conception of trigonometric functions that is based on a dynamic conception of angle,…

In the mathematics classroom, making sense of story problems can be a challenge for all students. Strategies that promote student discourse offer teachers one way to support their students' sense-making processes. In this article, the authors present a mathematical discourse strategy that was introduced to elementary school teachers during Project…

Our research includes undergraduate students who major in primary school education. Their academic background is prevailingly in the humanities. This poses specific demands on their mathematics instruction at university. To attract them to their mathematics course and raise its effectiveness, we use a series of activities. Writing assignments…

Mathematics word-problems continue to be an insurmountable challenge for many middle school students. Educators have used pictorial and schematic illustrations within the classroom to help students visualize these problems. However, the data shows that pictorial representations can be more harmful than helpful in that they only display objects or…

Magic captivates humans because of their innate capacity to be intrigued and a desire to resolve their curiosity. In a mathematics classroom, algorithms akin to magic tricks can be an effective tool to engage students in thinking and problem solving. Tricks that rely on the power of mathematics are especially suitable for students to experience an…

Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

This chapter explores problem-based learning (PBL) as effective pedagogy to enhance leadership learning. Through institutional examples, research, and personal experiences, the authors provide a rationale for faculty and staff to utilize PBL across the curriculum.

Help turn students into problem solvers. With lesson imaging, teachers anticipate how chosen activities will unfold in real time--what solutions, questions, and misconceptions students might have and how teachers can promote deeper reasoning. When lesson imaging occurs before instruction, students achieve lesson objectives more naturally and…

Instructional choice is a low-intensity strategy that can improve academic engagement. In this study, we investigated the effects of within-activity choices offered during math by third-grade teachers to participating students with behavioral and academic needs. We utilized a professional development model to train teachers to implement…

This research was an experimental research that aimed to know and measure the effectiveness of the application of Problem Based Learning model (PBL) with the assistance of animation media on tetragon material. This research type was quantitative research with one group pretest-posttest design. The population in this study was the students of class…

We tested a method for solving Bayesian reasoning problems in terms of spatial relations as opposed to mathematical equations. Participants completed Bayesian problems in which they were given a prior probability and two conditional probabilities and were asked to report the posterior odds. After a pretraining phase in which participants completed…

In this article, the authors emphasise the importance of purposeful mathematical discussion and using sequences of connected, cumulative, and challenging tasks in advancing students' spatial reasoning in the early years of schooling.

Mathematics has a unique and powerful role to play in the teaching of social justice issues. There is substantial quantitative evidence for social injustice, but many citizens lack the quantitative skills to understand that evidence. A course in quantitative literacy is a unique opportunity to provide this quantitative understanding to a wide…

The themes discussed in this study relate to how students reason about the information encoded in rate constants, which is important for developing a deep understanding of chemical kinetics at the molecular level. This study is part of a larger project centered more generally on students' understanding and use of mathematics in chemical kinetics.…