Too often the discourse of the mathematics classroom is defined as the teacher asking the questions and the students answering them--or trying to. Certainly teachers should not be prohibited from asking questions, but if students are always placed in the position of responding rather than initiating, then one can hardly be surprised if at times…

Of the eight scientific practices highlighted in "A Framework for K-12 Science Education: Practices, Crosscutting Concepts, and Core Ideas," the first is for students to develop abilities to ask questions and define problems (NRC 2012). Constructing a range of questions about an object or phenomenon validates not only what students have…

By working through well-designed tasks, students can expand their thinking about mathematical ideas and their approaches to solving mathematical problems. They can come to see the value of looking at tasks from different perspectives and of using different representations. This article discusses four tasks that encourage high school students and…

The necessity of using inquiry-based learning (IBL) was recently recommended by studies and reports made for the European Commission. Several European projects are devoted to the widespread use of IBL methods. The effects of using IBL are studied worldwide. In the framework of the Seventh Framework Program (FP7) project PRIMAS, a series of…

According to self-determination theory, social contexts that support students' basic psychological needs of autonomy, competence, and relatedness foster motivation toward behaviors that are valued in that social context. This study investigated the socio-contextual elements of a learning environment that support or undermine students' basic…

A multiple-baseline design across math-fact sets was used to evaluate the effects of a taped-problems intervention on students' performance with addition facts and their inverses in an intact, rural, second-grade classroom. Results suggested that the procedure was effective in improving fluency on math facts as well as their inverses. Across 3…

The aim of this study is to explain students' ability to transfer their knowledge about mathematical series to the problems that they encounter. The data of the study were obtained by using two different tests, namely "Problem Solving Test (PST)" and "Series Character Identification Test (SCT)" which were developed by the…

The mathematical topic of inverse functions is an important element of algebra courses at the high school and college levels. The inverse function concept is best understood by students when it is presented in a familiar, real-world context. In this article, the authors discuss some misconceptions about inverse functions and suggest some…

Nonroutine function tasks are more challenging than most typical high school mathematics tasks. Nonroutine tasks encourage students to expand their thinking about functions and their approaches to problem solving. As a result, they gain greater appreciation for the power of multiple representations and a richer understanding of functions. This…

This article introduces a trigonometric field (TF) that extends the field of real numbers by adding two new elements: sin and cos--satisfying an axiom sin[superscript 2] + cos[superscript 2] = 1. It is shown that by assigning meaningful names to particular elements of the field, all known trigonometric identities may be introduced and proved. Two…

The authors examined the role of problem sets on student learning in university microeconomics. A total of 126 students participated in the study in consecutive years. independent samples t test showed that students who were not given answer keys outperformed students who were given answer keys. Multiple regression analysis showed that, along with…

The author describes a classroom activity in which students generate and then analyze insulting words to gain insights into how gender is socially constructed. After discussing how and why undergraduate students struggle with the concept of gender, the author highlights the usefulness of an active learning pedagogy in clearing these…

This study identifies the kinds of problems teachers pose when they are asked to (a) generate problems from given information and (b) create new problems from ones given to them. To investigate teachers' problem posting, preservice and inservice teachers completed background questionnaires and four problem-posing instruments. Based on previous…

In this paper, we describe our experience with the creation and utilization of online assignments for several calculus classes at Simon Fraser University (SFU). We present our findings regarding available software by considering the needs and perspectives of the instructors, students, and administrators. We provide a list of questions that guide…

Bayes's theorem is notorious for being a difficult topic to learn and to teach. Problems involving Bayes's theorem (either implicitly or explicitly) generally involve calculations based on two or more given probabilities and their complements. Further, a correct solution depends on students' ability to interpret the problem correctly. Most people…