This article describes the technique of introducing a new variable in some calculus problems to help students master the skills of integration and evaluation of limits. This technique is algorithmic and easy to apply.

In this article, we discuss a collection of active learning activities derived from classic psychology studies that illustrate the appropriate use of descriptive and inferential statistics. (Contains 2 tables.)

In this article, the authors aim to identify the causal effect of the use of graded problem sets on academic performance of Spanish students. The identification strategy relies on an experiment in which the authors exploit variation arising from observing the performance of nearly 300 students taking the same class during the same semester and…

Using a design-based research approach, we developed a data-rich problem (DRP) set to improve student understanding of cellular respiration at the ecosystem level. The problem tasks engage students in data analysis to develop biological explanations. Several of the tasks and their implementation are described. Quantitative results suggest that…

This paper justifies the need for, and offers some suggestions on, the selection and implementation of mathematical problems known as dynamic solution exercises (DSEs). The intent of this article is to help provide insight into how mathematics teachers can go about making "vertical articulation" a cooperative and tangible part of the…

The great gorilla jump is an activity designed to allow calculus students to construct an understanding of the structure of the Riemann sum and definite integral. The activity uses the ideas of position, velocity, and time to allow students to explore familiar ideas in a new way. Our research has shown that introducing the definite integral as…

Practical project work based on eBay selling prices is described. It is suitable for secondary school students of a wide range of statistical expertise and it may be used to introduce a statistical package. (Contains 4 figures and 5 tables.)

Could problem solving be the object of teaching in early education? Could appropriate teaching interventions develop to scaffold children's efforts to solve problems? These were the central questions of this article. The sample consisted of 18 children attending public pre-school in Cyprus. The problem they were asked to solve was to find all…

Last semester, the author had a particularly vocal class that made it clear that they disliked small group exercises. In an attempt to understand their discomfort, she had this class generate a list of the top 10 reasons they disliked small group exercises. Some of the reasons listed by the students are exactly why the author uses small group work…

This article presents different approaches to a problem, dubbed by the author as "the consecutive pages problem". The aim of this teaching-oriented article is to promote the teaching of abstract concepts in mathematics, by selecting a challenging amusement problem and then presenting various solutions in such a way that it can engage the attention…

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…

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…

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…

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…