Blended learning is becoming increasingly prevalent in engineering education due to its flexibility and enhanced learning outcomes, however it can face challenges in maintaining student engagement and satisfaction. This study investigates the impact of worked example videos (WEVs) as a blended learning approach within undergraduate engineering,…

These classroom notes are focused on undergraduate students' understanding of the polysemous symbol of superscript (-1), which can be interpreted as a reciprocal or an inverse function. Examination of 240 scripts in a mid-term test identified that some first-year students struggle with choosing the contextually correct interpretation and there are…

An underlying goal in most chemistry curricula is to enable students to think like chemists, yet there is much evidence to suggest that students can learn to solve problems without thinking conceptually like a chemist. There are few tools, however, that assess whether students are learning to think like Ph.D. faculty, putative experts in the…

In this paper, the authors examine a property that holds for all cubic polynomials given two zeros. This property is discovered after reviewing a variety of ways to determine the equation of a cubic polynomial given specific conditions through algebra and calculus. At the end of the article, they will connect the property to a very famous method…

The authors examined the long-term learning effects of two different practice set assignment approaches on business students' long-term learning: a comprehensive, multiple-period practice set and a topic-specific practice set. Student learning was measured longitudinally across semesters. The authors found evidence that students using a…

A facility with signed numbers forms the basis for effective problem solving throughout developmental mathematics. Most developmental mathematics textbooks explain signed number operations using absolute value, a method that involves considering the problem in several cases (same sign, opposite sign), and in the case of subtraction, rewriting the…

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, 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…

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…

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…