In this study, I present how eight U.S. college calculus instructors with different patterns of inquiry practices used instructional situations to frame instructional tasks for introducing derivatives graphically to students. During four interviews, the instructors proposed up to eight tasks for introducing derivatives physically, graphically,…

Approximate mathematical treatments are commonly taught in undergraduate chemistry, but the validity ranges of these approximations have rarely been properly defined. We present error contour plots of commonly used quadratic approximations for calculating equilibrium proton concentrations of monoprotic acids. Students and instructors can easily…

A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students' algorithmatizing activity. In both…

The benefits of using Microsoft Excel built-in functions in an undergraduate Multistage Separations course are analyzed based on 15 years of experience teaching mass transfer in Chemical Engineering programs at both the Bachelor's and Master's levels. Eight reasons for using spreadsheets in a Mass Transfer virtual course are given. Through the…

Although numerous studies have investigated how technology affects academic achievement, very few have focused on the purpose of the use of technology in mathematics education. This current study examines how student teachers (STs) benefit from GeoGebra as one of the Dynamic Geometry Software (DGS) while solving continuity problems. In order to…

To teach adaptively, teachers should be able to take the students' level of knowledge into account. Therefore, a key component of pedagogical content knowledge (PCK) is the ability to assume the students' perspectives. However, due to the so-called expert blind spot, teachers tend to misestimate their students' knowledge, such as when estimating…

Typical difficulties in learning probabilistic subjects are concerned with big data, complicated formulas and inconvenient figures in statistical analyses. The present research considers the usage of innovative teaching methods (e.g. electronic summary of lectures, presentations of lecture courses, task solution templates, electronic training…

Graph data such as argument diagrams has become increasingly common in EDM. Augmented Graph Grammars are a robust rule formalism for graphs. Prior research has shown that hand-authored graph grammars can be used to automatically grade student-produced argument diagrams. But hand-authored rules can be time consuming and expensive to produce, and…

Linear algebra students are typically introduced to the problem of how to convert from one coordinate system to another in a very abstract way. Often, two bases for a given vector space are provided, and students are taught how to determine a transition matrix to be used for changing coordinates. If students are successful in memorizing this…

Successful algebraic problem solving entails adaptability of solution methods using different representations. Prior research has suggested that students are more likely to prefer symbolic solution methods (equations) over graphical ones, even when graphical methods should be more efficient. However, this research has not tested how representation…

This article presents "concept landscapes"--a novel way of investigating the state and development of knowledge structures in groups of persons using concept maps. Instead of focusing on the assessment and evaluation of single maps, the data of many persons is aggregated and data mining approaches are used in analysis. New insights into…

Understanding Maxwell's equations in differential form is of great importance when studying the electrodynamic phenomena discussed in advanced electromagnetism courses. It is therefore necessary that students master the use of vector calculus in physical situations. In this light we investigated the difficulties second year students at KU Leuven…

Can individuals guess the gender of a writer based on a sample of his or her handwriting? We administer an electronic survey twice to the same individuals to find out. The resulting data set is interesting to students, rich enough to be amenable to a wide array of activities, and open to a variety of exploratory tacks for statistics students and…

Using calculus only, we find the angles you can rotate the graph of a differentiable function about the origin and still obtain a function graph. We then apply the solution to odd and even degree polynomials.

Blind students are bound to make up a very small part of the population most university lecturers will encounter during their careers. Research to date shows that good communication between staff and student improves the chances of a successful outcome for both parties. The research does show, however, that the exercise seems to be one of…