Properties of curved functions considered to be parallel over their domains are investigated. Parallel curves in a given plane may appear identical but are actually not superimposable and thus are not congruent. Translational shifted functions in a plane are not parallel curves because the shortest perpendicular distance between them is not…

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,…

Learning curves are an important tool in cognitive diagnostics modeling to help assess how well students acquire new skills, and to refine and improve knowledge component models. Learning curves are typically obtained from a model estimated on real data obtained from a finite, and usually limited, sample of students. As a consequence, there is…

Manfred Hauben proposes an approach to teaching non-transitive relationships between 'paradoxical' dice using simple statistical graphics. This method usefully supplements traditional approaches of conditional probability calculations and trees, and students are thereby better able to see what is going on and the mechanism of these relationships.

Informal best fit lines frequently appear in school curricula. Previous research collectively illustrates that the adjective informal does not translate to cognitive simplicity. Using existing literature, we create a hypothetical framework of cognitive processes associated with studying informal best fit lines. We refine the framework using data…

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…

Implementing an integrated sequence of concrete-representational-abstract depictions of mathematics concepts (CRA-I) can improve the mathematics achievement of students with disabilities, and explicit instructional strategies involving problem-solving heuristics and student verbalizations can help facilitate students' conceptual understanding of…

Who will make a better estimate concerning the number of jelly beans in a jar, a single person or a group of people? On one side of the debate is the notion that a person would make a better decision because he or she uses unique knowledge that the group may not possess. On the opposite side of the argument is the claim that because of their…

Fitness trackers can provide primary students with exciting opportunities to calculate, measure time and distance, graph, make sense of data, and improve their activity levels. This article suggests ways to use fitness trackers in the classroom.

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…

Previous research has demonstrated how young children can identify the signal in data. In this exploratory study we considered how they might also express meanings for noise when creating computational models using recent developments in software tools. We conducted extended clinical interviews with four groups of 11-year-olds and analysed the…

Chocolate chip cookies are used to illustrate the importance and effectiveness of control charts in Statistical Process Control. By counting the number of chocolate chips, creating the spreadsheet, calculating the control limits and graphing the control charts, the student becomes actively engaged in the learning process. In addition, examining…

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)…

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.

Students with cerebral palsy (CP) without severe intellectual impairments often experience difficulties in mathematics performance. Given the high prevalence of learning difficulties in students with CP, few studies have examined interventions to improve the math competency of these students (Jenks et al., 2009). A single-subject reversal design…