Helping students reach a clear understanding of the cause-and-effect relationship between changes in parameter and the graph of an equation is the focus of the activity outlined in this article. The behavior of phase shifts has been regarded as counterintuitive for many people, and often, because of this, conflict between student intuition and…

Over a sixteen-week term, the study dove into how chess could enhance math skills for eleventh graders at three public schools in Cartagena, Colombia. It assumed that chess would sharpen their minds and problem-solving prowess. Seventy-one pupils took part, trying out a chess-centric way of learning. Researchers used multiple statistical…

Results in Mathematics Education, from different theoretical perspectives, highlight students' difficulties with graphs, both in interpreting given ones and in producing their own graphs. In this paper, we take an affective lens to understand both a student's relationship with mathematical graphs and a teacher's role when a task with a graph is…

This study sets for itself the task of constructing a learning trajectory for the fundamental theorem of calculus (FTC) that takes into account the interaction with an educational digital tool. Students were asked to explain the connections between interactive and multiple-linked representations in an educational digital tool, and to conjecture…

Learning mathematical thinking and reasoning is a main goal in mathematical education. Instructional tasks have an important role in fostering this learning. We introduce a learning sequence to approach the topic of integrals in secondary education to support students mathematical reasoning while participating in collaborative dialogue about the…

Graphing functions is an important topic in algebra and precalculus high school courses. The functions that are usually discussed include polynomials, rational, exponential, and trigonometric functions along with their inverses. These functions can be used to teach different aspects of function theory: domain, range, monotonicity, inverse…

The use of external representations has a potential to facilitate inquiry learning, especially in hypothesis generation and scientific reasoning, which are typical difficulties encountered by students. This study proposes and investigates the effects of a three-dimensional thinking graph (3DTG) that allows learners to combine in a single image,…

Within the South African school curriculum, the section on graphical functional relationships consists of signs which include symbols, notation and imagery. In a previous article we explored the role visualisation played in the way learners understood mathematical concepts. That paper reported on the learners' fixation with the physical features…

In this article, the author describes the "Be your own groundhog" project in her grades 9-12 Earth and environmental sciences courses, in which students use citizen science databases to research the physical changes that signal the arrival of spring. This project starts with a simple question, "When will spring spring?" This goes beyond the…

Composition of functions is one of the five big ideas identified in NCTM's "Developing Essential Understanding of Functions, Grades 9-12" (Cooney, Beckmann, and Lloyd 2010). Through multiple representations (another big idea) and the use of The Geometer's Sketchpad[R] (GSP), students can directly manipulate variables and thus see dynamic visual…