To prepare students for participation in our society, where interpreting, representing, and manipulating of dynamic phenomena are becoming key activities, we believe that one should start developing a mathematical understanding of change at an early age. We therefore started a design research project to teach the concept of instantaneous speed in…

This paper describes investigations in visualizing logpaths of students in an online calculus course held at Florida State University in 2014. The clickstreams making up the logpaths can be used to visualize student progress in the information space of a course as a graph. We consider the graded activities as nodes of the graph, while information…

Stephanie Whitney teaches in the department of teacher education at DePaul University in Chicago, Illinois. Her interest is in how students reason and make sense of mathematics, and how teachers can promote this behavior. Students should engage in reasoning and sense making daily in their mathematics classes. It is often through students'…

Graphing polar curves typically involves a combination of three traditional techniques, all of which can be time-consuming and tedious. However, an alternative method--graphing the polar function on a rectangular plane--simplifies graphing, increases student understanding of the polar coordinate system, and reinforces graphing techniques learned…

The purposes of this research are: (1) description of reading skill the students who join in CIRC learning model, Jigsaw learning model, and STAD learning model; (2) finding out the effective of learning model cooperative toward a reading comprehensions between the students who have high language logic and low language logic; and (3) finding out…

Global climate change and its effects are real and immediate. Students must gain an understanding of climate science so they can participate in public debate about how to reduce the emission of heat-trapping gases and how their communities can mitigate the effects of global warming. In this activity, students model these effects on Earth's oceans…

The pervasive use of visual representations in textbooks, curricula, and assessments underscores their importance in K-12 science education. For example, visual representations figure prominently in the recent publication of the Next Generation Science Standards (NGSS Lead States in Next generation science standards: for states, by states.…

The school environment adapted to the diversity of students is an important goal, but it is a challenge when it comes to the diversity of students with disabilities. The aim of this study was to describe the use of graphic systems in the routine of a preschool classroom through a collaborative program. The study included a teacher, 22 children of…

Mapping the knowledge formations of language teachers within their pedagogic practices is underresearched, particularly for subject English, a multi-faceted, elusively defined discipline. Deeper knowledge of the pedagogy of subject English teachers is critical, especially within South African education, given the socio-economic power of English in…

In light of the recent growing interest in conceptual learning and teaching of calculus, and especially with the focus on using technological environments, our study was designed to explore the learning processes and the role played by multiple-linked representations and by interactive technological environment in objectifying the accumulation…

It is surprising to students to learn that a natural combination of simple functions, the function sin(1/x), exhibits behaviour that is a great challenge to visualize. When x is large the function is relatively easy to draw; as x gets smaller the function begins to behave in an increasingly wild manner. The sin(1/x) function can serve as one of…

It is now well known that fractions are difficult concepts to learn as well as to teach. Teachers usually use circular pies, rectangular shapes and number lines on the paper as teaching tools for fraction instruction. This article contributes to the field by investigating how the widely used three external graphical representations (i.e., circle,…

Undergraduate students are increasingly being used to support course transformations that incorporate research-based instructional strategies. While such students are typically selected based on strong content knowledge and possible interest in teaching, they often do not have previous pedagogical training. The current training models make use of…

Research that has explored students' interpretations of graphical representations has not extended to include how students apply understanding of particular statistical concepts related to one graphical representation to interpret different representations. This paper reports on the way in which students' understanding of covariation, evidenced…

This article describes the Lissajous generalized figure and the original instrument for its investigation. Two specially prepared electrodynamic loudspeakers--a horizontal and a vertical--cause oscillations in two mirrors. It is possible to precisely control the motion of the mirrors, achieve a high frequency of oscillation and investigate…