Researchers have argued that students can develop foundational understandings for a variety of mathematical concepts through quantitative reasoning. I extend this research by exploring how students' quantitative reasoning can support them in developing meanings for inverse relations that influence their inverse function meanings. After summarizing…

This article reports on a study which used the APOS (action-process-object-schema) theoretical framework to investigate university students' understanding of derivatives and their applications. Research was done at the Westville Campus of the University of KwaZulu-Natal in South Africa. The relevant rules for finding derivatives and their…

In this paper, we present materials and teaching ideas utilizing multiple representations in the contexts of kinematics and the force concept. These ideas and materials are substantiated by evidence and can be readily used in teaching with no special training. In addition, we briefly discuss two multiple-choice tests based on physics education…

This teaching brief describes a 30-minute game where student groups compete in-class in an introductory time-series forecasting exercise. The students are challenged to "beat the instructor" who competes using forecasting techniques that will be subsequently taught. All forecasts are graphed prior to revealing the randomly generated…

Two problems from high school mathematics on finding minimum or maximum are discussed. The focus is on students' approaches and difficulties in identifying a correct solution and how dynamic geometry systems can help.

Complex numbers are essential in many fields of engineering, but students often fail to have a natural insight of them. We present a learning object for the study of complex polynomials that graphically shows that any complex polynomials has a root and, furthermore, is useful to find the approximate roots of a complex polynomial. Moreover, we…

Thirty-six secondary school students aged 14-16 were interviewed while they chose between a table, a graph or a formula to solve three linear function problems. The justifications for their choices were classified as (1) task-related if they explicitly mentioned the to-be-solved problem, (2) subject-related if students mentioned their own…

At an early stage of learning quantum chemistry, undergraduate students usually encounter the concepts of the particle in a box, the harmonic oscillator, and then the particle on a sphere. Rotational levels of a diatomic molecule can be well approximated by the energy levels of the particle on a sphere. Wave functions for the particle in a…

In the Fall semester of 2009, I taught a first-year course that focused on skills required to successfully complete undergraduate research. This paper will discuss the Simpson College first-year course requirements, my course goals, the graph theory topics covered, student feedback, and instructor reflection.

Data literacy is complex. When students investigate the natural world, they must be able to gather data, organize it in tables and spreadsheets, analyze it in context, and describe and interpret it--usually as evidence to support a scientific argument. These skills are echoed in the science and engineering practices of the "Next Generation…

The purpose of this research is to assess the student products created by digital storytelling, and to determine the awareness towards learning the topic and the cognitive loads of students during the process. Research was performed with a total of 52 teacher candidates attending 2nd class at "Classroom Teacher" department of Mersin…

Although dynamic geometry software has been extensively used for teaching calculus concepts, few studies have documented how these dynamic tools may be used for teaching the rigorous foundations of the calculus. In this paper, we describe lesson sequences utilizing dynamic tools for teaching the epsilon-delta definition of the limit and the…

Most personal student information stays local. Districts, states, and the federal government all collect data about students for important purposes like informing instruction and providing information to the public. But the type of data collected, and who can access them, is different at each point. This graphic shows how student data--from…

This paper reports an instrumental case study of the strategies employed by Year 11 students engaged in solving a functions population task. The task was implemented as part of a study of students studying functions in a Technology-Rich Teaching and Learning Environment (TRTLE). Student strategies related to the perception and enactment of…

There is limited research on teaching narrative writing skills to students with moderate to severe intellectual disability. In the current study, we used a multiple probe across participants single case design to evaluate the effects of an intervention package comprised of modeling, story templates, and self-graphing, on the inclusion of story…