In this study, we developed a three-dimensional framework to characterize post-secondary Calculus I final exams. Our "Exam Characterization Framework" (ECF) classifies individual exam items according to the cognitive demand required to answer the item, the representation of both the task statement and the solution, and the item's format.…

Students sometimes struggle with visualizing the three-dimensional solids encountered in certain integral problems in a calculus class. We present a project in which students create solids of revolution with clay on a pottery wheel and estimate the volumes of these objects using Riemann sums. In addition to giving students an opportunity for…

A rich understanding of key ideas in linear algebra is fundamental to student success in undergraduate mathematics. Many of these fundamental concepts are connected through the notion of equivalence in the Invertible Matrix Theorem (IMT). The focus of this paper is the ways in which one student, Abraham, reasoned about solutions to Ax = 0 and Ax =…

Certain mathematical concepts were not introduced to solve a specific open problem but rather to solve different problems with the same tools in an economic formal way or to unify several approaches: such concepts, as some of those of linear algebra, are presumably difficult to introduce to students as they are potentially interwoven with many…

This research project involved teaching linear algebra to second year undergraduates. Using Tall's three worlds of mathematical thinking as a theoretical framework, students were taught fundamental linear algebra concepts using each of the embodied, symbolic and formal dimensions. By varying the order in which these approaches were used in each…

In this paper we report on the outcomes of two surveys carried out in higher education institutions of Ireland; one of students attending first-year undergraduate non-specialist mathematics modules and another of their lecturers. The surveys aimed to identify the topics that these students found difficult, whether they had most difficulty with the…

Applying the Mathematical Knowledge for Teaching framework, we discuss the components of teacher knowledge that might be useful in supporting mathematical inquiry, and examine ways in which we strive to develop this knowledge within a middle grades mathematics program for undergraduate students who are prospective teachers. Using sample activities…

This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…

One of Martin Gardner's most famous columns introduced John Conway's game of Life. The inverse problem, finding a previous generation in the Game of Life given some extra constraints, was introduced a few years ago and is referred to as Retrolife. In this paper we present a puzzle played on a chessboard that is isomorphic to a variation of…

Mathematics experts often choose appropriate procedures to produce an efficient or elegant solution to a mathematical task. This "flexible procedural knowledge" distinguishes novice and expert procedural performances. This article reports on an intervention intended to aid the development of undergraduate calculus students' flexible use…

The study aimed to detect the effect of using an educational site on the Internet in the collection of bachelor's students in the course of basic concepts in mathematics at Al al-Bayt University, and the study sample consisted of all students in the course basic concepts in mathematics in the first semester of the academic year 2014/2015 and the…

Although the mathematics community has long accepted the concept of limit as the foundation of modern Calculus, the concept of limit itself has been marginalized in undergraduate Calculus education. In this paper, I analyze the strategy of conceptual conflict to teach the concept of limit with the aid of an online tool--Desmos graphing calculator.…

Without using limits, we prove that the integral of x[superscript n] from 0 to L is L[superscript n +1]/(n + 1) by exploiting the symmetry of an n-dimensional cube.

We define moves for king, queen, rook, bishop, and knight on a triangular honeycomb chessboard. Domination and independence numbers on this board for each piece are analyzed.

Boggle logic puzzles are based on the popular word game Boggle played backwards. Given a list of words, the problem is to recreate the board. We explore these puzzles on a 3 x 3 board and find the minimum number of three-letter words needed to create a puzzle with a unique solution. We conclude with a series of open questions.