The algebraic group Spin[subscript 3 × 3] arises from spinning collections of the numbers 1-9 on a 3×3 game board. The authors have been using this group, as well as a corresponding online application, to introduce undergraduate students to core concepts in group theory. We discuss the benefits of using this deceptively simple, toy-like puzzle in…

Most any students can explain the meaning of "a[superscript b]", for "a" [element-of] [set of real numbers] and for "b" [element-of] [set of integers]. And some students may be able to explain the meaning of "(a + bi)[superscript c]," for "a, b" [element-of] [set of real numbers] and for…

This mixed qualitative and quantitative methods study addressed the effect of technology on college algebra and survey of calculus students' understanding. This research study was conducted in fall 2016 on eight college algebra classes with a total of 315 students, and in summer 2017, on two survey of calculus classes with a total of 40 students…

Over the last several years, iPads have become increasingly popular in the classroom. The number of available apps that could be used in the mathematics classroom are countless, but some make better mathematical learning tools than others. This research presents a set of sixteen criteria that can be used to evaluate the potential of an iPad app to…

Interactions with technology have become a focus of education research, revealing specific constructs relevant to these interactions. Attributes of users and tools contribute to physically embodied interactions with technology and both users and tools modify attributes throughout these interactions. This study examines patterns of user-tool…

This article proposes a framework for classroom teachers to use in making pedagogical decisions regarding which mathematical materials (concrete and digital) to use, when they might be most appropriately used, and why. Two iPad apps ("Area of Shapes (Parallelogram)" and "Area of Parallelogram") are also evaluated to demonstrate…

Computer algebra systems are described. Features of such systems and information on MACSYMA, Maple, muMath, REDUCE, and SMP are given. (MNS)

The theme of the sixth annual meeting of the North American Chapter of Psychology of Mathematics Education was "The Importance of Psychological Models for Research in Mathematics Learning." The conference proceedings contain papers organized around five major topics. In the first section, eight papers on the learning of arithmetic are…

Computer algebra systems (such as MACSYMA and muMath) can carry out many of the operations of calculus, linear algebra, and differential equations. Use of them with sketching graphs of rational functions and with other topics is discussed. (MNS)

This study, part of a longitudinal investigation, examined the kinds of thinking which children aged 10 and 11 could carry over from Logo instruction to an algebraic context. Interviews focused on their ability to construct meaningful symbolization for the concept of variable and to construct formalized algebraic rules. (MNS)

Computer Algebra Systems (CAS) are computer systems for the exact solution of problems in symbolic form. The newspaper is designed to serve as a conduit for information and ideas on the use of CAS in education, especially in lower division college and university courses. Articles included are about CAS programs in several colleges, experiences…

Provides a program listing in True BASIC which constructs several kinds of matrices: (1) matrices with integral entries that have inverses that have integral entries; (2) matrices with integral entries that have inverses that are rational numbers with reasonable denominators; and (3) matrices with integral entries and prescribed integer…

Argues that computer instantiations of abstract concepts could assist mathematics education by providing concrete experiences and by inducing the mental process of construction that Piaget called reflexive abstraction. College students with computer experiences scored higher than those taught with traditional methods on a test of functions and…

Presented are some current facts about symbol manipulators and their relation to high school mathematics. The development of computer algebra systems is discussed. Five areas of computer algebra needing investigation (skill proficiency, understanding, curriculum content, student homework, and equity) are identified. (MVL)

Discusses the use of the computer to encourage a versatile approach to learning involving both symbolic/logical and visual/holistic types of mental activity. Provides experimental data showing the effect of an enhanced Socratic mode of teaching. (YP)