The author believes that Venn diagrams are a useful, yet hugely underused resource, to encourage purposeful talk, reasoning and logical thinking both within mathematics and across the curriculum. Here, she describes ways in which Venn diagrams can be used to add challenge and develop reasoning, discussion and mathematical thinking at Key Stage 2.…

In this article, we describe preservice elementary teachers' reactions to Liping Ma's (1999) book, "Knowing and Teaching Elementary Mathematics" (KTEM), from five universities. Ma's discussion of solely teaching elementary mathematics procedurally and its consequences awakens the preservice teachers' memories of learning elementary mathematics.…

This article describes one prevalent practice that a group of 6th- and 7th-grade students engaged in when they used fractions in the context of area and perimeter, decimal operations, similarity, and ratios and proportions. The study's results revealed that students did not simply take the concepts and skills learned in formal fractions units and…

The mathematics methodology subjects the author undertook in the early 1980s encouraged him to adopt a very expository style of teaching in which each new concept is introduced by its formal definition. The teacher should then explain a few carefully chosen examples for students to copy into their books, and then provide plenty of graded practice…

In this paper, we examine the potential use of animation for supporting the teaching of some of the mathematical concepts that underlie computer games development activities, such as vector and matrix algebra. An experiment was conducted with a group of UK undergraduate computing students to compare the perceived usefulness of animated and static…

In a general sense, the research interest of this article concerns the preschool class, which is an intermediate form of schooling for six-year-olds in Sweden, between preschool and school and their two traditions of "play" and "learning," respectively. In a more specific sense, the issue of learning one aspect of basic…

In this article a potentiometric method for reducing sugar quantification is described. Copper(II) ion reacts with the reducing sugar (glucose, fructose, and others), and the excess is quantified using a copper wire indicator electrode. In order to accelerate the kinetics of the reaction, working conditions such as pH and temperature must be…

An echo can often be heard in career and technical education (CTE) hallways, "How am I going to fit academic skills into this program." They have a choice! They could pick up a math or English book and start selecting something to separately add in. Perhaps an academic consultant could be tapped to separately add to the task list. Another option…

Students often struggle with the connection between algebraic and graphical representations of functions. This overview of the history of the Cartesian coordinate system helps the classroom teacher consider new ways to aid students in making the "Cartesian connection." (Contains 7 figures.)

Games are a useful and fun way to review material in class, and encourage students to actively participate in review sessions. In fact, researchers have concluded that playing games can be an effective learning tool, especially in mathematics, in situations where the goal is to reinforce specific ideas or concepts. Two places this type of…

The Laplace Transform is an object of fundamental importance in pure and applied mathematics. In addition, it has special pedagogical value in that it can provide a natural and concrete setting for a student to begin thinking about the modern concepts of "operator" and "functional". Most undergraduate textbooks, however, merely define the…

We describe exercises in which students use PascGaloisJE to formulate conjectures about certain binomial identities which hold when the binomial coefficients are interpreted as elements in the cyclic group Z[subscript p] of integers modulo a prime integer "p". In addition to having an appealing visual component, these exercises are open-ended and…

This article discusses student difficulties in grasping concepts from linear algebra. Using an example from an interview with a student, we propose changes that might positively impact student understanding of concepts within a problem-solving context. In particular, we illustrate barriers to student understanding and suggest technological…

This article discusses a classroom activity in which students in a small-sized (n = 4) Abstract Algebra class were able to discover some properties related to permutations and transpositions by physically moving from chair to chair according to suggested guidelines. During the lesson students were able to determine ways to write a permutation as a…

This article is the third in a series of articles describing a research project entitled "Entering into Symbols" (EIS) on the use of mathematical applets at key stages 2 and 3. The first two articles, in "MT200" and "MT203", described applets designed to teach place value ("Tuckshop subtraction") and basic algebra ("Matchbox algebra"). In this…