Introduction: In this document we stress the importance of developing in children a structure for advanced numerical-algebraic thinking that can provide an element of control when solving mathematical situations. We analyze pupils' conceptions that induce errors in algebra due to a lack of control in connection with their numerical thinking. We…

Transfer of reading strategies from the first language (L1) to the second language (L2) has long puzzled educators, but what happens if the L1 is an alphabet language and the second is not, or if there is a mismatch in the languages' grapheme-phoneme connection? Although some students readily adjust to reading and writing in their second language,…

Invented by English mathematician and pedagogist, Caleb Gattegno (1911-1988), the geoboard was designed as a manipulative tool for teaching primary geometry in schools (Williams, 1999). Traditionally made out of plywood and nails, geoboards today are usually made out of plastic and come in a variety of different sizes and colours. Rubber bands are…

This qualitative study investigated young children's mathematical engagement in play with wooden unit blocks. Two boys, ages 6 and 7, were independently observed completing the task of filling outlined regions with the various sets of blocks. Three major mathematical actions were observed: categorizing geometric shapes, composing a larger shape…

The triangle congruence conditions are a central focus to nearly any course in Euclidean geometry. The author presents a hands-on activity that uses straws and pipe cleaners to explore and justify the triangle congruence conditions. (Contains 4 figures.)

This article, which describes integrating virtual manipulatives with the teaching of probability at the elementary level, puts a "virtual spin" on the teaching of probability to provide more opportunities for students to experience successful learning. The traditional use of concrete manipulatives is enhanced with virtual coins and spinners from…

Getting and keeping the attention of an eight-grade algebra class can often be a challenge. Doing so while trying to meet curriculum expectations and standards can be a daunting task unless projects are designed to both pique and maintain student curiosity. Projects designed around standards that initiate interest and have multiple entry points…

In this paper, the development of an innovative Virtual Manipulatives and Whiteboard (VMW) system is described. The VMW system allowed users to manipulate virtual objects in 3D space and find clues to solve geometry problems. To assist with multi-representation transformation, translucent multimedia whiteboards were used to provide a virtual 3D…

This article depicts the rewarding experience of creating mathematical environments for kindergarten and elementary students by focusing on one of the most important and often difficult-to-grasp concepts (fractions) through play methods incorporated into a math fair. The basic concept of a math fair is threefold: (1) to create preplanned,…

Approximately 93 percent of Americans indicate that they experience some level of math anxiety. Math anxiety is defined as negative emotions that interfere with the solving of mathematical problems. Studies have found that some students who perform poorly on math assessments actually have a full understanding of the concepts being tested; however,…

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…

The use of toys in physics teaching is common. This brief review of the physics of toys intends to show that they are not only very useful in lectures and demonstrations in order to motivate students but also very interesting from a scientific point of view. However, since their physics is sometimes too cumbersome, the effect can be the opposite.…

We have designed a laboratory experiment to illustrate the use of spectroelectrochemical techniques for determination of aqueous iron. The experiment described in this article is applicable to an undergraduate laboratory course in analytical chemistry. Students are asked to fabricate spectroelectrochemical sensors, make electrochemical and optical…

In this article, the author describes a lesson he observed involving a function machine. This function machine was a box with a slot at the top of one side and a large cut-out hole at the bottom of the opposite side. A card with a number written on it (the input) was pushed into the slot and the teacher put their hand through the hole of the other…

This collective case study analyzes the use of manipulatives in math lessons developed and taught by 4 groups of elementary teachers (K-8) involved in lesson study as part of a professional development program. The study found that in three of four lessons studied manipulative use was turned into an end in and of itself, rather than a tool, and…