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…

Successfully implementing the practice of inclusion by differentiating instruction is dependent upon both the skills and attitudes of general education teachers. New general education teachers who are entering the field are particularly vulnerable to the demands and stress of the profession, and exemplary preservice teacher education programs must…

Geometry, classification, and the classification of geometrical objects are integral aspects of recent curriculum documents in mathematics education. Such curriculum documents, however, leave open how the "work" of classifying objects according to geometrical properties can be accomplished given that the knowledge of these properties is the…

The authors constructed an 11 x 17 in. tactile map to teach routes in an outdoor play environment to a 5-year-old blind child. After learning the routes on the tactile map, the child independently navigated them in the outdoor play environment. With practice, the child reduced the time necessary to learn and navigate the routes. The authors…

"Ionic Blocks" is a teaching tool designed to help middle school students visualize the concepts of ions, ionic compounds, and stoichiometry. It can also assist high school students in reviewing their subject mastery. Three dimensional blocks are used to represent cations and anions, with color indicating charge (positive or negative) and size…

This article describes an activity that can be performed with an inexpensive plastic toy popper. The activity builds skill at analysing motion and results in the calculation of a surprisingly extreme acceleration. (Contains 1 figure.)

Over the past 5 years, the author has visited scores of Montessori classrooms, most of them in the United States and Canada, and has observed many commonalities among them. For example, in almost every classroom, children freely chose their activities and engaged hands-on with material objects. They took care of the environment, wiping up their…

Early childhood educators use several learning centers in a classroom to target growth in different developmental areas, but as a preschool teacher, the author was always impressed by how children addressed multiple areas of development at the sensory table. Understanding that sensory experiences were important for preschoolers, the author wanted…

The purpose of this paper is to share the results of a fourteen-week study that focused on the effects of teaching mathematics instruction with the implementation of manipulatives in an elementary classroom. Students that fill our classrooms deserve the opportunity to use manipulatives to help them grasp all the different concepts that are taught…

This article describes the positive impact of Montessori manipulative materials on four seventh grade students who qualified for academic intervention services because of previous low state test scores in mathematics. This mathematics technique for teaching multi-digit multiplication uses a placemat-sized quilt with different color-coded squares…

In this article, the author describes his categorization of practical mathematical tasks using drama, body maths, and a host of outlandish props. He categorizes the lessons under three headings--demonstration, teamwork, and creative display--partly as a means of furthering the invention of more activities within each classification. His…

Changes in DNA base-repair may serve as an indicator of the time elapsed since divergence from a common ancestor. DNA sequences can now be analyzed. The simulation presented in this article allows students to observe the accumulation of changes in a randomly mutating sequence of playing cards. The cards are analogous to DNA nucleotide or protein…

Many secrets can be told by the physical surroundings of library media centers. Whether the center is kid-friendly is one of the first obvious tell-tale signs. When a library center has Arthur & D.W., Clifford, Pooh & Eeyore, shells, special rocks, etc. hidden by the circulation center or in the back in boxes, it's time to revolt. The movie Free…

This article presents an investigation carried out with a group of able mathematics students who were studying at a level 1 year in advance of their peers. The purpose was to investigate the extension of usual three peg Towers of Hanoi to four pegs and attempt to find a rule that could be used to predict the minimum number of moves required to…