"They are the same" is a phrase that teachers often hear from their students in arithmetic and algebra. But what do students mean when they say this? The present paper researches the notion of sameness within algebraic thinking in the context of generating equivalent numerical equalities. A group of Grade 6 Mexican students (10- to…

This article provides a range of activities designed to engage students in using an early form of graphing. While the "Australian Curriculum: Mathematics" (2014) highlights understanding, fluency, problem-solving, and reasoning, the National Research Council (2001) describes five strands of mathematical proficiency, with the additional…

The degree to which second and third grade children learn transformational geometry concepts under specific instructional conditions and the effects of transformational geometry instruction upon the children's spatial abilities are studied. Results imply that the students learned aspects of transformational geometry but that their spatial…

Activities designed for levels 1-4 give experience in recognizing shape and form after standard transformations are applied to geometric figures. The activities for the upper levels use a physical projection to provide experience with the properties of similarity. (DT)

In this study Piaget's method of the clinical interview was used to examine children's understanding of rotation about apoint at three age levels (6, 7, and 8). In two half-hour sessions, subjects (N = 108) were given four tasks: (1) an adaptation of Piaget's locus and circular motion experiment, and tasks concerned with (2) the circle as a locus…

Assessed was the performance of subjects who had been exposed to transformational geometry treatment. The performance test consisted of geometry achievement and spacial ability measures. Second and third grade subjects were randomly assigned to experimental and control groups. The experimentals received a twelve lesson treatment and the controls a…

After a discussion of philosophy and learning processes and theories, the author presents rationale for teaching axiomatics in geometry including traditional and modern transformational approaches. (JG)

Presents an activity on transformations that employs a story from children's literature. Emphasizes that books and stories that use mathematical problem solving not only engage children in the narrative but also give them opportunities to see how mathematics is used in everyday life. (ASK)

This game offers an opportunity for students in grades 4-6 to sharpen their spatial skills and enrich their geometric experience. It presents such concepts as reflection, translation, and rotation (flip, slide, turn). Templates for the game are included. (MNS)

Examines the cause of confusion arising from ambiguity of units and semantics in length, area, and volume concept formation. Introduces the mimik, a standard area of one thousand square millimeters, and advocates its use as an interim symbol system. (JM)

Geoboards are viewed as excellent vehicles for developing intuitive understandings of various topics in transformational geometry. The activities described are designed to show pupils that when a triangle or parallelogram is subjected to a transformation called a shear, its area is not changed. Ways for finding areas are detailed. (MP)

Development of geometric congruence and motion was studied through tasks that tapped transformational imagery, correspondence matching, measurement operations, and transformation combinations. Results showed even the youngest children studied could generate strategies for verifying congruence. The dominant strategy in younger children was edge…