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Test Review: A. J. Connolly KeyMath-3 Diagnostic Assessment: Manual Forms A and B. Minneapolis, MN: Pearson, 2007:

The KeyMath-3 Diagnostic Assessment (KeyMath-3 DA) is a norm-referenced individually administered diagnostic test. The KeyMath’s first edition was published in 1971 and was designed to diagnose students with mathematics learning disabilities. The author, Dr. Austin J. Connolly, updated the original version in 1988 to be more user-friendly for the examinee and examiner (Perez, 1996). The recent KeyMath-3 DA (Connolly, 2007) offers significant improvements that align with the current mathematics curriculum standards, including the National Council of Teachers of Mathematics’ (NCTM) content and process standards. This review focuses only on the KeyMath-3 DA Form-A starter kit, which includes a manual, two easels, and record forms.

Middle-Grade Preservice Teachers’ Mathematical Problem Solving and Problem Posing

Empirical data were gathered from 51 middle-grade preservice teachers who were randomly assigned into one of two groups. The first group solved a task and then posed new problems based on the given figures, and the second group completed these activities in reverse order. Rubrics were developed to assess the written responses, and then thoughts and concerns related to problem-posing experiences were collected to understand their practices. Results revealed that the preservice teachers were proficient in solving simpler arithmetic tasks but had difficulty generalizing and interpreting numerals in an algebraic form. They were able to pose some basic and reasonable problems and to consider important aspects of mathematical problem solving when generating new tasks. Thus, teacher educators should provide substantial educational experiences by incorporating both problem-solving and problem-posing activities into engaging instruction for preservice teachers.

Children Early Mathematics Development Based on a Free Play Activity

Learning early mathematics is essential as it acts as a basis to young children in understanding higher mathematical concepts in the future. This paper discusses the learning of early mathematics through play activities that are widely integrated into the fields of education and psychology to describe how children acquire knowledge from their surroundings. Origami, singing, and construction blocks are part of play activities in preschool where teachers can utilize for basic mathematics development. The experiences relating to actual items or objects with quantity and quality such as color, sizes, and shapes before continuing to pictorial and symbolic stages will help to nurture children understanding of early mathematics.