In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators…

This article shows how to modify classroom evaluation items to avoid four potential difficulties that limit a teacher's insight into students' mathematical understanding by addressing these issues: (1) poor choice of numbers; (2) implausible or inappropriate contexts; (3) inclusion of graphics that do not help make learning visible; and…

Finding ways to help primary-grade students overcome difficulties in solving mathematical word problems can be a daunting task for teachers in a regular classroom setting. Student challenges may include: (1) difficulty with vocabulary; (2) lack of confidence when solving problems; (3) confusion on the proper operation to use when solving a…

When the word problems of forty-five sixth-grade students were examined, multiple levels of understanding and misunderstanding multiplication were exposed. The purpose of this article is to demonstrate the potential of problem writing as a technique for assessing the depths of students' mathematical understandings. Discussions include sample…

Specific examples are used to discuss assessment, an integral part of mathematics instruction, with problem posing and assessment of problem posing. General assessment criteria are suggested to evaluate student-generated problems in terms of their quantity, originality, and complexity.

To assess students' developing literacy, teachers regularly listen as individuals read. Similarly, listening to students talk about their mathematical reasoning is a powerful way for teachers to assess students' problem-solving abilities and mathematical understanding. Traditional paper-and-pencil tests have long been the main avenue to evaluate…

Describes the use of the children's book "Geraldine's Blanket" to promote discussion and allow the teacher to assess the children's understanding of area, place value, number sense, fractions, and problem-solving strategies. (MKR)

Presents an assessment activity to determine the ability of students to devise a plan for solving a problem and recording their work while solving the problem. Uses the theme of planning and organizing a birthday party. (MKR)

Describes a 7-year-old whose mathematical performance in class embodies much of what is important according to "Curriculum and Evaluation Standards for School Mathematics". She speaks little English and therefore scores low on standardized, norm-referenced tests. Concludes that changes in curriculum and classroom instruction require changes in…