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…

In this article, the authors share a variety of ways to formatively assess basic fact fluency. The define fluency, raise some issues related to timed testing, and then share a collection of classroom-tested ideas for authentic fact fluency assessment. This article encourages teachers to try a variety of alternative assessments from this sampling,…

The wealth of assessment options that exists offers teachers and students a "menu" of selections. Just as matching appetite needs with appropriate food selection is fundamental to a successful dining experience, matching assessment options to targeted achievement needs is crucial to an effective assessment experience. The author uses a…

A child's demonstration of his conceptual understanding of number bodes well for his future success in school mathematics. As youngsters' thinking becomes more logical, they apply one-to-one correspondence relationships to quantification. Yet, reliable assessment of young children's mathematical ability is difficult because of social and emotional…

Diezmann presents a series of classroom number-sense activities that encourage young students to use and refine their estimation, prediction, and observation skills. The activities explore the relationships between the number of objects in an opaque container and (1) its fullness and (2) the size of the objects in the container. Informal,…

Discusses the language-inquiry approach to learning geometry and describes the use of geometry stations to promote this inquiry. (Author)

This article describes a tool teachers can use to analyze student work and provides activity suggestions to guide instruction based on their findings. By integrating the voice of the child and the voice of the discipline, teachers can use their inner voice to build a model of the child's understanding. (Contains 8 figures.)

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 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…

This article describes the significant gains in student achievement in an urban elementary school when teachers worked together to develop, administer, and review assessment items. In grade-level teams, teachers completed item analyses and engaged in instructional conversations about students' needed instruction. (Contains 3 tables and 2 figures.)

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.

Presents mathematics activities to teach place value. (Author/YDS)

Investigates whether student interviews provide teachers with a more detailed, accurate, and complete picture of children's mathematical understanding and whether this knowledge helps teachers improve the way they teach mathematics. Shows how to use student interviews as a guide to further instruction. (KHR)

Describes a method for helping children become powerful thinkers who explore mathematical ideas deeply and creatively as they develop their mathematical promise, and approach mathematics in a manner similar to that of mathematicians in the field. Discusses ways of assessing this kind of learning. (ASK)

The open-ended assessment item supports students in achieving mathematical understanding that the National Council of Teachers of Mathematics (NCTM) advocates. The items encourage students to demonstrate their understanding in creative and informative ways.