For fans of the bestselling book "The Formative 5: Everyday Assessment Techniques for Every Math Classroom" comes this updated and expanded edition for understanding and implementing highly effective, research-backed formative assessment techniques into seamless, daily practice with students in grades K-12. "The Formative 5 in…

A story problem about borrowing money, presented in this article, may be represented with positive or negative numbers and thought about in different ways. The authors describe ideas related to integers (both positive and negative) and how students used them in relation to a story problem, and how they related these ideas to equations.

Ben, a good mathematics student, participated in a seven-week study. Describes three tasks that reflect impact of textbooks, real-life connections, and mathematical symbols. Shows that Ben's notion of one-half was task-dependent, concrete, and based on physical actions. (NI)

Questioned is a method of having students tap reference points on numerals to count out sums, differences, and products. How the method works, educators' reactions, and problems noted in interviews with children are discussed. (MNS)

The advantages of using interviews to diagnose children's needs are discussed. General interview strategies and specific questions for gaining insight into a student's understanding of the four operations are presented. (MNS)

Requirements for assessment under Public Law 94-142, the development of an Individualized Education Program for each handicapped child, the least restrictive environment, handicapping conditions, implementation procedures, diagnostic teaching strategies and learning conditions, teaching ideas, and a format for diagnostic interviews are each…

This book is a hands-on field manual for elementary school teachers. It features a range of activities that offer opportunities for reflection while enhancing student field experiences, through observation and practicum. The first section of the book provides activities that focus on collecting information about the school and its resources, and…

This text is a verbatim transcription of an interview with John Bates, a former math coordinator for Metro-Toronto schools, and the Director of Inner City Education, Toronto, Canada. (The interview was conducted by Thomas C. O'Brien under the auspices of the Teachers' Center Project of Southern Illinois University at Edwardsville.) Much of the…

The five levels of the van Hiele theory are described. Then interviewing tasks designed to be presented to students in kindergarten through college are presented. Finally, responses from 14 interviews are discussed, with implications for teaching geometry. Extensive references are included. (MNS)

Discussed are number meaning and part-whole relationships concerning place value. Findings from a research study with students in grades two-five who were interviewed about place-value tasks are given. Stages of interpreting two-digit numbers are presented, with implications for the classroom. (MNS)

The need to provide understandable problems and ways to help children understand problems are explored. An interview with a sixth grader depicts his incorrect strategies and leads to suggestions for teaching problem solving using a range of mathematical models for each operation. (MNS)

A case study of one child who had difficulty adding two- and three-digit numbers is given. Analyzing, diagnosing, and remediating the problem are each considered. (MNS)

Describes five formats of alternative assessment (journal writing, open-ended problems, portfolios, interviews, and performance assessments) for mathematics and science, how these methods can be implemented, and benefits of each type. Samples are included. (13 references) (Author/MKR)

Recommends conducting interviews with students in order to grasp their understanding of fractions and provides interview questions. Presents results of a study using those interview questions and concludes student responses fell into three main categories: (1) described a mental image of an object; (2) drew a model of the fraction using a circle…

Preschool children (n=115) in Poland were tested in five areas: counting, equipotency of sets, dividing, adding, and comparing. Results showed that these children already had informal knowledge of many of the concepts and skills included in the mathematics curriculum in the early grades. (PDD)