This guidance report focuses on the teaching of mathematics to pupils in Key Stages 2 and 3. It is not intended to provide a comprehensive guide to mathematics teaching. We have made recommendations where there are research findings that schools can use to make a significant difference to pupils' learning, and have focused on the questions that…

The National Assessment of Educational Progress (NAEP) mathematics assessment measures students' knowledge and skills in mathematics and students' ability to apply their knowledge in problem-solving situations. At each grade, students responded to questions designed to measure what they know and can do across five mathematics content areas: number…

Examples of possible methods for unobtrusively evaluating student progress through real problem solving outcomes without formal testing are illustrated. These methods include the use of interviews, artifacts, observations, I learned statements, checklists, flow of discussion charts, and self-awareness exercises. (MN)

This paper provides an extensive literature review and recommendations for authentic assessment, and then provides recommendations for administrators in order to implement authentic assessment in elementary schools. A lack of comfort, with the way in which standardized tests seems to dictate what teachers teach as part of the curriculum, was a…

Results from the third national mathematics assessment are presented. Overall, the performance of nine year olds changed little since the second assessment, while significant gains were made by 13 year olds. Data on whole numbers, fractions and decimals, other basic concepts, and problem solving are discussed. (MNS)

This guide is organized around a list of skills that all students should know and be able to do at each grade level from kindergarten through sixth grade. It provides parents, teachers, and students with knowledge of what is being taught in a logical scope and sequence by grade level. The purpose of this guide is to help build a basis for…

Suggests that, although questions are often used to help students or stimulate student thinking, questions can also be used to help evaluate student thinking and attitudes about problem solving. Sample problems and questions are given. (PK)

Results of the National Assessment of Educational Progress related to student ability to use information from graphs and charts is discussed. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

Open-ended individually administered questions can ascertain whether students can reason about arithmetic problems. Free response test items are useful in assessing students' thought processes as they solve mathematics story problems. Since story problems do not state explicitly which arithmetic operations are required for solution, students must…

This is one of a series of reports summarizing the results of the second mathematics assessment conducted by the National Assessment of Educational Progress (NAEP). Nine, 13- and 17-year-olds were assessed during the 1977-78 school year. The assessment measured achievement in various content areas at four levels of cognitive processes (knowledge,…

Offers seven criteria for developing mathematical thinking, plus suggestions for teaching and assessing students' progress that are compatible with each learning criterion. Provides evaluation sheets that help the teacher assess and grade students on the criteria. (10 references) (MDH)

Evaluates the effectiveness of a sixth grade experimental language arts program designed to teach higher-level thinking skills. Reports on different types of instruments for measuring higher-level thinking skills, including verbal and nonverbal tests of divergent thinking, a nonverbal test of flexible thinking, and a verbal divergent production…

The statewide implementation of instructional support teams (ISTs) in Pennsylvania is analyzed in terms of the challenge of bringing team-based problem-solving models to scale. The history of the phase-in of ISTs in more than 1,700 elementary schools is presented, and the salient research conducted on ISTs is reviewed. The results indicate that…

This book reviews alternative assessment. Suggestions include portfolios, interviews, observations, journals, and tests utilizing various rubrics. This book contains suggestions and materials that teachers can use to assess students' progress in problem solving, reasoning, and communication. Many performance tasks and problem-specific rubrics for…

Using data collected in 1977-78, the Evaluation System has computed fall and spring mathematics scores on the Prescriptive Mathematics Test (PMT) for classes of students in grades one through six. In addition, relationships of performance on the PMT to class size, attendance, percent of males in the class, number of different test levels used in a…