Teachers' ability to elicit and build on students' mathematical thinking during instruction is critical in order to support students' mathematical growth. An emerging hypothesis in the field is that the construct of a "learning trajectory" (LT) has the potential to support teachers in making sense of and using student…

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…

This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…

Based on the efforts to infuse engineering practices within the technology education curriculum it is appropriate to now investigate how technology education teachers are assessing engineering design activities within their classrooms. This descriptive study drew a full sample of high school technology teachers from the current International…

Discussed are the results of the second National Assessment of Educational Progress (NAEP) mathematics assessment concerning children's ability to solve verbal problems. The data indicate that the commonly held view that children cannot solve word problems may be an oversimplification. (Author/TG) Aspect of National Assessment (NAEP) dealt with in…

"Progress in Mathematics[C] 2006" is a new core curriculum for students in kindergarten through grade 6. "Progress in Mathematics[C] 2006" differs substantively from "Progress in Mathematics[C] 2000" in both content and assessment material. "Progress in Mathematics[C] 2006" uses a sequence of systematic…

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,…

A conceptual framework is provided for generating assessment tasks that provide an instructor with a richer description of student reasoning/thinking than is possible by simply giving students problems to solve. The application of this framework is illustrated with material from introductory statistics courses which focus on: (1) sampling; (2)…

This paper discusses how concepts and procedural skills in problem-solving tasks, as well as affects and emotions, can be subjected to meaningful measurement (MM), based on a multisource model of learning and a constructivist information-processing theory of knowing. MM refers to the quantitative measurement of conceptual and procedural knowledge…

The National Assessment of Educational Progress (NAEP) administered the selected supplemental mathematics exercises to 13-year-old students during October and November 1975 and to 17-year-old students during March and April 1976. This assessment represents a specially modified supplement to 1972-73 full-scale mathematics assessment and was…

This report describes the results of Connecticut's second statewide assessment of mathematical knowledge, skills and attitudes. The Connecticut Assessment of Educational Progress annually tests a sample of Connecticut students in grades 4, 8, and 11 in one or more subject areas. Students at each grade level were randomly selected to participate in…

Presented is an overview of the 1979 Illinois Inventory of Educational Progress (IIEP) for eleventh-grade mathematics. The IIEP is a systematic effort by the Illinois State Board of Education to collect information on the educational achievement of Illinois students in certain areas and to make that information available to educational…

One of the most ambitious attempts to assess students' understanding of mathematics was carried out in England between 1974 and 1979. The results of this study indicate that there is a need in an overall assessment program to evaluate students' algebraic understanding as well as to measure their achievement in algebraic manipulations and problem…

The National Assessment of Educational Progress (NAEP) reports on the status and progress of educational achievement in the United States. Based on its surveys, "The Nation's Report Card" provides comprehensive information about what students in the United States can do in various subject areas. The framework for the 1990 mathematics…

This document ties the essential skills needed in mathematics to the National Council of Teachers of Mathematics' (NCTM) Curriculum and Evaluation Standards to help facilitate future curriculum development. The overall goal for the 21st century is to make mathematical power a reality for all students. The rationale for this document can be found…