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…

Within the current test-centered educational reform movement, considerable emphasis is placed on using assessment results to make instructional decisions for individual students. Test scores are used to estimate a student's current level of skill, monitor his or her progress during instruction, and identify whether the student has gained the…

In the generative classroom, teachers provide well-designed learning environments that result in the combination, recombination, and reorganization of repertoires such that new untaught repertoires are likely to occur. One component that can contribute to such generativity is Precision Teaching (PT), a frequency building instructional…

The purpose of this randomized experiment was to compare the performance of high-, average-, and low-achieving middle school students who were assessed with parallel versions of a computer-based test (CBT) or a paper-pencil test (PPT). Tests delivered in interactive, immersive environments like the CBT may have the advantage of providing teachers…

This book presents a schoolwide model of instructional support designed to make the most of available time, resources, and personnel--one that is also fully compatible with other problem-solving models, such as response to intervention. The authors provide a comprehensive and cohesive framework for linking assessment and intervention. They show…

Postsecondary level remediation has recently received a great deal of attention with the public questioning the efficacy of spending money on remedial classes, and scholars questioning whether such courses are effective in helping students graduate. The California State University (CSU) system has responded to the challenge of remediation by…

This paper reports a study aimed at revealing special-educational-needs pupils' learning potential by means of an ICT-based assessment including a dynamic visual tool that might help pupils when solving mathematics problems. The study focused on subtraction problems up to 100, which require "borrowing". These problems, in which the value…

During the years 1993-96, there has existed an active discussion group entitled "Using Open-Ended Problems in Mathematics" as a part of the scientific program of the Psychology of Mathematics Education (PME) conference. This report contains revised versions of presentations given in the discussion group. Since the PME is an international…

"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…

Comments on the results of the second mathematics assessment done by National Assessment of Educational Progress by the president of the National Council of Teachers of Mathematics. A "critical need for attention to higher-order cognitive skills" is pointed out. (MK) Aspect of National Assessment (NAEP) dealt with in this document:…

This volume contains the proceedings of the 7th international conference on Adults Learning Mathematics--A Research Forum held in July, 2000 in Massachusetts. It includes posters and short oral reports under these section headings: (1) Research into Practice; (2) Large- Scale Issues: Frameworks, Standards, and Assessment; (3) Theoretical…

Data from some geometric exercises administered during the 1977-78 mathematics assessment of the National Assessment of Educational Progress (NAEP) are analyzed, and suggestions for correcting student deficiencies are presented. (MP) Aspect of National Assessment (NAEP) dealt with in this document: Results (Interpretation).

This paper suggests that the mathematics teacher needs to do much reading and studying of important trends in improving the mathematics curriculum. Recommendations are made for what teachers need to look for in research studies in mathematics in order to help them recognize what would make for a quality study. Collaborative and individualized…