Research has established that children's development of addition and subtraction skills progresses through a hierarchy of strategies that begin with counting-by-one methods through to flexible mental strategies using a combination of knowledge of basic facts and understanding of place value. An important transition point is the shift from the…

The aim of this study was to test a training program intended to fine-tune the mental representations of double-digit numbers, thus increasing the discriminability of such numbers. The authors' assumption was that increased fluency in math could be achieved by improving the analogic representations of numbers. The study was completed in the…

This manual is an instructor's guide for the utilization of the "CCA High School Mathematics Curricula: Advanced Algebra and Calculus" courseware developed by the Computer-based Education Research Laboratory (CERL). The curriculum comprises 34 algebra lessons within 12 units and 15 calculus lessons that are computer-based and require…

Focusing primarily on current problem areas in mathematics instruction, this third yearbook of the Finnish Association of Mathematics and Science Education Research contains five articles addressing four themes in mathematics education. The first theme is concerned with proportional reasoning in mathematics teaching and describes school test…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

A random sample of middle school special education teachers from various classroom settings completed a survey asking them about what instructional practices and materials they used to teach students with disabilities how to solve word problems, how much time they allocated to problem solving instruction, and what type of problems they gave their…

Many mathematics educators and researchers agree that current mathematics instruction in elementary and secondary schools focuses too much on efficient computation and not enough on mathematical understanding, problem solving, and reasoning. But beyond this agreement exist diverse views about what it means to know, understand, and learn…

These units were developed during the summer of 1987 as one component of a project on "Integrating Problem Solving Into Mathematics Teaching." Each unit has the objective of developing students' thinking abilities in mathematics. These units have been revised subsequent to field try-outs prior to dissemination. The summaries of 56 different…

This bibliography identifies reports of research on correlates, causes, effects, and treatment of test anxiety. The listing was developed for a synthesis of research, performed by meta-analysis at Adrian College, Michigan in 1986-87. Guidelines for including studies were applied as follows: (1) the research concerned academic test anxiety, using…

This is the final test for students in the twelfth-grade course Mathematics 30, offered in schools in Alberta, Canada. It contains 52 multiple-choice questions and five written-response problems, with two-and-one-half hours allowed for completion. Approved calculators may be used. Scoring is done by the provincial education department. (RH)

This bibliography presents 21 references and abstracts for improving mathematics instruction in two ways. The first aim is to serve as a guide in locating higher-order thinking skills material in mathematics; the second is to encourage the integration of higher-order thinking skills techniques into the mathematics curriculum. Entries are included…

Argues for teaching different approaches to solving problems. Using a geometric example, alternative solutions are given which use synthetic geometry, transformation geometry, analytic geometry, complex numbers, trigonometry or vectors. (PK)

Argues that, because problem solving has two aspects, a thinking process and a final product, a good evaluation requires consideration of both aspects. A holistic scoring point system is described. (PK)

Suggests and discusses several strategies for helping students become better problem solvers. (PK)

Outlines two mathematics teaching strategies: the exploration/discovery approach to mathematical concepts, and the use of pair group problem-solving. These require teachers to shift from the traditional role of lecture/demonstrator to a role demanding new skills in planning and facilitating student work. Includes 10 references. (MD)