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close this bookImproving Student Achievement in Mathematics (IAE - IBE - UNESCO, 2000, 48 p.)
View the document(introduction...)
View the documentThe International Academy of Education
View the documentPreface
View the documentIntroduction
View the document1. Opportunity to learn
View the document2. Focus on meaning
View the document3. Learning new concepts and skills while solving problems
View the document4. Opportunities for both invention and practice
View the document5. Openness to student solution methods and student interaction
View the document6. Small-group learning
View the document7. Whole-class discussion
View the document8. Number sense
View the document9. Concrete materials
View the document10. Students’ use of calculators
View the documentConclusions
View the documentAdditional resources
View the documentReferences
View the documentThe International Bureau of Education-IBE

Introduction

This booklet summarizes the mathematics chapter from the Handbook of research on improving student achievement, second edition, published by the Educational Research Service. The Handbook is based on the idea that, in order to succeed, efforts to improve instruction must focus on the existing knowledge base in respect of effective teaching and learning. The Handbook was specifically designed to help school administrators and teachers carry out their evolving instructional leadership roles by giving them a ready source of authoritative yet practitioner-based information about research on effective teaching and learning.

The practices identified in this booklet reflect a mixture of emerging strategies and practices in long-term use. The authors briefly summarize the research supporting each practice, describe how this research might be applied in actual classroom practice, and list the most important studies that support the practice. A complete list of references is provided at the end of the booklet for readers who want to study and understand the practices more fully.

In most cases, the results of research on specific teaching practices show only small or moderate gains. In education, we need to understand, carefully select, and use combinations of teaching practices that together increase the probability of helping students learn, knowing that these practices may not work in all classrooms at all times.

The strongest possibility of improving student learning emerges where schools implement multiple changes in the teaching and learning activities affecting the daily life of students. For example, if the aim is to improve students’ scientific problem-solving skills, the school might plan to introduce training for teachers in (1) use of the learning cycle approach; (2) use of computer simulations; and (3) systemic approaches to problem solving. To simultaneously plan for the training and other provisions needed to sustain all three of these changes would be no small undertaking, but would hold great promise for improving the quality of student problem-solving.

The research findings presented in this booklet provide a starting point for developing comprehensive school plans to improve mathematics instruction. Teachers and school leaders will inevitably need time for further study, discussion and other exposure to what a particular practice entails before deciding to include it in their school’s plans.

The complexities involved in putting the knowledge base on improving student achievement to work in classrooms must be recognized. As Dennis Sparks writes in his chapter on staff development in the Handbook of research on improving student achievement, schools and school districts have a responsibility to establish a culture in which teachers can exercice their professional competence, explore promising practices and share information among themselves, while keeping the focus on the ultimate goal of staff development-the improvement of student learning.

Improving teacher effectiveness

The number of research studies conducted in mathematics education over the past three decades has increased dramatically (Kilpatrick, 1992). The resulting research base spans a broad range of content, grade levels and research methodologies. The results from these studies, together with relevant findings from research in other domains, such as cognitive psychology, are used to identify the successful teaching strategies and practices.

Teaching and learning mathematics are complex tasks. The effect on student learning of changing a single teaching practice may be difficult to discern because of the simultaneous effects of both the other teaching activities that surround it and the context in which the teaching takes place.

Thus, as teachers seek to improve their teaching effectiveness by changing their instructional practices, they should carefully consider the teaching context, giving special consideration to the types of students they teach. And, further, they should not judge the results of their new practices too quickly. Judgements about the appropriateness of their decisions must be based on more than a single outcome. If the results are not completely satisfactory, teachers should consider the circumstances that may be diminishing the impact of the practices they are implementing. For example, the value of a teacher focusing more attention on teaching for meaning may not be demonstrated if student assessments Concentrate on rote recall of facts and proficient use of isolated skills.

The quality of the implementation of a teaching practice also greatly influences its impact on student learning. The value of using manipulative materials to investigate a concept, for example, depends not only on whether manipulatives are used, but also on how they are used with the students. Similarly, small-group instruction will benefit students only if the teacher knows when and how to use this teaching practice. Hence, as a teacher implements any of the recommendations, it is essential that he or she constantly monitors and adjusts the way the practice is implemented in order to optimize improvements in quality.

These cautions notwithstanding, the research findings indicate that certain teaching strategies and methods are worth careful consideration as teachers strive to improve their mathematics teaching practices. As readers examine the suggestions that follow, it will become clear that many of the practices are interrelated. There is also considerable variety in the practices that have been found to be effective, and so most teachers should be able to identify ideas they would like to try in their classrooms. The practices are not mutually exclusive; indeed, they tend to be complementary. The logical consistency and variety in the suggestions from research make them both interesting and practical.

The authors wish to acknowledge the following colleagues who made helpful suggestions: Tom Cooney Professor of Mathematics, University of Georgia; James Hiebert, Professor of Mathematics Education, University of Delaware; Judy Sowder, Professor of Mathematics, San Diego State University; and Terry Wood, Professor of Mathematics Education, Purdue University.