Cover Image
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


This booklet is excerpted from the mathematics chapter of the Handbook of research on improving student achievement, second edition. It provides a synthesis of the knowledge base regarding effective practices for improving teaching and learning in mathematics. These materials are intended for use by teachers, principals, other instructional leaders and policy makers who are undertaking the quest to improve student achievement.

The research findings presented are intended to be used as a starting point, which can initiate staff development activities and spark discussion among educators, rather than as a prescription that is equally applicable to all classrooms. As Miriam Met writes in her chapter on foreign languages in the Handbook of research on improving student achievement:

Research cannot and does not identify the right or best way to teach [...] But research can illuminate which instructional practices are more likely to achieve desired results, with which kinds of learners, and under what conditions. [...] While research may provide direction in many areas, it provides few clear-cut answers in most. Teachers continue to be faced daily with critical decisions about how best to achieve the instructional goals embedded in professional or voluntary state or national standards. A combination of research-suggested instructional practices and professional judgment and experience is most likely to produce [high student achievement].

Thus, this booklet cannot give educators all the information they need to become expert in research-based instructional practices in mathematics. Rather, these materials are designed to be used as a springboard for discussion and further exploration.

For example, one approach to professional development might be to distribute the booklet to teachers, find out which teachers already use certain practices, and then provide opportunities for them to demonstrate the practices to their colleagues. Next, a study group might be formed to pursue further reading and discussion. Both the extensive reference list on page 39 and the list of additional resources on page 35 can serve as a starting point. The study group’s work might lay the foundation to plan a staff development programme for the next year or two that would enable teachers to learn more and become confident enough to use the selected practices in their classrooms.

Suggestions from users of the Handbook

Since the publication of the first edition of the Handbook of research on improving student achievement, the Educational Research Service has asked users how the Handbook and related materials have helped them in their efforts to improve instructional practice. Here are a few of their experiences in using these materials for staff development:

· Some teachers suggested reviewing one practice a month through the school year at department meetings. The practice would provide a focus for discussion, with teachers who already used the practice available as resources and as mentors for other teachers who were interested in using the practice in their own classrooms. As one teacher remarked, ‘staff development doesn’t work when teachers are told what they need-often, they then just go along for the ride’.

· One school reported using the materials as a resource when teachers met to discuss alternative approaches that might be used with students who were struggling. The Handbook ‘provided ideas and was a guide to other resources’.

· Curriculum specialists studied the Handbook together, and then met with teachers in their own content areas to review both the contents of the subject-area chapter and the ideas shared among the specialists. Each teacher was asked to identify one research-based practice that would expand his or her personal repertoire of instructional strategies and to introduce its use during the first three months of school. Follow-up discussions were held by content-area teachers and specialists, as well as by the specialists who met as a group to share ideas generated by the teachers with whom they worked.

· One respondent identified an important use for these materials: to validate the instructional practices that teachers already employ. In his words, ’it is as important for teachers to know what they know as well as what they still have to learn’.

· Teachers in one district reviewed and discussed the research findings, then received training and follow-up support in strategies in which they were interested.

· One principal, while expressing concern about the time that teachers in her school spent at the photocopying machine, kept a copy of the Handbook by the machine. She reported that teachers liked the short format, which allowed them to read quickly about one of the practices.

· Another suggestion made by teachers was the use of the materials to help less-experienced teachers ‘take the rough edges off. More-experienced teachers would work collaboratively with them to help the newer teachers expand and refine their repertoire of strategies.

The context: a school culture for effective staff development

Experience has shown that teachers need time to absorb new information, observe and discuss new practices, and participate in the training needed to become confident with new techniques. This often means changes in traditional schedules to give teachers regular opportunities to team with their colleagues, both to acquire new skills and to provide instruction. As schools continue the task of improving student achievement by expanding the knowledge base of teachers, the need to restructure schools will become more and more apparent.

Successful use of the knowledge base on improving student learning in mathematics, as in the case of all the other subjects included in the Handbook, relies heavily on effective staff development. As Dennis Sparks, executive director of the National Staff Development Council, says in his Handbook chapter:

If teachers are to consistently apply in their classrooms the findings of the research described in this Handbook, high-quality staff development is essential. This professional development, however, must be considerably different from that offered in the past. It must not only affect the knowledge, attitudes, and practices of individual teachers, administrators, and other school employees, but it must also alter the cultures and structures of the organizations in which those individuals work.

Changes needed in the culture of staff development include an increased focus on both organization development and individual development; an inquiry approach to the study of the teaching/learning process; staff development efforts driven by clear, coherent strategic plans; a greater focus on student needs and learning outcomes; and inclusion of both generic and content-specific pedagogical skills.

The contents of this booklet and the Handbook of research on improving student achievement can provide the basis for well-designed staff development activities. If schools provide generous opportunities for teacher learning and collaboration, teachers can and will improve teaching and learning in ways that truly benefit all students. To achieve that end, professional development must be viewed as an essential and indispensable part of the school improvement process.