Examined multiple modalities of nonspoken forms of representation-specifically gestures, pictures, objects, and writing-used by three teachers in three years of first grade math lessons. Students must attend to visual as well as vocal means of expressing information to gain access to all information presented in mathematics lessons. (BF)

Examines mathematics instruction and its relationship to issues of language, culture, and power in a low-income urban elementary school with large numbers of bilingual students. Results of discussions of student work during a summer training institute for university researchers, teachers, and administrators provide suggestions for approaching…

Describes an experiment designed to change prospective teachers' views of what constitutes a good explanation of a mathematics topic, presenting examples of participants' explanations at three stages of the experiment using a "levels of subject-matter understanding" framework, and suggesting that to effectively teach a topic, teachers'…

Comprehension of chance language, such as is found in newspapers, is a fundamental aspect of statistical literacy. In this study, students' understandings of chance language were explored through responses to two items in surveys administered to 2,726 students from grades 5 to 11. One item involved evaluating the chance expressed in phrases from…

We present a methodology for designing better learning environments. In Phase 1, 6th-grade students' (n = 223) prior knowledge was assessed using a difficulty factors assessment (DFA). The assessment revealed that scaffolds designed to elicit contextual, conceptual, or procedural knowledge each improved students' ability to add and subtract…

Background: Since the early 1980s, there has been a growing interest in the potentiality of computers as facilitators of students' learning. The importance of using technology effectively as a learning tool has been emphasized by many researchers. However, finding good software that encourages pupils to explore and express mathematical ideas is…

To meet the challenge to reform mathematics education, effective opportunities to learn are needed to promote prospective elementary school teachers' development of the knowledge base that supports teaching, for mathematical proficiency. This article describes three professional development interventions and their influence on prospective…

Most people think that engineering and mathematics go hand in hand. To many, being an engineer means manipulating equations and calculating measurements to design and build structures of all kinds. And they are right. Engineering does involve a great deal of mathematics. But, building structures to withstand certain environmental conditions or…

It is said that meteorology is the only profession where a person can be wrong half the time and still keep his or her job. The truth is not quite so bleak, but one can still ask, "Just how accurate are weather forecasters, anyway?" This article presents two projects for middle level students to investigate this issue in a hands-on,…

Affective consequences of two types of mathematics instruction, guiding instruction and directing instruction, were studied for two types of students with special needs: mildly mentally retarded students and students with specific learning disabilities. Seventy students were instructed in small groups in either a guiding or a directing instruction…

"Johnny" may be learning more about reading and mathematics, but he may have little time to study the discoveries of Columbus, the tenets of the U.S. Constitution, or the social and political causes of the Civil War. Those time-honored topics--as well as lesser-known events and figures throughout history--are fighting to maintain their…

This article describes an activity in which students plot collections of ordered pairs according to prescribed set conditions. The coordinate plane sets can have rich variety, and their construction fosters critical thinking, attention to detail, and algebraic reasoning. (Contains 3 figures.)

This article describes geometry-oriented problem-solving tasks that can encourage students to develop a positive attitude toward mathematics. The tasks concern working with polyominoes, two-dimensional shapes that consist of squares joined fully at the edges. (Contains 7 figures.)

This article describes an investigation into mathematics for teaching in current teacher education practice in South Africa. The study focuses on formal evaluative events across mathematics teacher education courses in a range of institutions. Its theoretical orientation is informed by Bernstein's educational code theory and the analytic frame…

This article describes the use of commercial games in mathematics to help teach algebraic reasoning, spatial sense, and multistep problem solving. It also provides a description of how one teacher implemented the use of games.