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Classroom discourse and communication are issues central to current reform in mathematics education. For reform to happen in classrooms, teachers will have to teach from a conceptual curriculum. To do so they must be sensitive to children's thinking during instruction and shape their instructional actions accordingly—to ensure that children hear what they intend them to hear. This article examines how one teacher's way of knowing mathematics was reflected in the language he used in teaching concepts of rate to one student during a teaching experiment. The teacher's conceptualizations of rate, although strong and elaborate, were encapsulated in the language of numbers and operations, and this undermined his effort to help the student understand rates conceptually. We examine the teacher's language in light of his intentions and the student's interpretations of the tasks. We discuss implications for instruction that is based on a conceptual curriculum and is sensitive and responsive to children's thinking.

The field of educational assessment is rapidly changing. Calls for reform have been heard for some time, and they are now being heeded in unprecedented ways. One outcome is that we are suddenly undergoing a deluge of books and articles about assessment in mathematic education, ranging in topics from broad impassioned tatements about the need for change, to specific hypotheses about how to change and what the anticipated outcomes might be, to actual implementations representing specific efforts to change, to sharp criticisms about some of the unexpected results of change. The current situation leaves us, as reviewers, in something of a quandary. On the one hand, there is certainly a need to keep abreast of important contribution to the literature, and we want to review a many of the new books as is feasible. On the other hand, it seems somewhat unfair to review books that attempt to deal with ongoing and urgent changes in educational assessment. becaue they are all too often outdated by the time they appear. All researchers are aware of the lag between the time a manuscript is written and the time it reaches its audience. Sometimes the lag is great, and sometime it is s mall. For rapidly changing fields—like educational assessment—a large lag is especially problematic because what seems new and revolutionary at the time of writing may no longer appear so new by the time a reader encounters it. Such is the case with some of the books we review here.

Part I of this report (Thompson & Thompson, 1994) described the attempts of one teacher, Bill, to teach concepts of speed to one child, Ann. We analyzed sources of their eventual dysfunctional communication, concluding that Bill had encapsulated his deep understandings of rate and proportionality within his language for numbers and operations. Part II presents the session of the researcher, Pat, with Ann, analyzing his instructional actions in light of his agenda for having Ann build a scheme of operations by which to understand distance, time, and speed. We contrast Pat's agenda with Bill's, focusing on the mathematical knowledge that guided their instructional decisions and actions and briefly discuss implications for the preparation of teachers with regard to content knowledge.

A useful strategy in solving problems is “look for a pattern.” In using the strategy, we start with simple cases or versions of the problem and from these cases discover a pattern or rule that can be applied to find the general solution.

Case studies were conducted to investigate the conceptions of mathematics and mathematics teaching held by three junior high school teachers. Examination of the relationship between conceptions and practice showed that the teachers' beliefs, views, and preferences about mathematics and its teaching played a significant, albeit subtle, role in shaping their instructional behavior. Differences among the teachers in their conceptions and practices are explained followed by a discussion of properties of their conceptual systems.

mathematical symbolism, we may be teaching them that understanding plays no role in problem solving or, more generally, in mathematics learning. We may all benefit if we follow the advice given by Brownell (1942, p. 439): "Highly formal and abstract techniques should never be imposed upon the child. Instead, they should be viewed as the end-products of development. Teaching should start with

Acentral theme of NCTM's evaluation standards (National Council of Teachers of Mathematics. Commission on Standards for School Mathematics 1989) is that assessment is an integral part of teaching. One of the many reasons to assess students' learning is to find out where we teacher are in relation to our goals. Another reason is to be able to inform students, parents, or administrators about students' progress. Regard less of the relative merits of these and other reasons for assessing students' learning, the main purpose of assessment should be to inform teaching.

It is increasingly popular for research reports to acknowledge the importance of affect in mathematical problem solving. Unfortunately, merely acknowledging its importance does not get us far in understanding the role affect plays in problem solving. In the absence of efforts focused on understanding the role and importance of affect in problem solving, our attempts to deal effectively with students’ affect during problem-solving instruction will be guided by hunches and good intentions.