As reform recommendations collide with traditional practices, the questions on the minds of many interested teachers and parents are these: Should we really adopt this new textbook series? Should we change the way we teach? What mathematics should students really be learning? It would be nice if research could give clear and simple answers to these kinds of “should” questions, but it does not and it cannot.

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### James Hiebert

The current debates about the future of mathematics education often lead to confusion about the role that research should play in settling disputes. On the one hand, researchers are called upon to resolve issues that really are about values and priorities, and, on the other hand, research is ignored when empirical evidence is essential. When research is appropriately solicited, expectations often overestimate, or underestimate, what research can provide. In this article, by distinguishing between values and research problems and by calibrating appropriate expectations for research, I address the role that research can and should play in shaping standards. Research contributions to the current debates are illustrated with brief summaries of some findings that are relevant to the standards set by the NCTM.

### James Hiebert

Measurement skills provide children with a powerful link between the abstract world of numbers and the concrete world of physical objects. Before young children learn to measure, they can only describe objects or quantities with relatively vague, uninformative terms such as “big” or “many.” As they learn to measure, children acquire the skills to describe quantities in more precise and more useful terms. They can now talk about the size of quantities as the number of units measured.

### James Hiebert

Two of the most striking and informative results from recent research on children's mathematics learning are the following. On the one hand, many children possess a surprising degree of competence with mathematical situations outside of school. For example, before beginning school, most young children can solve simple addition and subtraction stories, such as “Mary has 8 pennies. She gives 3 pennies to Roger. How many does she have left?” (Carpenter and Moser 1984; DeCorte and Verschaffel 1987; Riley, Greeno, and Heller 1983). In other words, before children have been taught how to add and subtract, they can solve addition and s ubtraction problems. Similarly, older children, as well as adults, can solve a variety of real-world problems using strategies that they have not learned directly in school (Carraher, Carraher, and Schliemann 1987; Lave, Murtaugh, and de Ia Rocha 1984; Scdbner 1984).

### James Hiebert

Johnny is good at measuring. He usually gets all his worksheet problems right, especially when the problems involve using his ruler to measure things.

### James Hiebert

As reform recommendations collide with traditional practices, the questions on the minds of many interested teachers and parents are these: Should we really adopt this new textbook series? Should we change the way we teach? What mathematics should students really be learning? It would be nice if research could give clear and simple answers to these kinds of “should” questions, but it does not and it cannot.

### James Hiebert

As suggested by the titles, the chapters in all three books deal with children's mathematical thinking and learning. The authors are leading psychologists and mathematics educators in this broad field of research, and the volumes present some of the most comprehensive, systematic, and careful research recently conducted on problems of current interest in the field. There is no question that these books will serve as major reference works for those interested in research on the learning of mathematics. With some exceptions, the volume edited by Lesh and Landau presents work of mathematics educators, and the volumes edited by Brainerd and by Ginsburg contain work of cognitive psychologists. The three volumes were selected for a single review because they represent significant approaches to studying a common problem—children's mathematical thinking and learning.

### James Hiebert

AS REFORM RECOMMENDATIONS COLLIDE with traditional practices, the questions on the minds of many interested teachers and parents are these: Should we really adopt this new textbook series? Should we change the way we teach? What mathematics should students really be learning? It would be nice if research could give clear and simple answers to these kinds of “should” questions, but it does not and it cannot.

### James Hiebert

This study examined whether Piagetian logical reasoning abilities and/or an information-processing capacity are needed to learn basic measurement concepts. First-grade children, equated for prior knowledge of measurement but differing in developmental status, were instructed individually on linear measurement. Results showed that the Piagetian reasoning abilities of length conservation and transitivity were required to learn some measurement concepts but not others. It appears that the effects of these cognitive abilities are task specific and, in this sense, are not useful as general measures of learning readiness. Information-processing capacity, as measured by backward digit span, had no detectable effect on learning success.

### James Hiebert

This study examines the position of the unknown set and children's representation and solution processes for verbal addition and subtraction problems. Forty-seven first-grade children were given three joining problems and three separating problems in an individual interview. Each joining and separating problem had a different quantity as the unknown. Small blocks were available for children to use to model the problems. Results indicated that the position of the unknown had a profound effect on children's modeling behavior, which in turn affected the choice of the solution process and the relative difficulty of the problem.