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### Jinfa Cai

*Although the Journal for Research in Mathematics Education (JRME)* published its first issue in January of 1970, the first scholarly book review appeared in the January 1977 issue under the editorship of James Wilson. In it, Thomas Kieren (1977) reviewed the 1975 National Advisory Committee on Mathematical Education (NACOME) report, *Overview and Analysis of School Mathematics Grades K–12.* In his editorial for the issue, Wilson (1977) wrote,

### Jinfa Cai

In the late 1980s and early 1990s, the National Council of Teachers of Mathematics (NCTM) published its *Standards* documents, which provided recommendations for reforming and improving K–12 school mathematics. With extensive support from the National Science Foundation, a number of *Standards*-based school mathematics curricula were developed and implemented to align with the recommendations in the *Standards*. The implementation of *Standards*-based instructional materials requires change not only in how mathematics is viewed but also in how mathematics is taught and learned. Thus, teachers and school districts face challenges when trying to implement *Standards*-based curricula. Moreover, because the *Standards*-based curricula claim to have different learning goals and they also look very different from traditional mathematical curricula, some parents, professionals, and school communities challenge both the new goals and the efficacy of these new curricula. In the past several years, there have been heated debates over the mathematics education reform movement in general and *Standards*-based curricula in particular. As the debates continue, there is an increasing demand for data that show how well *Standards*-based school mathematics curricula work.

### Jinfa Cai

Direct modeling with concrete objects can be a powerful problem-solving strategy for young children (Chambers 1996). However, as problem situations become more complex. the value of more powerful strategies becomes apparent. An algebraic approach in which students first describe the problem using an unknow n in an equation and then solve for the unknown (Lesh, Post, and Behr 1987) is one such strategy.

### Stephen Hwang and Jinfa Cai

Mathematics education has existed as an independent field of research for over a century. Although young compared with some other domains of research, mathematics education research has nevertheless developed into a fertile and active discipline. In particular, the last 40 years have seen a rapid expansion of output from a growing body of mathematics education researchers. Indeed, the productivity of mathematics education researchers working in a host of subdomains has encouraged the development of a wide variety of research journals (Cai, 2010). The field has clearly expanded beyond a small handful of key journals for disseminating research findings. At the same time, books and monographs on mathematics education have also long been staple venues for published research.

### Jinfa Cai and Patricia Ann Kenney

The reform movement in school mathematics advocates communication as a necessary component for learning, doing, and understanding mathematics (Elliott and Kenney 1996). Communication in mathematics means that one is able not only to use its vocabulary, notation, and structure to express ideas and relationships but also to think and reason mathematically. In fact, communication is considered the means by which teachers and students can share the processes of learning, doing, and understanding mathematics. Students should express their thinking and problem-solving processes in both written and oral formats. The clarity and completeness of students' communication can indicate how well they understand the related mathematical concepts.

### Edward A. Silver and Jinfa Cai

The mathematical problems generated by 509 middle school students, who were given a brief written “story-problem” description and asked to pose questions that could be answered using the information, were examined for solvability, linguistic and mathematical complexity, and relationships within the sets of posed problems. It was found that students generated a large number of solvable mathematical problems, many of which were syntactically and semantically complex, and that nearly half the students generated sets of related problems. Subjects also solved eight fairly complex problems, and the relationship between their problem-solving performance and their problem posing was examined to reveal that “good” problem solvers generated more mathematical problems and more complex problems than “poor” problem solvers did. The multiple-step data analysis scheme developed and used herein should be useful to teachers and other researchers interested in evaluating students' posing of arithmetic story problems.

### Jinfa Cai and Edward A. Silver

During the past several decades, there has been considerable attention to crossnational comparisons of mathematics achievement. A number of studies have examined the performance in various mathematical topic areas by students from different countries (e.g., Lapointe, Mead, & Askew, 1992; Robitaille & Garden, 1989; Stevenson et al., 1990; Stigler, Lee, & Stevenson, 1987). In general, when crossnational studies in mathematics have included samples of Chinese and U.S. students, the findings have been that Chinese students perform mathematical tasks at much higher levels of proficiency than U.S. students (e.g., Lapointe et al., 1992; Stevenson et al., 1990).

### Carol Santel-Parke and Jinfa Cai

During a recent NCTM regional conference, a speaker addressed the significance of performance assessment in the mathematics classroom. Afterward, a mathematics teacher posed a question to the speaker: “I agree with you that performance assessment is very important in the classroom, and your sample tasks are very interesting. However, as a classroom teacher, how can I design these kinds of interesting tasks or modify existing tasks to ensure that they accurately measure my own students' performance throughout the year?” Although only one teacher voiced this concern during the session, many other teachers may have similar concerns. The purpose of this article is to share a few of our experiences in developing performance-assessment tasks. We hope that the examples will be helpful to teachers in designing their own performance tasks to measure students' higher-level thinking and reasoning skills in the classroom.