Cognition and Instruction

Spillane, James P.

doi: 10.1207/S1532690XCI1802_01pmid: N/A

Using a cognitive lens, this article explores school districts' response to recent mathematics reforms. Analyzing the ideas about instruction that district leaders construct from the mathematics reforms, I identify dominant patterns in their understandings. Whereas district leaders in the study understood the mathematics reforms as representing change for their mathematics policies and programs, their understandings tended to miss the full import of the reforms. Focusing on the forms of the mathematics reforms rather than their epistemological and pedagogical functions, district leaders' understandings tended to focus on piecemeal changes that often missed the disciplinary particulars of the reforms. Based on this analysis, I argue for the inclusion of implementers' interpretation of the reform message, along with the more conventional variables such as local resistance to reform and limited local capacity to carry out reform proposals that dominate in the literature in models of the implementation process.

Perry, Michelle

doi: 10.1207/S1532690XCI1802_02pmid: N/A

In this research, I examine some of the classroom processes that may be responsible for the stellar mathematical performance among Asian children compared to U.S. children. The study documents differences in the frequency and type of mathematical explanations during lessons observed in 80 U.S., 40 Chinese, and 40 Japanese 1st- and 5th-grade classrooms. Explanations occurred more frequently in the Japanese and Chinese classrooms than in U.S. classrooms. Furthermore, typical explanations in the Asian classrooms were more substantive than those in the U.S. lessons, and Japanese children were learning about more complex topics than their peers in Taiwan or the United States.

Nathan, Mitchell J.; Koedinger, Kenneth R.

doi: 10.1207/S1532690XCI1802_03pmid: N/A

Elementary, middle, and high school mathematics teachers (N = 105) ranked a set of mathematics problems based on expectations of their relative problem-solving difficulty. Teachers also rated their levels of agreement to a variety of reform-based statements on teaching and learning mathematics. Analyses suggest that teachers hold a symbol-precedence view of student mathematical development, wherein arithmetic reasoning strictly precedes algebraic reasoning, and symbolic problem-solving develops prior to verbal reasoning. High school teachers were most likely to hold the symbol-precedence view and made the poorest predictions of students' performances, whereas middle school teachers' predictions were most accurate. The discord between teachers' reform-based beliefs and their instructional decisions appears to be influenced by textbook organization, which institutionalizes the symbol-precedence view. Because of their extensive content training, high school teachers may be particularly susceptible to an expert blindspot, whereby they overestimate the accessibility of symbol-based representations and procedures for students' learning introductory algebra.

VanSledright, Bruce A.; Frankes, Lisa

doi: 10.1207/S1532690XCI1802_04pmid: N/A

This study explored how historical concepts and research strategies were taught and made sense of by students in 2 fourth-grade classrooms. We examined the teaching and learning of a unit on Native Americans in the Chesapeake Tidewater area in each classroom. In 1 classroom, the teacher intentionally sought to enhance students' concept and strategic historical knowledge through integration of history and research strategies (based in reading-language arts), and in the other, the teacher did some inquiry-based study of history but expressed no direct intention of using it to enhance student conceptual or strategic knowledge. Daily observations of teaching practices were conducted throughout the units. The teachers were interviewed both formally and informally about what they were trying to accomplish. Six students from each class were interviewed in depth directly after they studied Native Americans and again at the end of the school year to get their perspectives on what they thought they had learned, and to assess differences in concept development and strategic knowledge about research practices. These data were augmented by informants' descriptions of their attitudes about doing research. Results suggest that the differences between the classrooms with respect to the ways the teachers taught the units were rather obvious. However, the differences reported by the 6 students from each classroom regarding concept- and strategic-knowledge development were quite subtle. The teacher in the first classroom noted appeared partly successful in helping her students develop historical concepts and strategic knowledge about research practices. The teacher in the second classroom also promoted some development of conceptual and strategic knowledge. The partial successes in both classes as well as the between-class differences are the focus of the discussion. Based on the study results, commentary is offered about how to improve concept and strategy development in historical study along with a consideration of the subject matter knowledge demands such improvements would make on elementary school teachers.