Curtis C. McKnight

Curriculum coherence: An examination of US mathematics and science content standards from an international perspective

In recent years, US curriculum policy has emphasized standards‐based conceptions of curricula in mathematics and science. This paper explores the data from the Third International Mathematics and Science Study (TIMSS) to argue that the presence of content standards is not sufficient to guarantee curricula that lead to high‐quality instruction and achievement. An examination of the content topics covered in each grade of a group of six of the highest‐achieving TIMSS countries in mathematics and science shows a pattern in which new topics are gradually introduced, are a part of instruction for a few grades, and then often leave the curriculum as separate topics. This contrasts sharply with mapping of topics in the various US national standards in mathematics and science. Topics enter and linger, so that each grade typically devotes instructional attention to many more topics than is typical of the six high‐achieving countries; in addition, each topic stays in the curriculum for more grades than in the high‐achieving countries. An examination of mathematics and science content standards from 21 states and 50 districts in the US shows a pattern more like that of the US national standards than those of the high‐achieving TIMSS countries. While content standards have become integral to US curriculum development and reform, they have yet to reflect the coherence that is typical of countries that achieved significantly better than the US in the TIMSS study.

Surveying Educational Opportunity in Mathematics and Science: An International Perspective.

To have meaningful policy implications, an [education] indicator is placed in a particular context. That is, within a mature set of indicators, each bears an understandable relationship to the health of the system and to each other so that together they can be viewed as a model of the system (Burstein, Oakes, & Guiton, 1992).

Curriculum sensitive assessment: Content does make a difference

Abstract This chapter explores the use of rankings and total test scores in large-scale international comparative studies and some of the issues related to them. It examines their value as a basis for policy decisions and educational research. Country ranks on total test scores have been seen to be relatively robust to changes in test content, even changes directed at greater curriculum relevance. Unfortunately, other analyses suggest this robustness is likely a consequence of high levels of aggregation and broad, shallow domain sampling. Student achievement in mathematics and science is inherently multi dimensional. Highly aggregated scores of broadly sampled domains are inherently misleading and mask fundamental, educationally relevant diversities at more specific levels of the curriculum.

Content Coverage Differences across Districts/States: A Persisting Challenge for U.S. Education Policy.

This article utilizes the 1999 TIMSS-R data from U.S. states and districts to explore the consequences of variation in opportunities to learn specific mathematics content. Analyses explore the relationship between classroom mathematics content coverage and student achievement as measured by the TIMSS-R international mathematics scaled score. District/state-level socioeconomic status indicators demonstrated significant relationships with the dependent variable, mathematics achievement, and the classroom-level measure of content coverage. A three-level hierarchical linear model demonstrated a significant effect of classroom content coverage on achievement while controlling for student background at the student level and SES at all three levels documenting significant differences in mathematics learning opportunities as a function of the U.S. education system structure.

Facing Facts in U.S. Science and Mathematics Education: Where We Stand, Where We Want to Go

The Third International Mathematics and Science Study (TIMSS) provides data that seems clearly important to science and mathematics education in the U.S. TIMSS gathered extensive data on curriculum, textbooks, teachers, and instructional practices in science and mathematics education and some of these data are presented and discussed. Eighth grade achievement data show the U.S. to be somewhat above average in science achievement but consistently average or below in mathematics. U.S. official curricula cover comparatively many topics and are relatively unfocused. U.S. science and mathematics textbooks typically take a cautious, inclusive approach keeping traditional content while adding new reform topics. They thus lack. Teachers, without guidance to help them focus, typically divide their attention among many topics. Empirically, there is little agreement in the U.S. on what is truly “basic” judging by common topics among curricula and textbooks. U.S. teaching, at least in mathematics, is teacher and moves among many different activities, failing to tell a coherent story. We must face these as we seek to find ways to become what we want to be in providing science and mathematics education.

Content Representation in Mathematics Instruction: Characteristics, Determinants and Effectiveness

Publisher Summary This chapter describes characteristics, determinants, and effectiveness of content representation in mathematics instruction. A characteristic feature of mathematics instruction is that its mathematical content can be represented in a variety of forms. The forms often differ widely in their complexity. Two key aspects of content representation, each captured in one variable, were selected as the foci for studying decisions about content representation. The first variable, VARIETY, was simply a count of the number of different content representations emphasized, or at least used for instruction on a given subtopic. The other aspect of content representation considered here was the relative balance in instruction on a subtopic between perceptual form representations, and symbolic form representations. Perceptual forms were those which depended on a central perceptual or iconic element. Symbolic forms were those which depended primarily on abstract and symbolic elements without the presentation of a figural element.

Mathematics Achievement in U.S. High Schools from an International Perspective.

Performance of U.S. students on international tests of math ematics achievement continues to lag, say these authors, who review the results of a study conducted by the International Association for the Evaluation of Educational Achievement.