Sharon L. Senk

The Mathematics Education of Future Primary and Secondary Teachers: Methods and Findings from the Teacher Education and Development Study in Mathematics

In 2005, the International Association for the Evaluation of Educational Achievement (IEA), Michigan State University, and the Australian Council for Educational Research took an important step in advancing the field of education by partnering to develop and implement the first international and comparative study of mathematics teacher education. The study was made possible by the substantial funding received from the National Science Foundation, the IEA, and the collaboration of 17 participating countries. The purpose of this article is to illustrate the methodology used in this major cross-national study of teacher education—the IEA Teacher Education and Development Study in Mathematics, known as TEDS-M—and to share its main findings related to the mathematical preparation of future teachers.

The Effects of Curriculum on Achievement in Second-Year Algebra: The Example of the University of Chicago School Mathematics Project

We examine the performance of 8 pairs of 2nd-year algebra classes that had been matched on pretest scores. One class in each pair used the UCSMP Advanced Algebra curriculum, and the other used the 2nd-year-algebra text in place at the school. Achievement was measured by a multiple-choice posttest and a free-response posttest. Opportunity-to-learn (OTL) measures were used to ensure that items were fair to both groups of students. UCSMP students generally outperformed comparison students on multistep problems and problems involving applications or graphical representations. Both groups performed comparably on items testing algebraic skills. Hence, concerns that students studying from a Standards-oriented curriculum will achieve less than students studying from a traditional curriculum are not substantiated in this instance.

Curriculum and Achievement in Algebra 2: Influences of Textbooks and Teachers on Students’ Learning about Functions

Textbooks are a major factor in creating opportunities for learning in high school mathematics. However, teachers sometimes skip or modify lessons in the textbook. Thus, the enacted curriculum can be quite different from the intended curriculum of the textbook. This chapter describes a study of the intended, enacted, and attained curriculum conducted in ten matched pairs of Algebra 2 classes in five high schools in the United States. In particular, because functions are a major content strand of high school mathematics across the world, we discuss relationships between students’ achievement on items testing their knowledge of functions and the opportunities to learn provided by their textbooks and teachers.

Examining content validity of tests using teachers’ reported opportunity to learn

ABSTRACT Validity evidence based on content is critical for making inferences about examinees’ responses to test items. Traditionally, content validity has been established by specifying the content domain of an instrument, through reviews by subject-matter experts, through alignment studies, or by reporting measures of internal consistency, such as Cronbach’s alpha or Rasch reliability. In this article, we use data from curriculum research to propose another measure of content validity, specifically, teachers’ self-reported measures of students’ opportunity to learn the mathematics needed to answer test items.

A Multidimensional Assessment of Teachers’ Knowledge of Algebra for Teaching: Developing an Instrument and Supporting Valid Inferences

Numerous researchers have suggested that there are multiple mathematical knowledge and skill areas needed by teachers in order for them to be effective teachers of mathematics: knowledge of the mathematics that are the goals of instruction, advanced mathematics beyond the instructional material, and mathematical knowledge that is specific to what is needed to teach students. The research reported here is about the development of a test of teachers’ knowledge in these three areas related to the teaching of algebra. The test development process is described and the results of several analyses are reported that had the goal of checking whether valid inferences can be made about the hypothesized components of teacher knowledge.

Exploring Models of Secondary Geometry Achievement

Thompson and Senk (ZDM Math Educ 46:781–795, 2014) described variations in the curriculum enactment of 12 secondary school teachers using the same geometry textbook. In this paper, the researchers investigated factors that might account for the achievement of the 544 students enrolled in the 25 geometry classes these teachers taught. Multilevel regression analyses showed that the students’ prior achievement, teachers’ reports on their use of questions applying the mathematics studied, and students’ opportunity to learn the content of the posttest have significant positive effects on the geometry posttest achievement. The percent of lessons taught, writing emphasis, and frequency of use of activities with concrete materials had negative effects on the posttest achievement. The researchers’ final model accounted for about 95% of the variance. School size or type, instructional time, teacher’s certification and experience, and other aspects of curriculum enactment were not significant. Other factors and more reliable ways to measure and combine those factors in determining curriculum enactment may lead to developing more precise models of students’ achievement.