Denisse R. Thompson

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.

Communication and Representation as Elements in Mathematical Literacy.

The process standards of communication and representation in the Principles and Standards for School Mathematics are critical tools to help students develop mathematical literacy. In the mathematics classroom, students need to be encouraged to use speaking, listening, reading, and writing to communicate their understanding of mathematics words, symbols, and concepts. In addition, they should be encouraged to use multiple representations (such as diagrams) to move fluently between verbal, symbolic, graphical, and numerical forms of mathematics concepts.

Assessment in Mathematics Education: Large-Scale Assessment and Classroom Assessment

This volume draws on research to discuss these topics and highlights some of the differences in terms of challenges, issues, constraints, and affordances that accompany large-scale and classroom assessment in mathematics education as well as some of the commonalities.

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.

Interdisciplinary Mathematics and Science Education Through Robotics Technology: Its Potential for Education for Sustainable Development (A Case Study from the USA)

Interdisciplinary Mathematics and Science Education Through Robotics Technology: Its Potential for Education for Sustainable Development (A Case Study from the USA) This case study pictures the challenges and successes described by two Grade 8 teachers as they attempt to use robotic technologies to integrate their mathematics and science curriculum in an interdisciplinary manner. We share our observations regarding the difficulties the teachers faced and their perceptions as they used the technology as part of classroom instruction. Our analysis indicates that the technology served as an effective management tool for teachers and a strong motivational tool for students. However, the data also reveal that the teachers struggled to integrate the technology in a manner that supported interdisciplinary instruction, particularly because they lacked time and appropriate curricular materials. Consequently, we argue that for robotic technology to be used as a model to support education for sustainable development, specific curriculum, adaptable to local contexts, needs to be readily available.

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.

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.

Formative Assessment: A Critical Component in the Teaching-Learning Process

This introductory paper to the volume contrasts formative assessment with summative assessment and describes the importance of formative assessment to classroom instruction. In particular, it argues that a task is formative to the extent that data from the task are used to enhance and inform further instruction rather than simply to provide an evaluation of a student or of instruction. The use of design research as a mechanism to develop sound classroom assessment is outlined because a design science framework provides a means to tie together varied exemplars of innovations in assessment. A cycle of task implementation and revision can lead to improved assessment practices.

Looking to the Future: Lessons Learned and Ideas for Further Research

This concluding paper to the volume highlights some lessons learned from the various papers relative to the issue of formative assessment and draws them together as a range of attempts to make students’ learning visible. In addition, possible avenues for further research related to this important topic are discussed, including formative assessment as an instrument or a process, the development of tools for assessment, and a more nuanced understanding of classroom assessment.

Precalculus Teachers' Perspectives on Using Graphing Calculators: An Example from One Curriculum.

ABSTRACT Graphing calculators are hand-held technological tools currently used in mathematics classrooms. Teachers’ perspectives on using graphing calculators are important in terms of exploring what teachers think about using such technology in advanced mathematics courses, particularly precalculus courses. A descriptive intrinsic case study was conducted to analyse the perspectives of 11 teachers using graphing calculators with potential Computer Algebra System (CAS) capability while teaching Functions, Statistics, and Trigonometry, a precalculus course for 11th-grade students developed by the University of Chicago School Mathematics Project. Data were collected from multiple sources as part of a curriculum evaluation study conducted during the 2007–2008 school year. Although all teachers were using the same curriculum that integrated CAS into the instructional materials, teachers had mixed views about the technology. Graphing calculator features were used much more than CAS features, with many teachers concerned about the use of CAS because of pressures from external assessments. In addition, several teachers found it overwhelming to learn a new technology at the same time they were learning a new curriculum. The results have implications for curriculum developers and others working with teachers to update curriculum and the use of advanced technologies simultaneously.