The dissertation study reported here describes various policies and strategies used by school districts that impact student performance on the Missouri Algebra 1 End-of- Course (EOC) assessment. Analysis of state testing data, teacher survey data, and interview data were used to describe policies and strategies used by 42 teachers and…

10 Great Curricula is a collection of stories written by educators who have come to understand curricula differently as a result of their engagement with a graduate course and its instructor. The book represents the best of what can be found in teaching and learning, in general, and in the quest for meaningful ways to understand curricula in…

The California Department of Education (CDE) has long asserted that success Algebra I by Grade 8 is the goal for all California public school students. In fact, the state's accountability system penalizes schools that do not require all of their students to take the Algebra I end-of-course examination by Grade 8 (CDE, 2009). In this dissertation,…

This study examined the effectiveness of the course, Math Recovery, on a group of ninth-grade students enrolled in the course Algebra/Geometry I measured by course grades and subsequent tenth-grade MAP scores. In addition, gender and race differences were investigated in this study to determine the impact, if any, on academic achievement. The…

The goal for selecting the released set of test items was to have approximately 25% of each of the full item sets for mathematics content knowledge (MCK) and mathematics pedagogical content knowledge (MPCK) that would represent the full range of difficulty, content, and item format used in the TEDS-M study. The initial step in the selection was to…

This study examined preservice teachers' reactions to and reflections on a set of five animations as representations of algebra instruction. The results showed that most comments in the preservice teachers' reflections were related to: (a) student learning and motivation, or (b) the classroom and instructional environment. Few comments in the…

In 2002/03, the Charlotte-Mecklenburg Schools in North Carolina initiated a broad program of accelerating entry into algebra coursework. The proportion of moderately-performing students taking algebra in 8th grade increased from half to 85%, then reverted to baseline levels, in the span of just five years. We use this policy-induced variation to…

Defining what teachers need to know to teach algebra successfully is important for informing teacher preparation and professional development efforts. Based on prior research, analysis of video, interviews with teachers, and analysis of textbooks, we define categories of knowledge and practices of teaching for understanding and assessing teachers'…

International comparisons have highlighted that the U.S. mathematics curriculum, both in terms of curriculum influences (e.g., textbooks, standards) and actual instruction, is broad and shallow. Standards-based reform is explicitly designed to improve coherence and reduce redundancy across grades. This article evaluates the redundancy of…

The conventional approaches to mediation analysis such as path analysis and structural equation modeling typically involve specifying two structural models, one for the mediator and the other for the outcome. We employ an alternative approach that avoids some strong identification assumptions invoked by the conventional approaches. By applying a…

Two experiments were conducted, contrasting a minimally guided discovery condition with a variety of instructional conditions. College students interacted with a computer-based tutor that presented algebra-like problems in a novel graphical representation. Although the tutor provided no instruction in a discovery condition, it constrained the…

Our research project aimed at understanding the complexity of the construction of knowledge in a CAS environment. Basing our work on the French instrumental approach, in particular the Task-Technique-Theory (T-T-T) theoretical frame as adapted from Chevallard's Anthropological Theory of Didactics, we were mindful that a careful task design process…

The paper on "Magnetism and Simultaneity" by Adler provides an excellent new thought experiment involving the lack of simultaneity in Einstein's special relativity. Adler uses the lack of simultaneity rather than the Lorentz contraction to derive the formula for the magnetic force on a moving charged particle. Advantages of his derivation are that…

A problem posed in an influential textbook is analysed in more detail than is given there. The textbook answer to the problem has been represented as counterintuitive, as is probably the case; however, it is here shown that it depends critically on an assumption. If this is relaxed, then a wide variety of possible answers is available. All the…

Several jeeps are poised at base camp on the edge of a desert aiming to escort one of them as far as possible into the desert, while the others return to camp. They all have full tanks of gas and share their fuel to maximize penetration. In a friendly desert it is best to leave caches of fuel along the way to help returning jeeps. We solve the…