Algebra is critical in shaping future mathematics success and is integral to the K-12 curriculum. Despite its inclusion, a common challenge arises as students' progress to higher grades without a solid foundation, resulting in challenging learning experiences. This action research study focuses on the algebraic learning experience of a Grade 7…

While research in mathematics education has shown that mathematics assessments are highly consequential, traditional assessments often lag behind advancements in instructional methods. One such advancement is the promotion of mathematical habits of mind such as students' abilities to critique others' reasoning. This study explored the use of…

Project-based learning (PBL) is an instructional method that has grown in popularity across all grade levels and subject areas, in both K-12 schools and higher education institutions. PBL embraces the integration of curriculum across subjects, the engagement of home and community in school learning, and the involvement of students in cooperative…

Continual assessment of student understanding is a crucial aspect of teaching. The adoption of the Common Core State Standards for Mathematics (CCSSM) represents raised expectations for the level and depth of mathematical understanding that is expected of our students. But new standards also mean new tests. What those tests will be like is of…

This paper discusses issues arising in the design of questions to use in an on-line computer-based formative assessment system, focussing on how best to identify the stages of a learning hierarchy for reporting to teachers. Data from several hundred students is used to illustrate how design decisions have been made for a test on interpreting line…

This chapter argues that for the science of learning to become a fully "human" science, it needs to move from viewing learning from an exogenous perspective to an endogenous one. Taken from Latin, the term "endogenous" translates roughly to "from within," and in the meaning the author gives to it here, it refers to a perspective on learning from…

This article reports the results of a study examining the utility of curriculum-based measurement (CBM) in algebra for predicting performance on a state math assessment and informing instructional placement decisions for students in seventh, eighth, and tenth grades. Students completed six Basic Skills algebra probes across different time…

The purpose of this study was to explore a cognitive approach to analyzing students' written responses to mathematics performance assessments to inform learning, instruction, and assessment design and development. The existing data used in this study were seventh grade students' written responses to, and item scores on, four released mathematics…

There is a lack of implementation of instructional strategies to assist middle school teachers in improving mathematics education for their students. Coaching is one solution to this problem, but its impact on student achievement is unclear. This case study evaluated the relationship between coaching and teacher efficacy and the impact of these…

Observation measures of instructional quality tend to fall into two broad categories--those for use across subject areas and those intended for use in specific subject areas. The move toward content-specific measures is a result of research suggesting that effective teaching looks different across subject areas and that both content knowledge and…

This study explored the performance of seventh-grade students with and without disabilities, educated in inclusive mathematics classes, on a mathematics assessment aligned to state standards with graphing calculators as an accommodation. The study used random assignment of classes to condition with students nested in classes. Students did not use…

This document offers a planning tool for grades 3-7 that can be used by regional comprehensive centers, other technical assistance centers, and state departments of education to plan professional development for teachers. It is based on the "National Mathematics Advisory Panel Report" which was published in 2008. The panel synthesized its final…

This article argues that intervention pilot test evaluations have focused insufficient attention on the measurement of project fidelity and the subsequent use of fidelity results for (a) interpreting variations in project outcomes and (b) understanding the rationale for teachers' deviations from implementation protocols. The authors report on the…

The PD program evaluated in this study is designed to address the problem of low student achievement in topics in rational numbers. The study focuses on seventh grade, the culminating year for teaching those topics. The study randomly assigned 77 mid- and high-poverty schools from 12 districts to treatment and control conditions and collected…

This paper will describe results concerning the impact of the PD on the three primary study outcomes: teacher knowledge of rational number topics, teacher instructional practices, and student achievement in rational number topics. All analyses are completed. However, the results cannot be shared at this time because the report is currently under…