Middle school math placement and progression are topics that are part of an active policy and practice discussion in California and elsewhere. Beginning in the 2008/09 school year, California's State Board of Education recommended that students complete algebra I by the end of grade 8. Between 2003 and 2009 the proportion of grade 8 students…

Speakers in conversation typically repeat and modify earlier comments. In mathematics conversations, these repetitions, or poetic structures, can facilitate the collaborative discovery of mathematical relationships. A close analysis of 90 turns of an algebraic problem-solving conversation reveals eight types of poetic structures. This report…

Instructors are a chief input into the higher education production process, yet we know very little about their role in promoting student success. This is in contrast to elementary and secondary schooling, for which ample evidence suggests teacher quality is an important determinant of student achievement. Whether colleges could improve student…

Proving that a given set is indeed a subgroup, one needs to show that it is non-empty, and closed under operation and inverses. This study focuses on the first condition, analysing students' responses to this task. Results suggest that there are three distinct problematic responses: the total absence of proving this condition, the problematic…

"Cognitive Tutor"® is a secondary mathematics curriculum developed by Carnegie Learning that focuses on how students think about and learn mathematics. Teachers facilitate student learning as students acquire and apply new information and discuss their work. The curriculum can be implemented using a textbook, adaptive software, or…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

This report examines the outcomes of the Summer Programs, a two-pronged initiative developed by the Superintendent to provide supplemental instruction for students in need of remediation and access to selected digital application for practice outside the regular school context. The Summer Programs are comprised of seven In-Class components and one…

This study examined student actions, interpretations, and language in respect to questions raised regarding tabular, graphical, and algebraic representations in the context of functions. The purpose was to investigate students' interpretations and specific ways of working within table, graph, and the algebraic on notions fundamental to a…

Planning a lesson can be similar to planning a road trip--a metaphor the authors use to describe how they applied research and theory to their lesson planning process. A map and mode of transportation, the Common Core State Standards for Mathematics (CCSSM) and textbooks as resources, can lead to desired destinations, such as students engaging in…

Numeracy is the understanding of the meaning and interpretation of natural phenomena and is an important skill for full participation in society. Everyday there are numerous situations that require individuals to interpret quantitative information for personal decision making and understanding of significant public issues. However, the gap between…

In this paper, we discuss the relevance of 'Grundvorstellungen' (GVs), a didactical category to analyze students' mental models in comparison to the intended mathematical meanings in the context of Linear Algebra and Analytic Geometry. Diagnostic tasks were used to reveal students' conceptual understanding in this field of expertise. In…

The meaning given to letters is significant for students' ability to be successful with algebraic tasks. Recent studies have noted that even when students have a sense of generalised number, they often have a natural number bias in the values they think a letter can take. This study analyses interviews from 13 students across two schools to…

Studies of the impact of various types of computer use on the results of learning and student motivation have indicated that the use of computers can increase learning motivation, and that computers can have a positive effect, a negative effect, or no effect at all on learning outcomes. Some results indicate that it is not computer use itself that…

As STEM educators, we know it is beneficial to train students to think critically and mathematically during their early mathematical lives. To this end, the author teaches the College Algebra/Precalculus course in a flipped classroom version of an inquiry-based learning style. However, the techniques described in this paper can be applied to a…

In this study, the representations preferred by prospective teachers in the teaching of note values were determined and the accuracy of these representations was analyzed in the context of mathematics and music. The case study, one of the qualitative research designs, was used in the study. Study group of the research consisted of 113 pre-school…