A multiple probe across participants design was used to examine the effectiveness of a treatment package to teach students with moderate intellectual disability how to solve simple linear equations. The investigator read realistic scenarios of a problem, used actual items as manipulatives, presented a visual aid of the equation, and used a system…

This paper focuses on description and evaluation of a Web-based professional development system for teachers centered on the collection and use of frequent student performance information in algebra for instructional decision making. With U.S. federal grant funding, researchers developed Web-based instructional modules, which provided interactive…

Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…

Low success rates in developmental mathematics courses have caused a growing concern for many institutions including moderately selective four-year universities. As a result, institutions have adopted various course redesign models, such as the emporium and replacement models, which take advantage of interactive online learning tools. Though these…

Comparison is a fundamental cognitive process that can support learning in a variety of domains, including mathematics. The current paper aims to summarize empirical findings that support recommendations on using comparison of multiple strategies in mathematics classrooms. We report the results of our classroom-based research on using comparison…

Why are math modeling problems the source of such frustration for students and teachers? The conceptual understanding that students have when engaging with a math modeling problem varies greatly. They need opportunities to make their own assumptions and design the mathematics to fit these assumptions (CCSSI 2010). Making these assumptions is part…

A new transition course centered on complex topics would help in revitalizing complex analysis in two ways: first, provide early exposure to complex functions, sparking greater interest in the complex analysis course; second, create extra time in the complex analysis course by eliminating the "complex precalculus" part of the course. In…

The purpose of this study is to investigate the development of relational thinking skill, which is an important component of the transition from arithmetic to algebra, of 5th grade students. In the study, the qualitative research method of teaching experiment was used. The research data were collected from six secondary school 5th grade students…

The perpetuation of mathematical rules that expire (Karp, Bush, and Dougherty 2014; 2015), or rules that are taught in previous grades that no longer hold true, suggests that many secondary students harbor misconceptions from their elementary and middle-grades mathematics experiences as they progress to mathematics classes that are more…

Simplifying symbolic expressions is usually perceived in middle school algebra as an algorithmic activity, achieved by performing sequences of short drill-and-practice tasks, which have little to do with conceptual learning or with creative mathematical thinking. The aim of this study is to explore possible ways by which ninth-grade students can…

As noted in the literature, students struggle to learn developmental mathematics. A positive experience with developmental mathematics has been shown to increase students' confidence in learning mathematics (Duranczyk, 2008). Additionally, students who have a successful developmental experience are more likely to experience success in subsequent…

The Office of English Language Acquisition (OELA) has synthesized key data on English learners (ELs) into two-page PDF sheets, by topic, with graphics. This document presents highlights relating to English learners and college and career readiness covering school-year (SY) 2013-2014. The topics for this report include: (1) Percentage of ELs…

Improving the nation's math prowess and preparing the youth to be college or career ready, may need to be solved by a culmination of theories from different perspectives. As the controversial meshing hypothesis contends that teachers should present information according to each students' learning styles; this can be extremely difficult in a…

A theoretical model of metacognition in complex modeling activities has been developed based on existing frameworks, by synthesizing the reconceptualization of metacognition at multiple levels by looking at the three sources that trigger metacognition. Using the theoretical model as a framework, this multiple-case study explores students'…

In our study, 32 German and Swiss 8th/9th-grade classes of lower-secondary school worked with their teacher on the same proving problem. The sample belongs to the Swiss-German study "Quality of Instruction, Learning Behavior and Mathematical Understanding". Our data analyses relate to the teachers' approaches to generating a specific…