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…

The relevancy of linear algebra (LA) in different areas and also the difficulties faced by undergraduate engineering students studying this content are well known. Grounded on this premise, we aimed at articulating papers related to the teaching and learning of LA in engineering undergraduate programs through a mapping of the main investigations…

Elementary pre-service teachers in an upper-division algebra mathematics content course explored graphing through the use of Calculator-Based Rangers™ (CBRs). This study explores how they used the "Distance Match" feature of the technology to engage in algebraic thinking. Operating CBR technology, pre-service teachers' perceptions…

The ties between literacy and numeracy exist in the development of vocabulary and language for understanding mathematical concepts. Research indicates that explicit instruction in mathematics vocabulary supports success with mathematics problem solving (Biemiller 2009; Pierce and Fontaine 2009; Rubenstein and Thompson 2002) for native…

Building sets, video games, and scatterplots may seem unrelated, but when they are combined into a problem-based learning (PBL) lesson, these elements join to create a unique learning experience. PBL lessons drive instruction by focusing learning and activities around a central challenge or question while providing a relevant, captivating, and…

An individual's learning is determined by cognition, motivation, and social context. Taking these aspects into account, we assessed scaffolding in tutoring situations via contingency to determine how successful and unsuccessful teacher-student interactions are shaped. We aimed to find out how the problem-solving process in successful tutoring…

This study examined effects of gamified comparison on sixth graders' performance of algebra word problem solving and attitude toward algebra learning. Seventy-two sixth graders were invited to participate in a four-week experimental instruction and assigned to three groups: gamified comparison, comparison, and control. The results showed (1) a…

Guided by a theoretical framework emphasizing the importance of fidelity of implementation (FOI), this paper explores how teachers of grades 3, 4 and 5 implemented an early algebra intervention, and the relationship between FOI and student learning. The data shared in this paper come from a longitudinal experimental research project in which 3,208…

A design experiment with 18 students in a regular seventh grade math class was conducted to investigate how to differentiate instruction for students' diverse ways of thinking during a 26-day unit on proportional reasoning. The class included students operating with three different multiplicative concepts that have been found to influence rational…