To efficiently solve mathematical expressions and equations, students need to notice the systemic structure of mathematical expressions (e.g., inverse relation between 3 and 3 in 3 + 5 - 3). We examined how symbols--specifically variables versus numbers--and students' algebraic knowledge impacted seventh graders' problem-solving strategies and use…

Purpose: WebQuests are employed for many different instructional aims by offering students to take an active role and encouraging their critical thinking skills to construct their own meaning about an inquiry. The purpose of the study was to explore pre-service mathematics teachers' decisions about the organization of information sources in which…

In this synthesis, we analyzed 10 prealgebraic reasoning interventions for students with mathematics difficulty (MD) in Grades 6 through 8. All interventions focused on one or more prealgebraic concepts including integer operations, algebraic expressions and equations, and functions. Of the 10 intervention studies, six employed single-case design…

This study, firstly, aimed at investigating the various types of the multiple math representations and transitions among them in the 8th grade math textbook, and secondly, teachers' use of these representations in teaching. The current study employed the content analysis approach to investigate the multiple mathematical representations and…

Middle school is a critical time when students begin formal study of functional relationships in algebra. However, many students struggle in understanding functions as relationships between quantities that change according to a dependency relationship. We report on the influence of Scaling Continuous Covariation in fostering productive ideas about…

In this paper, we discuss the utilization of an innovative learning tool, the Sphero BOLT robot, in a 10-day algebra-based mathematics education course for graduate students. Students created routes for their BOLTs to travel and determined ways to measure the distance, rate, and time of their robots' movements. The student prompt, sample student…

The aim of this study was to examine 6th-grade students' mathematical abstraction processes related to the concept of variable by using the teaching experiment method and to reveal their learning trajectories in the context of the RBC+C model. A teaching experiment was administered to a class of 29 middle school students for 3 weeks. Observations,…

To succeed in mathematics middle-years' students must move from additive to multiplicative thinking and from arithmetic calculations to generalised algebraic strategies. If we ask the right questions this progression can be monitored and prompted through fraction tasks. Students' solution strategies for fraction tasks vary from a dependence on…

In this study we investigated the relationship between urban eighth grade students' Hands-On Exposure to Algebraic Thinking (HEAT) competition performance and their subsequent performance on standardized measures of mathematics achievement (ACT Composite Score, ACT Math Scores, and Louisiana Algebra End of Course Exams). It was found that the…

This study examined the effects of two teaching treatments [multiple-representation instruction (MR) and traditional algorithmic instruction (TA)] on students' performance on mathematics problems that integrated fractions, decimals, and percent. Using a 2 × 2 crossover design, the effect of the teaching treatments and their sequences on student…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

An exploratory study was conducted to investigate the use of magic activities in a math course for prospective middle-school math teachers. This research report focuses on a lesson using two versions of math magic: (1) the "5-4-3-2-1-½ Magic" involves having students choose a secret number and apply six arithmetic operations in sequence…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities and…

"University of Chicago School Mathematics Project (UCSMP)" is a core mathematics curriculum that includes materials and a routinized instructional approach with an option for teacher training. The curriculum uses an inquiry-based approach with a focus on active learning where students frequently engage in hands-on activities 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…