This study was performed to determine preservice elementary mathematics teachers' solution performance of systems of linear equations using geometric representation, algebraic representation and transition from geometric representation to the algebraic representation and the predictive role of preservice elementary mathematics teachers'…

Learners' choices as to whether and how to use visual representations during learning are an important yet understudied aspect of self-regulated learning. To gain insight, we developed a "choice-based" intelligent tutor in which students can choose whether and when to use diagrams to aid their problem solving in algebra. In an…

Students often perform arithmetic using rigid problem-solving strategies that involve left-to-right-calculations. However, as students progress from arithmetic to algebra, entrenchment in rigid problem-solving strategies can negatively impact performance as students experience varied problem representations that sometimes conflict with the order…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Prior research has shown that game-based learning tools, such as DragonBox 12+, support algebraic understanding and that students' in-game progress positively predicts their later performance. Using data from 253 seventh-graders (12-13 years old) who played DragonBox as a part of technology intervention, we examined (a) the relations between…

Does the timing of children's formal understanding of mathematical equivalence matter for algebra readiness? A change-resistance account (McNeil & Alibali, 2005) predicts that it is beneficial for children to construct a formal understanding of mathematical equivalence in the early grades before overly narrow operational patterns become…

We studied the impact of metacognitive reflections on recently-completed work as a way to improve the retention of newly learned problem-solving techniques. Students video recorded themselves talking through problems immediately after finishing them, completed ongoing problem-solving strategy maps or problem-sorting exercises, and filled out…

In the present research, we provide empirical evidence for the process of symbolic integration of number associations, focusing on the development of simple addition (e.g., 5 + 3 = 8), subtraction (e.g., 5 - 3 = 2), and multiplication (e.g., 5 × 3 = 15). Canadian children were assessed twice, in Grade 2 and Grade 3 (N = 244; 55% girls). All…

The study determined the problem-solving performance and skills of prospective elementary teachers (PETs) in the Northern Philippines. Specifically, it defined the PETs' level of problem-solving performance in number sense, measurement, geometry, algebra, and probability; significant predictors of their problem-solving performance in terms of sex,…

This study investigated the cognitive factors that impact the completion of mathematics problems, specifically algebraic-reasoning, by individuals who use tactile materials (i.e., braille) compared to those who use print materials. The inquiry investigated working memory, task time, cognitive load, efficiency, and the predictive quality of…

This study focused on how two algebraic concepts- equality and variable- predicted 8th grade students' equation solving performance. In this study, predictive design as a correlational research design was used. Randomly selected 407 eight-grade students who were from the central districts of a city in the central region of Turkey participated in…

Children in the elementary grades are expected to solve equations to demonstrate prealgebraic proficiency. Prealgebraic differences may emerge based equation type (i.e., standard vs. nonstandard), the operation shown or required for solution (i.e., addition or subtraction), and the position of the unknown. Prealgebraic differences may also be…

The study assessed the relative effectiveness of understanding the problem statement on students' mathematical behaviours in Borno State Secondary Schools. The study was guided by an objective: to determine the Understanding the problem statement on student's performance in senior secondary school and a null hypothesis: there was no effect of…

Proportional thinking, which requires understanding fractions, ratios, and proportions, is an area of mathematics that is cognitively challenging for many children and adolescents (Fujimura, 2001; Lamon, 2007; Lobato, Ellis, Charles, & Zbiek, 2010; National Mathematics Advisory Panel [NMAP], 2008) and "transcends topical barriers in adult…

Three questions were addressed in this study. Is there evidence of epistemological beliefs congruency between students and their instructor? Do students' epistemological beliefs, students' epistemological congruence, or both predict mathematical anxiety? Do students' epistemological beliefs, students' epistemological congruence, or both predict…