The purpose of this study was to explore the paths by which word-problem intervention, with versus without embedded pre-algebraic reasoning instruction, improves word-problem performance. Students with mathematics difficulty (MD; n = 304) were randomly assigned to a business-as-usual condition or one of two variants of word-problem intervention.…

Human-driven carbon emissions have resulted in increased levels of dissolved carbon dioxide in the Earth's oceans. This dissolved carbon dioxide reacts with water to form carbonic acid, which impacts ocean acidity as well as the solubility of carbonate-containing compounds, with far-reaching impacts on marine ecosystems and the human communities…

Algebraic Thinking (AT) and Computational Thinking (CT) are pivotal competencies in modern education, fostering problem-solving skills and logical reasoning among students. This study presents the initial hypotheses, theoretical framework, and key steps undertaken to explore characterized learning paths and assign practice-relevant tasks. This…

Powell, Berry, et al. (in press) conducted a randomized control trial assessing the effects of two variants of word-problem intervention with third graders (n = 304) experiencing mathematics difficulty. Students were assigned to a business-as-usual condition (BaU) or one of two variants of word-problem intervention. One variant included a…

This quasi-experimental design study aimed to examine how exposure to supporting productive struggle teaching practice impacts students' conceptual understanding, procedural fluency, and strategic competence when solving high-demanding quadratic functions problem solving tasks. Results suggested that students in the supporting productive struggle…

Students in the elementary grades often experience difficulty setting up and solving word problems. Using an equation to represent the structure of the problem serves as an effective tool for solving word problems, but students may require specific pre-algebraic reasoning instruction about the equal sign as a relational symbol to set up and solve…

Comparison is a powerful and important way that we learn. To support teachers in the use of comparison in their instruction, the authors developed an instructional routine called compare and discuss multiple strategies (CDMS). Similar to other instructional routines, CDMS is a structured, specific, repeatable minilesson that teachers can use to…

Productive failure has shown positive effects on conceptual and transfer measures, but no clear effects on procedural measures. It is therefore an open question whether, and to what extent, productive failure methods may be used to enhance the learning of procedural skills. A typical productive failure study focuses on a single, complex concept;…

Analyzing and interpreting student thinking through written work is a key, often challenging, practice of teaching. It entails noticing students' mathematical thinking and drawing on mathematical knowledge for teaching. This study investigates how pre-service secondary teachers at the beginning of their preparation reason about students' written…

The purpose of this quantitative, quasi-experimental study was to determine if, and to what extent, technology-enhanced problem-based formative assessment instruction would have an impact on college students' algebra learning and development of critical thinking skills, when compared to traditional classroom instruction in a first-year college…

Context personalization--the incorporation of students' out-of-school interests into learning tasks--has recently been shown to positively affect students' situational interest and their performance and learning in mathematics. However, few studies have shown effects on both interest and achievement, drawing into question whether context…

We examined the influences of pre-solving pause time, algebraic knowledge, mathematics self-efficacy, and mathematics anxiety on middle-schoolers' strategy efficiency in an algebra learning game. We measured strategy efficiency using (a) the number of steps taken to complete a problem; (b) the proportion of problems completed on the initial…

The present study examines the effectiveness of incorporating worked examples with prompts for self-explanation into a middle school math textbook. Algebra 1 students (N = 75) completed an equation-solving unit with textbooks either containing the original practice problems or in which a portion of those problems were converted into a combination…

We designed a rubric to assess free-response exam problems in order to compare thinking skills evidenced in exams in classes taught by different pedagogies. The rubric was designed based on Bloom's taxonomy and then used to code exam problems. We have analyzed historical and recent exam problems in both algebra-based and calculus-based exams. In…

Cara, a seventh-grade student with learning disabilities (LD) in mathematics, believes that the ratio 2:3 is equivalent to 4:5 because there is a difference of one between the two numbers in each ratio and there is a difference of two between corresponding numbers in the two ratios (2 + 2 = 4 and 3 + 2 = 5). This misconception affects her ability…