This article sheds light and reflects on how students in grades seven and eight read and understand implicit data when solving a story problem. Problem solving experiences help in adding up to the child's mathematical knowledge and promote a higher level of critical thinking abilities. Seventh and eighth grade students were selected from two…

The purpose of this research was to develop and test a model of factors contributing to science, technology, engineering, and mathematics (STEM) learning and career orientation, examining the complex paths and relationships among social, motivational, and instructional factors underlying these outcomes for middle school youth. Social cognitive…

Research shows that the greatest gains in student learning in mathematics classrooms occur in classrooms in which there is sustained use of high cognitive demanding tasks throughout instruction (Boston and Smith 2009). High cognitive demanding tasks, which this article will refer to as rich tasks, are mathematics problems that are complex, less…

Although students' invented strategies typically prove to be effective in the improvement of students' mathematical understanding, little is known about how preservice teachers interpret and respond to student-invented strategies on whole number multiplication. This study investigated the nature of 25 preservice teachers' interpretations of and…

This study aims to understand students' constructs regarding mathematical problems. Fifty-one Taiwanese primary students' constructs are elicited using interviews with the repertory grid technique based on their responses to creative and non-creative problems. The results of qualitative data analysis show that students' initial constructs can be…

We examined the use of problem solving videos (PSVs) as a substitute for general chemistry exam review sessions. We investigated student perceptions of course aspects regarding usefulness for supporting their learning of chemistry content. We also examined "how" students used the PSVs to further their learning. Students ranked the PSVs…

"English Language Learners" (ELLs) at risk for "math disabilities" (MD) are challenged in solving word problems for numerous reasons such as (a) learning English as a second language, (b) limited experience using math vocabulary, and (c) lack of strategies to improve word-problem-solving skills. As a result of these…

The purpose of this study is to assess students' conceptual learning of electricity and magnetism and examine how these conceptions, beliefs about physics, and quantitative problem-solving skills would change after peer instruction (PI). The Conceptual Survey of Electricity and Magnetism (CSEM), Colorado Learning Attitudes about Science Survey…

Physics students can encounter difficulties in physics problem solving as a result of failing to use knowledge that they have but do not perceive as relevant or appropriate. In previous work we have demonstrated that some of these difficulties may be epistemological. Students may limit the kinds of knowledge that they use. For example, they may…

Research has demonstrated that instruction that relies more heavily on example study is more effective for novices' learning than instruction consisting of problem solving. However, "a heavier reliance on example study" has been implemented in different ways. For example, worked examples only (WE), example-problem pairs (WE-PS), or problem-example…

Pat was a 19-year-old attending a Special School for the Intellectually Disabled in Indonesia. She was interviewed by the first author regarding her mental calculation strategies when solving 1- and 2-digit addition and subtraction problems. Results indicate that she was able to see ten as a unit composed of ten ones and was facile in using…

What "is" mathematics? What does it mean to "do" mathematics? The answers to these two questions critically influence the ways in which learners respond to a mathematical problem. On the other hand, if they see questions as having only one correct answer and as needing to be solved in one particular way, they will be prone to…

The worked-example effect, an application of cognitive load theory, is a well-supported method of instruction for well-structured problems (Chandler and Sweller, 1991; Cooper and Sweller, 1987; Sweller and Cooper, 1985; Tuovinen & Sweller, 1999; Ward and Sweller, 1990). One limitation is expertise-reversal effect, where advanced students…

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem-solving and metacognitive…

This experimental study evaluated the effectiveness of a research-based intervention, schema-based instruction (SBI), on students' proportional problem solving. SBI emphasizes the underlying mathematical structure of problems, uses schematic diagrams to represent information in the problem text, provides explicit problem solving and metacognitive…