In a PBL environment, learning results from learners engaging in cognitive processes pivotal in the understanding or resolution of the problem. Using Tan's cognitive function disc, this study examines the learner's perceived cognitive functions at each stage of PBL, as facilitated by the PBL schema. The results suggest that these learners…

The present research investigated analogical transfer during problem solving by bilinguals. In a study with 50 Spanish-English bilinguals, participants solved a target problem whose solution was similar to that of a preceding source problem. The source problem was always presented in the 2nd language; the target problem was always presented in the…

The main goal of this study is to find out the effect of the instructional design method on the enhancement of problem solving abilities of students. Teaching sessions were applied to ten students who are in 11th grade, to teach them problem solving strategies which are working backwards, finding pattern, adopting a different point of view,…

Mathematical discussions in which students compare alternative solutions to a problem can be powerful modes for students to engage and refine their misconceptions into conceptual understanding, as well as to develop understanding of the mathematics underlying common algorithms. At the same time, these discussions are challenging to lead…

A local urban school district recently reported that 86% of third graders did not demonstrate proficiency on the Math Standardized Test, which challenges students to solve problems and justify solutions. It is beneficial if these skills are developed prior to third grade. Students may be more academically successful if kindergarten teachers have…

Generalization has been identified as a cornerstone of algebraic thinking (e.g., Lee, 1996; Sfard, 1995) and is at the center of a rich conceptualization of K-8 algebra (Kaput, 2008; Smith, 2003). Moreover, mathematics teachers are being encouraged to use figural-pattern generalizing tasks as a basis of student-centered instruction, whereby…

A challenge in mathematics education research is to coordinate different analyses to develop a more comprehensive account of teaching and learning. I contribute to these efforts by expanding the constructs in Cobb and Yackel's (1996) interpretive framework that allow for coordinating social and individual perspectives. This expansion involves four…

Existing technologies pose challenges for the education system related to what contents, strategies and skills students should learn and what types of teaching scenarios should be considered in learning. In this study, prospective high school teachers were encouraged to systematic use various digital technologies in a problem solving course during…

Our study investigates preservice teachers' perceptions of real-world problems; their beliefs about teaching real-world contexts, especially ones sociopolitical in nature; and their ability to pose meaningful real-world problems. In this paper we present cases of three preservice teachers who participated in interviews that probed their thinking…

Considering the update of curricula and the importance of problem solving skills in mathematics education; the need for examining the problems in mathematics textbooks in the context of presentation, content, and solution becomes a current issue. In this study, it was aimed to designate the problem types used in middle school mathematics textbooks…

The "Program for the International Assessment of Adult Competencies" (PIAAC) is a cyclical, large-scale study of adult skills and life experiences focusing on education and employment. Nationally representative samples of adults between the ages of 16 and 65 are administered an assessment of literacy, numeracy, and problem solving in…

Highly capable mathematics students are not usually considered strugglers. This paper reports on a case study of a Year 6 student, Debbie, her response to a lesson, and her learning involving a challenging mathematical task. Debbie, usually a highly capable student, struggled to complete a challenging mathematical task by herself, but as the…

This paper explores young children's drawings (6 years old) in early number and addition activities in Malaysia. Observation, informal interviews and analysis of drawings revealed two types of drawing, and gave insight into the transitional process required for children to utilise drawings in problem solving. We argue the importance of valuing and…

This study explored the potential of a rich assessment task to reveal students' multiplicative thinking in respect to a hypothetical learning trajectory. Thirty pairs of students in grades 5 and 6 attempted the task. Twenty-two pairs applied multiplicative structure to find the number of items in arrays. However counting and computational errors…

The purpose of this paper is to show how important "monitoring" is as metacognitive skills in solving physics problems in the field mechanics. Based on test scores, twenty one students were divided into two groups: more successful (MS) and less successful (LS) problem solvers. Students were allowed to think-aloud while they worked on…