Extant research has demonstrated that problem-posing and problem-solving mutually affect one another. However, the exact nature and extent of this relationship requires a detailed elaboration. This is especially true when adidactical problem-posing arises within a problem-solving context. In this study, we analyze the scripting journey used by two…

What difficulties do architecture students encounter in the structural design for their final master project? How do they address these difficulties? This paper presents the topic and focuses on these two research questions by examining the students' experience, using thematic analysis with a qualitative approach. We obtained the data through…

The book that inspired millions of educators to refine their approach to teaching returns for an all-new third edition. Built on a more rigorous research base and updated to emphasize student diversity, equity, and inclusion, "The New Classroom Instruction That Works" offers a streamlined focus on the 14 instructional strategies proven…

Helping students learn to think like a physicist is an important goal of many introductory physics courses. One characteristic distinguishing more experienced physicists from novice students is that they make better use of problem solving as a learning opportunity. Experts were found to spend more time than novices in monitoring their work,…

What are the nature, forms, and roles of metaphors in mathematics instruction? We present and closely analyze three examples of idiosyncratic metaphors produced during one-to-one tutorial clinical interviews with 11-year-old participants as they attempted to use unfamiliar artifacts and procedures to reason about realistic probability problems.…

This study investigates problem-solving difficulties of novices in a classroom setting, using a German instructional tool, the Fischertechnik kit of approximately 400 parts. In order to analyse the students' thinking processes as they solved the problems, verbal protocol analysis (VPA) was used to record the students'' thinking processes and…

In an attempt to further understand connections between children's proficiency and development with single- and multidigit addition, this study investigated the conceptualizations and solution strategies of 26 first-graders presented with several single-digit, multiple addend addition problems. The changes in students' solution strategies over the…

Digital systems offer computational power and instant feedback. Game designers are using these features to create scaffolding tools to reduce player frustration. However, researchers are finding some unexpected effects of scaffolding on strategy development and problem-solving behaviors. We used a digital Sudoku game named "Professor Sudoku" to…

In this article, pre-service teachers' mathematics content knowledge is explored through the analysis of two items about ratio from a Mathematical Competency, Skills and Knowledge Test. Pre-service teachers' thinking strategies, common errors and misconceptions in their responses are presented and discussed. Of particular interest was the range…

This study investigated the students' learning process of the concept of concentration at the elementary school level in Taiwan. The influence of different representational types on the process of proportional reasoning was also explored. The participants included nineteen third-grade and eighteen fifth-grade students. Eye-tracking technology was…

The Models and Modeling Perspectives (MMP) has evolved out of research that began 26 years ago. MMP researchers use Model Eliciting Activities (MEAs) to elicit students' mental models. In this study MMP was used as the conceptual framework to investigate the nature of students' models of curve fitting in a problem-solving environment consisting of…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

In the present article, we articulate three assumptions underlying theories proposing that restructuring processes play a key role in insightful problem solving: representational difficulty, representational change, and discontinuity in solution processes. We argue that these assumptions need empirical validation to justify the proposition of…

Offers a progressive series of eight lessons designed to guide students in generating questions, creating investigations, and finding answers. (AIM)

Algorithmic and investigative approaches to mathematics are compared and discussed. Their mutually contradictory spirit is explored. Examples of the application of each method to a mathematics problem are presented. (CW)