This paper describes the preliminary stages in physics problem-solving related to the use of external representation. This empirical study was carried out using a phenomenographic approach to analyze data from individual thinking-aloud and interviews with 8 senior high school students and 7 physics teachers. The result of this study is a set of…

The paper presents and analyses a sequence of events that preceded an insight solution to a challenging problem in the context of numerical sequences. A three­week long solution process by a pair of ninth­-grade students is analysed by means of the theory of shifts of attention. The goal for this article is to reveal the potential of this theory…

Despite the importance placed on how children come to solve single-digit addition problems, many children count on to solve these problems when they are expected to use accurate retrieval-based strategies. In this study, we assessed if a subitising intervention improved the rate at which problem-solving practice promoted retrieval, using a…

This study discusses the construction of deductive warrant derived from inductive warrant in mathematical argumentations expressed by pre-service teacher. In completing a mathematics task, a problem solver needs argumentation to determine, reveal, and support a reasonable solution. A mathematical argumentation can be analyzed by Toulmin scheme…

Initiatives to integrate engineering design in the elementary science classroom have become increasingly evident in both national reform documents and classroom practice. Missing from these efforts is a purposeful attempt to capture students' designerly thinking and dialogues as they engage in the process. The purpose of this study was to…

This study explores the civic thinking heuristics that civic leaders use when pre-planning action. Across eight think-aloud protocols, findings suggest that three heuristics are employed. "Frame alignment" refers to the process of harmonizing personal beliefs and interests with the particulars of a civic action issue to find personal…

The authors investigated the differences in using problem decomposition and problem recomposition between dyads of engineering experts, engineering seniors, and engineering freshmen. Participants worked in dyads to complete an engineering design challenge within 1 hour. The entire design process was video and audio recorded. After the design…

Comparing datasets, that is, sets of numbers in context, is a critical skill in higher order cognition. Although much is known about how people compare single numbers, little is known about how number sets are represented and compared. We investigated how subjects compared datasets that varied in their statistical properties, including ratio of…

Research on problem solving typically does not address tasks that involve following detailed and/or illustrated step-by-step instructions. Such tasks are not seen as cognitively challenging problems to be solved. In this paper, we challenge this assumption by analyzing verbal protocols collected during an Origami folding task. Participants…

A coding scheme is presented and used to evaluate solutions of seventeen students working on twenty five stoichiometry problems in a think-aloud protocol. The stoichiometry problems are evaluated as a series of sub-problems (e.g., empirical formulas, mass percent, or balancing chemical equations), and the coding scheme was used to categorize each…

Problem solving research has encountered an impasse. Since the seminal work of Newell und Simon (1972) researchers do not seem to have made much theoretical progress (Batchelder and Alexander, 2012; Ohlsson, 2012). In this paper we argue that one factor that is holding back the field is the widespread rejection of introspection among cognitive…

Open-ended problem solving is a central skill in engineering practice; consequently, it is imperative for engineering students to develop expertise in solving these types of problems. The complexity of open-ended problems requires a unique set of skills. The purpose of this qualitative study was to investigate the approaches used by engineering…

This paper describes the results of a qualitative study using ground theory to investigate the different approaches used by chemists when answering open-ended problems. The study involved undergraduate, industrialist and academic participants who individually answered three open-ended problems using a think aloud protocol. Open-ended problems are…

The Common Core Standards require students to learn content and mathematical practices, and so teachers must have content knowledge and be able to engage in practices themselves. This raises the question of how novice teachers learn to engage in mathematical practices. I investigate pre-service secondary teacher learning of mathematical practices…

This study aims to describe the constructive metacognitive activity shift of eleventh graders in solving a mathematical problem. Subjects in this study were 10 students in grade 11 of SMAN 1 Malang. They were divided into 4 groups. Three types of metacognitive activity undertaken by students when completing mathematical problem are awareness,…