Constructing multiplicative reasoning is critical for students' learning of mathematics, particularly throughout the middle grades and beyond. Tzur, Xin, Si, Kenney, and Guebert [American Educational Research Association, ERIC No. ED510991, (2010)] conclude that an assimilatory composite unit is a conceptual spring to multiplicative reasoning.…

In order to investigate the nature of complex problem solving (CPS) within the nomological network of cognitive abilities, few studies have simultantiously considered working memory and intelligence, and results are inconsistent. The Brunswik symmetry principle was recently discussed as a possible explanation for the inconsistent findings because…

Most theories of intelligence do not directly address the question of whether people with high intelligence can successfully solve real world problems. A high IQ is correlated with many important outcomes (e.g., academic prominence, reduced crime), but it does not protect against cognitive biases, partisan thinking, reactance, or confirmation…

Procedural problem solving is an important skill in most technical domains, like programming, but many students reach problem solving impasses and flounder. In most formal learning environments, instructors help students to overcome problem solving impasses by scaffolding initial problem solving. Relying on this type of personalized interaction,…

In research on mathematical problem posing, a broad spectrum of different situations is used to induce the activity of posing problems. This review aims at characterizing these so-called problem-posing situations by conducting three consecutive analyses: (1) By analyzing the openness of potential problem-posing situations, the concept of…

This paper describes LOGAX, an interactive tutoring tool that gives hints and feedback to a student who stepwise constructs a Hilbert-style axiomatic proof in propositional logic. LOGAX generates proofs to calculate hints and feedback. We compare these generated proofs with expert proofs and student solutions, and conclude that the quality of the…

This paper presents a qualitative study developed with a group of 16-year-old students who were asked to estimate large numbers of elements on a bounded surface. Taking the realistic mathematics education framework as a reference, we presented the students with an activity sequence comprised of four different tasks--each one with a different…

The contribution aims at subject-specific analyses of student solutions of an exercise from an electrical engineering signal theory course. The basis for the analyses is provided by praxeological studies (in the sense of the Anthropological Theory of Didactics) and the identification of two institutional mathematical discourses, one related to…

Visual programming environments are popular instruments in teaching Computational Thinking (CT) in schools today. Applying Sense-Reason-Act (SRA) programming can influence the development of computational thinking when forcing pupils to anticipate the unforeseen in their computer programs. SRA-programming originates from the programming of…

In this study we aimed to understand teaching mathematics through problem posing based on an analysis of 22 teaching cases. Teaching mathematics through problem posing starts with problem-posing tasks. This study provides not only specific examples of problem-posing tasks used in classrooms but also related task variables to consider when…

To be able to solve complex information problems in a digital environment is a key 21st century skill. Technology users usually expect to achieve their goals in a fast and accurate way. However, the actual relationship between time-on-task and task outcome is currently not well understood. We analyzed data from a large-scale international study in…

The ability to selectively focus on and remember important information, referred to as value-directed remembering, may be crucial for effective memory functioning. In the present study, we investigated the relationships between metacognitive monitoring and control accuracy, selectivity for valuable information, and fluid intelligence. Mediation…

Teacher-research clubs are an effective and infectious way to solve problems and fuel passion. Educators Sally Donnelly and Megan McCormick discuss how their do-it-yourself teacher research club helped their colleagues gain perspective on problems of practice and grew to be an influential part of their school district.

Functional fixedness involves difficulty with conceptualizing creative object uses. When it obstructs problem-solving, individuals must reframe their approach. We examined how different training techniques--chunk decomposition (i.e., considering an object's basic parts and physical properties) and constraint relaxation (i.e., considering an…

The Productive Failure (PF) approach prompts students to attempt to solve a problem prior to instruction -- at which point they typically fail. Yet, research on PF shows that students who are involved in problem solving prior to instruction gain more conceptual knowledge from the subsequent instruction compared to students who receive the…