The Dirac delta function is a standard mathematical tool that appears repeatedly in the undergraduate physics curriculum in multiple topical areas including electrostatics, and quantum mechanics. While Dirac delta functions are often introduced in order to simplify a problem mathematically, students still struggle to manipulate and interpret them.…

The research paradigm invented by Allen Newell and Herbert A. Simon in the late 1950s dominated the study of problem solving for more than three decades. But in the early 1990s, problem solving ceased to drive research on complex cognition. As part of this decline, Newell and Simon's most innovative research practices--especially their method for…

We developed an intervention based on the learning by teaching paradigm to foster self-regulatory processes and better learning outcomes during complex mathematics problem solving in a technology-rich learning environment. Seventy-eight elementary students were randomly assigned to 1 of 2 conditions: learning by preparing to teach, or learning for…

In this paper we investigated the contribution of a dynamic testing procedure, including multiple graduated prompts protocols, in identifying differences in need for instruction of second grade children (N = 120) with arithmetic difficulties. The training was adaptive and prompts were provided according to one of six protocols, each focusing on a…

This pilot study, involving PGCE primary student teachers, applies "Livescribe" pen technology to facilitate individual and group reflection on collaborative mathematical problem solving (Hickman 2011). The research question was: How does thinking aloud, supported by digital audio recording, support student teachers' understanding of…

Twenty-four mathematics teachers were asked to think aloud when posing a word problem whose solution could be found by computing 4/5 divided by 2/3. The data consisted of verbal protocols along with the written notes made by the subjects. The qualitative analysis of the data was focused on identifying the structures of the problems produced and…

In configuration problems, such as the construction of a weekly study schedule, decision makers must assemble a combination of parts under a set of constraints. Interactions may be present between the parts, and more than a single objective function may exist, such as minimizing the number of days on campus and maximizing the interest level of the…

Empirical evidence on the way in which expert designers from different domains cognitively connect their internal processes with external resources is presented in the context of an extended cognition model. The article focuses briefly on the main trends in the extended design cognition theory and in particular on recent trends in information…

Thirty-six secondary school students aged 14-16 were interviewed while they chose between a table, a graph or a formula to solve three linear function problems. The justifications for their choices were classified as (1) task-related if they explicitly mentioned the to-be-solved problem, (2) subject-related if students mentioned their own…

This study considers the role and nature of co-thought gestures when students process map-based mathematics tasks. These gestures are typically spontaneously produced silent gestures which do not accompany speech and are represented by small movements of the hands or arms often directed toward an artefact. The study analysed 43 students (aged…

This article explores the use of protocol-structured dialogue in promoting reflective practices and shared theories of action within a district leadership team. Protocols have been used to make individuals' theories of action visible and subject to evaluation. This is important for leaders trying to establish coherence across a system; in…

The study explores the development of 11-year-old students' informal inference about random bunny hops through student talk and use of computer simulation tools. Our aim in this paper is to draw on dialogic theory to explain how students make shifts in perspective, from intuition-based reasoning to more powerful, formal ways of using probabilistic…

The effective use of reading strategies has been recognized as an important way to increase reading comprehension in hypermedia environments. The purpose of the study was to explore whether metacognitive strategy use and access to hypermedia annotations facilitated reading comprehension based on English as a foreign language students' proficiency…

The authors present a project that aims at understanding the way language learners write in social media in their every day lives using the target language. How do our students proceed when writing a Social Network Site (SNS) post? What resources do they use for references on word, sentences and text level? By answering these and related questions…

This paper describes the outcomes of a qualitative investigation into the range of different approaches that students use to solve open-ended, context rich problems. The study involved a small cohort of students individually solving open-ended, context-rich problems using a think aloud protocol. The problems required the students to develop a…