This study investigates the effects of metacognitive and cognitive strategies for computational thinking (CT) on managing cognitive load and enhancing problem-solving skills in collaborative programming. Four different scaffolding conditions were provided to help learners optimize cognitive load and improve their problem-solving abilities. A total…

In mathematics, problem-solving can be considered to be one of the most important skills students need to develop, because it allows them to deal with increasingly intricate mathematical and real-life issues. Often, teachers attempt to try to link a problem with a drawn diagram or picture. Despite these diagrams, whether given or constructed, the…

Objective: Explicit instructions to students to use the index finger to trace out specified elements of mathematics worked examples have been shown to improve mathematics learning outcomes; however, there is limited research on whether the magnitude of tracing actions impacts these outcomes. Method: Using an experimental design, 34 adults were…

This lecture reports on aspects of a larger research programme focused on studying mental mathematics in elementary and secondary mathematics classrooms. It specifically addresses an unplanned aspect that became salient through the work conducted in these classrooms. In this research programme, mental mathematics sessions are designed on a variety…

There is a growing awareness that many children are not developing fast and accurate retrieval-based strategies for solving single-digit addition problems. In this study we individually assessed 166 third and fourth grade children to identify a group of children (called accurate-min-counters) who frequently solved simple single-digit addition…

Covariational reasoning has been the focus of many studies but only a few looked into this reasoning in the polar coordinate system. In fact, research on student's familiarity with polar coordinates and graphing in the polar coordinate system is scarce. This paper examines the challenges that students face when plotting polar curves using the…

In two experiments, we studied how people's strategy choices emerge through an initial and then a more considered evaluation of available strategies. The experiments employed a computer-based paradigm where participants solved multiplication problems using mental and calculator solutions. In addition to recording responses and solution times, we…

This paper reports on a study to examine mental computation strategies used by Year 1, Year 2, and Year 3 students to solve addition and subtraction problems. The participants in this study were twenty five 7 to 9 year-old students identified as excellent, good and satisfactory in their mathematics performance from a school in Penang, Malaysia.…

Individual differences in strategy use (choice and accuracy) were analyzed. A sample of 362 Grade 6 students solved complex division problems under 2 different conditions. In the choice condition students were allowed to use either a mental or a written strategy. In the subsequent no-choice condition, they were required to use a written strategy.…

One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…

This study identified 10 savants with developmental disabilities and an exceptional ability to calculate calendar dates. These "calendar calculators" were asked to demonstrate their abilities, and their strategies were analyzed. The study found that the ability to calculate dates into the past or future varied widely among these…

Described in the context of a computer simulation are highlights of a program of research focusing on the storage of mathematics problem solving information in young children's memory and the development of such knowledge structures in older children. Specifically discussed are the problem size effect, the network nature of the memory…

Presents a student module modeling knowledge states and learning skills of students in the field of Newtonian dynamics. Uses data recorded during the exploratory activity in microworlds to infer mental representations concerning the concept of force. A fuzzy algorithm able to follow the cognitive states the student goes through in solving a task…

This study focuses on the mental processes used during estimation. This research: (1) developed an operational definition of estimation; (2) created an instrument to identify exceptionally good estimators; (3) collected performance level data on 1187 subjects; (4) constructed interview problems and developed protocols to identify the thinking…

Data were generally consistent with the view that preschoolers and elementary schoolers can respond to memory probes by applying arithmetical processing to running gist from recently solved problems. Discussed are two competing interpretations of the development of working memory: fuzzy-trace theory and the generic-resources hypothesis. (Author/RH)