This paper discusses findings from an ongoing study investigating mental mechanisms involved in the conceptualisation of linear transformations from the perspective of Action (A), Process (P), Object (O), and Schema (S) (APOS) theory. Data reported in this paper came from 44 first-year linear algebra students' responses on a task regarding the…

This study investigated how and how often to present prompts to enhance students' source evaluation and multiple-text comprehension. Participants were 72 undergraduates who read a set of digital texts on a controversial topic of smartphone use and mental health, wrote a justification statement for their selection of trustworthy texts, and answered…

Network models of the WAIS-IV based on regularized partial correlation matrices have been reported to outperform latent variable models based on uncorrected correlation matrices. The present study sought to compare network and latent variable models using both partial and uncorrected correlation matrices with both types of models. The results show…

Meta-reasoning refers to processes by which people monitor problem-solving activities and regulate effort investment. Solving is hypothesized to begin with an initial Judgment of Solvability (iJOS)--the solver's first impression as to whether the problem is solvable--which guides solving attempts. Meta-reasoning research has largely neglected…

This paper provides a tutorial on epistemic network analysis (ENA), a novel method for identifying and quantifying connections among elements in coded data and representing them in dynamic network models. Such models illustrate the structure of connections and measure the strength of association among elements in a network, and they quantify…

The research examined relational processing following stroke. Stroke patients (14 with frontal, 30 with non-frontal lesions) and 41 matched controls completed four relational processing tasks: sentence comprehension, Latin square matrix completion, modified Dimensional Change Card Sorting, and n-back. Each task included items at two or three…

Many educational data mining studies have explored methods for discovering cognitive models and have emphasized improving prediction accuracy. Too few studies have "closed the loop" by applying discovered models toward improving instruction and testing whether proposed improvements achieve higher student outcomes. We claim that such…

This article analyses students' thinking as they interacted with a dynamic geometric sketch designed to explore eigenvectors and eigenvalues. We draw on the theory of instrumental genesis and, in particular, attend to the different dragging modalities used by the students throughout their explorations. Given the kinaesthetic and dynamic…

This study is part of ongoing research in undergraduate mathematics education. The study was guided by the belief that understanding the mental constructions the pre-service teachers make when learning matrix algebra concepts leads to improved instructional methods. In this preliminary study the data was collected from 85 pre-service teachers…

In this article, the authors present a tool, the Cognitive Rigor Matrix (CRM; Hess et al. 2009), as a means to analyze and reflect on the type of questions posed by mathematics teachers. This tool is intended to promote and develop higher-order thinking and inquiry through the use of purposeful questions and mathematical tasks. The authors…

A key issue of cognitive diagnostic models (CDMs) is the correct identification of Q-matrix which indicates the relationship between attributes and test items. Previous CDMs typically assumed a known Q-matrix provided by domain experts such as those who developed the questions. However, misspecifications of Q-matrix had been discovered in the past…

The authors discuss empirically determined competence areas to K-12 computer science education, emphasizing the cognitive level of competence. The results of a questionnaire with 120 professors of computer science serve as a database. By using multi-dimensional scaling and cluster analysis, four competence areas to computer science education…

Through a series of six guided classroom discoveries, students create, via targeted questions, a definition for deciding when two sets have the same cardinality. The program begins by developing basic facts about cardinalities of finite sets. Extending two of these facts to infinite sets yields two statements on comparing infinite cardinalities…

Mood affects the way people think. But can the way people think affect their mood? In the present investigation, we examined this promising link by testing whether mood is influenced by the presence or absence of associative progression by manipulating the scope of participants' information processing and measuring their subsequent mood. In…

Cognitive diagnostic analyses have been advocated as methods that allow an assessment to function as a formative assessment to inform instruction. To use this approach, it is necessary to first identify the skills required for each item in the test, known as a Q-matrix. However, because the construct being tested and the underlying cognitive…