A basic mental model (BMM--in German 'Grundvorstellung') of a mathematical concept is a content-related interpretation that gives meaning to this concept. This paper defines normative and individual BMMs and concretizes them using the integral as an example. Four BMMs are developed about the concept of definite integral, sometimes used in specific…

Concept maps are powerful tools used to reveal challenges in students' learning. However, their use introduces complexities when a large group of students' conceptualizations need to be examined. In this study, concept maps of 344 general chemistry students were analyzed after grouping them based on achievement in chemistry, math proficiency, and…

This study was carried out in order to determine how the 3rd grade students of the Department of Elementary Mathematics Education structured their "if and only if propositions". The data were obtained by examining the students' answers given to the midterm exam questions and discussing the solutions with the students in the classroom.…

Cognitive Diagnostic Assessment (CDA) is an alternative assessment which can give a clear picture of pupils' learning process and cognitive structures to education stakeholders so that appropriate instructional strategies can be designed to tailored pupils' needs. Coincide with this function, the Ordered Multiple-Choice (OMC) items were…

This study explored a diagnostic assessment method that emphasized the cognitive process of algebra learning. The study utilized a design and a theory-driven model to examine the content knowledge. Using the theory driven model, the thinking skills of algebra learning was also examined. A Bayesian network model was applied to represent the theory…

The purpose of the study is to present research focused on validating the four algebra cognitive models in Gierl, Wang, et al., using student response data collected with protocol analysis methods to evaluate the knowledge structures and processing skills used by a sample of SAT test takers.

Most research on differential item functioning (DIF) focuses on methods for detection rather than on understanding why DIF might occur. This study was designed to investigate whether two alternative approaches to parsing items based on structural characteristics related to particular cognitive strategies could be used to help explain gender DIF.…

This study investigated the propositions that (1) the expressed preference for formal-deductive style of thinking and mathematics anxiety are negatively correlated; (2) the preferred cognitive style is positively correlated with the respondent's self-assessment of mathematical ability; and (3) those expressing a preference for the analyst style of…

Many significant changes in perspective have to take place before efforts to learn the content and capabilities of children's minds can hold much sway in educational testing. The language of testing, especially of high stakes testing, remains firmly in the realm of "behaviors", "performance" and "competency" defined…

This book contains a compilation of papers presented at the International Conference on Education and New Developments (END 2017), organized by the World Institute for Advanced Research and Science (W.I.A.R.S.). Education, in our contemporary world, is a right since we are born. Every experience has a formative effect on the constitution of the…

The cognitive structure of an algebra test was defined and validated using the linear test model (LLTM) and quadratic assignment (QA) techniques. The LLTM is an extension of the Rasch model with a linear constraint that describes item difficulty in terms of the cognitive operations required to solve the item. The model permits the specification of…

This report reviews a theoretically inspired empirical investigation of individual differences in knowledge, abilities, and nonability traits as part of an ongoing effort to better understand adult intellectual development and to develop more accurate measures of adult intelligence. Twenty Knowledge Scales were constructed, drawing on…