This paper reports on students' conceptions of minima points. Written assignments and individual interviews uncovered salient, concept images, as well as erroneous "mis-out examples" that mistakenly regard examples as non-examples and "mis-in examples" that mistakenly grant non-examples the status of examples. We used Tall and…

This study answers the following research questions: 1) What types of mathematical errors do future teachers identify when they reflect on their practice? and 2) Which levels of development of the didactic suitability assessment competence for the "errors" component can be inferred when they reflect on their practice? To answer these…

We know that making mistakes in mathematics is an inherent attribute of doing mathematics deeply. Yet, making mistakes is at the root of mathematical fear and anxiety for elementary preservice teachers (PSTs). Valuing mistakes in mathematics is an essential part of shifting from deficient views to asset views of mistakes and having better…

Background: Mapping fraction symbols to magnitudes is easier for students to master than comparing fraction magnitudes. Fraction mapping assesses students' understanding of part-whole interpretations of fractions; fractions represent the parts of an object or set of objects. Fraction comparison assesses students' understanding of measurement…

The aim of this study is to investigate the effect of positive error climate in classrooms on middle school students' error orientations and attitudes towards mathematics. The data of the research were collected in the 2021-2022 academic year. The participants of the study consisted of 44 students in two 6th grade classes in a middle school in the…

Background: Committing errors is a common part of the learning process, and adults are more likely to correct errors that they can recall. However, preadolescent children's recall of previous errors (i.e., memory for errors) may be limited. Aims: We examined children's ability to recall their past errors and tested whether recalling an error aids…

We encounter variables with little variation often in educational data mining (EDM) due to the demographics of higher education and the questions we ask. Yet, little work has examined how to analyze such data. Therefore, we conducted a simulation study using logistic regression, penalized regression, and random forest. We systematically varied the…

One major aim of international large-scale assessments (ILSA) like PISA is to monitor changes in student performance over time. To accomplish this task, a set of common items (i.e., link items) is repeatedly administered in each assessment. Linking methods based on item response theory (IRT) models are used to align the results from the different…

As a theory of skill acquisition, the instance theory of automatization posits that, after a period of training, algorithm-based performance is replaced by retrieval-based performance. This theory has been tested using alphabet-arithmetic verification tasks (e.g., is A + 4 = E?), in which the equations are necessarily solved by counting at the…

Evaluation of the cosine function is done via a simple Cordic-like algorithm, together with a package for handling arbitrary-precision arithmetic in the computer program Matlab. Approximations to the cosine function having hundreds of correct decimals are presented with a discussion around errors and implementation.

In this study, we replicate and extend prior work that investigates the extent to which content-specific and non-content-specific measures of instruction mediate the relationships between teacher knowledge and student achievement gains. We further probe the extent to which classroom and district context moderate the individual and collective…

We investigated the influence of context on students' understanding of cross products of vectors using three isomorphic multiple-choice tests asking for the direction of a cross product in different geometrical settings. One version of the test involved the Lorentz force, the second version involved the torque on an electric dipole, and the third…

Students' difficulties in quantum mechanics may be the result of unproductive framing rather than a fundamental inability to solve the problems or misconceptions about physics content. Using the theoretical lens of epistemological framing, we applied previously developed frames to seek an underlying structure to the long lists of published…

The purpose of this study was to understand and compare the types of errors students with a specific learning disability in reading and/or writing (SLD-R/W) and those with a specific learning disability in math (SLD-M) made in the areas of reading, writing, language, and mathematics. Clinical samples were selected from the norming population of…

Although Error Analysis (EA) has been broadly used in Foreign Language and Mother Tongue learning contexts, it has not been applied in the field of engineering and by STEM (Science, Technology, Engineering, and Mathematics) students in a systematic way. In this interdisciplinary pilot study, we applied the EA methodology to a wide corpus of…