The purpose of this research is to classify the mathematical modelling problems produced by pre-service mathematics teachers in terms of the number of variables and to determine the mathematical modelling skills and mathematical skills used in solving the problems in each class. The current study is a qualitative research and the data was analyzed…

The aim of this paper is to review some studies conducted with different learning areas in which the schemes of different participants emerge. Also it is about to show how mathematical proofs are handled in these studies by considering Harel and Sowder's classification of proof schemes with specific examples. As a result, it was seen that the…

The gap between skilled workers needed and skilled workers available increased since the start of the fourth industrial revolution. Employees now need different knowledge, skills, and abilities to enter the workforce and stay current with new technologies than they did in the past. One way this knowledge gap and skilled worker shortage could be…

Communities develop social languages in which utterances take on culturally specific situated meanings. As physics students interact in their classroom, they can learn the broader physics community's social language by co-constructing meanings with their instructors. We provide an exposition of a systematic and productive use of idiosyncratic,…

The problem of taking a data set and separating it into subgroups, where the members of each subgroup are more similar to each other than they are to members outside the subgroup, has been extensively studied in science and mathematics education research. Student responses to written questions and multiple-choice tests have been characterised and…

Holyoak and Koh (1987) and Holyoak (1984) propose four critical tasks for analogical transfer to occur in problem solving. A study was conducted to test this hypothesis by comparing a multiple components (MC) approach against worked examples (WE) in helping students to solve algebra word problems in chemistry classes. The MC approach incorporated…

Linear algebra is one of the most challenging topics to learn and teach in many countries. To facilitate the teaching and learning of linear algebra, priority should be given to epistemologically analyze the concepts that the undergraduate students have difficulty in conceptualizing and to define their ways of reasoning in linear algebra. After…

A study was conducted at the Technical University Berlin involving students who twice failed the written examination in the first semester course Linear Algebra for Engineers in order to better understand the reasons behind their failure. The study considered student understanding in terms of Bloom's taxonomy and the ways in which students…

The ability to categorize problems based upon underlying principles, rather than surface features or contexts, is considered one of several proxy predictors of expertise in problem solving. With inspiration from the classic study by Chi, Feltovich, and Glaser, we assess the distribution of expertise among introductory physics students by asking…

Representational fluency (RF) includes an ability to interpret, create, move within and among, and connect tool-based representations of mathematical objects. Taken as an indicator of conceptual understanding, there is a need to better support school algebra students' RF in learning environments that utilize both computer algebra systems…

Literature in mathematic problem-solving suggests that learners store information in memory which helps them solve stereotyped algebra word problems. Cluster analysis has been used as an exploratory tool to infer the types of problems which have common representations in memory. This study compares the results of a hierarchical cluster analysis of…

Three experiments investigated the ability of 79 college students to solve similar algebra word problems. Data indicate that students are able to perceive and use similarities in such problems at the level of a conceptual structure. A training session to explain relevant structural principles was effective in improving performance. (SLD)

During several years of experimentation, we accumulated a large collection of data on the analysis of problems generally encountered in algebra and on the reasoning developed by students at different levels when confronted with these problems. Analysis of this data led us to a new way of looking at differences among word problems, and to the…

The goal of this study was to develop a framework for classifying algebra story problems and to determine observed frequencies for each problem type. One thousand ninety-seven algebra story problems were selected from nine standard algebra textbooks. These are divided into eight families based on the nature of the source formula involved; for…

Four human judges agreed highly among themselves about the presence of errors committed by 60 adults solving algebra word problems, but were in less agreement about categorizing faults. An expert system agreed with judges about correctness of answers, but was in even less agreement about categorizing the faults. (SLD)