Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 4

Kassel Project Related Abstracts

4 Conspicuous and Significant Learner Errors in Algebra

Authors: Michael Lousis

Abstract:

The kind of the most important and conspicuous errors the students made during the three-years of testing of their progress in Algebra are presented in this article. The way these students’ errors changed over three-years of school Algebra learning also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students, who were purposefully culled according to their participation in each occasion of testing in the development of the three-year Kassel Project in England and Greece, in both domains at once of Arithmetic and Algebra. Hence, for each of these English and Greek students, six test-scripts were available and corresponded to the three occasions of testing in both Arithmetic and Algebra respectively.

Keywords: Algebra, Errors, Kassel Project, progress of learning

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3 Learners’ Conspicuous and Significant Errors in Arithmetic

Authors: Michael Lousis

Abstract:

The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic are presented in this article. How these errors have changed over three-years of school instruction of Arithmetic also is shown. The sample is comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. These students were purposefully selected according to their participation in each testing session in the development of the three-year Kassel Project in England and Greece, in both domains simultaneously in Arithmetic and Algebra. The data sample includes six test-scripts corresponding to three testing sessions in both Arithmetic and Algebra respectively.

Keywords: Arithmetic, Errors, Kassel Project, progress of learning

Procedia PDF Downloads 125
2 Mathematical Competence as It Is Defined through Learners' Errors in Arithmetic and Algebra

Authors: Michael Lousis

Abstract:

Mathematical competence is the great aim of every mathematical teaching and learning endeavour. This can be defined as an idealised conceptualisation of the quality of cognition and the ability of implementation in practice of the mathematical subject matter, which is included in the curriculum, and is displayed only through performance of doing mathematics. The present study gives a clear definition of mathematical competence in the domains of Arithmetic and Algebra that stems from the explanation of the learners’ errors in these domains. The learners, whose errors are explained, were Greek and English participants of a large, international, longitudinal, comparative research program entitled the Kassel Project. The participants’ errors emerged as results of their work in dealing with mathematical questions and problems of the tests, which were presented to them. The construction of the tests was such as only the outcomes of the participants’ work was to be encompassed and not their course of thinking, which resulted in these outcomes. The intention was that the tests had to provide undeviating comparable results and simultaneously avoid any probable bias. Any bias could stem from obtaining results by involving so many markers from different countries and cultures, with so many different belief systems concerning the assessment of learners’ course of thinking. In this way the validity of the research was protected. This fact forced the implementation of specific research methods and theoretical prospects to take place in order the participants’ erroneous way of thinking to be disclosed. These were Methodological Pragmatism, Symbolic Interactionism, Philosophy of Mind and the ideas of Computationalism, which were used for deciding and establishing the grounds of the adequacy and legitimacy of the obtained kinds of knowledge through the explanations given by the error analysis. The employment of this methodology and of these theoretical prospects resulted in the definition of the learners’ mathematical competence, which is the thesis of the present study. Thus, learners’ mathematical competence is depending upon three key elements that should be developed in their minds: appropriate representations, appropriate meaning, and appropriate developed schemata. This definition then determined the development of appropriate teaching practices and interventions conducive to the achievement and finally the entailment of mathematical competence.

Keywords: meaning, Representations, Computationalism, Error Analysis, Kassel Project, appropriate developed schemata, explanations for the probable causes of the errors, mathematical competence

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1 Teaching Practices for Subverting Significant Retentive Learner Errors in Arithmetic

Authors: Michael Lousis

Abstract:

The systematic identification of the most conspicuous and significant errors made by learners during three-years of testing of their progress in learning Arithmetic throughout the development of the Kassel Project in England and Greece was accomplished. How much retentive these errors were over three-years in the officially provided school instruction of Arithmetic in these countries has also been shown. The learners’ errors in Arithmetic stemmed from a sample, which was comprised of two hundred (200) English students and one hundred and fifty (150) Greek students. The sample was purposefully selected according to the students’ participation in each testing session in the development of the three-year project, in both domains simultaneously in Arithmetic and Algebra. Specific teaching practices have been invented and are presented in this study for subverting these learners’ errors, which were found out to be retentive to the level of the nationally provided mathematical education of each country. The invention and the development of these proposed teaching practices were founded on the rationality of the theoretical accounts concerning the explanation, prediction and control of the errors, on the conceptual metaphor and on an analysis, which tried to identify the required cognitive components and skills of the specific tasks, in terms of Psychology and Cognitive Science as applied to information-processing. The aim of the implementation of these instructional practices is not only the subversion of these errors but the achievement of the mathematical competence, as this was defined to be constituted of three elements: appropriate representations - appropriate meaning - appropriately developed schemata. However, praxis is of paramount importance, because there is no independent of science ‘real-truth’ and because praxis serves as quality control when it takes the form of a cognitive method.

Keywords: Cognitive Science, Cognitive Psychology, Arithmetic, Kassel Project, information-processing paradigm, level of the nationally provided mathematical education, praxis, remedial mathematical teaching practices, retentiveness of errors

Procedia PDF Downloads 204