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Symbol sense behavior in digital activities
No full textThe algebraic expertise that mathematics education is aiming for includes both procedural skills and conceptual understanding. To capture the latter, notions such as symbol sense, gestalt view and visual salience have been developed. We wonder if digital activities can be designed that not only require procedural algebraic skills, but also invite symbol sense, and if the notions of gestalt view and visual salience are helpful in understanding student behavior in such a digital environment. To investigate this, a prototypical digital algebra environment was designed, consisting of thirty tasks, which focus on these two characteristics of symbol sense. The activities were piloted in five one-to-one think-aloud sessions with students from pre-university grade 12. The results suggest that the students’ behaviors indeed can be understood in terms of (lack of) symbol sense, and that the notions of gestalt view and visual salience apply to behavior in digital environments as well. Therefore, we believe digital activities can invite symbol sense; the educational exploitation of such environments is not trivial
Are geometric concepts of vectors bookable? An analysis of the didactic transpositions in mathematics textbooks
No full textIn Germany, the use of vectors is traditionally introduced in lower secondary education in Physics and in upper secondary education in Mathematics. In this curriculum, a geometric point of view plays an important, but somewhat unclear role whereas at the beginning of the Bachelor’s degree programmes structural-symbolic approaches dominate in courses like “analytic geometric and linear algebra”. Based on an analysis of Mathematics textbooks in upper secondary education from a point of view of geometry, differential geometry, and dynamical systems, the underlying geometric concepts are worked out as praxeologies. Some typical problems in working with vector geometry relate to the change between different conceptual models in the organisation of the textbooks
Are geometric concepts of vectors bookable? An analysis of the didactic transpositions in mathematics textbooks
No full textIn Germany, the use of vectors is traditionally introduced in lower secondary education in Physics and in upper secondary education in Mathematics. In this curriculum, a geometric point of view plays an important, but somewhat unclear role whereas at the beginning of the Bachelor’s degree programmes structural-symbolic approaches dominate in courses like “analytic geometric and linear algebra”. Based on an analysis of Mathematics textbooks in upper secondary education from a point of view of geometry, differential geometry, and dynamical systems, the underlying geometric concepts are worked out as praxeologies. Some typical problems in working with vector geometry relate to the change between different conceptual models in the organisation of the textbooks
Are geometric concepts of vectors bookable? An analysis of the didactic transpositions in mathematics textbooks
No full textIn Germany, the use of vectors is traditionally introduced in lower secondary education in Physics and in upper secondary education in Mathematics. In this curriculum, a geometric point of view plays an important, but somewhat unclear role whereas at the beginning of the Bachelor’s degree programmes structural-symbolic approaches dominate in courses like “analytic geometric and linear algebra”. Based on an analysis of Mathematics textbooks in upper secondary education from a point of view of geometry, differential geometry, and dynamical systems, the underlying geometric concepts are worked out as praxeologies. Some typical problems in working with vector geometry relate to the change between different conceptual models in the organisation of the textbooks
Are geometric concepts of vectors bookable? An analysis of the didactic transpositions in mathematics textbooks
No full textIn Germany, the use of vectors is traditionally introduced in lower secondary education in Physics and in upper secondary education in Mathematics. In this curriculum, a geometric point of view plays an important, but somewhat unclear role whereas at the beginning of the Bachelor’s degree programmes structural-symbolic approaches dominate in courses like “analytic geometric and linear algebra”. Based on an analysis of Mathematics textbooks in upper secondary education from a point of view of geometry, differential geometry, and dynamical systems, the underlying geometric concepts are worked out as praxeologies. Some typical problems in working with vector geometry relate to the change between different conceptual models in the organisation of the textbooks
Introduction to the proceedings of the thirteenth Congress of the European Society for Research in Mathematics Education
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