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Additional resources for Proficiency and Beliefs in Learning and Teaching Mathematics: Learning from Alan Schoenfeld and Günter Törner
Noncommutative valuation rings. Trans. Moscow. Math. , 1, 273–287. Dubrovin, N. I. (1993). The rational closure of group rings of left orderable groups. Mat. Sbornik, 184(7), 3–48. , & Törner, G. (1993). On the ideal structure of right distributive rings. Comm. Algebra, 21(8), 2697–2713. Gräter, J. (1984). Über Bewertungen endlich dimensionaler Divisionsalgebren. , 7, 54– 57. , & Törner, G. (1984). Stochastik – Ein Grund- und Leistungskurs. Göttingen: Vandenhoeck & Ruprecht. Leder, G. , & Törner, G.
Proc. Amer. Math. , 128(11), 3167–3175. 28 ABOUT GÜNTER TÖRNER Brungs, H. , & Osmanagic, E. (2007). Gauss extensions and total graded subrings for crossed product algebras. J. Algebra, 316(1), 189–205. Cohen, I. S. (1946). On the structure and ideal theory of complete local rings. Trans Amer. Math. , 59, 54–106. Dubrovin, N. I. (1984). Noncommutative valuation rings. Trans. Moscow. Math. , 1, 273–287. Dubrovin, N. I. (1993). The rational closure of group rings of left orderable groups. Mat. Sbornik, 184(7), 3–48.
Strategical decision-making The quantitative results presented above were complemented by qualitative analyses directed at the identification of students’ understanding of contingency tables. In the following, we will present some first results, which illustrate the quantitative findings. We present excerpts from the interviews with three 4th graders who performed differently on the contingency table tasks. For this analysis, we will use three items from the abstract-formal context of varying difficulty (according to the empirical results).