![]() An examination of the levels of cognitive demand required by probability tasks in middle grades mathematics textbooks. International study of achievement in mathematics: A comparison of twelve countries. G., Sahin, A., Kalaycioglu, S., Osgood, B. Educational Studies in Mathematics, 112(1), 73-102. Analyzing the written discourse in calculus textbooks over 42 years: The case of primary objects, concrete discursive objects, and a realization tree of the derivative at a point. Haghjoo, S., Radmehr, F., & Reyhani, E.Context problems in realistic mathematics education: A calculus course as an example. Gamoran (Eds.), Methodological advances in cross-national surveys of educational achievement (pp. Hurford (Eds.), Modeling students’ mathematical modeling competencies: ICTMA 13 (pp. Research in Mathematics Education, 10(1), 19-35. The capacity of two Australian eighth-grade textbooks for promoting proportional reasoning. Romberg (Ed.), Reform in school mathematics (pp. Mathematical Thinking and Learning, 12(2), 117-151. A comparative analysis of the addition and subtraction of fractions in textbooks from three countries. International Journal of Science and Mathematics Education, 14(8), 1475-1497. Coordinating multiple representations in a reform calculus textbook. South African Journal of Education, 33(2), 1-18. ![]() High school learners’ mental construction during solving optimization problems in calculus: A South African case study. What do students really understand? The Journal of Mathematical Behavior, 21(2), 151-165. Educational Studies in Mathematics, 79(2), 239-261. How do elementary textbooks address fractions? A review of mathematics textbooks in the USA, Japan, and Kuwait. Transparency and replicability in qualitative research: The case of interviews with elite informants. Implications for several stakeholders, including calculus textbook authors and calculus instructors are discussed. Overall, findings of this study suggest the existence of a relationship between known students’ difficulties with solving optimization problems and the opportunities to learn about optimization problems provided by calculus textbooks. In addition, both textbooks provide ample opportunities to interpret critical numbers and extrema in context. Setting up objective functions is either not necessary or it is straightforward for most problems in the two textbooks. Findings of this study indicate that a majority of the problems in both textbooks lack realistic and essential contexts, have matching or missing information, and require a low cognitive demand to solve. To accomplish this, we analyzed examples and practice problems from two calculus textbooks widely used in the teaching of calculus in the United States. This study investigated opportunities to learn about optimization problems provided by undergraduate calculus textbooks.
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