By E. H. Lockwood

This ebook opens up an immense box of arithmetic at an trouble-free point, one during which the part of aesthetic excitement, either within the shapes of the curves and of their mathematical relationships, is dominant. This booklet describes equipment of drawing airplane curves, starting with conic sections (parabola, ellipse and hyperbola), and happening to cycloidal curves, spirals, glissettes, pedal curves, strophoids etc. quite often, 'envelope tools' are used. There are twenty-five full-page plates and over 90 smaller diagrams within the textual content. The ebook can be utilized in faculties, yet may also be a reference for draughtsmen and mechanical engineers. As a textual content on complicated airplane geometry it may entice natural mathematicians with an curiosity in geometry, and to scholars for whom Euclidean geometry isn't really a central examine.

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16) to students and the potential influence it might have. Perhaps letting your students read it and comment on may be worth a try. 14. Select a unit or a series of tasks and problems from your favorite algebra textbook. Discuss the extent to which they convey a “sense of purpose” for algebra. Elaborate the nuances of the construct “sense of purpose” (for whom? what purpose? ). Suggestion: browse through the study conducted by Project 2061 (2013). , & Wilson, K. (2005). Designing spreadsheet-based tasks for purposeful algebra.

E. ), Algebra and Algebraic Thinking in School Mathematics (pp. 37–49). Reston, VA: NCTM. , & Nachmias, R. (1989). Re-exploring familiar concepts with a new representation. Proceedings of the 13th International Conference on the Psychology of Mathematics Education (PME 13), Volume 1 (pp. 77–84). Paris: PME. , & Nachmias, R. (1993). What is your family name, Ms. Function? – Exploring families of functions with a non-conventional representation. Journal of Computers in Mathematics and Science Teaching, 12, 315–329.

A student was surprised to notice that 2 − 3 = 2 × 3 and he wanted to know whether there are other pairs of numbers for which their difference equals their product. Explore this task and consider the following as potential issues for discussion with colleagues and students that arise during or after the exploration: Can you at first sight exclude pairs, or single numbers that you know right away will not be candidates for this property to hold? Which kinds of algebraic expressions can be created in order to explore when does this property hold?