By Sue Johnston-Wilder, John Mason

This article and interactive CD-ROM aid academics expand their educational practices via leading edge methods for educating geometry as constructed via the Open University's Centre for arithmetic schooling.

Show description

Read Online or Download Developing Thinking in Geometry PDF

Best elementary education books

Teaching Young Children Mathematics

Young children research arithmetic such a lot successfully in contexts which are significant to them. figuring out the possibility of those contexts for fostering younger kid's mathematical studying whereas nurturing and not easy them, calls for wisdom of arithmetic in addition to of kid improvement. keeping off the debates surrounding hands-on studying vs.

About Teaching Mathematics: A K-8 Resource, 3rd Edition

A compendium of greater than 240 classroom-tested classes, this crucial source is helping lecturers construct pupil figuring out and abilities and know how youngsters most sensible examine math. during this 3rd version, Marilyn Burns has thoroughly revised the 1st part to mirror what she has realized through the years from her lecture room adventure with scholars and her expert improvement adventure with academics.

Eureka Math Curriculum Study Guide: Grade 2: A Story of Units

Eureka Math is a complete, content-rich PreK–12 curriculum that follows the point of interest and coherence of the typical center nation criteria in arithmetic (CCSSM) and thoroughly sequences the mathematical progressions into expertly crafted educational modules. The significant other examine courses to Eureka Math assemble the foremost parts of the curriculum for every grade right into a unmarried place, unpacking the factors intimately in order that either clients and non-users of Eureka Math can profit both from the content material awarded.

Childhood, Education and Philosophy: New ideas for an old relationship

This ebook explores the belief of a childlike schooling and provides severe instruments to query conventional different types of schooling, and other ways to appreciate and perform the connection among schooling and youth. enticing with the paintings of Michel Foucault, Jacques Rancière, Giorgio Agamben and Simón Rodríguez, it contributes to the advance of a philosophical framework for the pedagogical thought on the middle of the booklet, that of a childlike schooling.

Extra info for Developing Thinking in Geometry

Example text

It is not always possible to draw an interior rectangle if you start from any point on the longer side. Since it is possible to construct an interior rectangle from any point on the shorter side of the original rectangle, this process can be repeated, as in the next task. 3 Sequence of Rectangles As before, imagine drawing a rectangle inside a given rectangle. Now imagine drawing another rectangle inside this one and continuing the process. What conclusion can you draw about this sequence of rectangles?

Sometimes it is necessary to insert or construct extra elements that enable you to discern sub-figures whose known relationships (for example, similar triangles and ratios and parallelism) you can use to make deductions about other relationships. Notice also that it is important at the end of a chain of reasoning to look back at what was invariant, and to clarify what it is that is allowed to change and in what ways. 4 Look back over the reasoning given in this section and consider what particular features of language are involved in reasoning on the basis of properties.

If a second circle is added, as suggested in the comment above, then you could see the diagram as consisting of two similar figures. Each figure is a square with a circle inside it. Since the ratio of the areas for the two squares has already been established, it follows that the ratio for the two circles will be the same. In his book How to Solve It, George Polya (1957) poses the problem illustrated in the next task. 3 Polya’s Square–Triangle Problem Given a triangle, draw a square inside the triangle such that two of its vertices are on the base of the triangle and the other two vertices are on the other two sides of the triangle.

Download PDF sample

Rated 4.38 of 5 – based on 26 votes