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1994 Book DidacticsOfMathematicsAsAScien

Level One:
Level Two:
Level Three:
Level Four:
Level Five:
Yes. Sides are straight at a right angle.
Yes, as long as all of the sides are the same length.
No, because all sides must be equal.
(a) No, because there must be one side of the triangle
(hypotenuse) that is longer in a right triangle and equilateral has
all sides the same.
(b) No, all the angles have to be the same and all three have to
equal 180 degrees.
(a) No, you can't have 3 right angles because the sum of the an-
gles would be 270 degrees and it must equal 180. The angle mea-
sure are all the same in an equilateral triangle.
(b) No, because an equilateral triangle has all the same angles. If
you had a triangle with 3 right angles, you would have 3/4 of a
square of the sides would not connect.


SCIENCE AND TEACHER EDUCATION
REFERENCES
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on research on effective mathematics teaching (pp. 27-46). Reston, VA: National
Council of Teachers of Mathematics.
Bauersfeld, H. (1980). Hidden dimensions in the so-called reality of a mathematics class-
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Brown, C. A. (1985). A study of the socialization to teaching of beginning secondary math-
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(pp. 639-656). New York: Macmillan.
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Mathematics.
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Fisher, L. C. (1988). Strategies used by secondary mathematics teachers to solve proportion
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CA: 
Intersystems
Publications.
114
deeper understanding of the process by which teachers learn to teach so that
we can have a better basis for developing teacher education programs.
Appropriately defined and applied, science can enable us to develop this
understanding and allow us to impact on the practical art of teaching and
teacher education in a way not foreseen by Highet and many of our profes-
sional forefathers who ascribed to an analytical view of science.


THOMAS J. COONEY
Glasersfeld, E. von (1989). Constructivism in education. In T. Husen & N. Postlethwaite
(Eds.), International encyclopedia of education (pp. 162-163). (Supplementary Vol.).
Oxford: Pergamon.
Graeber, A., Tirosh, D., & Glover, R. (1986). Preservice teachers’ beliefs and performance
on measurement and partitive division problems. In G. Lappan & R. Even (Eds.),

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