MasterClass in Mathematics Education by Paul Andrews & Tim Rowland

Author:Paul Andrews & Tim Rowland
Language: eng
Format: epub
ISBN: 9781441103338
Publisher: Bloomsbury Academic
Published: 2013-03-21T16:00:00+00:00

Conclusion

The four core readings addressed a set of related conceptual and instructional issues, and exemplified an important body of research within mathematics education that focuses on the notion of proof. Specifically, the readings addressed the following issues: the meaning of proof and adverse consequences of the use of unclear terminology for mathematics education research in the area of proof (Balacheff 2002; Stylianides 2007); students’ different ways of thinking about proof, some of which derive from deeply rooted misconceptions such as that empirical arguments are proofs (Sowder and Harel 1998); and the role of instruction to support the development of students’ ways of thinking about proof and to help them overcome misconceptions they have in this area (Stylianides 2007; Stylianides and Stylianides 2009).

Although not all readings focused on the same level of education, they form in my view a coherent reading package that can inform research and practice across all levels of education. This can be partly attributed to the fact that, unlike many mathematical topics (e.g. fractions) or operations (e.g. addition) whose curricular treatment is typically age specific, the notion of proof is, or can be, relevant throughout students’ mathematical education as a vehicle to mathematical sense making.

There are several other important issues within the selected body of research that I have not discussed in this chapter. These include the elements of teacher knowledge about proof that can be important for effective mathematics teaching (e.g. Stylianides and Ball 2008), the role that technology can play in the teaching and learning of proof (e.g. Jones 2000; Mariotti 2000; Marrades and Gutiérrez 2000), practices involved in reading or evaluating proofs (e.g. Inglis and Mejia-Ramos 2009; Stylianides and Stylianides 2009; Weber and Mejia-Ramos 2011), the place of proof in curriculum or textbook materials (e.g. G. Stylianides 2009), and so on.

Notes

1.The page numbers in this section refer to the online version of Balacheff (2002).

2.Betsy’s argument (line 14) would likely meet the stricter standard of proof set by the second researcher epistemology.

Further reading

Hanna, G. and Jahnke, H. N., 1996. Proof and proving. In A. J. Bishop, K. Clements, C. Keitel, J. Kilpatrick and C. Laborde, eds, International handbook of mathematics education. Dordrecht, Netherlands: Kluwer, 877–908.

Healy, L. and Hoyles, C., 2000. A study of proof conceptions in algebra. Journal for Research in Mathematics Education, 31, 396–428.

Marrades, R. and Gutiérrez, Á., 2000. Proofs produced by secondary school students learning geometry in a dynamic computer environment. Educational Studies in Mathematics, 44, 87–125.

Stylianides, G. J., 2009. Reasoning-and-proving in school mathematics textbooks. Mathematical Thinking and Learning, 11, 258–88.

Additional references

Ball, D. L. and Bass, H., 2000. Making believe: the collective construction of public mathematical knowledge in the elementary classroom. In D. Philips, ed., Constructivism in education: Yearbook of the National Society for the Study of Education. Chicago, IL: University of Chicago Press, 193–224.

—, 2003. Making mathematics reasonable in school. In J. Kilpatrick, W. G. Martin and D. Schifter, eds, A research companion to principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics, 27–44.

Ball, D. L., Hoyles, C.

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