Design properties
- Name
- Proofs that Square Root of 2 is irrational
- Topic
- Algebra
- Learning time
- 4 hours and 40 minutes
- Designed time
- 4 hours and 40 minutes
- Size of class
- 25
- Description
- The activity looks at the meaning of concepts of "key ideas" and "memorablity" and how they relate to the metric "width of a proof". It attempts to show whether and how they are congruent with other aspects of proof discussed in literature on the teaching of proof and proving. We presented 4 differents proofs of the irrationality of SQRT(2). Three proofs utilise algebraic tools, and one proof utilise geometrical tools.
- Mode of delivery
- No mode selected
- Aims
- 1) To what degree does the width of a proof (as Gowers uses of term) represent a new idea in mathematics education. 2) How does memorability (as Gowers uses the terms) relate to understanding, and how could the concept be of benefit to mathematics education?
- Outcomes
-
- Reproduce Reproduction proofs containing sophisticated skills. Reproduction proofs containing key ideas.
- Investigate Investigate the width of proof after the Gardner's proof.
- Editor
- zenonlig
Timeline controls
Timeline
Read some characteristic proofs - creation of the working groups
80 minutes)
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Read Watch Listen4025Read the activity in SPARK Adobe text.
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Discuss3025Attention in proof no 1 and the proof 8 of "Laczkovich & Gardner" in "Cut the knot" .
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Produce1025Students are divided into groups of 2 and carry out their first job. Write the proofs 1 and 8. (reproduction in PADLET step by step the profs 1 and 8)
Notes:
Resources linked: 0
Two activities that support the width of proofs, according to Gowers
60 minutes)
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Investigate3025The two proposed activities is the "spring from nowhere", for Tennenbaums's solution and the proof of Gardner
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Collaborate2025Find the similarities between the proofs of the two activities and the proofs of Tennenbaums and Gardner
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Discuss1025Write both proofs (Tennenbaums and Gardner) and find the "deus ex machina"
Notes:
Resources linked: 0
assessment
30 minutes)
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Produce3025Show that the sqrt (2) is irrational number, using an proofs that you think you can replay with the most complete way.
Notes:
Investigation of Cowers proof
Resources linked: 0
irrational Number and continued fractions
110 minutes)
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Investigate3025Read in wikipedia, the paragraphs: 1) Calculating continued fraction representations 2) Finite continued fractions 3) Infinite continued fractions 4) Generalized continued fraction for square roots Can you help the investication, by the activity abour SQRT{2} in padlet
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Collaborate40251) Define the collaborative project. 2) Identify project elements and components in detail; 3) For each component identify the resources that are essential. These can be; a. materials b. equipment c. strategies d. knowledge e. experience
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Produce4025Solve the problems of activity and presented the work in Power Point.
Notes:
Resources linked: 0
Learning Experience
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