proof blocks a visual approach to logic and proof
DESCRIPTION
Proof Blocks A Visual Approach to Logic and Proof. Jenni Dirksen San Mateo High [email protected]. Jinna Hwang Francis Polytechnic High [email protected]. Agenda. Difficulties teaching two column proof Activity to set the stage What are these ProofBlocks anyway? Your turn - PowerPoint PPT PresentationTRANSCRIPT
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Proof Blocks A Visual Approach to Logic and Proof
Jenni DirksenSan Mateo High
Jinna HwangFrancis Polytechnic
![Page 2: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/2.jpg)
Agenda
Difficulties teaching two column proof
Activity to set the stage What are these ProofBlocks
anyway? Your turn Research
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The Problem
Given: PRF is equilateral RO bisects PRF
Prove: PRO FRO
O R
P
F
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Setting the Stage: An Activity
Warm-up activity for proof (~10 min)
Order the blocks of each color
Complete conditional statements on worksheet
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Setting the Stage: An Activity
What makes this activity easy?
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The Solution
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Proof Blocks
Given: MT AH H is the midpoint of MT
Prove: MAH TAH
HM T
A
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Proof Blocks
HM T
AGiven: MT AH H is the midpoint of MT
Prove: MAH TAH
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Proof Blocks
HM T
AGiven: MT AH H is the midpoint of MT
Prove: MAH TAH
![Page 10: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/10.jpg)
Proof Blocks
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Proof Blocks
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Proof Blocks
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Proof Blocks
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Proof Blocks
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Definitions
H is the midpoint of MT
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Definitions
H is the midpoint of MT
![Page 17: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/17.jpg)
Connecting Blocks
MH HT
![Page 18: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/18.jpg)
Connecting Blocks
MH HT
![Page 19: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/19.jpg)
Proof Blocks
![Page 20: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/20.jpg)
Definitions
MT AH
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Definitions
MT AH
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Connecting Blocks
AHM AHT
![Page 23: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/23.jpg)
Connecting Blocks
AHM AHT
![Page 24: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/24.jpg)
Proof Blocks
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Proof Blocks
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Proof Blocks
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Proof Blocks
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An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
![Page 29: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/29.jpg)
An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
![Page 30: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/30.jpg)
An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
Corresponding Parts of
Congruent Triangles are Congruent
![Page 31: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/31.jpg)
An Extension
Corresponding parts of congruent triangles are congruent
![Page 32: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/32.jpg)
An Extension
Corresponding parts of congruent triangles are congruent
![Page 33: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/33.jpg)
An Extension
Corresponding parts of congruent triangles are congruent
![Page 34: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/34.jpg)
On your whiteboards
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
![Page 35: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/35.jpg)
Connecting Blocks
MAH TAH
![Page 36: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/36.jpg)
An Extension
HM T
A
Given: MT AH H is the midpoint of MT
Prove: AM AT
![Page 37: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/37.jpg)
Try It Yourself!
Given: O is the midpoint of BK B K
Prove: BL CK
C
O
B L
K
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Proof Blocks in Action
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Proof Blocks in Action
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Proof Blocks in Action
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Go ProofBlocks!
Theorems as manipulatives
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Go ProofBlocks!
Theorems as manipulatives Student approved
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Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL
![Page 44: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/44.jpg)
Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL Easily checked logic
![Page 45: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/45.jpg)
Comparison of Reported Confidence versus Achievement on Proof Assessment
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2 Column ProofBlock
School B
Somewhat Confident / Confident on Post-Survey Scored 2 and Above on Assessment
Confidence vs. Achievement
2 Column ProofBlock
Confident / Somewhat Confident
![Page 46: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/46.jpg)
Comparison of Reported Confidence versus Achievement on Proof Assessment
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2 Column ProofBlock
School B
Somewhat Confident / Confident on Post-Survey Scored 2 and Above on Assessment
Confidence vs. Achievement
2 Column ProofBlock
Confident / Somewhat Confident
52%
59%
![Page 47: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/47.jpg)
Comparison of Reported Confidence versus Achievement on Proof Assessment
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2 Column ProofBlock
School B
Somewhat Confident / Confident on Post-Survey Scored 2 and Above on Assessment
Confidence vs. Achievement
2 Column ProofBlock
52%
59%
More than ½ the proof correct on test
![Page 48: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/48.jpg)
Comparison of Reported Confidence versus Achievement on Proof Assessment
0%
10%
20%
30%
40%
50%
60%
70%
80%
90%
100%
2 Column ProofBlock
School B
Somewhat Confident / Confident on Post-Survey Scored 2 and Above on Assessment
Confidence vs. Achievement
2 Column ProofBlock
52%
59%
More than ½ the proof correct on test
19%
43%
![Page 49: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/49.jpg)
Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL Easily checked logic Special Education accommodations
![Page 50: Proof Blocks A Visual Approach to Logic and Proof](https://reader035.vdocuments.site/reader035/viewer/2022062217/568148fa550346895db62109/html5/thumbnails/50.jpg)
Questions?
Photograph taken by Melissa Holmes