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
Proof Blocks A Visual Approach to Logic and Proof
Jenni DirksenSan Mateo High
Jinna HwangFrancis Polytechnic
Agenda
Difficulties teaching two column proof
Activity to set the stage What are these ProofBlocks
anyway? Your turn Research
The Problem
Given: PRF is equilateral RO bisects PRF
Prove: PRO FRO
O R
P
F
Setting the Stage: An Activity
Warm-up activity for proof (~10 min)
Order the blocks of each color
Complete conditional statements on worksheet
Setting the Stage: An Activity
What makes this activity easy?
The Solution
Proof Blocks
Given: MT AH H is the midpoint of MT
Prove: MAH TAH
HM T
A
Proof Blocks
HM T
AGiven: MT AH H is the midpoint of MT
Prove: MAH TAH
Proof Blocks
HM T
AGiven: MT AH H is the midpoint of MT
Prove: MAH TAH
Proof Blocks
Proof Blocks
Proof Blocks
Proof Blocks
Proof Blocks
Definitions
H is the midpoint of MT
Definitions
H is the midpoint of MT
Connecting Blocks
MH HT
Connecting Blocks
MH HT
Proof Blocks
Definitions
MT AH
Definitions
MT AH
Connecting Blocks
AHM AHT
Connecting Blocks
AHM AHT
Proof Blocks
Proof Blocks
Proof Blocks
Proof Blocks
An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
An Extension
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
Corresponding Parts of
Congruent Triangles are Congruent
An Extension
Corresponding parts of congruent triangles are congruent
An Extension
Corresponding parts of congruent triangles are congruent
An Extension
Corresponding parts of congruent triangles are congruent
On your whiteboards
Given: MT AH H is the midpoint of MT
Prove: AM AT
HM T
A
Connecting Blocks
MAH TAH
An Extension
HM T
A
Given: MT AH H is the midpoint of MT
Prove: AM AT
Try It Yourself!
Given: O is the midpoint of BK B K
Prove: BL CK
C
O
B L
K
Proof Blocks in Action
Proof Blocks in Action
Proof Blocks in Action
Go ProofBlocks!
Theorems as manipulatives
Go ProofBlocks!
Theorems as manipulatives Student approved
Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL
Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL Easily checked logic
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
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%
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
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%
Go ProofBlocks!
Theorems as manipulatives Student approved Visual, kinesthetic, and ELL Easily checked logic Special Education accommodations
Questions?
Photograph taken by Melissa Holmes