Daro CC Alg presentation
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Transcript of Daro CC Alg presentation
![Page 1: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/1.jpg)
2011 © New Leaders | 1
Mile wide –inch deep
causes
cures
![Page 2: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/2.jpg)
2011 © New Leaders | 2
Mile wide –inch deepcause:
too little time per conceptcure:
more time per topic = less topics
![Page 3: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/3.jpg)
Two ways to get less topics:
1. Delete topics2. Coherence: when studied a little deeper,
mathematics is a lot more coherenta) coherence across conceptsb) coherence in the progression across grades
![Page 4: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/4.jpg)
Why do students have to do math problems?
A. To get answers because Homeland Security needs them, pronto
B. I had to, why shouldn’t they?
C. So they will listen in class
D. To learn mathematics
![Page 5: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/5.jpg)
Why give students problems to solve?
• To learn mathematics• Answers are part of the process, they are not the product• The product is the student’s mathematical knowledge and
know-how• The ‘correctness’ of answers is also part of the process: Yes,
an important part
![Page 6: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/6.jpg)
Wrong answers
• Are part of the process, too• What was the student thinking?• Was it an error of haste or a stubborn
misconception?
![Page 7: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/7.jpg)
Three responses to a math problem
1. Answer getting2. Making sense of the problem/situation3. Making sense of the mathematics by learning to
work through the problem
![Page 8: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/8.jpg)
Answers are a black hole:hard to escape the pull
• Answer getting short circuits mathematics, and lacks mathematical sense
• Very habituated in U.S. teachers versus Japanese teachers
• Devised methods for slowing down, postponing answer getting
![Page 9: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/9.jpg)
Answer getting vs. learning mathematics
U.S.:• How can I teach my kids to get the answer to
this problem? Use mathematics they already know – this is easy,
reliable, works with bottom half, good for classroom management
Japan:• How can I use this problem to teach the
mathematics of this unit?
![Page 10: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/10.jpg)
Butterfly method
![Page 11: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/11.jpg)
![Page 12: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/12.jpg)
Use butterflies on this TIMSS item:
1/2 + 1/3 +1/4 =
![Page 13: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/13.jpg)
2011 © New Leaders | 13
Mile wide –inch deep
causes
cures
![Page 14: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/14.jpg)
2011 © New Leaders | 14
Mile wide –inch deepcause:
too little time per conceptcure:
more time per topic = less topics
![Page 15: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/15.jpg)
Two ways to get less topics:
1. Delete topics2. Coherence: when studied a little deeper,
mathematics is a lot more coherenta) coherence across conceptsb) coherence in the progression across grades
![Page 16: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/16.jpg)
Why do students have to do math problems?
A. To get answers because Homeland Security needs them, pronto
B. I had to, why shouldn’t they?
C. So they will listen in class
D. To learn mathematics
![Page 17: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/17.jpg)
Why give students problems to solve?
• To learn mathematics• Answers are part of the process, they are not the product• The product is the student’s mathematical knowledge and
know-how• The ‘correctness’ of answers is also part of the process: Yes,
an important part
![Page 18: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/18.jpg)
Wrong answers
• Are part of the process, too• What was the student thinking?• Was it an error of haste or a stubborn
misconception?
![Page 19: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/19.jpg)
Three responses to a math problem
1. Answer getting2. Making sense of the problem/situation3. Making sense of the mathematics by learning to
work through the problem
![Page 20: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/20.jpg)
Answers are a black hole:hard to escape the pull
• Answer getting short circuits mathematics, and lacks mathematical sense
• Very habituated in U.S. teachers versus Japanese teachers
• Devised methods for slowing down, postponing answer getting
![Page 21: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/21.jpg)
Answer getting vs. learning mathematics
U.S.:• How can I teach my kids to get the answer to
this problem? Use mathematics they already know – this is easy,
reliable, works with bottom half, good for classroom management
Japan:• How can I use this problem to teach the
mathematics of this unit?
![Page 22: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/22.jpg)
Butterfly method
![Page 23: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/23.jpg)
![Page 24: Daro CC Alg presentation](https://reader035.fdocuments.in/reader035/viewer/2022062420/55b55b6abb61eb81758b4608/html5/thumbnails/24.jpg)
Use butterflies on this TIMSS item:
1/2 + 1/3 +1/4 =