por Tyler Trettin hace 5 años
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Vygotsky- Self Talk & Guided Participation Kids talk them selves through problems and I just help guide them. This is the ultimate goal.
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Have them show their understanding of the why.
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What's their understanding of multiplication?
Do they understand the why behind solving the equation?
Example of the "why".
23 multiplied by 17. Why when solving this problem do we put a two over the two in 23. What does it represent? Why do we put a zero, in the second row of numbers? This is the kind of understanding I want from the students. I don't want them to just know how to do it, I want them to know why they are doing each step.
Multiplication is repeated addition.
25*4 is the same as 25 + 25 + 25 +25
Using this example I would teach the students how to multiply using the standard algorithm.
Over generalization - If I taught my students that you must carry every time you multiply a number together then that would be a over generalization.
Under generalization - If I were to say that you only need to carry sometimes without explaining the reasoning, that would be under generalizing.
Students may over or under generalize in their algorithms by having faulty algorithms.
Example: If you don't explain what the numbers represent when carrying they may just add the carried over number to the ten place and multiply that number by the number on the bottom. This would be under generalizing because they know that they need to carry but not what the number represents.
----->2 37 * 4 ______ 208
One way I would teach my students how to do this is through blocks.
Giving the students a problem like 106* 17. This problem would be very hard with blocks and would take forever.
We will use 10 * 5. Using blocks of ten I would ask them to solve the problem. They would see that they need 5 blocks of ten and count the total number of blocks to get their answer.
If Jenna has two closets with 10 shirts in each closet, how many shirts does she have total?
If there are 3 cars and each car has 4 tires, how many tires are there all together?
Child is able to use logical thought when solving problems.
