No matter what I did to grasp what was going on in class from Primary school through Junior college, I had not been successful. I learned to live with the red mark in my report cards: FAIL!
Why was I failing Maths when I was acing other subjects? Last evening, I discovered the reason for my failing grades: My Maths teachers had not taught me well!! They didn't know how to teach Maths, the correct way, that is.
PROBLEM 1: Which letter in the name is 99?
more than just a bunch of numeralsCount off each letter of the name forward and then backwards and continue...
1) How can you deduce from the pattern in the numerals where the 99th numeral will be?
2) What methods will you use? How many methods will you use
Can you see some patterns formed by these numerals so far? I did.
Method 1
Simply count from 1 to 99 and you will get the answer although this is tedious and there are faster ways to arrive at the answer.
Method 2
Looking for multiples of 10.
Knowing where the multiples of ten are, I will be able to locate 100. I then count backward and discover that letter N is the 99.
Method 3
Under the letter B, we can see the following pattern 11, 21, 31, etc.
We then locate 91 and count forward to 99 or locate 101 and count backwards to 99.
Method 4
Look for numbers with the digit 9 in the ones place and you will get 99 in no time.
Method 5
Look @ multiples of 3 or 5 etc.
Just when I thought there was only one way to arrive at the answer, was I surprised that there were at least 5 methods to solve this problem!
PROBLEM 2: Card Trick
How do the 10 numerals arrange themselves? Example o-n-e-1-t-w-o-2-t-h-r-e-e-3 etc...
Take out your deck of cards and start problem solving!
Can't figure it out? Give up?
After several attempts, I worked this out:
PROBLEM 3: Tangram
Can you use 3 pieces to create a rectangle? 5 pieces?
Can you create congruent rectangles (using different pieces to form the same)?
Can you use all 7 pieces to form a rectangle?
Must Read: The classic "Grandfather Tang: A tale told with tangrams" by Ann Tompert
What do we need to solve the Math problems?
1. time to explore to get to the solutions
2. use different methods
3. discuss with someone (2 heads ARE better than one)
4. use concrete materials
5. see patterns
Theories
A. Dienes Stages:
1st: "Play" --- incidental or informal...explore, explore, explore!
2nd: Structured Learning --- unfolding information
3rd: Practice --- avoid practice too early or it will lead to practising the wrong things or what
they are unsure
B. Vygotsky -- social learning (working with people)
Zone of Proximal development (ZPD)
C. Jerome Brunner's CPA Approach
C oncrete
P ictorial
A bstract
What Children Learn In Mathematics
1. Looking for problems
2. Visualization
3. handling abstract ideas
4. persistence
5. belief that there is more than one way to solve problems
Suggested links:
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