| How to Teach Math (Elementary Math) | | | | head with a method. How they possess these |
| | | | | “methods” in their head without being taught |
| Frank Ho | | | | is interesting. What happens to those children who |
| | | | | were not born with these “methods’ in their |
| Canada certified math teacher and founder of Ho | | | | brain? We can train them but how? |
| Math and Chess | | | | Most math worksheets today are not designed in a |
| | | | | way to require children to do a lot of thinking and |
| | | | | basically are done with repetitions to get proficiency |
| Yesterday I was teaching a grade one girl and she | | | | and fluency. Many times, we see word problems |
| had some trouble to figure out the answers with | | | | require children to do backwards calculations but do |
| questions such as ? + 5 = 11 but when given the | | | | we have basics worksheets to encourage backward |
| question 6 + 5 to her, she could do it with ease. So | | | | calculations or reversing thinking? |
| clearly the reverse thinking presents a bit difficulty to | | | | I did an experiment on the first girl I mentioned that |
| her. She does not have any learning disability and is | | | | I gave her some training on ? + 5 = 11 similar type of |
| eager to learn question. In 2-hour lesson she sit in | | | | questions then eventually she was happy since she |
| front of me, she never asked for any breaks but | | | | could do all kinds of similar problems with different |
| continually asked me for more problems to work on. | | | | numbers but the interesting experiment is the minute |
| At the same time I was thinking about a boy who | | | | I changed the question to the following circle + |
| was about grade 3 and could get the following | | | | triangle = 11, triangle = 5 and what is the value of |
| answer in his brain and his mom could not figure out | | | | circle? She got confused but we know all I did was |
| how sometimes he got answers. | | | | simply replace numbers by symbols and she got into |
| The question is something like A + B = 10, B + C = | | | | trouble again. The next level will be to replace |
| 16, C + A = 20, what is A, B, C? | | | | symbols by variables to go into algebra. From this |
| Asked how he got the answer, he told me that | | | | experiment, I learned that it is very important to |
| because A + B = 10 which is smaller than B + C so | | | | train children with symbols at very earlier age so that |
| he knew C is bigger than A by 6 so he substituted C | | | | they are not afraid about symbols. The problem is |
| = A + 6 into C + A =20 to get A which is 7. I do | | | | most worksheets one can buy is not designed this |
| not know if he really figured the answer all by himself | | | | way and does not foster the thinking to go from |
| or he already had some training before he came to | | | | “figures” or pictures to symbols. |
| see me but still it is impressive he could do it all in his | | | | The biggest problem is that we are failing to teach |
| head and found out the relationship. Some grade 11 | | | | how to do reverse thinking and how to solve word |
| students in high school have trouble to work out this | | | | problems. It seems strange to children that once |
| kind of problem. His mom told me that he is gifted. | | | | they master their basics computation skills they face |
| I remember a boy who is 4 years old and could | | | | another hurdle that is they still have to learn another |
| already do additions, subtractions, and multiplications | | | | set of skills to do word problems. This is the problem |
| all in his head but had difficulty to “see” what | | | | that we as educators have not come up with a |
| shall be the next move on the chessboard (even | | | | transition way to show children on how to go from |
| made wrong moves). Why? Do our brain process | | | | “computation” to “word problem”. |
| numbers and images (chessboard) differently? A | | | | Many math teachers are making mistakes by using |
| grade 3 girl who came to my class and just could not | | | | the methods of explaining the concepts to do |
| do multiplication but finally could do it very fluently at | | | | calculations as well. For example, the method of using |
| grade 6 and I asked her what happened so she told | | | | “tiles” to explain how to do integers is fine |
| me she decided to memorized at grade 6 and the | | | | but it is entire different mater to use the “tile |
| same story happened to a boy, he told me that he | | | | method” to do actual computations. It is too |
| finally “decided” to memorize it at grade 6 | | | | slow and cumbersome and children will lose |
| etc. | | | | confidence if to use the tile method every time to |
| My purpose of recording many of my teaching | | | | do integers calculations. The same problems with |
| examples above is to say that there are still a lot | | | | times table using skip counts or subtractions using |
| that we do not know on how children learn and how | | | | count back, all these are good for explaining concepts |
| to effectively motivate them and get their interest in | | | | but to get the fluency children required to move |
| learning and how we teach them effectively. The | | | | ahead, then children can not rely on count back |
| most surprising I discovered is we have not taught | | | | every time to do subtractions. I ask one child who is |
| children math in an effective way and perhaps in the | | | | using finger method to do multiplication by 2 hands |
| wrong way. I will explain my thinking and | | | | (he is grade 5), “Are you going to put your pencil |
| observations below. | | | | down and so you can use your 2 hands to do |
| Other than gifted children, the math skills need to be | | | | calculations at grocery counter with you wife and |
| taught to children and also learned by children. The | | | | children standing in front of you?” If not then |
| examples of Pascal who could add from 1 to 100 | | | | what good is the finger method when it actually |
| without being taught and the boy cited above who | | | | allows children to use outside instrument (similar to |
| could do simultaneous equations in his head are | | | | the idea of using a calculator), not their mental power |
| examples that some children could do math in their | | | | to help them to develop their brain? |