Wednesday, March 29, 2017

Modeling the Model Diagram

I remember when I was learning to be a teacher, the math professor gave the class of trainee teachers a Primary 4/5 question. She wanted us to solve the question with model drawing. There were about twenty of us, with different backgrounds and age groups. The time given was 15 min. None of us managed to solve it. NONE. Mind you, all of us were university graduates. 

It's been almost 10 years since then and since then, I always believed that it does help kids with their Math. Unfortunately, most people I speak to, don't agree with me. There was a mother whom I met at a school's event recently who actually dissuaded her girl from drawing the model as she thought it was a waste of time. 

Audrey is P3 this year, and it's also this year that her teacher is requiring the class to do their models in the Math sums. I naively thought P3 Math means simple math questions = simple intro to model diagrams = a piece of cake. 
I was wrong. I should have known that the hardest thing to teach are always the basics. Audrey came home with a math worksheet one day, which required her to do her model diagram and solve the questions. It was already painful to see her come up with a diagram because she was quite particular about being neat and later erase all away because she didn't get it. After 30 minutes, she was still at the first (unsolved) question. I tried to do it slow with her, but she was not getting it. After a while, I gave up and basically did her homework with her. (I 'taught' and she wrote) Because we again had an unpleasant learning experience together, I felt lousy and was up the whole night thinking of what I could do to change things. 

We went back to basics  of the model diagram after school one day. So far it has worked for me. And in case you are one of those who were born too early for the model diagram method, see if this works for you. 

1) I did away with the drawing of the diagram
I used strips of construction papers (4 colors would be safe since so far, I haven't used more than 3 colors) of standard varying lengths. I halved a strip for the pink and further halved the lengths for the orange and blue respectively. Whilst the green I divided the paper into threes.
I did this for many reasons. Firstly, it was less time consuming for Audrey to present her model and secondly I'm not sure if it was just her, but she couldn't see at times that certain parts need to be the same (because it represents the same amount) and certain parts need to be longer proportionately to represent a greater amount.

2) She only shows me the diagram
This doesn't mean she doesn't solve the question, but my focus was really the diagram and not her working. The diagram is essentially a working and while she doesn't need to do her working, I still ask her what her steps are.
I got her to do on her white board from school since I really didn't want to keep wasting paper and I thought it was easier to erase any mistakes with the duster than the eraser.

3) Step-by-step intro to model diagram
With all my materials prepared, I had a step-by-step demo. I showed her an example, guided her on the next and let her do the second. She fumbles sometimes, but with practice she does get it.
In short, this is how you show it:
a) Translate line by line of the question to the diagram. (It helps to break down the question. If sometimes the first line does not help much, you can use the second line to help) 
b) Labeling  (It helps to understand the premise of the question)
c) "Layering": When comparing the strips, all similarities must be found in the model (it helps the child to relate to the question)
The above shows an example of how "layering" works. Comparing the first and third strips with the second, the difference is shown by the green and orange strips respectively. However, since the green is longer than the orange strip, it would also mean that the green strip consist of the orange portion inside it. Visually, it helps the child to see which has the most and by how much. 
d) Finally, indicate the question with a question mark (It helps to understand what we are finding out)

Here's an example:
There were 15 more pupils in Class 3A than in Class 3B. 20 pupils from Class 3B moved to Class 3A. How many more pupils were there in Class 3A than Class 3B in the end?
Starting from top left to right.
I always tell Audrey to approach the question line by line since most of the questions are pretty straight-forward. (There are some questions which you do not work on the first line, but because it won't be 'basics' I won't be talking about it here. If you do want to know how to do it, let me know, and I can always share it)

As you can see, she used the green strip to represent 20 pupils from Class 3B in the second picture and immediately did the "layering" step of placing it in the first strip as well. She then "moves" the 20 students to the first strip by adding another green strip to it, while indicating using a dotted line that the students have moved to the first class. (I would tell her to cover the bottom green strip so that she would remember that the 20 students are no more in that class, allowing her to see the 'excess' students  in 3A as compared to 3B)

Obviously, it's not possible to use the strips in a pencil and paper exam mode. Only after she is comfortable moving the colored strips, I would let her attempt drawing it out. 
Yes I know, the question mark for the diagram is missing :P
And I am proud to say, she is slowly becoming a little expert in model drawing. :P

I know it's a little wordy today… Nonetheless, I hope it has helped you to help your child a little. :) Let me know if it did!!!