Models - One of the mainstays of our Singaporean Mathematics learning system. This method has been around for a long time and yes, even I remember learning them when I was a student myself! A quick search on Wikipedia reveals that this came about in our syllabus in the early 1980s so I suppose that makes my cohort one of the pioneers who learnt this system! (If you don't know what the model method is all about, here is a link to help.)
I do concede that my students who draw models during tests do better. However, marking their worksheets and thinking about the way schools in Singapore have carried this out has made me wonder: Are we putting too much emphasis on the model method, in the wrong way? I know my school isn't the first to have the students draw bars and bars of models in their work, sometimes even writing up whole worksheets dedicated to the drawing of accurate models. I know I'm not the first teacher to underline and redraw their students' models and sometimes, giving up altogether and making them erase everything to start again.
However, I want to say that by doing so, we have to be clear on our reasons for doing so.
First, let us consider what the model is. For this purpose, I found a video by Dr Yeap Ban Har very useful. This video shows him giving a talk on 'Singapore Math' in UK and here he explains what the model is:
So now I know that they are really a tool, or in his words, "a mere excuse... to develop visualization ability" and to provide a stepping stone to the algebra they will eventually encounter.
Which also makes me wonder why on earth some schools would force their students to draw models for every single problem sum, even deducting marks for models drawn wrongly even if the equations are correct. Isn't that like checking to see if you were counting on your fingers in the way that they want? Yes, it is an important tool for understanding but at the same time, there are other problem solving methods out there. Just as some kids would understand better through model drawing, there are also kids that understand just as well without the models. (Or worse, be led into misunderstanding the problem because of the model being drawn wrongly)
Another issue is the accuracy needed in drawing a model. Other than the lines having to be straight, the units have to follow mathematical logic as well. For example, if Robert has 3 times as many units as Stella, you cannot draw a model where Robert's 3 units are equal in length to Stella's 1 unit. This may lead students into developing a flawed understanding.
Yet I'm sceptical about making my students draw and erase until they draw perfect mathematical models. Remember that the syllabus is about developing problem-solving skills, not about mathematical drawing skills. Do we really have to make them draw all their models from scratch? Can we not, for example, provide blank rectangles for them to start the thinking process and then add on their own model drawings?
So as a summing up:
- Models are a method for teaching, amongst many others
- We teach them so that the students can visualize problems better (and there's a fine difference between problems and problem sums, I feel, but that's another topic for another day)
- We are not teaching them so that our students will be accurate artists
- Maybe there are other ways to let them use the model method, without making them draw everything from scratch
- Maybe we can also teach them, they have a choice to use it or not
Anyway, if you have become intrigued by Dr Yeap, here is another video where he talks about Singapore Math.
What do you think about the Model Method? Comment below!