“Don’t draw models!” I sure hope I heard wrong . But there has been talk among our students that their previous tutors encourage them not to use model. In fact, throughout our teaching history, it seems that that is sometimes, not all the time, the modus operandi of many tutors or teachers – To teach the units method instead.
Like I said I sure hope I got this wrong. After all, it is wrong to judge the actions of others based on the hearsay of others as well. Perhaps, most teachers teach the units method mostly and advocate it as a preference to solving questions. Perhaps, these students we taught misinterpreted what their previous teachers and/or tutors said and we will leave it as that. And I say that if the child is ok with that mode of solving questions, then so be it. But a lot of times, students can see better with models. And as adults, we have to understand that the mind of a child is comparatively undeveloped as compared to the mind of a full grown adult. Numbers sometimes hold little meaning to our young. Some students even use both the model and the units method within the workings to enhance problem solving ability. I don’t see anything wrong with that. In fact, that is a good strategy to have. The mind has a problem with abstractions in many instances and it is wise to put pen to paper, draw a model or a diagram, detail down the workings step by step in order to work towards the final answer.
One thing about the use of models is that it sure does take a longer time to solve a question with models. This of course is a generalisation and this generalisation is made when considering the time involved in the units method, which can be a lot more efficient than the model method. Another restriction is that while using models, sometimes, one has to slice and dice the model to too many boxes. And, if a student counts wrongly the number of boxes, that can lead to errors at this stage and even down to the answer. In a sense, that error is carried forward to the end. A dreamy student then takes the final answer as correct without checking. Is this the right way? Obviously not. Checking is always a must. However, that is another article altogether.
Back to the part on drawing models. I think the answer as to whether the students sheould rely exclusively on the units method is determined solely by the ability of the students.Let us put students into three categories. Students deemed to be below average, average and above average broadly speaking. A student of average ability and less and has problem “seeing” what the question is asking for should attempt the drawing of a model. Certain questions are before-after type questions. For those questions, drawing at least a 2 stage model will help the student. This is what we have found out. For average ability students and up, while a student may be able to “see” better than others in these categories, model drawing is not as essential but for tough questions, drawing model can really help the student to see the “light”.
So don’t be stifled by general rules. Be flexible and encourage flexibility among your children. Drawing the model and using the units method can occur together to aid problem solving. In fact, that is what we do at Singaporemathguru. Our videos, which are one too many, and within the video ( which is an explanation to a particular question) , students are able to understand the pitfalls and the misconceptions of a certain way of thinking. We try to address all of that here at Singaporemathguru. At Singaporemathguru, we try to teach thinking about thinking(metacognition) and not just solving the question itself. We teach logical reasoning, deductive and inferential skills to questions besides just solving the question mechanically. For the A star, students must be able to go beyond mechanical thinking. They would have to think out of the box to get to the answer at times. Also, many a time, we connect the dots for students as well. For example, did you know that many students are not able to solve assumption questions using methods taught in schools but do better with the drawing of a table and making inferences from it? Both methods are interrelated. We teach both methods and in a sense, both methods reinforce each other. That is also the reason why some of our videos are long in duration. But if you’d like, please just fast forward the video to the part which you want to watch.
And let us further answer the question as to whether to draw a model from real life examples. Student A and Student B. Both students have above average ability. Both have marks in the range of 80 to 90. Student A draws models but Student B doesn’t When it comes to the crunch though, an examination that forces you to think, the student with the ability to draw models edges out the other and gets the A star. Case in point, whatever ability you are, draw it anyway even if there is just a 1% incremental chance of getting the answer right through the model. What is there to lose in drawing a model? Nothing! What is there to gain? All the marks. Perhaps, students and parents can think about this from a risk and reward perspective. The risk is low and the reward is high. “If I don’t do it, I will definitely lose those marks. If I do it, the marks could very well, possibly be mine!”
The Singaporemathguru Team