How do we assess if children have learnt a fact or not? Usually it is their ability to recall a matching answer to a question we post them.
“What is 10 x 10?” “One hundred.” (Learnt! Tick!)
“If ten friends give you ten sweets each, how many sweets do you have?”
“Er .. er… er … ”
“Come on, if you have ten rows of ten objects, how many objects have you got?”
“Er … ”
While the above may seem to be a discussion of an adult with two separate children, the two children were actually one and the same. The same child could moments earlier churn out the answer for ten mutiplied by ten, yet when presented with a word problem to an answer she already knew, could not connect the two together.
Unfortunately this are the limitations faced by the education system. Assessing learning and understanding is difficult, and time-consuming, and perhaps too individual a task to be managed within the confines of a classroom ratio of 30:1. So instead of understanding if students have learnt, teachers have to demonstrate that students are capable of reproducing facts that they have more often than not memorised and kept within short term memory, then reproduced in an exam question paper that is largely fact based and recollection-biased.
As educators, we have to communicate understanding and learning alongside the acquisition of facts and knowledge. We also have to communicate a love for learning, a desire to find things out, and a desire to be creative and experiment. In many of these cases we should withhold our inner desires for the right or wrong answer, but encourage the development of ideas first, then the facts.
Here is an example. Instead of teaching by rote questions such as 10 x 10 x 20 and other mental maths facts, another technique often used is the Problem-Solving Method. This can manifest itself in methods such as these:
Give a group of eight students twelve items each, and ask them to divide up these items equally into six boxes.
Some students will realise that one way to do this is for the first student to place his item in the boxes, then the second student to continue where he left off, and for each successive student to do that in turn. This is the linear way, where the items are “added” equally into each box.
Some may decide to count how many items they have first, and then see if they can divide them into four piles. This is the multiply and then divide method.
After a ten-minute timeframe, students may report back on their answers and be encouraged to look for other methods and examine their effectiveness.
This is a time-consuming process to teach 12 x 8 = 96, and 96 divided by 4 = 24. And in many classrooms, there isn’t really that much time to do all the mental sums in this way. But in the next lesson, you could assign one group to do another similar problem, while giving another group a multiplication chart to obtain the answer from.
In this way, you have demonstrated to them that there is purpose and meaning in what they are doing, and that there is reason to learn the mental maths – so that it is a quicker way to get the answer.
Purpose, Meaning and Relevance. These should form the basis of learning upon which facts are built. This ensures that another information memorised or learnt by the textbook delivery at least has some sort of personal relevance.