MATHEMATICS Adapted from an article by George Anderberg published in the Pueblo Chieftan (Pueblo, Colorado) in 2002.
I USED TO BE GOOD AT MATHS.
“I was good at math in primary school then I started to fail.”
“Once I started Algebra it was over.
How often do you hear that statement?
What is it that goes wrong after Primary School? What can we do to improve our children’s math skills?
Maths reform really begins in primary school, maybe even earlier. We must be careful not to make the mistake that because primary students perform satisfactorily that they are OK. They could well be using inefficient strategies. Strategies that work satisfactorily at 4th, and 5th grade level but which will ultimately hinder a student’s ability to think mathematically and become mathematically proficient. Teaching students their tables by rote is not teaching numeracy skills. We must teach the associated logic.
This is where mental computation comes in.
What is mental computation you ask?
It is simply processing numbers using only your mind, choosing the easiest way to get the answer without writing anything down.
Many of us may recall the focus on mental arithmetic in our own schooling. What was important then was speed and accuracy; the human calculator took in numbers and produced an answer. If a method was inefficient it was quickly replaced with a better one. By constantly exercising our brain we developed a high level of mental maths fitness, much as an athlete would do when training to develop physical fitness.
During the past 30 years, research has started to recognize the value of mental computation in developing a rich understanding of place value and our number system as well as the associated logic. Mental computation is a broader concept than mental arithmetic; mental computation emphasizes the mental processes used to achieve the answer.
Too many students enter secondary school with calculating methods that consist solely of schemes of counting by one. While these methods often result in the correct answer, they take so much effort that there is little chance of learning new material. The learning of these students has reached a plateau. These students have not developed efficient computational skills in their early years and as a consequence their mathematical development is slowed. They take so long to perform the simplest of computational tasks that they are left behind. Their mental computation is inefficient and they must resort to pen and paper or a calculator for even the simplest task. In addition they have no way of quickly checking the reasonableness of their answer. (Counting On DET 2000)
In their early years students learning develops along similar pathways but there comes a time when the path divides. One path continues with the count by one or unitary method which, while producing correct answers, is very limited and inefficient. The other pathway uses “collection based procedures” and the use of place value to produce a quicker, more efficient method of computation.(Counting On DET 2000)
For example a student using collection-based procedures would think like this;
· 19 + 7 becomes 19 +1 +6 or 20 + 6.
· 57 + 28 becomes 50 + 20 + 5 + 10 or 55 + 30
A student using unitary method however would start at 19 and count on another 7, arriving at the correct answer but by a much slower route, and the route gets slower as the problem gets bigger.
These are the students who ”used to be good at maths” but who start failing in high school.
Mental computation is the beginning of mathematics, and along with it reasoning and logic skills. Skills that are as important (perhaps more important) as reading and communication skills. Yet, when students are at the most important stage of their learning, pre school to 5th grade, we educators barely give lip service to mathematics education. Where are the specialist maths teachers in the primary schools, where are the special maths programs. In some schools the program is so loaded that teachers are lucky to be able to teach 40 minutes of maths a day.
The Hunter is a community vitally interested in education and as a community we can instigate maths reform in our primary schools. We have some highly gifted and trained teachers but they lack the time, the programs, and the knowledge that they have broad community support.
We have recognized that reading begins at an early age but numeracy skills and the associated reasoning ability also begins at an early age and I fear that we have not sufficiently recognized this, to our detriment and the detriment of our children.
Ways to improve your child’s mental computation skills.
Rule # 1. Always ask your child how they got the answer.
Car Maths. While traveling this summer look at the mile markers and ask how far have we come and how far do we have to go.
For example, if you are passing exit 212 and you live near exit 94 how far have you got to go. Always ask how your child got the answer. If they are using efficient computation skills you should hear something like this:
If it was exit 194 then we would have 100 miles to go, 194 to 212 is 6 + 12 or another 18 miles so we have another 118 miles to go.
You can, as a family, calculate average speeds, travel times, estimated time of arrival. Remember the process is as important as the answer.
ADDO. Draw a 3X3 grid similar to naughts and crosses toe grid and write in 9 different numbers from 1 through to 20. From a deck of playing cards draw two cards and add their values, if the sum is one of your chosen numbers you can cross it off. The first to get 3 in a row wins. Increasing the number of cards drawn at a time can extend this game, so you might be adding 3, 4, or more numbers, or you can combine the cards to produce 2 digit numbers. Of course you will have to enlarge your grid and/or change the range of possible numbers. The variations are endless.