The importance of understanding and “feeling” the basics in mathematics.

As a high school teacher focusing on grades 10 – 12, this article is motivated by my observation of too many senior learners making basic mistakes and thereby losing unnecessary marks. This lack of basic understanding unfortunately emanates from the lower grades and although it is not my intention to criticise primary and junior secondary maths teachers, I believe that this issue is important enough to warrant some serious discussion.

Primary school and grades 8 and 9 are where a solid foundation needs to be laid for mathematics. Given the abstract nature of the subject, it is essential that one does not teach too much too soon. Learners need to be given enough time to absorb and get a feel for mathematical concepts. 

For example, grade 4 and 5 CAPS states that learners should add and subtract fractions with the same denominators. It is only in grade 6 that you are meant to introduce different denominators, but not any denominators, one needs to be a multiple of the other. If you are a teacher who feels that this is too simple and goes beyond what is required, please be aware that this will very likely lead to problems later on. If learners are not mature enough to grasp the concept, they will end up following rote methods that have no meaning for them. This will then result in them losing confidence and therefore the guts it requires to succeed in mathematics. And because of the hierarchical nature of maths, gaps start to develop in that all important foundation.

When learners graduate to grade 10, the demands of the curriculum are such that there is little time for going back to plug gaps. They mostly stay gaps . . . and sadly often become bigger gaps!

I would like to mention three typical problems which have their roots in the lower grades.

1. Fractions, especially adding and subtracting them. Just mentioning the word “fraction” rattles a lot of learners and if they can’t add (a) imagine the problems they will have later  with something like (b)! As I mentioned earlier, if learners are not given enough time to absorb a concept, they resort to memorising methods which they do not understand.

2. Negative numbers, and in particular, adding and subtracting them. I have noticed that learners are quick to grab their calculators to find the answer to – 2 – 3. A senior learner should have no problem doing this in their head if they have a feel for the concept of negative numbers.

3. Solving equations. Learners get so tangled up in the methods that they completely lose sight of what they are busy with. I had a learner the other day who could not understand why x = 5 in the equation 1 = (c).

And another who did the following: (d) because the method he was taught is “take the 9 to the other side and change the sign”.

As teachers, our job is to motivate and inspire learners, especially when teaching mathematics. By laying a solid foundation in the early years, learners will have a much better chance of success with their mathematics . . . something we desperately need in this country!

Written by: Peter Prentice

You Can Do Maths

Money Tips to Teach Your Kids

Ask any three year old “Where does money come from?” and they are bound to say “Out of the machine in the wall.”  If only life was that simple!! 

The sooner we teach our children about the source of money and its spending capacity, the more likely it is that they will grow into financially responsible adults.

In order to educate your children about finances, you need to set a good example for them.  If you can’t save money, then how can your children be expected to save money?  Or if your children see you buying everything you desire in a shop, how can you expect them to spend any differently?  So start by setting the right example.

Involve your children in the household finances

Quite often, parents chose not to talk to their children about finances, but it is important that they learn from an early age.  They do not need to hear the finer details about what you earn, otherwise the whole school may get to know.  Do involve them in the cost of living and the cost of basic household items. Teach them an understanding for budgeting so that they can see how you spend your money. 

Children understand by what they see.  To try and illustrate how quickly money is spent, try drawing out all your earnings in cash.  Make up a pile of R100 notes.  Sit your child down and show them how one pile goes towards paying the bond, another towards food, another towards the telephone account etc.  They will then see how the pile diminishes very quickly.

Life is about the choices we make

Children need to learn from a young age that there is a big difference between ‘wants’ and ‘needs’.  A want is an ice cream, whereas a need is a healthy balanced meal.  A want is the latest designer clothes, a need is a school uniform.  It is OK to want, but you need to teach them that ‘wants’ are met only after ‘needs’ have been seen to.

Try and explain the advantages of buying the item and the disadvantages.  For example, instead of spending money on chips and chocolates, rather save it for a while and buy something lasting like a new bike helmet or a sleeping bag for a school trip  -  you can tell that I am the mother of a boy!

By teaching our children about choices, when they are older and wiser, they will be able to make informed decisions when purchasing bigger items such as a microwave or a gas braai.  It will give them the background to be able to decide between a new car and a used car.  They will have learned to do research and to avoid spur-of-the-moment decisions.

Work equals Reward

It is imperative that children learn that we as parents work hard for our money!  Money is a precious resource.  Success at school work can bring from you some monetary rewards if that is how you want to start this lesson in life.  Otherwise, repeatedly pointing out what you as parents own and are able to purchase because of your job  -  which is because of your education -  is an on-going additional resource. 

If you constantly just give money to your children as and when they ask for it, they will not learn how to earn money, and therefore, will not understand the real value of money.  Children need to understand that money doesn’t just pour out of the machine in the wall.  They need to realise that there is a direct relationship between the work that we do and how much money is available to spend.

Banking

Involve your child in opening a bank account for them.  I would suggest that you open a debit card account, and once your child is old enough, in most cases around 10 or 11, you can start paying their pocket money directly into the bank account. Encourage them to start using the debit card when purchasing items.  Link the electronic bank statements to their email address, and open a ‘file’ for them to save the statements.  Discuss the statements with them, showing them the debits (amounts they have spent) and the credits (the pocket money you have paid to them or any other money they have paid into the bank account).

Budgeting

Most children and teenagers will definitely have better things to do than drawing up a budget, but I really would encourage you to help your children with a budget.  Although it doesn’t need to be electronic, once children enter high school, they will probably feel very comfortable using an Excel spread sheet and this will certainly be of benefit to them, as it is quicker and easier for regular budgeting.

It is imperative that children understand that a budget is a saving and a spending plan, with the emphasis on saving.  The earlier children start budgeting, the less likely it is that they will end up in debt  -  more on that later.

With budgeting, at the outset, children need to learn two very important principles:

1.       Pay myself first (i.e. save at least 10% of your money)

2.       Tithe (i.e. invest at least 10% into your church or other charity of choice)

Saving is not optional. They must save on a monthly basis.  When it comes to saving money, a young child can be taught the concept of saving toward something, for example, saving towards a new computer game.  Over the years, as children learn this concept, they will then be able to fully grasp the need to start saving for their first car.

Saving should be based on a percentage of their pocket money, and I would suggest that it should be at least 10% of each pocket money payment.  A percentage works best as it can then also be used when they receive money for birthdays or at Christmas time.

Set a goal.  Identify what it is that they are saving for;  smaller items for younger children and bigger items such as an ipod or cellphone for older children.

http://www.corewealth.co.za/

Use your money cleverly!

Written by: Kirsty Scully