One simply trick that makes fractions easy.

Why does my child have so much trouble with fractions?

Of all the areas of maths that cause problems for the young learner, fractions causes the most and I have often seen students in middle and upper secondary school still struggling to understand them. Fixing one simple misunderstanding can solve this.

When children start to learn about numbers, they do so by counting and recognizing quantities (e.g. ‘How many apples are there?’, ‘Can you count to 10?’, etc.).  Kindergartens and schools reinforce counting quantities and digits are formally introduced.. Over and over our children are told numbers tell us how many things there are. This is all important and good…. Until we start with fractions.

Fractions are a way of describing things that are less than one. The tricky part is the bottom bit of a fraction (the denominator). The denominator stops being a normal number and tells us a size instead[i]. For example the ‘4’ in ¼ tells us that the whole object (e.g. cake) should be divided into 4 equal parts (the size is 4).

When we learn, we tend to use what we know already to make sense of new things. For young children, who have been told over and over that a number is a quantity they can count, the denominator is seen in the light of what they have learnt already. This prior knowledge tells them that the denominator is a quantity because it is a number.  This leads them to all sorts of odd results. For example, ½ + ½ = 2/4 (because you can add quantities together).

If your child is struggling with fractions, sit down with them and explain how sizes work in fractions (using clothing sizes as a comparison can help). Once they understand that the denominator just describes the size, the rest becomes easy.

[i] For the purists, we know that the denominator uses quantities to describe the size and does not change from a normal number in this sense, however, for clarity in young learners it is far more important for them to understand the concept of a denominator as describing a size.

NAPLAN: Parents are giving it a thumbs up but should they?

NAPLAN: Parents are giving it a thumbs up but should they?

Parents backing NAPLAN as a guide to children’s progress is a very understandable thing. As parents, we are sometimes unsure of whether the school is giving us the honest information about our children. Having an organisation external to the school doing a check gives us an independent measure of both our child and the success of our school. It seems simple, but the concept of NAPLAN has a raft of unintended consequences that should be considered.

NAPLAN is Inaccurate

The NAPLAN test uses a small number of questions to assess students on a particular week each year. The nature of this means that individual students’ results can be inaccurate. The child may have had a distracting event in their life that week, or they might be a little unwell, or they had a late basketball game the night before, etc. It might also be that one class just happened to focus on one of the areas in the test the week before while another class was going to do it next week and this also skews the results.(See here for more:

As the number of students goes up, the overall accuracy of the results improves as these anomalies get absorbed in the larger numbers. NAPLAN gives accurate information for a state or the country as a whole but is less accurate at a school or individual level.

NAPLAN Causes School Panic

Because school results are readily available to parents, schools have become very concerned about NAPLAN results. Apart from the inaccuracies outlined above, it is right that schools should be concerned, but what schools actually do about this is sometimes alarming.

If a school is worried about poor NAPLAN results, you would think it would lead to them reviewing their teaching and learning practices and making long term plans to improve things. The NAPLAN tests could then be used as a benchmark for the success of those changes. This would be a fantastic result and does happen in some cases. (See here for more:

For many other schools, though, this worry only makes things worse. The school, worried about losing students, tries to game the system. They do this by spending weeks before the NAPLAN tests giving their students practice on sitting the tests. This gaming of the test leads the school to get inaccurate results and the NAPLAN test grows to become a stressful event for the student. (Read more here

Students see themselves as failures
Our schooling system uses a method of teaching where all students are expected to be doing the same work based on their grade level. There are many reasons for this, with the main one being economics – it is just too expensive to provide appropriate learning to every student individually. The NAPLAN testing measures students’ progress in this system. To be fair, it does measure across several levels, but this does not help struggling students much. Struggling students exist in this system that constantly tells them that they are not smart because they are not at the level of other students in the class. For such students, NAPLAN testing gives them an external opinion that confirms their self-belief that they are just dumb

My child can’t understand their homework… Neither can I!!

So here you are, your child is sitting staring at their maths homework and not understanding how to solve a problem. You can see the frustration building and you want to help. The problem is you can’t solve the problem either!

While it is understandable that a parent can feel inadequate in such a situation, it is my belief that this is one of the greatest opportunities for a parent to assist their child to become a good learner. Here are some reasons why:


The Dreaded Homework Sheet

This week’s topic is a bugbear for many parents where nights are spent helping a tearful child cope with homework in the form of a sheet of activities that need to be completed by the end of the week. The activities usually include some Mathematics and English questions as well as small puzzles. Your child usually doesn’t want to do the sheets and it becomes a point of contention in the household. If your child happens to be coping well at school, the homework sheet may be completed quickly on a Monday night and then there is no ongoing homework for the remainder of the week.


Homework: Is it good or bad?

In all the schools I worked at, the schools had a “Homework Policy” which stipulated how much homework was required each week at each year level. It was a weekly time-consuming ritual of setting, collecting, marking and following up the students who failed (often regularly) to complete homework assignments. The effort put in to the homework routines always seemed to be a lot of work for a very small return to me.

Like everything in education, the validity of homework comes up regularly in the media. In an article this week published by the ABC (read it here) some schools in Western Australia are moving away from having their children do homework. Are such schools doing the right thing? Homework is a contentious issue. In the following few weeks I will be publishing a series of articles related to homework where we will examine the benefits and problems with homework in our schools.