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.
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 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: https://www.aare.edu.au/blog/?tag=misleading-naplan-reports.)
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.
Causes School Panic
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.
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: https://ro.ecu.edu.au/cgi/viewcontent.cgi?referer=http://scholar.google.com.au/&httpsredir=1&article=3074&context=ecuworkspost2013.)
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 https://files.eric.ed.gov/fulltext/EJ1017709.pdf.)
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
A video blog this week. Click on this link to watch it. > An underclass of learners
The first step to lasting changing something as hard as this is an open exchange of ideas. If you have any thoughts or ideas around this, please add it in the comments.
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:
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.
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.