Throughout my own subject knowledge, fractions is a concept in which I enjoy resolving problems to. As a child I remember thriving of the solutions to equivalent fractions. This was through the method I was taught and the familiarization of specific multiples. This continued throughout high school from the reoccurring practice that took place within maths classes.
Once I joined university I identified within my first year that this is a concept that I would like to refresh and become familiar with once again. I realised that my understanding of improper fractions and transferring fractions into decimals and percentages is a target for my own personal subject knowledge.
Throughout reading, I have realised the importance mathematical language such as ‘numerator‘ and ‘denominator‘, nevertheless Haylock (2010) suggests that it is acceptable to use informal language , such as ‘top number’ and ‘bottom number’. From this it has made me realise the importance of grasping understanding first and then moving onto more complex ideologies. I hope to develop my pedagogical understanding through reading and different theoretical perspectives.
I have realised through seminars that integrating fractions is essential towards development in other mathematical areas, this includes:
- Data Handling
- Mixed number to improper fractions.
Terminology and Examples:
- Improper Fraction: 11/8 —-> 1 3/8 (mixed number)
- Proper Fraction: 3/8
- Mixed Number Fraction: 3 5/8 —-> 29/8 Solution: 8 x 3 + 5 = 29/8
- equivalent Fractions: 2/6, 4/12, 8/24
- A fraction is part of a WHOLE with the top number being the ‘numerator’ and bottom number being the ‘denominator’.
How to visualise improper fractions:
For example 9/4 could be visualised using pizzas, circles, or other shapes to show children the link between a mixed number and an improper fraction. It represents two whole cakes cut in quarters alongside a quarter of a cake.
Visual representations helped my personal subject knowledge, this allowed me to understand the importance in allowing children to notice patterns and sequences, especially in equidistant fractions As Haylock (2014) suggests, this can establish the idea that you can change one fraction into equilivant fractions by multiplying or dividing the denominator and numerator by the same thing.
Within professionals practice Phase 1A, fractions were introduced to year 3 children using squares on the board. Children were given a fraction such as 2/4, they were then told this means ‘2’ out of ‘4’. We then drew four squares on the board and modelled to the children if it is two out of four, how many squares will need to be shaded. Children were asked randomly using match sticks with their names on to ensure the same children are not answering. Children responded well and the majority of children had similar ideas. Afer children responded with the correct answer they were asked mastery styles questions such as ‘how and why did you get this answer’, ensuring that they are actually developing understanding and are able to recognise why. Some other children also identified this to being a half, after a visual representation took place on the board, which was able to lead onto more complex ideas.
From this method by the end of the week all children were able to solve at least 2:5 equivalent fraction problems correctly.
Teaching method used within practice.
This allowed me to recognise that even the simplest resources can be powerful and effective. With the use of colour, shapes and open questioning children were able to think in-depth about the answers they got. This again, showed be the absolute importance of mastery style questions in the children’s learning. It allowed me to recognise in maths that some children may be able to say the correct answer but may not be able to explain their understanding. It is up to us as teachers to break this down for them and scaffold their understanding with use of language and discussion.
National Curriculum Links:
Y1:Introduce to equal amounts and 1/2, 1/4.
Y2: Introduce to 3/4 as well as quantities of amounts. Should be able to simplify 2/4 to 1/2.
Y3: Introduce to equivalent fractions, addition of fractions and comparison of fractions.
Y4: Introduce relationships between fractions and division. For example 1/100 of 600 is 600 divided by 100.
Y5: Introduce to improper fractions as well as percentage, fraction and decimal equivalence.
Y6:Add and subtract fractions with different denominators. introduce multiplication of fractions as well as simplifying and dividing.
What I knew before:I had a basic idea of how to solve different problems with fractions. My strongest area was equivalent fractions.
What I’ve learnt: I now have a wider understanding of the relation of fractions in regards to the curriculum. I have an idea of what each Key Stage should be learning for their age stage development. I have also learnt the importance of scaffolding through visualisation and questioning.
What I now want to know: Do all children learn maths in the same way, are certain strategies effective to all children, how can I differentiate to meet specific needs? What are different mathematical concepts in relation to theorists?