5 top tips for a mastery approach in KS2 mathematics
Russell Timmins, August 2016
1. Embed concepts at the outset
Take time to embed all concepts fully.
An unselfconscious use of practical equipment at the start of all new mathematical ideas helps to achieve this goal, it also helps to de-stigmatise the use of concrete equipment for all in the classroom.
2. Concrete - semi concrete - abstract
Avoid going for route one.
In other words do not teach any abstract concepts until pupils have understood what the mathematics is doing, where it is being done and where links to other mathematical ideas can be joined.
A generic approach of understanding from the use of concrete apparatus followed by its withdrawal and replacement with diagrams or visual aids. When this is confidently happening with pupils they will be ready to go for a more abstract and fluent approach to their mathematics in each area of study.
3. Assess for mathematical reasoning
Mathematical reasoning is the foundation stone of all mathematical understanding.
“If I multiply 2 odd numbers, the product cannot be an even number. True or false? How do you know?” Mathematical reasoning as a major player in mathematics education enables the learner to make links quite smoothly to other mathematical areas. It also determines whether calculations are necessary for example, “Is 2472 ÷ 9 a whole number?” (A simple yes or no answer.)
If mathematical reasoning is not used then the calculation must be carried out in order
to answer the question. However, if they reason, that if the sum of all digits in a
number totals 9 then it is divisible by 9 and if not it is not divisible by 9, then
mathematical reasoning has saved a lot of work but still given a satisfactory answer
to the question.
4. Assess for problem solving
What do we mean by problem solving?
The vast majority of people when asked this believe it to be wordy problems, where the mathematics is not clearly defined in the question. The classic example is this type of question:
“If 3 men take 5 days to build a wall, how long would it take 4 men?” However in reality a problem is something that requires a solution and finding the solution is the problem. How the problem is solved is where we are making our assessments. Is the problem a straight forward case of using an applied process like column addition for example? Perhaps, but is it being checked with the inverse application of column subtraction?
In year 6, given a problem involving percentages, are pupils able to convert to
fractions, if this makes the solution easier to achieve? Problem solving involves
mathematical reasoning and the ability to use links to other mathematics in order to
get to the end result. A simple correct answer is not always enough to make
5. Assessing mathematical fluency
The fluent use of a process is not always worthy of a tick in the assessment box.
Fluency in mathematics is the pinnacle of learning based on mathematical reasoning
and the ability to problem solve through a process that is well understood and easily
checked for errors.
Think back to secondary school trigonometry. I was taught the acronym SohCahToa in order to help me to remember how to find unknown sides and angles in right-triangles. Look at the wording. Remember not understand because if I am frank I did not really understand how I kept getting all my answers correct. All I knew was that the process worked. Today that is simply not good enough and quite right too. True fluency of approach is solidly understood mathematics, the offshoot of which is a much reduced requirement of revision because it is understood and not something to remember.
Fluency in mathematics relies on the learner’s ability to see problems from more than one angle and by choosing the most efficient route every time. True fluency.