Explain this
Assessment informing planning: Action Research
The Gaps and Misconceptions Tool was developed by Devon LDP ©2011 and has been made available here by kind permission.
Research references: Devon Learning and Development Partnership
The Gaps and Misconceptions tool was written and created by the Devon Primary Maths Team (part of Devon Learning and Development Partnership) and is made available, with thanks, on the ATM website.
Formative assessment
The NNS has always suggested ways to ensure that assessment informs planning (formative assessment). For example:
- Simple highlighting systems on medium term plans that can be used to keep a track of what the class has achieved and then be used to help plan the next half term or term’s work.
- A teacher plans the first few days of the week and then adjusts his/her plans as the week progresses.
Sample medium term plans and unit plans have been produced to help teachers with medium term and short term planning on the understanding that they are to be adjusted to fit the needs of the children in the class.
However this ‘adjusting’ is something that teachers can find difficult.
OFSTED reports that: ‘There are weaknesses in teachers’ assessment of pupils progress’ and in particular: ‘teachers do not do enough to diagnose pupil difficulties or use this information to adjust their teaching’
This could be because it can be hard to ask the right questions to identify difficulties. It is even harder to think of yet another way to teach the concept that is misunderstood. The subject knowledge of the teacher is key; teachers need to be able to use a variety of visual images when explaining and to make links between different mathematical concepts.
Studies have shown that strengthening formative assessment produces significant and often substantial learning gains (Black and Wiliam 1998). So formative assessment became the focus for the Assessment Action Research Group that worked together in 2002-2003. It looked not just at how to diagnose problems but also what to do when problems had been identified (using probing questions to identify misconceptions which are then tackled using mathematical images).
Assess and Review Lessons
The NNS has started to help teachers begin formative assessment with the document ‘Using assess and review lessons’ (Ref: DfES 0632/2001)
It has a section that:
- poses questions to reveal difficulties (probing questions)
- gives ideas to help re-teach a mathematical concept
all related to the key objectives.
Helpful Material
The Action research group identified that teachers could be helped further if provided with material that had:
- Probing questions for the mathematical concepts that most children find difficult e.g. subtraction, division and decimal fractions;
- Generic probing questions that can be used for any mathematical concept;
- Images to undo misconceptions or fill gaps in common areas of difficulty.
Action Research Methodology
The group used existing questions in
- NNS ‘probing questions’
- QCA research report ‘Using assessment to raise achievement in Mathematics’
- ‘Errors and misconceptions in Maths (Mike Spooner)
to help begin the process of writing further good probing questions.
The mathematical concepts chosen reflected individual schools’ curricular targets and those identified by QCA in their booklets ‘Implications for teaching and learning from the 2002 SATs’
The format for this document is based on documents produced by the NNS and NLS on inclusion (‘Including all children in the literacy hour and daily mathematics lesson’).
Many of the questions presented here have been tried on children in the teachers’ schools and their responses have been written up as clearly as possible. It became clear, when asking these questions, that follow up questions are required to help precisely identify the misconception or gap. These were often: ‘how do you know/how did you work that out?’ type questions. Having white boards available for the children and the teacher can help if jottings/pictures are needed to aid explanation.
How to use the questions
The questions can be used with the whole class, a group, pairs, or individuals.
Children can respond orally to a partner and then to the teacher or on a white board. It always a good idea to expect children to answer in whole sentences with correct vocabulary. This is more likely to happen if they have a chance to try out a response on a partner before talking to the teacher in front of the class or with a group.
The teachers in the group used the questions with small groups so that we could easily make a record of their responses, but this was only for the purposes of the action research. For teachers trying our questions, the best use of the children’s replies would be to inform/adjust further teaching/planning as opposed to recording any actual responses.
When to use the questions
These questions can be asked at the end of a unit of work during an ‘assess and review’ session. However they might more usefully be posed before a unit of work.
For example: on the Friday before a unit of work on fractions a Y4 teacher asks the probing questions to see how much the children have retained from the last time the children were taught the topic and to identify any prevalent misconceptions. They can then begin to plan the unit of work based on their own children’s understanding.
In addition teachers can feedback their results to other teachers, especially those in younger year groups. The question sheets have a column entitled ‘Implications for other year groups’, this lists teaching ideas/images that might be useful for the teachers of younger children.
Generic probing question starters
Teachers on the project noticed that asking probing type questions can become second nature and can used throughout teaching not just when one is consciously assessing.
As Black and Wiliam (1998) note: ‘instruction and formative assessment are indivisible’. Teachers asking these questions really want to hear the replies, they are not ‘guess what is in my head’ type questions. Question starters were developed to help generate probing questions.
In order to create questions that probed into children’s understanding the teachers tried out a number of sentence starters. It was noticed that these questions could be grouped into 5 types of questions. These are set out below, with a few examples from different areas of Maths:
Real life
Can you give me a real life context for...
- Can you give me a real life context for 34 - 28=6?
- Can you give me a real life context for measuring angles?
- Can you give me a real life context for why you need to measure things?
- Can you give me a real life context for when would you need to read and interpret a graph?
An after the event: ‘how?’
How did you decide... How did you work it out...
- How did you work out the answer to that calculation?
- How did you decide which units to use when measuring?
- How did you decide that the caterpillar was longer than your rubber?
- How did you work out how many tickets you would need for the pantomime?
- How did you decide how to order the numbers?
Generalisations
What are the rules for deciding... How do you find... What clues are you looking for... Do you have any tips... Why is this a... How do you...
- Why is this an equilateral triangle?
- Why is this a prime number?
- How do you find out whether a shape is symmetrical or not?
- Do you have tips for someone trying to calculate the area of the shape?
- How do you identify groups of multiples?
- Are there any rules when you are ordering fractions?
- Do you have any tips for someone comparing lengths?
- How do you work out how many children in the school have school dinners?
- Are there any clues you can use to help interpret a graph?
Identifying another child’s misconception
Which of these are wrong and why... Richard said something incorrect: what does he need to know to get it right?
- All quadrilaterals have at least one right angle.
- Richard put these numbers in order: 4.7, 4.05, 4.3, 4.24, what does he need to know to get it right?
- All triangles are symmetrical.
- Multiplication makes the number bigger.
- The chance of a head coming up every time a coin is tossed is unlikely.
- Richard said that these 2 containers hold the same amount. Is he right? Why?
Always/sometimes/never
Is this statement always... never... sometimes... true? How could you change it to make a true statement?
- Prime numbers are odd.
- Shapes with three edges are triangles.
- Adding numbers gives you a bigger answer.
