Developing problem solving in your school
Maths Week Ireland aims to help teachers unpick what problem solving really looks like in the classroom and how they can develop it within their pupils. We want to provide teachers with the tools and resources to organise their own problem solving workshops in schools.
A fixed mindset describes someone who believes that their level of intelligence cannot be changed. They are born with a certain limit on what they can achieve and nothing they do will change this. Somebody with a growth mindset believes that their intelligence can grow depending on the amount of effort they put in.
As adults and teachers, we have to be careful about the mindset we have about maths. It is important to note at this stage that maths is not a gene that is passed down from a mother or father. A person can succeed in maths depending on the effort they put in. It is therefore important that, as adults, we are saying and doing the right things to encourage this.
Teachers should think carefully about the types of praise they use in the classroom. They should not always praise the child that finishes everything first or gets everything right the first time around. This implies that you have to be quick and accurate in maths which is not the case. Maths is about exploring possibilities and so effort needs to be praised. Mistakes are a valuable learning experience and should be acknowledged as such.
Words/phrases that encourage a growth mindset and should be used by teachers and parents include:
- How did you do that?
- Can you show me more?
- Wow – that’s great – well done!
- That looks like it took a lot of effort.
- How many ways did you try before you found the right way?
- What do you plan to do next?
- Would you change anything if you had to do it again? Why?
Words to avoid using regularly and that will encourage a fixed mindset include:
As always it is about the context in which you give praise and be conscious of the impact you are having on the other children in the class when giving praise.
There are several great videos clips on YouTube about Growth Mindset:
Mathematicians are people who think deeply about the maths they are working on – speed is not a contributing factor. Mathematicians make connections and think logically. Very often mathematicians will not find the solution the first time but they will persevere and try again until they succeed. Perseverance is imperative in maths and we need children to understand this from an early age.
The Primary Irish Maths Curriculum states “Information acquired is interpreted by the learners themselves, who construct meaning by making links between new and existing knowledge”. This statement requires pupils to think for themselves and make sense of the maths that they are doing as well as make connections between topics.
Mathematics is a series of interconnected ideas; every mathematical area algebra, geometry, trigonometry, etc. is part of a whole that constitutes an evolving system, a way of thinking and communicating ideas. However, in most classrooms maths is taught through topics, and children can develop a view that each topic is separate to the next. This is part of the mindset that needs to change. Unless the teacher establishes these connections, they may be missed by the learner.
Top Tips to encourage mathematical thinking:
- Ensure children know that there are several ways to solve a calculation. For example, 18 x 5: you could write it out using the short multiplication written layout; you could round 18 to 20, multiply by 5 and then subtract ten; you could halve 18 and double 10 to multiply 9 x 10. Can you think of any other ways?
- ‘I just know’ or ‘I did it in my head’ – Do not accept these for answers – always ask pupils to explain or show you how they solved a question. Very often when a child becomes comfortable with a calculation strategy they will ‘skip’ steps internally and not realise what maths they are doing when solving a question. Asking them to explain regularly will ensure they fully understand how they got to an answer and perhaps realise where they went wrong.
- Show me a different way of solving it. This is a great way to challenge pupils and get them to think flexibly about maths and numbers.
“One of the causes of failure in mathematics is poor comprehension of the words and phrases used.”
Primary School Maths Curriculum, P.6
An integral aim of the maths curriculum is to enable the child to use mathematical language effectively and accurately. The ability to talk about ideas gives the pupils the potential to be efficient mathematical problem solvers, and thereby enables them to take on more challenging work. In order to do this there are two important elements to consider: the teacher and the child.
The teacher is the single most person that will influence how a child talks about maths and what vocabulary they will use. The teacher therefore needs to ensure that they are always speaking correctly and modelling the language using the correct mathematical vocabulary. Children may not pick up the language easily, however, and thus the importance of consistency and repetition of the correct vocabulary is vital.
As outlined above, the teacher is single most person that will influence how a child talks about maths. However that influence will go unnoticed unless the child has the opportunity to practise the language. Children need opportunities in every single lesson to talk about the maths using appropriate vocabulary. Why not give each pair of pupils an activity where there is no recording expected and just allow them to talk and discuss the maths for 3-4 minutes?
Questioning can combine both of the elements above. We all know that teachers ask a lot of questions during the day (approximately 400 every day!) so it is really important that we think about what these questions are really asking and are they valuable for the lesson? Most of the questions asked are closed questions, that is, they have only one answer. For example, how many sides does a rectangle have?
However by slightly adapting these closed questions in a maths lesson they can tell us a lot more about a child’s level of understanding, for example, what can you tell me about this rectangle? Now the child can answer the question with multitude of responses and the teacher will have a better insight about their understanding of shape in this case.
You can also take the questioning a bit further and ask some clarifying questions. These will probe the child to think more deeply about the topic. For example, could this six-sided shape be a triangle? Why/why not? Now the child will be defending their knowledge of rectangles and applying it in a different situation.