Teaching Problem Solving Strategies
Teaching Problem Solving Strategies in Math class is my least favourite thing, and for good reason. Studies have shown that students find math word problems so difficult that they just shut down, and won’t even attempt to solve the problem. Researchers have found that the if the struggle is too intense students suffer anxiety and begin to believe they are ‘too dumb’ to even have a go and adopt a fixed mindset about mathematics; believing that they are “not a Math Person!” This belief is frustrating for teachers because teachers know their students have been taught ways to solve math problems, like, ‘highlight key words’, ‘guess and check’, and ‘make a table’. But in order for students to use these ‘solution’ focussed strategies they also need to be taught a series of steps to follow before this can happen; steps that they can use to help them decipher and decode the actual problem.
Solving word problems involves multi-steps which involves a higher order level of thinking. Problem solving requires the application of deep mathematical understanding rather than just the recall of facts or procedures to find a solution. To help students to become successful problem solvers they need to be explicitly taught a series of problem solving strategies that complement the problem solving solutions. Australian educator Dr Anne Newman’s research (1977) into successful problem solving found that students progress through 5 hurdles during problem solving, and when teaching numeracy, teachers need to incorporate these steps into their planning so that for students can become successful problem solvers!
Teaching Problem Solving Strategies Using Newman’s Prompts
Try using Newman’s analusis and these 5 prompts to help you with teaching Problem Solving Strategies to your students.
- Hurdle 1: Reading – Even good readers often find it being able to read and decode mathematical texts, words, and graphics
- Hurdle 2: Comprehension – Students may not understand the meaning of the words and graphics in a mathematical context. They may confuse everyday meanings of words and substitute this for mathematical contexts. Students need to know what’s important and what’s irrelevant detail. This is so much more complicated than just highlighting the key words! If you are able to highlight what is important it doesn’t mean you know why it’s important or what you need to do with that information. What if you think everything is important? This will prevent them from building an understanding of what the question is asking them to do.
- Hurdle 3: Transformation – Students find it difficult to work out how to transform the words of a problem into an appropriate mathematical strategy to solve the problem. They need to know a range of George Polya’s strategies to do this, some include:
- Draw a picture
- Guess & Check
- Act it out – use materials
- Write a number sentence
- Find a pattern
- Make an orderly list
- Eliminate the possibilities
- Work backwards
- Hurdle 4: Processing Skills – Most teachers are excellent at teaching math skills such as multiplication, addition, division and subtraction and students are quite able to follow the process of these skills. The problem is that more often than not they do not know when to apply these skills? Most students do not know which operational process is required to solve a problem.
- Hurdle 5: Encoding – Arriving at a solution and testing that the answer works
5 Problem Solving ‘Prompts’ for Success
Dr Anne Newman came up with a way to analyse the errors students made and a set of prompts that you can use during these 5 stages. they will help you to identify where students are having difficulties and provide the appropriate level of scaffolding to help them progress through their difficulties and be successful! I use the following prompts with the students during problem solving:
- “Read the question to yourself. If you don’t know a word leave it out or use another word.”
- “Tell me what the question is asking you to do.”
- “Tell me how you are going to find the answer?
- “Show me what you are going to do to get the answer. Talk aloud as you do it so I can understand your thinking.”
- “Write your answer, does it make sense? Have you answered what was being asked?”
Watch our Problem Solving Video for More on Newman’s Prompts
We found a number of problem solving acronyms to help students develop their problem solving skills. We have created a set of Think-boards and posters that incorporates Newman’s prompts and 3 acronyms: S.O.L.V.E it!, R.i.D.E, & F.i.S.H. Use these problem Solving Strategies & A Growth Mindset to help your students become ‘Good Mathematicians’.
Watch the video to see how the S.O.L.V.E it! strategy works…
CLICK Here To SEE our Problem Solving Pack- Includes Problem Solving Strategies, Classroom Posters, Flip Book & think-boards
FREE Problem Solving Thinkboard!