Using the PLTS framework to promote mathematical learning
Independent Enquirers
Students ask questions. Not only questions about following a method or finding an answer, but questions about mathematical ideas, like ‘can you have an irregular square?’ ‘can a quadrilateral have a curvy side?’.
Students identify questions to answer. Given a mathematical situation or object, students can generate interesting questions to explore. For example given a geometrical picture they might come up with questions to ask such as ‘what fraction of the picture is blue?’ ‘how many different triangles are there in the picture?’
Creative Thinkers
Students question their own and other people’s assumptions. They argue with each other about whether a mathematical statementis true or false, such as whether a triangle and a square can have the same area. They find out how other people have come to their point of view and can explain to them why they are wrong, or why they cannot be sure they are right.
Students make connections between their own and other people’s ideas. The lesson doesn’t end with me reading out a list of answers to questions. The lesson ends with discussion about the different ideas that people have had and the different ways that people have thought about the problem.
Team Workers
Students show fairness and consideration to others. Students listen to each other’s ideas and contributions respectfully. Students are not just sat in groups, but they work in groups. They ask each other for help and actively try to help each other. They do not ask me for help unless their whole table is genuinely stuck. They care about each others’ learning.
Reflective Learners
Students communicate their learning clearly. They can clearly explain what it is they are trying to do in mathematical terms. They do not see their work as about trying to answer questions 4-6, but instead they are trying to find something out, such as ‘I am trying to find out how many right angles there would be in a pattern with 4 squares.’ At the end of the lesson, I am not telling students what they should have learnt; they can tell me what it is they thinkthey have learned. Not just what they have done, or how they did it, but what they have learned from it – ‘I found out what the word congruent means and I found that you can have three congruent quadrilaterals around a point because…’.
Students evaluate their experiences in terms of how they will help future progress. Students understand what they are doing and why it will help them to find a solution to their question. For example, they can explain why they are drawing a particular pattern and how that will help them find the largest number of right angles in any given pattern. They are not searching for number patterns in a list of numbers without thinking about where the numbers are coming from or why they help us find a solution.
Students assess themselves. They recognise, and admit, what it is they do not understand and what it is they need to know in order to solve a problem.They might for example explain that they cannot solve the problem because they do not really understand the meaning of the word quadrilateral. A typical question might be, ‘but what actually is a tessellation?’
Self Managers and Effective Participators
Students work towards goals, breaking them down into manageable steps, showing initiative and commitment throughout. Students are set a real challenge that I have not broken down for them, which can be tackled in different ways. We do not start with a simplified version of the problem and then work through ever more challenging variations, with me telling them how to do it.They are given a problem that they do not know how to solve and they must invent their own methods to come up with a solution. They will keep trying different ideas until they succeed.