Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching mathematics for a growth mindset is central to how I teach maths. It is always in the forefront of my mind when I plan a new lesson.
I was very grateful to be given the opportunity to share some ideas about how I teach mathematics and lead my department to develop a growth mindset in my students at #BCME9.
In my presentation I talk about the link between a student's growth mindset and their self efficacy. I suggest a range of strategies for how a maths teacher can convince students they do have the skill set to attempt and solve problems they previously thought were beyond them.
The strategies I share in this blog are things that have worked well for me and I have seen work well in my department. I hope you find some ideas that you think could work well for you in teaching mathematics for a growth mindset.
When teaching for a growth mindset I challenge students to apply their learning to solve multi-step problems rather than repeating the same skill for similar questions.
Rather than repeatedly finding the area of a triangle using the formula, A = 1/2 bh I challenge students to find the area of composite shapes where finding the area of a triangle is only one step of a much larger problem.
When students are able to find the factors of a number we can develop their growth mindset by applying that skill to investigate the different perimeters for a rectangle with a fixed area. This could lead on to finding the smallest possible perimeter using irrational numbers or even the largest perimeter using decimals while exploring the concept of infinity.
I suggest when a student has learned how to solve an equation using trial and improvement they could apply it to solve much larger and more complex problems such as the example in the PowerPoint.
In 1976 Richard Skemp wrote a paper called Relational Understanding and Instrumental Understanding. Skemp describes Instrumental Understanding to be learning by rote. Relational Understanding is when a student can connect what they are currently learning to what they previously knew to be true. This type of understanding is more likely to develop a growth mindset as it constantly reinforces and extends their knowledge. Students are then more able to solve complex problems than a student who has an instrumental understanding.
To teach for a Relational Understanding I believe a lesson needs to be structured so students recall their prior learning at the start, extend it through the key learning objective in the main and apply the new skill in the plenary. I have blogged about flow of a mathematics lesson in more detail here.
The examples in the PowerPoint highlight a couple of activities that I use to get students talking about the topic at the start of the lesson. From listening to their conversations I can assess their prior knowledge which helps me decide the level of pitch for the beginning of the main phase. Read more about making the most of a mathematics starter here.
In the main phase I demonstrate how to progress from teaching the main learning objective to using it as a skill to solve a range of scaffolded questions. This approach helps to avoid plateauing so students remain engaged and constantly challenged.
The plenary provides an opportunity to assess the learning for each individual while challenging them to connect the new skill to other areas of mathematics. In this video I talk more about using a plenary in a mathematics lesson to assess progress and extend student's learning.
To develop a student's growth mindset they need to believe they have the intelligence and skill-set to solve a problem which they would not have previously attempted.
Comprehension of these questions must be accessible to all students if this is to be achieved. It is important therefore to present the question both visually and orally whenever possible.
Giving students some control over the amount of time they have to solve a problem helps to take the pressure off so they work calmly and maintain their focus.
As teachers we inherently want to help students with their work as and when they think they need it. I propose being less helpful. Encourage using peer support to help them get started with a challenging question.
If they do need help from the teacher they should be specific with what help they need and how it fits in their strategy for solving the problem. If a student believes they do not know where to start, get them to read the question to you or ask them what the solution may look like.
If you would like a student to share their working with the class give them prior notice so they can prepare in advance. They make want to rehearse presenting their method with a friend or another adult. I know I rehearsed my presentation at BCME9 several times!
When teaching mathematics for a growth mindset the resources we provide students with to answer the question is key to how successful students will feel.
I use mini-whiteboards in every lesson. I ask students to show me the whiteboards at the same time. I do not comment on individual whiteboards so no student feels embarrassed by what they have written. Students can either work in pairs on individually. If they do decide to work in pairs they must both agree with what is written.
When a student does share their work with the teacher it is important to value their processing rather than the final solution. A final answer can be ultimately wrong but the method could be valid and insightful. If we only ask students for their final answer we miss out so much of their method. Students can feel successful if they know their processing is correct even if their final answer is not.
I encourage students to be critical of each of other and to have a discussion when different solutions or methods arise. This encourages them to talk about the problem which is key to developing their mathematical reasoning. When I look at the student's working on their whiteboard I will ask those with different approaches to discuss and share ideas.
Generic praise patronises. When teaching mathematics for a growth mindset be specific about what your awarding the praise for. This will show the students it has been earned and they deserve it. Awarding praise in this way will make students more likely to apply the same level of effort (or higher) next time.
Be clear and creative with your praise. What one student considers praise another may find humilating. For instance, one student may thrive on public praise whereas another could benefit from a discrete smile or nod.
Priase persverence and persistence not quick answers with little working. When a student refuses to progress on with a lesson because a previous problem is bothering them I will always give them the time to solve it. In the student's mind this adds value to their processing which means they will be more likely to apply the same level of effort in future problems.
Here's a video about a study on praise and growth mind-sets. I did not include in my presentation but I would like to share it here as the research findings echo the points above.
A written note from the teacher in a student's book that directly comments on a piece of their work will add so much value to their processing and effort. Being recognised in this way will encourage greater efforts in the future.
In my department we display an Outstanding Mathematicians Board in the faculty corridor. Students know they will only be on the board if they take risks in their learning and have persevered both in their class and home work. Any student who gets their name on the board also recieves a letter home courtesy of the mathematics department.
There are lots of great websites with resources available to for teaching mathematics with a growth mindset.
There are over 450 lessons available for members on my own site http://mr-mathematics.com. The UK Maths Challenge site is excellent for providing challenging and indepth problems. Geogebra has a huge range of interactive animations that promote a relational understanding.
I hope you have found this blog useful and are able to take away some ideas to try for yourself. Please do leave a comment below to share how you go about teaching mathematics for a growth mindset.
Inspiring students to enjoy maths and feel the success that comes with attempting a difficult challenge is why I teach. The feeling of success is addictive. The more students experience it the more they want it and the further out of their comfort zone they are willing to go to get more of it. Teaching […]
To find the equation of straight line graphs students need to calculate the gradient using two pairs of coordinates and the intercept which is the y value of where it crosses the vertical axis. Examiner’s reports of past exam questions show students are more able to find the intercept of a straight line than they […]
Students learn how to generate and describe arithmetic and geometric sequences on a position-to-term basis. Learning progresses from plotting and reading coordinates in the first quadrant to describing geometric sequences using the nth term. This unit takes place in Term 4 of Year 10 and is followed by the equations of straight line graphs. Arithmetic […]