Hi, my name is Karl and I have just completed a year’s journey as part of the Champion of Maths program through Scitech and Alcoa. This is my second Blog post for the year, and you can read my first one here.
At the start of the year, I was confident in my Mathematic ability but have come to realise how much more effective I can be. Upon reflecting, there are many strategies and lessons that I would teach differently to develop students who are confident in tackling a problem and have the reasoning to say, “Yes, I am right and I can prove it.” I thought that I would share some of the things I have learnt this year and one area I feel I can still grow.
Problem Solving is more than just word problems.
I mentioned this in my first post and wanted to elaborate. When it came to teaching problem solving, I would often devise or find a list of worded problems to give to the students. Students who understood the content simply applied a list of steps to solve these problems. There usually was no need to think of the operation that was needed to be used, as it was often the same operation for the whole sheet, or a single step operation that students had to identify. Students could solve these problems but lacked flexibility in their maths and couldn’t use the skill in different contexts. Problem solving is the ability to face a problem where you don’t quite know how you will find the answer. It’s about finding strategies to move you in the right direction, analysing, failing and trying again. When I provide students a whiteboard and a problem with just the right amount of guidance, I have found students genuinely problem solve. And, what’s more, students understand the maths and not a list of steps to follow.
Teaching students to understand is not just explaining it to them.
I am not saying there is no place for explicit teaching, although having students explore the maths and create connections for themselves which they can explain to those around them builds a foundation that explicit teaching can enhance. Showing students how to write an algebraic expression for a number pattern is so much easier when they have found these patterns and voiced them to you. To begin with they may not use the correct vocabulary, but through discussions and exploring with the students they walk away knowing why and not just how.
Maths can be fun without the need to “hide the maths”.
So often students view maths lessons with a level of disdain. For many it is that difficult subject that teachers force students to do. Often students say things like, “When would we ever use this in real life?” or “Why do we have to learn this?”. One thing I love about the Champion of Maths program is students do not ask this anymore. They can quite easily see how and when the maths is used outside of school and can explain this to me. I think this is a part of the engaging aspect of the program. I have heard teachers say before they have done a lesson where they hid the maths to make it fun. Maybe turning some mental maths into a crossword. Champions of Maths stands out for me because it doesn’t hide the maths. It is purposeful and very clearly maths, but the students are highly engaged and challenged. Students are not fooled into doing maths in secret, yet they love and enjoy the maths quite openly. Students in my class get excited when the whiteboards come out.
The skills and techniques are a part of what I view as best practice teaching.
Many aspects of the program that I have been taught are not limited to mathematics. The research that has gone into providing such high-level mathematics teaching has helped broaden the strategies that I use in a range of areas. One great example is the use of a standing white board to engage and involve all students. I have used this strategy to engage students in group projects in science and technology projects. Students were accustomed to this approach through problem solving lessons and were able to share ideas and prepare themselves for the task at hand. It led to a more effective group project.
As I moved through the program, I noticed more that teaching mathematical thinking and reasoning is vital to creating confident and capable students. I think the biggest improvement I plan for future teaching is going to be focussing on teaching reasoning. I find several of my students are very capable in their mathematical thinking and through Champions of Maths have become capable problem solvers, however, some of these students still feel unsure when sharing answers to problems provided.
One example is a question I gave my students recently:
By placing just one pair of brackets, make as many different answers to this problem as you can.
3 + 4 x 8 – 6 ÷ 2 =
Write each question and answer the equation.
This was a consolidating task and students were familiar with how brackets worked in mathematics. Groups quickly found a range of answers and a few stepped up and were very systematic about their approach. They would find all the ways two digits could be contained in the brackets and move on to finding how three digits could be contained and so on. I was excited to come to groups and see they had all the answers. I probed and asked, “So, do you have all the answers?” to which many groups replied along the lines of, “I don’t know”, or “I think we’ve missed some.”
From this point on I plan to focus on the benefits of being systematic, looking for a strategy that starts at a clear point and changes one thing at a time until all options are investigated (much like some of the groups were doing). I want students to see they can generalise an approach to a problem and justify their thinking. I plan to focus a lot of my questions around, “Are you right?” and “How do you know you are right?”. By doing this I am opening discussions that will lead to stronger reasoning. I hope to have this as a focus early on for my next class, so students learn ways to prove they have found the solution and become confident in their abilities.
I have grown so much in my mathematics teaching thanks to Champions of Maths and am pleased to say that the adventure is not yet over. Next year I will be continuing my work with Shyam, but this time I will be supporting a new cohort of teachers as a coach in the program. I look forward to seeing how a different perspective will show me new and exciting ways to approach the education of mathematics.
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