Over the past two years, I have been learning about what it means to be a teacher. There are a number of different things that I have learnt about the number of different roles a teacher has every day. Most of the important things that I have learnt about being a teacher is actually about my students. As teachers, we are there to respond to the needs of the students. When they need to learn something, we teach them. When they need to be assessed, we assess them. When they need to be listened, we listen. This is something that most teachers are very good at doing.

As teachers, we are also faced with a number of Edu-Acronyms. Letters preceding “BL” flood twitter feeds and Professional Learning pages more than anything else… Challenge Based Learning, Project Based Learning, Team Based Learning… One which captured my attention as a beginning mathematics teacher was Problem Based Learning.

Since hearing about this, I looked further into it. As a student, I developed my love for mathematics through solving problems and arguably enjoyed the use of logic more than anything else. So it was no surprise that it was something that I would require my students to do regularly.

I went to professional learning activities run by Dan Meyer, followed his blog, and subjected my students to countless 3-act math lessons. I had at last found how I enjoyed teaching my class – working through problems with them and teaching them content when they begged me to, as solving the problem without the method or skills taught would seem impossible without it. I had found a way to respond to my students needs.

I then shared my thoughts with some fellow teachers and a mentor at the school that I teach at. I quickly learnt that such pedagogy is not utilised by the majority of mathematics teachers in High Schools across South Australia. I was then encouraged to begin my own Professional Learning Community to work with like-minded teachers to develop our own understandings and “spread the good word” (in a non-biblical sense).

I thought a good place to start was to put my thoughts onto paper about what I have to share and how I might respond to anticipated questions:

Why Problem Based Learning?

When should it be utilised?

• Problem based learning in mathematics allows students to learn the mathematical knowledge and develop their understanding as “problem solving tools”. When they are required to learn such skills, they apply it to a particular problem to either help them solve the problem or understand more about it. This allows learners to place value and meaning to the skills that they are learning about and developing. They are also required to think critically about problems and think deeply about what information is presented, what is important, and what information is needed to be able to solve the problem.

How best should it be presented?

• Problem based learning should require students to ask questions about their current understanding when approaching a problem. If students are able to identify the important information of a problem and are required to develop their understanding by building on pre-existing knowledge, the connection between what was learnt, what needs to be learnt and why, is much greater. Problem based learning should, of course, allow students to apply their understanding to solve problems.

Should it replace what I already do?

• Problem based learning activities make for great introduction lessons. They should be accessible to each student in the classroom and challenge even the most knowledgeable students. Rather than having students revise the previous year’s content, problem based learning should require students to identify that something that they already know (i.e. pre-existing knowledge) and see that it can be applied to a certain problem. This would allow students to access the problem until such a time that they need to learn a new skill or develop their prior understanding to advance further in the given problem. Such activation of prior understanding allows students to re-connect their knowledge of that subject to the current content.

…activation of prior understanding allows students to re-connect their knowledge of that subject to the current content.

What format is best to follow?

• There are a few different models for problem based learning activities. Some of which include: 3 Act Math Lessons (Dan Meyer), Low Threshold High Ceiling Tasks (Lynne McClure), Thinking outside the square (Pearson). Although these vary in the way that problems are presented, they require students to do the following things:
  • Presentation of the Problem
  • Reaction to the Problem
    • What do you think?
    • Can you guess what will happen / the answer?
  • Discussion of the Problem
    • What is important? Why?
    • Do we have enough information?
    • What else do we need to know?
  • Trial of solution
    • Can you try to solve the problem?
    • How did you approach it?
  • Teaching of skill / mathematical shortcut
    • What about if we did this?
    • This is what we call…
  • Application to problem
  • Development of Problem
    • What else needs to be considered?
    • What if…

As well as the occasional lesson that I write a blog post about, I do try to collate my lesson materials in a Google Sheet. These can be found below: