Concept-Based Teaching in Mathematics

Some members of my team and I were recently meeting with the IB subject manager for Maths HL assessment. She mentioned that one possible development for the next round of curriculum updates (pdf, IB OCC login required) is a greater focus on inquiry learning and concept-based teaching. When we started discussing this I realised I don’t really know what concept-based teaching looks like in maths. Do you?

I am just beginning my learning journey about concept-based teaching in maths. Here are my stops so far.

Jennifer Wathall has written a book about concept-based maths – it will be published in 2016. I knew Jennifer when I worked in Hong Kong and I attended workshops given by her. I think it is likely to be a very practical and useful book.

This brief blog post by Jeff Hadad argues that the idea of concept-based learning is a good one for maths teachers.

The blog post above links to a book called How Children Learn: Mathematics in the Classroom by the US National Research Council (free download).

Here is a short article by an MYP teacher that gives an example of concept-based learning using simultaneous equations.

What can you share about concept-based mathematics?

Peer Assessment: The “Production Line”

My grade 9 students did an individual investigation last week and I wanted to involve them in the process of marking it. I heard about a peer assessment structure called the production line from a colleague last year. In brief, the students mark each other’s work in groups, and each group concentrates on one aspect of feedback. The assignments travel around the group, gaining lots of detailed feedback.


2014-01-22 14.08.20

Preparation

The investigation task already had an assessment rubric. It is based on the MYP year 4 criteria. The rubric focused on Investigating Patterns (MYP criterion B) and Communication in Mathematics (MYP criterion C). I divided the task specific criteria into themes – five in total:

  • B1: Finding and stating patterns
  • B2: Problem-solving techniques
  • B3: General rules
  • C1: Language and representation
  • C2: Reasoning

The Lesson

I rearranged the tables in my room and assigned groups of three students to sit together. I gave each group the details of one of the criteria. An example is shown below (and you can get them all in the investigation file).

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I had some instructions on the board (shown below) and we talked about what we were going to do. I had students help me staple an extra sheet of paper to the back of each task so that we could use it give feedback.


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I gave each group three tasks and asked them to read them, as a group, one at a time. Then they were to discuss the criterion and give some feedback. When they were finished with a task, I passed it on to another group.

Reflection on the Lesson

Since the rubric was already set up for this task, the preparation was quite easy for me. Making a task-specific rubric is a job that can take some time! Thankfully it only needs to be done once.

The number of criteria I wanted to mark didn’t match the number of groups I made in the class. I opted to have three criteria marked by two groups each and two criteria marked by one group each. This turned out to not work very well. The repeated criteria groups finished all the class tasks much more quickly (obviously!) and the other groups had much more to do. When I realised this, I asked two groups to take on a different criterion so take up slack from the inundated groups. Next time, I need to think more carefully about this. I didn’t want to make bigger groups because I felt like they would not work together well. In that case, I should have more criteria so that each criterion is only assessed by a single group.

I just managed (in 80 minutes) to get all the tasks marked by all the criteria groups. Next time I will not need to explain the production line in as much detail and I expect it will be more comfortable in terms of time.

The feedback that was given was extensive, though, I think I need to talk with the students about what the criteria is looking for. I can see the value of a class discussion about what constitutes good reasoning or communication or pattern stating.

The students gained a much more clear view of what criteria they are marked against. (The same criteria are in use throughout MYP maths.)

How do you use peer assessment in your classroom?