Aiming for Mastery?

The other day, a good friend of mine shared this picture with me asking me what my thoughts were:


On first glance, my thoughts were mixed.  On one hand, I really like that students are receiving messages about mistakes being part of the process and that there is more than one opportunity for students to show that they understand something.

However, there is something about this chart that seems missing to me…  If you look at the title, it says “How to Learn Math” and the first step is “learn a new skill”.  Hmmm…… am I missing something here?  If the bulletin board is all about how we learn math, the first step can’t be “learn a new skill”.  For me, I’m curious about HOW the students learn their math?  While this is probably the most important piece (at least to me), it seems to be completely brushed aside here.

I want you to take a look at the chart below.  Which teaching approach do you think is implied with this bulletin board?  What do you notice in the “Goals” row?  What do you notice in the “Roles” row?  What do you notice in the “Process” row?

Teaching Approaches - New

If “Mastery” is the goal, and most of the time is spent on practicing and being quizzed on “skills” then I assume that the process of learning isn’t even considered here.  Students are likely passively listening and watching someone else show them how… and the process of learning will likely be drills and practice activities where students aim at getting everything right.

I’d like to offer another view…

Learning is an active process.  To learn math means to be actively involved in this process:

  • It requires us to think and reason…
  • To pose problems and make conjectures…
  • To use manipulatives and visuals to represent our thinking…
  • To communicate in a variety of ways to others our thinking and our questions…
  • To solve new problems using what we already know
  • To listen to others’ solutions and consider how their solutions are similar or different than our own…
  • To reflect on our learning and make connections between concepts…

It is this process of learning that is often neglected, and often brushed aside.


While I do understand that there are many skills in math, seeing mathematics as a bunch of isolated skills that need to be mastered is probably neither a positive way to experience mathematics, nor will it help us get through all of the material our standards expects.  What is needed are deeper connections, not isolating each individual piece… more time spent on reasoning, not memorizing each skill… richer tasks and learning opportunities, not more quizzes…

“One way to think of a person’s understanding of mathematics is that it exists along a continuum. At one end is a rich set of connections. At the other end of the continuum, ideas are isolated or viewed as disconnected bits of information. A sound understanding of mathematics is one that sees the connections within mathematics and between mathematics and the world”
TIPS4RM: Developing Mathematical Literacy, 2005

So, while I don’t think putting up a bulletin board (or not) is really going to do much, I really do hope we are spending more of our time thinking about HOW our students learn and WHAT are goals are for our students (see the chart above again).

I still wonder what it means to be good at math?  I wrote about my questions here, but I am still looking for ways to show others how important mathematical reasoning is for students to develop.  Skills without reasoning won’t get you very far.  Maybe more about this another time…


3 thoughts on “Aiming for Mastery?

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