Thinking Mathematically

So you want your students to have a Growth Mindset?

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There has been much talk about Growth Mindset the past few years.  Many teachers recognize that there are a lot of students who exhibit a fixed mindset.  I often wonder when we introduce another educational term into the mainstream how many different ways the term can be misinterpreted.  Ask someone what they think about the terms growth or fixed mindsets and really listen to what they say.  I bet you would be surprised!

When others talk to me about mindsets, I often hear about students who struggle, needing to change their mindset… Makes sense doesn’t it.  We see a group of students in our school who don’t apply themselves, and we wish that they would just realize they could do much better if they just put forth more effort.  But is this what the whole growth/fixed mindset conversation is all about?

Those who see growth and fixed mindsets being about effort often think that encouraging their students with phrases or posters is what they need to succeed.  When we believe this, we might start to see a neat looking poster or bulletin board like these:

 

However, a poster alone might send a message to students that THEY are doing something wrong, THEY need to do something different… and that if they only tried harder, changed their words, became better people… that they would do better in math.

Personally, I don’t think this is all what the issue is with our students.  And I don’t believe this is what the research behind mindsets is pointing to either!  If we are looking to change our students’ mindsets, we need to do two things:

  1. Learn what it means to have a growth / fixed mindset.  We might be misinterpreting the whole idea here!
  2. Change OUR actions to promote growth mindsets.  Our students will only improve when WE change!

1.  Learning about Growth and Fixed Mindsets

While there are a lot of places you can go to learn more about a growth mindset, I think we need to make sure we are hearing from the experts. Here are a few I think you need to take a look at:

While I don’t want to spend much time restating what is already in these articles/videos/books, I do really hope you will check out at least one of the new ones you haven’t already seen.

I will give a few key points about the whole mindset movement though:

Do these 5 points fit your current understanding of Mindsets?  If any of these do not fit your thinking, please make an effort to read/watch some of the articles, videos linked above.


2.  Change OUR Actions to Promote Growth Mindsets

I think this is the part of the conversation that is completely missed!  We tend to focus on what everyone else needs to do instead of how we need to change.

Think again about the message above.  What are the common practices that happen in many math classrooms that help our students believe they are smart at math, or that they are not smart at math?

Practices that promote fixed mindsets:

Think about how each of these practices helps our students identify with mathematics.  Their mathematical identity is based on how WE present their successes.  Each of the practices above treats mathematics as a performance subject.  Students in classrooms like these are far more likely to believe that they are either a math person or not because the tasks ask them to recognize if they are better or worse than others in the room.

For example, students who are routinely given a page of closed questions to complete come to believe their role is to get them right.  Students who get them all right are likely to see that they are naturally good at math, while those who struggle through the questions are likely to see their “ability” in more negatively.  There is little room for students to see that they are growing!

On the other hand, teachers who view mathematics as a learning subject are more likely to have practices that allow students learn and grow.

Practices that promote growth mindsets:

 

Providing experiences like the items above will more likely allow your students to see that they are capable of growing and learning since the focus is on allowing your students time to develop.  These experiences help move the focus away from whether or not students are already good at math, toward a focus on the the learning today.  Allowing our students room for growth promotes a growth mindset.


Think about the lists above.  There are possibly a few that might challenge your thinking! Many hear some of the messages about the types of practices that promote fixed mindsets and struggle to know what to do instead.  Moving toward classrooms that promote growth mindsets is not about lowering the bar, in fact, classrooms that are successfully moving in this direction are expecting much more of their students… and are especially helping our students who begin the year struggling.

If you or your school or your district are interested in taking a focus on growth mindset, I encourage you to not just consider the pedagogy involved, but to actually focus on the practices that will help us to understand the math deeper ourselves!


For example, to focus on growth mindset, we as teachers need to be able to understand the math deeper in order to be able to teach mathematics in way that allows our students to see mathematics as a learning subject.  Here are a few things we as teachers, as schools and/or districts that we can focus on to help us make these shifts:

  1. Consider focusing on tasks that help us see that we can develop number sense through the use of strategies, visual representations and the big ideas behind the numbers.  Number Talks or Strings are wonderful practices that both allow our students to develop appropriate number sense, think flexibly about operations, yet allow for creativity and reasoning to develop.  Our learning here needs to include understanding the developmental models, strategies and big ideas appropriate for our students to develop number sense.
  2. Consider focusing on opening up problems.  Accessing resources like Marian Small’s Open Questions for the 3-Part Lesson/Eyes on Math/Good Questions… or Cathy Fosnot’s Contexts for Learning units… or other sources that might help us see how we can use open problems as part of a sequence of learning.  These, along with structures like the 5 Practices for Orchestrating productive mathematics discussions, can help us recognize how we can learn THROUGH problem solving.
  3. Consider focusing on mini-lessons that focus on student reasoning, conceptual understanding, the use of visuals and spatial reasoning.  This can include using tasks like Estimation 180, Which One Doesn’t Belong, Fraction Talks, Visual Patterns, 101Qs Problems, SolveMe Mobiles… in a way that promotes student thinking, students sharing, and the development of reasoning together.  This can also include the development of and use of instructional routines like Notice and Wonder or Contemplate then Calculate.  Whichever of these we explore, we need to learn how to give our students the opportunity to think and reason… share with each other… learn FROM and WITH each other.  And to do these well, WE need to continue to learn the important mathematics behind the tasks, not just use them because they are fun or neat.
  4. Consider a focus on assessment.  If we want classrooms that promote a growth mindset, we need to reconsider what information we send our students about what is important.  Learning about developmental progressions, how to give feedback effectively, tasks that allow us to make observations, listen to students as they are thinking, have conversations in-the-moment as students are problem solving.  When we deepen our understanding of the mathematics our students are learning, we will become better at using assessment effectively.  While many believe they are focusing on growth mindset by looking at spreadsheets, this is exactly the opposite of what needs to be focused on.

 

Whatever your focus, keep in mind the unintended messages we send our students about who is a math student… and continue OUR learning about the mathematics itself so we know how to help our students as they struggle (developmentally appropriate tasks/problems).

Teaching for a growth mindset will require us to make changes in our beliefs, but also in our practices!  Let’s keep learning my friends!!!

 

If interested, here are a few more posts that might help us see how to make these ideals a reality:

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