27 Oct Preventing the Shut Down – Part 2

Tip # 2: Multiple Methods

Last week we dove into the first tip to help us reengage students in mathematics, the power of empathy. You can read more about that here.

This week we are continuing the conversation with tip #2: Multiple Methods.

If you grew up in a classroom like me, your math classroom was really about two things.

1. The right answer
2. The teacher’s way

This didn’t really leave room for me to try on what I thought might work, to take a risk, or to offer any out of the box thinking.  In fact, I learned early on that rule-following was the way to ensure I passed each mathematics class.  Each class was more about doing the mathematics the teacher’s way: remember the rules, the algorithms, the procedures.  Classes weren’t very focused on problem-solving or thinking deeply.

I didn’t fully realize the implications of this until well into high school and beyond, but it did eventually become clear:  I knew about mathematics through the lens of computation.  But I didn’t really understand mathematics beyond computation.   I never really had to make sense of the mathematics, I was really only trying to regurgitate what I had been told, or what I had been shown.  I didn’t realize that this made me a passive learner in the classroom.  I wasn’t really owning my learning.  You might resonate with this too.  Think about your own mindset when you are learning something new.  Maybe you are in a professional learning atmosphere and the instructor asks you to do some math.  You may have 1 of 2 responses.

1. Ok, let me think about this and work through it. Your neighbor might be doing something different from you, but that’s intriguing, not intimidating.
2. Crap.  I don’t know, I don’t remember….now is a good time for a (bathroom break, coffee break, side convo with my neighbor).

If you saw yourself as a mathematician, you would engage with the mathematics because you know you are capable and that trying and working through it is part of math.  You aren’t ashamed that you don’t know right away, rather you are willing to engage and try to figure it out.

If you struggle as a mathematician, it may be more likely that you have your own coping strategies when asked to dive into math tasks as an adult.  You feel like you ‘should’ get it right away.  There is shame, fear, etc. This may be because you grew up like I did.  You didn’t really play with math ideas, you just regurgitated them. So, when asked to engage in a task in which you don’t automatically remember that trick, rule, or algorithm, you deal with it through one of your own coping strategies.

How do we change this script for our students?

I wonder how many of our students are the same.  They aren’t owning their learning because they are never really engaging with the mathematics to make sense of what THEY think the solution methods should be.  They aren’t wrestling with concepts, they are just bystanders. They are waiting to be told when, why, and how.   “The teacher obviously has a method in mind, so I’ll just wait until she shows me how.”

Conversely, when we launch a problem in math class, such as a story problem, and we allow students to solve however they would like, we are sending the message: “Because you can solve this without me.”

Students who struggle to get started are often struggling not because they don’t know what to do, but because they lack confidence that they can do it the way the teacher is asking it to be done.   There is a prescribed method that is desirable by the teacher and if as a student I don’t know that way, then I must not be smart enough and I’ll check out of math class now.  They can’t go on a coffee break, but they sure have perfected their own coping mechanisms.

As teachers, one of the best ways we can keep these students in engaged is to offer this one simple phrase,

“Try this problem. Show me at least two ways.” This says— there isn’t just one way.  Think flexibly.

“I’m not looking for the right answer, I’m looking for initial thinking.” This says this is safe.

“Use pictures, words, numbers, your math tools, anything that will help you demonstrate what you think we should do.” This says your methods are valued, valuable, and legit.

Using these phrases send the message that we are ok with the start (more on that next week).  It sends the message that they can try because we are looking for multiple ways, not just one way.

Teachers often ask me, “But what if they don’t even have one way and won’t put down anything?”

Remember, this is a coping strategy.  It’s easier to say I don’t know than to try on something that we aren’t confident about.  It’s similar to when you call on a student who has their hand raised just for the student to say,”I forgot.”  They didn’t forget.  They lost confidence.  It’s also easier to not try if each time my intuitive thoughts were shot down and conformed to the teacher’s way.  Why should I try if you’re just going to tell me how I should do it anyway?

My responses:

“Mathematicians try.”

“I wonder if a picture would help you get started?”

“See anything around you that is giving you an idea?”

I don’t care if they use their neighbor’s idea.  It’s an idea.  I need them to find success and confidence in trying something.  I’m trying to set a new standard of effort.

If those all fail, then I plan an idea.

“Why don’t you start with the equation?’

“Hmmm, I wonder if starting with ten frames ( or other tool for this topic) would help?”

‘Why don’t you go walk around the room and get a sense of what everyone else is doing.  If you get an idea, come back and try it out.”

My next move is to ensure I have discussed several of the methods that were produced around the room.  I don’t foster multiple methods by giving it lip service but then only ever discussing one way, my way.  My job as students work, is to understand what they are drawing/writing and to select and sequence their ideas.   I’m looking to connect the most concrete, pictorial method to the more abstract methods.  My goal is to honor the most basic approaches as much if not more than the abstract/short cut methods.  One of my favorite books on this topic of selecting and sequencing ideas comes from 5 Practices for Orchestrating Discussion.5 Practices for Orchestrating Productive Mathematics Discussions (affiliate link).

When I am successful at doing this, students start to believe me that I really do just want their thinking—I really do care about how they are solving and I recognize there are multiple ways to do this.   When I start with the most concrete/pictorial method, I’m giving access to ALL students in my room.  When I start by explaining the most sophisticated or efficient method, I prevent access to the thinking and I, in turn, get students who begin to shut down and disengage.   In NCTM’s Principles to Action,Principles to Actions: Ensuring Mathematical Success for All  (affiliate link)  using and connecting mathematical representations is one of the key principles to improve mathematics instruction.

“When students learn to represent, discuss, and make connections among mathematical ideas in multiple forms, they demonstrate deeper mathematical understanding and enhanced problem-solving abilities.” (Fuson, Kalchaman, and Bransford 2005; Lesh, Post, and Behr 1987).

We will get more engagement, keep the engagement, and have a healthier environment if we push for, discuss, and expect multiple methods and therefore entry points into a problem.

How have you found encouraging multiple methods, and connecting them for students has increased student engagement and access during your math lessons?