Category Archives: Growth Mindset

Reflective –> Effective

Okay. It’s time I hopped back on the blogwagon. I have been in graduate school this past year earning a Master’s degree in Private School Leadership (yeah, that exists) but I haven’t felt like I had anything to contribute to the discussion around math TEACHING up in my ivory tower. I want to end the year by reflecting on some of the things that I have been thinking about, ranging from little random thoughts to unanswerable questions, all of which I am excited to test out next year in my triumphant return to a math classroom!

So that’s what the next series of posts will be. But first… I have wondered if it was a good/necessary move for me to take a full year away from the classroom to reflect. One the one hand, it’s great to have the space and time to really delve into issues from human cognition to the use of data to improve student learning. On the other hand, I haven’t been able to workshop any of the ideas running around in my brain. Regardless, it has driven home to me the importance of reflecting, so I thought I would share the small change last year I made in my lesson planning that helped me become a more reflective, and thus more effective teacher.

You don’t need to take a year off or find more hours in the day to journal. You just need to add a column to your lesson plans.

lesson plan2

This is an actual screenshot from my Evernote planning notebook.  I chunk my class into activities, so that’s what you see on the way left. The next column describes any other necessary details or files that the activity requires. The third column is initially blank, and this is where I reflected. Every day, before planning the next lesson, I would go back to the one before and jot down a bullet point or two about each activity. Sometimes I would have a lot to say and would write some notes for my future self, but I would, at the very least, note how much time the learning activity took. Before long, this became a habit of my lesson planning that took no more than a few minutes.

I initially conceptualized this as a way to keep notes for myself in the future, should I teach the same class again, but found that I reaped the benefits far more quickly. Just sitting down for even 5 minutes to think about what happened that day started a recursive process where my reflections allowed me to make decisions in a different way in the future.

So I hope that some of my reflections from grad school might be helpful (for both readers and myself) — but I am also looking forward to reflecting next year in the classroom in a way that has a more immediate effect on my teaching and student learning.

Teaching Beliefs in Poster Form

Day one of the school year is rapidly approaching so I’m continuing my mad scramble to outfit my classroom (complicated by the fact that I’m trying to stock up here in the US because random things are very difficult to find in Jordan). My classroom walls were pretty bare last year, so I decided to make some posters and get them printed in large format (18″ by 24″). I wanted some of them to reflect core aspects of my teaching philosophy so that I can more easily continue great conversations that start in the beginning of the year and seem to peter out. Here is what I got printed:
(I’m counting this as #made4math for this upcoming Monday – I’ll be on a plane then!) 


Memorizing vs. Understanding

One of the big themes in my classroom is the difference between understanding and memorizing. I don’t need to rant about this now, but I think that students just are not aware that when they cram algorithms in place of problem solving, they aren’t really learning. Getting them to understand the difference between understanding and memorizing is one of the most important metacognitive lessons of my math class. I thought it would be nice to have a visual reminder I could point to with a sort of classroom meme.

To explain, this is a picture of my family dog Whiskey. Whiskey is awesome at learning how to do all sorts of tricks. I think he could easily be a commercial dog. But when he messes up, he has trouble getting back on track, because he has no idea what he is actually doing. He has memorized what gets him a treat (like how students perform mathematical algorithms for grades) but has no deeper level understanding to be able to tinker with the process or apply his knowledge to a new situation. My favorite Whiskey-isms:

  • BANG, YOU’RE DEAD: When my mom puts her gun finger out, Whiskey responds by sticking his paws in the air innocently. Then, my mom yells “bang!” and Whiskey awkwardly flops to the floor, flips over and plays dead. He’s really good at this, but if, for some reason, he messes us up, he just tries to throw all the steps of the trick at my mom until she gives him a treat (like students who just try to write stuff on a test for points). I show my students the video in this post, which shows Whiskey messing up, to illustrate the problem with troubleshooting a process you don’t understand.
  • OUR NEIGHBOR’S NEWSPAPER: Whiskey brings in the paper every morning for my parents, and loves life every time he does it. When he brings it in, he will chomp down on that paper until my parents give him a treat. The only problem with this has been that while on walks, he will sometimes see a neighbor’s newspaper and apply the same logic. He grabs it and the sprints home (however far away) and then wont let go until he gets a treat. I am going to use this example to talk about how you can misuse processes if you don’t understand them and try to apply them to different situations (like canceling out added terms in a rational expression).

If Whiskey could just ask “Why?” he could avoid these errors in his tricks! Good thing my students are capable of doing that.


The Growth Mindset

The Growth Mindset, a brainchild of Psychologist Carol Dweck, has become one of the lynch pins of my teaching philosophy. The philosophy espouses that believing intelligence is fixed hinders learning – “smart” kids will be scared to take risks and fail, and “dumb” kids will not see real results in their learning because they are comparing themselves to others instead of themselves. The growth mindset puts the emphasis on hard work leading to real learning, and normalizes (no, necessitates) mistakes as part of the learning process. I really like this image (which I did not make), despite how small it is, and I could see a student reading through this one day at the beginning or end of class. Even if not, I made the headers “Fixed” and “Growth” bigger so at the very least it will be a reminder to me while I teach about this important idea!

In the first week, I will give a survey that will get us talking about the Growth Mindset, as I did last year, but I hope to do a better job of continuing that conversation this time.


Math is Magical

I love the completely-not-subtle message that is so subtly expressed in this poster (which I also did not make). Yes, Math certainly is magical. In surveys, students always cite my enthusiasm for the subject as something that makes the class better, so I have embraced that as part of my teaching philosophy.


Foundations are Important

Okay, maybe this isn’t a huge part of my teaching philosophy, but I made this poster last year on regular printer paper and I really liked it, so I wanted a more durable poster. I like it especially because it worked as both a comforting thing for my Calculus students and an inspirational thing for the Algebra students. If you want a copy of your own, I have this image split into nine regular pieces of paper that you can print out and glue onto a poster.

Growth Mindset – Normalizing Mistakes

My first year teaching, I remember one of the elder, wiser, experienced teachers at my school looking at my first week plan and telling me that I think more deeply about setting routines in the class and creating a good class atmosphere. I kind of brushed this off as a sort of silly – I was there to teach Physics, and that’s what I would do. The other stuff would happen automatically. Well, luckily, I wasn’t totally wrong – I think that I inadvertently did a decent job of setting good routines, though I don’t think I did a great job of creating an atmosphere where mistakes were not only encouraged but celebrated. I realized by the end of the year that the hardest part of teaching Physics was not Physics at all, and tried to focus a bit more on all the “other stuff.”

This year, my third year teaching, one of my main goals is to really get my students to buy into the idea of a “Growth Mindset,” especially in my non-AP Calculus class. I started well with an awesome discussion, which was based on Dweck’s original mindset survey (which John Burk over at Quantum Progress turned into a cool data driven exploration of his students’ mindsets, which then he turned into a collaborative mindset data collection experiment in which you can participate). As my beginning of the year review rolled on though, I kind of ruined what I had started through my frustration with my non-AP Calc students. For some reason, they are incredibly weak, far weaker than the students I had going into the same class last year. Many don’t know the basic shapes of parent function graphs, don’t know how to correctly simplify rational or radical expressions
(\sqrt{x^2+y^2}=x+y    right??), have never seen a piecewise function, can’t find the domain of a rational function, can’t recognize a basic vertical shift etc. Sigh. I guess my surprise and confusion that they were at this level was pretty obvious, and both of my classes seemed embarrassed by not knowing things that I thought they “should have” and, yeah, worried that they were “dumb.” I sort of realized that I hadn’t bought into the growth mindset as much as I had thought – They’re weak? No. I was comparing them to the students from last year instead of just assessing their level of math and working from there.

The worst side effect of our really rough week of review is that the class started to get really, really quiet. I could only get a few students to respond to questions and take risks. I couldn’t tell when they didn’t understand something, even instructions, because they would just be silent – I have never had that happen in the classroom before. I decided to take some action and remind them (and remind myself) that we are a classroom committed to the Growth Mindset. Using, a wonderful interactive polling website where students can vote and immediately see the results at the front of the classroom, I carved out 10 minutes from mathematics and took them through a series of questions that I designed to help normalize mistakes. We looked at the results of each question before moving on to the next. The results…

Observations: Though some of the questions were certainly leading, the students seem to really buy into the ideas and remember our growth mindset conversation. The questions were ordered perfectly, because after everyone realized that no one else judges other people for making mistakes, they were forced to think about really why they were having a hard time participating in class. We went through each of the statements for the last question and talked about if we believed that statement, how the results from the previous two polls might help us participate more. It was a really nice conversation and seemed effective. I saw that look that the students get when their gears are turning and stuff is clicking. Side note: I was a little surprised that students voted for the “Mr. B, you are intimidating option” but I used that as a spring-board to remind them that I buy into the growth mindset idea too. (Also, sra7a means “honestly” in Arabic).

We wrapped up with a PollEverywhere open-ended question, where they type things into the poll and they show up on the screen. I thought this might be a nice, low pressure way to share some thoughts with the class so that we could all be supportive of each other:

How do I know this was a wonderful use of 10 minutes? The first response to the question above was “Thank You” which was surprising and actually pretty touching. And theeeen, it quickly devolved into things like “Bring lasagna to class” and “apple juice breaks.” Really senior-in-high-school? Apple juice? Thanks for ruining a rare sentimental math moment.

Next step: Now that I have them a bit more prepped to be okay with mistakes, I want to find ways to go one step further and celebrate mistakes. I really love the Mistake Game , from Kelly over at Physics! Blog!, to use with Whiteboarding in Physics. Basically, students work in groups and present the solution to a problem that contains a mistake hidden in it. Students are encouraged to find the mistake through asking thoughtful questions instead of just saying “HA! I FOUND THE MISTAKE.” I love this because it is not only instructional, but teaches students how to constructively criticize each other’s work. The math department plans on getting mini-whiteboards any day now, so I am excited to experiment with this. Also, Kate over at f(t) has some great tips from the Virtual Conference on Core Values from this past summer where she describes the center of her classroom as being “We Make Mistakes.”

Moral of the Story? Growth Mindset takes more than a description and a survey to create buy-in. I will remember that teachers can unintentionally send subtle signals through their behavior. I’ve learned from my mistakes with this, which, paradoxically, will lead me to encourage lots more mistakes. I’ll certainly be coming back to this throughout the rest of the year.

What If Angry Birds Didn’t Grade With SBG?

Last year I tried out Standards Based Grading the first time and really thought it was a game changer for my classroom. Though I haven’t worked out many of the tweaks yet, and some departmental pressure is conflicting a bit with my ideal way of running things, I am still very excited about using SBG this year in class. One of the mistakes last year was that I did a terrible job explaining the whole system in the first few days of school – the whole thing was far too abstract and different from what they were used to that the first presentation went over their heads and it took some students a while to actually figure it out. One of my goals of this year was to sell/explain SBG much better so that I could have everyone on board, and I figured that this would be a worthy use of about a day total of class (I ended up integrating it with problem solving and review).

It’s easy to get caught up in trying to explain all the details of SBG, but of course making a simple analogy to scaffold off their existing knowledge is far more powerful. I realized that they already know Standards Based Grading from playing games like Angry Birds. Here is how Angry Birds grades with SBG:

Right? Levels graded separately that you can play over and over until you gain mastery? I’m sure others have thought of this analogy, but it seems pretty solid to me. So now contrast this to what the Angry Birds score screen would look like if it “graded” in the traditional manner:

This would suck because I never get 3 stars the first time around. I’m really hoping that these pictures can do almost all of the explaining for me, especially when we compare them to the way I graded their diagnostic tests from the first day. I have never done a diagnostic test in the beginning of the year like this, but I wanted to do it this year for both its diagnostic purposes and to have them learn how SBG works experientially. I graded it today two ways for them – in the traditional points manner and with SBG (and I will give them back tomorrow with my 4 point rubric and a full description of the standards):

I hope to have a discussion about what SBG tells you that traditional points based scores do not, and talk about the very different reaction you would have to quizzes graded in the two ways. I hope that with sample grades in front of them that mean something to them and a fitting metaphor, they will be totally sold on SBG before the second full day of school finishes.

Other Materials I Used to Introduce SBG…

1. Getting them in a Growth Mindset

I have decided that metacognition is going to be a big goal of mine this year, of which one of the lynch pins (especially while grading with SBG) will be getting students to realize the difference between a fixed mindset and a growth mindset. This boils down to the idea that those that believe they can always grow and always get smarter will end up growing far more easily than those that believe that intelligence is fixed. I gave them a little math learning questionnaire adapted from Math Hombre (gracias!), who mathified Carol Dweck’s original research questionnaire for use with his math students:

I had them first fill it out silently for a few minutes. Then, in partners, they found and discussed a statement about which they had differing opinions and a statement about which they had similar opinions. Then each pair found a new pair and shared with them the two statements that they had discussed previously. This really helped pave the way for an awesome class discussion. My favorite comments were when one student said that intelligence has to change because he is a lot smarter than he was in 9th grade, and then when others came to the consensus that in a fixed mindset you are comparing yourself to other people whereas in  a growth mindset you are comparing yourself to yourself (beautiful!). Though some students were really resistant to the idea of not thinking in terms of “smart” and “dumb” anymore, I think many students really bought into the idea of a growth mindset and will hopefully be able to connect that idea to SBG in general…

2. The Nitty Gritty Details of my Hybrid SBG System

And theeeeennnnn, finally, after getting into a growth mindset and experiencing SBG through a diagnostic test, I am going to give them all the details of the grading system – percentages, processes, resources, philosophy etc. This is basically what I did last year without all the prep. I made a pretty awesome Prezi to do all of this, which I am really excited to show tomorrow (not in small part because it includes a hand drawn picture of an angry octopus).

I hope this will really stick because then it’s onward and upward to the magical land of Calculus!