Bravery and The Growth Mindset: Why is the Pool so Different from School?

Today marks the end of the second week of spring sports.  As the JV swim coach I have a love/exhausted relationship with this time of year, but when I step on deck and get to engage with our students in this different arena, I am reminded why I keep coming back to it.

Now in my third season, my JV roster has increased from about 30 swimmers (in each of the first two seasons) to 50 swimmers.  For a reason I can’t quite identify, there was a huge influx of new swimmers this year, particularly freshmen and sophomores.  And, to be clear, when I say “new” I mean, “no swimming experience whatsoever”.

When I share my shock with people, the common reaction is, “Well then cut some girls.”  There are about 15 – 20 girls this year that are swimming competitively for the very first time and standard operating procedure would dictate that I cut them (suspending the reality that swimming is advertised as a “no cut” sport).  But I can’t do it.  I cannot bring myself to cut them.

First, we cannot minimize the vulnerable position a teenage girl is putting herself into by walking out in a swim suit in front of her peers and jumping in to try a sport that she has no idea how to do.  In a world that feels increasingly judgmental (especially of our young people), how and why are they able to muster this kind of bravery? … (and here is my connecting point) … how can I get them to be this brave in math class?  More often than not, when my students see a problem they do not know how to do, they shut down.  They say they don’t know how.  They say they were never taught.  They question my validity as a teacher for daring to put something in front of them that I did not explicitly teach them how to do.  And yet in the pool, they jump right in.

I am not exaggerating when I tell you, this group of swimmers knows next to nothing about how to swim.  Only a few know how to swim freestyle, a smaller few have attempted the other strokes before this season, and none of them know how to dive or turn.  THEY FAIL CONSTANTLY.  And yet, they keep trying.  They take every word I say to heart and I watch in awe as they try to incorporate my advice to the best of their ability.  I can actually see their brains churning as they try to figure out how the heck to do a flip turn and not come up in the adjacent lane.  They keep failing and keep trying again.  Over and over.  Belly flop after belly flop until finally they dive in clean.  It is everything I want to see in my math class.  How can I get them to apply to school the same growth mindset they have in swimming?

I am so proud of their bravery.  Cut them?  No way.

Individual Interviews vs. Typical Test

What I did:

1.  I collaborated with my students to develop a rubric for their understanding of the Chapter 10 content.  The left side lists the four main skills from this chapter and the top shows the criteria necessary to earn each score.

2.  I created a schedule (in a shared Google Sheet) for students to sign up for their 10-minute appointment window.  Most were during class time, but some were before school or during a lunch/break/X-block.

3.  I created a sheet (for myself) with sample questions from each section so that I had questions ready to ask during the interview.  This also allowed me to ask different students different questions.  Students also used this sheet when they assessed themselves at the end because I broke the questions in to sections that matched the topics on the rubric.
4.  I interviewed each student for 7 minutes (with a 3 minute buffer).  During that time, I asked them questions about each topic (not just “Solve this…” but “Why did you do that step?”), students assessed themselves on the rubric, then I assessed them (as they were walking back to get the next student).
Why I did it: 

A few chapters ago, I asked students to make me a video (similar to a Khan Academy video) explaining the concepts we learned in that chapter (exponential expressions).  They did this in place of a typical written test.  The feedback was very positive and since then their ability to simplify exponential expressions has really impressed me.  Whereas a lot of math concepts tend to get forgotten after the chapter ends, these concepts seemed to stick.



PROS of the interview process: 

  1. I watched students hold each other to a higher standard when they were explaining and reviewing the concepts.
  2. The students said that they studied harder/better knowing they would have to explain themselves.
  3. Students were way more involved in the assessment process.
  4. I was finished grading as soon as the interviews were finished–there was nothing to take home!

CONS of the interview process:

  1. I had to limit myself to 7 minutes per student which limited the number of questions I could ask each student.
  2. The timing also limited how long we could spend on any given section.  If a student didn’t understand the concept, I would eventually have to move them along to the next section.
  3. I do not have the same amount of evidence to support my score of the student as I would have on a typical test.  Since the majority of the “work” for this assessment was a conversation (not every problem was worked out) I do not have a lot of evidence to base my score of the student on.  I wrote little notes and the students worked through some problems on paper (and they assessed themselves), but I definitely do not have written evidence to support every score.

Next steps:

I am going to continue with an “alternative assessment” for our last chapter, but my students and I are redesigning it with some changes.  Here are our ideas so far:
  1. Students pair up and assess each other.  This will allow students to have more time in their “interview” since multiple interviews will be going on at one time.
  2. Students will have the opportunity to re-explain a concept for a higher score on the rubric.

Do you have any ideas for us to consider?

Alternative Assessment

Chapter 7 in our Algebra 1 textbooks is all about exponents and exponent rules.  It is super dry (lots of rote memorization), but critical to their success in future math chapters and classes.  So I decided to try something a little different because I wanted my students to be able to fully understand and explain these exponent rules, not just regurgitate them on a typical test.  As I often do in class, I referenced my favorite Einstein quote, “If you can’t explain it simply, you don’t understand it well enough,” and decided to ask the students to explain the rules to me–via video.  The expectation was that they would explain why the exponent rules work, not just show me that they work.

Not quite sure the best way to do this, I attended Joan’s lunch demo of screencasting (such perfect timing!) and she really helped me get the ball rolling.  We found a great app (ShowMe) to record videos with, but when the time came to submit these videos, there were quite a few issues.  The biggest being that most of these videos are 5-10 minutes long and few platforms have the capacity to store that amount of content.  We are still working through this part of it.

I haven’t made it through all of the submissions yet, but so far they have been amazing.  Allowing the students to prove their understanding in a creative way really helped me see them in a different light … and we don’t even need to get into the brain science that supports using both “sides” of your brain in a math classroom.  The creativity of this one in particular blew me away:

Chapter 7 Alternative Assessment Student Sample
*It is over 7 minutes long so you obviously do not need to watch all of it, but the creativity comes across right away.

Even after all of the logistical snafus, the feedback from the students was very positive:

Almost 70% said that this type of assessment helped them understand these concepts more than if they had taken a traditional test.

Creating Innovators–Let’s Play!

Over the
break I finished the book Creating
Innovators
by Tony Wagner.  The
author interviewed many people considered to be “innovators” as well as their
parents, teachers and/or mentors in order to identify trends that help to create
innovative people.
Throughout
the book, the most common trend that developed was the fact that these
innovative people were given time to “play”(by parents or teachers or mentors)
and through that play they developed a passion and through that passion blossomed
into a purpose for their careers and other life goals.  That’s when I realized that we don’t take
enough time to play in a math classroom so I made it my 2nd semester
goal to incorporate more “play” into my classes.  I am trying to do this in three ways:

1.     Number talks
with my algebra classes.
  The basic idea is that I put a problem on the
board (i.e. 18 x 5) and the students have to figure it out without any
calculator or paper/pencil.  Once they
think they have the answer they put a “thumbs up” in front of their chest.  When everyone is showing a “thumbs up” I
invite volunteers to explain their thinking while I transcribe it on the board.  For example, one student did 5 x 10 then
added it to 5 x 8.  Another student did
20 x 5 then took away 10 (2 groups of 5). 
We had about 6 different strategies up on the board after this
problem.  The purpose is to show students
that there are many different ways to think of one problem—not just one.  I am very transparent with them, explaining
that my goal is for them to “play” with these numbers and start to see the
flexibility and creativity in math.

2.     Creating
time in my schedule for non-curricular math
.  Students need to see how
math (and mathematical thinking/strategies) apply outside of the
classroom.  If I believe this, I need to
prioritize it and create time for it—so that’s what I did.  In planning for this semester, I set aside
nearly every Friday for this purpose.  To
start out we will be working through Khan Academy and Pixar’s collaboration Pixar in a Box, which provides students with
videos and practice activities to see how math, science and technology come
together to create a Pixar movie.  Last
week we learned how Hooke’s Law (physics) was used to animate Merida’s hair in Brave. 
I’m not grading this.  We are just
playing.




3.     Would You Rather?
(Math)
  With my financial algebra students I am
trying to incorporate more opportunities for them to defend their thinking with
mathematics.  I am using this to start
class (similar to the number talks with algebra).  Again, I am emphasizing the fact that there
is no one correct way to think about these questions, but they do need to
support their decision with math.  For
example, in the picture below, students cannot just say “I would pick the beach
one because I like the beach better.” Most students select the beach based on
the basic multiplication (they can use calculators for this exercise) but then
some students argue that they would pick the city location because it is more
likely to be full throughout the year).


So my
question is, do you incorporate any aspect of “play” into you classes?  How?  I
need more ideas.  Also, if you are
interested, the best chapters were the ones about “social innovation” and “innovating
learning”.  You do not have to read the
entire book to get value from those chapters.

A Mathematician’s Lament

During our
math department PD (“How to Learn Math for Teachers”) we read an article by
Paul Lockhart titled
A Mathematician’s
Lament
.  In this article Lockhart
writes about a man who wakes from a terrible nightmare in which music education
and art education were made mandatory.
“We are helping our students become
more competitive in an increasingly sound-filled world.” Educators, school
systems, and the state are put in charge of this vital project. Studies are
commissioned, committees are formed, and decisions are made—all without the
advice or participation of a single working musician or composer. Since
musicians are known to set down their ideas in the form of sheet music, these
curious black dots and lines must constitute the “language of music.” It is
imperative that students become fluent in this language if they are to attain
any degree of musical competence; indeed, it would be ludicrous to expect a
child to sing a song or play an instrument without having a thorough grounding
in music notation and theory. Playing and listening to music, let alone
composing an original piece, are considered very advanced topics and are
generally put off until college, and more often graduate school.
Throughout
the article it becomes increasingly clear that the author is using this music
education analogy to articulate that mathematics instruction is a
“nightmare”.  The author even mentions,
“It is considered quite shameful if one’s third-grader hasn’t completely
memorized his circle of fifths,”—a clear parallel to third-graders’ memorization
of their multiplication tables.  The
author makes a similar analogy to art education in his “nightmare”, writing
that “The really excellent painters—the ones who know their colors and brushes
backwards and forwards—they get to the actual painting a little sooner. …
Nothing looks better that Advanced Paint-by-Numbers on a high school
transcript.”

This article
makes me feel sad and motivated at the same time.  I’m sad because his nightmare is
reality.  Math, which I would argue is a
very creative subject, has been whittled down to the memorization of basic
facts and formulas.  What if that was
done to art and music?  Wouldn’t that be
devastating?  Then why is it not seen as
devastating when its being done to math? 
A book I read over the summer mentioned that many people see math as a
finite subject, in the sense that they feel that everything about “math”   has already been figured out—all you have to
do is memorize the facts and formulas.  Where
is the fun in that?  What if art and
music were seen that way?  That all of
the songs had already been composed and all of the art had already been
created—all that was left to do was memorize the steps. 

Once I get
over my initial sadness, I feel motivated. 
I want to show my students the beauty and creativity that math has to
offer.   I want them to see math used in unconventional
ways and be curious about how they can apply math outside the confines of the
textbook and classroom. I want them to understand WHY certain formulas work—not
just that they do. I want them to see math as a tool for solving questions THEY
have, not as a set of facts for solving problems that have already been figured
out.  Sometimes I feel like I have more
questions than answers for how to make this a reality, but that’s my personal
charge.  I want to figure it out.

The Fibonacci Sequence = Math + Religion

An Introduction to the Beauty of the Fibonacci Sequence

Recently we’ve been talking a lot about cross-curricular projects and classes: math + science, English + history, religion + history, etc.  What about math and religion?  Where is the intersection?

Last year, a colleague shared a video with me called “The Fingerprint of God”.  In the video the narrator shows many examples of the Fibonacci Sequence (and spiral) in nature, including spirals in nautilus shells matching the spiral curve of a wave matching the spiral curve of our galaxy, and comments that this spiral is like a fingerprint of a common creator.  It blew my mind when I first watched it.  God does math?  Math came from God?  How does this all work?

The Fingerprint of God Video

I desperately wanted my students to have that same enlightening moment so I tried to design a project/activity that would allow them to have that experience.  I asked Adam Chaffey to help me and together we planned our Fingerprint of God activity which spanned the Monday and Tuesday before Thanksgiving break.  The girls were definitely confused when I told them we would be doing a religion + math hybrid activity, but getting to “break the silos” and show them that math and religion can work together was exciting.  On the first day, I showed the girls the Fibonacci Sequence (my students had already “discovered” this earlier in the year) and some examples of the sequence and spiral in nature before sending them out to find examples of their own.  On the second day, Adam showed the Fingerprint of God video and we discussed how seeing this “fingerprint” affected our faith.  Finally, the students were tasked to create a song/video tying together all that we had talked about over the last two days.  (I’ve attached a couple below)


Things I have to figure out how to improve for next time: 

  1. Make it a more discovery-based project instead of a discussion-based project.  I think I was so excited about sharing this with the students that I front-loaded this activity too much.  The discussions were good, but it felt anti-climatic.  There didn’t seem to be any “ah-ha!” moments.  The students did everything we asked of them, but didn’t really figure anything out on their own.  How can I guide them without giving them too much?
  2. Figure out how to collaborate with another class/teacher more smoothly.  I know this was made more difficult by the fact that I have the same group of students 1st and 2nd period, but the logistics of collaborating with a two religion classes was a real challenge.  Adam and I both had girls that were in both of our classes in different periods and therefore ended up hearing the same information and doing the same activity multiple times–not ideal.

…any ideas?

Student Submissions:

…thanks for your help Adam!