Growth Mindset Part 1: Math

We have all failed at something, and my personal list could take up this entire blog.  Here are just a few from the list: getting a job I wanted, receiving an “A” in a class, catching a plane on time (that only happened once in my life), weaning myself from Pepsi 0 (but still trying), driving a stick shift car, driving in the snow, etc.  How about you?  What have been your failures?  And…..what have you learned from these failures?  THAT’S THE IMPORTANT QUESTION!  When we fail, we need to learn the lesson that the failure taught us!

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Photo courtesy of Laura Gibbs on Flickr; check out her blog at http://growthmindsetmemes.blogspot.com/

“Raise your hand if you’ve failed at something.”  That was how I began my work with my 2nd through 6th-grade gifted students at the beginning of the school year.  I ended up getting a response from everyone, and also shared my own story.  I used this discussion to launch my theme for the school year, Growth Mindset, a term coined by Carol Dweck.  I had been introduced to this concept the previous year when my GT Facilitator job at an elementary school (we will call it School #1) was cut to two days (funding, funding, funding) and found a second part-time job, also as a GT Facilitator at another elementary school (School #2) in the same district.  This school had Growth Mindset as their theme for the year…with both students and staff.  At every staff meeting, we saw a video based on this theme or did an activity, and we all received cool staff shirts that said “Fail.Learn.Grow”.

I quickly realized how important this concept was in working with gifted students.  Some, not all, are perfectionists and tend to not try new things if they might fail.  Check out this excellent blog post by Gail Post with more about this fear of failure in gifted kids. I decided immediately that my job as their teacher was to invite them to failure…to ensure that they would fail!  My almost daily question to the students that year became, “What my job at this school?”  And the response:  “To frustrate us and make us fail!”.  In other words, told them they would be failing at several things this coming school year!  In order to prevent concerned emails from parents, I had already emailed all parents with information on this concept and links to resources.

Next, I had to come up with activities to ensure their failure, learning, and growth.  I decided to focus on math, as that has always been my “fear of failure” area. In addition, I had students who really needed some advanced math challenges! Below are some of the activities we did, along with photos taken during our learning and growth!

Noetic Math Contest
I was pulling my 2nd and 3rd GT/Highly Able students from their math block a few days a week, so I wanted something incredibly challenging for them…and this fit the bill.  This contest is THE BEST!  They offer practice questions, Problem of the Week (sent right to your email) and many other resources.  I already had some past contest problems from other teachers, so we used our sessions to work on these, and believe me, there were a few failures, lots of frustration, some tears, but a great deal of growth!  I varied between letting them work with a partner or alone.  I think the most important thing I did was never confirm or deny if they had the correct answer to a problem.  Instead, I had them check with other partner sets or individuals to see what answer they had.  If the answers were the same, they could be fairly confident they had the correct one (although a few times there were partners/individuals that both got the same wrong answer), and if they were different, both had to rework the problem.  For those students that were successful first, I sent them out to offer help and support to others.

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They provide an answer and explanation for confused teachers! Source: Noetic Learning Problem of the Week

Below are examples of the problem solving of these 2nd and 3rd-grade students!

One of the Noetic problems was SO difficult; the student and I were working on it for days…even though I had access to the answers, I could not understand WHY it was the answer (it wasn’t only the students who were frustrated!).  I finally emailed Noetic for an explanation!  Below are the problem and the students’ work (I’m sure many of you reading this can instantly come up with the answer…I was a victim of New Math in the 1960s, so be kind!)Screen Shot 2018-03-20 at 7.54.04 PM

Before they took their first contest, I had to have a serious talk with them about possible results.  I told them that these contests were difficult and they should be very proud of even trying it out!  When the results came back, with the first contest results ranging from 1/20 to 10/20 correct, I did the pep talk thing again. I handed back the contest papers and challenged the students to try incorrect ones again, and then explain to us where they went wrong the first time around.  What an incredible growth experience this was!

Math Olympiad
While I had heard of this contest for students in grades 4-8, I finally had a chance to be involved during that year at the Growth Mindset-themed school.  As part of my job, I was one of the coordinators of the practice sessions and contests.  And wow…those practice and contest problems were challenging!  I tried working them before each practice session and was often flummoxed myself (fortunately the practice book provides strategies and answers, and so do the actual contest problems.  During practice sessions, we had students choose between working in pairs or individually, and I did the same thing as in Noetic when students came up for answers, I had them go verify and check with others. When the contests were returned, once again a motivation talk was needed as even the most gifted of students often ended up with on 1/5 or 0/5!  I highly recommend either participating in the contest or just using past/practice problems with your students as challenges.  You could even have your own classroom “unofficial” contests!  Here are some sample problems and information.  You can find other sample problems via Google searches.  I was proud that this math-phobic teacher (more on that in future blog posts) then began the contest for the first time ever back at School #1 and I encouraged my GT students to join.  I was especially pleased that two of my 4th-grade girls joined up.  It was extremely challenging for them, but their growth that year was incredible!

Continental Math League
I had used sample CML problems with my GT students at School #1 for a few years, but when I began working at School #2, I was able to be part of the official contest that was offered for primary students (although CML has contests for grades 2-9).  Just as in Math Olympiad, we held practice sessions, working on strategies and building up problem-solving stamina. Once again, these incredibly challenging problems caused, yes, frustration, but also an incredible amount of learning, growth, and pride when an answer was finally correct!  Here’s some work my 1st & 2nd graders were doing on CML problems; that chicken one was a tough one…two of my girls worked on it for weeks; we even had a folder to store all of their work!

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How classroom teachers can use Noetic/Math Olympiad/CML: Have your whole class, or just interested students do the official contest; use as enrichment for advanced math students; send the Problem of the Week home as an optional challenge assignment; post in Google Classroom or Edmodo and award badges for those students who try to solve and explain their thinking! 

Algebra Tiles
So my 6th-grade students at School #2 had an incredible math teacher; she was wonderful at giving those GT kids advanced math work and challenges.  One particular day in her classroom, I noticed the students using some colored tiles…and had them explain them to me.  They were algebra tiles, and the students were using them to solve equations.  I was blown away…I had only ever solved equations in the traditional way and this added an incredible visual dimension!  The students demonstrated solving several equations using the tiles; I was beginning to understand but my traditional methods kept interfering with understanding the visual, hands-on method.  Upon arriving home, I immediately ordered a set as I was already planning to use them with my 6th grade GT kids at School #1.  So at both schools, as I worked with these students, I would have 1/2 the group solve equations with the tiles, and half solve using the traditional method and then compare answers; they would then switch.  Wow!  Incredible growth mindset going on for myself AND for the students!  Take a look at our work below using some paper-made tiles before I bought the real tiles! There are lots of videos on YouTube to help you and your students learn how to use these, and IXL has a great practice activity on using the tiles!  Intermediate teachers can use these as enrichment for advanced math students and/or set up as a math center!

Polynomials - Photo by Jan

The Fibonacci Sequence
Here is a perfect growth mindset opportunity to challenge your intermediate and middle school students, as well as younger gifted students. That same teacher who had her 6th graders using algebra tiles introduced them to the classic rabbit problem and then partnered the students up to try to solve it using any method they wanted to try.  It’s a tribute to her teacher, as well as their previous math teachers that I saw every kind of method being used to solve this, and there were a few students (yes, the amazing ones I was lucky enough to work with) who were able to come up with the answer.  The teacher had students come up and show their methods and work with the document camera.  Check it out!

Please stay tuned for future posts on how I embedded and used this theme of Growth Mindset all year long, down to and even including some fun at our holiday party!  In the meantime, keep on growing your mind!

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Photo courtesy of Laura Gibbs on Flickr; check out her blog at http://growthmindsetmemes.blogspot.com/

 

Author: Jan Anttila

I recently retired after 25 years of teaching (yay!) I started my own tutoring and consulting business and am now anxious to share my passion for teaching and many lessons, projects and activities I did with my students over the years, as well my current practices for tutoring.

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