Seeking Challenges in Math

I was working with a grade 7 teacher and his students a while back.  The teacher came to me with an interesting problem, his students were doing quite well in math (in general) but only wanted to do work out of textbooks, only wanted to work independently, and were very mark-driven. The teacher wanted his students to start being able to solve non-routine problems, not just be able to follow the directions from the textbook, and he wanted his students to see the value in working collaboratively and to listen to each other’s thoughts.

Our conversations quickly moved to the topic of mindsets. It sounded like many of his students had fixed mindsets, and didn’t want to take any risks.

For those of you who are not familiar with growth and fixed mindsets, students with fixed mindsets believe that their ability (in math for example) is an inborn trait.  They believe how smart they are in math is either a gift or a curse they are born with.  Those with growth mindsets, however, believe that their ability improves over time with the right experiences, attitude and effort.

When confronted with challenges, those with growth mindsets are willing to struggle, willing to make mistakes, knowing that they will continue to learn and grow throughout the learning process.  On the other hand, those that have fixed mindsets tend to avoid challenges.  They believe that struggle, making mistakes, and being challenged are signs of weakness.  Psychologically, they will avoid the feeling of discomfort in not knowing, as this threatens their belief about how smart they are.

Knowing this, we devised a plan to see whether or not his students were able to take on challenges.  We started the class by giving each student their own unique 24 card (see below).

24 card.jpeg

We explained that each card had 4 numbers that could be manipulated to equal 24.  For instance, the card above could be solved by doing 5 x 4 x 1 + 4 = 24.

We then explained that we would give them time to solve their own card (which had a front and a back), and that we would give them additional cards if they completed both problems.  We also explained the little white dots in the center of the card, 1 dot being an easy card, 2 dots being more complicated, and 3 dots being the most difficult.

As students continued to work, we noticed some students eagerly trying to solve the cards, and others starting to become frustrated by others’ successes.  After a few minutes, the first few students had completed both problems and asked for their next card.  We asked, “Would you like another easy card, or would you like to challenge yourself?” to which the vast majority asked for another easy card.  In fact, some students completed many cards, front and back, all at the easy level, never accepting a more challenging card (even bragging to others about how many they had completed).  Others, after giving up pretty quickly, asked if they could work with a classmate to make a pair.  While we were happy at first with this, none of the pairs had students working cooperatively together for most of the time.

Take a look at some of the challenging cards.  What do you do when confronted with something challenging?  Do you skip it and move on, or do you keep trying?


As soon as we were finished, we showed the class this video:

Watch the 3 minute video above as it ties in perfectly with the 24 problem from above.  We had a quick discussion about the video and why some of the students wanted to choose the easier puzzles.  The class quickly saw the parallels between the problems we had just done and the video.

While we had a great discussion about fixed and growth mindsets, it took most of the year to be able to get this group to see the value in collaboration, to focus on their learning instead of their marks, to be able to take on challenges and not get frustrated when they didn’t have immediate success.

Changing our mindset takes time and the right experiences!

I am really interested in why students who believe themselves to be “smart” at math would opt out of challenging themsleves.

Do any of your students exhibit any of the same signs as these students:

  • Not comfortable with tasks that require thinking
  • Eager for formulas and procedures
  • Competitive with others to show they are “smart”
  • Preference to work alone
  • Preference to work out of textbooks/ worksheets instead of on rich problems/tasks
  • See math as about being fast / right, not about thinking / creativity
  • Eager to do easy work that is repetative


So I leave you with some reflective questions:

What previous experiences must these students have had to create such fixed mindsets?

What would you do if your students avoided challenges?

What would you do if your students groaned each time you asked them to work with a partner?

How are you helping your students gain a growth mindset in math?

Can you recognize those in your class that have fixed mindsets?  Are you noticing those from different achievement levels, or just those who are struggling?

If our students find everything we do “easy” what will happen to them when they get to a math course that actually does offer them some challenge???



P.S.  Did you solve any of the 24 cards above?  Did you skip over them?  What do you typically do when confronted with challenges?

8 thoughts on “Seeking Challenges in Math

  1. I think one of the things students struggle with relates to the reason I didn’t solve any of the challenging 24 cards above: time. I wanted to read this blog, but my off period is short and I have other things I need to do. When we give our students tasks, sometimes we give them mixed messages. We say “this is easy” or “hurry up and finish” or “whatever you don’t get done is homework”. All of these messages are damaging in ways that might not seem obvious at first. Kids are busy and they are used to rushing, so they can get to something more fun. So it behooves us to do two things: Give them rich tasks that they are actually interested in (fun) and give them time to relax and think and process.


    1. I hope nobody assumes that the puzzle will help foster a growth mindset. It was the first way to help us show our students what a growth mindset is…
      The real work took all year being able to identify when we were being fixed… and much change in how the students experienced mathematics and mathematics learning.
      Thanks for the comment!

      Liked by 1 person

  2. I thought about this post quite a bit after reading it then trying to solve the first difficult card. I kept at it for a good long time without solving it. I was really surprised that the answer eluded me. I had considered every strategy that I could come up with, but I knew that it couldn’t be so hard that I wouldn’t be able to get it. But I worked too long on it for my comfort, so I decided to put it aside until later, and started to get on with the rest of my day. I just put it out of my mind….for about two minutes. Then the answer just appeared. I fumbled for a pencil just to check what I had seen, and to check if it was right, which it was. Then I thought, what just happened here? What happened that happens differently than in a classroom? First, when I didn’t “get the answer” right away I didn’t berate myself for being stupid, or fear that this proved that I was less than I wanted to me. I am completely comfortable with not understanding things right away (especially in the privacy of my home!) because I know most of the things I figure out takes time. So, persistence is the what I value, not speed. But this is so different that what I experienced as a student: one tends not to linger over homework, and all tests happen within a classroom period. But deep learning through discovery needs time for thoughts to marinate. I have absolutely no idea how a teacher could help students be comfortable with taking time to understand things without them feeling like losers, but this seems like a worthwhile goal. I’ll be thinking about it….

    Liked by 1 person

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