What Makes a Math Person? How Can a Growth Mindset Impact the Classroom?

We may have all seen the sudden cringe of disgust when we share with a recently met acquaintance that we are a Math teacher by trade. Many times this is followed up by the dreaded statement, "I'm just not a math person." For many reasons, mathematics gets lumped under a category of some rare magical gift that just appears in certain individuals, rather than a skill that can be developed, and a real tool that can be applied in various situations when learned.




Decades ago, Dr. Carol Dweck coined the term "Growth Mindset" to describe a contrary point of view to our typical attitude of "you either have it or you don't." This view tells us that the end goal is not to somehow suddenly possess the ability to do a certain thing, but rather that the effort and the process is the goal: that the journey should become the destination. We somehow seem to have lost that way of thinking in American schools. We find ourselves focusing on the end goal as a "passing" grade on a standardized exam, or a SAT Math score high enough to get us into a university where we can "really" start learning something worth learning. We are churning students through our factory style education system without developing their critical thinking skills near to the extent that they could reach when supported by teachers that embrace the idea of allowing students to explore content and embrace their curiosity at all levels of education.

But why math? Why does math as a content seem to widely be held to this idea that some people are just naturally good at it, and some are not? I have wondered about this topic for much of my career, and this weekend, on Saturday, March 4th 2017 I will be holding a round table discussion about how Mathematics relates to a Growth Mindset, and how our education system may be impacting the development of our youth and the first annual Houston STEM Conference at the University of Houston Clear Lake campus. The conference is from 8-4. Check the schedule for more information.

Hope to see you there!


Daniel Becker

For more information:

Houston STEM Conference
Presentation Schedule

Maria says...

Is Maria’s statement Always, Sometimes or Never true?

Block Pyramids

The drawings below show a 1-layer, 2-layer, and 3-layer pyramid made out of color cubes.  There is one visible block on the first one, 5 on the second one, and 13 on the third one.  "Visible blocks" are those that you can see if you were to walk around the pyramid.

•How many blocks would be visible on a 6-layer pyramid? 35-layer pyramid? n-layer pyramid?

•How many square units of paint would be used (total faces painted) in an n-layer pyramid?

My New Account

I recently opened a new bank account and ended up with $25 after the first month.  Six months later, I noticed that I had $235 in the same account.  The bank teller looked at my statements and commented that the amount of money in the account at the end of each month was the sum of the preceding two months.  What was the account balance after each month?

Month	Account Balance
1	$25
2
3
4
5
6	$235

I really like this type of problem for students of any age who we want to start thinking algebraically. 

How can your students move from guess-and-check to algebraic methods of solving this type of problem?

What Makes You So Special?

Discovering Special Cases of Polynomials in Ms. Wilson's Algebra I Class...

"This lesson was implemented the day after my students learned how to FOIL binomials. Students already had an understanding and mastery of exponent property rules, as well as adding and subtracting polynomials. The day after FOIL, I told students that we were simply going to “practice more multiplication of binomials” so that they really get it. What they didn’t know at the time was that all of the binomials they were multiplying would create perfect square trinomials and a difference of two squares. Students were given 15 problems to FOIL (all special cases) like the ones shown below:

I chose to sit students in groups of 4 for this activity and encouraged them to collaborate and help one another.  As the FOIL’ing began, the lightbulbs started to turn on. I could hear conversations evolving about patterns they were seeing involving additive inverses and things “dropping out”. One student announced to his group, “guys, if the signs are different the x’s always cancel out!” Many groups stopped FOIL’ing altogether and went on to apply the patterns they’d discovered for the remaining problems. Some needed guidance (more so with perfect square trinomials), so I asked them some leading questions that allowed them to own the discovery of these patterns and algebraic rules. The magic that happens in a classroom when you hear that, “ohhh!” – that’s the sweet spot." 

 When have you experienced one of those "aha" moments in your class?

(Catherine Wilson teaches Algebra I at Westbrook Intermediate School in Clear Creek Independent School District)

American Greatness? Not in STEM Education…

America has become the land of obsession with gadgets combined with general passivity in STEM fields. It seems that the more integrated we become with technology, the less interest there is in the actual application of science and mathematics that has made our current culture possible. When introduced as a Mathematics teacher, many of us are met with the reaction, “I’m just not a math person.” It seems that while many students are emotionally invested in math and science at an early age, the middle school years show such a dramatic change in curriculum that many students lose interest, and get stuck in a fixed mindset that makes them feel that success in STEM is out of their reach. In contrast, many countries around the world have taken different steps than the United States, and have experienced great success. What has created this fixed mindset when it comes to math and science, how does the classroom culture in these other countries compare to ours, and how can we support critical thinking and STEM integration in our classes and still “cover” the required content by many of our districts?

           

The recent PISA scores show a slight decline in performance in Mathematics and a slight increase in Science scores. Even with what we may consider a break-even mark in the STEM field academically, we can easily compare ourselves with the “GoldStandard” countries like Singapore, Japan and a greatly improved Estonia and find ourselves lacking. While those countries may seem to have many cultural differences with us, in terms of SES status, one of the measures that we generally connect to higher or lower STEM results, Estonia has very similar student demographics to much of the United States. While we push for more standardization and accountability through data via the common core curriculum, they adopted the opposite of many of the techniques that our government has consistently been pushing our education industry towards.

The world will be facing many challenges sooner than we realize that many believe can only be faced through STEM development. Technology, namely disruptive technology, has changed the workforce dramatically, and will soon have an even greater impact. To be successful in the future workplace, students need to have knowledge of the impact of STEM on our society and economy, and how they can apply STEM skills for the development of our country and our planet.

Some questions we as educators should explore:

• What creates a “fixed” mindset when it comes to Mathematics and Science in our classroom and culture?

• What can we do to promote a growth mindset in our classrooms while integrating STEM application into the real-life perspective of our students?

• Does our focus on testing and standardization take away from our ability to allow our students to embrace their curiosity and explore and discover new interests in STEM fields?

What do you think? Does the American education system stifle creativity in the foundational years when we should be strengthening it?

Diamond in a Box

Each figure in the pattern is created by joining the vertices of a triangle that is rotated as seen below:

•Provide at least 2 methods of finding the area of the diamond in the middle.  Is it a square?

•If the pattern continues, what would be the area of the diamond in Figure 20?  Figure x?