Why Struggling in Math is Good!

In today’s society we can find answers at our finger tips.  With smartphone, tablets, laptops, WiFi, and other tools at our finger tips, we can quickly find out thing we need to know quickly.  This has created a society and a group of students that are not comfortable with struggling, at least in the sense of finding information.  Who remembers going to the library, using the card catalog to find a book to do research, then having to know the Dewey decimal system to find where the book was, then going into the stacks with a bunch of note cards and writing down the important information.  Today’s students can accomplish this feat in seconds using technology, they have become spoiled!

They want the same type of quick resolution in math, but when they can’t google a math problem or use Photomath to do it for them, they get frustrated.  Struggling to solve a math problem is a necessary evil in becoming a good mathematician!  It is the struggle that makes us recall all the tools that we have to solve problems.  One of my favorite things to do as a math teacher is to discuss with students the different ways of solving the same problem.  These are some of the best discussions in a math classroom, I love asking students why they chose a specific technique or a specific order in doing a problem.  It gets them verbalizing and thinking about mathematics in a different way.

When students are really stuck on a math problem I love to ask them to give me some type of  informal analysis of what is going on in the problem.  This can sometimes start us down the right path to the solution.  We have to teach students that informal analysis like sketching, making conjectures, and estimating is necessary when we first observe a problem.  Once we complete the informal analysis we can develop a plan how to transition from informal to formal, and create a need for certain computational skills and processes.  This is just part of what I enjoy about the design thinking behind most Desmos Activities (click here for more).

I also think it is important for students to be wrong in mathematics.  I don’t mean that they added wrong, or missed a negative sign, I mean did a problem completely wrong.  We learn from our mistakes, and in mathematics I think this is a great learning tool.  When we can have a dialogue and observe others solving a problem, especially one which we got wrong, we see a different perspective.  As I progressed through high school, college, and even now as a teacher; I have learned the importance of doing something wrong, and trying to avoid that from happening again.  NOBODY IS PERFECT!!  It frustrates me when students are upset about getting a 97% on a test, but they don’t want to ask why they got something wrong.  numerical percentage grade for me are a waste, and a hindrance.  When students stop being afraid of being wrong and losing points, that’s when we can learn.

This week we are giving the PARCC test in my school.  I am administering the test to my Algebra 1 students.   People have mentioned that the PARCC is too hard, and not fair.  Let me tell you what I have notice:

  • My students worked really hard!  Harder then I saw them work all year
  • My students struggled, going back and forth between the questions
  • My students had some great mathematical conversation when they were done the test
  • My students used a ton of different skills to solve the problem
  • My students weren’t afraid to be wrong and tried almost every problem
  • My students enjoyed being challenged!!!

Adversity is not a bad thing, we learn from it.  My students took a really challenging standardized test this week, and hopefully they learned from it.  I hope they learned that everything in life is not easy.  I hope they learned how smart they really are.  I hope they learned never to give up.  I hope they learn that struggling is a good thing!!

Desmos Sliders…not the little sandwiches

To me, one of the most underrated tools on Desmos.com are the sliders.  Sliders give the ability to make things move, including a function. (Check this link out to learn more about SLIDERS)   There a couple of reasons I think sliders are so important and useful:

  1. Students love to see things move!  Usually the first time I use Desmos in graph I show students a really cool graph I made a couple of years ago.  It has a bunch of moving parts and really gets the students to “buy-in” to using Desmos.  Check out  MY GRAPH.
  2. I don’t have to tell students what the parts of an equation mean anymore.  By putting sliders in for the different parts of an equation, students can explore for themselves how each part of a function affects the graph. (see below for examples)
  3. It makes me a more efficient teacher.  It seems like every couple of year we have a change in our standards, inevitably that means more standards to teach in the same amount of time.  Before Desmos and before sliders that meant doing a bunch of graphs using x/y chars and plotting them so students could make the connections.  Now, something that used to take a whole class period takes about 5 minutes.

There are so many reason I hear why people love to use Desmos in their class, but I really don’t hear people talk about he sliders that often.  For me, the sliders are a tool that makes Desmos an invaluable tool in the classroom.

Below are a list of graph I use with the students that have sliders:

Linear Equation – transformation form

Absolute Value Function – vertex form

Quadratic Function – vertex form

Exponential Function – vertex form

Order of Teaching Quadratics?

Almost every year I spend a significant amount of time thinking about the order in which I teach Quadratics in my Algebra 1 class.  I break down the topic of quadratics into 3 specific topics/standards: 1) Multiplying/Factoring    2) Graphing    3) Solving Quadratic Equations.  The order in which I listed them above is also the order in which I presented them this year, but in past years I have started with graphing and then  hopped back and for between the other two.  Last night, while I was laying in bed not being able to fall asleep, I found myself debating this topic to myself.

As I have mentioned before, I teach in a K-8 district and I am the only Algebra 1 teacher.  This make the idea of discussing it with another teacher sort of a challenge.  In the past year or so I have realized that social media is an integral part of how I develop as a teacher.  Thus I am throwing this out to any reader to comment back to me with your ideas, share it will your colleagues, and give me some much needed insight!

Last year I had the honor of being chosen as a Desmos Fellow, which BTW is accepting applications for its 2nd Cohort, and I have posed the same question to them.  I have always been of the philosophy that the best teachers use other teachers as resources….so that is why I am reaching out to you.

Thanks in advance!!!