So How Exactly Should We Teach Math?

This summer, I read a book on how to conduct your math class in a workshop manner where emphasis is on student thinking and less on just getting the right answer.  As soon as I finished the book, THIS article went viral on why America students sort of stink at math.  I also saw a handful of videos by math teachers who seem to be moving in the right direction.  It all left me with a ton of thoughts and questions about math education.

How do you effectively teach math?

I reflected on the various ways I’ve taught math for the past three years as an educator, thinking about what worked and what didn’t.  Here are a few things that came to mind:

1st Year:

Being that it was my first year teaching in general, I taught math in the same ways that I learned it growing up.  I used traditional methods of showing the whole class a problem on my own, doing a few more problems together, and then giving them practice problems to do either by themselves or with a partner while I met with those who were really struggling.  Tried & true methods right?!  I remember having a mentor come and observe me during a math lesson.  She asked me what I usually do about the kids who fall asleep during the lecture.

2nd Year:

Started doing that whole flipped classroom thing.  New and trendy things are always better!  My class wasn’t really flipped; students watched the videos in class instead of at home.  It was still lecture based but hey, at least they could pause, rewind, and rewatch. Some kids benefited from the videos, others found them boring and struggled to stay on task.  I wrote an in depth reflection on why my flip sort of flopped.   One success that sticks in my mind from that year though was when 3 students were arguing (enthusiastically but respectfully) over whether 1 was a prime number or not.  (Check out my prime number song )

3rd Year:

Revised my blended learning classroom.  I organized my small group time so I was able to meet with almost every student on the concepts we were learning while other students continued to watch the video lectures and do the practice problems.  Had a better classroom atmosphere where students were more self-motivated to learn the material.  I heard more consistent and quality conversations on the math concepts.  I began to understand what it looked like to have students share their thinking, discuss disagreements, and find their own errors.

Hopes For This Year:

My first 3 years were in a large public elementary International Baccalaureate school where I was also teaching science, social studies, reading, and writing.  This year I will just be teaching foundational math skills and pre-algebra in a private middle school.  Quite a big change, not to mention beginning to figure out how to incorporate the new Texas math standards.  As I reflect and synthesize all I’m learning about math education, I’ve developed a few goals for this year:

• Viewing my students as apprentice mathematicians, and calling them that as well.  Creates much more of a growth mindset.
• Keeping the following analogy in mind: Computation is to math AS typing is to writing.  This will put less emphasis on computational skills and more emphasis on numerical literacy.  I’d prefer that students strive for solid number sense and maybe have less efficient computational skills than students who can solve any division problem but can’t explain how division and multiplication are different.
• Stop trying to rescue the students by explaining the problem to them.  Learning happens through the struggle.
• Move away from an “I, We, You” way of teaching; I explain, we try together, you do problems on your own.
• Move to a “You, Y’all, We” (Or “you all” for folks in the north) way of teaching; you try to solve it by yourself, you have discourse with your peers, and then as a group we hear the different approaches made.  This gives them an opportunity to stop and think, share their thinking, and discover their own misconceptions (or the misconception of their peers).
• Never say anything a kid can say.  Let the students explain to one another without ‘clearing it up’ for them.  I can let go of the lie that they won’t get it unless I explain it to them.

“My definition of a good teacher has since changed from ‘one who explains things so well that students understand’ to ‘one who gets students to explain things so well that they can be understood.’ -Steve Reinhart

• Get students to stop becoming ‘providers of answers’ and start becoming ‘explainers of thinking’

Obstacles & Resources:

Sometimes conversations like this can sound a bit esoteric.  We all nod when we hear things like ‘we need to teach our kids to actually think and not just plug and chug’ but too often, we have difficulty translating that into our actual lesson plans for the day.  I highly recommend Minds on Mathematics: Math Workshops for many practical examples of how you actually structure this in your classroom.

I feel finding beefy problems is always a challenge as well.  I plan on using Khan Academy for a lot of practice as well as way to monitor mastery of particular concepts. They’ve got plenty of resources to help you implement it into your class.

Here are some other resources that will provide problems you can have quality math conversations about:

• mathproblems.info
• braidedmath.com
• The Book of Perfectly Perilous Math – pretty enjoyable problems to work through and discuss for grades 5-7.  I’ve seen “non-math” kids get pretty excited about tackling some of these problems.  You can see PDF’s of a few example problems from the book HERE.
• Many textbooks have quality problems but they do most the thinking for the student; they give all the info and break the steps down into A- do this first, B-do this next, etc.  See how one teacher uses textbook problems to provide the bare minimum of information along with the question, leaving out the rest so students can have quality math conversations using intuition:
  

What have you discovered in your adventures in teaching math?  What works?  What doesn’t?