A funny thing happened on the way to the chalkboard.

As I sit in my classroom while my Number Sense class is taking their final exam, I find myself reflecting on the changes I have made over the course of the last five years teaching this course.  For most math teachers, we have experienced success as students of mathematics.  While this doesn't necessarily seem to be a very bright or insightful statement.  It is.  Embedded within that idea is that most math teachers were students of mathematics in a procedure-driven classroom environment.  This kind of classroom has a very recognizable format for most.

1. Students enter the room with last night's homework.

2. The first fifteen minutes (or more) are spent on going over the homework problems. These problems of discussion are typically selected by the highest achievers in class, leaving those with deeper misconceptions left to sit back and watch (or not watch).

3. The next 20 to 30 minutes is the teacher explaining a procedure or concept to the best of his or her ability.This often includes the teacher writing his or her notes/examples on the board.  The students are then putting down in their notes exactly what is written of the board.  When the highest achievers have questions about a process or product, the teacher will do another example similar to the first, but with different numbers.

4. Fifteen to 20 minutes are dedicated to doing homework in class that is an additional set of problems just like the examples during the lesson.  When problems diverge in thinking from the examples, these are seen as the really, really hard problems.

Truth be told, this was my teaching style of mathematics for many years.  In fact, the first few iterations of my Number Sense class were much like this.  Any teacher who has taught in this traditional format can relate to the frustration that, "My students got it yesterday when I taught them, but today it is like they have never seen it before."  Sound familiar?  It does to me.  

Over the years, I have used an article in my methods and curriculum class for future teachers of middle school and high school students.  This article is written by Stephen Reinhart and was originally published by the National Council of Teachers of Mathematics.  The article can be found here. In "Never say Anything a kid can say," Reinhart proposes a student-centered classroom where the power of collaboration is king.  While Reinhart wrote this article over a decade ago, the themes and strategies highlighted are still very true in math education.  In fact, the Standards for Mathematical Practices (SMP) within the Common Core State Standards for Mathematics CCSSM), emphasize the very same conversational environment within SMP3.  SMP 3 can be found here. In SMP 3, students are required to construct viable arguments and to critique the reasoning of others.  

This requirement of argument and critique begs a certain question in respect to traditional mathematics instruction.  Is it possible (or at least likely) that students are regularly given the opportunity to construct mathematical arguments that are viable?  Do they critique the reasoning set forth by their classmates?  I would respond to those questions with an emphatic, "NO!"

This brings me back full circle to my Number Sense class.  I used to a "good job" telling my students exactly what I knew about improper fractions and division with decimal squares, but I never gave them the opportunity to discover, inquire, and converse about what they knew.  This has changed completely in my most recent versions of the course.  I always have in mind, "Don't tell them, have them do something to create a group understanding at their tables."

I plan to blog in much more depth about my use of technologies (Nearpod, Plickers, Padlet, Aurasma, Kahoot, Desmos, and others) and other engagement strategies (Big Whiteboards [2 feet by 3 feet boards for tablework], speed dating, and "Let the chalk (not really chalk) do the talk").

So, a funny thing did happen on the way to the chalkboard, because now I am no longer on my way to the chalkboard to be a grand orator of math knowledge.  I want to create an environment where the voice of the student is the predominant voice heard in my room.  Research shows that with the right coaching, kids can thrive in this kind of environment and actually see math as much, much more than notes, blind procedures, and something that they are just not good at.