Understanding Takes Time

I know math workshop is for me!  Why?  Because I share these beliefs:

1) Students Are Capable of Brilliance

2) Understanding Takes Time

3) There is More Than One Way

Welcome to part 1 of our Minds-On Math Workshop bookstudy.  Here are some of my thoughts from this week! 

Students Are Capable of Brilliance

     My best teaching friend and Kindergarten teacher extraordinaire has this as her mantra.  Her students constantly outperform other Kindergarten students in the district and she is always being asked to share her secret.  Her #1 reason her kids do so well is because she holds them to very high standards.  She truly believes that all kids can learn and in many ways their teacher's attitude about their learning becomes a self-fulfilling prophecy.  Her students learn because she believes they can.  ALL OF THEM. 

     Every time I feel like giving up on a kid and just "Teaching him how to do it" (aka arithmetic without understanding) I remember my friend and how beliefs become her students.  All students can learn and we need to keep expectations high for our students.

Understanding Takes Time

     You can "teach" your students the standard algorithm for subtraction in ten minutes and have them practice it for an hour.  It will look like your students understand subtraction.  Next week or next month you will give them three subtraction problems and they will tell  you that they forgot how to subtract.   Worse yet, they might not tell you that.  They might keep missing a step in the procedure or do a step wrong repeatedly.  Now they are in a position where they think they know how to subtract and they have no idea all their answers are wrong. They don't know how to tell if an answer is reasonable because you didn't "teach" them how.
     Alternatively, you can spend an hour per day for three weeks guiding your students to develop flexible and efficient strategies and giving them opportunities to share these ideas with their classmates.  They will also have a chance to hear their classmates ideas and compare how they are similar or different from their own.  In the process of doing this, they will strengthen their understanding of addition, place value, estimation and inverse relationships.  Next week or next month, you will give them three subtraction problems.  They will solve them all mentally applying a strategy that is efficient for the numbers in each problem.  They may or may not use the same strategy for all three problems.
     The example above illustrates the difference between telling and guiding.  With telling, you are doing most of the talking and learning.  Sure it is faster but your students will lack understanding.  Guiding students to develop and refine strategies takes much more time upfront.  The students do most of the talking, and you get through fewer problems during a class period.   You might in fact spend 20 minutes talking about one problem.  It takes time but it also develops understanding.  Understanding is what will be there for your students next week and next month.  For me, it is worth the investment of time to produce understanding.

There is More Than One Way

     This is one I learned from my students.  There is one student in particular who I will always remember helping me see a new way to look at subtraction.  I was taught that there was one way to solve each math problem and it has taken me years of teaching and learning to undo that thought.  "With faith that each child, given time, has an innate ability to reason out a solution to a problem, even if their initial approach and strategy may differ from how we believe things "ought" to be done, we can begin to turn over the responsibility for learning mathematics to our students." This quote from the book really resonated this change for me and helped me see how my thinking has changed since I started my teaching career.  I know embrace multiple strategies and love that my second graders can currently solve a problem like 17-9 using six different strategies.  Most of them are very efficient and none of them involve counting! 

Do you share these beliefs?  How has your own experience in the classroom enhanced or changed your beliefs? Other thoughts about this weeks reading?  Leave your thoughts below in the comments!