Tuesday, January 31, 2017

What does math practice mean to you?

What comes to mind when you hear the phrase "drill and practice"?  Did you cringe just reading it?  To me, I think of an entire worksheet of the same type of bare number problem. For the most part, this practice is no longer the cornerstone of math instruction.  Conceptual understanding has become the focus as we work towards deeper understanding and mathematical sense making.   After some conversations this week, however, I have been reflecting on the role of practice in math class.

  • Practicing a skill allows students to:
    • apply strategies learned
    • work on precision and accuracy
    • increase efficiency (as we work towards fluency)

If students have conceptual understanding shouldn't they practice?  
I have told my students that the best way to prepare for a test is to practice problems.  I have always believed that if you want to get better at something, you need to practice.  So where is the disconnect?  Why does the thought of practice sheets seem so wrong when I do in fact believe in practice?  

I started to realize my true feelings on this issue when I read this blog about math facts in elementary school.  You can see my thoughts in the comment section.  It turns out I have very strong feelings about what practice should (and should not) look like in elementary grades.  Perhaps it is because my own children are that age, and I see first hand the effect practice worksheets have on my daughter's attitude towards math. With so many great and easy ways to practice skills through games I don't feel repetitive practice sheets and flashcards should be used.

If you are familiar with Jo Boaler's work, you are most likely nodding your head along with my statements so far.  As a middle school teacher, I do not pretend to know what this all actually looks like in an elementary class.  How do you know when a student has conceptual understanding and is ready for practice?  How do you monitor and keep track of progress?  How do you make the math accessible to all and begin to close the gaps that students come with in kindergarten?  I have great admiration for elementary teachers and the work they do every day to stoke the fire of excitement these young minds have.  It was after a conversation with one of my favorite elementary principals, @LukeHerlache1, about the work his school has been doing in math, that I started to think about the structure of math skill practice in middle school.

For some reason it seems more acceptable to give a practice worksheet in middle school.  Why is that?  How can I feel so strongly about practice in elementary school and have not taken time to reflect upon what it looks like in middle school.  When students want extra practice I gladly give them worksheets.  While it is rare that I have practice sheets as part of my lesson, I have links to them on my website.  The interesting thing is that some students really like them.  There is something comforting to them about doing a mass amount of the same problem and checking to see if they are correct.  Is that a learning style or a conditioned way that students have been taught to practice?

I encourage you to take some time to reflect on what practicing math skills looks like in your class.
  • What does "practice" actually mean?  
  • When is a student ready to shift from learning to practice?
  • How engaging is it for the students?
  • Do students have enough time to build conceptual understanding?  
  • Does the practice draw on their conceptual understanding or memorized rules? 
  • Does it focus on flexibility with numbers or following a set of steps? 
  • Does it encourage sense making?
In reflecting on my own teaching practices, I think my core beliefs about math instruction have lead me down the right path.  What I need to work on is being more purposeful in the planning process.  Each student is at a different point in their journey with a skill.  It is important for me to think about what practice is appropriate for that child at that time and what support they need.  If they are truly ready to practice a skill an Open Middle task will accomplish far more than a sheet of repetitive practice.  Have you tried one?  Students are still solving the same type of problem repeatedly, but now there are the added components engagement, purpose, and sense making.  It has a different feel and students continue to deepen their understanding as they "practice".  

As for those sheets with the same problem over and over again, those will be going into retirement.  


  1. Adrianne, It's so interested this idea of "practice". I define it differently when it comes to sports, music, yoga, VS math. I actually had a colleague tell me that at a recent STEM workshop the presenter said, "Students will not MATH if there is nothing to MATH about." The idea of math as a verb. Therefore the math is the doing. In which case if it's not noun, can you practice?

    Overall, I struggle with the idea of repeating a procedure over and over to practice completing the procedure accurately. I know that this is how we learned (and I use the word learn loosely) math, but were we doing any sense-making? I would love for someone to do a study of 3 groups of students: a) this group would work on rich tasks and numeracy in only a conceptually focused way; b) this group would do the work of group a PLUS spend time practicing procedures; c) this group would focus mostly on procedures and test prep. It would be interesting to see the results. Would group B do better than group A? And as I said in my post, can games (and zero use of worksheets) get students to the same place in terms of facility with algorithms?

    1. That would be an interesting experiment. This past summer I was on a plane next to a gentleman who attended elementary school in China. His parents sent him to a boarding school in the US for the rest of his schooling. He said that at that time (not sure what it is like now) school was like experiment c. He commented that everyone was good at taking tests, but if you were going to go to a doctor you wanted someone in the US who could problem solve and think critically.
      You bring up some good points too about practice. I like the idea of math as a verb. I'm currently reading Visible Learning for Mathematics and it cites that spaced practice versus mass practice has an effect size of 0.71. Games are something that I would think are easy to throw into the rotation to give that spaced practice.
      And then there is this quote, "Our challenge as a profession is to become more precise in what we do and when we do it. Timing is everything, and the wrong practice at the wrong time undermines efforts. Knowing when and how to help a student move from (sufficient levels of) surface to deep is one of the marks of expert teaching."
      I'll let you know when I have all that figured out ;)

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