Monday, December 20, 2021

The Magic of Students Doing Challenging Questions in Groups of Three on Vertical Surfaces in the Math Classroom

I read Peter Liljedahl's book Building Thinking Classrooms in Mathematics  this past summer and it has been transformational in my teaching. Getting all my students to go to a vertical surface in groups of three has been MAGICAL!!!!  I absolutely love the idea of students thinking more on their own than myself blabbing on about the material.  Brilliant!   It is a must read that is appropriately called the #thinkingclassroom. Let me give you major things that I changed in my classroom this year.  

1.  Select RANDOM Groups of Three 

The first thing is the randomness of your groups.  This is important because groups get old fast.  If a student has the opportunity to work in a new group of students they are more apt to participate and give and take instruction with their peers.  I change groups every time I have students go to the vertical surfaces which is about 3 times a week.  I hand a deck of cards to a student and they are in charge of shuffling the cards and then passing them out. See the video below.  Now before you hand the student the deck of cards you have to make sure there are the right amount of cards for the students.  I actually have 5 sets of cards, one for each class.  Then I don't have to mess with it too much because of absences.   I then have different locations that the Aces would go to, and the two's would go to and so on.  (see the image on point 2)   The deck of cards help the students know that it is not you that is making the groups.  After they get into the groups with all their stuff, this is the seat and location for the rest of the day.    Also, groups of three is perfect.  Two is too little and four is too much, three is just perfect.

2.  Have all Groups go to a Vertical Surface

This is tricky because you will need up to 8-10 spots in the room where students can do problems.  I use the wall which have white board paint on it.  I also use my windows which create a perfect surface to write on.   Sometimes teachers buy a 4 foot by 8 foot white board panel at Home Depot and cut it up and put it on the walls.  There is such a thing as plastic whiteboard sheets that cling or stick to the wall that work as well.  Since the students are switching groups locations so much I put a small group location map on the wall for students to navigate every time we change groups.    

3.  Give Challenging Problems.

In previous years, I usually would build up to problems that were more difficult with students.  However, I ended up not doing the most difficult ones because of time.  So start with the challenging ones first and you set a standard right away with vertical surface problems that will be difficult but reachable.  If you start with a challenging question, the process usually flushes out other easier concepts that are needed in the lesson.  Also, it is good for students to be stuck and figure out how to proceed.  This is what Liljedahl calls PROBLEM SOLVING!  What do you do when you don't know what to do.  So many times we take the challenging part out of their work and we as teachers do it for them.  Let them be challenged and think on their own.  Lastly, try to give open ended questions.  For instance, create an equation of a line that has an x-intercept of (0,5) and only passes through quadrants I, II, and IV instead of a question like find the equation of a line through these certain two points.

4.  How to Deal with Questions?

I think you better read Peter Liljedahl's book for this question.  However, the one thing I have learned so far this year is that I try to redirect questions back at their teammates (their other group members).    This gives power back to the group.  I have found that I know when students are just looking for confirmation or when they really need to know how to proceed.  When a student asks me if something is correct, I don't directly answer that.  I tell them to check with their teammates or to look at what other groups around them have done.  This is a good way to get dialog happening because many times other groups will have a variety of answers so students have to decide how to proceed.  Liljedahl has a list of excellent replies to questions.  See below.  I refresh myself with this list all the time.  My favorite is how did you do that? 

5.  Only one Whiteboard Marker per Group and Change 'Writers'

Only allow one pen per group.  This forces collaboration.  Also, make sure you call out for students to change who is writing the problem down on the board.  Sometimes groups change on their own, but more often I've found that you need to call out the change.  Sometimes I have a timer on my phone and it rings every 1-2 minutes for a change of writer.   This time amount always depends on the problem.  The non-writers are encouraged to bring their spiral (blank paper) up to the vertical surface to write notes with.   

Benefits to Vertical Problems
  • Math talk is huge...even 1st period.
  • Movement in the classroom.  
  • Students are willing to take math risks with new group members
  • Mistakes are easily changed via dry erase.
  • Students love to write on the wall
  • Class collaboration because groups can all see how all the other groups are doing the problem.
  • Did I say math talk?  Huge!!
  • Students like to take pictures of their work for future reference

Challenges to Vertical Problems
  • Some students are not collaborative and thus do not help their teammates. 
  • Off task groups 
  • Students don't always write down the problems/solution.  Thus they don't have notes from their work on the vertical surface.

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