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I've been teaching high school math for over 20 years. I write about my experiences here and also share activities that I have done with my classes that have been successful (and some that have been not so successful).
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How I Get My Students to Work at the Board



I call it Board Problems.

In 2017 I went to a teaching conference: Twitter Math Camp (TMC). (They haven't had one since 2018, and I don't know if they will have one again, but it was an awesome conference.)

One of the sessions I went to was by Jennifer Fairbanks (http://8ismyluckynumber.blogspot.com/ and on Twitter @hhsmath) and Katy Campbell (on Twitter @kd5campbell). It was about Vertical Non-Permanent Surfaces or #VNPS.

I had never heard of #VNPS before this session, but in the session description, there must have been some talk of getting your students out of their seats and working on the board because I was excited about going to the session.

Let's continue the conversation. Join me in my Facebook group.


At the time I had been trying to find a way to get my students to work at the board. I know other teachers would ask students to work homework problems on the board, but I always felt that would take too long and I would be anxious to get the lesson started.

Vertical Non-Permanent Surfaces #VNPS

During this session, Jennifer and Kathy explained that a man named Peter Liljedahl (http://www.peterliljedahl.com/) had done a study where he timed how quickly students got to work when they were given a set of problems. There were 5 different scenarios: 
  1. vertical non-permanent surfaces (whiteboard on a wall)
  2. vertical permanent surfaces (flipchart paper hanging on the wall)
  3. horizontal non-permanent surfaces (a whiteboard on a table)
  4. horizontal permanent surfaces (flipchart paper on desk or table)
  5. horizontal permanent surfaces (in students' notebooks) 

What he found is that students got to work the quickest when they were working on vertical non-permanent surfaces #VNPS. It seems that if students can quickly erase what they've written (non-permanent) then they are more likely to start writing right away, and if students can easily see what other groups are doing (vertical) that also contributes to them starting quicker.

When I explain this to my students they always say, "isn't looking at other groups' work cheating?" to which I say, "it's not cheating, it's collaboration." To which they say, "can we collaborate on the test?!"

If you want to read his published study, go here: Building Thinking Classrooms: Conditions for Problem Solving and also check out his article on Edutopia: Building a Thinking Classroom in Math

Honors PreCalculus students verifying trig identities


Visibly Random Groups #VRG

Also in Peter Liljedahl's study, he discovered that putting students in groups should be done randomly and in full view of the students. In other words, do not pick the groups ahead of time; use a deck of cards or a website to randomly group them. Part of the purpose of this is that students will "buy into" the group and be more willing to contribute if they can see how the group was formed rather than speculate why the teacher formed the groups the way he or she did. Read more here.


How I use #VNPS and #VRG

Here's what I do:
  • I call it Board Problems because #VNPS doesn't roll off the tongue as well.
  • I prefer groups of 3 but will do a group of 2 if I don't have enough students. At the beginning of the year, I put the student names in the Random Name Picker template that I got from flippity.net
  • I only allow students to have 1 marker per group. Students have to rotate who is doing the writing. I sometimes will stop the groups in the middle of a problem and ask another group member to take the marker and finish.
  • I give each group a sheet of paper with 5 to 10 problems on it (or however many problems will take them 15 to 20 minutes)
  • Groups work at their own pace. Generally, every group starts with the first problem, but that is not required.

Calculus students doing Board Problems


Here's how it usually goes:

  • The slowest groups don't finish the problems before we run out of time, but that's not detrimental because I don't take a grade for it.
  • Sometimes I will stop the class after a few minutes and ask the youngest person in each group (or the person whose birthday is coming up next) to move to the group to the left (I got this idea from Jennifer and Kathy). 
      • But what I have found is that since the groups work at a different pace, a student might end up in a group doing a problem that he has already completed. This is usually very discouraging to that student because they feel as if they are behind and their motivation drops.
  • I have more time to do Board Problems in my on-level calculus class because we move very slowly through the curriculum. 
      • When I graded homework less often, doing Board Problems was an ideal solution for getting the students to actually practice the skills - they rarely did their homework. But for the past couple of years, I check homework every day and I like to give them time in class to work on it so they don't have to take it home. So we don't do Board Problems as often as I would prefer.
  • In my Honors PreCalculus class, I only have time to do it 2 or 3 times per semester; the students usually prefer to get started on their homework if there is any extra time at the end of class.

You can see on the left side of the photo that now one wall is covered in glass.
The glass was added in Spring 2018.
If I needed even more space, the students could write on the windows.

Read more about my classroom with all of the writable surfaces.

Have you done something similar in your classroom? Let's continue the conversation. Join me in my Facebook group.