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Movement with Mathematics:  

Adding and Subtracting Positive and Negative Numbers

In the early 1970s, I had just completed my Bachelors Degree in Education and was working as a substitute teacher in Oklahoma. I was very new to teaching.  I had the opportunity to substitute teach junior high school mathematics classes.  It was a big assignment, an entire week.

The topics for the math class that week included adding and subtracting positive and negative numbers.  I had an idea that would help put some physical context to this abstract idea.   I drew a big number line on the floor of the classroom, about the size of hopscotch boxes, but just one long line of boxes.  The line of boxes was big enough that a student could easily stand in a box area.  Toward the middle, I identified a box as zero.  To the right of the number line, I identified the boxes as +1, +2, +3 and so on.   To the left, I identified boxes as -1, -2, -3 and so on.

In order to draw this on the floor we needed to move the student desks out of the pattern of rows of desks, and move them out of the way to clear space for the number line.  Noisy!

A student would stand in a numbered box.  Then, the student would be told to “add positive one” and the student would move one space to the right and see what the answer was after doing that.  Other movements would be called out as well, with the other students joining in the calling out!  “Subtract positive one” and the student would move a space to the left on the number line, and see what that number was. 

Then, we would call out “add such and such negative number.”  This took some thinking, and the student in the number line boxes would move to the left to add the negative numbers.  Students caught on to moving to the right to add a positive number, and moving to the left to subtract a positive number, moving to the left to add a negative number, to the right to subtract a negative number.

The other students seemed to really enjoy calling out to the student in the number line to add or subtract the numbers.  If the number line student moved in the incorrect direction, students would call out things like “No, go the other way to ….” or whatever the appropriate comment would be.  Other students would take turns on the number line, along with continued calling out by the other students.  This took nearly the entire class time.  This was noisy and fun!

This was noisy!  Students were cheering on fellow students and shouting out directions as to which way to move, and so on.  It was very interactive for the student in the number line, and the other students in the room.

It so happened that there were big windows across one wall, next to the hallway.  Others, including other teachers, would walk by, slow down and look at what we were doing, and continue walking.  I’m not sure what the other teachers passing by thought about all this noise and movement.  Students were not quietly sitting at their desks while I lectured about adding and subtracting positive and negative numbers, but they were moving around the room, making noise calling out to fellow students, but they seemed to catch on to those concepts while having some fun, making noise and moving around.

I was informed that I would not be needed to finish the week as the substitute math teacher.

I don’t know how the rest of that week went for the students, learning these somewhat abstract concepts with positive and negative numbers.   But my guess is that it was quieter, without moving desks and drawing a number line on the floor.

That was in the early 1970s.  Pedagogy was different nearly 50 years ago.  These days, we know that movement and noise can indeed be useful learning experiences!

Keep I mind that you don’t need a classroom to do this.  You can get some sidewalk chalk and draw your own number line boxes on your drive way, or your sidewalk, or the basketball court at the neighborhood park, or someplace like that!

Ray Crawford, Ph.D.

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