Is Math Linear?

Some Twitter users suggest that math isn’t always linear.  The curriculum that math teachers teach may resemble something linear, although some curricula (example: Chicago Everyday Mathematics) may engage in some type of spiraling format.   Even if a curriculum spirals, it is still somewhat linear. Most teachers would suggest that background knowledge is needed to learn higher level concepts.  This is especially the case at the elementary level. Generally, teachers are expected to teach specific math concepts at certain grade levels. Most of these concepts are assessed by the state for that particular grade level.

This past week I was teaching a math session with a group of upper elementary students.  We were having a conversation regarding triangles and angles.  We covered the topic that the measures of the interior angles should equal 180 degrees.  One of my students then asked how do we find an unknown side of a triangle.  I thought that was a decent question, so we took out our math books and started looking for clues in the geometry section.  The book led us to a dead end. So … I thought of my own learning and remembered something about the Pythagorean Theorem helping with this question.  As a class, we traveled on the internet and Googled Pythagorean Theorem.

We explored the following pages:

http://en.wikipedia.org/wiki/Pythagorean_theorem

http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.html

http://www.pbs.org/wgbh/nova/proof/puzzle/use.html

http://www.teachscienceandmath.com/2010/03/03/pythagorean-theorem-real-world-application/

After digging up a few resources, we finally found a  group of students that created a short video on the Pythagorean Theorem.

After reviewing the video above we decided to practice a few problems using our new knowledge.  The students seemed to enjoy and were motivated to continue on this Pythagorean adventure.   I asked the students to research the Pythagorean Theorem that evening and practice a few practical problems. I also asked them to bring in any practical problems relating to the theorem to school the next day.  The next day the students came in with papers of practiced problems and examples. Overall, I felt as though this was a great opportunity to expose the students to a higher level skill, that isn’t necessarily linear, but may benefit them in preparing for middle school.

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