The moment I noticed this week was during a math lesson. We were doing lesson 2.2 in Everyday Math about using numbers in everyday life. Students were completing a worksheet where they wrote their first, second (middle), and last name, how old they were, how many candles were on their birthday cake last year, their phone number, as well as emergency, school, and library phone number. On another worksheet students were asked to write the numbers 7 and 8 and then to draw 7 "things" in order to represent that they know how much "7" or "8" means. There were several students who completed this task fairly quickly because this worksheet was not challenging enough or asking too difficult questions. Students write their name everyday on worksheets, they know how old they are, they can get their number from home, and then they may take some more time to write numbers but not a long struggle. When students were completed with this task they told Ms. Hall which she instructed them to just color their objects they drew and the cake and candles when students were asked how old they were. Many students were coloring for a long time while waiting for the rest of the class to finish. Since they kind of got bored with coloring I noticed that they started talking more and losing focus on the math work.
I think what is most important in this situation is the fact that this activity was not challenging enough for more than half the class and not really a higher level task. Students were told to color instead of trying to work on some challenging math homework that could have advanced their thinking and maybe they would not have gotten distracted. The challenging task though would be to give students a higher level task or something that encourages mathematical thinking but is doable so that students don't feel it's too challenging to complete. It frustrated me a bit to hear that students were asked to just color their worksheets and not do something that was mathematically engaging. Several students could have extended their learning with another activity that connected to the use of numbers in everyday situations. Students could have been asked to write where else they see numbers in everyday life and how they use numbers in everyday life. This way students demonstrate their understanding and it can be used as a pre-assessment to what they understand. I think what happened was that my teacher didn't anticipate students to completing the task so early so she just thought why not have them color. This is not usual for my teacher, she's normally very on her toes and thinks of activities students can do that are challenging or at least extending the lesson. Witnessing this situation helped me to remember that I need to always be anticipating students completing tasks early and needing to be challenging them or thinking of ways to extend the lesson further to encourage mathematical thinking.
Another important principle that I feel this demonstrates is the importance of backwards design: starting with the mathematical goal / objective and deriving the learning activity from there. What was the mathematical goal of coloring? Perhaps the intention is that it would keep students engaged, but even this does not speak to a meaningful mathematical goal. Of course, coloring can still be a part of this mathematical task, but it all needs to be framed with the goal of the instruction in mind, first and foremost.
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