Yesterday we spent time making sense of the ideas of Clotheslines Math, and we were able to get a few quick reps in. Today, we dove straight in, students were broken up into groups of four, each person was assigned a job, and the students were tasked with placing the trig functions in their appropriate sequence on their number line. Students were given 15 minutes to make this magic happen
I had one group finish early, which was perfect, they became the “experts” and I shipped them out across the “country” to troubleshoot groups where the sequence was stalled. Once the 15 minutes were up, groups verified their sequences with others, and with their “experts” were given another 2 minutes to confirm their sequence. Each group would use their device to take a picture of their successfully completed sequence, and then we tried this process whole class, randomly chosen people were given a tent, two students were holding our much longer class sized chord, and we tried to place the tents in a proper sequence.
So a couple of things that I loved about this process: 1) Students understanding of how to construct a viable number line is sorely lacking from establishing benchmarks to proper scale and this is a powerful way to build it; 2) The multivalued aspect of the trig functions were highlighted in context, so some students made this connection; 3) The periodicity of the trig functions were brought to light when we connected all of our group together, and what did they notice and wonder.
We were able to get to try this in 8th grade today, as well, but with different algebraic based tents. Students in 8th grade were much more accepting and understanding of the process (tents were integers) but struggled with the tents that were given as variables. Students had no problem placing m, 2m, and m/3 in a variety of orders. So we will be addressing this misconception in the next period. I am thinking of having students draw a distance, then draw twice that distance, and a third of that distance. Then we place the tents m, 2m, and m/3 on their number line and see where the conversation goes.
On another note, today was the last day of a content specific course in mathematics for new teachers and I wanted to highlight some of these pieces in our last class together. So we started with a warm up on the sheet placing various terms in order. Our random groups were given an envelope with 3 linear equations, highlighting various slopes and y-intercepts and three fractions and asked to place in the correct sequence.
The teachers seemed truly engaged in the process, and the attending to precision (MP6) evident everywhere. After teachers shared their thinking and we compared, we talked about how this might be used in their content areas. I do not know if I facilitated bringing to light the flexibility of this strategy, but I think the teachers found some value in it as another tool in the trade. The evening was our last class together, as half of them will be graduating with their preliminary credential in a few weeks, and half will be doing so for another year but will be graduating to summer soon, so our theme of the night was graduation.
As per our traditional sequence, we like to have a group photo to commemorate the evening by, and this one was no different. In the spirit of the class, I showcased a family fail photo, to prompt our discussion and as a reminder for myself, and we tried to take an awkward family photo together, and I think we nailed that result.
It was an epic end to a great sequence of classes and I hope the new teachers were able to get as much from this as they gave my partner in this class. I hate to end this amazing post on a down note, but I felt the night went well, we did spend too much time on the “speed dating” portion discussing our use of a strategy from Teaching Reading in Mathematics (TRIM) with a problem from Fostering Algebraic Thinking (FAT) book. We didn’t debrief their assignment as well as I would have liked, and I don’t think I facilitated the connects between all the classes well. In the sequence of the night, time moved too quickly and trying to do too many things got the best of me. The part that really gets me is that it felt like we had put our hearts into this class, each night had a theme, we tried to make every moment purposeful, connected, meaningful and engaging, the teachers seemed to indicate they were picking up what we were putting down, but their feedback indicates more to the contrary than I would have expected. This is to say that no matter how well you dress something up if the content isn’t good, people will notice and will not connect to it. I am going to have to do a lot of reflection on this class and use these failures as opportunities to grow, learn, and question.