This week was the week of Professional Developments (PDs) with my creation and delivery of Interactive Math That’s Meaningful (Horrible Title, I know) and 3 Powerful Math Routines. Each one has some amazing pieces to it that I am very proud of, and both have some areas I do not feel meet my goals. Time and reps will let me know if my feelings are accurate, and it will reveal where other holes are and where great stuff is as well. It’s pretty hectic this week, so this is just short note to remind me to breath.
The end of the school year is rapidly approaching which brings a mixed bag of emotions to me every year. On the one hand, I am excited about sleeping in, long summer days, and more leisure time with family. On the other hand, I will miss the relationships, connections, and goofy things my students seem to do. My one consolidation this time of year is being able to experiment with instructional methods.
The use of an actual clothesline to model a number line is one idea I have had on my mind all year but just started diving into this past week. I started with these tents from the Clothesline Math.
I tried the same format and same numbers in both my HS and MS classes, the contrasts were interesting, as this process clearly indicated where gaps in understanding and evaluating numbers came in. I was not surprised by the placement of the term -3^2 term, and this provided a natural landscape to discuss this misconception.
In my trial run of Clothesline Math, I fell in love with it immediately, the learning and conversations that it promotes, the physical explanation of numbers relative to one another, and the kinesthetic components are all so impactful in the learning experience. I am looking forward as I build my very first trigonometry set, I have finished the first round of tents, and will work on more at a later time. I also see how logarithms could be used with this, and I want to use this with my MS students for solving linear equations, a la Mr. Matt “Yes, it is. And now you know why.” Vaudrey.
The other new endeavor, now in its fifth week is the creation and manifestation of a co-created Twitter chat. I never thought I would actually start one, but with the persistence of my right coast math dancing partner, Shane Ferguson (@MrFergusonMJHS), we are moving along quite strongly as we grow our weekly chat. The idea we wanted for the chat had to be centered around mathematics, but we didn’t want to cover what other chats already hit upon, when the idea struck we should talk about the many, many misconceptions there are in the world of education, especially related to mathematics education. I also am a huge fan of having the word ‘math’ show up in the title, a la @mathkaveli, which is how we ended up with #MathConceptions. Our 30-minute weekly chat is every Monday at 6:30 PM PST, and it’s a great group of people and powerful discussions. We also have a growing weekly chat in our Voxer group for #MathConceptions.
Although I have attempted to teach this topic in many ways at a variety of levels, I always find it interesting to see how learners attempt to grapple with the concept and understanding. Learners who struggle with understanding linear graphs typically have an even more difficult, and when you add-on this is the first time the learners have literally ever met the material I am at the source of the stream that I see in higher education. The topic is linear inequalities, the grade level is sixth grade, and I am attempting to teach these young minds this topic in 50 minutes, or less, and it is their first time (Does anyone else hear the Mission Impossible theme song here?) Well, I accepted the mission, I would attempt this process, twice actually, as I would teach this lesson back-to-back in two different group of 6th grade learners. As you are aware, I am a huge fan of 3 Act math lessons, with one of my favorite resources coming from La Cucina Matematica, where they shared Estimation 180 and found this amazing 3 Act lesson. As with any lesson, I have to adapt it a little to make it match my teaching style, and went in feeling ready to give it a tackle. In my career, this is the first time I have attempted to teach this lesson with a 3 Act component, and it is the first time I felt compelled to not give any instruction, but let the students conversation and discovery lead the way. One of the big pieces I was looking forward to was having students see their responses projected in front of them with Desmos, using their group responses to guide the inquiry. One note on this topic, I would prefer to have assigned each student their own opportunity to play on Desmos and then share out whole class, but I would need some additional front loading days to teach students how to interact and use Desmos, which I am unfortunate in that I didn’t have that opportunity, so we did that part whole class. My lesson followed this the PPT I made here or you can see below, which went off overall pretty well.
Immediately, I must say that the kids in the first class thought that Woody had cussed in the first act, so the second time I gave the lesson I had to front load that the bleep was covering up the answer to a question we were looking to answer. Another thing I picked up on right away, is that students struggled with figuring out what the humor was, they needed the mathematical background to understand what the reason for the humor was, which is an avenue to pursue with them later. The way that the various groups interacted, the way in which the conversations went within each group depended a lot on what they noticed from the clip. I was surprised by the number of kids who actually knew the show, a big thanks to reruns and older parents, as those students were more interested in the problem since they had more background knowledge of the show. The beautiful thing about this lesson, is that the discussion and interactions gave the students the opportunity to discuss and find the break even point, with about half the students understanding why the deal was better or worse. Quantitatively speaking more than 90% of the learners were able to understand that $25 per week was the break even point, and they were able to understand that certain values like $30 a week was greater than while $20 a week was less than the value of the original deal. We started to talk about how $24.99 per week was still less than the original $100 a month raise, while $25.01 per week was greater than the original $100 a month raise; however, there were only about six kids per class that were able to articulate this point and why in their exit slips. The next steps in this lesson would be to flush out the idea mentioned above, that any value greater that then $25 per week is a better deal (more money) for Woody, while any deal of $24.99 per week or less is a worse deal (less money) for Woody. The discreteness of money helps make this more concrete which was one reason I thought it might be very valuable for these learners, not to mention money is something they are familiar with. Overall, I would say the lesson went well and promoted a lot of great discussions among the students, it removed any prior need for mathematical knowledge so all kids had an entry-level assessment into the game, and the students discussing the break even point was a huge win. The use of Desmos really helped visualize it for students, and will give them some place to start building on. I feel confident this was by far the best attempt at securing an understanding of this difficult concept and I imagine that with follow-up and repeated visits this topic will be mastered by most of these young learners.