2017-05-24 – Day 14 – 360 Math Collaboration Finals Review

State testing finished two weeks ago, warming weather, and multiple field trips all indicate the sun is setting on the 2016-17 school year. The looming giant of finals is the final hurdle many of our students are left with in ending this school year, and here we sit investigating this idea.

Getting students the opportunity to do the work, we covered examples yesterday, and today we are doing a combination of 360 Math (thanks, @edcamposjr) for the inspiration there and karaoke presentations when we are finished.

In Math 3, students used Flippity (thanks again to Ed for that tip) to form our groups. Each group was given 90 seconds to capture the 7 problems on paper 360-style around the room, students used mobile phones to take pictures of the problems, and then shared the with their group. Students broke up the problems, some students would solve 2 problems, others would solve 1 problem, in the 15 minutes.

When time was finished, random selection for each group assigned the problem they would build the solution to the poster. Their goal is to write a solution clear enough that anyone could present it, which is the next phase with the presentation karaoke.

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The Math 3 students hit some of the road blocks I was anticipating, but this process uncovered a couple more as well. The students did not get to the point they were going to present, we will capture those tomorrow. Students did see me solve all 7 problems in 3 minutes, not emphasizing the quickness of solving, but the efficiency of ease of these problems the concept of multiple iterations of inverse operations. I do feel I needed to give them more opportunities, and I should have started with this approach on Monday, then used it to set the stage for any clarifications or additional input the students would need from me, not the other way around.

In Math 8, we followed a similar format as in Math 3, the students opened up with a Quizizz review, getting a single shot of the year. Next, we chose 7 problems posted on the walls, viz a vie 360 Math. The 7 problems were taken from review problems previously covered, with small alterations, each team was assigned a problem and given 10 minutes to solve. Their goal is to write a solution clear enough that another group could present their solution viz a vie Presentation Karaoke.

Getting students to present would go smoother is more reps, this is our first time trying this Presentation Karaoke. While herding cats is challenging, it is worth the effort in that students are really engaging in their learning.

One of my students stayed after to tell me that another student explained what “simplifying” means in a way that he now understands it. When students stay after to share about their learning you know something went well.

2017-05-17 – Day 7 – Clothesline Math & Goodbyes

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

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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.

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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.

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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.

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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.

2017-05-16 – Day 6 – Clothesline Math

Over the weekend I created my first tent series for Clothesline Math. In my Integrated Math 3, I want students to explore the input/output of trig functions and their values from the unit circle. Ideally, students would be interacting to make sense of the relationship between the input/output of trig functions and the connections to the various values of the unit circle.

(Dramatic music cue) The answer seemed obvious once I understood how I foresaw students working with the content: Clothesline Math.

I built my first series of tents for the clothesline math, I went to the store and bought eight $1 jump ropes for my groups to use as a clothesline, and created the tents. On Monday, we tried it…

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Dreaming of all the ways to utilize this idea, we had so much fun. The HS students were a little hesitant at first, but once they got into it, they were enjoying it. Our next step is to take their individual groups and make it whole class, this is where the learning will make the most impact, I am anticipating. I also am waiting for the moment when students realize there are two sets of infinite answers (periodic functions) for each of the cards, with a few exceptions like the cosine and sine obtain their max and min values at only one set of infinite answers.

All in all, I am so in love with clothesline math and will be utilizing it in a much more poignant way next year. If interested in using this same structure, or if you want to talk about ideas, I have a series of resources from many of my math heroes like Matt Vaudrey and Andrew Stadel.

2017-05-12 – Day 2 – Guest Presenter Steve Wyborney!!

Our special guest today, Mr. Steve Wyborney, delivered a fun and interactive learning experience for my Integrated Math 3 course. The students got to experience a variety of wonderful questioning strategies, they were enabled to challenge their teacher and integrated deep mathematical thinking into the whole process.

Mr. Wyborney’s incredible sense of creating engaging and powerful learning experiences was on display today, challenging the students to think differently and to understand things in a variety of ways.

The learning was deep, the conversations were rich, and the time flew by, a perfect ending to a rather long week. On that note, I am also learning to use SnapChap to capture the learning, which is why I’m continuing this video sequence. I like that every 10 seconds you have to finish your thoughts, forcing you to be more concise and embeds the idea of practice perfect. I also like the idea of the silly filters, as it helps me get past the weirdness I feel when taping myself. Combining this with my desire to blog more, I’ve created a snowball of learning experiences for myself, and with Day 2 in the bag, I’m excited that I just might make it.

Sequencing Transference

I am curious if there is a way for transference of skills to be acquired over time, especially for a difficult solution technique.

To satisfy my curiosity, I am trying the following scenario. In August I gave my Integrated Math 3 students a task, working with a partner, they had to sequence out the strips of paper hidden in an envelope. I made enough for each to student to work with a partner, one student would move only the words and one student would only move the equations.

The students had an entire period to work, and asked when they finished to take a picture with their device and email it to me. This first round easily took the entire period, as students became familiar with the task and had to make sense of the problem. As students worked, I circulated and asked guiding questions, but offered no direct support. A little over half way through the period, I had two groups that were close an accurate sequencing of the problem, so I prompted that students should walk around and look at what other groups were doing, develop a dialogue, and see if some fresh ideas developed.

By periods end, almost every group had some form of an accurate sequence, and I was quite impressed by their perseverance in this task. Thinking of the SMPs, we had hit three of them hard (SMP 1, SMP 3, and SMP 7), and I really think the students enjoyed it, even if “their brains hurt.”

A month later, I gave them the same envelopes, this time as a warm up problem. After 5 minutes, most groups were done, many of them could recall the flow of the solution, with minor errors; however, what stood out to me was how students were smiling once they felt they were able to do this task again, with much less effort.

A few weeks later, the students come to class they saw the familiar envelopes, they grabbed them and started sequencing the steps without being prompted. Less than three minutes later, the entire class was finished, so I took pictures of each group’s result, and projected them. As a class, I asked the students if they were similar or different than their own, this lead to a great discussion about many of the pieces that were in place, and why certain strips went where.

Following our discussion, I posted two similar problems to the one they had been sequencing to see if their understanding would transfer. The students tended to fall apart in attempting to solve these problems, their understanding of doing and undoing, i.e. the use of inverse operations and a mushy understanding of the problems became apparent, though they were clearly on the path to understanding the sequencing problem.

One thing that shocks me is that there is little connection from the sequencing of the problem to the examples shown, even after guided questioning. Meaning I’m not asking the right questions to uncover their thinking to make these connections, or I didn’t set the stage well enough for them yet, or I jumped ahead of myself and need to revisit at a future time. In any case, my curiosity is not satisfied, I do not know if students are able to transfer their understanding of one way of looking at a problem to another way, or if this task is too cognitively demanding to test this process with. In any case, there is evidence of learning in many other areas, and the collaboration over this task has been a pleasure to observe.

I am curious about your experiences with sequencing, transference, and promoting perseverance in with your students.