When I first read Sara VaDerWerf's blog post on how she approaches a task she has created, #1-100, I was excited to give it a whirl with my Algebra 1 8th graders. After much thought, I decided to give Greta Bergman's approach to the same task, but with expressions to represent the numbers 1-100. The task itself on the surface screams mathy and is initially overwhelming to students. The task itself is pretty straightforward. Students pair up and together (without talking) must take turns finding and highlighting the expressions that represents the numbers 1 to 100. The catch here is that they must do it in sequential order (e.g 1, 2, 3, etc...) and they must take turns. So if partner 1 finds 1, partner 2 must then find 2.
I set a timer for 3 minutes as my students tend to have low working memory and processing speed, though in the future I may go longer. I let them find as many as they could. Most groups got to 15-20. We debriefed about their initial approach to the task and I asked what was successful, what was challenging, and how they may approach it differently the next time. Challenges they identified:
Successes:
New approaches:
New round! I reset the timer and they anxiously wanted to try the task again. This time I allowed them to think out loud. Most students improved, but not by much. On average many improved by 3-4 numbers. I asked them why they thought that was. Many identified that they were able to memorize generally where the first few numbers were. I asked how that was and they weren't quite sure. I then asked if the students thought there might be a pattern to how the numbers showed up. Many exclaimed no! this is just torture, then one students started to connect the dots, literally. She began drawing lines from 1 to 2 to 3, etc.. Her partner exclaimed that it looked like a weird connect the dot picture that kind of resembled a box or rectangle. I asked the class if we continued to find more and more numbers what would happen. They all came the the conclusion that most of the time the numbers moved from the upper left, to the upper right, to bottom right, to the bottom left then back around and around. "How might this help us?" I asked "Well, if we divide the paper into those sections we can look in each one to narrow our search!" Student 1 "Yeah! We could break the paper into quadrants!" What a great launch into vocab! "Can we try it again?!" So we did. As I mentioned before, my students tend to have lower processing speeds and working memory scores. Despite having a new approach and strategy many of my students were only able to reach 20-30 numbers. They seemed frustrated and let down. I asked them if they had an unlimited amount of time, do they think they would solve it. They all exclaimed yes. So what happened? Well, when I asked for the challenges again, my students were quick to say that although they had already solved many of the problems and COULD tell me answers when given a bit of extra time. So what did that look like during the activity? At one point, the students were searching for 16. They had zoomed into 3 to the third power. I overheard the student quickly trying to recall her facts. "3x3=9... 9x3 is.... IS IT 16?! Ms. M it's 16, right?" The students knew what three to the third power was but the actual computation of the facts escaped them. Under the pressure of the timed task they could not find strategies to answer the question themselves. "WHERE IS 25, MS. M WHERE IS IT?" Struggling because too much and the urge to finish first overwhelmed their ability to slow down and search some more. I brought these scenarios forward to the class and asked them to tell me what it meant to them. Many giggled as they themselves had the same struggles and agreed that, in the end, they knew what 9x3 was but in the moment suffered a block for how to retrieve it. So what does that look like in math class? How could this approach show it's ugly head day to day when you're doing math? Students overwhelming started sharing their fears of being wrong and weighing that against taking too long in a class. Many admitted to throwing obtuse answers out they knew were wrong in order to buy more time to think about it. Some shared the parallel anxiety of trying to fall asleep but overthinking it and then you get caught in a loop of thinking about how you cannot sleep and it prevents you from sleep. Every single kid in the room agreed that strategies went out the window when they tried to go fast or became innerly competitive about how many they could find. 'How did it feel in the moment?" I asked. "I felt frustrated that I couldn't remember the facts" "I felt lost on the paper, even though I had a smaller section to search" "I felt like I overcomplicated everything because it started to get hard and then I made it harder" "I literally forgot every math thing in my brain" I asked them how we could change our approach to the task and how this might inform how we approach math in the future. Many decided that it would be better to ask for time or take the time before rushing into problems. To continue to use the strategies they know work and when they can't immediately remember a fact, to figure it out/derive it. I told my students about the work my school has done with Jessica Minahan author of The Behavior Code and her assertion that anxiety causes IQs (particularly in the area of PS and WM) to drop significantly. Kids were looking at me like I was inside their head and knew everything about them. It was nice for students to separate out the effects of anxiety of their math performance, themselves as math learners and their ability to perform mathematics, and recognize that there are times where they will struggle. More importantly, we discussed best practices as learners when these moments do happen and how to advocate for themselves in these moments.
5 Comments
11/28/2017 08:07:17 pm
This blog is consisting of some formulas and you know that math is very difficult subject. But this subject is really nice and students should to taking interest in this subject. You give the good information and solve this equation.
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1/22/2018 11:11:58 am
Gather all the knowledge of mathematics from this special zone. You will find the help for the 8th grade and decide to learn with the Greta Bergman's approach. Enjoy the algebra section of accept the mathematical challenges.
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1/30/2018 02:22:10 am
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2/26/2018 07:31:11 am
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2/28/2018 07:12:47 pm
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Jen McAleerMS Math Department Head located in Massachusetts. I mainly work with LBDB students teaching them meaningful mathematical procedures through context. I also look to open students' eyes to the mathematical world around them Archives
January 2017
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