September, 2016

I looked over and saw J with her head on the table, worksheets pushed to the side. I walked over. “What’s happening here?” I asked, slightly alarmed to see the girl who frequently proclaimed her love for math looking despondent for the first time in my fourth period numeracy class. “This is stupid,” she muttered, gesturing to the worksheet that ten minutes ago she excitedly chose from the pile. As I asked J what exactly was stupid about the worksheet, she pointed to a column of half-solved problems that I could already see were mostly incorrect. After a bit more prying, she admitted that she didn’t know how to subtract negative numbers. “I was absent last year when we learned that,” she quietly told me.

When I first met J, I would not have guessed that she had the ability to quickly turn into the girl I just described. For the first two weeks of numeracy class, she attacked each math problem that I threw her way, solving it remarkably quickly and doing impressive mental math. For example, when I asked the students to find 70% of 85, she noted that 10% of 85 is 8.5, so doing 8.5 x 7 would give her the answer. I had her explain her method to the rest of the class, and I ended up basing the next day’s starter problem off of her method.

Then came the incident with the negative number worksheet. After she told me she didn’t know how to do the subtraction, I re-explained the rules we had just taken notes on as a class, drew out a number line, and worked through a few examples with her. When I collected her paper at the end of the class, I saw that she had only done one more problem after I left her.

I didn’t think too much of this, for I understood that it takes time to learn a new rule. However, during the rest of the week of my formal observations of J, I saw three more instances of her deeming a challenging assignment “stupid,” and she even crumpled up her paper and gave up completely twice. Each of those instances differed from the first interaction I described above in one important way. In the first scenario, she legitimately did not know how to do the required mathematical operation. In the other three scenarios I observed, however, she was so close to getting the answer and was using all the right operations and tools. She just needed to give herself a little more time to figure out the final step, but she lost patience.

When I interviewed J, she told me that she’s strongest at math because it “comes easiest” to her. Although she said that she likes to write, she doesn’t think she’s good at English because she struggles with spelling, grammar, and punctuation. She emphasized that she especially dislikes essays because her teacher usually makes her rewrite them “because [she doesn’t] word stuff correctly.” With regard to her participation in class, she said, “I mostly only participate in subjects I know my answers are right…which is mostly just math and science.”

From J’s statements, it seemed that she feared being wrong. From my observations, it seemed that when she thought she was wrong, she shut down and often gave up, perhaps as a coping mechanism. By giving up, not solving the problem became a choice, rather than a reflection of her ability. In addition, her responses revealed that she found math enjoyable because of the ease with which she could do it, not because of the actual content. Hence, when the content got challenging, she stopped enjoying it.

J’s lack of perseverance became complicated by the fact that she often needed to be challenged in math more than the other students. She frequently finished assignments faster and requested an extension, yet when she thought the extension was too hard, she gave up. It appeared that she wanted to do more math, but only if it was easy for her. Mr. Strogoff, her seventh grade numeracy teacher and her current math teacher, recalled that last year he constantly had to have tons of worksheets at the ready to keep her busy while the rest of the class finished the normal assignment. She generally worked on those worksheets alongside X, another high-achieving student, and he didn’t hear much complaint or see her give up often. J understood where her math abilities placed her compared to the rest of the class, and consequently, liked to work alone. “I just like to do problems and worksheets individually,” she said, “because I work at a faster pace than everyone else in the class.”

J’s situation made me think about the debate around tracking in schools. Claremont generally aligns with Oakes’ belief that tracking is detrimental to all students, and almost all classes at Claremont are untracked. This year, however, the eighth grade teachers decided to put the high-achieving math students in one numeracy class (which I teach) so that they could be adequately challenged. J, along with all the other students in the class, was unaware of the tracking. I was still trying to decide for myself how I felt about it. As for J, she was usually much more engaged in my numeracy class than she was in Mr. Strogoff’s math class. This was probably due to the fact that she finished Mr. Strogoff’s assignments faster than anyone else, and since he was not always prepared with extensions, she spent a few classes bored with her head down, waiting for the class to catch up. Because my numeracy class was smaller and filled with students closer to J’s abilities, she typically did not finish as far ahead of everyone else. In this particular case, I would say that J benefitted from tracking.

In both of her math classes, I noticed that J was hesitant to show her work and explain her thinking; all she cared about was the answer. This reflected her negative attitude toward challenging problems. She didn’t care that she had done a lot of great thinking on them; she just cared that she hadn’t gotten the right answer. One of my goals for the rest of the year was to make J realize that how she got to the answer was just as important, and sometimes even more important, than getting the right answer. This goal actually extended to my entire class. To achieve it, I planned to repeatedly ask my students to explain their thinking in words and give them positive reinforcement when they did. I also emphasized that good mathematicians were able to effectively communicate how they reached their solution, and since they were young mathematicians, they must practice doing that as well.

The problem of building perseverance seemed trickier to address. This went beyond math class; it entailed entirely changing how she confronted challenges. I wanted the class to understand that just because something was hard for you, it didn’t mean that you were bad at it. I actually had an interesting conversation with my roommate about that as I was seeing this in my classroom. My roommate worked for the Worcester Public Schools as a data analyst and had been doing a lot with statistics. However, she deeply believed that she was bad at math. When I asked her why she thought she was bad at math, she responded, “Because it’s not easy for me. It takes me a long time.” This seemed similar to the misconception that J had. How could I get her to see that when something stopped being easy, it in no way meant that she was bad at it? For a starter later that week, I told my students what my roommate said and asked them what they thought. They ended up writing her notes, and without my prompting, included encouraging messages telling her that just because math was hard for her didn’t mean she was bad at it. It couldn’t have worked out any more perfectly! To address J’s needs more specifically, I vowed to continue to encourage her to not give up, and to talk to other teachers to see how they have handled similar situations in the past.

January, 2017

 On the third day of solving equations unit in my numeracy class, J and a few other students finished all the assigned work while the rest of the class still needed another day to finish, so I had them work on an extension problem. I haven’t been doing a great job of consistently having engaging and time-consuming extensions ready, but I had taken the time to plan different extensions throughout this unit. J and her group chose to work on a problem that entailed working backwards to find the number of coconuts originally on an island. I was really impressed by the students’ perseverance on this problem – especially J’s, for she is the most apt to give up. Some students were trying to draw out the problem or write an equation, and J decided to use blocks to represent the coconuts. This was no small task, for there ended up being 79 coconuts to account for, but she stuck with it! The problem took J and the other students a full class period to solve, and they didn’t give up until they figured it out. This left me wondering how I can replicate that “good struggle” experience for her in future lessons with the same level of buy-in.

March, 2017

As part of our exponent unit in numeracy, J discovered the zero power rule with a partner and taught it by herself to half of the class. After the lesson, she gave each of her “students” a worksheet to complete using the rule she had just taught them. As she passed out her worksheets, she sternly warned, “If you don’t show all of your work, you won’t get any credit.” Upon hearing this, I laughed to myself. Since the beginning of the year, J had argued with me whenever I asked her to show her work. Used to doing math in her head and doing it correctly, she often acted annoyed and gave up when she wasn’t getting the right answers to problems I posed to the class. In February as she encountered complex solving equations problems and I demanded that everyone show their work step-by-step when solving them, she started to see and accept how much more successful she could be once she did that. When she made a mistake, I watched her look back at her work and quickly locate the error, instead of declaring that she was giving up or that the problem was stupid. I never thought that I would hear her tell her classmates to show all their work. Even if she said it to mock me, at least that meant that she had internalized it enough to do that!