Once again, we started a new semester with some reflection on what had gone before. This time I first asked them to choose five skills we’d worked on to rank in order of most understood to least understood. Then I asked them to write about the skills that were actually enjoyable to learn, and ended by having them reflect on their own actions and habits, good and bad.
Editable version: Beginning of Semester Journal
Journal 9 came right before the semester-one final, so I gave students a list of skills they’d been reviewing beside a continuum of fear adjectives and asked them to give vent to their states of mind. The value of the assignment lay in the combination of skill labeling, self-assessment, and end-of-semester therapy. There’s something to be said for letting students feel heard on a personal level in a math class.
Like several other journals I assigned this year, this one started as a fuzzy idea in my mind, then grew to have structure and support after I consulted with my assigned speech-language pathologist. Using the three sentence starters near the top, (N leaves me … because I …; One way I deal with this is …; I would rather N than…) the students first tried filling in blanks aloud in a class discussion. They seemed to enjoy that. Then I moved them to fleshing out their ideas in writing. I don’t think a single student wrote about the same topics they brought up in our discussion, which was interesting. Maybe they figured they’d already gotten those ones of their chests by the time they were writing.
*8/6/14. I listed all the skills as gerunds (solving…, remembering..., etc.), which fit perfectly into the “N leaves me …” sentence starter, but not into the “I would rather N than…” starter. The majority of my students failed to correct the grammar in the second case by changing solving to solve, and so on. In the future, especially when working with students with language learning disabilities, I’ll want to draw the class’ attention to the necessary change.
Editable version:Semester 1 Review Journal Therapy
In September, while taking that Jo Boaler class I’ve mentioned, I finished a section about asking open questions that allow students to use different approaches and learn from each other. That’s a valuable idea, I thought. Unfortunately it’s just not compatible with my upcoming unit. Simplifying expressions is all about getting a single answer and there’s really just one way to do it.
The idea of asking open questions kept turning in my mind, though, until an application was suddenly obvious. I would keep the goal of having students write expressions in simplest form intact, but would add a dimension by having students also write expressions in non-simplest equivalent forms. This would allow students to follow their own thought processes and provide individualized responses, while also developing the concept of equivalence.
I wrote an expression in simplest form on the board, then asked students to write it in equivalent ways using
- Subtraction (the requirement of like terms for addition and subtraction was a worthwhile challenge)
- Negative Exponents*
We used this activity during the simplifying unit, and returned to it during reviews of previous material. Some students understood the meaning of the activity quickly, while at least one didn’t perceive it until just before the spring final: “Oh! We’re just writing things that will give us that first thing.” Bingo. Sometimes comprehension takes time. That’s why I’m in favor of continual review and intelligently designed cumulative finals rather than the take-a-test-and-forget-about-it model.
*I didn’t think to include negative exponents in the list until late in the year.
I organized this year’s trigonometry final according to theme. The sections of the final were:
- Vocabulary [synonyms, examples, descriptions, comparisons]
- Equivalence [simplifying expressions, factoring expressions]
- Functions [linear, quadratic, exponential, trigonometric] and Graphing [linear, quadratic, sinusoidal; domain and range]
- Interpreting Graphs [distance vs. time]
- Solving Quadratic Equations
- Exponents and Logarithms
- Angles and Trigonometric Values [sine and cosine; deriving the values for angles in quadrant one, providing the values for other standard angles]
I find I’m a big supporter of the cumulative final, even and especially for students who struggle with long-term retention. How else will they train their minds to hold on to things? I’m an equal proponent of intelligently designed cumulative finals. My final this year was not a test designed to congratulate those with natural retention and punish those without it. We spent time throughout the year, plus a good chunk there at the end, building student retention of important skills and information, making my final an opportunity for students to take pride in having actually learned things.
Not that my final was a cake walk. The expectations in the test were high to match the value I intended it to have.
Even after my vocab-building epiphany, I was inclined to be overly forgiving of slow vocab development. Fortunately my school has speech-language pathologists on staff to collaborate with teachers, and my SLP was quick to direct me toward more exact standards.
For example, one of our favorite vocab-building activities was Math Catchphrase (later dubbed “Mathphrase”). I laminated little cards with mathematical terms on them (some were review words, others were new for current material). Then we played Catchphrase, but instead of reading the word from the disk you pass around, students grabbed their word from a turned-over stack of cards in the middle of the table. On each corner of the table was a piece of paper with the words “Skip Zone,” where students could put the words they had to skip so we could talk about them at the end of the round. After watching us play it once, my SLP saw that the game needed an obvious external incentive for the students to use mathematical descriptions of the words instead non-mathematical ones. So I spruced up the scoring system to reward mathematical descriptions, which made a big difference. Unlike regular Catchphrase, we would reshuffle the words and play again with the same stack for the sake of repetition and reinforcement.
For her end-of-year review, a student came up with her own vocab game (“Draw, Act, or Describe”) that I’m excited to throw into the mix this coming year to prevent overusing Catchphrase.
For the first time in their high school careers, my students (juniors and seniors) are taking a math final that is cumulative over the entire year. To support them in preparing for this, I took a page from my own senior-year-math-teacher’s playbook and organized a student-led review. Each student signed up for one or two carefully defined topics from the study guide for which they would lead a 10-15 minute review in the final days of class. Each was required to meet with me in advance of their presentation to discuss the details of their plan. So far, those one-on-one meetings have yielded great teaching moments. The presentations themselves have mostly been rough. (I think it’s a healthy eye-opener to the travails faced on the teacher’s end of things.)
Next year I’d like to do this kind of review at the end of first semester as well as at the end of the year. That way they’ll have a chance to learn from their first attempt at teaching and hopefully do better and feel more at ease the second time.
*On a sort of related note, I broke the study guide for the final exam into two parts. There is a list of specific skills that will be tested, but there is also a list of concepts and definitions students will need to know/understand/be able to describe. The student presentations focus on specific skills; I field questions about the concepts/definitions.