# Journal 1: Reflect on Last Year’s Math Class

To get kids writing and self-assessing right off the bat, I gave this journal assignment on the first day of class. My collaborating SLP advised the inclusion of the word bank and sentence starters. Download an editable version here: 1 Day One Journal

# Goals for the Future

At the end of last year I posted a handful of goals I had for improvement. Here is this year’s version.

1. Create clearer expectations for the logarithms unit — or at least make sure the unclarity is purposeful.
2. Improve scientific notation materials.
3. Revise the vocab lists for my word wall.
4. Be careful about continuing instruction while students are still taking notes on prior info.
5. Plan for more “discuss/work with a partner.”
6. Provide examples of written work by previous students — practice critiquing them as class starter activities or as a way to get the writing juices flowing before a journal assignment.

# Philosophy of the Final 2013-14

I organized this year’s trigonometry final according to theme. The sections of the final were:

1. Vocabulary [synonyms, examples, descriptions, comparisons]
2. Equivalence [simplifying expressions, factoring expressions]
3. Functions [linear, quadratic, exponential, trigonometric] and Graphing [linear, quadratic, sinusoidal; domain and range]
4. Interpreting Graphs [distance vs. time]
6. Exponents and Logarithms
7. 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.

# Mathphrase

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.

# A Case for Mathematical Vocab-building

I knew my students had language-related learning disabilities but didn’t know how that would manifest itself in the classroom. Many of these students hear words they don’t understand so often that they don’t like to make a show of it. They let the moment pass, acting like they understand what you’re saying and assuming they’ll figure it out later if it’s important. In time I began to notice signs that my students didn’t understand certain terms, but for a while I effectively ignored their vocabulary needs. My thinking was that with as many gaps as there were in their understanding, conceptual mathematical vocabulary didn’t rank highly on the list. I mean, they knew the most common vocab terms (add, subtract, multiply, divide, distribute [on good days], equation, etc.), so I tried to express new ideas in those terms. I did use more advanced vocabulary in class, but I heard myself saying those terms quickly, self-consciously, like I know this word means nothing to you so let’s just get it over with.

Finally, I was working one-on-one with a student (a high school senior in trigonometry, one of the highest math courses taught at my school) because she didn’t understand a homework problem. We read through the problem, I tried rephrasing it, breaking it into manageable pieces, but made no headway. Then she pointed to two words and said, “I don’t know those words.” She was dyslexic, so maybe it was a symbological thing. Maybe she knew the words but was confused by their written forms, so I said the words out loud: “Radius and variable? You don’t know those words? Do they sound familiar at all, like you’ve heard them before but can’t remember what they mean?” “No. I don’t know those words.” I know for certain she’d heard them before, multiple times, but the fact is that she had no recollection of hearing them, was aware of no meaning associated with them. Radius and variable. This is a student who has taken Algebra 1, Geometry, and Algebra II, and made positive impressions on her teachers. She should know the words radius and variable.

What a wake-up call. Maybe she’d had other teachers who, realizing what a jumble her command of language was, had decided to de-emphasize vocabulary, to get her to do the math without worrying overmuch about the words associated with it. Or maybe they’d given vocabulary the normal amount of emphasis and this was what that level of emphasis resulted in for students like her.

She had taken all the prerequisite courses for trig and had been able to “do the math” so well that teachers had given strong recommendations of her ability. But here she sat without even basic tools for expressing the math she had learned to do. She could neither produce the words on her own, nor recognize them when written and pronounced for her. She could not communicate the ideas she had worked to learn, and without communication, ideas wither.

Boy, was I wrong about the ranking of vocabulary in the hierarchy of important mathematical subjects. Getting these students to “do the math” without enabling them with tools for communicating the math is nearly worthless. After this, cumulative vocab-building ceased to be a dismissable time-drain in my class and became recognized as central to the students’ learning and reviewing. It absolutely takes time away from other pursuits. It is essential.