# Project/Journal 11

This was the year’s largest and most technical writing assignment. I required students to submit drafts which I edited and returned to them so they would have the chance to make their writing more precise. The project consumed a large chunk of our time, but the process of explaining their methods and results in writing, getting a draft edited, then trying to make their language more precise was a turning point for my students’ mathematical communication.

All but one of my students were seniors and were pretty well invested in learning about student loans. On Day One I introduced subsidized vs. unsubsidized student loans. (The project presents case studies using unsubsidized student loans.) I also addressed how student loan interest is actually calculated* and explained that A=Pe^(rt) would give good enough approximations. In the mish-mash curriculum I worked from, A=Pe^(rt) is used as an application for the natural log, so I wanted to give students experience using that formula even though the unit was not connected to other types of interest growth.

The project gives 3 cases:

1. You take out an unsubsidized student loan of \$3000 your first semester of college and it grows while you attend school for 5 years.
2. You take out that same loan but you make an early payment of \$500 two years into college.
3. You take out the same loan but a semester later.

*09/10/14: An improvement might be to ask students to give estimates or judgments on the three options before any calculation.

The first day’s assignment was to calculate what the debt would grow to by graduation in each case and estimate the cost of repayment. I left students pretty much to their own devices to figure it out, which frustrated them to no end.

On Day Two we compared their solutions, went over the correct solutions, and they worked on the first two paragraphs of the write-up, turning in drafts the next day. Then they worked on the edits and writing the next paragraph, turned in a new draft, etc. (See what I mean? Large chunk of our time.)

Although self-conscious about it, I decided to provide a scripted template for the write-up for two reasons: to get them to wrap their brains around formal technical writing before requiring them to produce it themselves, and to allow them to focus on the portions I cared about most without completely doing away with the rest. The first paragraph is almost entirely scripted, with just a couple blanks to fill in. The other paragraphs allow much more freedom. I’m sure the template could be improved, so don’t judge! However, feedback is welcome.

Editable version of the assignment sheet: Ch. 12 Student Loans Project

Editable version of the template for the write up: Ch. 12 Studen Loans Write-up Template

*Unfortunately, my initial understanding of how student loan interest accrues was faulty. I was able to get this explanation from the bank managing my husband’s student loan:

Student loans are considered simple interest loans. Interest accrues daily on the outstanding principal balance.
The calculation used to determine the amount of interest that accrues per day is as follows:

Total Unpaid Principal Balance x Interest Rate, Divided by 365 or 366 (Days in a Year)

# Journal 10: Reflect on Semester One

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: Pre-final Vent

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

# Journal 6: Rank the Solving Methods

Journal 6 asked students to rank the three quadratic solving methods they’d been working on: factoring, graphing, and the quadratic formula. This was the most heavily curriculum-related writing they’d had to do, which is probably why they struggled to describe the math with any specificity.

I liked having written evidence that preferences for solving methods differed, so I posted opposing excerpts in the classroom (for example, one student talked about preferring the factoring method, while another described how he hated that method the most).

Editable version: Ch. 7 Pre-test Rank Solving Methods Journal

# Journal 5: Script of a Lesson

Journal 5 was inspired by this fun post by Ben Orlin over at Math with Bad Drawings (it’s a script of trying to teach students that some ideas take time). I provided the text of his post for us to read/act out together, then asked students to come up with other lessons a math teacher might want her students to learn (I had to help the ideas along a bit). Finally, the assignment was for each student to pick one of those lessons and write a script of a teacher trying to teach that lesson to students.

The idea of a creative writing assignment in a math class is pretty cool already, but one that gets kids to consider the big-picture lessons they’re learning and engage in some teacher role playing sounds like a real winner. The kids were genuinely excited about this journal, and the scripts they turned in are some of the most enjoyable student writing I’ve ever graded. I made copies of them, and in my end-of-year nostalgia I’ve already flipped back to read them twice.

Some highlights:

• A script that showed Niall Horan of One Direction learning that coming in to ask for help is not so bad after all.
• A couple scripts that took all the personalities in our class and played up their characteristics.
• A couple scripts that seemed like therapeutic coming-to-terms with past math class experiences.
• Scripts that revealed different student approaches: some chose lessons they’ve already mastered and could make a good case for, while others chose those they need to work on.

Download an editable version of the assignment here: Ch. 5 Part 2 Post Test Journal. Write a Script

*The optional math problem for students to include in their scripts was suggested by my co-conspiring SLP to provide students with some solid framework to hang their ideas on. Most students opted out of using it. For some it was essential.

# 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

# 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.