Journal 2 should have been counted as a regular homework assignment, so I’ve jumped to Journal 3, where I started trying to change the anxious, mistake-fearing culture of the class. The text I excerpted from the Pacific Standard was difficult for students to digest, so we spent a good piece of time pulling the meaning out of the text. An editable version of the assignment can be downloaded here: Try Something Journal Prompt

# 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

# End of Unit Routine

- Vocab Day: vocab review games, with emphasis placed on words from the current unit, although other words are included as well.
- Study Guide, Day One: The study guide begins with a list of concepts, terms, or skills students will need for the upcoming test, then provides practice problems. To start things out we always read through the list of skills one by one, with a pause for self-assessment after each. The students discreetly show how confident they feel with each skill with a thumbs-up, thumbs-down, or thumbs-somewhere-in-between. They can use the rest of the period to work through practice problems.
- Study Guide, Day Two: Open for continuing practice, checking answers, asking questions, etc.
- Test Day
- Journal or Project Day
- Students get Tests Back, Begin Test Corrections

# 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.

- Create clearer expectations for the logarithms unit — or at least make sure the unclarity is purposeful.
- Improve scientific notation materials.
- Revise the vocab lists for my word wall.
- Be careful about continuing instruction while students are still taking notes on prior info.
- Plan for more “discuss/work with a partner.”
- 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.

# Graphing Stories

Graphing Stories was a great addition to my class this year. It started as the Possible or Not activity that I used during our first unit (about functions, operations, input, output, etc.) and grew as I made my own graphs on Desmos to draw out understandings of new function types.

In addition to the learning value of the stories, they were also kind of fun — especially those for graphs that weren’t functions.

At first I required students to write or type their stories; then I provided individual whiteboards so they could just jot them down; then, sometimes, I let students share their stories without writing them anywhere first. Sometimes I meticulously demonstrated an interpretation of the graphed information, while other times it was merely a discussion.

I dictated that we were looking at distance vs. time graphs, but had the students make decisions about what units the time and distance were measured in and what they were measuring distance from. (In the future I might alternate between determining those measurement details myself and asking the kids to do it.) I almost always had to remind students to include observations about speed. (Relatively slow or fast? Constant? Getting faster or slower?)

On tests I included the extending challenge of providing a story and asking students to sketch the matching graph.

During the end of year review, the student who chose this section (Interpreting Graphs) for which to plan his own review activity took the opportunity to bring us all outside. He had prepared 5 graphs using different function types and distributed copies of those graphs to the two teams. On the basketball court the teams took turns acting out a graph’s story while the other team figured out which graph it was.

An extension that I’ve considered but not tried is taking the graph’s action from a book or film students are studying in another class.

# Using Open Questions to Teach Simplest and Equivalent Forms

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

- Addition
- Subtraction (the requirement of like terms for addition and subtraction was a worthwhile challenge)
- Multiplication
- Division
- 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.

# Philosophy of the Final 2013-14

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.