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.

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How do you feel about the length of these events? My school has a 2 hour block and typically asks students to spend at least 90 minutes. I wrestle with this as I’d like to have an assessment that my most deliberate students can still finish. This would mean that my best (and my most hurried) students would finish short of the 90 minute expectation. I know that there is a great gap in the efficiency with which students can organize material at this time of the year. I want all my students to have ample time to think.

I also find that I try to write these finals in a more broad fashion than unit tests. When the assessment concentrates on two to three weeks, I feel that granular detail is reasonable. When the test attempts to take in the entire course in its scope, I think broader themes – like those you outlined above – are more appropriate. I worked at a school where our department made finals look pretty similar. One short answer/MC/fill in the blank section and then single pages devoted to major themes where all problems on a page were related. I have not been able to convince my current colleagues to adopt this idea.

Getting the right length can be tricky with any test, and more so with a final. There are just so many great questions to ask that it’s hard to cut any of them out! My school schedules 100 minutes per final, and most of my students this year worked on theirs for close to that amount of time, although some stuck around to work on theirs some more. (I made notes to try to adjust that next time.)

This year I didn’t have the problem where a handful of students were finishing the test wildly faster than the others. Perhaps something that helped was that there were questions allowing for self-differentiation. For example, I provided distance vs. time graphs and asked students to write stories that explained the motion in the graphs. My fastest-working student wrote longer stories than many of the others, which meant he didn’t whiz though as quickly. At the end of the test I also included some bonus questions to challenge any who might finish early, including a couple reflection questions that required writing.

Yeah, I like the opportunity on final exams to underscore broad themes and to synthesize smaller ideas into larger ones.