This year in my PreCalculus class, I have many students who are excellent at solving exercises such as “find the roots of the following quadratic trinomial,” where students are asked to apply various skills in isolation. (My quizzes, which are worth 25% of the course grade are made up of mostly these skill-based questions) However, those same students genuinely struggle with word/story problems where students must decide what information is relevant and decide which skills to apply. (Much like the excellent situations and problems you give us to consider in your blog) While I try as much as possible to include these in classwork, I also try to show that these problems and the problem-solving and questioning skills developed by working on these problems are important and worth measuring by including them on more formal assessments.

I try to make it so that a student earning an “A” in my class has demonstrated mastery of basic skills and has demonstrated the ability to know in what context those skills should be applied. Many times students ask why bother taking advanced math, when they might never factor a polynomial or solve a quadratic equation ever outside of math class. For many students, the critical-thinking skills and communication skills they build by figuring out how to apply the procedures they’ve learned is the main skill that they’ll draw on when it comes time to communicate detailed, techincal information in the future.

For that reason, my assessments are heavily procedural. I litter my curriculum with applications, extensions, project-based work, sure, but I won’t force a student who can find the roots of a quadratic trinomial but who couldn’t do that in the context of a poster project on projectile motion to repeat Algebra 1.

Yours isn’t an uncommon concern with this kind of assessment. If it doesn’t work for you, there’s nothing cooler than splitting from your mentors and saying, “This is how I would do it.” Set up a blog, do your own thing, and tell us about it.

It seems like you value–above all else–the ability to look at an assessment score and know exactly what that number means. I like that and would like to find a way to do that. In doing so, however, it seems that you break everything down into such compartmentalized, small individual skills, that students are never assessed on their ability to solve rich, layered, challenging mathematical problems that require critical-thinking skills and/or require them to communicate their thinking.

Perhaps I’m assuming too much. Perhaps you have changed in the 2 years since you initially posted this entry. Are you assessment items still this procedural? Also, do you give Problems of the Week or portfolios or projects or any alternate ways of measuring what kids know?

[Thanks for your blogging. As I said earlier, reading it (and the comments) really improves my teaching abilities.]

I’m Belgian and although I already know my maths but I’m still learning how to teacht it properly. In Belgium, teacher are thought to identify and classify their goals before starting to design lessons or evaluation. Your evaluation scheme fits this perfectly and I’m going to give it a chance in my own classroom. It’ll probably need some adjusting and since some of my goals are ‘integration’ as steve called it (I teach math to math-majors in High school) I’ll have to put in some goals in that direction as well.

Thanks for sharing your thoughts.