Over the past couple of weeks, I’ve been completely inundated by an inquiry into assessments. I’ve been trying to answer Michael Fenton’s call to create better assessments by analyzing some of the assessments I’ve given this year. Like I said before, our school is exploring standard-based grading techniques. I teach four different preps, and each is taught and assessed in different ways.

- AP Stats
- Pre-Algebra
- 6th grade skills class – called Foundations
- Geometry

My goal in this post is to reflect some on what type of pedagogy, assessment, and rigor are applied in class.

Note:When I say rigor, sometimes I think I mean “pacing” or maybe my own stress level?

__Primarily Direct Instruction__

Statistics is almost exclusively taught using a direct lecture. I basically talk and ask very directed questions. I tell them what buttons to push, and how to graph Gaussian distributions and write down definitions very explicitly. I assess using materials that were purchased alongside the text book. *High rigor*.

Pre-Algebra is predominantly question driven, followed up with working example problems and smaller lectures. The class is somewhat strangely put together. We’ll cover matrices and exponents in the same chapter (I’m not totally sure why we cover either). Aside from this class needing some pruning, it’s essentially directly taught as well. I assess with frequent small, fragmented quizzes. *Low rigor*

__Primarily Exploratory__

In my Foundations class, I ask lots of questions, and we brainstorm how to solve them. We cover standards (like multiplying fractions) and the more light side of mathematics (like making hexaflexagons). Sites like estimation180.com have been a godsend for finding really simple, practical ways to frame questions – in that case for estimating. We take our time, and have lots of remediation when possible. *Low rigor*

In Geometry, I base the course loosely on the Modified Moore Method. If you’re unfamiliar, the MMM purposefully and carefully gives students definitions and axioms, and the student’s’ responsibility is to prove theorems, corollaries and such. I’ve modified the course in a way that students prove traditional theorems less, and are put into difficult environments in which they must navigate. *Medium rigor.*

**For example:**

“You are given a regular polygon with each exterior angle measured at 10°. (4 points each)

a. What is the measure of each interior angle of the polygon?

b. How many sides does the polygon have? (Hint: double check your answer)

c. What is the sum of the measure of all of the interior angles?

d. What is the sum of the measure of all of its exterior angles?”

This might look like a typical Geometry problem that you might see in any vanilla Geometry class. However, I feel like it’s not an assessment of how they use the interior angle/exterior angle sum formulas –

*because I never gave them one*. The closest I came to giving them a formula was to ask them in class what the sums of various regular and irregular polygons is. They filled out and made some guesses and then I gave them this questions on a quiz.

When I hear from students afterwards about the time they spent on this problem – drawing out different scenarios, testing and re-testing hypotheses, (productively) struggling and learning from the quiz itself, it makes me feel good. AND I COULD HAVE TAUGHT THIS FORMULA IN ABOUT 38 SECONDS. So what exactly am I doing here?

Relating this to Standards Based Grading – what standard coincides with this assessment? Formula creating ability? Rigor? Tenacity? Badassery? When I try to separate my assessment with a basic pedagogical philosophy, I really run into trouble.

__Closing thoughts__

According to standards-based grading, the students either picked up that information or they didn’t. They essentially strip the time component as well as the character component. SBG is pedagogically agnostic. It leaves me really wondering what a best practice is for each of my classes. Sometimes I feel a little timid and afraid that I’ve picked the wrong pedagogy for the class I’m teaching. I still feel strongly attracted to standards-based grading, but there __has__ to be room for giving students feedback on these other issues such as tenacity and grit. The lingering question for me is: how will they receive it?