Danielle Buckman: "A rubric for the level of understanding tells a student not only where they are, but where they can end up."

**Part 1**This is a two part post--the learning piece is second, so if you want PD and to learn more about writing rubrics for understanding, skip to the second half, I completely understand, time is the one definitively limited resource we have. The first half is how I got to be so awesome. Joking aside, I must give credit for how I have become a more conscientious teacher/human.

How do I know this? I feel it. I can feel it within and from the relationships I have with my students. And my husband, who has been my partner for all but my first year of teaching, has been more appreciative of my work too, less "you are always working," to more, "I notice how calm and confident you are."

I am deeply appreciative of so many people who make me a better teacher: The students for sure, they are my audience and have my full attention when I am crafting. Their feedback is unfiltered and immediate, whether they are humming or delivering crickets.

The #MTBoS community is my rock, where I also get unfiltered and immediate professional and sustaining support. Since 2012, the quality of the human in this sphere makes me strive to be my best self more than any other realm. This is a blessing, but can also bring some sadness, as this is what I want more regularly with my home colleagues and especially my district.

Thank you to College Preparatory Mathematics (CPM) for rich tasks and curriculum I enjoy.

Which brings me to another appreciation, my colleague extraordinaire, Danielle. She is a go-getter. She brings all the best from being a millennial straight into the teaching profession. No moss grows on that woman. We have very different backgrounds, she complements my wiggles and dreaminess with her clearly defined, no nonsense organized approach. We both love the roots of learning. We both love what good pedagogy and technology can do to inspire a student's curiosity. What makes students motivated to learn? We run from room to room, sometimes 5 minutes before the bell, with, "hey, I can't even do this that I spent over an hour writing yesterday, I'm going to do this instead." and for each other, we are like, "Heck yeah, that is awesome!" In the last six years, she is the one who gets the my love affair with #TMC and understands that the risk of failure is worth the growing pains. This post is about how having a colleague with patience and humility makes all the difference. And Oh, it is about writing rubrics.

**Part 2**My College Readiness students have been working on functions and their transformations.

I started with this kind of function:

And had students make tables and explore with technology (TI-84 and Desmos) what a, b, h, and k do to the graph. Next we looked at the parent graphs and the equations. We even looked at Spaceman Snoopy

f(snoopy) = (snoopy + 4) +8 |

g(x) = f(-Snoopy) |

(We live in Sonoma County the home of Charles Schultz). The students agreed, given an equation, they could mostly move the graph around, and that given a graph to move they were okay with that too. But given a graph of function already transformed was not so easy. We working on this for days and I wanted the students to get serious. Nothing like throwing in a little formative assessment. to light a few fires. What did I want to assess???

In comes Danielle, our TOSA for the year. That is exactly what she asked me: "What do you want to assess?" So now I understand the difference (Thank you TOSA) between writing a rubric for SBG and writing a rubric for level of understanding. I will do my best to explain:

I wanted to give students a clear picture of what I considered

**conceptual understanding.**Danielle kept asking, "What are you trying to measure? A standard or a level of understanding?" Further she points out the most important difference, "A rubric for the level of understanding tells a student not only where they are, but where they can end up." I want the students to understand what they know. Of course there are overlaps in Content Mastery and Understanding the Concept. But what information does, "met standard" mean to a learner? Not enough. I want to provide the most useful information to the student. (There is so much I want them to understand!) Slowing down to put it in writing is a very good practice for me.

First attempt at rubric for level of understanding:

5--I can write an equation given the graph of a transformation.

4-- I can explain and accurately graph any transformation from a graph or equation.

3--Basic understanding: I can explain what a, h,

**and**k do to a graph

2- Approaching understanding: I can explain what a, h,

**or**k do to a graph.

1- I am breathing

This was the task was taken from CPM Math 4, Pre-Calculus with Trigonometry

Students were completely engaged, learned how to ask the questions they needed to clarify their understanding. I got mostly 3 and 3.5's with one 5!

Next day after asking D again what is the difference between SBG and Level of Understanding?

I made a few improvements:

5- Deep Understanding: I can write the equation of a transformation given the graph of a parent function.

4-General Understanding: I can accurately graph a transformation given a graph or equation.

3-Basic Understanding: I can explain what h, k, a

**and**b do in the transformation of a function.

2-Approaching Understanding: I can explain what h, k, a

**or**b to the graph of a function.

I wished I had asked them what they thought their levels of understanding were before and after, not just after. This time I will have to be satisfied with end of informative assessment and just after summative assessment.

Always more to think about.

What is an assessment win and fail you've experienced in your teaching?

approaching met exceeding not yelow SBG

5--more room for student to grow--level of understasnding 5-points