Write first, title later.

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
Happy New School Year! Sam over at https://samjshah.com/ (You should check out his blog because, he is Sam and he is awesome!) reminded me us that there is a hashtag for folks like us: #MTBoSFD (Math Twitter Blog O Sphere First Days). He also promised to blog twice for

Thanks to @druinok. So here are my our First Days Stations inspired by @magicalmsmurphy.

This is Danielle:
She is the most amazing math 

teacher ever. See that precious bundle on the right? Danielle is so creative, she made a baby and took a year off from teaching. I am so over the moon that she will be my neighbor once again this fall. I have to share her 1/2 time with precious baby bundle o' joy, but that is okay. 

Inspired by  @magicalmsmurphy, an English Teacher in Los Angeles, California we took her idea and sat down today 
for three hours plan our own first day stations. We have 90 minute blocks and will have the students move 
stations every 7 minutes. We will give the students 90 seconds to get to the next station. 

Created by Danielle Graff and Amy Zimmer for grades 9-11

The Purpose:
1) To establish that our classrooms are learning communities.
2) To establish that we Math everyday in our classrooms.

The Set Up:
Students will be randomly assigned to groups of 4.
We will practice how to move around to stations before we let the students actually get to work/play.
Students will go through an introductory activity before they move to their station work. 
We decided that the students will have a record sheet to bring with them for each station. Not all stations
will have something to record, but we want the students to get accustomed to having evidence of their 

Behind The Scenes:
Danielle being Danielle, and the master of all things organizational, started a Google Doc. We designed 
the stations, then went back and determined what was needed for each station (my idea--just so you get 
that this was truly a collaboration). Then we went back through and assigned the needed tasks to each of us.

Husband: You spent 3 hours working on the first day? 
Me: Yeah, I and that was 50% of the work. 

Left To Do:
Determine an exit ticket (will it be part of the activity sheet or separate and what will it be?
How will we debrief? 
And our assigned tasks of course. 

Here you go: 


First Day Stations:

1. Syllabus + Scavenger Hunt – Stickies notes for parking lot questions and comments
Regular post-its, white board for notes, syllabus copies, supply list, scavenger hunt on recording sheet
How do we want intructions to go? IE student reads a question and all try to find answer? Each spends 4-5 minutes looking on own and then all together round robin read so that everyone has the correct answers?

2. Target Number Station – whiteboards, pens, rags NEED CALCULATORS AT MATH STATIONS!!
Space to write down on record sheet that has target number (which is 851 using 50, 1, 20, 5, 63, 10) How close can they get to target number, what is the lowest number they can make and what is the largest number they can make with the given numbers

A- Target number Station & laminate
D - Recording Sheet for ALL stations
3. FlipGrid – need ipad or chromebook and to download the app
Students give us there: name, age and something they are looking forward to this year – we, as teacher need to record an example. SO they watch ours and then record their own.

A&D - Learn how to use and create our own intro video
4. Community Agreements: make a list of agreements that support a safe classroom and create an optimal learning environment, group will need to pick a typist based on who is the oldest.
- Google Form, minimum of 4 suggestions

D- Google Survey
5. Consecutive Chains – For HW students will do two more chains and then create their own + 2-3 order of operations problems

D - Add blank consecutive chains to recording Sheet

A - Station & Directions & Example

6. Notice & Wonder: color print and laminate maps, create google form, students don’t have to write anything just respond on google form.

A - Color copy & Laminate

D - Google Form

A and D--prepare “reveal slides”
7. Order of operations – analyze the math problem that has been going around NEED CALCULATORS AT MATH STATIONS!!

A - station with directions
D - Add space for this on recording sheet

 8. Mindset Reading: Read mindset rubric as a group and make sure students understand what each category is saying, pencils down! Students take clipboard, highlighter and rubric outside to evaluate themselves privately. On the back of sheet they chose one category that they want to move over in and write some ideas on how they think they’ll do that.


A - Station Directions
D - Break up Rubric and Laminate
 We are going to practice going to stations before we actually do them, how do you go to the station, how do you leave the station, leave the station the way you found them for the next group, rules for stations discussion (no talking outside your group, no cell phones) before the stations we have the students introduce themselves (How do we want this done??)  to each other, NEED CALCULATORS AT MATH STATIONS!!

Brain Break in between stations? Brain Break halfway through? Ask questions that get them standing? (If you play a fall sport, stay standing, etc.)

 How/When to Debrief

Please let us know if you use stations on the first day how it goes. Also hit us up with any suggestions or comments! 

Ever since I read about Stand and Talks on https://www.saravanderwerf.com/ (The amazing Sara Vanderwerf's website) they have become the single most important routine/device/exercise/strategy I use in my classroom. You can also hear about them in this Global Math Department's webinar:
Just like warming up before exercising in earnest, like if you take a class at a gym or are getting ready for a race, the coaches ALWAYS warm you up. "Run 500 meters." Then we stretch and THEN we exercise, Stand and Talks open students up. They warm up their minds and activate an openness to learning through safe dialogue with a partner first. I love them. 

What is a Stand and Talk? 
Here is my proposal for the CPM 2020 conference: (Still holding my breath, I was rejected, but asking to be included in some other way--advise accepted)

Stand and Talks--5 minutes that will reshape your classroom culture

Think/Pair/Share is a common go to strategy to give students a cognitive boost.
But what if instead of sitting, you could create a similar, potentially richer, easy access,
sky’s the limit, non-disruptive experience moving and standing? Stand and Talks take five minutes
and will increases math discourse, always gives a student something to share out, and shifts the
cognitive lifting from teacher to student. 

Stand and Talks begin with a prompt to look at and hold so there are no awkward silences.
The directions are simple, the possibilities are endless. I have used them for review, preview,
introduction, and vocabulary. I have used them as an icebreaker with students and with colleagues.
I have used Stand and Talks with Notice and Wonder, What is the same and what is different,
Examples and Non-Examples, Who did it better, and What can you label?
I was introduced to the this strategy by Sara VanDerWerf @saravdwerf
and I can’t wait to share it with you! As Sara says, “My goal is for students to say it before I say it.” 


My directions are modeled after Sara's: You will be standing up and pushing in your chair
when I finish giving you the instructions. You are going to move at least 15 steps away from
your table mindfully and quietly with no devices or writing utensils.
You will find someone to partner with that is NOT at your table. If there are an odd
number of folks, someone needs to find me and I will tell you what to do. When everyone is
partnered and standing, I will give you a card with a picture, graph, or problem on it. You will find
at least 5 things to say about what is on the card. If you can't find more, repeat the ones you have.
You only have 90 seconds so we are not going to worry about who our partner is and you will not
complain about standing the entire time.

I walk around and listen, make sure the students are on topic, nudge them in their thinking. I also
can have "plants" for the whole class discussion that comes after. When the 90 seconds are up,
I ask students to freeze and then I give them a silly instruction for who picks up the paper copies on
the table in front of the room. "The tallest replaces the card and gets two paper copies, the one who
slept the longest, the one with the oldest living grandparent, the one who lives closest to school...(see
the community building there?)

When the students get back to their seats, we annotate them together. This can reinforce, re-engage
or front load a lot of student thinking! The oohs and aahs are super fabulous and a lot of good information
comes from not just the top students. We then glue them into our Everything Notebooks (see earlier
post). And move on with our day. 5-10 minutes max. (We have 95 minute blocks every other day)

They look like this on a half sheet of card stock:

1) I used this S and T just as I was introducing graphing a quadratic by complete the square. in Math 2 (CPM) (Used as
review for all things quadratic in College Readiness):

Here it is annotated:

2) I used this Stand and Talk for introducing piece wise functions in College Readiness: Thank you @ cluzniak @math_mrestrada

3) This is a beautiful student generated Stand and Talk from College Readiness:

4) This is another student generated Stand and Talk from the Spring Final for College Readiness.

5) This is one of my favorite Stand and Talks EVER. I wish I had done a pre and post for Math 2. This was at the end of Right Triangle Trig.

Here it is annotated:

6) I admit, I completely stole the next one. I thank @NatBanting. I used this with Math 2 (and again with College Readiness) introducing the Zero Product Property. 

Anything can be a Stand and Talk. I saw this on Twitter and wrote that if you take out the
original prompt and replace it with "What do you notice? What do you wonder?" you get a
really cool Stand and Talk.

Here is another image from @riehlt:

Gotta Stop, going down the rabbit hole...

Is there anything I should add? That you have questions about???