Tri-state EQuIP rubric

Every time our math committee meets we are energized by the progress we’ve made but at the same time we feel deflated because there is so much more work ahead of us. Last week we were again reminded that our math units need bolstering.

On Wedesday we once again analyzed our progress using the Tri-state EQuIP Rubric designed by Achieve. For the 7th grade rational numbers unit there are four areas we need work on:

Linking Mathematical Practices to learning opportunities and assessment items.

We hadn’t formally identified the applicable MPs to each learning sheet and activity so we went back and did that. Examining our assessments was next. My colleague and I experienced a giant YIKES on the decimals assessment because hardly any items could be linked to a MP. Since we ran out of time we need to revise those items plus look at the other assessments in the unit.


Explicit writing, speaking, and listening opportunities

We made some progress here by modifying directions on some activities. For example our subtracting integers portfolio was modified to include two peer reviews. The next time I assign this task students will create a draft of their video using Explain Everything then two students will watch, listen, and provide written feedback before creating the final video.


Instructional supports

We have some intervention and enrichment resources but we need find more and better organize the ones we currently have. The rubric also identifies the need for a performance task for the unit. I think we inadvertently listed it in the instructional supports section.


Scoring rubrics and pre-assessment reflection plans

Formally identifying the characteristics of partial credit, high partial credit, and full credit are on the drawing board. We also need to create a pre-assessment reflection plan for students to identify their strengths and what they need to review. This also includes helping them design an action plan before they take the assessment.


Lots of work ahead.

Authors who have influenced my practice

One of the most contentious areas in middle school is work completion. When I first began teaching I was of the mindset, I need to get kids ready for high school. If their homework is one day late, the max the student could earn would be 80%, two days late: 70%, three days late: 60%; more than three days late: teacher discretion. Retakes–no way, they had their chance; they should have studied. Or when I did allow retakes the maximum grade a student could earn would be 70%.

In effect I was using grades as a punishment. Equally troublesome was the fact that this system created a tainted report card. I’m supposed to be reporting academic progress not academic progress with two scoops of behavior and a cherry on top. Now I’m not only questioning my overall grading policy I’m starting to rethink how I assess.

There wasn’t a single turning point. It was an evolutionary process. However two author/educators who caused me to reflect are Thomas Guskey and Rick Wormeli.


Several years ago Guskey came to our district and presented a talk, Developing Grading and Reporting Systems for Student Learning.  He discussed the merits of standards based grading and a narrative report card that separates behavior from learning. His book and talk nudged me to reconsider my practice. Over the next five years I continued to contemplate grading and assessment. Guskey’s book led me to Marzano’s Formative Assessment and Standards Based Grading and that is where I am today.

Wormeli has been equally influential. Chapter 8 from his book Fair is Not Always Equal is particularly compelling. Why Do We Grade, and What About Effort, Attendance, and Behavior?

He contends there are six reasons why we grade:

  • To document student and teacher progress
  • To provide feedback to the student and family, and the teacher
  • To inform instructional decisions

  • To motivate students
  • To punish students
  • To sort students

“Notice the dividing line between the top three and bottom three…The bottom three reasons cross a line. When we grade to motivate, punish, or sort students, we do three things–we dilute the grade’s accuracy; we dilute its usefulness; and we use grading to manipulate students, which may or may not be healthy” (p102).

I’m still a work in progress, but I’m getting there.

Click the link below to read other bloggers who are writing about professional development books.


Integer choice assessment part 2

The other day I posted a work in progress–an assessment menu for adding and subtracting integers. Matt Coaty’s comment inspired me to explore how students would share their understanding, as well as develop assessment criteria.

Today I’m unveiling a new and improved version. I’ve taken the idea of a literary book club meeting where students bring a discussion tool to talk about a novel and have turned it into a “Mathematics Symposium” where students bring activities they’ve created about a concept and share their mathematical understandings with the group.

Here’s a revised 2-5-8 menu with descriptions of the criteria for success, suggested product ideas, and a check on whether students have met the expectations, or if they are not yet there.


Each student will have up to ten minutes to share their activities. When the group is finished they will assess each other using this two sided rubric/checklist. If a student marks any area as superlative (italics) they are to indicate on the reverse side what distinguished it from the other choices.

symposium reflection

symposium notes

To determine a “final” grade, I’ll review the artifacts along with the students’ input. I’ve successfully used this format when I taught literature and it was quite successful. I’m looking forward to seeing how this translates in a math class.


Standards based choice assessment

For the past couple of years our math curriculum committee has been focusing on creating performance based assessments with leveled problems. Now that we have a clear vision of the standards and what we want our students to know and be able to do I want to start offering some variety, some choice.

I’m toying with the idea of offering choice once per quarter. Here’s a 2-5-8 menu I created for adding and subtracting integers.

integer menu1

integer menu2integer menu3

In addition to the differentiated content, I like how this format requires the student to do much more thinking and problem solving because they have to come up with their own scenarios and problems. Even the Knowledge and Comprehension levels ask students to think.

One element that is missing is differentiating by product. What options do you suggest? Ideally they shouldn’t take hours to assess. Also if you have other activities to suggest or other input please comment.

Students learn to give feedback with a growth mindset

Yesterday Algebra’s Friend introduced me to a new professional development blog Read…Chat…Reflect…Learn! While I enjoy reading blogs for lesson ideas, I also love reading journal and magazine articles, books, research studies, etc. as another way to stay current. I’m glad I found this blog and I’m thrilled to see that it’s in its infancy, only because it makes me feel that I haven’t missed out on too much!

The current topic is feedback. The article for discussion was How Am I Doing? It offered a good overview, but what was missing was how to provide feedback using a growth mindset. This excerpt, Types of Feedback and Their Purposes,  gives clear examples. One type of feedback I tend to focus on is descriptive as opposed to judgmental feedback.

When examining student work for feedback I’ve collected their work in progress, and provided descriptive feedback. I won’t kid you. It’s time consuming. But an idea was floating in my head. What if I taught students to give each other feedback with a growth mindset?  I don’t want you to think I am shirking my responsibilities, but could math students offer feedback similar to students who participate in peer editing compositions?

After reading Algebra’s Friend post I thought I would give it a try. Yesterday and today I showed my students this Would You Rather problem. They were to work in groups of four to solve.

After the groups worked for about 10-15 minutes, I collected their work, redistributed them to different groups and asked the new group to provide feedback. Here’s an example:


Kids being kids, their feedback was somewhat judgmental and not of a growth mindset. Had they rephrased their wording to questions such as, “How could labeling help explain your thinking?” or a statement such as “The final answer is not clear,” would definitely put them on the track towards feedback with a growth mindset.

Doing this activity in groups made it quite manageable as only six responses were being critiqued. While I monitored each group I asked them what questions they had about the other group’s work. I also asked them to be positive with their feedback. Each problem was circulated twice. Doing so also gave groups the opportunity to see how others approached the problem and perhaps revamp their thinking.

Here’s how the above group implemented the feedback:



The next time I see them we’ll continue the conversation of how to offer feedback with a growth mindset. With more practice they’ll get better at it.

I should have thought of this at the start of the year.




Relying on spring break for more practice

I hate giving homework over break, but this time I had to do it.

Before spring break I gave my pre-algebra students an assessment on rate of change, slope-intercept, etc.  The results were disastrous. Students could calculate the slope, but many had difficulty graphing. Some were lost when converting the standard form of a line into slope-intercept form. I have to take most of the blame. I thought they were ready, but they weren’t. If you ask me why I thought they were ready the only response I could give you is, “Because we covered it in class.” In hindsight, I was an idiot. Not only did the kids check out before spring break I did too. In my haste to squeeze in an assessment I didn’t provide enough practice opportunities. Plus my in class checks for understanding had been limited.

I collected the assessment and began to grade the first page of the test. I was livid. They should have known the concepts, or so I thought. The following day, the day before break, I was going to be absent–out of the building attending a social studies workshop on Rwanda 20 years later. I couldn’t take a chance on the sub reteaching the concepts so I created a screencast for the sub to show in class. In it I walked through similar problems from the test. Their homework was to rework every problem. I also made a practice packet for them to complete over break.

Additionally I wanted to communicate the situation to the parents. So I emailed them a copy of the packet along with the answer key as well as the YouTube link to the test corrections screencast. I explained that I may haven been too hasty in trying to get an assessment in before break and appreciated their support. I closed with, “I hope this homework won’t be too much of a nuisance over break.”

I know I was gambling here. Not so much if the homework and test corrections would be completed, but if it would be completed correctly. I had no doubt if the students watched the video, stopped, and replayed when making corrections they would be successful. Would they use it? I can’t control that. That’s why I’m not a fan of a flipped classroom where the essential learning is done at home.

Fortunately this story has a happy ending. Over break I watched the YouTube hit counter increase from zero hits to 23 hits. When I saw the students on Tuesday we went over the test corrections and some of the homework problems. No major issues. I gave the kids an additional practice test to work on in class plus their homework was to make and take their own practice test creating similar problems of each type.

When they assessed on Thursday the results were soooo much better. Only five students didn’t quite meet the standard, earning 80-85%. The practice tests they made didn’t include all problem types.

The rest earned some form of an A and they took the time to create a thorough practice test.

My spring fever caused this. Don’t ask me where I went over break. I didn’t go anywhere.

PARCC assessment influences local assessment design

The math committee met today to continue our work creating local assessments. During our learning time we walked through 6 sample PARCC assessment items. Note: The math questions come after the ELA so keep hitting the right arrow until you get to the grade 6-8 math questions.


If one of your classes has been chosen to pilot the assessment, be sure your students play with it. When PARCC suggests students get used to the scrolling and buttons they mean it. I was using a 15 inch laptop and had to scroll.

But the real focus is on the assessment itself. For the past year and a half we’ve been designing local assessments with the common core in mind, but today’s preview of actual sample problems was an eye opener. Turns out we’ll need to revise some of our current assessments to address the performance requirements.



Instead of going back and revising some our previous local assessments we thought it would make more sense to begin applying what we now know to the next unit of study–inequalities.

Our students need to be exposed to multiple choice problems with multiple constructed responses. We spent a good twenty minutes on this problem and we’re still not satisfied with the wordsmithing. It may be better framed as Part A and B instead of problem 5 and 6. Anyway, here it is:



I’m beginning to second guess myself with some of these problems. We do a form of standards based grading. Is #13, in the image below, really a level 4? I’m now thinking it should be a level 3. And problem #14, is it too much of a reach to expect a 7th grader to write this inequality?


I’m looking for help. Please comment, point me to good assessment questions, or to bloggers who write about  assessment design.

Thanks in advance.

Pre-assessment yields two random, but important, lessons learned

Lesson 1: be flexible when grouping students.

Earlier in the week I posted on my 180 math post-its blog that students were pre-assessed on fractions. I was disappointed to see that only two pre-tested out of many of the concepts. Given the caliber of this class there should have been at least five more ready for enrichment on the skill of adding and subtracting fractions.

I probably should have started the class immediately by differentiating for the two students, but I didn’t. I had enrichment ready for them,  yet I launched into a whole class whiteboard/quick check activity of adding and subtracting fractions. I admit I short changed those two girls, but I’m glad I did the whiteboard work because within 10 minutes five more students revealed to me that their pre-assessment was a signal that they simply forgot.

It troubles me that students do not retain their learning, but that’s for another post. In this instance I truly believe those five kids had, as they say, a brain fart.

For the rest of the block they worked at two tables on challenge problems. Which leads to…

Lesson 2: Students can be completely engaged with non-real world problems.



The kids loved the challenge. I know there is little context with these problems, yet they were engaged for the entire block. You can’t describe them as puzzles, but for 7th graders the problems were puzzling and they wanted to solve them.

By the way this same class is enjoying the NCTM palette of problems I’ve been using for determining importance.

determining importance2

Recently I’ve been presenting them at the start of class. Students work independently then we share solutions, discuss their “arguments” etc. Some students want me to do this everyday.

What to do when you don’t know what to do

My students do not have much experience with non-routine problems. On occasion they’ve completed complex tasks, but certainly not enough, or a variety, for students to build self-efficacy. I’m trying to change that by living a SMART goal I created for myself. Last Thursday, day 8, I presented a formative lesson designed by the Mathematical Assessment Project.

The problem began: Emily doesn’t trust banks with her money. She has stored $24,000 in one dollar bills under her mattress. The rest of the problem can be seen below. This student’s attempt was typical.

money munchers4
Most students guessed and provided no mathematical reasoning to support their answer–revealing a lack of understanding of how to approach the problem.

After they worked on the task independently for fifteen minutes, I collected their work. I found myself providing the same feedback over and over. (My handwriting is atrocious. I know. )

As I reviewed their work, I came upon this response:

money munchers5
This student has recognized that mattresses come in a variety of sizes, but provides no math to justify her thinking.

One or two students thought to estimate the size of a mattress, but their dimensions weren’t reasonable. For them my feedback was, “How tall are you? What do you think the dimensions of your bed are?”

For estimating a stack of one dollar bills, nearly every student has this feedback: “How could a book help you? How could the pages in it help you estimate a stack of money?”

When I see the students tomorrow, they’ll take that feedback and work independently for about 10 minutes. They’ll then work in their groups to share their progress and come to a solution.

One thing I will add is criteria for success. Your work is: a reasonable estimate that is organized and clearly labeled.

I love this lesson. I get to see individual thinking. The feedback offers progress while not enabling. Plus, when they collaborate every student should be able to contribute to the solution.

Getting kids and parents to focus on the learning–the grade will come. Trust me.

Open House idea. I’m trying to think of a subtle way to impress upon parents that the focus is on the learning not on the grade. Maybe for some the focus is on the grade. However I think parents and students would agree that if we focus on the learning the grade will come.

Since I’m bored, I created two GoAnimate videos that I might use at Open House.  The first is a 30 second discussion about grades.

This one is less than a minute long and focuses on the learning.

This will lead into a nice segue where I can talk about the success students had  last year when they set goals and monitored their progress. I constantly tweak this document so you may notice that it’s not exactly like what’s represented in the image below. Maybe I’ll show the parents what progress monitoring looks like.

progress monitoring
This student needed to be assessed 3 times before she achieved mastery. As you can see the student was honest with respect to the amount of effort she put forth.

My assessments are designed in a standards based grading format (that’s why you see Scores 1-4). Students set a goal of either 3.0, 3.5 or 4.0. Three is the target. My formative assessments are ongoing and students can reassess as long as they complete and follow through on a study plan which is their evidence of study.

I cringe when I hear, “What can I do to raise my grade?” or, “Is there extra credit?”

I want to work with parents and students to reframe those questions to be more like, “What can I do to improve?”

Maybe Open House is the place to start.