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.

Assessing the 8 mathematical practices

Like Fawn, I’ve been thinking about how to assess the 8 mathematical practices. Eventually I will want to “grade” them, but at the start the students will need opportunities to practice the practices. In addition I can’t just let them practice without giving them feedback. So I’m going to use this ASCD resource to drive my formative assessments, It provides a great framework and walks through the entire process using the Boomerangs lesson, a high school MARS task.

As you can see the feedback is mostly through written questions. When I first read the section on suggested questions I was thinking, “They sound a lot like the 8 mathematical practices.” For example the issue of difficulty in getting started could fall under the math practice of making sense of problems.


These questions and my comments will hopefully provide the necessary feedback for students to improve on the mathematical practices, but I’ll have to do it on a regular basis for the feedback to be effective. Plus I’ll have to provide them with a rubric. Our district created this rubric for students and teachers.

practice tool

In the fall I’m going to focus on only two or three practices to start with, then add other practices. I’m stealing that idea from language arts teachers who use Six Traits of Writing. From what I understand middle school language arts teachers only focus on a few traits at a time.

What I’m also planning on doing is using this recording tool for anecdotal, informal observations. Sometimes I feel like a mad scientist walking around with a clipboard and jotting down my observations but I’ll have to get over it. The tool and rubric were created last month so I have not had a chance to take them for a test drive.

Assessing the math practices will be new to me. If you have experience or see some red flags feel free to chime in.


I’m beginning to get incredible feedback. Your comments deserve attention so I’m placing them within the post. Please continue to share your thoughts.

  • Assessing them is not about “can they” do a specific SMP, but “do they” and can they eventually do so habitually?–Just one of Jessica’s suggestions.
  • Reading their reflections not only gave me great insight into how the students believed they were using the practices but also how they were beginning to think about solving problems in general–Jennifer shared her blogged about journaling.

The Differentiation Domino

Daniel Schnieder and I are on a similar journey. He recently wrote a thoughtful piece in which he discovered the domino effect while implementing Standards Based Grading. His post focused on three dominoes—standards, assessments, and grading—and how his move to SBG has resulted in a reevaluation of every aspect of teaching and learning. He concludes by suggesting there are at least 50 more dominoes in the chain.

domino differentiation

I think one of those fifty dominoes combine differentiation with formative assessment.

I thought I knew differentiation—content, process, product, readiness, etc. But today I realized how much there is to learn. I watched portions of a Carol Ann Tomlinson webinar, Common Core State Standards: Where Does Differentiation Fit? and learned how the MARS project is transforming differentiation by using formative assessment to facilitate student thinking and problem solving.

In the past I used formative assessment to differentiate instruction by groupings or as a reactionary tool for when students didn’t get it. If you read the previous sentence closely, I’m differentiating before or after a lesson or task. What’s different is how Tomlinson suggests using differentiation and formative assessment during a mathematical task.

Here’s an example. In this MARS task students work independently for 15-20 minutes to solve and graph an inequalities problem. After the allotted time, the work is collected and analyzed based on the 8 Mathematical Practices (Not all practices may be present in the task).

Is the student having trouble getting started, or misinterpreting the problem (Make Sense of Problems)? Is there an organization of thought, or is work haphazard (Construct a Viable Argument/Attend to Precision)? Did the student present a variety of mathematical models (Reason Abstractly and Quantitatively/Model with Mathematics)?

The differentiated feedback is given to the student in the form of questions. Can you organize your numbers in a certain way? How would someone unfamiliar with your solution understand your work?

When the students resume the task the next class period they are given 10-15 minutes to review the feedback and answer questions. They are then paired or organized into triads to collaborate—combining ideas and creating a new and improved solution.

This particular task is designed for high school, but MARS has a variety of problem solving and concept development tasks for middle and high school. You can take your pick of Classroom Challenges.
Classroom Challenge

What I’ve been doing

The mathematical tasks our math department created this year use questioning to differentiate and guide problem solving but not in the same manner. Those tasks are much more group worthy in nature and the questions are presented to the groups as resource cards to allow for multiple entry points.

They both serve a purpose but the MARS example allows for differentiation based on a formative assessment, not on anticipated misconceptions.

In the fall, I had planned on introducing the students to the mathematical practices and collaborative work through a series of short group worthy tasks. It will serve them better if I differentiate by using the approach suggested by Tomlinson and the MARS classroom challenges.

Preparing for assessments

Side bar: My spring break was fabulous and I hope yours was too. I spent the week skiing with my daughter in Whitefish, Montana. The weather and mountains were majestic, but the warmth made the snow soft and sticky. Towards the end of the week I was skiing in a smoothie but falling down didn’t taste very good. However I had an absolutely wonderful time and would drop everything to go back again.

Now back to business and the business of teaching students how to prepare for an assessment.evidence of study

I wish kids were born with an innate ability for how to study for a test, but they aren’t. I wish kids knew instinctively what study tools to implement, but they dont. I wish, I wish, I wish. If I got everything I wished for I’d be out of a job.

I’ve found that as the end of a unit approaches and the assessment nears, I have to make time to review how to prepare for an assessment. What’s worked for me and my students is this Evidence of Study worksheet. Basically I let the students know one week in advance when the assessment will be and they are to study five days out of seven.

The first colum gives suggestions for how to study because most middle schoolers don’t know how to prepare for an assessment. They can do such things as create a practice test, complete online activities, or review/redo homework problems they got wrong.  We take time in class to write down what they are going to do each of the five days, plus they note the specific concept they are practicing. I’m not telling you anything new when I say students can be vague with their descriptions.  For example they’ll want to write ratios as the concept, but the concept is really rates and unit rates, or solving ratio problems with tape diagrams. I want them to identify the specific learning objective.

The Evidence of Study sheet and physical evidence are due the day of the assessment. I use the old Ronald Reagan, “Trust, but verify” approach by having the students obtain a parent signature for each of the five days. Physical evidence helps too! 😉

I’m always looking for ways to improve so please share your thoughts and ideas.

Educating parents and students about standards based grading

My phone and email were quiet one week after Open House. A parent however ran into my principal while attending another grade level’s open house and gave him some feedback which he passed along to me. They were two great suggestions: 1) continue to send emails over the next couple of weeks announcing when updates have been posted to the online grade book, and 2) explain once again why I am doing this.

The end of this post details what I sent home. It’s been only one day, but I’ve received just two emails requesting clarification. The clarification was what I anticipated–taking a score of 2 or 3 out of 4 and intepreting it as a 50% or 75%. I reiterated that it was not a grade, but merely a record of where the student is at.

Parents and students are accustomed to a gradebook that captures the end result. They need time to digest the idea that a grade book can be thought of as a running record of progress. This hit home today when a student said to me, “Rumor has it you are counting a pre-test as a grade.”

I told Emma, “No, I entered it in the grade book only as documentation that this is where you are at as of this date. It is not a grade.” She slowly began to understand this grading practice. This is an adjustment period and I hope everyone will come to appreciate SBG over the course of the quarter.

Another student questioned why I don’t just make each assessment worth 10 points. I understand where he is coming from, but returning to a point value defeats the purpose of SBG and students still end up focusing on the grade.

I’m curious as to how others have handled this question. Again I’m doing SBG using a percentage based grade book.

I haven’t forgotten. Here’s the email I sent to parents:


For those interested in learning a bit more about standards based grading, please read the information below. Again, if you have questions or concerns, please contact me via email or phone.

Why SBG?
1.  SBG measures and reports the learner’s progress in a clear, precise manner. An assessment reported in the traditional grade book would have very limited information such as rational numbers test, 85%. This type of grade book entry does not describe the student’s strengths and areas that need more practice.

Continuing with the rational numbers example, in SBG the concepts are recorded and reported individually. This way everyone knows where the student excels and struggles. The grade book reflects individual levels of mastery such as adding and subtracting fractions, mixed numbers, decimals, and integers, as well as a separate entry for multiplying and dividing these concepts.

2.  Another important feature of SBG is maintaining a running record of the student’s understanding of the major topics in each unit. Parents often ask, “How is my child doing?” Seeing your child’s trend moving from 2/4 to 4/4 indicates your child’s learning is moving closer to the learning target and beyond.

Today and tomorrow, Monday and Tuesday, I am explaining the process to the students and returning to them their “pre-test” on the first learning concept(s). In Home Access today you will see your child’s current level of proficiency. If I see your child on “B” days, I will share the pre-test results tomorrow, Tuesday. As I mentioned at Open House, 3 is the target and 4 is more complex content.

Thank you for the opportunity to teach your child and I look forward to a great year of learning.

Standards Based Grading in a percentage based world

I’m participating in the math blogging initiative and thankfully the list of writing prompts is not intimidating. I could write about how I chose the name for my blog—I am extremely curious and I want my students to be too. But I really want to talk about something else. Something that has piqued my curiosity.

Standards based grading. It’s what I want to implement this year and yet I need to do this within the limitations of our district’s percentage based gradebook reporting system. It appears my colleague from the other middle school and I will be the first in our district to implement it. I’ve been reading blogs and Marzano’s work all summer so I think I know what I’m getting into. But I need your feedback.

I have the formative and summative assessment pieces identified with the standards, I’ve created standards based student goal setting sheets (they can be found here), and I know how to score using the 4 point rubric. The hurdle is “How do I report grades based on Marzano’s 4 point scale and not freak out the students and parents?”

The following idea isn’t pure SBG, but it’s the best workaround for now.

If a teacher is “stuck” in a percentage based report card environment but wants to report standards based grades, Marzano offers a conversion chart:

Scale Score Percentage Score
4 100
3.5 95
3.0 90
2.5 80
2.0 70
1.5 65
1.0 60
Below 1.0 50

I plan to set up a weighted gradebook as follows:

  • All formative “assessments” are 4 points, based on the scale.
  • All summative assessments are 100 points.

The weights are:

  • Formative: 0%
  • Summative: 95%
  • Practice: 5% (The practice piece is an FYI. It is incidental to what I am trying to accomplish.)

The formative category allows me to keep a running record on how each student is progressing towards mastery.

The summative grade is determined by the students’ current level of mastery based on the most recent formative.

For example:

Susie’s initial formative assessment for Standard 6G1 is a score of 2. In the gradebook I create an assignment “6G1—Area 1”. The assignment is “worth” 4 points and it is placed in the formative category with no weight. I then create an assignment for the summative category 6G1—Area. Since Susie’s first score is a 2, according to the conversion chart, I enter a grade of 70.

Four days later Susie takes another formative assessment on 6G1. This time she earns a score of 3. In the gradebook I create an assignment “6G1—Area 2,” assign it to the formative category with no weight and enter her score of 3. Since Susie is now at a 3, I overwrite the previous summative entry with a grade of 90.

At this point the gradebook entries are:

2 formative assessments for standard 6G1—Area 1 and Area 2

1 summative assessment for standard 6G1—Area

Plus any homework practice logged as completion

In effect there will be one summative for each standard plus at least 2-3 formatives for that standard. I know two to three formative assessments may not be enough for some students to demonstrate proficiency or mastery. If need be, they can arrange a time during homeroom or after school to “show what they know.”

In the end the 95% weighted summatives will be averaged and the 5% weighted practice is factored in to the students’ grade. Since the summatives all have the same 100 point score, no standard is “worth more” than another.

Do you think it will work? What’s your experience with SBG?