Tag Archives: assessment

The 6 C’s of Claims-Based Grading

6-cs-picFor the past three years, I have been using a claims-based grading system in my math classes. Rather than using the traditional categories of Tests, Quizzes and Homework, or the standards-based categories such as A.REI.1 or Solving Linear Equations, my grade book is now comprised of the following claims-based categories that I refer to as the 6 C’s:

  • Concepts & Procedures
  • Critical Thinking
  • Communicating Reasoning
  • Constructing Models
  • Creativity
  • Collaboration

I call these “claims” because the first four of the six draw directly from my state of California’s testing system, The Smart Balanced Assessment Consortium. The SBAC exams and reports are based on four Claims for Mathematics Summative Assessment:


I figured that since the signers of my paycheck now expect me to impart these four abilities to students, that maybe my grade book should reflect these capacities as well.

I also know that the famous 4 C’s of 21st Century Learning are important skills for students to possess when they graduate our schools, therefore I thought that should be reflected in my grade book as well.


Two of these 21st Century C’s overlap with the SBAC claims. By choosing the phrasing “critical thinking” over “problem solving” and tweaking the SBAC phrase of Modeling and Data Analysis just a bit, I had my own 6 C’s of Claims-Based Grading.


This new grading system has demonstrated terrific benefits in the classroom for both my students and myself…

Student Focus & Reflection

Having the picture shown above displayed as a poster at the front of the classroom serves as a constant reminder to students as to why they are in the course. There is much more to math the just busting out algorithms. If they never have to solve an equation in their adult life, hopefully, they will understand the mathematical principles that they hear about in the news, be able to think and communicate in a quantitatively manner, interpret data and represent the story that the numbers tell, solve problems creatively and work collaborative to meet a goal.  Claims-Based grading keeps these ultimate purposes front and center in the students’ minds.

My students also have a grade sheet that reflects the 6 C’s on which they record the scores they received on each assignment. Any given assignment may have more than one score on it, much like what is done with standards-based grading, with each score being based on a 5-Point Rubric (to be shared in a future post). In other words, after each assignment, students are required to look at how they performed in terms of, say, critical thinking or constructing models, rather than studying for a test.

The portfolios in the class are structured around the 6 C’s as well, with the first six of the eight sections being the 6 C’s themselves. After each assignment is recorded, it gets filed in their portfolio in one of the sections that it was graded on. For example, if an assignment was scored on Communicating Reasoning and Creativity, then the student gets to choose into which of those two sections the assignment will be placed.


While a Traditional grading system focuses student attention on study habits, and Standards-Based grading focuses them on specific skills, Claims-Based grading focuses them on broader capacities that will serve them well as adults.

Teacher Focus &  Reflection

The greatest benefit of the Claims-Based grading system is how much it reminds me to teach and assess the capacities that I often forget. I naturally teach to conceptual understanding, critical thinking, communicating reasoning, and collaboration, but I need to be frequently nudged to present students with tasks that require them to construct models and create unique examples or solutions. For example, a group quiz will pose several claims-based problems on the same mathematical topic with a few cumulative questions as well.


The Collaboration grade is always a self-assessed grade by the group, with me holding the power to veto. Quite often, though, they accurately score themselves. This is not surprising since we score it according to the school-wide norms on collaboration.

Reflecting upon the results of the Claims-Based grading has great value to me also. Take my end-of-semester results for one class, for example. (Note, there appears to be a large number of assignments, but remember that each assignment may have multiple scores, like the quiz example above.)


With the exception of the collaboration grade, the scores appear to be fairly consistent. This is interesting since individual students do not show this consistency. They usually have a claim or two that lags the others. The numbers that give me the most pause are the number of items. The few number of collaboration scores is not a concern, because most of the assessments are individual anyway. However, I am assessing procedures twice as much as critical thinking, three times as much as communicating reasoning and constructing models, and five times as much as creativity. I’m not convinced this is an issue, but I’m not convinced that it is not one either.

There is another interesting phenomenon that has me reflecting on my practices. The final exam scores are far less correlated under this system than with my traditional system. In previous years, I would have only a handful students whose final exam score was different from their classroom grade significantly enough to raise or lower their course grade, and most of those would be an improvement in the grade. Under my new system, there is about a 45% volatility. That means that nearly half of the students score differently enough to change their course grade, with the number being split between raising or lowering the grade. I think this is because the district finals are so heavy on the procedural side, with absolutely no questions addressing modeling or creativity. Students who are strong or weak in the Concepts & Procedures category will then see a gap between their course grade and the final exam grade. I am keeping a careful eye on this dynamic as I move forward with the new grading system.

Moving Forward

For all the reasons that I have shared, I will be keeping this Claims-Based grading practice for a while. l see myself adjusting the system less, and using it to improve my instruction more.

Future Posts on Claims-Based Grading
  • The Claims-Based Grade Book
  • The 5-point Rubric
  • Value-Based Grading


Recap: CA Mathematics Network Forum, 2015

Logo CAMNThe 2015 California Mathematics Network is a community of math education leaders from twelve regions in the State. This Conference focused on the NCTM publication Principles to Actions. The book is an amazing resource that discusses what needs to be done in math classes, and what actions need to be taken by teachers and administrators alike to make that happen. It should be read by anyone who has an investment in math education. A good primer is p 5, 10, & 109-116, or check out the Executive Summary. Following are some terrific ideas from the conference speakers on how to implement these Principles.

The Best of the Common Core Closes the Achievement Gap — Dr. Lee Stiff, former NCTM President

  • Lee StiffThe Achievement Gap can best be narrowed through Effective Teaching of the CCSSM Practices.
  • Where do these effective teachers come from? … “from our good work!” (as instructional leaders)
  • The primary purpose of Principles to Actions is to fill the gap between the adoption of rigorous standards and the enactment of practices, policies, programs, and actions required for successful implementation of those standards.
  • NCTM Guiding Principles
    (from Principles to Action)
    Teaching and Learning
    Access and Equity
    Tools and Technology
  • NCTM Teaching Practices
    (from Principles to Action)
    1. Establish mathematics goals to focus learning.
    2. Implement tasks that promote reasoning and problem solving.
    3. Use and connect mathematical representations.
    4. Facilitate meaningful mathematical discourse.
    5. Pose purposeful questions.
    6. Build procedural fluency from conceptual understanding.

    7. Support productive struggle in learning mathematics.
    8. Elicit and use evidence of student thinking.
  • Student placement and support should be based on DATA not DEMOGRAPHICS.
  • We create the gap!!
    Screen Shot 2015-05-21 at 10.50.39 PM

Teaching Practices that Support Student Learning of Mathematics — Peg Smith, University of Pittsburgh

Peg Smith PicDr. Smith had us read through a well-known task, the Hexagon Train, and then analyzed it through the lens of each of the Teaching & Learning Principles in Principles to Actions (Summarized Below):

Hexgon Train



1. goals
2. tasks
3. representations
4. discourse
5. purposeful questions
6. procedural fluency

7. productive struggle
8. evidence of student thinking

  • It’s all about the task. Choosing the task really matters.
  • “What you put in front of the students frames their opportunity to learn the mathematics.”
  • Have your questions “locked and loaded,” and your responses “in your back pocket.”
  • It’s time to break out of the “postage stamp” lesson plan, (the homework, & examples fit in a little box), and write analytical, anticipatory lesson plans. (This one needs a cute name, too)
  • It’s difficult for teachers to use a high level task. It’s even more difficult for them to use it well.
  • Decrease the complexity of language without decreasing the cognitive demand of the task.
  • “Never Say Anything That a Kid Can Say.” (Article)
  • Writing “SWBT” objectives limit what students learn. Is the goal really to be able to find the length of the hypotenuse or to understand the relationship of the areas of the squares formed by the three sides of a right triangle?
  • Dr. Smith is the co-author of 5 Practices for Orchestrating Productive Discourse in Mathematics Class.
  • Dr. Smith shared this Principles to Action Tool Kit:

Dr. Smith then asked us to restructure a standard series of textbook questions into a more robust task. The conversation at my table was very rich. It was a briefer version of a lesson makeover, and would be an awesome PD activity.

Smarter Balance Update — Mary Tribbey & Jane Liang

This slide makes two BIG statements:

  1. The Red Dot () is along a timeline from the start of the assessment initiative to full implementation. We are still in the early stages of perfecting it.
  2. There do exist Interim Assessments that few schools (including mine) are using to check for student readiness.

Screen Shot 2015-05-19 at 9.52.34 AM

This day was the first I heard of the scaled score for the reporting of the test. It appears that there will now be some reporting on the standards as well as the claims, after all.

Screen Shot 2015-05-19 at 9.53.08 AM


Equity-Based Teaching Practices — Karen Mayfield-Ingram, EQUALS Program, UC Berkeley

  1. Mayfield PicGoing Deep with Mathematics
  2. Leveraging Multiple Mathematical Competencies
  3. Affirming Mathematics Learner’s Identity (multiple access points)
  4. Challenging Spaces of Marginality (diminish status within class)
  5. Drawing on Multiple Resources of Knowledge (including culture and experience)

Lesson: “He Was Suspended for Being Mexican” (excerpt from The Impact of Identify in K-8 mathematics Learning and Teaching) This was an anecdote of a teacher who took a students statement, “He was suspended for being Mexican,” and turned into a statistics lesson in which the students had to analyze data to determine if the school policies truly were racist or not. While we can’t tie every topic into a student-oriented context, I think it is a powerful idea that should be done more often.

Technology & Computation — Joe Fielder, Cal State Bakersfield

  • Pic FeidlerAll computation outside the classroom is done by a machine.
  • Machine computation is mostly done with spreadsheets.
  • Hand calculations are only done in math classes. (referenced TED talk by Conrad Wolfram)
  • If we are going to teach students mathematics that is relevant beyond the college entrance exam, we need to give explicit instruction on the tools of computation.
  • TI InspireDr. Fiedler is currently working with the college board to change the SAT to reflect computations done by hand-held graphing calculators.
  • The introduction of the first scientific calculator 1972 was controversial, because teachers were worried that students would no longer be able to use tables.
  • “Students are idle, indifferent, irresponsible in response to absurd work. This is a rational response!”
  • There is no change without a loss. If there is no loss, there is no change. Similarly, literacy diminished the need for memory, but we still teach students to read and write.
  • Yes, part of education’s job is to pass on old knowledge, but it’s not the entire job. It’s time to get with the times.

BREAKOUT: Exploring the Common Core Statistics & Probability Standards — Jim Short, Ventura County Office of Ed

  • Pic Jim Short“Statistics means never having to say your certain.” The irony is that this is what makes math teachers uncomfortable with stats.
  • Teachers are avoiding the teaching of statistics, but the ponderous of the Performance Tasks on State Tests are based on Statistics and Data Analysis.
  • Statistics is more important than Calculus. (referenced TED talk by Benjamin Arnold)
  • From the GAISE Report,
    4 Components of Statistical Problem Solving
    I.   Formulate Questions
    II.  Collect Data
    III. Analyze Data
    IV. Interpret Results
  • You aren’t teaching statistics unless you are teaching modeling.Here are some great tools that we used in the session to generate statistical displays in a spreadsheet:
    g(math) {Google Sheets add-ons}
    Geogebra {box-n-whisker}

    Core Math Tools {NCTM}
    =norminv(rand(), means.d.)” {Excel Macro for generating a set of normalized data}
    Stats vs Prob

BREAKOUT: The Right Answer is Not Enough — Ivan Cheng, Cal State Northridge

  • PIc Ivan ChengWhat the teacher assesses is what the students think that the teacher values.
  • How is “doing math” defined differently under Common Core versus NCLB? How you answer that questions, determines how you teach and assess under the new standards.
  • After a test, if the teacher can’t state what the student misconceptions are, then the teacher needs to do some more digging.
  • Teachers should use assessment questions that intentionally reveal misconceptions.
  • Why “a” student missed a question is as important as which question they missed.
  • Clicking Smarter Balanced ASSESSMENTS (in SBAC navigation bar) will take you to documents that map targets to standards.
  • “Think about getting through to the kids instead of getting through the textbook.”
  • This sample question demonstrated why the students have issues with the new assessments. The students instantly think that the answer is “20,” because x = 20. Since 20 is not a given situation, they often choose “D: Neither.”

Inequality Sample

My Big Take-Aways

  • The achievement gap can be closed by the effective teaching of the Math Practices.
  • It’s all about the task!!
  • Two Big Words kept coming up: Meaningful & Equity. Equity is achieved by giving all students access to meaningful, high-level mathematics.
  • Get with the times, and start using technology in order to move from computation to deeper, higher mathematics.
  • There are some amazing tools available for Statistics tasks. This is a pervasive topic that needs serious attention and support.
  • Our assessments communicate what we value. The assessments are changing, because our goals are changing. Therefore, we teachers must change our values and practices.
  • We should all read Principles to Action.
  • The Region 10 Team is an amazing group of intelligent, passionate people. I look forward to seeing how we will put all these principles into action.

Region 10

Tiger Woods Gets a C- in Golf

Tiger SsshhMy district is seriously looking into standards-based grading. I have dabbled in it and see both the value and the pitfalls. Interestingly, I wrote the article below in 2002, long before SBG came into vogue and before the Common Core started flirting with Performance Tasks. While Tiger may not be the top golfer in the world anymore, it speaks directly to my hopes and concerns. I invite some push back here from the SBG gurus.

Earl Woods? Hello sir, thank you for coming to my classroom to speak with me about your son Tiger. Yes sir, I know that he appears to be doing well at home, but Mr. Woods, to be honest with you, Tiger is in danger of failing golf.

Currently his grade is a C-. I can show you the grade breakdown if you like. Certainly. As you know, there are approximately two hundred professional golfers. Each is ranked in various skill categories. Your son, Tiger, ranks as follows.

Driving Distance 2nd
Driving Accuracy 72nd
Greens in Regulation 1st
Putting Avg. 159th
Eagles 132nd
Birdies 2nd
Scoring Avg. 1st
Sand Save Avg. 4th

As you can see, Tiger does very well in most skill categories, but appears to perform poorly in two. Now, failing in two out of the eight leaves him with a score of 75%. There is a third category in which he is only slightly above average; therefore, he only gets partial credit. This diminishes his seventy-five percent to a 70%, and thus, he gets a C-.

My concern is that if Tiger were to falter in any one of these eight categories, he would surely fail golf. However, there is plenty of room for him to improve in these problem areas. He has an excellent work ethic, so I am confident that with a little more effort, Tiger will succeed. Mr. Woods, thank you for your support in this matter.

Can you imagine ever having this conversation regarding Tiger Wood’s ability as a golfer? How does the best golfer in the world get a near failing grade in golf? The answer is in the assessment.

The rankings given in the previous scenario are true. Furthermore, from this list, the All-Around Rankings of each professional golfer is determined by adding the golfer’s relative rank in each category. The lower the score, the better. Adding Tiger’s categorical rankings places him 10th in the “All-Around Rankings.”

In other words, there supposedly are  nine other golfers in the world better skilled than Tiger Woods. Being in the top five percent of all golfers in the overall skill category would certainly raise his grade in golf to at least a B, if not an A. However, he still does not rank as the top All-Around player in the world.

If we change the assessment, though, Tiger fares much better. For instance, Tiger is the richest golfer in the world. He is number on in season earnings and is the all-time career money winner. His is also number one in the World Rankings. The World Rankings are based on how well a golfer finishes in tournament play in comparison with the strength of the field. In other words, how well does the golfer compete?

Tiger Trophy

Tiger wins the most tournaments and wins the most money. In my mind, and that of many others, that makes Tiger the bets golfer n the world. Yet, I am basing my opinion on his performance as a golfer rather than his skill as a golfer. Analyzing two other golfers can show the difference between the value of skill and that of performance. Do the names Cameron Beckman or John Huston ring a bell to you? No? Me, neither, and I am an avid golf fan. The reason that you do not know these names is that these two people are average golfers in the World Rankings. (They don’t win much.)  Yet, they both outrank Tiger in the All-Around (2nd and 9th respectively). According to certain forms of assessment, Beckman and Huston are better than Tiger Woods.

Beckman Q2

We can see this scenario being played out in our classrooms. The Beckmans and Hustons get higher grades than the Tiger Woods, because too much of our assessment is based on individual skill rather than on mathematical ability. The Tigers excel in the performance assessments that we occasionally offer, but these are so out weighed by itemized tests that the All-Around Ranking (skill) wins out over the World Ranking (performance),

A more appropriate balance of skills, testing and performance assessment in our classes may send our most underachieving mathematicians to the head of the class.

Beavis and Barbie Revisited

“I thought your article was brilliant. My teachers hated it.” Those bb_heads closewere the words of my friend who is the Instructional Coach at his high school. He was referring to an article that I wrote several years ago titled Barbie and Beavis: Holding Students Accountable … to What? In essense, the article questioned whether teachers were basing grades on competency or compliance. The point I made was aligned with Robert Marzano’s question “What’s in a grade?” By having his colleagues read my piece, the coach was obviously challenging the traditional practice of grading students on effort rather than performance. Interestingly, the teachers pushed back, insisting that a grade absolutely should be all about the effort.

I am not surprised that these old school habits are still pervasive in the age of accountability. I just found it curious that the teachers were so vocal in publicly defending a practice that has been repeatedly debunked by both research and antecdotal experience. Afterall, where is the evidence that any school has shown drastic improvement by flunking a bunch of kids for not doing homework?

I wonder if the arrival of the common core and it’s significantly different assessment strategy will force teachers to rethink and retool their own grading practices or will they simply continue with the same-old same-old and just tolerate another annoying state test once a year.

(To read the original Beavis & Barbie article click the title below)

Beavis & Barbie: Holding Students Accountable … to What?