Monday, July 9, 2012

4 Point Rubric

When I started this journey three years ago, I sat and listened to what Dr. Marzano was saying about the need for a new scale for assessing and grading.  I heard him talk about the 100 point scale being inaccurate.  He says "it is like measuring the physical growth of a student throughout the year but using a measuring tape that changes how long an inch is from one measurement to the next."  Formative Assessment and Standards Based Grading by Robert J Marzano, page 41.  He did an activity with the people in attendance to prove his point.  I was amazed at how a group of educators could be so far apart when scoring on the 100 point scale!   He then furthered this activity, showing how we would all agree on the same score if we used a 4 point scale.  (Formative Assessment and Standards Based Grading, Chapter 3)  I was sold!   

With some help from a couple of colleagues, I spent the next 6 months developing rubrics, trying them, revising them, before being challenged by my admin to come up with a general math rubric.  When I look back now, I realize how poor those first few rubrics were!  We were trying to take what we had from an assessment and fit the results into a 4 point scale!  It wasn't working!   So we sat down and read more from Dr. Marzano (he speaks of this scale consistently in many of his books!) and adapted his 4 point scale to fit our needs.   This is what we came up with:

Level 1:  This is pretty much bang on to what Dr. Marzano recommends.  We don't define skills/processes/knowledge/etc. at this level.  The student is simply inconsistent or needs help with the outcome.  

Level 2:  Dr. Marzano defines this as "simpler content" (Formative Assessment and Standards Based Grading, page 48).  We defined it as the "basic level of understanding" for the outcome.  We expect all students to be able to achieve this level to receive their course credit.  These really are the basic skills, and if a student is unable to be successful with these types of questions, they are not ready to move on.

Level 3:  Dr. Marzano defines this as "target learning goal"  (Formative Assessment and Standards Based Grading, page 48).  We have also set this level as the target level of understanding for the outcome.  We look at what the OUTCOME says needs to occur (not necessarily the indicators), and make sure that they can achieve this for level 3.  

Level 4:  Dr. Marzano defines this as "more complex content" (Formative Assessment and Standards Based Grading, page 48).  I would have to say we again, are pretty similar.  Here is where we look for deep understanding.  Many application questions are at this level.  Error Analysis is often found here.  We look for explanations of work, theoretical understandings as opposed to simply memorizing a process.  

Once we had agreed upon what each level would mean, we then had to sit down with each outcome, decide if we would leave the outcome as one piece, or "chunk" it ("unpack it") into smaller, more communicable pieces.   We then had to create outcome specific rubrics that following our general rubric.  This is what takes the most time!   We have discovered through experience that sometimes you will try one rubric only to discover that it needs to be tweaked/combined/broken up and that that is okay!   We will likely never have the "perfect" rubric!  What we do have are rubrics that are allowing us as teachers to be more consistent with each other and between students.  We are also now very transparent for students and parents with what is expected!

We have also discovered that we often have two types of outcomes.  The first is an outcome that has definite progression in the learning.  These outcomes are easier to make the rubric.  For example, solving linear equations - our math 9 rubric has level 2 is solving when there are up to three steps and no fractions; level 3 is solving any linear equation; and level 4 is situational/error analysis/explanations/modeling, etc.  

The second type of outcome is harder to define.  This outcome is one where there are many distinct pieces and not always in sequential learning.  We have also been encouraged to stay away from quantifying levels (ie.  "able to do three of five of the following...").  So this has made these type of outcomes the most difficult to write a rubric for.  Here is an example of an outcome from the Saskatchewan Math 20 Foundations course that is of this type.  The description in the colored boxes are our general math rubric I described earlier.

What we decided for this outcome was that the level 2 skills were basic definitions.  There was no manipulation of formulas/equations/etc.  We felt that because of the formative procedures in place a student would have lots of feedback and by the time the end came along, they should be able to answer all of those terms successfully.  The level 3 skills require some sort of manipulation or solving.  There is more to these skills.   Level 4 is still a deeper understanding.  You'll also notice that we wrote these in student friendly terminology.  When a student reads the rubric they read "I can determine..."

Every "graded" assessment, no matter what type of assessment (quiz/exam/performance task/oral/etc.) will be graded using the specific outcome rubric.  This allows for tracking growth of learning.  It is a consistent scale.  It does not change from assessment to assessment.

We have now created these specific rubrics for all of the Saskatchewan Math 9 - 30 curriculums!  We are constantly tweaking them, but there is a starting point!   We have also decided as a department and extended division PLC group that we will share these rubrics if others want them.  A person might not agree with every one of the rubrics, but they are a starting point to be used.

On a side note, we do assign levels of understanding using half points as well... 0.5, 1.5, 2.5, 3.5... but we do NOT define these with skills/processes/etc.  We use what we learned from Dr. Marzano in that these are used for students who are completely successful with a lower level and partially successful with a higher level.  I believe the half points are very important for a student so that they can see growth in their learning.

It has been two full years of using the 4 point rubric instead of the percentage.  Our students do not see a percentage on ANYTHING, even report cards, until the final report (grades 10 - 12 only) and ONLY because the Ministry of Education requires it.  It did take some time for students and parents to adjust to this change, but my last set of parent teacher interviews in April were the first time I did not have one parent ask about a percentage!  I feel we are making progress.  We have been communicating a lot better with parents, through letters, videos and emails as to why we are changing.  Once you explain to them that this is a much more accurate representation of what their son/daughter does or does not know they buy in.   I will tell them that in the past, if they saw a 75% did they really know what it meant?  Did it include behaviours?  Did it mean that the student scored 75% on every outcome?  Or did it mean that the student had 50% on three outcomes and 100% on three outcomes?   Did it mean the student had been successful with all outcomes?  Did the student improve their learning through the course?  A 75% does not tell you much of anything other than it norm references kids and people have their own opinion as to whether 75% is good or bad.  It is often referred to as "average".  However, if you see that your son/daughter has level 3 on outcome FM20.9, you can read the rubric to see what they have been successful with and what they still need to work on.  Our progress reports (which I will blog about soon), will also show what the student's levels of understanding were over time so that the parent and student can see if learning is occurring.  The mark is pretty transparent.  Nothing is hidden.  Since making this change I am very confident in defending a student's "grade".   When a parent comes in and asks what their son/daughter still needs to work on, I can give them an accurate answer!

Parents are also concerned about University entrance.  How will this affect their son/daughter getting into University?  I tell them two things.  First, we will still give a percentage at the end of the course so that they can apply (we have a conversion that is common to our department).  Second, I tell them that this is far superior to the past system, as now if a student knows that they want to go into a program that has very competitive entrance requirements, the student knows what they need to learn to have a deep understanding of each outcome and can work towards those higher "grades".  In the past it was often a one shot deal.  You learned the outcome, wrote the test, and moved on.  Now we track growth, encourage growth, provide opportunities to improve, and basically give a checklist of what needs to be done at each level of understanding.   Parents accept this when it is explained this way.

This has been a huge philosophical shift for everyone involved and although we are not all at the same place in this shift, we are moving towards a common goal!  That is we want all kids to learn!  We need to find the best way for this to happen and to me, the 4 point rubric is a definite piece of this journey.


  1. Thank you for sharing this! My grade level team and I are considering adopting a 4pt scale as you describe here for all subjects for our 8th Graders. This piece was very helpful. Our administrators have also expressed a need to give a percentage grade at the end of the term (ugh!), so if you don't mind my asking, how do you go about determining that at the end? We're considering using a "Percentage of objectives passed" to determine a final grade. Thoughts?

  2. We convert to a percentage only for our grade 10 - 12 classes. There are two steps. First, the student must have met at least level 2 on EVERY outcome. If they have not done so, then they are incomplete and do not get a mark. There will be a blank spot on their report card. We no longer "fail" a student. I plan on blogging about this soon! Anyways, once a student has at least level 2 on all outcomes, we then average the current levels of each outcome. We do NOT average all assessment pieces within one outcome to get the current level. For that we look for most recent and most consistent and use our professional judgement. However, because we must end up with one overall percentage, we have found the best way to do this is to average the current level scores. We have then developed a conversion chart (which is always open to discussion!). Because a main purpose of a percentage in our Province is for University entrance, we wanted to be fair to our students. Our benchmarks are this: level 2 = 60%, level 2.5 = 75%, level 3 = 90%, level 3.5 = 95% and level 4 = 100%. There are not many schools on this system (in fact ours is the only division that I know of at this point!). Some of our teachers think that level 3 = 90% is too high, but my argument is that many students in our province that are doing level 3 work are scoring 95 - 100% as our level 4 questions are often not traditional math questions. I would have rarely asked these types of questions in the past or assigned very little value to them.

    Good luck with this! It is a lot of work to begin with, but very rewarding in the end! If there is anyway you can convince your administration that a percentage for 8th graders is not necessary it will make a lot more sense!

  3. Thanks for the post, Carey!

    - How do you keep track of all these rubrics so they're aligned across grade level and department? And, what's the process for continually improving these rubrics? My school is moving to SBG next year and I'm wondering how to do this.
    - I'm finding that there are two types of rubrics as well, and am trying to come up with better names for them. If you come up with some, please let me know.

    1. Good luck with next year! It will be a lot of work, but it is worth it in the end!

      I'm not sure I'm going to answer your first question properly, so let me know if you need more! Our PLC group started this at the grade 9 level and have moved up one grade level at a time. We follow our general math rubric when assigning skills to a level. This allows our rubrics to keep a consistent format. Within our particular school we have 14 math teachers and all teachers teaching a certain class will use the same rubric. We meet during our PLC time to do some common grading to make sure we are all on the same page. At this point the rubrics we are using have not been made mandatory outside our school, but there are some other teachers in our division that are using them.

      As for continually improving them... we meet or do group emails when we don't feel one is working well. This can be during the course of teaching the outcome or later in the semester. At the end of the first semester of implementation we will meet as a group to discuss if any major changes need to be made. Some of the changes we have made are combining outcome chunks or splitting an outcome. Other changes are reassigning levels.

      I hope this goes well for you! If you have a group to work with it is a lot easier than doing it all on your own! If you are in the States, I believe Marzano Research has some exemplars on their site for the Common Core Standards that might help get you started.

    2. i believe marzano's approach is a waste of valuable time. as if grading were the problem. haaaaa have not seen any evidence that this approach has any effect whatsoever. rubrics, power standards....please. let us teach stop reinventing the basic. no respect for marzano or his marketing of education for his sole profit

  4. I am concerned about grade inflation and Marzano's integer grading scale. Do scales like this inflate grades? How do you ensure that students who pass have enough understanding of the material?

    I'm asking these questions because the integer rubric appears to be very forgiving for underachieving students.

  5. I'm not sure I understand what you mean by the integer grading scale and grade inflation. The way we use the rubric is to show growth of levels of understanding. Can you define underachieving? We do not combine behavior with understanding of outcomes/standards. If a student demonstrates that they understand the outcome, it doesn't matter what their behavior is or how long it might have taken them. When we HAVE to convert to a percentage, we have a conversion chart that we use. Maybe I'm not understanding your question properly.

  6. We are starting to write rubics and would love to see more of your examples as we are also reading Marzano's book and like what we see in your example above. If you'd be willing to share, it would give us so much more to go on.. My email is and I teach Math in Muscatine, Iowa.. Thanks so much for being a Pioneer in this process.

  7. Our math website has links to our rubrics:

  8. pile of crap! marzano is selling same product as anyone else. bizarre how he considers himself to be an expert. barf

  9. Well I just hope the carpenter has the patience and understanding when watching an apprentice make boxes inside boxes to make a plus sign that gives the answer to do a multiplication problem on the two by four, instead of the number over a number and working it.

    And relating to old medical practices is not even a comparison in my book. The right comparison would be more like, we use to scratch marks on cave walls now we use pencil and paper to make the same scratch marks and still getting the same result.

    It is new math. Math tricks. Like the one math trick where you guess a number and then go through a series of functions and get the same number every time to make yourself look like a magician to match the number wrote down in the envelope. Math has many ways to solve for the answer. Why not let people find out for themselves if they want to know the other properties the make the same conclusion. It's like math has started over from say that learning the place values of numbers ( the one, tens, hundreds and so on) was not enough. Lets draw some boxes.

  10. Sorry wrong post. ignore previous. Its late here.