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.

My thoughts on Final Exams in Math

We (meaning math department) have been questioned lately on the necessity of final exams.  

"Are they necessary?"
"If a student demonstrates mastery earlier why do they need to write them?"
"Can you find an authentic task instead?"

These are just a few questions we've been asked the past couple of years.  Math is likely one of the last subjects where a comprehensive final is still given.  Now, having said that, we have changed our procedures and approaches to writing the final exam.

Instead of calling it a final exam, it can be looked upon as a summative assessment.  I believe that all of the assessments, whether termed formative or summative, that are done during the course of the semester are really formative in nature as the students are able to and encouraged to improve their level of understanding on any outcome at any time until the "summative assessment" (final exam) is given.  Even at that point, if a student is still not meeting the basic level of understanding (level 2), they are given opportunities to improve.  We have also moved our summative assessment to about three weeks prior to the end of the semester.  There will be one or two outcomes that are not on the summative assessment, as that is what will be done in the last three weeks.  We also spread the summative assessment out over two - three days and the students are told which outcomes will be on each chunk.  Our summative assessment consists of questions at each level of understanding (2, 3, and 4) for every outcome.  By moving the assessment up we have accomplished a number of things.  1)  They are not stressed about all their other final "projects" that need to be done in a short period of time.  They can focus on math.  2)  We are still testing understanding over time and at the completion of the semester (as stated in our curriculum!)  3)  We have time following this assessment for those who still have not met the basic level of understanding on an outcome to continue learning it  4)  it gives teachers time to evaluate and enter levels of understanding for all outcomes

Some will question why a student who got a level 4 two months into the semester should have to write that outcome on the final.  When I think about the 10 000 hours needed before you master a skill (Malcolm Gladwell, The Outliers) I shake my head at labeling a student "master" of a skill they have practiced for maybe 5 hours!  Most outcomes are less than 10 hours of in class time!  And yet we expect a student who has "mastered" the outcome at the time will actually remember this in a few months after new learning has been done!  Maybe our level 4 questions/activities need to be stepped up a notch, but at this point I am not comfortable that being a level 4 two months in will mean you are a level 4 at the end of the semester.  I only had a few students who demonstrated a level 4 more than once on an outcome and of those, most, but not all, were able to achieve a level 4 at the end.  Until my data shows that they will ALL remain at a level 4 I feel they still need to complete the summative assessment.

I try to teach the more complex outcomes or ones that are so critical for the next class, early in the semester so that we can spiral back through them over the course of the semester.   We do this through entrance slip questions.  I believe this really helps students improve their understanding of the outcome.  In fact, many students improve their level of understanding on the summative assessment at the end of the year!  This year I had 50% of my math 9 class score level 4 on outcomes on the final exam!  The majority of students improved their current levels of understanding so learning was achieved over the course of the year.  I was super impressed!

We do not average the scores of all of their assessments, we use professional judgement and look at most recent and most consistent levels.  The students know that if they improve on their summative assessment then that will be their current level.  I am always impressed at how well the students do at writing these assessments, when they know it can impact their grade in a positive way.  In the past, when a final was worth only 25% of their mark, the students would know what they needed to pass the class and thus I marked many crappy final exams!  Or they would know that a great score on the final would only boost their mark a few percent so it wasn't worth their time to prepare for it.  Now the students know they must demonstrate a basic level of understanding (a little bit of pressure, but this is truly a BASIC level, if they don't know these questions they aren't ready for the next level), so they actually try and don't leave entire pages blank!  They also know that they can improve their score and overwrite previous "mistakes" so there is motivation to prepare.

Math is built upon prior knowledge and I think it is really important that a student demonstrates at least a basic understanding of the outcomes at the end of the semester.  I want to know that they are ready for the next class.  If they have a  basic understanding it means that I might only have to do a quick refresher of the skill instead of having the student look at me as if I'm speaking Greek and they've never seen what I'm doing before!   This occurs in students that have not even met the basic level of understanding.  I want these students to do additional learning before I see them at the next level.

So my question is "Is math a unique subject where some sort of a summative assessment needs to take place towards the end of the semester?"   Does this have to be a written assessment?   Does anyone have a project/task/assessment that they do instead of a sit down written assessment that will test each outcome?    Should all students have to complete all outcomes or should we allow "recommends" or "opting out" if previous levels of understanding were 4's?  I would love to hear thoughts and suggestions from other math teachers!  I'm always willing to learn and share ideas!

Ready For A Change

In June 2009, my principal suggested to me that I attend a Marzano/Pickering conference in September.  I didn't have a clue who they were, but I didn't tell her that!  I didn't really want to go, until she said it would be a night away from my kids.  At that time they were 1 and 4 and I wasn't getting any sleep!  She sold me!  I was going.  It was one of the best decisions of my teaching career.

I went and sat there and listened to Dr. Robert Marzano speak about formative assessment and standards based grading.  I saw the data on what research showed to be effective and ineffective.  Sadly I realized that many of the ineffective strategies were things I was doing.  He inspired me to make some changes.  I must have been at a point in my career where I was ready for a change.  I thought I was going to make a simple change.  I enlisted the help of our division math consultant to create a visual chart of the student's progress in each outcome.  The research showed that this strategy would help to improve student learning.  I thought it would be a simple process.  Boy was I wrong!  We soon discovered that it was a lot harder to show progress on a scale out of 4, when everything I was doing was based out of 100%!   Thus this lead me to one of the most difficult, but enjoyable years of my teaching career!  The learning curve for me this year was not a curve, but pretty much a vertical climb!  However it was a very rewarding climb.  It took us half a year of many bad rubrics to finally get to a place where we could develop a general math rubric to guide all of the specific outcome rubrics.  A few more math teachers jumped on board and through collaboration we became more comfortable with creating rubrics and assessing outcomes using a scale instead of 100%.  We were on our way...

Why I am blogging

I have been thinking about blogging about education for a few months now.  I blog about my kids, so why not about my job.  My job is not what it used to be.  The teaching profession and education system have been changing since I started.  There are a lot of misconceptions about what is going on and I wanted to share everything that I love about my job and the education system.  I want to be able to explain why the system is changing and why I believe it to be a good thing.  I want to share the wonderful stories from my classroom and share the successes that I see on a daily basis.  I want everyone to know that I see students LEARNING on a daily basis and I love it!  

I AM a teacher.  This is MY journey.