[AnE] SBG - where I am and where I want to go

Previously on AnE...

"Assessments are not just in written form.""It is what we do with [assessment] that determines the function."

This time I plan on tackling a different but related topic of standards based grading (SBG).  This is quite a monster of a post... so be prepared.  I will begin with some background first...

I am open to different definitions.  In fact, I love reading about slightly varying definitions because it helps frame the conversation.  But for the sake of what I am about to talk about, it's important to indicate what I take SBG to be.  Let's first establish the difference between norm-referenced vs criterion-referenced interpretations of assessment.

Norm-referenced is something that we math teachers don't -- and shouldn't -- use.  It's the idea of the bell-curve.  Criterion-referenced involves the idea of establishing scores according to how well the student matches up to established criteria.

I've never graded with "marks" where a question is out of a certain number of "points." Okay, "never" is pushing it.  In the very beginning while I was at my first practicum I had to grade with marks, but ever since that point I haven't done percentages or marks.  I have always believed it's better and (with experience) easier to evaluate based on achieving a standard or not.  There are lots of examples we can take a look Math Mistakes, a beautiful website edited by @mpershan.  I will use one of my own students's example instead:

Nothing special.  It's a relatively closed question with one right answer.  Regardless, we can take a look.  The student knows a couple of things.  They know about the general concept of what an optimized shape with the biggest volume is - given a set surface area.  They are not efficient with establishing the formula, and somehow their solving step went to a 6 instead of dividing by 2.  But who's to say that the mistake of cube-rooting is worth more than others?  I believe it's more meaningful by looking at what the students understand and what they don't understand.  First and foremost, we're looking at how much of the standard they have achieved.  Instead, we begin with the expectation of what we want the student to achieve.  Which according to our curriculum, it's this:







Note the "investigation" part.  That's important.  The Ontario ministry of education also provides some "specific expectations," which can be helpful.  One of them reads like this:


















This problem is not quite an open question that will fulfill the expectation, but the next is more of an open question that will have opportunities for that.  That's really all it's about -- opportunities.  Opportunities for students to demonstrate their mastery of expectations, skills, or standards.

There's a lot of conversations that need to happen around the idea of SBG, which as I mentioned in the previous post, I am extremely excited about.  Daniel Schneider (@mathyMcMatherso) recently wrote several pieces on assessment, like this one.  He hits several important points in assessment, and the piece has gotten a lot of buzz - which is also exciting to me.

After attending several sessions at OAME today, I came to this realization:

Interesting, and exciting as well.  I want more though.  I need more.  I recently had several wonderful conversations with Jonathan Newman (@newmjh3) on Tiered assessments and Standard based assessments.  I quickly shared what I did last semester with him, and he came up with the wonderful idea of using Google spreadsheet to develop something similar.  We're still working on it.  There are a lot of awesome things that we'll talk more about too.  But in any case - let me finally frame the meat of this post.

SBG - Where I am

I begin with something like this in my spreadsheet:

and each assessment is recorded in the vertical columns.  But then I use a few formulas to make it automatically visual:

There are a few things here

1. Easy to use
Because of how I set it up, there is just 1 visual tab (and not one for each student).  I just have to change the student name, and everything will automatically change to reflect student achievement.

2. Proficiency levels
Instead of percentages and arbitrary points, I get an overall look at whether the student has achieved understanding.  In the example given, there are 2 main expectations shown.  Each assessment is chronological, so we can see a clear trend of improvement.  I also use different colours to indicate what forms and types of assessments they are (I will probably talk about forms and types of assessments later).  Students get a clear picture of what they need to work on.

3. Incompletes do not count against them
I separated the incomplete assessments as just missed opportunities.  They are not rigid "0's" that students received which transfers to some sort of percentage after mysterious averaging functions.  Incompletes are simply missed opportunities.  Lack of evidence does not imply that students do not understand the concepts.

4. Multiple opportunities
Students will always be able to come for reassessment.  It's a loaded statement, but I will unpack this in a later post.

In addition to this form of reporting student achievement, I have also started to integrate these elements into my Ninja Board.

It looks a bit like this on the back of my classroom wall:

As students gain understandings of masteries, they also gain these crests.  There are essentially 11 overall expectations in the course that I am referring to, and each correspond to a crest that I have created/found/edited.

There are clearly more that I need to explain about the various aspects that I am doing with assessment in class (construction of a sample assessment, for example), but I will get to those later.  I want to get to the next part - which is where I want to go with assessment.

SBG - where I want to go

This is more important to me.  This is the reason why I have been looking at how others have approached the same concepts.  This list is open to change, but I don't think the main points will alter very much.

1. Completely projects-based spiral curriculum
I alluded to this before here, and then here.  Essentially the idea is this.  Opposed to the U.S. curriculum, where topics of mathematics are separated to Algebra and Geometry...etc.  In Ontario, Canada, our curriculum revisits ideas in what is called a spiral curriculum.  Recently, I became interested in the idea of creating a tighter spiral within a classroom.  The main idea is this:

• Everything is activity driven.  No lectures.
• All concepts covered are done through rich activities.
• There are no units.  Just problems.

No Units.  that's really what I am trying to get at.  Rich problems for mathematics are everywhere.  it's up to us to harness them.  through this method, concepts of mathematics evolve naturally as students work through interesting problems throughout the year.  They learn to create their own problems, and learn to solve their own problems.

This approach is actually perfect for mediating the issues surrounding re-assessment.  If topics are revisited naturally through each problem and activity, then there is no problem with reassessment.  They are reassessed anyway!

2. Focus on Mathematical Processes

Within the Ontario curriculum mathematics document (grade 9-10 example), it describes 7 mathematical process expectations: Problem solving, communicating, connecting, reflecting, representing, selecting tools and computational strategies, and reasoning and proving.  These skills are common and are suppose to flow throughout every grade.  Students learn to employ these skills through the different "content expectations" described before.  I have been doing process portfolios to focus on these important transferable skills.  However, this is not a focus in all classrooms.  I want/need to bounce more ideas of how to assess these important skills.  Hopefully this blog post will garner some interested people who are doing similar things with these transferable skills so we can have good conversations around them.

3. Improving evaluative properties of alternative assessments

This is pretty much my M.A. direction.  What are valid methods of incorporating observational assessment evidences of student achievement?  What qualities do activities need to share in order for alternative assessments to thrive?  If students are demonstrating understanding, does it really make sense to make them sit down, and to write out their understanding?  Should the additional step of "writing it out" become the determining factor of student achievement?  ...etc.

Of course, there are lots of aspects that I am interested in as well.  My conversations with Jonathan has been focused on the feedback piece.  Implementing Google Spreadsheet is an excellent way to achieve this.  Hopefully we'll both get some off time soon so we can chat more about this.

Leave a note if you are interested in talking more about this.  I am currently pretty sick... so it's possible that I am lacking in a lot of explanations.  But don't hesitate and leave a note for elaboration.