My Implementation of SBG for Math

I have been thinking through how I want to implement SBG for my physics class, and that got me thinking about my implementation of SBG for my math classes and how I think it will have to change for physics.  I think this is an appropriate time for reflection on the past.  I will talk about how I set up my classroom and then talk about why I do what I do.


What I Do 

I feel that my SBG system for math is more accurately describes as Skills Based Grading instead of Standards Based Grading.  I have a one to one correlation between skills and test question types.  I would give a Skills Test every week, and that test would be a collection of skills.  The class before the Skills Test I would give a Skills Test Preview.  Every skill would get its own score (see grading scale below).


Here is the grading scale I have used when grading these Skills test

A – 100%

B – 85%

C – 70%

Not Yet – 40%


1)  Every skill is tested (at least) twice.

2)  The first time a skill is tested the skill is an easier version of the problem.  Because the first time a skill is tested the version is easier I will only give a maximum score of a B.  The second (and beyond) time a skill is tested will have a maximum score of an A.

3)  My gradebook will only remember your highest score on a skill.

4)  Any skill for the semester can be retested with prior notice.  I allow the retesting of one skill a day.


Why I Do What I Do

Of course no ideas are original.  I switched to a Skills Based Grading system during the 2009-2010 school year.  This article by Dan Meyer was my inspiration (The Comprehensive Math Assessment Resource) along with articles from Marzano.  I have made some changes and tweaks for this system to work in my world.

The one to one correlation between skill and problem type was necessary because I only have a two-dimensional gradebook (my school uses the gradebook in Aeries SIS), with the dimensions of student and skill leading to a single score.  I wish we had a three-dimensional gradebook, where each student and skill can lead to multiple scores, but I don’t see that coming to Aeries any time soon and I am unwilling to use a separate gradebook outside of Aeries.

Currently my school has a 7 period modified block schedule, where we see all classes on Monday, we see all odd period blocks on Tuesday and Thursday, and we see all even period blocks on Wednesday and Friday.  I never like to surprise my students with assessments so we would have a preview of the skills test every first block (Tuesday and Wednesday) and a skills test every second block (Thursday and Friday).  I will give students time in class during the first block to go over the preview and then I make sure we go over every problem in class.  Then the solutions are posted on my website.  As I tend to have a new class or two every year (I have taught 12 different preps in my 7 years of teaching at my current site) I use the previews as a time to write a first draft of the test.

I have modified my grading scale to something simple.  I use a 40% as the lowest score a student can receive on a test because of this article (The Case Against the Zero – CCRESA).  I used to have a score that corresponded to 55% (so a consistent 15% increase between scores) but I dropped it because I only wanted a minimum competency on a skill, as represented by a C (70%), to count in the gradebook.  I never liked deciding whether a student got a 40% or a 55% because they were both not showing competency.  And eliminating a score (and a choice) it made it even easier for me to grade.

My gradebook only remembers your highest score because I had no straightforward way to record the history of the scores on the skill.  As I enter in the scores I only change the score if the new score is higher.  And I love having the first time a skill is tested to make it an easier version of the skill and not allowing students to earn the full score on that version.  Everyone gets tested twice and gets feedback after the first testing.  Students get the confirmation that they know (or do not know) how to solve the skill.  And everyone is trying the second time a skill is tested because everyone is trying to get a score of 100%.  It is pretty amazing how that works for students regardless of skill level.

I have gotten away from students recording their own scores on a separate paper.  I never enforced that in an authentic way.  Students would fill it out by looking at their grades online instead of as they received their papers.  I didn’t feel like that was the behavior I wanted but I also knew that I didn’t want to enforce the desired behavior (recording their scores as they received their papers).

Every student can retake a skill throughout the semester.  This implementation is one of my biggest disappointments, though.  I cannot get students to retake tests.  I only allow retakes outside of class, and even though I am usually in my classroom during break and lunch I don’t have many students asking for retakes.  I only allow one retake for one skill a day because I really want students to learn one skill, show me, and then learn something else.  Also, it saves me from a student coming to me in the last couple of days before a semester and asking to retake eight skills.  I do not give a skill retake on a day that I help them through a skill.  I will give students complete practice problems before they retake the skill to make sure they are up on the knowledge.  I want them to see that their scores are not determined by a magic 8 ball or by a lottery.  Their skills are determined by their practice and learning.  I expect them to practice and show me their learning.

I wanted to make my life easier in the long term by creating problem types in ExamView that would let to create multiple versions of a test (my students all sat in groups of 2-4).  I learned how to program questions in ExamView and I have created test banks for my Algebra 1, Algebra 2, and Trigonometry classes.  Those test banks made it really easy for me to make test retakes and practice for students.  And while it is a lot of work up front to create those test banks the effort did pay off as I taught a class multiple times.

Below are examples of my tests and previews.  Notice how they are similar in format but notice how the skills and scores summaries are slightly different at the top.  These tests were all created in Word for my Integrated Math classes.

Sample Skills Test Preview

Worked out Solutions to the Preview (reviewed in class and posted on my website)

Sample Skills Test

I hope this helps to explain how I have implemented a skills based grading system in my math classes.  I have tried to be deliberate with all the decisions I have made.  I want this system to be focused on student learning while being manageable for a teacher to implement.  And I am looking forward to showing how my physics class will be similar and different.

Beginning to teach lines Part 1


So I know the second half of my Algebra 1a class is going to be focusing on the linear part of Algebra 1.  I want to look at multiple representations of linear relationships, and I want to tie these relationships to something they can see and measure.  Here is what I have done and I will also talk about what I want to do.

Start with solving proportions

I have known that I ultimately want my students to be able to interpret position versus time graphs, so I decided to start with introducing ratios and solving proportions.

I started the worksheet above with this idea from Sarah Hagan (of Math = Love Blog fame).  I wanted to stay away from even mentioning cross multiplying when solving proportions because I see students try and use it everywhere… regardless if it applies or not.  So I really emphasized solving an equation techniques.  I also wanted students to get used to working with units.  These numbers have meaning.  Please state the meaning.
We spent a lot of time writing and solving proportions.  Some were doing really well with it.  I then wanted to begin a graphical representation of ratios and all the proportion solutions.

Students were expected to come up with their own scale for the graphs.  Also, I have been emphasizing all year long that a graph always needs three things, the quantity for both axes, the units for both axes, and the scale for both axes.

So now I wanted students to find other solutions from looking at the graph.  Also notice that I am asking students to write the ratio of distance over time.  Again, that is to preface our slope discussion, and to show that this distance over time has meaning!

There is more to come… part 2 will be up soon.

Decimal Scales

I used some of the decimal scale slides from this site today.

It really got my Algebra 1a students thinking.  And it was a great lead in to us talking about graphing and determining a scale for the axes.  It really helped to bring out their misconceptions of scales having different size intervals.  This was a great exercise for them today.


Quit saying “but I am not a math person.”

Thank you, Rhett Allain

Quit saying “but I am just not a math person.”

I really believe that society just allows people to be bad at math.  It is socially acceptable for adults to say “but I never got through Algebra.”  That is a confession of math illiteracy.  But adults never say “wow, reading, that is so hard!  I don’t read.”  Math illiteracy is socially ok but language illiteracy is not socially ok.  Really, there should not be a difference.  Let’s do what we can to change it.