Monday, October 26, 2009

Our Grading System

Standards Based Instruction

We decided a few years ago that the sequence of our texts don't really work for us.  As a result, we began teaching one standard at a time. We have taken our state standards set up a sequence and pace  in a way that makes sense to us.  Some of the standards we have broken down into specific skills and these skills are what make up our gradebook.

Common Formative Assessment

Once we have done our initial classroom instruction, we give a common multiple choice assessment.  This assessment is graded on a 1-4 rubric.  A students next step is based on how well they do on the assessment which is a pretty fair cross-section of the different problems a student may be expect to do on the given standard.  We determine the initial score based on the percentage of problems they get correct.  85-100% = 4, 70-84% = 3, 55-69% = 2 and below 55% = 1. 

Less Than Proficient

The level of understand a student demonstrates determines what happens next.  If a student scores a 1 or 2, he will do a series of activities that may include defining basic terms and demonstrating pre-requisite skills.  Once finished with these activities, the student will then take the problems that were missed on the CFA and not only correct them, but explain what went wrong (verbally or in writing) and how to work the problem correctly.  Students who score a 3 on the initial assessment are just required to make the necessary corrections with explanation.  Once the corrections have been made, the student is then given a re-assessment and the new score replaces the old score in the gradebook. 


Although  students may get 100% of the problems correct on the initial assessment, we still give them a 4.  Our reasoning is that the multiple choice test doesn't allow our students to demonstrate understanding that goes beyond classroom instruction, but it does allow them to show proficient understanding.  Students who demonstrate proficient understanding on the assessment are given the opportunity to turn the 4 into a 5 by choosing from two categories of activities.  Examples of activities may be creating a mini lesson, peer tutoring or some other project agreed upon by teacher and student.  The second activity is some sort of writing assignment that may require the student to explain the process or describe what skills a student may need in order to be successful with this standard.  Once a student has completed these activities and has shown the ability to explain his work the score in the gradebook will be turned into a 5. 


At this point, I can say that the strengths of this system are:

  • Students grade is based on what they understand and not a mere accumulation of points.

  • Students are allowed to re-assess and new understanding replaces old understanding in the gradebook.

  • Students seem to understand where they are having trouble and what skills they need to remediate.

  • Learning has become a conversation between teacher and student because in order to re-assess, student needs to articulate previous misunderstanding and current understanding.

  • Students have a choice on when to re-assess.  They can work at their own pace.

  • Students also have some choice on which activities to do in order to demonstrate understanding.

  • The dross has burned off the grade.  Students' grades are based on what they understand rather than things like effort,  homework or extra credit.


  • Students have to take more ownership of their learning which means they have to un-learn some bad habits.  Not sure that it is a weakness in our system specifically or an indictment of the educational system in general.

  • Teachers are having to re-think classroom management when students are working on different activities.

  • We are having to decide if some of our standards actually lend themselves to "advanced" work or if later standards are the advanced version of some previous standards.

  • Need to develop more advanced activities for students to do while working towards a 5. We allow for students to create their own activity as long as it has been agreed upon by the teacher, however many students don't know what to do with that kind of freedom. 


  • What's the best way to take a series of 1's, 2's, 3's, 4's and 5's that are based on levels of understanding and turn them into a letter grade? Do you use mean, median or mode? 

  • If we go with some sort of average from 1-5, what percentage do you use for an A, B, C, D or F? Currently we are going with average where > 4.5 = A, > 4.0 = B, > 3.0 = C, > 2.0 = D and <2.0 = F.

Adaptation for the Advanced Class

Because my classes are advanced, I have to adapt this system to suit my students' needs.  Basically, I am using the standards as the "basic skills" for my class.  I have a posted a series of mathcasts and study guides on each standard and the students are expected to view the online examples and do the problems in the study guide prior to taking the pretest.  If a student scores above 90% on the initial assessment, there is no other work to be done on the standard--they receive a 5.  Students who score below  90%, need to correct their errors, explain to me that they understand why they made their mistakes and how to fix them.  Once I am convinced that they have truly corrected their errors, I give them a second assessment and the new score replaces the old one. 

My reason for allowing students to earn a 5 right off the bat is that 90% of our classwork is problem solving that uses the standards as the jumping off point.  Students in my 8th grade class receive two grades.  They are all enrolled in an algebra class as well as a geometry class.  We treat the algebra class as the "grade level" basic skills class and the geometry class is the "advanced" class.  The geometry we are doing is analytical so students are having to use the algebra at a much higher I'm ok with not making them jump through hoops in the algebra class. 

Note: My department is awesome.  I truly loved my math department at my previous school and it was really tough to leave them.  However, I couldn't imagine working with a group of teachers more willing to try new things.  We have pretty good discussions in our department meetings and there is plenty push back.  But at the end of the day, we are all trying to find the best way to educate our students.


Jason said...

I use a similar system (0-4 instead of 1-5). My standards are sorted into topics. I do about 4-6 topics per trimester. At the end of the grading period I use conjunctive scoring. Students need all 3s and at least one 4 for an A. Lowest 2.5 and at least one 3 for a B. Lowest 2 and at least one 3 for a C. Any score a 1.5 a D and any score lower an F. I like it because one high score doesn't make up for another. Thus, 4,4,4,1 would still be an F. The key is you have to keep them updated (not a downside) and also you'll need to end new instruction a little early before the grading period to give them a chance to review and bring up any low scores. I usually spend the last two weeks letting them work on specific standards and retest.

Question: I'm trying to help my math teacher design standards-based grading topics but we're running into the same problem I think as you. A lot of the standards sort of lead into other ones so we've got the dilemma of creating the top score as "mastered this who year's worth of sequence" or segregating them into smaller chunks. I think in terms of learning the first option is desirable because it forces the student and teacher into relating everything together. On the other hand, logistically it seems like a pain in the butt. Not to mention explaining to every kid and parent that a 1.5 at the end of the first quarter is ok since it's a whole year's standard.

Jim said...

This sounds like a pretty amazing system, and I would love to join a department really interested in assessing kids in this way. That being said, I do have a couple questions.

1) Do you find that this requires a lot more time spent on grading the writing assignments?
2) Are the students able to make good connections between the standards if they are taught discretely (an implication I gathered from what you wrote)?
3) Do you have parents complaining about the grade if little Jose or Maria "tried hard, and effort should count for something" even if they did not reach the standard?
4) More of a statement than a question. It appears that students deemed 'proficient' do not have an opportunity to show this on more complex and/or multi-step problems since the initial assessment is multiple choice and the follow-up activities do not seem to be problem-based. Is that not an issue?

Great ideas though, and something I am very interested in, although I do feel there is a place in the grade for effort (this year, at least, my thoughts on this are always in flux). Would love to hear more!

David Cox said...

As we have gotten into this system, I am thinking that a 0-4 would work just fine, but politically a 1 seems to go over better than a 0. Not sure if it really matters, but when you are changing the paradigm, there is no need to pick unnecessary fights.

The only thing I can really offer at this point regarding standards that lead into others would be for a student who shows proficiency in the latter standard validates their score on the former. For example: in CA we have a standard for simplifying expressions and one for solving equations (providing explanation for each step). If a student can solve equations fine, then they have to be able to simplify expressions. So if I give a reassessment on equation solving (and the problem(s) I give for a reassessment are pretty rigorous) and the student nails it, I change the score for the simplifying expressions standard as well.

Good questions...I knew I could count on you. :)
1. I have found that it actually cuts down the grading time. Our multiple choice assessment is aligned to Edusoft so the sheets are scanned and scores are posted on the web. The "grading" of the writing assignment involves me reading it and discussing it with the student. Finding class time to do that isn't too much of a problem because we have daily 94 minute blocks for the entire year. We have twice as much time with our students as I did when I was at the high school. The model our middle schools use was adopted to allow for intervention/enrichment. The regular classes (read non advanced) carve out an average of 20 minutes per day for re-assessment/intervention.

2. I don't think we are having any more of a problem getting kids to make connections than we did when we were doing it the old way of following the pacing of the book. The main difference is that students really know what they do and don't understand.

3. We have had no problems with eliminating the homework/effort part of the grade. I have to give credit to our principal on that one. He takes the bullet any time that discussion comes up. It hasn't been often, though. The toughest sell was convincing parents and students that a kid could score 100% on the initial assessment and still have a 4. Our rationale was that each assessment has two parts and the CFA was only part one. At the end of the first quarter, I have to say folks have made the adjustment.

4. That is one of the weakness as I see it as well. I would love to have a bank of projects/problems/challenges that allow students to truly work with the math on a higher level. Our text has some ancillary materials that involve challenge and interdisciplinary problems and I have combined them into a pdf for the rest of the department by standard. They are now beginning to use them. I have given the Phillips Exeter problems to some of our algebra teachers and encouraged them to start using those. By a long shot, this is the biggest concern that I have as well. However, when I look at it compared to what we were doing, we are still no worse off.

This is definitely a work in progress, but I think we are headed in the right direction.

Matt Townsley said...

It would be really great to work with a team like yours. Such great ideas and so nicely worded, I felt compelled to leave a comment. Keep in mind that your work is outstanding and my thoughts are in no way intended to discount your work:

A quick question for you that I've been wondering about - what is the role of a pre-test in this type of standards-based grading system? (I am thinking of giving it a try later in November once my student-teacher gives back my classes) Maybe there are topics that students catch on to quickly that could be reviewed rather than taught over an entire class period? If designed well, a pre-test could also indicate that the majority of students struggle with an idea or have the same common misconception.

Have you experimented with pre-tests at all?

David Cox said...

Thanks. We have been talking about using a pretest and in some ways that is how I use the CFA. I have posted examples online and don't do very much pre teaching before I give the first assessment. There are two reasons for this: #1 My 8th graders were introduced to most of the algebra as 7th graders and #2 These are advanced kids and they are very capable of learning a skill without having to do 50 practice problems. I do the same for the 7th grade class because my state's standards for 7th grade are very skill oriented and many of these skills the kids come with. The last thing I want to do is waste a class period on percent of change when they already know it.

Now with that being said, if the CFA shows that most of the class doesn't get it, then I do a whole class lesson. But if there are small pockets that don't get it, I do more of a mini lesson for that small group.

Would this work in the regular classroom? I really don't know. There is a mindset in most of our students where they simply don't take much ownership of their own learning. We are attempting to change that by making them aware of what they do and don't know as well as emphasizing understanding as opposed to just "getting a grade."

I agree that well designed assessments can say a lot and save a bunch of unnecessary work. Ya got any?

Matt Townsley said...

"I agree that well designed assessments can say a lot and save a bunch of unnecessary work. Ya got any?" Nope! I'm going to rely on a test-generating application that came with our textbook as a test bank and crank out some multiple choice questions for starters. As with any new project, have to start somewhere and the move to the ideal.

One more question about your CFAs: do these usually happen after a single lesson on those learning targets? I'm envisioning...

Monday - teach LT1
Tuesday - teach LT2
Wednesday - teach LT3
Thursday - CFA over LTs1-3
Friday - proficient & less than proficient scheme

or do you re-teach a bit before administering your CFA. From your blog post, I gathered it was pretty light on instruction before the CFA.

David Cox said...

What test generating app do you use? I started using ExamView over the last couple of years and I love it; especially because you can export tests to html and post on the web as study guides or you can actually administer a test and have the results sent to your email.

The light teaching takes place in my class specifically. In the regular classrooms, the teachers will cover the standard for the week and usually test on a Friday. The proficient-less than proficient scheme will occur daily. We have 94 minute blocks and teachers can carve out about 20 minutes daily for the intervention/enrichment. Now minutes can be banked and used on other days. For example: if a teacher has a lesson or activity that may take over an hour, he may forgo the intervention portion of the class for the day. Maybe the minutes will be made up on another day, maybe not. It really depends on the situation.

Our 7th grade standards are already very specifically targeted, ie. NS 1.2- Integer ops and basic fraction ops, AF 1.3 Properties (comm, assoc, distributive, etc) NS 1.4- identify rational and irrational numbers.

In algebra we have a few standards with many layers. Our Standard 2.0 involves most number sense stuff: exponent rules, negative and rational exponents, simplifying radicals, rationalizing denominators. We teach it as one standard but have broken it up into different skills in the gradebook.

Does that help?

Matt Townsley said...

Yes, that makes a lot of sense, David. I've also been using Exam View for creating some tests and worksheets. Here in Iowa we don't have state standards (they're on the way, but not in a format/mandate like other states have put into place), so all of our standards are created locally. Iowans still love their local control, but it creates a bit more work on our end to ensure that what we teach matches up with external assessments. In short, my course learning targets are setup similar to yours. Thanks for taking the time to share.

David Cox said...

If you don't have state standards, how is your external assessment created? If there are common skills that you would find on that assessment, I would argue that you do have state standards but no one has written them down yet.

Matt Townsley said...

Each district picks external tests to use to report AYP. Most districts that I know of use the Iowa Tests of Basics Skills/Iowa Tests of Educational Development (note that ITBS and ITEDS are "Iowa" only because they are developed in Iowa...other states use them, too, from my understanding). So, do we align our standards and benchmarks with Iowa Testing? Yes. Are these our "state standards"? No. Here's where it gets tricky:

Iowa just came out with quasi-state standards to be implemented over the next several years, but they don't match up with ITBS/ITEDs. For example, ITEDs do not assess inferential statistics, however you'll find "Understands and interprets inferential statistics" in the essential concepts and skills category of data analysis/statistics & probability. These essential concepts & skills are very vague, but I guess you're right - combined with the ITED/ITBS, we do have some unwritten goals for learning. The entire second half of my Statistics class is on inferential statistics (confidence intervals, hypothesis tests and the like), but in my grade book, I, like you break down this very large/vague concept into measurable learning targets.

We're really digressing from your original post here, but thanks for