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 level...so 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.