After reading a number of blog postings about Standards Based Grading (SBG), I tried a hybrid version of it during the Fall semester of 2010 in an Algebra I class and three Algebra II classes. What follows is a description of how I approached things, what worked, and what didn’t.
Approximately 40% of each student’s semester grade was based on SBG quiz scores, 30% on traditional chapter test scores, and 30% on the semester exam.
I was not obligated to test to specific standards, so I picked quiz “topics” which were timely and allowed for challenging questions. My goal was to have most questions be challenging enough to make perfect scores unlikely on the first try.
Each student’s best two scores for each topic counted towards their overall Quiz grade. All lower scores for the topic were dropped, regardless of the sequence in which the scores were obtained.
Each answer received a maximum of five points:
– One point for attempting the problem
– One point for using a valid approach to the problem
– Three points for working the problem to a solution
– One point taken away (up to three) for each algebra or arithmetic error
My grade book consisted of a three-ring binder with one page for each student. Each page had a grid with quiz topics down the side, and question identifiers across the top (A, B, C, D…) so that I could quickly determine which questions a student had completed for each topic. I recorded Chapter Tests at the bottom of each page.
I tried to schedule two “Quiz Opportunities” per week during class time, usually for 10 to 15 minutes. I projected between one to three questions on the board for students to complete, one question per topic. Students who had already received two perfect scores on a topic (i.e. who had mastered a standard) did not need to answer that topic’s question.
The first three questions on a topic were given during in-class Quiz Opportunities. Students who had not yet earned two perfect scores after completing all in-class questions on a topic were welcome to complete additional questions on the topic outside of class time, no more than one question per topic per day. I kept a preprinted supply of additional quiz questions for each topic handy in a drawer, ready to hand out on demand. Some students required as many as ten attempts to earn two perfect scores.
The 12 week semester allowed time for 7 or 8 quiz topics. Chapter tests, school events, and the pace at which new material could be introduced all affected how many “topics” could be assessed. I also could not introduce any new “topics” during the last two weeks of the semester, as there would not be enough time for all students to master them at that point.
Towards the end of the semester I was swamped with quiz questions that needed correcting as students realized time was running out to achieve perfection. Many students were asking me to correct questions immediately, which was not possible very often. Students wanted to know if they had mastered a topic or not, and thus whether they would need to complete another question or not. Although I set the next-to-last week as the deadline to complete questions on topics 1-4, and the last week as the deadline for topics 5-8, I was still swamped with questions to correct during both of those weeks.
Things That Worked
Students really liked the lower-stress approach to quizzes. I did not hear groans or pleas to postpone when a “Quiz Opportunity” was announced, and students even requested them with eager anticipation on occasion!
This approach to quizzes allowed me to ask more challenging questions. For example, most Algebra II questions were complex enough that students began to see the value of working in an organized way, had to complete a minimum of three rewritings of the entire expression or equation to arrive at a solution, and used a half page or more of paper to complete their work.
Most students were determined to master each topic, and continued completing questions on topics outside of class until they mastered it. Students were elated when they finally mastered a topic. Big smiles.
By the end of the semester, the majority of Algebra II students had mastered most of the topics assessed by the quizzes, even the ones with plenty of opportunities for sign errors, distribution errors, and errors in working with algebraic fractions.
Most students who did poorly on a quiz topic did not “give up” once the quiz was over. They continued to work on mastering the topic throughout the semester.
My grade book provided a clear visual history of each student’s mastery by topic over time. Parents liked it, I liked it, and students could easily see what needed work (each student was expected to maintain their own version of their quiz score history sheet).
Posting “old” quiz questions on my teacher blog gave students a useful study/review tool – both for the next question on a topic, as well as for chapter tests and the exam.
Things That Did Not Work
Grading consumed too much time, particularly toward the end of the semester (surprise!). While I wanted to see where students were making their errors, if I had asked students to find their own mistakes in erroneous answers, with help from peers or me if necessary, they could have learned more from the process.
I ended up with a pile of quizzes that students had completed outside of class, which I could not hand back because other students had not completed that question yet. While I showed students their graded quiz briefly, that is not the same as having it in your notebook to review and learn from before completing your next quiz question on the topic. This deprived students of an opportunity to learn from their mistakes later in the semester.
Choosing “topics” for quiz questions was not always as easy as I had expected it to be, particularly for the first month of Algebra I. Some math topics can be difficult to create challenging (yet meaningful) quiz questions for.
Many students did not improve their scores on a topic over the course of multiple attempts. It felt like they were not really focusing on why they lost points, then thinking about how to prevent it from happening again. They seemed to assume that their score would improve by simply trying again without making any changes to the way they work that type of problem beforehand.
Many students did not have as great a sense of urgency to master a topic as I had expected… until the end of the semester.
What Would I Do Differently?
- Not set myself up to be such a bottleneck
- Require students to review and reflect on their work more
- Encourage students to complete quiz questions only when they have demonstrated that they are ready
- Raise the stakes a bit for “retakes”
Instead of counting the two best scores on each topic, I would count only the most recent (not necessarily the best) quiz score for each topic. Students would always be welcome to complete additional questions, but should only do so if they know they have mastered what eluded them the last time.
Using “practice” and “real” questions might be more efficient and effective than what I tried in the Fall. “Practice” questions would be ideally administered via an internet-accessible multiple-choice quizzing system which would allow them to complete a question and receive immediate feedback on their answer. Students would log in to such a system so that I have a record of the problems they viewed and answered, along with the answer they gave.
Using multiple-choice practice questions would require more upfront work to create good questions, as the “wrong” answers would need to be crafted to provide diagnostic information for both the student and the teacher. However, the extra work in the beginning would hopefully save considerably more time correcting over the years to come, while also allowing students to work more independently.
A student would need to answer a specific number of practice quiz questions correctly (three?) and turn in their work (following the outline below) for all questions viewed on-line in order to earn the opportunity to complete a “real” quiz question on the topic.
Practice problems would be required to use this format/outline:
- rewrite the problem
- solve the problem, showing your work neatly
- check your answer using the techniques taught in class
- if your answer did not check, try solving the problem a slightly different way and check that answer.
- does the quiz system say your answer is correct?
- for each incorrect attempt above, complete the following steps:
- find and circle all errors in your work leading to the answer using a different color pen or pencil – if necessary, get help from a friend or a teacher to find your mistakes
- Describe how/why each circled error occurred
- What will you change about how you work such a problem to avoid making the above error(s) again?
If a student earns a less than perfect score on the “real” question, they would still be able to complete another “real” question at a later date, but would first need to analyze their errors on the “real” quiz question using the same approach, then complete another set of practice questions correctly. “Real” quiz questions would receive a letter grade of A, B, C, or D based on a rubric discussed in class and used for all graded work during the course.
The mistake analysis process described above should be time-consuming enough to discourage excessive retakes. But I also want students to focus on mastering each topic within a couple of weeks if possible… so perhaps subtract two tenths per week from their 4.0 scale quiz letter grade starting the third week after a topic has been introduced.
By having set dates for “real” quiz questions, I could return all graded work immediately since no other students would receive that question on a later date.
I would not project quiz questions on board. While it saves some toner and time at the copier, it does not save paper and can introduce rewriting errors into student work as they copy the problem down from the board (particularly for those sitting farthest from the board). However, the major reason for not using the projector for quiz questions is that it is more useful for displaying the next task to tackle when students have completed their quiz questions.
If you are interested, here is a good article that lays out the advantages of “SBG”: Seven Reasons for Standards Based Grading