Experiments in Grade Configuration in Math

We experimented this year with a new grade configuration in math in the middle school. We had a great in service PD in the beginning of the year which made the compelling case for certain assessment practices and how they would benefit math learning statistically through externalized (MAP) scores. Up to that point, we had a grade configuration which had a mix of percentages such as 40% on tests, 30% on projects, 20% on quizzes and 10% on homework. Digging around the internet, I found many middle schools have a similar policy (give or take 10%) but I could never find any research supporting while this was infinitely superior to one configuration or another.  One of our school goals this year was to use data to make informed decisions about teaching and student learning, and I decided to pilot the grading policies recommended in my grade 7 classroom.

In short, the premise was that by putting 100% on summative assessments, students will achieve more. I was skeptical at first and this sounded to me like "high stakes grading" but the argument was that if you give students enough practice and have deliberate, spiraling teaching, by the time students reached their final unit test, they were most prepared to demonstrated their understanding. Key data points that supported this were:
  1. Our adopted California curriculum standards clearly states that "Summative Assessments are the most valid and reliable indicator of in-depth understanding." (California Curriculum Framework)
  2. Statistics supported that through enough practice such as assignments, quizzes to check for foundational knowledge, projects and practice tests, students had the highest level of understanding in summative tests. 
  3. To grade everything puts undue stress on students and does not allow them to benefit from mistakes early in the learning process. A teacher must know that some work is "practice" on the road to understanding. 
All of these were valid points. I had just finished reading a policy on California grading standards that showed that "yet to date, there are no national, evidence based studies addressing grade-span configuration issues, and few studies actually use empirical data" (National Forum), but I decided to jump in feet first. We had problems in the past with grade inflation giving the illusion of higher understanding which often contradicted external test scores. For instance, little Johnny had a "C" or even a "B" through retesting or resubmission of work in class, although our MAP test data might put him in the 40% percentile which made for awkward recommendations on IEP's or math placement for the next academic year. We wanted to design a grading policy that was accurate and honest.

Our principal was very supportive of our efforts, although there were a number of parents in the community that did not like it. Typically, they were parents of middle and low achieving students as you can imagine. I did survey the students anonymously at the end of the year to get their opinion on the policy and most of them had softened to the notion. Many of them were tired of classmates not doing their share of the work in group based projects or investigations, and this inequity reared its ugly head to me as well. Students that "demonstrated mastery" through an project-based assessment or authentic assessment did poorly on a summative task on their own. Were they lucky? Or did someone else like a classmate, parent or tutor do the work for them?

Some of my key findings in action research after the school year were:
  1.  Although MAP test data did improve significantly in median score, mean scores were little changed. 
  2. Students did complete learning tasks that were not graded, as they were rungs on the ladder towards master, but there was almost an obsessive nature that some students had in test preparation. 
  3. For end of the year portfolios, I had students reflect on their "best learning experiences" on their blogs and told them not to focus so much on the grade, but rather the experience. Many students did reflect on their learning of topics, projects, but many of them chose a particular test that they did well on.
There were a lot of other conclusions that we made, but as they were more speculative than data based, so I shan't share them minus one-our students already consistently exceeded external test scores of typical 7th graders in the United States. Our seventh grade students usually test at the 10th grade level and as students math proficiencies increase, so does their tendency for growth. So, as the "smarter" and older your classes get, you can expect smaller gains from them (NWEA). Finally, if a hypothesis is not supported by the data, than it's unsupported by the data. Perhaps the data presented to us earlier was before and after a huge curriculum change or integration of differentiated instruction. We already had been differentiating instruction and our curriculum is fairly sound, so perhaps we were overly optimistic in expecting the same gains.
I want students to learn and appreciate math on it's own terms, and not create a culture of "math test takers." This seems to be the bottom line in American education these days and although test preparation is a necessary evil for high school and college, to create a classroom of test taking machines seems like a scene out of Pink Floyd's "The Wall". I can just hear the music playing-"We don't need no education!"

The challenge for me now is how to balance the academic rigor in a way that allows students to make mistakes and learn from them, connect math to real-world learning experiences, flesh out 21st century learning in problem solving and differentiate instruction for each an every student in my classroom so that every student learns. Oh, not to mention using assessment that is accurate and effectively indicates to students and parents areas for remediation. Through this whole experience, I am reminded that teachers do not merely teach, we are psychologists, scientists of our craft and politicians as we communicate with parents and the larger community.

I reminded of something Bill Powell told me in a workshop: "Good teaching is hard. If you want to do something easy, become a doctor."

  • Northwest Evaluation Association (NWEA) RIT Scale Norms 2011-Table 5.3 page 46
  • Mathematics Framework for California Public Schools Kindergarten to Grade 12. page 240
  • Policy Statement on Grade Configuration-Issue 5, July 2008 "The National Forum to Accelerate Middle Grades Reform"

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