The entire unit was assessed using a common test developed by my mentor teacher and shared with the math department. The test was a series of open-response questions equally covering the five chapters.
The first check for understanding that students have access to is the lecture. During my SMARTboard slides, I give example problems for students to try. Students compare answers with each other and with my answer. The second check is through homework problems. The math department posts all homework solutions online and keeps a solution guide in class so students can frequently check their own work and make sure they are doing problems correctly.
The first formal assessments are the chapter quizzes. The quizzes are also common assessments shared by the department. All quiz questions are multiple-choice to allow for a quick turnaround of results to students (next day). The questions are of the same type as the homework problems.
The large and detailed rubric above guided student work on the Minute to Win It project and paper. On a day-to-day basis, however, I commented on each group’s paper through Google Docs. When they logged in the next day, they immediately knew which sections of their paper needed more work to get up to 100% on my rubric. Using this model of continuous assessment, students were able to continue working hard each day and take very low grades to a perfect score (which every group did by the end). Since I knew students had plenty of time to revise and improve their work, I was able to be extra-critical of all aspects of the project, both in their math and their writing. During the first three days of in-class writing, this rapid-feedback and revision process led to a level of engagement I have yet to see repeated amongst all students.
Reflection on Assessment of Student Work
Note: for privacy reasons, I did not post student work samples to the site -- contact me at andypethan at gmail.com and I will send you the papers written by 3 teams, including my comments at all of the revision points.
Included in the folder are three student assignments at five different daily snapshot points. Since I gave students a week in class to write their papers in teams of 3-4, there was a lot of human-hours available for revision of the work. Each day, I read through the team papers and left comments on each one, pointing out where they fell short of expectations or made mistakes in calculations or understanding. I was impressed to see that students responded very well to the continuous feedback and constructive criticism, making major improvements between each day that I read their work. I felt that giving students a rough example paper to look at and a very clear rubric to work from greatly increased their chances of success. My continuous commenting on their work only reinforced these guides and helped students to clearly understand my expectations.
The final product that each team delivered was excellent. On the high end, teams like “Team 1” wrote something that could pass as a college-level technical paper. The entire team responded quickly and effectively to feedback and worked hard on the project. In the middle, teams like “Team 2” did a good job of hitting all of the requirements set forth in the rubric. The writing is not as strong and the sections do not flow incredibly well, but the entire team showed a clear understanding of the statistics material I presented to them. Their work and their test grades are in alignment. On the low end, teams like “Team 3” struggled to follow the purpose of the project. With lots of assistance and commenting, they eventually improved the core of their paper to something fairly coherent with meaningful and accurate statistics in the body. However, the overall big-picture understanding of the team members showed through in both their paper and test scores.
Grading
Homework: Since the solutions are provided freely to students, homework grades are based on completion. All but a two students completed their homework assignments. Homework was worth ~4% of the unit grade.
Daily participation: Points are awarded for effective use of work time in class. Daily points were worth ~12% of the unit grade
Project: Using the rubric, I graded every team before the final version was due. Since there was still time before the due date, students fixed their mistakes. In the end, every team scored 100% by fixing all errors I found in their work (including the new ones they created while fixing old ones). The project/paper was worth ~12% of the unit grade.
Quizzes: The scores of the five chapter quizzes are averaged together. They were worth ~27% of the unit grade.
Unit test: The final test score holds the largest weight, since all of the other components are designed to prepare students for this final assessment. It was worth ~45% of the unit grade.
Reflection on Assessment System
The grading system is tiered to encourage growth at each checkpoint in the learning process. Participation points encourage students to show productive behaviors in-class that lead them to success. Unfortunately, I did not have a great method of awarding or taking away these points except in more extreme situations, so this part of the grade was relatively ineffective as a motivator for my class. Homework is self-assessed and graded on completion because students use homework as a tool for learning, not formal measurement of progress. Quizzes are taken in test-like conditions, except they target a smaller chunk of material and are worth fewer points. This allows students to see how well they can expect to perform on a test of the material with time to improve areas of weakness. It is important to give it some weight because students would not properly prepare for it if it was worth nothing. Finally, the test is the major measurement of progress for the unit and rightfully holds the most points. Since there was not a major project in the previous iteration of the course, I had to squeeze this into breakdown by taking a few percent away from the weight of the unit test (students were okay with this change to the syllabus!).
For the next semester, I changed the grading breakdown to reflect my goals for the students:
Homework Quizzes: 5%
Section Quizzes: 10%
Project Portfolio: 30%
Unit Tests: 35%
Final Test: 20%
I shifted the points away from behaviors (daily points, homework completion) and towards demonstrable evidence of learning (project portfolio and daily quiz/section quiz/unit test).
When I first taught the unit, I found that I had problems with some students simply copying the answers from the solutions manual to get their homework completion points. Based on the old grading scale, this was silly, as homework was worth less than 5% of their grade. Now it is clear that each day, I will give students a 3-5 question quiz at the end of the period. Doing poorly on these quizzes has negligible effect on their grade, but provides them with a good check of how well they understand the material.
In order to further emphasize the iterative nature of learning, students will have an opportunity to bump up a low score on a homework quiz to 100% by showing me their completed homework. In addition, students will be able to get 50% of their lost points back on section quizzes by properly correcting their mistakes in class.
Once I started adding major projects into the class, I decided to create a way for students to showcase their work. The project portfolio consists of all projects, including the Minute to Win It paper, and reflections on what each student learned from the project. By giving the project significantly more weight (about 3 times as much as before), it shows the value I place on demonstrating understanding in a sharable project, not just a test. All projects, just like this one, will use a detailed rubric for clear and objective evaluation of student work. The rubric proved very effective in the Minute to Win It paper.
The relative weighting from homework quiz to section quiz to unit tests will remain similar to last quarter. The quizzes have been reduced in value to clarify their importance as a formal learning tool, not a summative assessment.