Assessment

toc =High School Math Grading System=

Below is my current (2012) grading system. It has evolved over 17 years of teaching high school and middle school mathematics, and it will continue to do so. Thank you to the many wonderful colleagues who have shaped it.

Philosophy
Experience has shown me that if it's not assessed, it's not valued. Here's what I value:
 * **Rigorous** and **challenging** mathematics
 * An appreciation of the **connections** within mathematics
 * A willingness to **investigate** mathematical ideas
 * An understanding that **practice** is necessary for success in mathematics
 * Successful **study habits**- consistent practice, preparedness, etc.

Grading
This is the grading system that I've implemented to support the above philosophy:

Responsibility (10%)*
I assume each student will come to class prepared, so each student earns 2 responsibility points per class. If they come to class unprepared (no text, pencil, notebook, laptop, etc.), they only earn one point, and if they come to class without their independent work attempted (something written for each problem), they don't earn any points. Turning in a required assignment late also results in not earning the responsibility points for that day.

At the start of the year, I often check independent work by asking students to copy down their working for three problems (from their notebooks, without their text)- this allows me to emphasize that something needs to be written for every problem. It also allows me to look at a student's work more closely outside of class time. As the year goes on, I just do a daily spot check to ensure that students are writing something for every problem- if they do this, they earn the responsibility points for that day.

My feeling is that students should work on math for an hour outside of each class. They may choose to spend the majority of that hour working on old IW questions; in that case, they would probably just write down the problems from the new IW assignment to show that they looked at the problems; this earns the responsibility points.

A responsibility point is sometimes given for returning a signed progress report. A student who has lost a number of responsibility points can also work out some individual agreement to earn back some points by acting responsibly.

This portion of the grade is easy to record. I just keep track using an attendance sheet- I make a mark if a responsibility point is not earned. There's really no reason to not earn responsibility points, and students regularly earn all possible points. Since the category is 10%, it doesn't impact the student's grade much (and rarely has any impact on the yearly grade), but it isolates that component of the grade from the academic component (rather than deducting 10% for a late assignment, for example) and students know that it isn't good to lose too many responsibility points.

Independent Work (10%)*
I collect the unit's independent work on the day of the unit test. Students staple it behind a cover sheet for the unit (like [|this one] distributed on the revision day). The expectation is that each assignment is done and then checked and corrected in a different color (the different color is more for them than me- I emphasize that when they are revising for independent work quizzes, they should focus on those colorful problems because they are the ones they are still learning). I give time each day in class for independent work questions (usually posted before class on a page like this), questions can also be asked at math extra help sessions, and answers are available all unit- thus, there should be no reason not to have every problem done correctly by the end of the unit.

The idea with independent work is that students work on it all unit. Most independent work assignments include some problems to stretch and challenge- students may not make much progress on these initially, but with the unlimited help available, they should eventually work through each assigned problem. This allows me to use independent work as a mixture of practice and investigation. Students work on challenging problems in a supportive environment.

Grading independent work does not take me much time- I try to mark the independent work while students take their tests. I use [|this rubric], although I am sometimes more lenient when I know students are working hard. Given my limited amount of checking time, I spend more time checking and giving feedback to students who are struggling in the course. All students get a grade, though. Independent work is assigned for every class.

Quiz (30%)
Each unit includes one or two quizzes which are merely independent work problems with a number or two changed. Wordings of problems are unchanged. I write quizzes by choosing 8 to 12 independent work problems from any assignment up to the previous night's (to allow students to ask questions on the new assignment). Students with limited time for revision know exactly what to expect on a quiz. In this way, students who keep up with independent work assignments and make sure they can do each problem are rewarded, and I can then identify which students are merely copying down the provided independent work answers or who copy work from friends. Additionally, students can use their original independent work while they take the quiz. This includes any notes or reminders or working they have included on their original independent work.

It does not take long to write a quiz from independent work questions, so I am able to give one each week or so. It gives students practice working in an unassisted (and, for honors students, timed) setting while also giving me feedback on how their skills are progressing. It takes a little time to grade, because I give partial credit. Each question is generally worth from 1 to 4 marks, and I aim to award marks for correct working rather than penalize marks for incorrect working.

Test (50%)
I refer to my tests as Opportunity Days- opportunities for my students to demonstrate what they have learned in a unit. They generally last all period. They are usually between 12 and 18 questions long (the final score is out of 100%). Students may use technology (calculator, Geogebra, etc.) on the first page. When they are ready to give up their technology, they receive the second page and they may then work on both pages for the remainder of the period. The questions assess the standards of the unit, and thus will usually not be identical to previous questions asked in class or on independent work. In lower level classes, a question may consist of several parts which may connect or may be a set of one step exercises on a concept. There will usually be at least one question which requires some explanation. Questions will be of varying difficulty levels; it is rare for a student to get all questions completely correct. These tests are "finely crafted opportunity days," and they generally take a while to write. [|Here] is one such unit test.

When students finish the timed portion of the test, I quickly mark each question either right or wrong. To be marked right, the question must be answered completely correctly. I then scan a copy of each student's test on the photocopier to keep a record of the work done in class. Students usually collect their tests by the end of the day and begin work on the next portion- Supercorrections.

Supercorrections are where students go back and correct their tests and then reflect on each problem that they missed. They may receive any assistance they'd like- from fellow students, me, parents, tutors, Wolframalpha or other websites, etc. They write a correct solution for the problem missed and then write a reflection on the problem- what concept they were missing, what silly mistake they made, etc. To make a correction super, I encourage them to do something extra- show alternate methods of solution, connect to a different problem, etc.


 * Here are the **instructions, rubric, and forms** for Supercorrections (these files provide the details for how Supercorrections work).

I usually devote two or three classes of independent work time (including the day of the test) and a day or two of class time to Supercorrections. Supercorrections are due a week or so after the timed portion of the test to allow students to come in for extra help if they need it.

Supercorrections take a while to grade, but I find the time well spent. Most students have spent a good amount of time and effort on their work. Here are several examples of recent Supercorrections received (you may want to print the PDF files or zoom in to read them more clearly):


 * **The student who didn't revise for the test and whose work during the unit was spotty at best** ([|here]). He used the Supercorrections to finally learn the basics of logarithms. The rubric means that his test score is still low- he can't afford to do this every unit- but hopefully he realizes that he can do better with consistent effort.


 * **The student who works hard but finds the tests challenging** ([|here] and [|here]). This student is rewarded for hard work and her ability to handle challenging problems improves through her effort on Supercorrections. This type of student is often surprised that problems that seemed quite difficult at first are actually not that hard.


 * **The strong mathematics student** ([|here]). This student can still learn from challenging tests and reflections on Supercorrections.

Supercorrections place emphasis on working accurately in a timed situation (full marks are only possible by getting a problem correct the first time). Students learn to check their work carefully so that they don't need to write a Supercorrection for a careless mistake. More importantly, though, they provide time and space for reflection and more reasoned analysis. It also allows me to make summative unit test into a formative learning opportunity.

It takes some time to explain the Supercorrection concept to students (and parents). I find that describing the timed portion of the test as the rough draft and the Supercorrections as the final draft is helpful. I also show [|a model Supercorrection]. I show how the grading rubric works and demonstrate some grade calculations- for example, a student who only answers 3 out of 12 questions completely correctly could still earn up to a 91%, depending on the type of error made and the quality of the Supercorrection.

After students have submitted Supercorrections and I have graded them, we then go through the test together, and I answer any additional questions. Students who have made any errors on Supercorrections have until the end of the quarter to correct those errors and resubmit their Supercorrections for full credit.

The final assessment of the unit is a follow-up test which consists of a subset of the original test questions with slight number changes (to discourage memorization of answers). This follow-up test occurs early into the next unit and counts as much as the Supercorrected test.

I also aim to use quarter/semester projects in classes as time allows. These are weighted as tests and have rough and final drafts.

*Not mandatory
Occasionally a student refuses to buy into my system of independent work and responsibility points and doesn't do or submit independent work assignments. Because I don't want such a student to be penalized by my system, students always have the option to not count the Responsibility and Independent Work components in their quarter grade and just have their grade be based off their performance on quizzes and tests. I don't make a big deal of this fact, but I do usually have one or two students a year in this category. Most students, though, find that these two categories boost their grades.

IOU (extra credit)
I have a box of extra credit IOU cards. Each one is worth 0.1 points added to any quarter grade. Students earn IOUs by making clever observations in class, finding errors in my board work, winning warm-up or revision games, doing problems from the NCTM Mathematics Teacher calendar, or working on some other extra credit problem (which usually arise from a class discussion).

IOUs require almost no effort on my part. I don't keep a record of IOUs awarded; students must keep their own IOUs. At the end of the quarter, I give students their grades to the nearest tenth. If they choose to use some IOUs to raise their grade, they do so then by giving me the required number of IOUs at that time.

Final Exam: aka Final Opportunity Day
The final exam has no Supercorrections. It is the students' final opportunity to show me what they know- a true summative assessment. It is very straightforward and should not be difficult for students who have been working hard all year.

Communicating
This system is transparent- it allows students and/or parents to calculate grades while leaving sufficient flexibility for my professional judgment (particularly in test writing and Supercorrection marking). I have no problem making my grade book available online or emailing regular progress reports. The system also provides many opportunities for hardworking students to affect their grades; regular communication gives students ownership of them.

At the start of the year, I communicate my course expectations with a course methodology. It has developed over a number of years, and it is [|available here].

Use of class time
I find that this system of grading frees my use of class time. Since independent work is not collected until the end of the unit, I may use an assignment to introduce a topic, knowing that we will go over it before students need to submit their final work. I give independent work every class, and I always give time for questions from all independent work assignments, but this is about the only constant. Some lessons are more investigative; others are more teacher centered.

I also find that responsibility for learning shifts from the teacher to the students in this system. Our class time together is a chance for students to ask questions and work on their ongoing independent work assignments, and it is also a safe setting for investigating the challenging questions that will eventually be asked on the end of unit tests.

Level of engagement
This approach to mathematics grading forces students to engage- it's not possible to just drift through class with this system. At the same time, no one needs to make math his life (or be a complete math nerd). Ideally, as students buy in to the system, their level of engagement with mathematics and thus their success rises correspondingly.