Each semester, I stand in awe of how many students do not understand how to calculate the impact a semester final exam has on their semester grade. Our math department grading policy roughly breaks down in each class to the following:

90% Formative/Summative measures from the semester
10% Cumulative Final Exam

Kids carry many misconceptions about the final exam. A common one is that the final can somehow miraculously overwrite a semester's effort (or lack of effort). Here's a visual representation, to scale, of the 90%/10% model.

Exhibit A: The orange team blows out the red team, 90 to 10.

I have often instructed students to make the following program to help them forecast the impact of the exam on their semester standing.

Exhibit B: Program on the TI-84 for computing a 90%/10% weighted grade.

Here's a numeric example for how this sometimes surprises a student.

Exhibit C: Not much movement of the overall grade, despite a solid final exam score.

This is where the discussion gets interesting. Students will often use trial and error, over and over and over again, with the above program to compute the final exam score they need in order to get an A (which is 90% in our grading scale).

Exhibit D: An A doesn't appear to be in the cards, especially since extra credit does not exist in my class. (I'll share my views on EC on a different day). But I digress.

This is where I like to invoke Ken O'Connor's philosophy from How to Grade for Learning. This is a terrific book for teachers of all disciplines because it carefully examines the potential dangers of deferring to the electronic or paper gradebook to make all the heavy decisions.

Guideline 6 (page 153): Crunch numbers carefully - if at all.

a. Avoid using the mean; consider using the median or mode and weight components to achieve intent in final grades.

b. Think "body of evidence" and professional judgment - determine, don't just calculate grades.

I have been using the following practice for nearly ten years. I have a one-on-one conference with the student. I speak to them about what they need to get on the final to earn a particular grade. Since the breadth and depth of my final exam questions are more considerable than on unit exams, the student with an 86 would earn a 90 if they earn a 90 or better on the final exam, despite the fact the numeric stuff doesn't turn out that way.

This policy works wonders with students at the upper end. Sitting on a 96 for the semester, Johnny? What if you had the chance to up your semester grade? What if you could get a 100 for the semester by acing the final exam? All of a sudden, the student has a carrot to chase. The students appreciate this approach because it is a system that rewards effort and hard work. This approach gives the control back to the student.

Otherwise, isn't it possible that neat-and-tidy 96% in the grade book is simply a graveyard of sign errors? Or computation errors? Philosophically, what do I want as a teacher? Do I want a student's grade to reflect their learning? I have worked with thousands of students, yet only a handful I have encountered get most things on the first attempt. I tell my students every semester I have yet to meet a person that learned something without making mistakes.

I approach this problem reasonably. Don't get me wrong - if a kid is sitting at a 62% for the semester and gets a 95% on the final, that doesn't necessarily mean the kid deserves a 95%. I would need to reflect on the student's formative and summative measures as a body of evidence to help me make an informed professional judgment. However, if that situation happens - and it hasn't happened to me yet - I would need to re-examine my professional practice. That situation would indicate there is a disconnect between the content mastery a student demonstrates and what the grade says the student knows.

Teachers need to think carefully about how their grading practices capture - or don't capture! - student content mastery. Virtually all measurements are imperfect. The burden of evidence to prove or disprove the student knows something should lie with the student. If this is true, then the burden of judging whether the evidence suggests the student is learning lies with the teacher, not the plastic or silicon genie.

Think carefully on your grading this holiday season. Good luck to everybody - teachers and students alike - with semester finals!