Emphasizing Concepts Over Computation Through Standards Based Grading

From my experiences as a Structured Learning Assistance (SLA) Facilitator (if you're unfamiliar with what that is, a description can be found near the top of this post) and Math Tutoring Center tutor at GVSU, I suspect the majority of students have the wrong idea of what mathematics is. If you would ask a high school students to describe what mathematics is, a typical answer would probably depict math as the art of calculation or a set of algorithms that allow us to calculate values. I would argue that this type of answer stems from math being taught with an emphasis on computation, or being able to correctly use an algorithm to find an answer. With the exception of my AP Calculus and AP Statistics courses, I can attest to math class being taught in this manner for the vast majority of the math courses I took. I cannot recall being asked conceptual questions very often on assessments or outside the lesson; the emphasis was placed on being able to compute the desired value. 

But there is so much more to mathematics!

One possible reason for this emphasis is standardized testing. With the increasing weight placed on student scores on standardized testing, some teachers are feeling more pressured to teach to the tests. In my experience with standardized testing (MEAP, NWEA, the ACT and its preparatory tests, and the PSAT), there are very few, if any, mathematics questions that ask for a conceptual understanding of the mathematics. Although it is important to prepare students for these tests given their implications (e.g. funding, college admittance, and, for some, job security), I believe that teaching to the test only contributes to students exclusively seeking the right answer, rather than a conceptual understanding, and perpetuates the notion that mathematics is the art of calculation. If math can be boiled down to computing a solution from a big bag of algorithmic tricks, we lose the opportunity to show the beauty of mathematics, as captured in one way by the video below.

Thus, in my future classroom, I would much rather place an emphasis on conceptual understanding since I believe the computational skills will follow. With a conceptual understanding of a given topic, a student should be able to figure out and justify the necessary steps to solve a computational problem as well as demonstrate his/her understanding on a conceptual question. As a result of this belief, I am leaning toward implementing a standards based grading system in my future classroom. With a traditional grading system, I agree with Shawn Cornally that it "teaches kids to love accumulating points instead of learning material."

This is exactly what I want to prevent

With a culture where accumulating more points or receiving a higher score on a standardized test is equivalent to being more knowledgeable about a given topic, it leaves room for students to feel like Billy Madison

or Sheldon Cooper.

Oh Sheldon...

In an effort to not promote this culture in my future classroom, I am seriously considering moving toward assessing students with Standards Based Assessment and Reporting (SBARs) more and more. I believe that this type of assessments puts the student more at ease since it allows for students to demonstrate understanding through explanation and the ability to reassess.

You mean you want to grade more?!?!

Now, this might be the novice teacher in me talking, but I am willing to put in the extra effort grading reassessments, if that means students are arriving at a conceptual understanding of the content. With traditional assessments, I believe they only give the teacher a snapshot of a student's understanding of the material on a given day, so there is value in reassessment since it will allow the teacher to obtain a more accurate look at a student's understanding and what he/she really knows through assessment and reassessment. I suspect there are instances where a student does have an understanding of the concept, but the student was not able to produce it with the initial assessment. Thus, reassessment provides an opportunity for students to demonstrate that coming into the day of the initial assessment, they really did have an understanding of a concept they missed. 

It's in there...somewhere...maybe 

This leads me to the another aspect of SBARs I really like: students explaining their way to the answer. I believe it is really hard to determine, for the most part, by a series of computational steps if a students truly has a conceptual understanding of the content in the set of concepts being assessed. By requiring students to supply their thought process on a problem and justify each step they take, a problem that was once purely computational, and thus could only assess algorithmic thinking, can be transformed into a problem that can accurately assess conceptual understanding as well. However, it is important to emphasize the process when deciding how well a students meets the standard because, as John Golden (@mathhombre) writes (in the SBAR link above), "scores do not mean an answer is right/wrong, but are meant to reflect how much understanding was demonstrated. It is possible to demonstrate good understanding of a concept without even finishing a particular problem." 

You mean you don't want the correct answer?!?!

Now don't get wrong, being able to find the correct answer is great, but I believe arriving at the correct answer will be a by-product of a conceptual understanding, so there should not be a decrease in standardized test scores using this system. In fact, I predict they would increase since students can rely on their conceptual understanding on the test instead of trying to figure out which algorithm from the big bag of tricks needs to be applied. Hence, I believe using this system can only benefit the student. 

There are definitely kinks to be worked out in implementing such a system, but if I want to promote a classroom culture where a conceptual understanding is more valued than excellence in computation, then I believe using SBARs is step toward achieving that goal. I definitely plan to look through this beginners guide to standards based grading when (likely) implementing this system in the future. 

I would love to hear your thoughts and opinions on standards based grading or suggestions on implementing such a system!