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!

Re-energized and Refocused

About a week ago, I had the amazing opportunity to not only attend, but also help present at the Math-in-Action (MIA) conference at GVSU. This math education conference brought together math educators of all levels from across the Midwest to help teachers discover new ways to improve their classroom. By the end of the day, my decision to become a teacher was reaffirmed, my passion for teaching was seemingly at an all-time high, and my itch to get in the classroom already was scratched to the point that I couldn't focus on my homework later that day.

Wake up, Nick! I had to snap myself back into Nick the pre-service teacher who still has a lot to learn. I had to remind myself that I have yet to write a lesson plan, create my own activity other than worksheets and a KaHoot review game built from textbook problems, and initially teach students material, among other things. In just over two short years, I will be looking for a teaching position. By that time, I would like to be ready to make an impact on my future students having acquired the necessary skills and feeling the same excitement and passion that I was feeling after MIA. But what I do know is that I have many fantastic takeaways to, well, take away from MIA. The biggest of which is the necessity to incorporate technology and mathematical literacy in the classroom. I had always realized the necessity for both, but now I have tangible ways to make these a reality. One way to infuse both came from the first session I attended. Zach Cresswell, a high school math teacher in Michigan, discussed the concept of an inquiry based flipped classroom, which I am very interested in bringing to the classroom, and his experiences with it. As a part of his model, he has students blogging about various aspects of class.

Really? How had this not hit me until he explicitly stated it?! What am I doing right now? Blogging. As Zach explained, students +  blogging = getting a better idea of a student's understanding. Here are a few examples of his students blogs that demonstrate what I believe to be the power of having students blog about class. These examples show that student blogging not only gets the student thinking critically about a given concept, but it also allows the teacher to obtain a more accurate reading of the student's understanding. This benefit is something I view as a must in my classroom. Much like the SBAR assessments in my math education class, I would much rather place an emphasis on conceptual understanding than being able to perform an algorithmic computation.

Let's be real; this is NOT math

Don't get me wrong, there is nothing wrong with being able to find the correct answer. But what is it worth if you cannot explain the concept behind it? I think that a student blogging about the connections between the unit circle and the trig function from an activity that uses a program like the one below (slowed down of course) is much more worthwhile for the student (and the teacher!) than answering a few computational trig function problems for homework since it gets at something deeper than meaningless values.

This is so cool, right?

Anyways, I really like how versatile student blogging is with what a teacher can do with it. It can be used for an explanation of a homework problem, a mini project, a check for in-class understanding, and any other form of concept check,to name a few, while allowing a student to further develop mathematical literacy. When Zach (@z_cress) reads a "good" blog post and shares it via twitter, the students are shocked at how the MTBoS responds to their blogs. The students are really excited that real math people are viewing their post, not just their classmates. I love how this initiates a sense of professionalism with students. It helps to teach them that their work matters and is of worth. With all of these benefits, I cannot imagine a classroom of mine where student blogging is absent. After all, what math teacher doesn't want his or her students excited to talk about math?