{"id":6083,"date":"2013-09-18T00:00:00","date_gmt":"2013-09-18T04:00:00","guid":{"rendered":"http:\/\/aurora-institute.org\/blog\/cw_post\/competency-based-grading-and-common-core-math-a-perfect-match\/"},"modified":"2020-02-05T12:50:59","modified_gmt":"2020-02-05T17:50:59","slug":"competency-based-grading-and-common-core-math-a-perfect-match","status":"publish","type":"cw_post","link":"https:\/\/aurora-institute.org\/cw_post\/competency-based-grading-and-common-core-math-a-perfect-match\/","title":{"rendered":"Competency-Based Grading and Common Core Math: A Perfect Match?"},"content":{"rendered":"

\"Screen<\/a>My Uh-Huh Moment<\/strong><\/p>\n

Over the summer I spent the day with my math team as we prepared for the implementation of the Common Core State Standards for Mathematics into our school. We were working on an intense math problem when I had one of those uh-huh moments<\/i> \u2013 the kind I used to describe to my students when I taught high school math in Andover, Massachusetts. The problem was a simple one to understand, but it had many layers of complexity to it for math teachers:<\/p>\n

Imagine you are a peasant, and your ruler told you that you could have as much land as you could mark off by walking in one day. What is the most amount of land you could reasonably claim? Give your answer in square miles and be prepared to support and defend your work.<\/i><\/p>\n

Among the questions that came to mind when thinking about how to solve this problem were these: How many hours can a peasant reasonably walk in a day? How fast can a peasant walk? How many breaks will the peasant need to take? Are there hills, mountains, or other physical obstacles that the peasant will encounter? What kind of tools will the peasant have to navigate with (i.e. a compass or a GPS)?<\/p>\n

Very quickly, a group of us began to debate these questions and create a list of assumptions that we would use to derive our answer. We debated what type of a shape would produce the biggest area. With some trial and error and use of some mathematical formulas, we agreed that a circle might be the theoretical shape that would yield the biggest area, but the square was the shape that would be easiest for the peasant to trace, assuming they had a compass or could make use of a reference point such as the sun for direction.<\/p>\n

My uh-huh moment<\/i> came not because my team arrived at an answer that we felt comfortable with. Rather, it came because I realized that we as a math team were embarking on a revolution that was going to change the way our students thought about math. The days of assessing students with multiple-choice, low depth-of-knowledge math questions would soon be gone. Instead, a new era of performance-based summative assessments that may have more than one correct answer will soon become the norm in schools across America. Students will not only have to be good at math, they will have to be experts in mathematical reasoning as they support and defend their thinking. This is a competency-based approach to learning. My mind filled with excitement and optimism as I realized that our recent shift to a competency-based grading and reporting system was going to put our students into the driver\u2019s seat as we implement the Common Core State Standards for Mathematics into our math classes this school year.<\/p>\n

 <\/p>\n

The Common Core State Standards for Mathematics<\/strong><\/p>\n

The Common Core State Standards for Mathematics (CCSSM) claims, by its own website, to be working towards greater focus and coherence<\/i>. My home state of New Hampshire, along with many of the states in our nation, has adopted the Common Core as a way to structure both state and local curriculum. CCSSM has gained popularity (and perhaps notoriety) for the fact that it has identified the fewest number of mathematics standards than just about any set of state-level math curriculum frameworks available. The CCSSM standards are focused, however, aiming for clarity and specificity over state frameworks that have been described as inch wide and mile deep<\/i>.<\/p>\n

In addition to math content standards organized into domains such as Number and Quantity, Algebra, Functions, Geometry, and Statistics and Probability, the CCSSM outlines a set of eight standards of mathematical practice \u2013 varieties of expertise \u2013 that students are expected to develop. These include things like:<\/p>\n