Editor’s Note: Math teachers across the country are learning the power of formative assessment in their classrooms. In this video series, we bring you an opportunity to see formative assessment in action, with the help of math consultant Ann Shannon and resources from the Mathematics Assessment Project (MAP). Ann provided the initial training for teachers in Kentucky’s Kenton County on how to implement MAP and frameworks from the Math Design Collaborative. She observed teachers in the classroom, gave real-time feedback, helped facilitate the after school meetings to analyze student work, and helped build capacity in the district so that the work would be sustainable.
When I first read the Common Core State Standards (CCSS) for Mathematics, I felt overwhelmed. I loved the idea of common standards and a focus on math practice standards as a way for students to interact with the content, but I wasn’t sure how this would look. How would I support teachers and their approach to this content? Soon after Kentucky adopted the CCSS in March of 2010, my district, Kenton County, got involved with the Math Design Collaborative (MDC) as a way to help teachers make sense of the standards and begin shifting instruction toward the Common Core. My work with teachers around MDC has been critical to our students’ success because of the focus on formative assessment and teacher collaboration time.
Formative Assessment is Central to MDC
Each MDC lesson (a free resource) is aligned to the CCSSM in both content and practice, and is designed to be used about two-thirds of the way through a unit of study. All lessons begin with a short pre-lesson assessment meant to bring student misconceptions to the surface. After administering the pre-lesson assessment, teachers collaborate in teams to analyze student work, identifying common misconceptions that are getting in the way of their understanding. Sometimes, we find it challenging to look at the misconceptions that students still have, but the information we get is instrumental in furthering student understanding.
After the pre-lesson assessment, the lesson moves to a collaborative activity where students work through their individual misconceptions with focused feedback from the teacher. When students complete the lesson, teachers collaborate again around the student work on a post-lesson assessment. They analyze the work for growth, and determine not only their next steps in instruction for these students, but also the next steps for shifting their approach to the content for future students.
See a Full Cycle of Formative Assessment
In this new video series, Teaching Channel went inside two of Kenton County’s middle school classrooms to capture MDC at work. In the videos, we watch students having productive struggles in order to make sense of math concepts. And, we see teachers determining which instructional strategies will help students master rigorous standards. In the 8th grade classroom, students are exploring linear equations in two variables. In the 7th grade classroom, we see students tackling proportional relationships.
Case Study: Proportional Relationships
In Teri Walker’s 7th grade classroom, you’ll see students working with the standards cluster 7.RP through the MDC lesson “Proportion and Non-Proportion Situations.” This Standard changed the most with the Common Core. Before the shifts demanded by the CCSSM, much instructional time was spent “setting up a proportion, cross multiplying, and solving.” While students still work with equivalent ratios, they now must connect their previous learning about unit rates and ratio reasoning to proportional relationships.
Understanding Proportional Relationships
See how Ms. Walker uses a real-world lesson and pre-lesson assessment to expose the gaps and misconceptions her students have about proportional relationships.
Common Issues with Proportional Relationships
Using the previous day’s pre-lesson assessment, Ms. Walker addresses misconceptions and deepens understanding through group work and a probing classroom discussion. Watch how she shifts the work load to her students — instead of answering student questions herself, she guides her students to do the explaining.
Deepening Understanding: Proportional Relationships
Listen in on Ms. Walker’s follow-up teacher conversation on the student work from the post-lesson assessment. Then watch her translate and adapt the feedback she gets to help students apply what they learned to the real world.
Case Study: Linear Equations In Two Variables
In these next three videos, using the same protocol, watch Susie Morehead’s 8th grade classroom work with the standard clusters A-CED and A-REI through the MDC lesson “Solving Linear Equations in Two Variables.” Historically, many students learned the methods to solve systems of equations, but never learned to interpret the meaning of algebraic equations and their solutions. Additionally, many students have difficulty in choosing the most efficient methods to solve problems. This lesson helps identify students who are having these difficulties and gives them the opportunity to work through these misconceptions.
Reviewing Linear Equations in Two Variables
Common Issues with Linear Equations
Deepening Understanding: Linear Equations
Approaching the standards through the MDC framework has made the CCSSM and the Standards for Mathematical Practice much more concrete. Teachers are gaining a better sense of what it looks like for students to demonstrate a particular standard and are using student work to reveal the need for instructional change. When teachers discover student misconceptions through pre-lesson assessments, they find the holes in how we have approached the content in the past and begin to consider a better way. This is the real power of MDC: teachers having time to collaborate around student work aligned to the standards, and to discuss instructional implications specific to their students and their course.