In November, the SUDDS learning science team worked with teachers and sixth grade students at Highland Middle School in Harnett County, NC to conduct a design study on sixth grade ratio topics. The goal of the study was to better understand how teachers use Math Mapper to guide their instruction and how students use Math Mapper to guide their learning. With a shared curriculum in use across teachers, the differences and commonalities in how teachers and students respond to and use the data could be examined. Thus, Dr. Confrey and her team wrote a curriculum targeting the development of a conceptual understanding of ratio. This ratio curriculum was built upon empirically supported learning trajectories that describe the benchmarks and strategies exhibited by students as their understanding of a concept increases in sophistication.
The SUDDS ratio curriculum addressed two Relational Learning Clusters (RLCs) within the ratio domain: 1) Finding key ratio relationships, and 2) comparing ratios and solving for missing values in proportions. In the first week of the curriculum, students explored the first RLC: Finding Key Ratio Relationships. Students engaged with the three ratio constructs within this cluster (equivalent ratios, base ratios, and unit ratios) through a problem-based curricular model. Each lesson began with an engaging task relating to an authentic context. The context served two purposes: 1) engage students by making the mathematics relevant and authentic, and 2) to provide meaning to the mathematical construct being explored. For example, ratio equivalence was introduced through the task of finding recipes for lemonade that taste the same. The context, recipes that taste the same, is authentic and relevant, and it provides a real world meaning for equivalence – two recipes will taste the same if you can multiply the quantities in one recipe by the same number to get the quantities in the other recipe.
In week two of the curriculum, students explored the second relational learning cluster: Comparing Ratios and Solving for Missing Values in Proportions. For this cluster, the SUDDS team employed a project-based learning approach. In a project titled “Arrive Alive,” students investigated statistics relating to distracted driving (texting, talking on the phone, etc. while driving a car) and to riding in a car without wearing a seatbelt. As a culminating activity, students presented their findings in a infographic aimed at informing high school students in their community of the dangers of distracted driving. To satisfy the requirements of the infographic and make the data meaningful to their intended audience, students needed to use and understand the two constructs within this second RLC: compare ratios and solve for missing values in proportions.
Near the end of the teaching of each RLC, teachers administered two SUDDS diagnostic assessments to measure student progress and inform teachers’ instruction and students’ learning. Using the results of the diagnostic assessments, teachers identified specific content that needed re-teaching and students that needed individual attention. Students, meanwhile, used their score reports to identify areas of weakness within each RLC. After analyzing their score reports, students were asked to complete a survey. Two of the survey questions and a few selected student responses are shown below.
What things did you notice looking at your data?
“I need to work on finding equivalent ratios”
“I was improving in certain attributes”
“I need to practice finding unit ratios”
“That I showed growth”
“I noticed that I am good at base ratios.”
“I noticed that I improved on finding unit ratios and identifying ratio equivalence, I improved a little on finding base ratio.”
“I have shown improvement”
“That I’m pretty good at finding the base ratio”
What do you plan to do next?
“I plan on studying on the area that I got wrong so I can get a greater score than my last score.”
“studying unit ratios”
“work on my ratio skills”
“I will do more work on unit ratio”
Not only did students demonstrate heightened awareness of their weaknesses, but they also exhibited a growth mindset by acknowledging their strengths and identifying ways to improve. These RLC diagnostic assessment score reports provided students with a targeted assessment of their progress and equipped them with the language necessary to specifically address areas for improvement and act upon those areas. Additionally, by situating the score reports within the interactive Math Mapper learning map, students were able to visualize a path to success.
At the conclusion of the study, teachers administered an independent ratio assessment designed by Achieve the Core to measure student understanding of ratio. Because the learning science team built both the RLC diagnostic assessments and the curriculum, an independent assessment was needed to validate the results of the diagnostic assessments. The results of the independent ratio assessment provided the learning science team with valuable information that will help guide the revision of the current curriculum, the creation of future curricula and addition of needed diagnostic assessment items.
The Highland ratio design study provided insights into the ways in which the use of Math Mapper 6-8 can support teachers in making instructional decisions while empowering students to take ownership of their own learning. Combined with the results of the independent ratio assessment created by Achieve the Core, the learning sciences team is excited to incorporate its findings and continue to improve Math Mapper 6-8.