Mastery of Knowledge & Skills - Claim 1:
Procedural Fluency, Conceptual Understanding and Application of Math
Test scores are just one way of measuring mastery of knowledge and skills, but they are not the whole story. In fact, we believe that the kinds of work students do on a daily basis in the classroom are absolutely critical to our students' success on standardized assessments. The evidence below gives us a better understanding of what our students do well in their math classrooms and illuminates, in part, how our students are able to demonstrate high levels of mastery in math.
Math Problems of The Week
In 6th grade, students learn early on to "do math" together in groups and to share collective responsibility for the individual success of each team member. This group work, and the innovative way it is assessed build essential collaborative skills that are the foundation for deeper learning in other classes and in future grades at REALMS.
Students practice some of the discrete skills and content necessary to complete a more complex problem involving application. Having students assess their own mathematical contribution and their peers builds accountability for learning the math and for working together.
Below are three samples of a "Group POW" (Problem of the Week) from 6th grade. You can click on each to expand. Be sure to click on the two group assessments below the student work to see an innovative way to ensure that collaboration drives learning for all group members!
Exploring Slope through Bicycles
The Common Core State Standards call for students to apply their mathematical understanding to solve real world problems. At REALMS, students do just that. However, beyond just applying math they have already learned to real world situations, they often USE real world situations themselves to discover and develop their conceptual understanding in the first place.
An example is an investigation into slope that our 8th graders pursue prior to leaving on a 3 day self supported bike tour on Orcas Island, WA. Many students know how the algorithm for calculating the slop of a line but fewer can explain the connection between the slope of a line, the linear equation y=mx+b and how slope and linear equations play out in real life applications.
Here students use bicycles and the front and rear chain rings to count and plot the number of tire revolutions per pedal revolution using different gear ratios. In the classroom they collect the data in small groups and then use this data to explore the math using a graphing app on their iPads called Desmos.
The photos here tell the story of data collection and the two student work samples below give a sense of how students have an opportunity to use the data to develop a deeper conceptual understanding of slope.
Student Work Samlpes From Bicycle Investigation
Self and Peer Assessment of Math AND Habits of Collaboration
Click either image to see student self and peer assessment of POW project as well as teacher synthesis.
6th Graders Collect Surveys and Analyze Data, at Home and on the Road!
Each Spring semester 6th graders pursue a learning expedition we call Nourish. It brings together our science, math, humanities and art teachers in collaboration around an investigation into global and local food systems.
As part of this expedition, our students design surveys to give to residents in both Bend and Portland, OR regarding their food consumption choices and habits. IN math class, they compile the responses from hundreds of surveys, analyze the data, and make conclusions that connect to their learning in science and humanities.
Below are some examples of the students' work from this investigation: