This year at High Tech High we decided to “give the Common Core a try” in our 6th and 9th grade math classes. Our hope was that the new Common Core standards (emphasizing coherence, rigor, and depth) would provide a good match for our project-based environment. Of course, we had questions. Would a common scope and sequence stifle the teacher autonomy that is so precious to our organization? Would teachers continue to be able to personalize and bring in adult world connections through math projects? Would the standards squelch the deeper learning we are striving for? Or would they finally put an end to our endless discussions about “what” to teach in the absence of good standards and help us move forward with defining our “how”?
Given the opportunity to step out of the classroom for a year and support this shift, I have engaged with many teachers and experienced firsthand how the project planning process has shifted with the entry of the Common Core. The approaches to planning can be broadly categorized in two ways. In the first, the “backward” method, teachers start with an idea or passion of theirs or of their students. Through brainstorming and research, the mathematics in the idea is explored, highlighted, and included in the project design. The second approach has been “forward planning,” whereby the teacher has sat down with a list of standards in a given unit or units of study and worked to brainstorm possible real-world connections. Through the use of a sample open-ended problem the project is birthed out of the standards themselves. In the two case studies that follow, I will describe projects planned in the backward and forward directions. In the implementation of these projects, there have been the usual snags along the way. Nevertheless, glimmers of hope shine through for deeper, richer math projects and a more coherent math program.
Enrico Fermi is best known for his work as a physicist. What is lesser known is that Fermi really enjoyed tackling the estimation of “big problems,” problems so big that the quantities seem impossible to compute. For example, a classic problem of his was, “How many piano tuners are there in Chicago?” Using some educated guessing and some basic mathematics, Fermi would make estimations on these large problems.
As our sixth grade teachers took on the common core, Fermi math problems surfaced as an interest of ours that might spark a project linked to the ratios unit in our common core framework. The focus of ratios in sixth grade is modeling equivalent ratios using tools like the ratio table and double number line. After an initial brainstorm session with teachers, I created a sample poster outlining the stages of a potential math project and how the math fit into each step. I also created a sample Fermi problem and product, “How many donuts fit into a swimming pool?” The teachers who agreed to take on this project sat down and “tuned” the project. Throughout the tuning process, we brainstormed possible products and ways that we could make sure that math was present, finally arriving at a concrete project description and phases of action for implementation.
The project entailed students creating their own Fermi questions based on their own personal interests and measuring or researching the necessary information before modeling the scaling of the ratio through tables or double number lines. Three teachers implemented the project, each putting their own twist on the final product and presentation for the work (two made stop-motion videos and one made posters in Photoshop). Allie, one of the co-designers and implementers, found that the project was engaging and the math work was rich. She went on to say, “Differentiation was really inherent in this project because students were able to come up with their own questions. I challenged my higher achieving students to come up with problems dealing with volume, while struggling students created problems looking at area or even just length or height.” She further reflected that another few days to implement critique and more drafts would have made their products even more excellent.
Ben, another teacher who helped design and implement the Fermi project, noted that one particular student who is often off task and unfocused was enabled to thrive in the project. “Even though he struggled with the math,” Ben stated, “he focused on the creation of the video in which he was implicitly outlining the math steps along the way.” Ben observed that because the problem was open-ended and kids could pick topics based on interest, there was deeper learning happening through the project. He further reflected that, “One weakness of the project was that it became very tedious and sometimes the videos weren’t top quality, but the math was always there.” Ben’s implementation of this project has provided a solid foundation for future iterations of the project and he is already thinking through ways to keep the mathematical processes the same, but tweak the product.
In starting with a topic that interested us—Fermi’s estimation work—and in following a structured design and critique process, we teachers were able to work together to design a rich math project that engaged the students in deeper learning at all levels.
Geometry presents the largest shift in the Common Core standards. As a result, it has been challenging for our 9th grade teachers to find a wealth of resources that properly convey the sought-after content and skills. In thinking about how to approach geometry this year, my colleague Amy Callahan and I sat down with two High Tech High Chula Vista Teachers. Our goal: take the Constructions and Rigid Motions geometry standards and create a project that highlights the core content in a rich and meaningful way to the students. When I first met with Gavin and Paul, project co-designers and implementers, they had already looked through the standards and had a vague idea of where they felt the standards leading them: something along the lines of constructed polyhedra that could be displayed in mobile form or be hung in some way. In our planning time together, the four of us dove into the math standards and the mobile idea to see how they matched up. Two of us worked on physically constructing nets while the other two focused on technology, tinkering around with Geogebra until we learned the program well enough to use rigid motions to create nets. As Gavin and Paul put the project design into final form, they dubbed it “PolyMEdron” because after students constructed the net, they would export the image into Photoshop, where they would put images that represented themselves on each side of the polyhedral before printing, folding, and displaying the project for their school-wide exhibition.
The content of the project focused on constructions and basic definitions of rigid motions. As Gavin reflected, “Students were able to utilize their knowledge about constructions while learning about computer programs such as Geogebra and Photoshop.” Through the use of these programs, students became engaged in Common Core standards of practice: modeling with mathematics and using tools appropriately.
The PolyMEdron Project was not without flaw or hiccup. Technology problems such as freezing computers seemed to make the project take much longer than intended, and it lost steam in the process. Gavin further reflected, “The outcomes of the project were that students had a better understanding of how nets can be constructed to become polyhedrons, and students became very familiar with Photoshop. I do not think students were able to deepen their understanding of geometric constructions through this project which was the initial unit that we designed this project around.”
Though the content learning outcomes were not directly in line with what we set out to address, there was deeper learning as defined by Mehta (see below), in that students faced the task of doing most of the mental work themselves and that they were “playing” with the mathematics with the goal of making something artistic and representative of themselves. In terms of next steps, the teachers now have a launching point for how to address these standards next year. Whether the decision is to modify and implement a similar project or to take the standards and head in another direction with them, there was a definite learning experience for both students and teachers in this process, as always in project based learning.
No doubt some combination of forward and backward project planning is the reality for most teachers planning projects. Nevertheless, the basic process of starting with either content or passions and then developing the rich math content through co-planning, brainstorm, questioning, and critique is one way that HTH teachers have combined our passion for projects with our desire to “give the common core a shot.” For teachers familiar with projects, it has brought an extra dimension to our math project planning time, leading to richer math projects. For teachers new to our organization, like Gavin and Allie above, it has provided a framework to structure and tune the project for next year.
Jal Mehta (2012) defines deeper learning as both challenging and open-ended. He further says that it matters to students because it is linked to questions. From the students’ perspective, there is a regular grappling with uncertainty, the real possibility of failure, and the knowledge that they are doing most of the mental work. Using our High Tech High philosophies and structures as a guide, the teachers and I have gone about the year planning math projects, this time with the Common Core in mind. In co-planning projects and then observing as the projects are put into motion, I have seen evidence of both reflective teaching and deeper learning.
The Common Core has helped to structure our conversation and guide the rich mathematics in the projects. All of our questions around teacher autonomy and deeper learning have not been answered, but our ability to infuse and even feature Common Core math within our project based learning environment is exciting. We hope the Common Core will broadly impact others as they see that the new standards really do call for deeper learning like that in project based learning.
Visit www.hightechhigh.org/math for resources that High Tech High has been using to support teachers’ transition to common core this year.
Reference Mehta, J. (2012). Teaching Differently, Learning Deeply. Kappan Magazine, 94(N2), 31-35