“Mathematics makes the mind its playground. Doing math properly is engaging in a kind of play: having fun with ideas that emerge when you explore patterns and cultivating wonder about how things work. Math is not about memorizing procedures or formulas, or at least that’s not where you start.”23 Let’s begin by looking at what Anderson calls the six disasters in mathematical pedagogy. Separate arithmetic from algebra; Teach mathematics without any historical references; Use textbooks that are elitist and cryptic; Do work and be tested as an individual as opposed to working and being tested as study groups; Accept the myth that mathematics is pure abstraction and, therefore, antithetical to one's cultural and working environment; and Memorize, memorize, memorize.24 This unit will try, whenever possible, to avoid these “disasters” as outlined by Anderson. As Berry states, “one main idea of “new math” was to reduce focus on the drill and practice approach to teaching mathematics and increase focus on approaches where students could develop conceptual understanding of mathematics. These pedagogical approaches included the use of manipulatives, guided discovery learning, teaching practices, and the spiral curriculum25 This unit will include the following Pedagogy:
Holding space for student voice in the classroom
Bob Moses famously said, “We don’t listen to kids enough. Really listen. It is a difficult thing for grown-ups to do, listen and actually pay serious attention to what young people are saying.”26 This unit will involve various opportunities for student voice in each lesson. Turn and talks, see/think/wonder, and think/pair/share are just some examples of how space will be made for student voices in the lesson plans. In Rough Draft Math Amanda Jansen makes an argument for prioritizing student voice in the classroom as follows: “Listening to our students is not only productive for their learning, but also powerful for developing their identities as learners. Communicating about thinking helps understanding develop and the distinction between listening to students rather than for an answer is useful for teachers to consider when promoting rough draft thinking.”27
Revision policy on all assignments
Allowing students to revise their work is a productive way to cultivate a mathematically positive classroom culture. By allowing students to revise homework assignments, teachers alleviate stress and pressure that can hinder the learning process. As Su states, “In the math education community, the term productive struggle describes the state of actively wrestling with a problem, persistently trying out various strategies, being willing to take risks, being unafraid of mistakes, and progressing incrementally in understanding the underlying ideas. This wrestling produces a certain kind of endurance, which enables us to be comfortable with the struggle. This endurance produces an unflappable character that benefits us in addressing life problems—calming us with the knowledge that it’s okay if we don’t solve a problem right away. We appreciate that not solving a problem can be just as important as solving it—that, as Simone Weil suggested, the effort to grasp truth is itself worthwhile, for increasing our aptitude, even if it produces no visible fruit.”28 Jensen elaborates on this idea further by identifying three key features of rough draft math: Imperfect but precise. Unfinished and unsure. Involves revisiting and revising. (#8 p.8)
Include time for thinking and writing
All too often students see math class as a place to be right or wrong. When it is far more nuanced than that. The mathematics classroom should be a space for thinking and collaborating, not for judgment. Therefore, each lesson will include time for reflective thinking and writing. Students will write in response to poetry and quotes as well as in response to the daily chapter of The Number Devil.
The unit will culminate in a final project that aligns with the students' Art major at COOP. Students will create a personal mathematics narrative, which they will submit on the final day of the unit. For instance, the theater majors will write and perform a monologue based on their mathematical heritage. The visual arts majors can create a piece of work that illustrates their personal narrative. This unit will be an exciting way for 9th graders to begin their high school careers by both honoring the arts and the strong academic tradition that is embedded at CO-OP. For educators who don’t teach at an arts themed high school it is encouraged to have students write their narrative as an essay and adjust the rubric accordingly.
Below is the unit project description that students will be given on the first day of class:
Welcome to Revealing Truth, the first unit of this Algebra I course. At the end of this unit, in approximately four weeks, you will be asked to submit your personal mathematics narrative that connects your major here at COOP to the topics we are studying in Algebra. The initial rubric for this project is below, we will spend time at the end of our first-class making changings to this rubric together until we are satisfied with its language.
Personal Mathematics Narrative Rubric
Name: Major: Project title:
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3 Exemplary
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2 Proficient
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1 Adequate
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0 No submission
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Writing/Thinking
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Student includes a thoughtful reflective writing as part of their project that explains their process and how it connects to the unit
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Student includes a thoughtful reflective writing as part of their project that explains their process
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Student includes a reflection on their process
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No reflection is submitted
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Content
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Project has clear connections to the unit that are creative and varied
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Project has one connection to the unit
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Project has vague connections to the unit
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No project is submitted
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Presentation/Display
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Presentation or display is engaging and demonstrates project buy-in
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Presentation is sufficient
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Presentation lacks effort
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No project is submitted
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