Project Based Learning and its Implications in a Multicultural Mathematics Classroom

Project Based Learning and its Implications in a Multicultural Mathematics Classroom

When I was a junior in high school, I was placed into AP Calculus. On the first day of classes, I came to that particular class to find that my favorite math teacher, Mr. Best[i], was the instructor for this years AP class. He began the class explaining that we will be preparing for the AP examination in June, as well as preparing a final exit project. He went on to explain that we would be having two assessments: a midterm and a final, as well as this project. Our grade would consist of the two exam grades as well as the project grade, attendance, participation and homework completeness. He began to give us examples of projects that students completed in the past, and told us that literally anything is “fair game” as long as you’re able to describe it using mathematics.

The remainder of the period, we explored different options and complied a list of words and phrases in the description of the project examples that we were not familiar with. The list grew and grew to include words such as derivative, integration, velocity, shells, and so many more. Mr. Best then began to explain that we will be learning what all of the words on this list that we created mean, and that this information will be very important for us to complete our projects. Though there were projects that were given as an example (which students were able to pick), Mr. Best encouraged us to think “outside the box” and propose our own projects.

Throughout the next week, everyone in the class decided on a project that they wanted to work on. Mr. Best used a combination of lectures and “mini projects” in order to teach us the basics and ins-and-outs of calculus. By the end of the year, students built catapults, constructed model bridges, and did inquiry projects surrounding topics such as rainbows amongst other things. We were required to turn in a paper explaining our processes as well as any calculation work we did in order to complete the project. I had recently seen a Myth Busters episode answering the question if you should run or walk when it is raining outside. In the episode, I found many factors that they didn’t analyze (i.e. the speed of the rain as well as how big the droplets are). I went on to analyze whether someone should walk or run in the rain by looking at multiple factors in regards to the weather and the phenomenon of rain. I was able to examine the shape of a raindrop, how the wind affects rain, and how the diameter of the raindrop also effects the speed in which is falls.

I credit this experience with math as to why I decided to study mathematics in college; I always knew I liked math and was good at it, but I didn’t know what the possibilities were. Before deciding that I wanted to teach, I held a Mellon Mays Undergraduate Fellowship in mathematics and was going to go on to pursue my Ph.D. in mathematics. My junior and senior year I completed projects surrounding sustainability and data compression. I felt that when I was personally invested and connected to the projects that I was working on, I was much more motivated in my day-to-day work. This research and inquiry based experience I had through my research experiences was something that I was not getting in my traditional lecture-style classroom; I was being asked to think deeply and creatively about all aspects a project.

Not all students learn the same way; what works for one student, may not work for another student. By diversifying the methods of teaching used in the classroom, we’re able to captivate the student’s attention, and hopefully inspire the student. By implementing a project-based model of teaching, we’re able to foster critical thinking without the traditional lecture based instruction. With a balance of lecture as well as projects, students will be able to make meaning in their learning and in turn be invested in their learning. By engaging the students in projects, it allows put to use the skills that they just learned. Projects allow the students to think about mathematics through different lenses and approach the problems that are arising through different avenues and use “mathematics as a key analytical tool” (Gutstein, 426). By putting into place a curriculum that is culturally relevant to the students, will allow the student to connect and relate what they’re learning to real life situations that are concerning to them. Sadly, because “… math is not taught in ways that all students find meaningful and relevant to their lives, and as a result, certain groups of students have traditionally been disadvantaged in math classes, including female students an students of color.” By giving meaning to the problems and situations that are being analyzed, “…we’re able to make math more “real” and, thus, more engaging” (Kumashiro, 114).

I was very much so inspired by a talk that I attended last semester presented by Simon Hauger of The Workshop School. The Noyce STEM Teaching Program of Bryn Mawr Hauger, an engineer turned inner-city schoolteacher, lead a team of students from West Philadelphia high school to enter a global competition on the engineering and design of a high efficiency hybrid vehicle. The students did extremely well, which in turn inspired Hauger to open up a new public high school in Philadelphia named The Workshop School. The Workshop School uses a project-based approach in order to motivate and teach critical thinking skills to the students. Hauger and one of his students Azeem, were invited to give a PopTech[ii] Talk in 2010 where Azeem stated in his presentation: “you can’t teach critical thinking skills without critical conditions.” This quote struck me because I feel that there is not enough critical condition in today’s standard curriculum; there are not enough connections being made to the real world. Why is what I’m learning important?  What are the applications of my classes in the real world? Why should I care? By providing critical condition as well as implementing critical thinking skills, you’re creating problem solvers and leaders, not better test takers. Anyone can learn for an exam, but when students are able to have a personal investment in their learning, they take much more than knowledge away from the class.

The basis of the work done at the Workshop School has to do with projects. Their approach to project-based learning is described via their website as follows:

At the core of everything we do at the Workshop is project work. Projects must address a problem that is important to both the student and to society, and they must result in work that can be evaluated using the real-world standards. While in the lower grades (9-10) teaches play a more prominent role in designing projects, by the time they reach the upper grades students largely design them on their own. When proposing projects, students must include a brief summary of the project, the problem it aims to solve, the core concepts they will need to learn in order to execute the project, the products or deliverables that will result from the work, and the academic standards and skill areas the project will address.

Examples of topics that projects have covered include identity, immigration in America and sustainable living, all of which are issues that are important to the students. These projects take the forms of models, magazines and formal presentations amongst other layouts. The projects seem to cover a range of different skill sets from public speaking, writing, mathematical inquiry and many more.

            By implementing projects into the curriculum, students are allowed to navigate the different avenues of problem solving; there is no right or wrong way to approach the situation. Because there are many stigmas surrounding mathematics and learning math (i.e. “I’m not a math person” and “girls are not as god at math as boys”), many times “math anxiety” develops as a result. Frankenstein suggests that we must address the pedagogical issues that make people uninterested and unengaged in mathematics:

The immediate pedagogical causes of the situation — such as meaningless rote drill, taught so that it requires extensive memorization, and unmotivated applications which are unrelated to the math one actually used in everyday life — create a situation where people “naturally” avoid mathematics (12).

By permitting the students to have a voice in what they’re learning, students become more engaged and personally invested in their education. By allowing the students to look at themes that are concerning and part of their everyday reality “…in such a way that mathematics involved starts at a very basic level, and by having students pose problems… teacher and students are truly co-researchers” (Frankenstein, 15). I feel that when students are able to use their prior knowledge and their curiosity in a classroom setting, avenues for comprehension and dialogue are opened. By incorporating dialogue into the curriculum, it seals “…together the teacher and the students in the joint act of knowing and re-knowing the object of study,” which allows for students to feel as if their opinions and ideas indeed matter and are valid (Shor & Freire, 100).

I’m currently completing my Praxis placement at Leaf Middle School in the Upper Darby area outside of Philadelphia. I’m currently observing and teaching two classes of 8th graders in an ESL (English as a Second Language) classroom. Though I haven’t been able to practice teaching mathematics, I’m taking a lot away from working with these students and seeing what topics concern them, what they’re wondering about and what knowledge they’re bringing into the classroom. Throughout the past year that I’ve spent at Leaf Middle School, I’ve come to love the mile school age group and I hope to teach 7th and 8th grade mathematics in the future.

For this unit that I am designing, I wanted to focus on a common core state standard and teach to the standard while incorporating a culturally relevant topic. The standard that I will be teaching to will be CSS.MATH.CONTENT.7.RPA.3 which is part of the 7th grade common core standards which states: “Use proportional relationships to solve multistep ratio and percent problems” (corestandards.org). Throughout the United States, high school dropout rates are rising and retention in public schools is dwindling. For this unit that will last 5 class days, I will be combining lectures as well as group mini-projects in order to allow students to analyze data surrounding the graduation rates of incoming freshman in the state of Pennsylvania as well as other states.  By looking at this data, students will be able to see patterns (increasing, decreasing or stability) in graduation rates and also will be finding the compliment of the data (drop out rates). The students will be forming proportions and ratios of students in the class as well as converting and computing percentages based on given data.

By having the students keep a “learning log”, they will have the opportunity to document their learning, explain their steps and express their concerns. When I was in middle school, my mathematics teacher had all of his students keep a learning log (journal). In the learning log we would list the main problem, the materials that we needed to complete the project, the step-by-step procedure that we followed in order to reach the solution, our solution, our reflection on the project and any concerns that we had at the end of the unit. Writing for understanding is crucial in a mathematics classroom. Written work for the learning log “ranged from answering open-ended questions to writing a full essay; these dealt with students’ views, interpretations, and feelings on a particular issue (Gutstein, 427). Journal writing demonstrates to the students what they understand and don’t understand by forcing them to express their thoughts in words. Students will then also evaluate each other’s journals, that way they can get exposure to how their peers are approaching the same problem and the language that they’re using as well as their views and opinions on the subject matter.

By combining classroom discussion, group work as well as writing, I hope to help students understand the concept of ratios and proportions as well as have them start thinking about the realm of statistics, how they’re represented, what they’re used for and why they’re important. I feel that in many multicultural and diverse communities, as well as across the nation, high school retention and graduation is a growing issue that students need to be aware of. By looking at an issue through a mathematical lens, it attaches meaning to numbers. By giving students the skills to interpret statistics and proportional relationships, they’ll now be able to see relationships like they haven’t been able to before.