This is a post in the ongoing Emergent Math mini-series: Routines, Lessons, Problems, and Projects.
I graduated high school twenty years ago this year. What’s remarkable is how little I actually remember about my classes. I remember certain feelings I had towards particular teachers or classes, but not the actual classroom action itself. There are three exceptions. There are four distinct activities I remember from my classes and they’re all projects:
- In my combined Physics/Calculus course we divined the accelleration due to gravity based on an experiment me and Eric Durbin concocted. And we were pretty close! We’ll call this the Learning Project.
- In AP Stats we conducted soil testing and surveyed the neighborhood to determine whether they cared about this issue. We’ll call this Project-Based Learning.
- In English we had to recreate various scenes from The Lost Horizon. We’ll call this the Dessert Project, for reasons which will become clear.
- In Biology we had to collect a bunch of leaves. I don’t remember why, but we had to do it. We had to get certain kinds press them is a special way. I hated it. We’re not calling this project anything other than The Leaf Project
That’s it. That’s all I remember about my classwork in High School. Don’t get me wrong: I remember other stuff too, like that time the time my friend Ash was talking so the teacher made him get up and teach the class,I recited “Shaft” in English class (“Who’s the black private dic that’s a sex machine to all the chicks?”), and my creepy Algebra 2 teacher making about ten too many jokes about “french curves.”
But by and large I remember the projects. Don’t get me wrong, there’s other stuff in there. I graduated college and everything, partially with some knowledge I acquired in school. But I only remember these actions.
Projects are an opportunity to illustrate how crucial your discipline is to the world or our understanding of it. They’re also an opportunity to waste several days or weeks of class time and force students to jump through imaginary hoops concocted by the teacher. In both cases, students will remember.
Projects apply mathematical knowhow to an in-depth, authentic experience. A project occurs over the course of two to four weeks. Ideally, projects are outward facing, community based, and/or personally relevant to students.
Let’s take a look at three types of projects. As with this entire mini-series, I’m painting with a broad brush and I’d happily concede that what I call one thing, might actually be another in another’s eyes.
The Dessert Project
I’ll withhold why it’s called the “dessert” project for now. These are typically given at the end of a unit intended to sum up the content. These often occur as a retelling of the content, such as my Lost Horizon example above. We read the book, we identify crucial scenes, and then we reenact them. We’re barely doing any analysis, let alone synthesis.
The best Dessert Projects take what a student has learned and unleashes it on an appropriate real-world scenario. Now that we’ve learned the content, we’re going to see how it looks in a different context. Most end-of-chapters offer this kind of project.
The Learning Project
In a Learning Project, we learn something germane to the topic at hand through the use of an in-depth investigation. The structure of a Learning Project is more-or-less dictated by the teacher, but there is enough agency awarded to the students to experiment on their own. The WHY and HOW are often provided and the WHAT is relatively self-contained.
In my gravity example above, we were given the task (calculate the accelleration due to gravity), the materials (a video camera that allowed you to fast forward one frame at a time – this was the 90’s mind you), and the format of the product (a lab report). We had
It was a deeply memorable and engaging task. Unlike Dessert Projects, we are asked to actually find out something new, rather than repackaging information. Despite the fact that Learning Projects may not have a community partner, a public presentation, or a shiny final product (ingredients of Project-Based Learning which we’ll get to in a moment), we construct or deepen our understanding of some new knowledge or knowhow.
I’d suggest these as other examples of Learning Projects:
- The Fall of Javert (Mathalicious)
- Farming Project (David)
- Weather Forecast (Geoff)
- Sprinklers (Nat)
- Des-man (Fawn)
- Hotel Snap (Fawn)
Project-Based Learning (PBL)
PBL has gotten the most headlines lately. Schools across the country want to provide deep, authentic, and motivating experiences for kids in all subjects. And to be sure, the best of PBL absolutely achieves that. Students are given a open ended, authentic challenge and students develop and present a solution. Through this process, students acquire new mathematical knowledge and skills.
In PBL (like Problem Based Learning), the task appears first and necessitates the content. Students learn the content in order to achieve their final product. Often – if not always – PBL occurs in groups.
But don’t be fooled: quality PBL entails a lot more than just giving the students and letting go of the process entirely. The teacher/facilitator crafts the daily lessons and activities to support the process. The following graphic is taken from the New Tech Network, my employer. It explains well the various phases of a project and a menu of options for lessons, activities and assessments throughout a project.
The project launch occurs at the beginning of the unit. It kicks off and drives the unit. In this case the project is the “meal” as opposed to the “dessert” (recall from early Dessert Projects). The project is how students will learn the material.
Project Launch: Have students read the Entry Document (the letter) and collect “knows” and “need-to-knows”.
To the students of Akins New Tech High School,
The US presidential election of November 7, 2000, was one of the closest in history. As returns were counted on election night it became clear that the outcome in the state of Florida would determine the next president. When the roughly 6 million Florida votes had been counted, Bush was shown to be leading by only 1,738, and the narrow margin triggered an automatic recount. The recount, completed in the evening of November 9, showed Bush’s lead to be less than 400.
Meanwhile, angry Democratic voters in Palm Beach County complained that a confusing “butterfly” ballot in their county caused them to accidentally vote for the Reform Party candidate Pat Buchanan instead of Gore. See the ballot above.
We have provided you the county-by-county results for Bush and Buchanan. We would like you to assess the validity of these angry voters’ – and therefore Al Gore’s – claims. Based on these data, is the “butterfly” ballot responsible in some part to the outcome of the 2000 election? What other questions do the data drum up for you? And what can we do to ensure this doesn’t happen again?
We look forward to reading your analysis and insight, no later than May 5.
Your county clerk
Example project pathway – the 2000 Election
In this example, we still retain many of the lessons and workshops that we would typically teach during this unit, but notably they occur as students are working towards various benchmarks and the final product. The lessons inform the student products.
There is enough to write about PBL to merit its own miniseries. Structures and routines are crucially important in a PBL Unit. Assessment must look different. Managing groups becomes an entirely different challenge. How the authenticity of the product and the external audience enhances the quality of student work.
For now, here are some other tasks that adhere to PBL.
The genesis of this entire mini-series stems from questions I receive about Problems and Projects. Mainly, “how often should I use problems? How often should I use projects?” The unstated part of that question is, “when do I actually, y’know, teach?” (Actually, sometimes that’s stated). I’ll save another post for “putting it all together” or “adjusting the levels” but know for now that’s why I put together this framework of Routines, Lessons, Problems and Projects.
As for the “how many projects?” question, I’ll give a squishy answer and a non-squishy answer.
My squishy answer: design a project whenever (A) the standards uniquely align such that you can create multiple lessons around one scenario and (B) when you can identify a project scenario that will maintain momentum over the course of several weeks.
My non-squishy answer: One or two a year. Most standard clusters don’t lend themselves to multiple investigations around one, single context. But some do! Content clusters around things like Data and Statistics, Area and Perimeter, and Exponential Growth and Decay are ripe for real-world scenarios that can be analyzed through the lens of multiple content standards.
As challenging as it is to design and facilitate projects, and as little time we have as educators to carve out the time for it, we don’t want to deprive students of the real-world insight math can have. We want to provide these experiences that will live on in students’ minds as the power of mathematics, whether or not they go into the field. So be on the lookout. Look for news articles and community opportunities that might embolden students to use math for maximum impact.
Also in this mini-series:
- Intro post: Routines, Lessons, Problems, and Projects: the DNA of your math classroom
- Routines: the driving beat of your class
- Lessons: the stuff we envision, only better
- Problems: then a miracle occurs
- Active Caring: the essential ingredient
(Editor’s note: The original post had “dessert” written as “desert,” which is a different kind of project altogether, I imagine.)