Awhile back, I wrote about the portfolios that I was having my students create over the course of the school year. I have now run this project for two years, and wanted to describe more details about how I set up this experience for my students, as well as talk a little bit about how I know that it is valuable for them, and changes that I plan to make for next year.
The portfolio that my students create is a little booklet. I leave the presentation entirely up to them, besides requiring that they submit it in person rather than electronically (just because I’m sick of kids claiming to have had email or google drive issues). Each portfolio consists of a cover page, a one to two page reflection on problem-solving, and written explanations of the four problems that the student solved that year.
I’d also like to note that a lot of the ideas described here come from Bryan Meyer’s blog Doing Mathematics and Jim Mahoney’s book, Power and Portfolios. Obviously I’ve tweaked everything so that it makes more suits my practice best, but I’ve definitely borrowed very heavily from them.
BEGINNING OF THE YEAR
There are a few important things that I do at the beginning of the year to set up the expectation that my students will be creating there own portfolios.
- On the first day of school, we spend most of the period on this activity that I’ve written about before. I give them an open-ended problem and provide them with very little information. They are forced to make decisions within the problem. These are manageable decisions, such as estimating how many students go to our school. It is also important that they need to write out all these decisions and the reasoning behind them, which is what they will be expected to do for the final portfolio.
- We read through the mathematicians’ habits using this handout.
- We set up our binders. There are instructions for how to do this on the handout mentioned in #2 and I have lots of examples from previous students.
- I show them portfolios written in past years.
Here are the habits I use:
Collaborate, Be confident/patient/persistent, Create data, Generalize, Look for patterns, Multiple representations, Seek why and prove, Solve a simpler problem
Students select a problem they solved in the last two weeks that is an example of them using one of the habits. They fill out a little cover sheet (I keep them in labeled pockets on my back wall) and put both the problem and the cover sheet in their binders. It’s super important that they actually submit the problem, so they can potentially write about them later.
Here‘s an example of one of the cover sheets. The others are nearly identical, with the name of the habit changed.
Each quarter, students select the problem of which they are the most proud and write a detailed account of how they figured it out. We call these ‘portfolio write-ups.’ At this time, I do not include any discussion of the mathematician’s habits in this assignment (see below for future changes I plan to make).
One issue is that sometimes the write-ups look more like how-to’s than I would like. It helps to encourage students to include things that they did that were incorrect, or times that they felt confused or overwhelmed. This also reminds students that you can still be a good mathematician even if you don’t understand something immediately.
I give them this handout, which contains instructions and a grading rubric.
In addition to their second-quarter portfolio write-ups, I also ask students to answer questions about the collection of problems in their binders and about how they are doing with the habits. I use this handout.
END OF YEAR
By the end of the year, my students have written 3 write-ups. Their final portfolio must have four, so they have one more to write. Of course, many students have more than one more to write, if they missed assignments earlier in the year or aren’t super well-organized.
Every quarter, I give fairly detailed feedback to the portfolio write-ups, so I do ask students to rewrite their work, unless they got a 100%. I don’t require this, though maybe I should.
This is the handout that I give to students.
This is the grading sheet that I use for each portfolio.
My only requirements for the presentation is that it has a cover sheet and that students hand in a physical copy. I give full points for presentation as long as they are neat and legible – I don’t care whether they simply typed “Meghan Riling’s Portfolio” in black ink, or created an intricate design in colored pencil. I recommend students type the write-ups, but have given full credit to immaculately handwritten ones.
HOW DO I KNOW IT’S WORKING?
First of all, what do I mean by ‘working’? Ideally it will do a few things for students: develop their problem-solving skills, make them believe in themselves as problem-solvers, make them believe that being good at math isn’t the same thing as being fast at math, and encourage them to try new things instead of give up when they are confused.
For one thing, my students take this project pretty seriously. For the most part, their write-ups go into a lot of depth. (I’m considering a length cap next year, as some honors kids handed in 15+ page portfolios.)
I also gather from what they write in their reflection letters that they do feel that their problem-solving skills are improving. It’s possible that they’re just sucking up to me. But I don’t think so — some kids were talking to me about how they thought they had pulled one over on me. In the reflection questions, I asked how they would use what they had learned in the future, and these dudes thought they were just so slick for saying they would use it in real life, rather than in math class. So, I guess they don’t even know that they’re saying things that would count as sucking up to me.
Here are some quotes I grabbed from their write-ups that give me hope:
Senior – precalculus
This year I learned I am actually very capable of figuring out Math. I used to be hard on myself when I couldn’t get the right answer and give up right then. That isn’t the case this year; I have learned there is possibility.
Junior – precalculus
I have learned not to shy away from things because failure is normal. I will fail numerous times in life but I need to bounce back and shake it off. If you set your mind to getting the problem right, you’ll get it right. … If I don’t get it right the first time, why can’t I get it right the second time?
Sophomore – honors algebra 2
What I learned about solving problems is that there is no correct way to solve a problem and there are almost always multiple ways to look at it.
Junior – precalculus
I have become much more creative as well as talkative and collaborative about how to solve the problems in front of me. I believe that the most useful skill I have learned was to really experiment with all different sorts of ways.
Freshman – algebra 1
See now one of my biggest problems when it comes to math is giving up easily. I used to get overwhelmed and anxious when I saw a difficult equation, which would result in me not completing a lot of problems. So by picking up the habit of being confident, patient, and persistent I’ve been able to be open minded to lots of new possibilities and outcomes.
I know that’s a bunch of them. The things that pop out a lot are that they now see there are multiple ways to solve a problem and that they are finding that they are solving more problems just by not giving up. I think the other side to not giving up is that they must be trying new approaches. And frankly, even if they are sucking up to me, I’m not that worried about it — at least they know that talking about perseverance and creative problem-solving are ways to suck up to me!
Anyway, I think that just about explains everything. I’m more than happy to explain anything at all in more detail, if anybody is interested.