It all started accidentally, with reading an article. It was 1998, my first year of teaching in the USA. That memorable year taught me many lessons. Among those was the realization that along with my extensive experiences of teaching in Europe, I needed to explore and integrate new methods that were available in America.
I got really excited about that article entitled Student Portfolios in Mathematics by Donita Robinson, from the April 1998 issue of the Mathematics Teacher. I found the topic very interesting and it motivated me to enroll in an online graduate course, Portfolio Assessment: Making it Happen.
In general, in the day-to-day teaching we don’t have the opportunity to stop, focus, and evaluate our progress and accomplishments very often. This is why it’s important that our students learn how to reflect on what they are learning. The reflection process gives them a greater awareness of the learning process and helps with the clarification of their goals. Portfolios provide the avenue for all of this.
I gave the first portfolio assignment during the 1998-1999 school year in my junior Honors Precalculus classes. At that time, at Seattle Preparatory School, we had trimesters. Each student created a showcase portfolio in the end of the first trimester, and one in the end of the year (second and third trimester combined). In later years, besides Precalculus, I also used this assessment in freshmen Intermediate Algebra and senior Math Topics classes.
I didn’t give too many instructions. I wanted a loose and a not very structured format, a collection of information that would paint a portrait, and show my students’ growth in mathematics. They needed to include a minimum of five entries in the portfolio that were important to them, explain why each was chosen and how it demonstrated their progress in the course, and write a summary reflecting on their overall accomplishments. They needed to place everything in some sort of folder with a creative cover, have a table of contents, and fill out the self-evaluation form. I evaluated the portfolios based on the above criteria, then the students took them home and showed their parents whose feedback was very positive, evident from the parent-feedback survey they completed.
Throughout the years, my students have, almost without exception, done a wonderful job with this assignment. They selected various entries: math autobiographies, tests, quizzes, notes, warm-ups, class activities, homework assignments, projects, or even a transcript from a distance learning math class. They came up with creative, funny, and thoughtful titles for the entries: Why does my brain hate me?, Take a Go-Ride in a Sine Curve, Logarithmic Nightmare, The Impossible Becomes Easy, Work That Speaks for Itself, Totally Awesome!, Wakeup Call, A cry for HELP!, My exponential growth, A log in my property, Mistakes Help Me Learn for Future Tests, How I Try to Do Better in Math Outside of School, Wait, Math Can be Hard?, Devious Domains, Quadratics’ Quirky World, Putting It All Together, My Pop-Quiz Nightmare, If At First You Don’t Succeed, Try Try Again, just to name a few.
The covers of the portfolios were either hand-drawn (often with mathematical themes, for example those from Leah, Ally, and Diana; Ayaka’s showed a girl – herself? – studying for long hours), had computer generated art, or featured a photo of themselves. Sometimes it was a collage (like Sydney’s second portfolio), and occasionally the work was dedicated to their cat (also featuring the cat!).
Some titles said it all, right from the beginning: The Wild Roller Coaster of Pre-Calculus, Pre-Calculus Expedition, My trip though the world of math, Time has passed…and a lot has been learned, Expanding my horizons, My World of Math, Precalculus with Pasztor: One Girl’s Story of How a Junior Honors Class Was Actually Fun, Learning from those around me…, or these two from Mazohra: Path to Pre-Cal: The First Steps of a Journey and Pushing the Limits: Reflections on a year of Pre-Calculus. Some simply stated My Math Portfolio.
A few students explained the meaning of the cover in words. Julie – whose portfolio, entitled Knowledge, featured dragons and volcanoes – said, “For me, to gain knowledge is to take a perilous journey, overcoming obstacles to finally reach the goal: comprehension of a concept. Be it dragons, volcanoes, or bad study habits, to defeat the barriers between me and understanding makes me a stronger student, as well as a stronger person, ready to take on the next challenger in the future.”
A few others – Pilar, Laura, or Neil – had a theme for their portfolio.
Pilar in Goldilocks and the Three Bears: My Journey through the First Trimester of Pre-Calculus just like Goldilocks, enters the “Forest of Junior Year.” In the “House of Pre-Calculus” she tries out chairs and tries to eat porridge. The first chair is too big but she finds a perfect one. The porridge is unbearable, too hot, later it’s mediocre, too cold, until the three bears give her opportunities to improve herself.
In her second portfolio, Pilar and the Beanstalk, she tells a charming story of a young girl who starves for knowledge, and exchanges the family’s treasured cow not for food, but for a handful of bean seeds. She plants them and they sprout and grow to a great height. She then scales the bean stalks while reaching new heights of knowledge. Sometimes she crashes but in the end has enough knowledge to “pursue the Giant Final.”
Laura in her Math Portfolio, in the “magical world of mathematics” finds her brain locked in a tower, fights a dragon, sees casting spells within spells, scales the steep and treacherous mountain, and then she “lives happily ever after (well, sort of).”
In Neil’s Portfolio of Pre-Calculus we follow him through “The treacherous fields of laziness” and “The valley of simple mistakes” as he tells the tale of trial and error.
Then The Return of Neil’s Portfolio shows how “He has translated indecipherable codes” and “gazed into the eyes of defeat undaunted”, until he was able to say The Final Trimester: No More Work.
Evaluating the portfolios was always a lot of reading. A lot of delightful, joyous, and sometimes surprising reading. Students clearly showed their growth in mathematics, in taking responsibility, and in self-confidence. They were very proud of their accomplishments. The high degree of self-reflection constantly amazed me and gave me great insight into how they were progressing and a richer picture about their abilities. They frequently reflected on the class procedures and atmosphere, and many of the reflections told me much about them as people.
Currently, I’m not using portfolio assignments in my classes, but I treasure some of the actual portfolios, and most importantly, I treasure the experience. It made me a better teacher, taught me the importance of reflection in the learning process, and gave me a powerful tool in my teaching. One day I might come back to this assignment.
As I was writing this blog post, I contacted some of my former students asking for their permission to use their work. They enthusiastically said yes, and to my great delight they even fondly remembered our time together. I can see the impact of portfolios to this day.
More about my students’ portfolios soon.