Math Portfolios

posted by Stephanie Forsman

At the start of every school year, I always have it in my mind that this is going to be the year that I create the ultimate math portfolio. A fluid place where the children’s entire math worked is housed; a place where all of their previous work is easily accessible and they can refer back to review or to aid them in solving a problem; a neatly organized, sequential archive that includes technology, reflection, and assessments. And every year, the idea of this “perfect” math portfolio becomes too daunting and I end up spending the year avoiding such an undertaking and putting it off until the following year.  Well, this upcoming school year 2017/2018 is the year! With the help of our Math Specialist, I am going to work on creating the ultimate math portfolio for elementary children. Wish me luck!

The problem with creating such a math portfolio is that we have so many different ways in which we record our mathematical thinking.  They have a math notebook, individual papers (worksheets, puzzles, scrap paper) that goes into a math binder, a math workbook that compliments our TERC math curriculum, math projects, math games, and math work that they record on their iPads either in Google Classroom or in the Explain Everything app. I understand that this portfolio is not designed to house ALL of the math work they do in 4th grade but rather, be a mindful collection of work that best highlights a student’s efforts, progress, and achievements.  And I want the portfolio to be an ongoing conversation between our Math Specialist, the student, and myself.

Before school ended last June, the Math Specialist and I decided that we would try and create a digital math portfolio. We have a one-to-one iPad correspondence program at my school and we already do a fair amount of our math work on the iPad.  I can also send them PDFs of assessments or worksheet that I want them to work on through a PDF Annotator on Google Classroom.  Explain Everything is the iPad app that we use most for our math work so I think that this will continue to use this app to create our math portfolios.

“Create, share, and present on any device using Explain Everything Interactive Whiteboard. Use real-time collaboration, a cloud sharing portal, infinite canvas and a wide range of tools to present your ideas and express your creativity.”

The children can draw and annotate; import images, files, and videos; record everything; add text and math equations; share cloud projects; collaborate; and it works with Google Drive. I love the idea of students having video of them talking about math strategies and their mathematical thinking.  Parent/teacher conferences are an added bonus of that video feature.

Now that I have pretty much decided on my format, what goals do I want to accomplish with this math portfolio?  I stated earlier that I wanted a place that houses all of their math work but is that necessary?  A math portfolio should help the children recognize quality work and take some time to select entries that best reflect their effort and process.  Writing this blog has helped me to work out some issues and specifics that I’d like to include. For instance, I think that setting aside a time once a month or once a unit to go through our work would be most beneficial.  The first session, the Math Specialist and I could model how to go through our math work and chose pieces that ill go into the portfolio. We need to communicate our expectations of what kind of work needs to be collected. (and what not to collect needs to also be communicated) A reflection should accompany the work. Work they are proud of and why, work they really worked hard on, worked where they made a mistake and learned from that mistake and where able to correct their work through that mistake.  The reflection can be a PDF that can accompany the work that will then go into a file or a verbal explanation using the actual work as a visual that can be done on Explain Everything.  How great would it be for report cards, assessments, and Parent/Teacher conferences to have a recording of the student explaining their process and mathematical thinking?  Children also love to hear and see themselves on video and will most likely look at and listen to the reflection several times throughout the year further solidifying concepts and skills.

Another important aspect that I want the children to be able to include in their portfolio is the Exemplars they do for weekly homework.  Exemplars are open-ended questions that engage students and help them to develop critical thinking and reasoning skills to solve real-world problems. An example of a weekly Exemplar:

 

The Exemplars are broken up into content and I assign a different problem a week that aligns with what we are studying.  The children can use any strategy that works for them but they must show all of their work.  If they just simply write down the answer then I have them go back and explain their thinking.  Exemplars become an important part of our math routine and conversations, (we once did a whole end of the year skit on how our class uses habits of Mind to solve Exemplars) and the children become very motivated and determined when solving.  After the Exemplars have been reviewed, I think that I will have the children put them in a folder and later, when reviewing our work for our portfolios, chose some Exemplars to contribute.  They can take a picture of their work and download it into their digital math portfolios.

A big part of our math program is cooperative collaborations, projects, and playing games.  Occasionally I like to give the kids team building challenges.  I get these challenges from the Internet, professional workshops that I have attended or from Odyssey of the Mindwww.odysseyofthemind.com.

Odyssey of the Mind is a creative problem solving competition with teams from all over the United States and they have practice problems on line.  Several times a year, I  present the children with a problem and give them a time limit to figure out that problem.  Divided into groups, each group receives materials, guidelines, and a time frame that is divided into planning, execution and review.  The last challenge we did was “The Newspaper Tower” challenge. Each group got a stack of newspapers and two meters of masking tape. The challenge was to build the tallest structure they could using the given materials.  The children love these challenges and ask to do them often.  I take picture of them at work but they very rarely see all the pictures and I end up sticking them in an end-of-the-year slideshow.

 

So, what if I made the photos available during our Math Portfolio time and the students could choose what photos they wanted and add them to their own portfolios? This serves not only as evidence of their experience but, if accompanied with a recording, serves as a way to document their learning in ways that do not lend themselves to traditional assessment. I really like the idea of the student’s math portfolios including lots of pictures that include captions or recordings.

In the same ways that we have Writing Celebrations and Parents as Reading Partners, I’d like the children to have an opportunity to celebrate their progress and set future goals.  Math Portfolio Monday? Maybe twice a year where parents, other teachers and students can come into our classroom see the math work we’ve been doing.  We can project some of the work onto our whiteboard via Airplay and others can show their work on their iPad.  And maybe there could be some place where people could comment on the portfolios?

I will not only need the help of my Math Specialist with this endeavor but the help of our IT person and our Director of Library and Research (technology) While writing this blog, I have become very excited about this digital math portfolio and already know that I am going to have my students include the beginning-of-the-year math questionnaire that I hand out on day one. That will be our starting point.

On last thing that I’d like to mention is that I make my own academic goals known to not only my students but to other faculty members and to parents. The children tend to be more technologically savvy than I am and they usually help out a great deal in that area. Colleagues can help you out with ideas or resources and by telling the parents, it keeps me accountable.  Writing this blog will also keep me accountable!

Stephanie Forsman

Stephanie Forsman—who wrote many of the math lessons on our Math at Home website—has been teaching in the New York City independent school system for more than 15 years. She is currently a fourth-grade teacher at The Berkeley Carroll School in Brooklyn, where she previously taught at the second- and third-grade levels. She has served as a facilitator for Mathematics in the City, a research and professional development center with a mission to "transform classrooms into communities of mathematicians, where children explore interesting problems and, like mathematicians, engage in crafting solutions, justifications and proofs." She has presented workshops on Math Puzzles & Logic Games, Technology and Math and Napier’s Bones at national conferences and served as the math subcommittee chair for the accreditation group conducting the New York State Association of Independent Schools’ 10-year school accreditation reviews in 2013. Stephanie earned her B.A. in art history and fine art at Trinity College in Washington, DC, and her M.Ed. in elementary education and museum education at Bank Street College in New York City. She also served as a Peace Corps volunteer in Mali, West Africa.

Read more posts by Stephanie Forsman

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