For fifteen years I taught in a district that stood firmly on the premise that all teachers were teachers of reading. As a middle school math teacher, I was also given a reading block each day. As is often the case in ELA, my students kept portfolios in which they collected evidence of their growth as readers.
I appreciated the teachable moments using portfolios provided. My students had many opportunities to track growth, identify points of understanding/confusion, explore personal reading/writing preferences, and reflect on strategies that scaffold reading success.
It didn’t take long to realize I wanted this same experience for my math students; hence, the birth of a math process-folio.
I used the term “process-folio” because I wanted my students to identify the practices and processes necessary for good mathematical thinking to flourish. My goal was for students to view themselves as capable in math, where they see and insist that math makes sense. The process-folio would provide that evidence where students could track their growth in analysis, relational thinking, and problem solving.
I intentionally created and found tasks that promoted reasoning, good number sense, and estimation. Students wrote journal entries with questions, connections, and representations they used to help make problem solving easier. I made sure to provide ample time for reflection as they discovered points of progress. Students identified growth by selecting pieces over time identifying where and how they went from confusion to understanding.
An even more important goal was for students to appreciate effort as a means to success in math. I took time each week for students to recognize and reflect on how effort and hard work made a difference in their confidence and success in math. It was important for my students to discover that anyone can be smart in math with effort and care.
Always My First Assignment: A Math Autobiography
The first entry for students every semester/year was a Math Autobiography. I believe students can learn much about their feelings about math from reflecting on their personal math histories. An example of my assignment is included below:
My Math Autobiography
|Before we embark on our wonderful math journey together, I’d love to get to know more about you and your personal history in math.
You will need to share that history in a Math Autobiography. It is helpful to first reflect on your feelings about math and to identify the experiences in your life that led to those feelings.
Your Math Autobiography should fill at least one page with Times New Roman font in 12 point size, double spaced. Sentence structure, spelling, and punctuation are important.
Be careful that your Math Autobiography is in paragraph form and not a bulleted list of answered questions.
The sentence stems below are a way to get you started. You do not need to use them all. If you have an idea not related to these that you would like to express, please do so.
Some Possible Sentence Starters
|5+ points 3-5 points 1-2 points
Thorough, Thoughtful, Somewhat Thorough Skimpy
Exceptional Effort Good Effort Little Effort
|0-5 points||SELF-REFLECTION: In-depth reflection with meaningful discoveries on the impact learning math has had on your life thus far.|
|0-5 points||MECHANICS: Response is written clearly using Standard American English including correct grammar, spelling, punctuation, and complete sentences.|
Upon reading the math autobiographies, I would write back to each student responding and reflecting on their math stories. I would ask them to consider how their math history might be impacting their math future. I challenged my students to use this experience to help form personal goals for the year. These goals would be included in the process-folio and revisited several times over the year. Collectively, we would create a class chart of principles to abide by so every student would have the opportunity to achieve their goals.
Suggestions for Additional Submission Pieces in a Math Process-Folio:
The following are other possible pieces that can be included in a math process-folio. Some years, I used them all; other years, I was more selective. It all depends upon the individual class and your intention as the teacher.
The choices do not matter as much—it is really the student’s reflection on those choices that matter. I have found some students do not know when their own learning occurs. They need to recognize their capabilities and pinpoint those moments of clarity. Success breeds success and getting students to recognize they can succeed in math increases their motivation, confidence, and self-efficacy.
25 Suggestions for Additional Submission Pieces in a Math Process-Folio
- A table of contents – if the teacher is setting the pace for submission pieces
- Journal entries – with time to reflect on the reasoning behind the math and personal progress and/or struggle
- Exit tickets – student choice and/or teacher directed
- A challenging problem showing good reasoning and problem solving skills
- Proof of how the student went from confusion to understanding
- Student preference of his/her best fit strategy with explanation
- Representations of good math reasoning
- Assessments with reflections and/or corrections
- Proof of good math collaboration, with justification of why it is considered good
- Samples of best/worst work with explanation
- Personal math strengths with samples
- Personal math struggles with samples and action plan
- Reflections on personal progress (revisit and/or revise goals)
- Attitudes changes towards math with revisit of math autobiography
- Student submissions by choice
- Noticing & Wondering Brainstorms
- Celebrations where hard work really paid off
- Problem-based learning opportunities and/or projects
- Proof of growth in one or more of the Standards of Mathematical Practices
- Relevance of math topics
- Something the student is really proud of, with explanation
- Something the student would have done differently and what the experience taught him/her
- Something the student wants the teacher to notice
- Connections recognized between math topics with explanation/sketches
- A parking lot of continued questions and answers discovered along the way
A Final Reflection on the Math Process-folio: Student-Led Conferencing
I always ended the semester with Student-Led Conferencing. Many districts are implementing student-led conferencing during parent/teacher conferences. As a consultant, I have seen the benefits of this experience as students take an active role in their assessment of their progress in learning. I believe all opportunities we offer where students gain a sense of agency, interest, and motivation to learn, are always worth the effort.
My student-led conferences were similar but without parents. For students to get the most out of the experience, I would take time in class throughout the year for them to prepare. Part of the planning time was used to identify and reflect on how, when, and why learning occurred. The conferences then provided the opportunity for them to showcase those discoveries.
Below is a template for how my students would prepare for this conference:
Student-Led Conference: Reflecting on your Growth as a Mathematician
During the last week of the semester, you will meet with me concerning your math process-folio. Prior to this meeting, we will take time in class to sit and reflect on your learning in math this semester as is evident in your math process-folio. You worked hard and you should be very proud. I want you to discover those points where your best learning occurred.
At the conference, you will lead the conversation that shows your growth points as a learner as a result of our time together. This meeting should take 15 minutes and will be led by you. It will take preparation and reflection to make this conference a worthwhile time of learning.
If you miss this meeting, 20 points will be immediately deducted from the process-folio grade.
This is also the opportunity to share your unit plan. Be prepared to show revisions and growth moments and parts that really make you proud!
YOUR MEETING TIME IS AT ______________ ON JUNE 7TH, 8TH OR 9TH. THIS MEETING WILL TAKE PLACE IN ROOM ________________ AT __________________.
Feel free to use the following questions/sentences to help you in making our meeting meaningful.
- What is something you are most proud of?
- What is something you would do differently next time?
- Show one of the Standards for Mathematical Practice and how that standard is reflected in your work. Discuss how this helped you in your mathematical thinking.
- What shows an ah-ha moment for you?
- Show evidence of how________ is like _______________.
- Show evidence of how _______ is different than ____________.
- What two things show growth? (Show a beginning understanding to a deeper understanding)
- How will you use your math process-folio?
- What would you like me to know about your process-folio?
- What advice would you give next semester’s students about the process-folio?
- What is something that was tough at first, but then you got it? Show evidence of that progression.
You do not need to answer all of the above questions, but using them as a framework for leading our meeting will make it much easier for you. Another good idea is to post-it where you will find the answer to the questions so you can find them with ease.
Best of luck! See you at the meeting!