Portfolios are a way of collecting evidence of student engagement. They can have one or various purposes by focusing on students’:
- reflections on progress and successes
- sense of meeting the mathematics curriculum’s outcomes and indicators that a teacher selects
- sense of attaining the mathematics teacher’s goals for the class.
“Mathematics is best learned when students are actively engaged in constructing their own understandings.” – Dr. Marian Small
It is important that students participate in deciding what is placed in their portfolio. And at the same time, they must take responsibility for managing their portfolio and articulating the significance of each bit of evidence placed in it; for example, how does an item show that students are working towards the mathematics curriculum’s indicators, towards your goals for the class, and towards numerical literacy?
Do you want engaged, enthusiastic learners? Do you want to work with learners who strive to produce quality work? Do you want your students to learn and achieve more? The research is clear. When students are involved in the classroom assessment process, they become more engaged in learning. (Davies et al., 2008; p. 77)2
Some teachers expect students to help set their own goals and help determine some of the criteria for evaluating their portfolio. The more that portfolios are student created, student led, and managed in collaboration with their teacher, the greater the student autonomy that results. Teachers’ stories illustrate how responsible autonomy guarantees engaged learners, which in turn increases academic success. This is a feature of portfolio use that is particularly important for Indigenous students.
All of this means that students become acutely aware of their mathematics teacher’s expectations. When students explain the significance of a piece of evidence (e.g., usually in a note attached to the entry), they are pointing out to their teacher, and to adults at home who might read it, what the entry represents; be it effort, progress, success, or an ability to reflect. In other words, from a student’s point of view, a mathematics portfolio initiates important conversations with their mathematics teacher and their parents/guardians over their effort, progress, and success in learning mathematics and Indigenous ways of knowing.
Portfolios can be stored physically, for instance, as paper or duo tangs in a 3-ring binder or in a strong folder. Or they can be stored digitally as on a computer or other types of digital hardware.3
Consequently, videos or photos with oral or written commentary can capture activities related to Indigenous ways of knowing, problem-based learning, or mathematics activities. Students’ observations and diagrams can quickly be scanned and sent a student’s digital portfolio. A record of the action or an excursion into Indigenous ways of knowing would honour the journey students make to produce a mathematics product or to acquire new perspectives.
Most often, only the product is assessed (e.g., How well were the problems solved?), not the complex of capabilities, actions, and accomplishments required to produce the product (e.g., What ingenuity and Western mathematics’ values were evident? What new insights into sustainability were gained?).
A portfolio allows a teacher to balance action and product in student assessment. Included in this balance is the expectation that students will reflect on what they did and will communicate this reflection orally or in writing. For students who have a recurrent learning strength that is more oral than written, digital media facilitate that asset. Portfolio content can be informal feedback (e.g., written comments or a rubric filled out by a teacher) that celebrates the process of learning. It can also include formal feedback (e.g., quizzes, tests, and reports) that monitors summative assessments.
Whichever storage method is chosen, paper or digital, a student’s privacy must be ensured. Portfolios contain sensitive information that could make students feel vulnerable. Students need to feel safe and secure. Only the student and teacher should have access to a student’s portfolio.
When group work is involved, a group portfolio can be produced. If the portfolio is digital, then copying it to a student’s personal portfolio is easy. Some teachers have established a classroom homepage on the internet to maintain greater communication with parents and other teachers. With student permission, a teacher could easily copy an item from a student’s or a group’s portfolio to the class homepage.
Portfolios often include the following:
- a visual that conveys the portfolio’s organization
- a table of contents
- rubrics, rating scales, and/or checklists to be filled out by teachers and/or students on a fairly regular basis (i.e., formative assessment)
- rubrics, rating scales, and/or checklists to be filled out at the end of a unit, semester, or year (i.e., summative assessment)
- student reflections and self- assessments
- written descriptions of, and reflections on, certain activities, projects, and class discussions (e.g., a section for “An important contribution I made today”)
- teacher comments
- digital recordings that document activities and projects
- digital recordings that communicate student reflections
- quizzes, tests, lab reports, science projects, research reports, and other formal products
- summary page written by the student at the end of the portfolio identifying their growth and their strengths, and suggesting a few goals for their improvement in certain areas.
|It is essential that students explain the significance of each entry. To facilitate this task, you could design a form that will be filled out by a student and attached to each entry. This graphic shows a sample form for you to modify to meet your own situation. 4|
From time to time when you review new entries to a student’s portfolio, you can write your comments on the form students have attached to an entry, if applicable. This is excellent feedback to a student.
Students should be encouraged to identify their progress and celebrate it, for a number of attainment goals that you have set for them, and for goals that they have set for themselves. Conventionally, people have tended to focus only on the products of learning and on the next hurdle for students to overcome. Portfolios tend to correct this over-emphasis.
This SaskMATH resource can help you move towards developing a portfolio assessment for your students. However, it can not offer a particular strategy or a particular set of assessment tools that will work for you, because these involve a host of decisions unique to each teacher or school.
Colleagues who teach other school subjects and assess their students with portfolios can give you general tips on implementation strategies. For instance, consider introducing portfolios in incremental steps. Students gradually learn responsibility for managing their portfolio, and teachers new to portfolios benefit from becoming familiar with their various features over time. You might introduce portfolio use after students have become accustomed to your classroom routines and expectations. As it turns out, teachers become strongly motivated to increase and expand their portfolio use when they experience students’ positive reactions to sharing responsibility for assessment.
The following ideas may be used to support the creation and effectiveness of portfolios:
- Remind students how you conduct assessment and evaluation in your class. Introduce portfolios as an extension to what you currently do.
- Invite students to describe what they already know about portfolios.
- Provide a brief overview of how you expect portfolios to work in your class.
- Show an example of a portfolio, if possible, for students to picture what it might be for them.
- Let students know what they will be evaluated on; that is, explain the purposes of their portfolios, and illustrate specific ways you and they will contribute to the assessment and evaluation of their portfolio entries. For example, share summative rubrics, rating scales, and/or checklists with students.
- Collaborate with your class when setting up guidelines for what entries will be included, and how those decisions will be made. Here is a sample of topics to address:
- What are the purposes of the portfolio? (effort, progress, successes, reflections, meeting expectations, final evaluation, etc.)
- What can be included in the portfolio?
- What are the criteria for selecting an item or piece of work for inclusion? When should those selections be made?
- How to learn to use the technology for digital portfolios, or for digital entries to paper-based portfolios.
- Who will determine what entries are included in the portfolio (e.g., the student, the teacher, the student and teacher in consultation)?
- When should entries be added or removed?
- How should the entries be organized and documented?
- Where will the portfolios be stored?
- How will your feedback to the students take place (e.g., written, oral, interviews, rubrics, rating scales, checklists, etc.)?
- How will the portfolio be evaluated in the end?
- Review with students their responsibilities in organizing, managing, and updating their portfolio, and periodically discussing its contents with you.
- Inform parents/guardians about your portfolio innovation
The above list is neither exhaustive nor prescriptive but intended to start a conversation among like-minded colleagues.
1While this heading indicates an Aboriginal context, the considerations in this section are universally applicable to a Holistic way of assessing all children
2Davies, A., Herbst, S., & Reynolds, B.P. (2008). Leading the way to making classroom assessment work. Courtenay, BC, Canada: Connections Publishing.
3More on this topic can be found in the Communication/Portfolios section of Digital Classroom/Communication (https://saskmath.ca/digital-classroom-communication/)
4Assessing, Evaluating, and Reporting Student Progress – Supporting English Language Arts, Saskatchewan Ministry of Education, 2011, p. 10.
5ePortfolios Explained: Theory and Practice. Centre for Teaching Excellence, University of Waterloo. https://uwaterloo.ca/centre-for-teaching-excellence/teaching-resources/teaching-tips/educational-technologies/all/eportfolios.