Why do we use math portfolios?
The Advantages of Authentic Assessment
We believe that the best way to assess what a student understands and can do is to examine evidence from a diverse collection of work. By viewing different types of student work created in a variety of contexts, we are able to see the strengths of students with different learning and communication styles.
Especially in mathematics, many teachers rely solely on tests and quizzes to assess understanding. At East Side, we do believe that students should be able to complete tasks independently, with time constraints, in a testing environment. However, we also believe that this is just one skill possessed by a strong mathematician. This belief is in line with the Assessment Principle of NCTM, which states, “overreliance on such assessments may give an incomplete and perhaps distorted picture of students’ performance” (p. 22).
In their book Integrating Differentiated Instruction and Understanding by Design (2006), Carol
Ann Tomlinson and Jay McTighe lay out three principals of effective assessment. The first is to “consider photo albums versus snapshots” (p. 60). By this, they mean that no single type of assessment can effectively measure something as complex as understanding. They explain this using a photographic analogy:
"A photo album typically contains a number of pictures taken over time in different contexts. When viewed as a whole, the album presents a more accurate and revealing “portrait” of an individual than does any single snapshot within. It is the same with classroom assessment—a single test at the end of instruction is less likely to provide a complete picture of a student’s learning than a collection of diverse sources of evidence is" (p. 60).
Especially in mathematics, many teachers rely solely on tests and quizzes to assess understanding. At East Side, we do believe that students should be able to complete tasks independently, with time constraints, in a testing environment. However, we also believe that this is just one skill possessed by a strong mathematician. This belief is in line with the Assessment Principle of NCTM, which states, “overreliance on such assessments may give an incomplete and perhaps distorted picture of students’ performance” (p. 22).
In their book Integrating Differentiated Instruction and Understanding by Design (2006), Carol
Ann Tomlinson and Jay McTighe lay out three principals of effective assessment. The first is to “consider photo albums versus snapshots” (p. 60). By this, they mean that no single type of assessment can effectively measure something as complex as understanding. They explain this using a photographic analogy:
"A photo album typically contains a number of pictures taken over time in different contexts. When viewed as a whole, the album presents a more accurate and revealing “portrait” of an individual than does any single snapshot within. It is the same with classroom assessment—a single test at the end of instruction is less likely to provide a complete picture of a student’s learning than a collection of diverse sources of evidence is" (p. 60).
Good Assessment Drives Good Instruction
When developing this math portfolio system, first we determined what an East Side student should know, understand, and be able to do to demonstrate that she or he is a capable mathematician. Now that the system is in place, we have to make sure to implement a pedagogy that provides our students with the opportunity to meet this standard.
Becoming Self-Directed Learners
This portfolio system also helps our students become self-directed learners. According to Bena Kallick and Arthur L. Costa (2004), “students must become continual and internally driven learners: self-analyzing, self-referencing, self-evaluating, and self-correcting” (p. 2). One way to motivate learners to be self-directed is to make their work purposeful and important. Our math portfolio system does this. When students know that their work is going into a portfolio that will lead to their graduation, they see their work as meaningful.