In the world of education, not all assessment is created equally. In the area of mathematics, folks seem to think marking or assessing student work is very easy to do: things are either right or wrong – full stop. This could not be farther from the truth.
Most of us grew up in a system that was based on that kind of marking, the kind that looked for a particular math problem to be only right or wrong. Tests and quizzes were comprised of many examples of problems, and we endeavoured to get as many as we could correct, generally using the same procedures over and over to solve the items.
That, however, is a very shallow level of assessing. Students can produce an answer to a problem without knowing or understanding the underlying mathematical concepts – and it is there, in the conceptual knowledge, that the “real math” lives. So a student who has done a page of problems (say, long division or quadratic equations) may be able to follow memorized rules and procedures to come to a correct answer without having the faintest notions of the “why” behind the rules and procedures. There was no assessment of the “real math”.
My friend Katie Wagner, who teachers a number of math courses at McMath Secondary School (isn’t that a cool place to be teaching math!), has written in her blog about two different kinds of math assessment:
Standards-Based Assessment — a grading method where students’ proficiency on a specific outcome is assessed based on a set of pre-established standards.
Outcome-Based Assessment – a grading method that assesses students discretely against the particular outcomes that they are to learn in a course, a unit, or such.
I encourage you to read Katie’s posts and think about the assessments you are doing with your students in your classroom (or, if you are a parent, think about the assessments your children are experiencing). Hopefully you will have some points of discussion and/or questions after you read about the other possibilities.
We need to be helping students understand the “why’s” of mathematics, to understand the deep concepts that underlie all of the rules and procedures, and we need to ASSESS students for those “why’s” and understandings.
Thanks for being a “guest speaker”, Ms Wagner!
Mathematically yours,
Carollee In the world of education, not all assessment is created equally. In the area of mathematics, folks seem to think marking or assessing student work is very easy to do: things are either right or wrong – full stop. This could not be farther from the truth.
Most of us grew up in a system that was based on that kind of marking, the kind that looked for a particular math problem to be only right or wrong. Tests and quizzes were comprised of many examples of problems, and we endeavoured to get as many as we could correct, generally using the same procedures over and over to solve the items.
That, however, is a very shallow level of assessing. Students can produce an answer to a problem without knowing or understanding the underlying mathematical concepts – and it is there, in the conceptual knowledge, that the “real math” lives. So a student who has done a page of problems (say, long division or quadratic equations) may be able to follow memorized rules and procedures to come to a correct answer without having the faintest notions of the “why” behind the rules and procedures. There was no assessment of the “real math”.
My friend Katie Wagner, who teachers a number of math courses at McMath Secondary School (isn’t that a cool place to be teaching math!), has written in her blog about two different kinds of math assessment:
Standards-Based Assessment — a grading method where students’ proficiency on a specific outcome is assessed based on a set of pre-established standards.
Outcome-Based Assessment – a grading method that assesses students discretely against the particular outcomes that they are to learn in a course, a unit, or such.
I encourage you to read Katie’s posts and think about the assessments you are doing with your students in your classroom (or, if you are a parent, think about the assessments your children are experiencing). Hopefully you will have some points of discussion and/or questions after you read about the other possibilities.
We need to be helping students understand the “why’s” of mathematics, to understand the deep concepts that underlie all of the rules and procedures, and we need to ASSESS students for those “why’s” and understandings.
Thanks for being a “guest speaker”, Ms Wagner!
Mathematically yours,
Carollee 