Submitted as an entry in the MathTwitterBlogosophere New Blogger Initiation:
First, a confession: I am not a math teacher. I will understand if being a math teacher is viewed as a non-negotiable prerequisite for participation in the mathtwitterblogosphere, and will accept my excommunication. Otherwise, please read on:
Last year, I was a Match Corps member at Match Middle School in Boston, MA. As the Algebra TA at Match, I was responsible for writing the math tutorials for our eighth graders, and it forced me to think about the problems that we give our students, and the work that they evoke. Early in the year, I had creative ambitions, but they were clumsily executed and incredibly time-consuming. By midway through the year, I could efficiently produce error-free scaffolded assignments, which seemed to mostly fulfill the primary goal of tutorial: high repetition procedural practice. But I was dissatisfied. Students were getting better procedurally (important), but they were totally missing the relevance of mathematics (very important). I wanted to communicate that math is a language that we use to represent real situations, and to solve real problems, but there's no way to communicate that without giving students real problems, and it's hard to come up with real problems in real time.
First, a confession: I am not a math teacher. I will understand if being a math teacher is viewed as a non-negotiable prerequisite for participation in the mathtwitterblogosphere, and will accept my excommunication. Otherwise, please read on:
Last year, I was a Match Corps member at Match Middle School in Boston, MA. As the Algebra TA at Match, I was responsible for writing the math tutorials for our eighth graders, and it forced me to think about the problems that we give our students, and the work that they evoke. Early in the year, I had creative ambitions, but they were clumsily executed and incredibly time-consuming. By midway through the year, I could efficiently produce error-free scaffolded assignments, which seemed to mostly fulfill the primary goal of tutorial: high repetition procedural practice. But I was dissatisfied. Students were getting better procedurally (important), but they were totally missing the relevance of mathematics (very important). I wanted to communicate that math is a language that we use to represent real situations, and to solve real problems, but there's no way to communicate that without giving students real problems, and it's hard to come up with real problems in real time.
I started wondering about other teachers: How did they get their problems? What did their problems look like? I kept my ears open, and it seemed like teachers relied on four problem sources: textbooks, subscription problem banks, online worksheet generators, and their brains. None of these seemed to be the way that you would produce problems if you thought they were critically important. The first three outsource problem creation and selection to anonymous workers writing problems for anonymous students, which seems like a good recipe for consistency, but not for excellence. The last solution pits an individual teacher, with limited time and resources, against a virtually unlimited task - a recipe for exhaustion and compromise.
Nevertheless, I admired and trusted the efforts of individual teachers far more than the books, banks and generators. It seemed like the people who devoted themselves to students two hundred days per year were the most likely to really care about fostering engagement and understanding. As I wrote my problem sets, I thought about generations of math teachers, hundreds of thousands of them, all writing problems for their students, but separated by time and space. And, at last, in conversation with teachers, I stumbled upon an alternative: a free math problem bank, created and curated by K-12 teachers.
Here's an attempt at a clear argument (to facilitate objections):
(A) Teachers (and most adults) want to improve students' engagement in and understanding of mathematics
(B) Students' engagement in and understanding of mathematics is shaped, primarily, by the problems that they solve
(C) If we want to improve the student experience of math, we need to improve math problems
(D) To improve math problems, we need to identify good problems, and we need to produce a lot of them
(E) The best way to identify good problems, and to produce a lot of them, is to have a lot of people contribute their best problems
(F) There are a lot of teachers already writing problems who might be motivated to contribute their best
(G) A simple website could give teachers the platform to collectively produce and curate a library of excellent problems
Habib and I started working on the website in May. We're calling it Opus - Latin for "work." We picked Opus not because we like to be pretentious, but because we think that the English word "work" has become associated with drudgery. When we give a student a cookie-cutter problem, we are asking her for "work." When we give a student a great problem, we are providing her with an opportunity to create an "opus."
In short, we believe that there is an intimate connection between the problems that we give to students, and the work that they give to us. Opus is a place where teachers select the "work" that their students will do. RealProblems is a blog about how to write problems that are worthy of an opus.
-Tyler
Nevertheless, I admired and trusted the efforts of individual teachers far more than the books, banks and generators. It seemed like the people who devoted themselves to students two hundred days per year were the most likely to really care about fostering engagement and understanding. As I wrote my problem sets, I thought about generations of math teachers, hundreds of thousands of them, all writing problems for their students, but separated by time and space. And, at last, in conversation with teachers, I stumbled upon an alternative: a free math problem bank, created and curated by K-12 teachers.
Here's an attempt at a clear argument (to facilitate objections):
(A) Teachers (and most adults) want to improve students' engagement in and understanding of mathematics
(B) Students' engagement in and understanding of mathematics is shaped, primarily, by the problems that they solve
(C) If we want to improve the student experience of math, we need to improve math problems
(D) To improve math problems, we need to identify good problems, and we need to produce a lot of them
(E) The best way to identify good problems, and to produce a lot of them, is to have a lot of people contribute their best problems
(F) There are a lot of teachers already writing problems who might be motivated to contribute their best
(G) A simple website could give teachers the platform to collectively produce and curate a library of excellent problems
Habib and I started working on the website in May. We're calling it Opus - Latin for "work." We picked Opus not because we like to be pretentious, but because we think that the English word "work" has become associated with drudgery. When we give a student a cookie-cutter problem, we are asking her for "work." When we give a student a great problem, we are providing her with an opportunity to create an "opus."
In short, we believe that there is an intimate connection between the problems that we give to students, and the work that they give to us. Opus is a place where teachers select the "work" that their students will do. RealProblems is a blog about how to write problems that are worthy of an opus.
-Tyler
