A Conversation with Jack Rotman: Part One

As promised, here is Part One of our interview with AMATYC's Jack Rotman! A developmental math teacher for more than forty years, Rotman has worked with AMATYC in various positions since 1987. He currently runs the New Life Project—"a national effort to develop a new model for developmental mathematics." 

This first portion of our conversation covers many topics, but we mostly speak about his response to Complete College America's infamous "Bridge to Nowhere" findings, as well as Rotman's thoughts on the joys and pleasures of mathematics. Part Two—scheduled to run this Wednesday—focuses predominately on the New Life Project. Note that we spoke with Rotman before AMATYC 2015. 

For more on Rotman's thoughts about the "Bridge to Nowhere," click on this link, which will take you to an AMATYC powerpoint presentation that addresses the topic. 

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ASP Blog: At AMATYC 2015, you plan to give a speech that directly responds to Complete College America's assertion that developmental math (and all remediation) serves as a "bridge to nowhere." What compelled you to respond? 

​Rotman: It is risky that they are using data to backup predetermined positions. It’s a pretty awful use of data. Overall, the data does show problems; however, I don’t know about all developmental education, but certainly in mathematics, [this bad data is not caused by] nature but by design. Many developmental courses are simply copied from elsewhere and then misused. Our work [at AMATYC] is all about deciding what students actually need at the college level—whether its mathematics, science, or technology, then building courses from these things rather than merely copying a high school course and calling it good enough for college.
 
One of the things they say in “The Bridge to Nowhere” report is that students come to college expecting college level courses not high school courses—well, I actually agree with that. It is important to give students the college experience, even if they need to do something prior to normal college work. So, our courses are at a somewhat higher level cognitively than traditional developmental math courses. This is one of the problems that we see in our traditional work—it is so procedural and memory based that students don’t get any preparation for the bigger challenges they face in college-level work. 

ASP Blog: I know another thing you are passionate about involves the math teachers themselves. We focus so much on students—and justifiably so—that sometimes we don't stop to think that teachers might do a better job if they too were genuinely engaged with the content they teach. Can you discuss this? 
 
Rotman: One of the things I used to work on was getting mathematicians excited about teaching mathematics. The traditional work in college—especially in developmental and college algebra—has been ruined in some ways. It isn’t as exciting as many professionals want it to be. You want to teach something you feel good about—not simply trinomials or how to solve an eight-step rational equation. Those are things we want students to be able to do when needed, but they are not things that make teachers wake up in the morning and say, “Oh, I can’t wait to teach that today.”  
 
The human mind is naturally curious about how things fit together. It’s not that we have to convince students that mathematics is interesting or not interesting. If we present something that we are genuinely excited about—most students respond to that. Right now, it is hard for students to get excited about traditional curriculum because it is the same stuff that they had before that wasn’t useful the first time they saw it.  

ASP Blog: So you are saying that teachers need to get excited about their work and students need to better understand the context of what they are learning? 

Rotman: This is difficult to articulate accurately. Some people hear me talk and come away thinking, "Jack is all for teaching everything within context.” Other people hear me talk, and they think I’m saying that context is irrelevant. The truth is somewhere in between. 
 
My own background isn’t so much in mathematics as it is in educational psychology. I’ve been reading research for forty years. In all of that reading I’ve never seen any research that shows teaching math in context actually improves learning—it improves motivation, but it can actually harm learning if you are not careful. That is true for most things that we do. It is easier to harm learning than it is to enable it.
 
When people teach fully from context, they often limit the mathematics they teach to what students can understand at that specific time. I feel really bad about that because if I can’t get a student at least interested in learning mathematics for its own sake, I haven’t shown them what a mathematician is, I’ve just showed them how you use mathematics. These are not the same thing. 
 
When students pass through one of my math classes, I want them to at least get an inkling that the material is something that somebody gets interested in by itself. Even if we can’t apply it right now, this math is something that can be fun for the next sixteen weeks.
 
I like context—but I never stay there very long. I start with context in my classes—I usually teach something simple, then bring it into context, then go into something more mathematical. This involves a kind of a dance around context, not a long term stay. 

ASP Blog: That is so interesting! I can see how someone who is passionate about math, someone who genuinely finds it fun, would almost resent the idea that math is some sort of pill hidden in peanut butter that one tries to force down the throat of a sick dog. If you genuinely care about math, I can see how this approach might come across insulting.  

Rotman: Mathematics has always been this amazing and awkward mixture of practical and unpractical. The interesting thing is that some math that was useless twenty years ago is now a matter of national security or enables a business to survive or enables a company to produce something. Today’s useless mathematics is tomorrows economy. You never know.
 
So do we really want to say to students, “I am only going to teach you what you can use today, which is actually what you could have used two years ago.” We are never completely up to date. When they need something in five years, students will have no idea what they should be looking for.
 
When people think of math, they usually think only of arithmetic then useless things that don’t apply to life. [This binary] bothers me a lot. History is full of mathematics being embedded in practical things as well as being an abstract pursuit for its own merit. That’s true for most sciences—all of them are like that. The arts too. There are two dimensions in math. You can’t teach just one and lose track of the other. 

ASP Blog: You’ve basically just described a paradox. Math is perpetually useful and un-useful—and neither of these categories is fixed.  
 
Rotman: Right. The whole world is a paradox in some ways, from top to bottom. There are days that everything makes sense, but more often than not, there are things that don’t quite fit together. 

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Click here for Part Two.