This seems so easy. What makes it hard to do? I will suggest some reasons and discuss each in turn.
Students Know, Teachers Don’t
As an instructor, I know I don’t understand some contexts that learners understand, and so I’m unwilling to work with or make up problems in these areas. I’m afraid I won’t be able to get the “right” answer, or that someone will ask me a question I can’t answer. I don’t trust my students who know about an area to be able to explain it to me or to other students who don’t know about it, so I like to be prepared with a back-up explanation. If the area is something that I am not familiar with, I feel lost and unwilling to take the risk. An example for me is sports statistics. I know there are acres of math in there somewhere—batting averages, win/loss ratios, salary caps, comparison of scoring records from former days with scoring stats from today, but it’s not my life, so I don’t feel comfortable working with it in math class.
For me to use this area of real life, I have to learn something new, maybe a lot of new things; if I decide to learn from my students, it’s going to be messy, with a lot of “not math” going on in the math class. Maybe I can learn some basics from a book or from a friend, outside of class, and then I’ll have to trust my students to help me through the hard parts. There’s that shared power structure again.
Teachers and Students Understand Differently
I get fooled sometimes. I’m talking with students about something, and I make all kinds of assumptions based on how it works in my life, but as we talk, I begin to see that things work differently in their lives. Of course, this happens with friends and colleagues, too, but in the classroom I want to find contexts that we share, so that the math part stands out. When I start from my life to find examples of math use, I often find examples that do not speak to my students’ lives. Cooking comes to mind. For me, cooking involves reading cookbooks, deciding on a recipe, checking the cupboard, and buying what I need for the recipe. I measure nearly everything with cups and spoons, so it’s easy for me to cut a recipe in half, or double it. When I talk to students, however, or watch them cook, I find most don’t use a recipe, and they measure by eye or by feel, not by cup or by teaspoon. When I look at the way they cook, I can’t find any math; when they look at the way I cook, they don’t recognize it as real life, so math work I make up about cooking is not real life math for them. They have to understand this foreign way of operating in the kitchen before they can attempt the math problems, and the result is that I make it harder for them, not easier.
Math Problems Include Hidden Motives
Many texts use problems taken from real life that I think have a hidden message: “Your life is a mess because you don’t know how to manage your money and I’m going to show you how.” There follow endless questions about balancing a checkbook, finding the best buy, figuring out interest payments, working on commission. For students living below the poverty line, the problem is not how to budget, but how to get more money, food or other necessities. Finding out how to get an extra bag of food from the food bank, or where to go for a free dinner, or how to get some help to transport the free couch someone has offered you, are all much more efficient ways to improve your life than learning to balance a chequebook.
A participant in an on-line discussion group posted this story:
I was contracted to teach the literacy portion of an employability skills course (students were mandated to take this course through social services) and I was mandated to teach a section on budgeting. I walked into the class, and began talking about coupons, saving, budgeting, etc.— all to blank faces. I could feel the anger in the room. I went home, pondered, and then the next day, I sat myself in the back of the room, (trusting my gut instinct on this one) and said, “Who am I to talk to you about budgeting?” (I knew they envisioned me as having a good income.) I said it was them who could teach me how to budget since they did it every day of their lives—them who had to scrape by on a measly $600.00 a month. I trusted them to have the answers within themselves. I apologized for having demeaned them by talking about what they could do, rather than learning how they heck they did do it. It was transforming, to say the least, as to what happened in the room after that: they all got to work telling, not just me, but everyone there, how they did do it. We then compiled a list of helpful budget hints, and everyone was extremely happy about the learning process. (“Getting Out of the Way,” an asynchronous on-line conference sponsored by Literacy BC, May 23, 2001).
Meaningful, realistic problems do not always lend themselves to mathematical solutions; other factors may be more important. If a student lives with a drunk who spends all the money on booze, budgeting is not the solution to her life problem, and not even the solution to her money problem. Similarly, time management may not be a matter of estimating how long things take, filling in a schedule, learning to plan for future events like tests, and so on. If a student is on-call at two part-time jobs and she must say yes to any call, or if she has on-call responsibilities in her extended family, or if she has to stand in line for hours at the welfare office or the food bank, she does not control her own time. Because she does not control her own time, she cannot plan to get her homework done by filling in a schedule. Rather, the solution to her problem lies in gaining some control over her time.
I’m not suggesting that the math class is the place to take on how to deal with a drunken mate (although it may be), or how to get better working conditions or get other family members to help with family responsibilities (although these, too, may be appropriate). However, I am recognizing that math content that purports to offer real life situations often misses the mark, no matter how well meaning it is. So-called “real life” problems may not be any more relevant to students’ lives than this one, from Even Cowgirls Get the Blues: “If a hen and a half lays an egg and a half in a day and a half, how long will it take a monkey with a wooden leg to kick the seeds out of a dill pickle?” (Robbins, 1981, p.16).
Real Problems Are Messy
Problems from real life do not fit neatly into 50-minute classes, nor do they build on math skills and concepts systematically. Because they require divergent thinking, and many different kinds of math skills, they do not fit neatly into the kinds of texts we usually use. Different students bring different math experience and different life experience to realistic problems, and this wide range of knowledge and ability adds to the messiness when we use them in the classroom. By using the ordinary kind of textbook problems, we control this messiness to some extent. “I’ve taught everyone how to find the percent one number is of another. So I’ll give them this page of questions that ask them to find what percent one number is of another, and everyone will be able to do it.” In order to use real problems in the classroom, we have to give up some of that control, and agree to the messiness of real life. Of course, that means that we will also have to deal with our own resistance to giving up a “neat” math class, and that we will have to deal with student resistance, and that somehow we will have to convince colleagues and administrators that we are doing real math.
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