When I began teaching basic math (whole numbers, fractions, decimals and percent) to adults twenty-five years ago, I started teaching as I had been taught, that is, the teacher did the math at the blackboard and the students watched the teacher do math, and listened to her talk about doing it. Then they worked in their own books, and took the tests at the end of the chapter and at the end of term. From the beginning, from the very first term, I knew it wouldn't work. Students were bored and frustrated by their lack of activity and their lack of understanding. I was bored and frustrated by their lack of engagement and their lack of understanding. I wanted more.
I began to change my teaching practice in a variety of ways—more emphasis on teaching concepts rather than algorithms; more group work, less lecture time; more emphasis on students discovering patterns; more emphasis on math thinking and problem solving; and more use of real life problems and a greater reliance on manipulative's and models. Indeed, some of the very things that I found in the literature when I went searching recently.
When I began to change my teaching practice, I met resistance on all fronts—my own resistance, students’ resistance, and resistance from the programs I worked in over the years. Overcoming this resistance to new methods became the first hurdle to changing my practice and feeling comfortable with the changes.
As I changed my ways of teaching to include more student participation, problem solving, math thinking, group work, and use of manipulative's and models, a voice inside my head kept talking to me.
What you are doing is not real math, I could hear the voice say. It is frivolous to ask students to make charts and diagrams, more like art than math. Asking them to talk about their own ways of figuring things out is a tangent—you know the most efficient ways to do the calculations, so just teach them those and forget about their folk math. And getting them to work in groups to figure things out is a complete waste of time; it takes too long, and there is no way for you to tell what they are really learning in those groups. Probably they are not learning anything, and you have no control!
These new things will not help students pass the exam, the voice went on, and you know how important the exam is. You know what is on the test; drill on those things, and forget about the rest. You will just confuse the students more when you expect them to understand math rather than memorize, it continued. Just give up these new ideas, and it will be easier on everyone.
Working in these new ways just causes problems, I heard the voice say again. You know that your students have huge holes in their math backgrounds. When you stray off the beaten path in math class, you fall into one of those holes, and when you try to fill it in, you fall into another hole, and you can never get out. Furthermore, every student seems to have a different set of holes! The only way to get through the material is to stick to the path, and help the students figure out how to stay on the path to the end of the course. You know you’re creating more holes by doing it this way, but it’s the only way.
I dealt with the voice in various ways: I talked back to it, I found support in other teachers (both at home and away), I talked to my students, I made change slowly so I could see what was going on, and I stuck with it. I still hear that voice from time to time, but it is weaker, and I know how to make it quiet now—I point to the positive results I get when I ignore it!
Some students throw themselves into school with such positive attitudes that I don’t have to worry about their resistance—I only have to make sure that they have successful experiences in class to maintain their enthusiasm. Many students, however, are less open to new strategies for learning math; their responses range from silent withdrawal, to questioning their value, to open refusal to use them. Over the years, I have used different strategies to honour student resistance and work with it rather than against it. I find that students need to be able to express their resistance in order to maintain their sense of self in the class, and that when they can do so with dignity, they are more likely to be able to stay present and attend to the work. When Arleen Pare (1994) did some research for her MA thesis in my classroom, she found a positive correlation between student expression of resistance and student retention. The more complex and open their resistance to me and my teaching, the more likely they were to continue to come regularly:
“This is not real math.”
Nearly every student who enrolls in a basic math class has years of (unsuccessful) experience as a math student; it stands to reason that they have a firm idea of what math class should be and what success in math looks like. They expect me to give them sheets of questions and some tricks to help them remember how to work with fractions. When I ask them to work with manipulatives or visuals, do group activities or field trips, they resist. “This is not real math.”
I deal with that resistance by acknowledging that what I am asking them to do is not what they are used to, and it feels strange. I ask them to tell me all the ways they have tried to learn math in the past. Then I ask, “Does anyone know a way to learn math that really works?” Invariably, nobody does because they have all been previously unsuccessful. This conversation with students is part of making my work and theory transparent, and makes them partners in designing their own learning. The discussion about past methods of learning math, an evaluation of what parts were more useful or less useful and the conclusion that something new needs to be tried, means that they are part of the team talking about what form teaching will take.
I began to change my teaching practice in a variety of ways—more emphasis on teaching concepts rather than algorithms; more group work, less lecture time; more emphasis on students discovering patterns; more emphasis on math thinking and problem solving; and more use of real life problems and a greater reliance on manipulative's and models. Indeed, some of the very things that I found in the literature when I went searching recently.
When I began to change my teaching practice, I met resistance on all fronts—my own resistance, students’ resistance, and resistance from the programs I worked in over the years. Overcoming this resistance to new methods became the first hurdle to changing my practice and feeling comfortable with the changes.
As I changed my ways of teaching to include more student participation, problem solving, math thinking, group work, and use of manipulative's and models, a voice inside my head kept talking to me.
What you are doing is not real math, I could hear the voice say. It is frivolous to ask students to make charts and diagrams, more like art than math. Asking them to talk about their own ways of figuring things out is a tangent—you know the most efficient ways to do the calculations, so just teach them those and forget about their folk math. And getting them to work in groups to figure things out is a complete waste of time; it takes too long, and there is no way for you to tell what they are really learning in those groups. Probably they are not learning anything, and you have no control!
These new things will not help students pass the exam, the voice went on, and you know how important the exam is. You know what is on the test; drill on those things, and forget about the rest. You will just confuse the students more when you expect them to understand math rather than memorize, it continued. Just give up these new ideas, and it will be easier on everyone.
Working in these new ways just causes problems, I heard the voice say again. You know that your students have huge holes in their math backgrounds. When you stray off the beaten path in math class, you fall into one of those holes, and when you try to fill it in, you fall into another hole, and you can never get out. Furthermore, every student seems to have a different set of holes! The only way to get through the material is to stick to the path, and help the students figure out how to stay on the path to the end of the course. You know you’re creating more holes by doing it this way, but it’s the only way.
I dealt with the voice in various ways: I talked back to it, I found support in other teachers (both at home and away), I talked to my students, I made change slowly so I could see what was going on, and I stuck with it. I still hear that voice from time to time, but it is weaker, and I know how to make it quiet now—I point to the positive results I get when I ignore it!
Some students throw themselves into school with such positive attitudes that I don’t have to worry about their resistance—I only have to make sure that they have successful experiences in class to maintain their enthusiasm. Many students, however, are less open to new strategies for learning math; their responses range from silent withdrawal, to questioning their value, to open refusal to use them. Over the years, I have used different strategies to honour student resistance and work with it rather than against it. I find that students need to be able to express their resistance in order to maintain their sense of self in the class, and that when they can do so with dignity, they are more likely to be able to stay present and attend to the work. When Arleen Pare (1994) did some research for her MA thesis in my classroom, she found a positive correlation between student expression of resistance and student retention. The more complex and open their resistance to me and my teaching, the more likely they were to continue to come regularly:
These results suggest a positive association between conscious, active resistance and regular attendance. It also suggests that the more that conscious resistance is encouraged, the more likely it is that regularattendance will result (Pare, p. 115).
As an example, take the student who keeps his coat on, sits silently at the back of the room, or near the door, and whose body language says, “I’m not here.” Pare found that this student is more likely to drop out than the student who says, “Why do we have to do this stuff anyway?” and then gets a response that respects his resistance.
Students sometimes express their resistance to participatory methods by simply dropping out of the class, but over the years, I have developed a teaching stance that recognizes, honours, and encourages open expression of their resistance. As a result, many students will question my methods when they are new to them. As you will see from the examples that follow, their resistance may be indirect, and often comes in the form of a question that is not a real question.
Nearly every student who enrolls in a basic math class has years of (unsuccessful) experience as a math student; it stands to reason that they have a firm idea of what math class should be and what success in math looks like. They expect me to give them sheets of questions and some tricks to help them remember how to work with fractions. When I ask them to work with manipulatives or visuals, do group activities or field trips, they resist. “This is not real math.”
I deal with that resistance by acknowledging that what I am asking them to do is not what they are used to, and it feels strange. I ask them to tell me all the ways they have tried to learn math in the past. Then I ask, “Does anyone know a way to learn math that really works?” Invariably, nobody does because they have all been previously unsuccessful. This conversation with students is part of making my work and theory transparent, and makes them partners in designing their own learning. The discussion about past methods of learning math, an evaluation of what parts were more useful or less useful and the conclusion that something new needs to be tried, means that they are part of the team talking about what form teaching will take.
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