Volume 1, Issue B ::: May 1997
Reconceptualizing Roles: Mathematics and Reading
by Mary Jane Schmitt
When I first started teaching mathematics to adults in basic education programs, about 25 years ago, I believed in and used individualized assessment, instruction, and -- to the extent possible -- curriculum. I diagnosed the computational gaps, took into account the adult's long term goals, made a plan to fill in those gaps, and then the student and I set upon the task of making it happen. It was called diagnostic or prescriptive teaching, and it seemed a great deal more learner centered and efficient than a brush up or a review course where everyone was expected to be on the same page at the same time. The thinking was that no one would ever be "left behind" or lost again because everyone could learn at his or her own pace.
Learners didn't talk much to each other in those early classes of mine. It was a two-way teacher-learner dialogue. The mathematical content emphasis was largely computation and workbook driven. The word problems at the end of a chapter provided students with a way to practice the computational algorithms just covered.
Another notion I had was that I was a math teacher, not a reading teacher. Rather than take on the responsibility of helping students improve their reading, I skirted the reading issue by controlling the reading level of the word problems. I had a slew of workbooks, and I dealt with different reading levels by using word problems that matched a student's reading level. I audio taped problem sets for beginning readers.
Today, while I am no longer a classroom teacher, I work closely with adult basic education (ABE) and k-12 mathematics teachers, and what I see emerging are some significant and positive trends. The first is that the definition of the mathematics essential for adults is expanding. A group of ABE teachers in Massachusetts posits that "math is more than computation. It is a set of concepts, principles, and relationships which serves as a powerful symbol system and tool for describing and analyzing our world." They and several other state and local ABE math teacher teams are working to adapt the NCTM Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics, 1989) to the ABE classroom. As a result, there seems to be more variety within mathematics curricula. Adults are not just learning how to manipulate numbers, they are also collecting, displaying, and analyzing data; creating and identifying patterns, relations, and functions; developing a stronger sense of number and operation; and exploring spatial and geometric relationships.
Secondly, I am working with teachers who are purposefully emphasizing more realistic and relevant problem solving situations rather than the controlled one- or two-step word problems. As a result, math students are more engaged in reading, writing, speaking, and listening. When problem situations depend on gathering information from a variety of everyday sources, such as articles and advertisements in newspapers and magazines, prose literacy and mathematical literacy are hard to separate. Understanding the problem becomes much more complex than knowing a list of key words -- more' means add, less' means subtract, of' means times -- to solve formulaic word problems.
Finally, what strikes me is that ABE students are talking and writing to each other about mathematics. What I see frequently are cooperative learning groups, which promote mathematical discourse, and assessments with open response and open ended items, which require students to explain and defend their thinking. Teachers are also emphasizing the ability to move freely between a variety of ways of describing a mathematical concept: in algebraic symbols, everyday situations, pictorial representations, graphs, tables, and written and oral explanations. "Doing mathematics" requires communication skills that draw not only upon computation, but also on reading, writing, listening, and speaking.
In all of this, it's interesting to think about the way roles are changing. ABE teachers and learners, faced with new ways of approaching mathematics, have to stretch well beyond business-as-usual because both are learning new skills, and are engaged as learners. It isn't easy to write or talk about mathematics when you've never done it before. Most of us -- teachers and students -- learned to do mathematics as a solitary activity and kept our mathematical thinking to ourselves. The roles of the math and language arts teachers begin to coincide, too. Teachers, facilitating a classroom environment where students learn to communicate mathematically, are employing techniques such as brainstorming, group story writing, journals, and interviews -- the same techniques found in literacy classrooms.
The Massachusetts Adult Basic Education Math Standards (1994), developed by a group of ABE math teachers, exemplify the direction mathematics is taking. Here is an excerpt from the Standards:
"In the adult basic education classroom, curriculum design must include approaches to teaching mathematics as communication that allow learners to:
develop appropriate reading, writing, listening, and speaking skills necessary for communicating mathematically in numerous settings;
discuss with others, reflect and clarify their own thinking about mathematical outcomes, and make convincing arguments and decisions based on these experiences;
define everyday, work-related or test-related situations using concrete, pictorial, graphical, or algebraic methods;
appreciate the value of mathematical language and notation in relation to mathematical ideas."
For ABE math classes to continue to evolve as communities of competent problem solvers and communicators, it will take the combined skills of literacy and numeracy practitioners. As a first step, I'd like to see a dialogue about integrating language and mathematics skill development, and perhaps the focus of that discussion could start with GED preparation, where mathematics is imbedded in several of the items on the social studies and science tests and where all the mathematics test items are contextualized problems. Or the dialogue could begin around the definitions of mathematical literacy and numeracy and literacy and the importance of each in the adult roles of worker, citizen, and parent. Wherever it starts, the point is the same: mathematics and literacy must proceed together.
A dialogue between the literacy and the numeracy communities is essential. One medium for discussion of this issue is the Numeracy electronic discussion list. To join, send a message to: firstname.lastname@example.org
In the subject box, write "Subscribe Numeracy."