Primary teachers know that young children love to talk about what they do and think. They understand not only the pleasure this provides students, but also its importance for language development and intellectual growth.
Marian S. Small, mathematics professor in education at the University of New Brunswick, proposes that a rich primary mathematics program virtually depends on talk. She encourages teachers to allow 1st and 2nd graders to experiment with mathematical ideas by describing their reasoning and solutions to the problems teachers provide.
Small states that most curricula now offer at least some experience with manipulative materials and opportunities to apply math concepts and skills to real life problems. And, Small states, these activities are important aspects of a math program.
However, incorporating language as a major component in our math program is also important, and this has so far not been done. Small believes that discussion is vital for improving students’ understanding of mathematical concepts and ultimately their ability to utilize their math knowledge.
Currently, teachers tend to limit their verbalizations in math classes to explaining procedures, giving directions and answering ‘how to’ type questions. Thus, there is little opportunity for students to express mathematical ideas.
Small recommends incorporating language into the teaching of math in order to involve students more fully in mathematical processes.
While workbooks, which demand repetition of mechanical procedures, produce children who are proficient calculators, the students must deal with mathematical ideas directly when paper and pencil are removed. Teachers and students are forced to verbalize their ideas, to explain what they are thinking, or how they resolved a problem.
When students work orally on a problem, instead of in a standard written form, they develop their own strategies or procedures for solving those problems. Students naturally adopt a procedure that makes sense to them. For example, in asking them to add 35 and 28, they many visualize manipulatives and count them, or they may round off the numbers to 35 and 30, which is 65, and 2 less is 63, or use 35 and 20 to make 55 and then add 8 more for 63. In this way, they create and express their own mathematical ideas.
Just as stories are read and events discussed in language arts and reading, Small believes that the same thing should occur in math lessons.
Real life experiences
Problems designed around lunch money or other real life experiences should be discussed daily. Productive math experiences can arise spontaneously in conversations during the day; “How many of you remembered to return your parent permission forms?” “What portion of you remembered?” “How many children are here today?” “That means how many forgot their slips?” Small reports that many problems normally outside the scope of 1st and 2nd graders’ written computation skills can be handled successfully through oral discussion and problem-solving.
Small does not expect or recommend that teachers delete paper and pencil tasks from their math instruction in the primary grades, but she does recommend that ‘speaking math’ come first. Discussing, explaining and reasoning aloud helps students to understand the concepts which underlie the procedures they do on paper.
Speaking about math ideas also enables the teacher to find out why a child is not able to compute correctly or to solve a word problem; the child’s description of what he/she is doing usually reveals the misconceptions he/she holds.
Small also recommends that children use written language in the form of “math stories” to explain math concepts or procedures. Young children can write a whole page about the number 5, for example. Sharing their ‘stories’ with the class helps students to develop a broader concept of that number and invariably raises other mathematical ideas for discussion.
“Do You Speak Math?” Arithmetic Teacher January 1990, pp. 26-29.
Published in ERN May/June 1990 Volume 3 Number 3