Math Communication

Man is a social being. There is a strong tendency to interact whenever we see another one of our own kind. That is why our students need to talk even when the most important concept of the lesson is being addressed.  We can discipline them in ways galore with no perpetual success and a lot of frustration for us or we can simply chose to let them be. We can chose to encourage them to use their inherent communication urge to learn and to share. Communication is the key to a future outside school. Why then we forget the power of this skill while engaged in the Maths classroom?

Since I like to talk, I have never ever forced my students otherwise. Instead, I have encouraged them to talk, to communicate, to question. When I leave my class after a period of intense gruelling Maths session (phew!) where we basically talk a lot, question and try to frame answers, sing songs or see a video and do problem solving with running commentaries, the students are left more energetic and lively. I have had my colleagues complement and complain as to what I do to them, leaving them in an excited and restless state. This sense of restlessness may seem negative superficially, however it sparks creativity, it sparks thinking. What gets you talking is surely bound to make you feel something. It makes them reflect and question. Communication for me and my maths students is the buzzword!

Most people complain of the alien characters that abound in math. Math symbolism is phobiac for majority. The key to dispelling all these fears tin Mathematics is to confront the symbols and the terms head on. I use questioning to encourage communication. I encourage my students to act out and sing their maths concepts. I do an interesting activity called JAM sessions in the Maths classroom, inspired from one of my colleagues and a very dear friend Ms Nampreeta Kaur, For those whose preferred choice of communication is non-verbal, I let them draw or make Math models.

And if you believe that I am the culprit behind the generation that doesn’t stop talking, please don’t blame only me. NCTM needs their share of blame.

The Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) emphasizes the need to address communication skills. These skills, including reading, writing, listening, and speaking, enhance mathematical understanding and problem-solving ability. Moreover, to communicate effectively, one must be able to interpret and analyze mathematical ideas. The curriculum and evaluation standards recommend that opportunities be afforded students to "use language to communicate their mathematical ideas" (NCTM 1989, 78).

Although these recommendations are valuable, most of us, including me still find them difficult to implement with students who are not proficient in English.

Students with "limited English proficiency," that is, students who do not possess the level of English proficiency needed for meeting academic requirements, lack some or all of a wide range of skills. Some students lack the ability to listen, speak, read, and write in English. Other students have speaking and listening skills but are below grade level in reading and writing. Given these characteristics of students that we have in our classrooms, what can we as teachers do to furnish opportunities to enhance communication skills in Mathematics? More specifically what can be done to help these students participate meaningfully in class activities? How can students be assisted in developing the language skills  they need to deal with the tasks and materials given in the class?

With the help of some specific topic based examples, I will try to answer these questions in my next post.

Suggested Instructional Strategies for developing communication Skills in the Maths Classroom

Afford opportunities for students to clarify key terms and words.

Unlike the language used in everyday communication, the language of mathematics is precise and concise. Each word and phrase used in mathematics has a definite meaning that must be grasped to assure that the student fully understands the mathematical concept. Therefore, it is essential for students to learn the key terms and words used in mathematics. This requirement, however, does not imply that students be "taught" the terms in isolation (e.g., "Here are the terms for the lesson; what do they mean?"). On the contrary, the terms should be used in the same context in which the students will encounter them. Students need to be given opportunities to read the terms and definitions, ask questions about them, use them in sentences, and if possible, describe them using visual or concrete materials. Language can be made comprehensible through a variety of means, such as demonstrations, hands-on materials, visual aids, and manipulation of content (Krashen and Terrel 1983). Furthermore, mathematical terms are best understood when students use the language of mathematics in a meaningful setting (Krashen 1981; Cummins and Swain 1986).

When I want to define a term in my class, I try to question the students as to

·         Their previous knowledge about the term

·         Some connection to a previously known term

·         Any resemblance to the English word

·         The root words involved

For example, let us assume I want to teach my students the definition of polygon which goes like this –

“A Polygon is a simple closed figure made up of line segments”

Now my questions and strategy followed is like this –

1.       Give an example of a polygon. – Most of the students are able to answer this question correctly. I try to take the distinct accurate responses and enlist them on the Blackcoard.

2.       I then encourage some of them to draw figures of some polygons on the board, including a triangle, a square, a rectangle, a pentagon, even may be a parallelogram or a trapezium.

3.       Now that visually all of them know what a polygon looks like, I encourage them to put their knowledge and understanding into words. Most of them are able to respond using their previous knowledge that a polygon is a figure made up of line segments.

4.       Now I need to help them focus their attention on the intricate details in the definition. After drawing a figure made up of line segments which is open, I challenge them to check whether every figure made up of line segments is a polygon.

5.       This gets me my first part of the detail that a polygon is a closed figure made up of line segments. I use similar questioning and prompting techniques to get the second part of the detail i.e. a polygon is SIMPLE.

6.       Now the word simple has a mathematical as well as an English meaning. I try to help them compare the two.

7.       While discussing the terminology for the different polygons, I encourage them to see a polygon as a POLYgon, a hexagon as a HEXAgon, and so on, taking their attention to the root words and their meanings – poly means many, hexa means six.

So I teach them not just the definition of a polygon, I teach them important communication skills. I teach them to think and verbalise what they can see and what they know. In the process their skills of drawing figures as well as their logical and critical reasoning skills are also addressed. So with this teaching strategy, essentially based on effective questioning and prompting, I cover the entire gamut of cognitive skills – Knowledge, Understanding, Application (when I make them judge whether a given figure is a polygon or not), Skills and the higher order thinking skills as well.

Offer opportunities for students to talk about mathematics with one another

Cooperative-learning groups are the optimal setting for this type of discussion to occur. Within the privacy of a small group, students feel more secure about making a contribution (Artzt and Newman 1990). Furthermore, each group can be composed of students of varying levels of language proficiency. Through role assignments, as suggested by Dishon and O'Leary (1984), different students can take on such tasks as recording, supplying materials, reporting, and translating. This way the members of the group are given the opportunities to practice such communication skills as reading, writing, and speaking as they interact with one another. The recorder is asked to record and summarize the work of the group; the person who supplies the materials reads the instructions for the activity; and the reporter orally communicates the group's ideas to the class.

Maintain a classroom climate in which students with limited English proficiency are encouraged to participate.

The teacher can design whole-class instruction in a manner that encourages the participation of all students. Reducing the amount of time the teacher talks gives students more time to use English in class. One basic "truth" applies in language learning: One can become proficient only if one uses the language. An essential part of the process of learning the language is to give students the freedom to make errors when speaking English. The teacher should deal with grammatical errors tactfully. Students can be corrected through modeling; for example, if a student states that "the root squares are five," the teacher can respond, "Yes, the square root is five. Would you repeat your answer, please?"

Give students opportunities to examine and discuss problem-solving processes.

A number of procedures can often be helpful when working through mathematical tasks. By verbalizing the processes used to solve problems, students who may not be confident about their English-language skills can be assisted in their problem-solving endeavors. For example, they can routinely be encouraged to discuss such questions as these:

1. What are the important facts or conditions in the problem?
2. Do you need any information not given in the problem?
3. What question is asked in the problem?
4. Describe how you solved the problem.
5. Do you think you have the right answer? Why? Why not?
6. How did you feel while you were solving this problem?
7. How do you feel after having worked on the problem?

(Charles, Lester, and O'Daffer 1987, 24-25)

The main purpose of such activities is to give students the chance to communicate orally the processes they use when solving a problem.

Create opportunities for students to reflect on the main points of a lesson.

During the course of a lesson, students with limited English proficiency are likely to lose track of the class discussion. It is, therefore, important that the teacher summarize the discussion frequently and highlight the main points of the lesson. One helpful means of doing so is through the use of diagrams and lists. Students should be encouraged to explain in their own words, oral or written, the main ideas presented in the lesson. A student who cannot offer an explanation in English should be allowed to use his or her native language. Another student can translate the explanation into English so that all can understand.