In elementary school, students start to learn mathematics as a discourse. They start to know what are addition, subtraction, division, and multiplication. Eventually, they begin to be aware of word problem. From a simple case of daily life, they are asked to solve it by transform it into mathematical symbol and operation.
For example, Anna is given two problems:
8 – 2 = …
Bobby has 7 balls. After giving it to Sally, he only has 3 balls. How many balls Bobby gives to Sally?
For the first problem, Anna easily solves it. However, for the second problem, Anna first should understand the problem and after that, transform this word problem with daily discourse into mathematical discourse. She may know that Bobby actually gives 4 balls to Sally but she cannot write the process of it as 7 minus 3 equals 4.Here, Anna is having difficulty in transforming daily discourse into mathematical discourse. She finds it difficult to interpret a case happened in real life and use mathematics to solve it. If this case happened, teacher will somehow get confused on assessing student’s understanding whether the student do not understand the meaning of the problem, or they understand the meaning but cannot transform it into mathematical discourse to solve it.
One of the solutions to overcome this problem is by fostering mathematical literacy. Mathematical literacy is the ability to think numerically to interpret and analyze real life case in order to solve it and not merely doing mathematical operation (Gouthro & Griffore, 2004). Based on the Anna’s case above, mathematical literacy is not merely the ability to solve the first problem but also real life problem like the second problem.
The main aspect of improving mathematical literacy is the thought that mathematics is not a collection of procedures and formulas but a tool that is useful to solve daily problems. It is also a language and communication system used for exploring knowledge (Whitin et al, 1990).
Strategy to improve students’ mathematical literacy is by making open-ended problems (Whitin et al, 1990). Different from closed-ended problem, open-ended problems allow students to try various method to find the answer. Along the process, teacher allows multiple representations as his/her appreciation on students’ unique background of knowledge. Learning mathematics does not concern more on procedural and fixed algorithm given by teacher anymore but more on guiding students to find their own meaning and knowledge of the lesson (D’Ambrosio, Johnson, & Hobbs, 1995, in Gouthro & Griffore, 2004). Students can try their way and reflect whether that way is effective and fitted to them. They will also independently learn some registers of mathematics and get adjusted to mathematics discourse. By doing this, students will have sound understanding because they learn in a flexible atmosphere.
Examples of multiple representation
Fostering mathematical literacy is very useful for not only students in learning but also teacher in assessing students’ understanding. From students’ side, by having good mathematical literacy, students will be directed to more abstract discourse easily (NCTM, 2009). For example, if students can understand that based on the Anna’s case above 4 comes from 7 minus 3, it will be easier for them to solve the following case:
Bobby has x balls. After giving it to Sally, he only has y balls. How many balls Bobby gives to Sally?
By slowly moving from concrete example to abstract problem, students with good mathematical literacy will know that the solution for this abstract case is x-y.
Nowadays, the gap between students and mathematics exists because students do not think that mathematics has connection to their real world. Moreover, mathematics discourse is relatively different with daily discourse. Since fostering mathematical literacy should be related to real life situation, students will value mathematics more. They will think that mathematics is useful and worth to be learnt (Gouthro & Griffore, 2004). It increases the interest of students to learn Mathematics more.
From teachers’ side, fostering mathematical literacy will help them to assess students’ understanding (Whitin et al, 1990). The current trend of assessing students’ steps on problem is by grading each step they have. For example there is a problem:
Mom has three children. Each child is given four candies by mom. How many candies Mom give to all of her children?
Teacher will expect students to write the solution as simple as 3 x 4 = 12. However, the problem is that the information got from this answer is too little to make sure students’ understanding. Since in improving mathematical literacy teacher should allow multiple representations, because each student has their own style in transforming daily discourse into mathematical discourse, the variety of ways in solving problems will also increase. Students may want to draw a picture of the three children and four candies on each child, and simply write down 4 + 4 + 4 = 12. Responding to this answer, teacher can introduce multiplication as repeated addition. Here, students will be adjusted to multiplication as his/her new register and internalize it. Teacher will obtain more information to assess students’ understanding.
Fostering mathematical literacy to help students in understanding mathematical discourse is indeed not an easy job. It comes as a respond of the difficulties had by students and their assumption to mathematics subject. However, if teachers conduct the strategy, students’ difficulties in understanding discourse may be overcome and their opinion on Mathematics will be improved as they get adjusted to mathematical discourse through flexible, open-ended atmosphere. Teachers will also get the benefits in assessing students.
Gouthro, M, and Griffore, J. 2004. Leading Math Success: Mathematical Literacy. Ontario: Ontario Education, retrieved on November 16, 2011 from http://oame.on.ca/lmstips/files/lms/LeadingMathSuccess.pdf
NCTM. 2009. Guiding Principles for Mathematics Curriculum and Assessment. USA: NCTM
Whitin, D. J, Mills, H, and O’Keefe, T. 1990. Living and Learning Mathematics: Series and Strategies for Supporting Mathematical Literacy. Portsmouth: Heinemann.