Milton Francis

Oftentimes, people think of mathematics as a symbolic discipline that is very difficult to comprehend. I must agree with them, because for the mind to understand symbols, it has to decode the language in which the data is presented. The mind must then interpret its meaning for the reader to be able to transfer it into plain text, which may be in the form of words, numbers, or variables. When mathematics is presented, it is often done by using one, two or all three representations mentioned: WORDS, NUMBERS, and VARIABLES. However, what are these and how are they used in the presentation of the ‘difficult’ discipline called MATHEMATICS?

First, let’s ask ourselves the question – what is mathematics? This definition by wikipedia brings out the four initial fields of the subject – quantum, structure, space, and change, without which, the body of mathematics would not have existed. Quantum refers to quantity, which involves numbers, one of the symbolic representations that will be addressed. Structure deals with groups which evolve into abstract algebra. Space refers to geometry and trigonometry, two very important branches of mathematics. Finally, change involves the understanding of the discipline through functions, complex analysis, and quantum mechanics, to name a few. But how do these impacts on the reading in mathematics?

As stated earlier, reading mathematics often involves words, numbers, and variables. A word, according to wikipedia, is a language unit with meaning. They are used singly or in groups. In mathematics, words are used in verbal problems, commonly called word problems. For example:

If the water level in a cylinder of radius two meters is rising in a
rate of three meters per second, what is the rate of increase of
the volume of water?

This is called a pure word problem, as it consists of words only. There are however, verbal problems that have a mixture of words and numbers. An example of which could be as follows:

If the water level in a cylinder of radius 2m is rising in a rate of
3m per second, what is the rate of increase of the volume of

You probably may have noticed that both problems are similar, except that one consists of only words, while the other includes the number symbols as well.
Another example of a word problem can be seen by clicking the link To find word problems online for Grades 1-5 visit KidZone Math. For word problems for Grades 5-12 visit Word Problems for Kids. {Carolyn Semet}

What is the number symbol? Number, as what it is often refer to as, is a very abstract concept. It is used in measures and for counting. It is what most non-mathematically inclined persons use, and is their concept of mathematics. When a child start pre-Kindergarten, the teacher exposes him/her to this concept in the form of counting. Counting leads to the writing of the symbols, thus begin the process of mathematics education. An example of the measuring concept of mathematics is as follows:
Calculate 4∙35 × 10 3 + 6∙74 × 10 2

The concept of variables is one of the most difficult to grasp in the initial stages of the learning of mathematics, so this concept is not introduced at the pre-kindergarten level, and to some extent, not even in the early years of elementary education. A variable , as it is used in mathematics, is a quantity that is not known. Because it is unknown, the number symbols cannot be used as its representation, so mathematicians use letter symbols drawn from various languages. For example, letters of the English alphabet like x, y, a, p, r, etc. Other language alphabets like the Greek’s α, β, γ, δ, and the popular θ are used as well. The way in which these alphabets, called variables, are used is represented as shown in the mathematical statements below:
Simplify 5x + 7y – 4x – 2y + x

Solve the equation x2 + 3x – 28 = 0

Find the positive value(s) of θ in the range 0° ≤ θ ≤ 360°, of the equation
2 sin θ + 3 = 4

This is what is involved when mathematicians talk about Reading in Mathematics.
Comments From Steven Schnee:
Mathematics presents it dirty language in multiple disciplines of instruction. One in particular is science. The chemistry of world events can be calculated by simple formulas and expressions. How much tension is found between molecules of a substance? Why does water adhere to containers? Much of the applications in science can be derived through the lingistics of mathatics. This is all fascinating and wonderful. The real problem arises when attempting to present these complex theorems to students in simple, half baked fragments. How can a sophisticated idea like the atomic theory be broken down in terms easy enough for our developing students to comprehend? The answer falls into the hands of the language which we call math. Students deal with formulas derived by Niels Bohr and other scientists to visualize and breakdown the energy transfer within an atom. The hardest part for a teacher introducing this information is delivering this instruction to a student who has still not mastered the mathematical language. A person who can not identify the unknown or variable in a mathematical situation or manipulate numbers to materialize an answer to science problems will struggle. A student can not master the science vernacular without bypassing the math language first. (Steven Schnee, July 15, 2007)

Reading in Mathematics should not overlook what students could be reading, other than text books, which contain mathematical threads. Most adult reading, or mathematical problem solving, takes place while reading articles in magazines like Consumer Reports or Discover. In fact, we usually read non-fiction. When we want to know how-come, what-if, why or so-what, we turn to magazines, newspapers, and a host of other nonfiction text. Therefore it is quite reasonable to include some reading, along with the math text books, to acquaint students with math in every day life and help them make connections between their studies and the real world.
In addition to these sources, "environmental print" should not to be overlooked. By environmental print I refer to real-time text, such as signage, junk mail, advertisements, packaging materials and containers. Consider nutrition information, credit card and CD/DVD club solicitations. Students are consumers, and always will be. They need the experience of weighing options and making reasonable decisions for themselves. Using this type of material in the classroom can provide them with that experience.
I taught a basic math class one year to seniors (all girls at The Young Women;s Leadership School) that was specifically aimed toward math in everyday life. We read other materials, such as A Girl and Her Money to learn about credit and its common pitfalls. I would definitely augment classroom text with additional types of materials and think that comparing a selection of potential checking accounts, cell phone plans and media clubs is a great way to go.
[Lynne Bailey]

Math language is quite a challege in the classroom sometimes. In many cases, keywords are definitely the solution for comprehending the subjects in school. Math on the otherhand has not only word terms but symbol terms. I agree this may cause a difficult situation for students to learn math. In my classroom we use vocabulary terms to help students relate to the proplem and understand the process. We used word walls for each concept and practice referring to the terms(hoping the will get it after hearing it several times). A useful website is also Illuminations this helps define lessons and standards that target math goals.
{Arleen Chan}

As an ESL teacher I am always working with content area vocabulary. It amazes me just how much language is involved in subject areas like Math. Teachers can not assume that students know the vocabulary necessary for each lesson. Just as in teaching reading, math vocabulary needs to be introduced beforehand and reintroduced and talked about during the lesson. Do not assume students know the meaning of equals when written in English when all their life they have seen it as =.
deirdre doherty
Many students have difficulty with mathematics because they have difficulty with reading in mathematics. Reading in math requires different skills than other forms of reading. It is important to learn strategies to improve the students’ reading skills directly related to mathematics. We need to focus on reading comprehension, reading a textbook, vocabulary development, and writing in mathematics. It is important to support the student in vocabulary development and use writing to support the learning of mathematics.
Tim Sullivan

Milton, I like your opening paragraph. Matter of fact the whole presentation is excellent. It's a nice opening summary into the world of mathematics. Being a musician I too must master musical words and symbols to play my instrument.

Deirdre brought up a good point about having a solid foundation with the vocabulary. As in any discipline, having a solid foundation of the basics is a key to success and mastery in that discipline.
Lee Nelson