Reading Comprehension in Mathematics
From WikEd
[edit] Descriptions, definitions, synonyms, organizer terms, types of
Read: "To apprehend the meaning of (a book, writing, etc.) be perceiving the form and relation of the printed or written characters." (Webster, 2002)
Mathematics: "Mathematics is a language that people use to communicate, to solve problems, to engage in recreation, and to create works of art and mechanical tools. It is a language of words, numerals, and symbols that are at times interrelated and interdependent and at other times disjointed and autonomous." (Adams, 2003)
[edit] Application in classrooms
On many occasions, reading teachers have commented that Johnny can't read, but that isn't a problem for the math teacher. Not only does reading comprehension hinder mathematics learning, but the inability to decipher text code can be exacerbated in math with the addition of symbols and nonlinear presentation of information. In fact, researchers have found that comprehending math word problems is quite difficult because the writing is compact and lacks elaboration (Fuentes). Students therefore need to infer meaning and context. Fuentes also noted that reading in math is difficult because of structural differences between math problems and text. Math problems are not read left to right, and words that students already have in their vocabularies take on additional meanings when applied to mathematical contexts. Adams points out that, "the reader is challenged to acquire comprehension and mathematical understanding with fluency and proficiency through the reading of numerals and symbols, in addition to words." To further complicate matters, letters are no longer parts of words, punctuation serves different purposes, and numerous symbols are added. If Johnny is having trouble reading "normal" text, you can see how his difficulties are compounded in math.
There are two types of problems in math--expressions and equations and word problems. Both pose their own issues from a reading comprehension viewpoint. With expressions and equations, students must understand the symbols used and the order in which to process the information. For example, the student needs to understand that an equal sign means "the same as" or "is," and that exponents must be completed prior to adding. Word problems tend to strike fear in the hearts of most math students because of the added layer of complexity. Words problems can be as simple as "Twenty-five is what percent of 50," to complex scenarios. Here not only do the problem solvers need to understand symbols and procedures, but now translation is required to put words into math sentences. According to Mayer, "In translating, the problem solver converts each sentence into an internal mental representation. This process requires linguistic knowledge (such as knowing that Vons and Lucky are proper nouns) and factual knowledge (such as knowing that there are 100 cents in a dollar)," (Mayer).
So how can we help mathematics students with reading comprehension difficulties? As math teachers, we need to be well versed in reading comprehensions strategies and modify them for mathematical comprehension purposes.
- K-W-L
The K-W-L strategy in reading helps to activate prior knowledge and peak interest in what's to come by asking "What do I know?", What do I want to learn more about?", and "What did I learn?" (Hyde). Applied to math instruction, the K-W-L can be modified to K-W-C. Here the K stands for what is known, the W represents what is to be determined, and the C cautions the learner to look for special conditions (Hyde). This structure helps activate students' prior knowledge about mathematics and how it is used.
- Making Connections
Reading teachers encourage students to make connections with stories, either text to self, text to text, or text to world. When we adapt these connections to mathematics, "we ask students to look for connections that are math-to-self (connecting math concepts to prior knowledge and experience); math-to-world (connecting math concepts to real-world situations, science, and social studies); and math-to-math (connecting math concepts withing and between the branches of mathematics or connecting concepts and procedures," (Hyde).
- Predicting
Predicting is key to knowing the reasonableness of a math solution. In math, we call this estimating. We assess the information presented and estimate the outcome. If our solution differs greatly from our estimate, we need to reassess the information and our process.
- Visualizing
In reading, we suggest that students create mind movies to help them visualize the text. This can be applied to math as well by drawing pictures and making tables. Due to the compact nature of word problems, students can also elaborate to help them get the full meaning of the problem. Shannon Foster, a fourth grade teacher from Texas, worked with her students to help them draw pictures of word problems. Of this process, Foster noted, "My students and I agreed that creating a visual to go along with the word problem gave them a better understanding of what the problem was asking as well as what information the problem was providing. Using this visualizing strategy from reading helped them illustrate the information given. It also allowed each student to connect with the text. The pictures showed their understanding."
- Vocabulary Instruction
Vocabulary instruction is important to all content areas including math. Students enter the math classroom with vocabulary from other disciplines and everyday life. These definitions, however, are altered for mathematical purposes. For example, the word volume has an everyday meaning of a noise level, but in math it means the "amount of mass taken up by an object," (Adams). Therefore, vocabulary must become part to of regular mathematics instruction to help students avoid confusion.
[edit] Evidence of effectiveness
Hyde worked with a second grade teacher using his K-W-C method along with visualization. He and the teacher showed the students a problem about a freight train and its cargo one line at a time. Students then completed K-W-C charts, used cubes to build the train arrangements, then drew pictures of the problem solutions. Using these strategies, students were able to understand and solve a problem typically thought to be too complex for second grade students. Hyde and other teachers continued to use adapted reading comprehension strategies throughout the year with great success.
And what about Ms. Foster and her fourth grade class? Recall they were drawing pictures of word problems to enhance their comprehension. "...I repeated that same assignment with individual work. My students, bless their stubby crayons, suddenly were involved in the text," (Foster). Students who had previously failed a test with word problems were far more successful on a test following instruction on drawing pictures to match the problems. "As I sat in my rocker...I scanned through the tests. They were covered with what looked like doodles, but my well-trained eye understood these were obviously illustrations," (Foster).
[edit] Critics and their rationale
Where should reading comprehension for mathematics be taught? This is one issue that has surfaced as the need for this type of instruction is recognized. Math teachers, feeling pressured by mandated testing to cover a wide range of material in a short amount of time, may decide that adding vocabulary and reading instruction to the math curriculum is overload. Reading teachers, on the other hand, may not embrace adding another layer to their curriculum, especially one that is seemingly out of their content area. A few years ago, a well-known textbook publisher created a program for reading and writing in math. The series failed to sell, however, as questions over where to use it (reading or math class) surfaced.
There are also critics of the key word methodology of solving word problems. Key words help the problem solver determine which math operation to use. For example, students learn that "altogether" indicates addition, and "out of" signifies division. While teachers introduce key words as a strategy, students often times, "adopt a key-word approach to solving these types of problems that bypasses any mathematical reasoning," (Clements). Students grasp hold of the key words and numbers and start calculating without thinking. According to Cathy Seeley, past president of the National Council of Teachers of Mathematics, "This type of practice falls apart on two levels. First, it misleads students. For any clue word or trick, most of us could create a test item for which the trick does not work. Second, the time that students spend memorizing tricks or words without understanding the related mathematics is precious time they lose from instruction that could support their mathematics learning." For any given key word, problems can be written for which the strategy will fail.
[edit] Alternative explanations due to Diversity considerations
Classrooms have an ever increasing number of English Language Learner (ELL) students. Some might assume that ELL students have an easier time transitioning in math because fewer words are used. However, in a review of test scores, Basurto found that ELL students traditionally score lower on math sub-tests of standardized tests compared to national averages. This is likely attributable to their difficulties processing word problems. Math teachers may steer away from teaching word problems to ELL students until they have sufficient language skills. "We know from research studies that mathematics instruction for second language learners is frequently limited to computation exercises," (Basurto). However, it is important to help these students apply mathematical situations to their language acquisition. "...approaches that contain conditions of reading comprehension will help develop and enhance the problem solving processes needed by second language learners, (Basurto).
Some students need to learn different uses of symbols along with the new language. "For example, in countries around the world, the comma (e.g., 236,69) or a raised dot (e.g., is used to separate a whole number and a fractional part, whereas in the English language, we use a decimal point to make this indication (e.g., 236.69)," (Adams). This may lead to additional confusion for students learning a new language.
[edit] Signed “life experiences”, testimonies and stories
[edit] References and other links of interest
Adams, T. L. (2003). Reading mathematics: More than words can say, The Reading Teacher, 56, 786-795.
Basurto, Imelda, (1999). Conditions for reading comprehension which facilitates word problems for second language learners, Reading Improvement, 36, 143-148.
Clement, L, Bernhard, J., (2005). A problem solving alternative to using key words, Mathematics Teaching in the Middle School, 10, 360-365.
Fuentes, Peter, (1998). Reading comprehension in mathematics, The Clearing House, 72, 81-88.
Foster, Shannon, (2007). The day math and reading got hitched, Teaching Children Mathematics, Nov., 2007, 196-201.
Hyde, Arthur, (2007). Mathematics and cognition, Educational Leadership, 65, 43-47.
Mayer, R.E., (2004). Teaching of subject matter, Annual Review of Psychology, 55, 729-70.
Seeley, Cathy, Teaching to the test, from The President's Corner of the National Council of Teachers of Mathematics website, retrieved May 4, 2008. [1]
The New International Webster's Student Dictionary, International Encyclopedic Edition, Trident Press International, 2002.
