For too many students, mathematics has little or no connection to their real-world experience. Previously, I thought that this stemmed primarily from a lack of understanding of mathematical concepts. While that deficiency certainly is an important factor, I am becoming more convinced that students don’t appreciate the power of mathematics largely because of an inability to represent, visualize and model word problems.
Research has found that students solve math word problems using one of two general methods: direct translation or problem modeling. Less successful problem solvers usually utilize the direct translation approach. Students identify numbers and key relational terms in the problem statement. Over the years, students have learned that certain key words indicate what computational operation should be used in a word problem. A solution plan is developed by combing the numbers and the key terms. In other words the student directly translates the key proposition in the problem statement into a set of computations. Due to its algorithmic nature, this method has garnered nicknames such as “compute first, think later” and number grabbing (Hegarty, Mayer, & Monk, 1995).
Successful problem solvers are more likely to use a problem model approach to solve word problems. In this method, the problem statement is translated into a mental model of the situation described in the problem. This leads to an object-based representation of the problem rather than a proposition based representation of the problem (Hegarty et al., 1995).
Consider how these two methods might be used to answer the following mathematics problem: “At Lucky, butter costs 65 cents per stick. This is 2 cents less per stick than butter at Vons. If you need to buy 4 sticks of butter, how much will you pay at Vons?” A student might go through the following steps to incorrectly arrive at an answer using the direct translation method. The student would assign 65 cents to the cost of Lucky butter and would assign 4 to the number of sticks of butter needed. The student would recognize the keyword less, which usually indicates subtraction. The student would use this incorrectly identified relationship to compute the cost of Vons butter as 63 cents by subtracting 2 from 65. Finally, the student would multiply this quantity by 4 to arrive at the final, incorrect cost of four sticks of butter at Vons (Hegarty et al., 1995).
However, a student using the problem model approach would be more likely to construct a correct representation of the problem and would be more likely to catch arithmetic mistakes during the computational process. After reading the problem statement, the student would mentally create an object to represent the problem. Using the same example, the student might mentally place the prices for Lucky and Vons butter on a number line. The price for Lucky butter would be placed at 65 cents. Since the problem statement indicates that Lucky butter is 2 cents less than Vons butter, the price for Vons butter must be placed two units above the price for Lucky on the mental number line. With this mental representation, the problem solver is better equipped to plan an arithmetic solution. Furthermore, the student is far more likely to notice a computational error. If a student calculated the cost of Vons butter to be 63 cents, they would recognize this calculation is incorrect because they already visualized the price of Vons butter as being 2 units above the price of Lucky butter on the number line (Hegarty et al., 1995).
With this knowledge in mind, teachers must identify reading comprehension strategies that can be employed to push students toward the problem model approach for solving word problems. The rest of this paper will discuss methods that have been used to scaffold students in this direction.
Before students can properly construct a model of a word problem, they must know how to deal with the vocabulary in the...
Cited: DiGisi, L., & Fleming, D. (2005). Literacy Specialists in Math Class! Closing the Achievement Gap on State Math Assessments. Voices from the Middle, 13, 48-52.
Fuentes, P. (1998). Reading Comprehension in Mathematics. The Clearing House, 72, 81-88.
Hegarty, M., Mayer, R., & Monk, C. (1995). Comprehension of Arithmetic Word Problems: A Comparison of Successful and Unsuccessful Problem Solvers. Journal of Educational Psychology, 87, 18-32.
Kuzniewski, F., Sanders, M., Smith, G., Swanson, S., & Urich, C. (1998) Using Multiple Intelligences to Increase Reading Comprehension in English and Math. Action research project, Saint Xavier University, Chicago, IL.
An example of a graphic organizer used to help high school algebra students understand math word problems.
(Kuzniewski et al., 1998)
Please join StudyMode to read the full document