Recently, the Common Core State Standards (CCSS) stated its’ motto for “standards for mathematical practice by means of a slogan: “Make sense of problems and persevere in solving those problems” (Common Core State Standards Initiative, 2019). Literacy is intertwined with content subjects and is crucial in making sense of problems. Students, especially English Language learners, develop a fear for word problems during the transition stage at the fourth-grade level, when they move from simple word problems to solving complex problems.
Word problems are used as practice exercises and as illustrations throughout mathematics curriculum, and mathematical reasoning and problem-solving are closely linked to language, and rely upon a firm understanding of ideas expressed in the text and basic math vocabulary (Dale & Cuevas, 1992 & Jarret, 1999). These studies demonstrated that the use of reading strategies can help students to think, analyze, and remember ideas expressed in the text (Shanahan, 2018). Therefore, this article is focused on comprehension strategies that enable students to solve word problems in mathematics.
Strategy #1: Connect Word Problems in Daily Life by Thinking Aloud
One of the purposes of word problems is to prepare children for daily life. Word problems are a great resource to introduce new concepts to students. As children encounter real world problems, teachers could exercise the think aloud strategy as they read the problem. Read the first sentence of the problem orally, and then comment on it by thinking aloud about what information it has delivered and how does it challenge students to think critically? Repeat the procedure for the second sentence. Let students hear what you are thinking as you read the problem, piece by piece. Think aloud by explicitly stating what and how the ideas are applied in daily life. Then keep thinking aloud as you put the pieces together. This strategy is applicable during reading problems, training, and testing understanding of new concepts.
Example. Class, listen to the opening sentence of this problem: “Juan wanted to buy a cake.” The word buy leads me to think this problem is going to involve money. “At the counter he saw a chocolate cake for ten dollars and ..."
Strategy #2: Rereading to Revisit with a Purpose
Language proficiency is a contributing factor in problem-solving. According to the United States Department of Education (2001) students’ performance on word problems is generally ten to thirty percent below their performance on comparable problems in a numeric format.
Students, specifically young English Language Learners, exhibit inadequate second language proficiency which could be tackled with rereading in solving word problems. They need to make a habit of rereading. Rereading refers to revisiting the text with a different purpose of visit each time, and writing the interpretations with a pencil to correct or change it later when a new interpretation arises. Reread to correlate language and mathematics and move towards mathematical direction with at least 95% accuracy rate (Hite 2009). Read the whole problem; then reread the problem again and again, highlighting keywords, evaluating, and writing mathematical equations with key variables
Example. Class, Read word problem 1 all the way through, and reread it making notes on whatever you think is important. Jose, what did you write? Barbara, How about you? Can you both read what you noted as important? It seems that the two of you disagree about what is important. Class, reread to see if you agree with Jose or with Barbara.
Strategy #3: Explicit Guided Instruction to Identify Critical Content
Explicit guided instruction can positively impact student learning. Careful listing of information and variables is a valuable step in solving word problems. Explicit instruction could also be student-centered in targeting what students need to learn new. And, the skills they might need to learn the new idea (Archer & Hughes, 2011). Guide your students in identifying the critical information. Guide them to find out if multiple steps are required to solve the problem. An estimation could help before actually proceeding.
Example. Class, we know to read and write fractions, and today we are going to compare fractions in word problems. Read word problem 3 and re read to make notes. Answer me, how many students are there in Ms. Ashley’s class? How many students in Ms. Ashley’s class are wearing glasses? We see that two-thirds of Ms. Ashley’s class…..I repeat it is two-thirds.
Strategy #4: Employing Re-representation in Problem Solving
“The activity of re-representation may be a crucial step in mathematization” (Gamo, Sander & Richard, 2010, p. 409). Re-representation could be practiced by asking students to identify relevant information in the problem, understand what is asked for, and making educated guesses to solve by comparing with the model problem solution. For example, identifying keywords and phrases like area, multiplied by, a product of for multiplication word problems; quotient, divided by, and how many do each get for division problems. These keywords should be used to identify the pattern.
Example. Class, The Oreo cookie problem you solved earlier is similar to this problem. So try to use the Oreo cookie problem to help you solve the Choco-chip cookies problem. In particular, try to use how you divided Oreo cookies into each bag. You can come up with the same kind of procedure for solving how many Choco-chip cookies for each person this time. Remember, last time you divided Oreo cookies equally into each bag, and this time instead of bags, you are going to share among people at a table.
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