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They experienced problem comprehension that provided them access to solve the problem. They found it easier to create an internal representation for each sentence and integrate the information in to a coherent structure. Students can demonstrate that coherent structure using various representa tions: concrete, diagrams/charts/pictures, or sym bolic, which goes back to the last part of Polya ’ s (1973) Step 1 in the problem - solving process. However, showing the word problem structure is not enough when students are learning to solve word problems to bolster their problem - solving skills. Next, we describe the Fab Four (Oczkus, 2010) set of reading comprehension strategies and how they can be modified to include problem com prehension when using the three - sentence word problem template. Problem Comprehension Integrated with Read ing Comprehension Strategy: Fab Four The Fab Four (Oczkus, 2010) is intended as a re ciprocal teaching strategy for reading comprehen sion (Palinscar & Brown, 1986) that is suited for middle and upper elementary students. It is typical ly used with fiction and non - fiction literature linked to science, social science, or history. In gen eral, mathematics is not included. Reciprocal teaching (Palincsar & Brown, 1986) is a scaffolding technique that teaches students to be come metacognitive, that is, aware of their think ing. The responsibility to comprehend the text shifts from the teacher to the students so they can comprehend the text on their own. The reciprocal teaching strategy begins with the teacher modeling each of these four strategies to the students. The gradual release of responsibility begins in the next step, when students are placed into groups of four. One student in each group is given the role of checker to ensure all four strategies are used. The final release of responsibility occurs when students use these strategies on their own when reading a text. The Fab Four strategies are: Predicting, Question ing, Clarifying, and Summarizing (Oczkus, 2010). They are taught to the students using puppets or pictures of characters representing each strategy: “ Paula the Predictor, Clarence the Clarifier, Quinn
the Questioner, and Sammy the Summariz er ” (Stricklin, 2011, p. 621). Next, we describe each of the strategies. Predicting is a type of guessing but includes pre viewing the text. For text outside of mathematics this may include looking at illustrations or the cov er of the book and the title. The students use this technique when implementing the frame: “ I think this is about … because …” (Oczkus, 2010, p. 18). Within mathematics, particularly for some content areas such as geometry or statistics, students can look at an illustration, graph, or chart when using the same predicting frame. Questioning involves using diverse types of ques tions, such as 1) wondering questions, 2) quiz questions, 3) inference questions or main points questions, and 4) they are encouraged to create dis cussion questions while reading the text. Student ’ s own questions increase their awareness of their own thinking, and it increases their attention to the text (Oczkus, 2010). When solving mathematics word problems, students can use questioning to identify what they fail to comprehend that goes beyond, “ What do I do? ” Students can ask ques tions about the context of the problem, or the rela tionship between the objects, or characters in the word problem. For example, the students can ask, “ How many marbles does Joe have? ” and “ How are Tom ’ s marbles related to Joe ’ s marbles? ” Clarifying is monitoring one ’ s comprehension. Specifically, the student is tracking their under standing and using strategies that can fix lapses of comprehension. It includes two basic steps: 1) ad mitting you fail to understand something (e.g., I am stuck) and 2) figuring out how to remedy the situation (e.g., how do I get unstuck). This goes beyond lack of word recognition; it includes grasp ing the main ideas. Using the frame: “ I didn ’ t get the sentence … so I …” (Oczkus, 2010, p. 21) helps students to identify where in the text their comprehension breaks down. Other additional prompts to support clarifying include: 1) “ I didn ’ t understand the part where …”, 2) “ This doesn ’ t make sense …”, 3) “ I can ’ t figure out …” (Oczkus, 2010, p. 21). The remedies to clarify components in a mathematics word problem may include the following frames: “ I reread the parts I don ’ t under-
Virginia Mathematics Teacher vol. 48, no. 1
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