Word Problems? No Problem! Helping Students to Set Up and Solve Word Problems
An important way students demonstrate mathematics competency is through solving word problems. The term word problem refers to a text-based mathematics problem in which students respond to a prompt within the word problem to develop a solution. Perhaps not surprisingly, students who experience difficulty with mathematics (as identified by an official or unofficial disability diagnosis) demonstrate low rates of success with setting up and solving word problems (Fuchs et al., 2014; Jitendra et al., 2014). In this brief, we describe effective word-problem instruction for students with a mathematics learning difficulty (MLD) to better equip educators with the appropriate content knowledge to support their most vulnerable students.
Types of Word Problems
In textbooks and on high-stakes assessments, students in the elementary and middle school grades often solve two types of word problems: Directional and Routine. A Directional word problem provides students with specific directions to complete a task. For example, in the word problem question: Which three shapes are quadrilaterals? students must identify the three shapes fitting the definition of a quadrilateral. A second example, Use the drawing tool to draw a rectangle with an area of 1575 square units and a side of 45 units, requires students to draw a rectangle.
A Routine word problem directs students to respond to a question about the provided information. Typically, Routine word problems are the problems most people think of when they hear the term “word problem.” The following offers one example of a Routine word problem: Ryan has 1/2 pound of chocolate. He divides it into 4 equal portions. Enter the amount of chocolate, in pounds, of each portion. In this Routine word problem, students need to use the information about 1/2 pound and 4 equal portions to determine each portion is 1/8 of a pound. In another Routine word problem example, Kevin makes muffins. It takes 8 minutes to mix the batter. The muffins bake for 17 minutes. The muffins cool for 5 minutes. What is the total amount of time Kevin spends mixing, baking, and cooling the muffins?, students must calculate the total amount of time (i.e., 30 minutes) to correctly answer the question.
Why Word Problems are Difficult
Word problems prove challenging for students with MLD for many reasons, including the need to identify relevant information, ignore irrelevant information, and/or perform the computation(s) necessary to find the solution (Krawec, 2014; Sharpe et al., 2014; Wang et al., 2016). In addition, students with MLD may experience difficulties reading the problem, understanding the vocabulary within the problem, and interpreting the text (Fuchs et al., 2015; Peake et al., 2015); further, working memory challenges may hinder the word-problem process (Swanson et al., 2014). Solving word problems involves numerous steps and skills, and without formal instruction, most students with MLD rely on the immature strategy of adding all the numbers presented in the word problems without reflecting upon the word-problem question.
Because mathematics standards in the U.S. expect students to set up and solve word problems and students with MLD may find word problems especially challenging, several research teams have developed word-problem interventions to support the specific needs of students with MLD. See the work of Brian Bottge, Lynn Fuchs, Asha Jitendra, and Marjorie Montague (among others) for exemplar examples of word-problem interventions (Bottge et al., 2007; Fuchs et al., 2010; Jitendra et al., 2014; Montague et al., 2011).
In this brief, we describe our research team’s effort to provide effective word-problem instruction to students with MLD. First, we discuss the importance of embedding modeling and practice about algebraic reasoning within a word-problem intervention. Then, we describe the five components of our intervention to support students in setting up and solving Routine word problems, as this type of word problem often proves most difficult for students with MLD. Lastly, we offer recommendations to general and special educators for implementing high-quality word-problem instruction in their classrooms.
Instruction on Setting Up and Solving Word Problems
From 2015-2018, we provided third-grade students with MLD an intensive word-problem intervention called Pirate Math Equation Quest (PMEQ). We identified students with MLD as scoring at or below the 25th percentile on a measure of word problems. Students in PMEQ received our intervention 3 times per week, for 16 weeks, with sessions lastly approximately 30 minutes. PMEQ students participated in five activities for each session: (1) Math Fact Flashcards, (2) Equation Quest or Pirate Crunch (3) Buccaneer Problems, (4) Shipshape Sorting, and (5) Jolly Roger Review. See Figure 1 for an example of each activity.Back