Our last post highlighted how strategies that ignore the connection between reading and math fail to prepare students to solve complicated word problems. Thankfully, there are effective approaches to helping children with varying support needs solve word problems (Lein et al., 2020), many of which resemble comprehension strategies used in reading instruction. This post describes two approaches supported by decades of research: attack strategies and schema instruction (Powell & Fuchs, 2018). Curious readers are encouraged to consult the references for more information about these techniques. Additionally, a link to free instructional resources appears at the end of the post. 

Reading to Solve: Effective Strategies for Word Problems

Attack Strategies

Attack strategies are step-by-step methods designed to help students solve word problems that are often taught using checklists and diagrams (Jitendra et al., 2015). For example, the Solve It! strategy (Montague et al., 2014) includes six steps: (1) Read for understanding; (2) Paraphrase the problem; (3) Visualize the problem in a picture or diagram; (4) Hypothesize a plan to solve the problem; (5) Estimate the answer; and (6) Compute the problem and check the result. Each step is accompanied by three prompts (say, ask, check) that describe specific questions to ask and actions to perform throughout the process. Attack strategies for word problems are similar to those used in literacy instruction to guide students through tasks such as answering comprehension questions (RAP; Hagaman et al., 2010) or writing essays (e.g., POW+TREE; Shora & Hott, 2016). 

Likewise, word problem attack strategies are often presented as easily remembered phrases that can represent steps to solve an entire problem or specific phases of the problem-solving process (Powell & Fuchs, 2018). The RUN strategy, for example, provides a simple method for identifying types of word problems: Read the problem aloud; Underline the question; Name the problem type and pick an operation (Fuchs et al., 2014). 

First, a student would read the following problem:

Rex has 3 boxes of markers. Each box holds 6 markers. He gives 4 markers to his friend. How many markers does Rex have left?

and then underline the question:

How many markers does Rex have left?

Finally, the student would assess the structure of the problem and link it to previously taught problem categories: 

Equal Groups (3 boxes x 6 markers) and Change (gives 4 away). 

But how does the student learn to recognize these problem types? Attack strategies help students recall and follow steps for solving problems. However, these strategies are usually paired with explicit practice in problem-solving skills. The RUN strategy, for example, concludes with a prompt to identify the problem type—a skill that must be acquired through extensive practice. That’s where schema instruction comes in.

Schema Instruction

Schema instruction is another extensively researched method that involves explicitly teaching students to classify word problems based on their schema, or underlying structure (Powell et al., 2022). At its core, schema instruction teaches students to read mathematically, supporting comprehension in ways similar to dedicated literacy instruction. Students learn to make sense of text, identify relationships between quantities, and select appropriate operations. The process is highly reminiscent of the meaning-making that occurs when comprehending narrative or informational passages. Some common schemas, with examples, include:

Teaching students to recognize schemas requires dedicated, reading-focused instruction embedded within typical math lessons, often beginning when operations are initially introduced (Powell & Fuchs, 2018). For example, Total schemas, which represent part-part-whole relationships and are often solved via addition and subtraction, can be introduced as early as kindergarten and revisited for several weeks throughout the year. Effective instructional strategies include modeling the identification of schemas, explicit vocabulary instruction, and the use of specific solution strategies for each schema. Additionally, students will use attack strategies during schema instruction to help them identify operations and solve problems. 

Powell (n.d.) describes how schema instruction might look in practice. Returning to the RUN strategy, instruction typically includes a graphic organizer describing the strategy, a worksheet listing questions to help students identify specific schemas, and specific steps for solving problems belonging to different schemas. Instructors usually present mixed sets of problems from total, difference, change, and equal groups schemas instead of separate dedicated blocks of similar problem types. This is because interleaving—or mixing problem types—has been linked to rapid improvements in students’ ability to discriminate between schemas (Fuchs et al., 2021). Students are taught to begin every word problem using the RUN strategy. After reading the problem and underlining the question, students would then use self-directed prompts to determine the appropriate schema (Powell, n.d.):

Teaching self-questioning can involve teaching specific gestures associated with each schema to support memory and comprehension. For example, the gesture for the Change schema involves (a) placing a hand horizontally near the chin to represent the starting amount and (b) moving it to the forehead or chest to demonstrate an increase or decrease. When presented with the following problem: 

Marco had 10 marbles in his collection. Then he found 7 more under his bed. How many marbles does Marco have now? 

application of the RUN strategy and self-questioning would lead students to conclude that this problem belongs to the Change schema. Within each schema, students receive additional training in solving various types of problems, such as Change problems when (a) the end amount is missing or (b) the starting amount is missing. For each problem, teachers guide students through structured steps in identifying a solution:

Marco had 10 marbles in his collection. Then he found 7 more under his bed. How many marbles does Marco have now? 

A student using the problem strategy might say: “Marco starts with 10 marbles. He finds 7 more. This is a Change increase problem because I know what Marco starts with, and that amount gets bigger.” 

They would then identify critical parts of the problem:

ST + C = E

ST = 10; C = 7 

10 + 7 = E

17 = E

Finally, the student would solve the problem: “Marco has 17 marbles.” 

Instruction begins with many materials and prompts, which are gradually faded out as students become more successful at solving problems. Additional examples, with detailed steps and materials, are available at the resource linked at the end of this post. 

Vocabulary instruction, though not the focus of schema instruction, is often embedded to help students identify problem structures (Powell & Fuchs, 2018). Instruction may target words such as “altogether,” “more than,” “fewer than,” “gave,” “received,” “taller,” or “heavier.” Looking at these terms, some instructors may assume students come into math class having already acquired these words in other settings. However, this is not always the case. In fact, many early elementary students likely have limited experience applying these terms, especially in mathematical contexts.

A key feature of schema instruction that strongly ties it to literacy instruction is its emphasis on vocabulary and conceptual understanding (Powell & Fuchs, 2018). Schema instruction avoids linking words to operations (e.g., more = add) or categorizing problems by operation. This is because words can have different meanings depending on context, and students can use different operations to solve the same problem correctly. Together with effective, explicit reading instruction, schema instruction is a powerful tool for helping students understand word problems and link literacy to math concepts. 

Resource 

Schema instruction may seem challenging for many instructors who feel they lack the resources to integrate reading into their instruction or support students who struggle with reading. Fortunately, free materials and plans related to effective word problem instruction are available. 

One example is Pirate Math Equation Quest, a research-based intervention that improves students’ understanding of word problem schema. Instruction concerning the identification of problem types and application of attack strategies is placed in the context of a pirate-themed adventure. The site includes student materials, teacher guides, and video models. 

Literacy is every subject—and math is no exception. Word problems, specifically, are not just math problems with words; they are reading tasks embedded in math. Ineffective approaches like the keyword strategy may appear to make word problems easier, but in reality, they undermine the literacy skills that support effective problem solving and mathematical understanding. Effective strategies integrate literacy into math using evidence-based instructional approaches. Adopting these approaches can improve outcomes for students in both math and reading. 

Acknowledgement

We thank Sarah Powell, Professor of Special Education at the University of Texas at Austin, whose presentation at the UI Baker and Teacher Leader Center in February 2025 greatly informed this post. 

References 

Arsenault, T. L., & Powell, S. R. (2022). Word-problem performance differences by schema: A comparison of students with and without mathematics difficulty. Learning Disabilities Research & Practice, 37(1), 37–50. https://doi.org/10.1111/ldrp.12273 

Fuchs, L. S., Powell, S. R., Cirino, P. T., Schumacher, R. F., Marrin, S., Hamlett, C. L., Fuchs, D., Compton, D. L., & Changas, P. C. (2014). Does calculation or word-problem instruction provide a stronger route to prealgebraic knowledge?. Journal of Educational Psychology, 106(4), 990–1006. https://doi.org/10.1037/a0036793

Fuchs, L. S., Seethaler, P. M., Sterba, S. K., Craddock, C., Fuchs, D., Compton, D. L., ... & Changas, P. (2021). Closing the word-problem achievement gap in first grade: Schema-based word-problem intervention with embedded language comprehension instruction. Journal of Educational Psychology, 113(1), 86.

Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87(1), 18–32. https://doi.org/10.1037/0022-0663.87.1.18

Hagaman, J. L., Luschen, K., & Reid, R. (2010). The “RAP” on reading comprehension. Teaching Exceptional Children, 43(1), 22-29.

Jitendra, A. K., Petersen-Brown, S., Lein, A. E., Zaslofsky, A. F., Kunkel, A. K., Jung, P. G., & Egan, A. M. (2015). Teaching mathematical word problem solving: The quality of evidence for strategy instruction priming the problem structure. Journal of Learning Disabilities, 48(1), 51–-72. https://doi.org/10.1177/0022219413487408

Lein, A. E., Jitendra, A. K., & Harwell, M. R. (2020). Effectiveness of mathematical word problem solving interventions for students with learning disabilities and/or mathematics difficulties: A meta-analysis. Journal of Educational Psychology, 112(7), 1388–1408. https://doi.org/10.1037/edu0000453

Montague, M., Krawec, J., Enders, C., & Dietz, S. (2014). The effects of cognitive strategy instruction on math problem solving of middle-school students of varying ability. Journal of Educational Psychology, 106(2), 469.

Powell, S. R. (n.d.). Pirate Math Equation Quest. University of Texas at Austin. https://www.piratemathequationquest.com/