Understanding Problems - Teach With Tech

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Learning how to solve word problems requires students to understand the context and then develop a strategy to solve the problem. Students build on their ability to organize, create visual representations, and use precise language. You can help your students build on these skills and understand how to use them in specific situations (see UDL Checkpoint 6.2: Support planning and strategy development).

Steps:

  1. Provide Clear Explanations
  2. Give Students Strategies and Models
  3. Provide Ongoing Formative Assessment

Step 1: Provide Clear Explanations

  1. When students face new or relatively complex tasks, it is critical that teachers pause and provide clear explanations of what is expected and of the mathematics being learned. When providing guidance, use short declarative sentences, scaffold the questioning, and give students sufficient time to understand and react (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships).
    Example of a sequence to support students
    • Announce: “Here is exactly what I need you to do.”
    • Give initial direction: “I need you all to read the problem silently to yourselves.”
    • Continue: “Now I would like you to read the problem again, paying particular attention to the meaning of the numbers.”
    • When students are ready, explain: “Now I need you to tell your shoulder partner what the problem is asking you to find.”
  2. A common and effective strategy to reinforce directions and explanations is to ask students to present the directions or explanations in their own words. Prompt students by asking, “Can you repeat the directions that I just gave to the class?” or “Can you put the explanation that I just gave in your own words and repeat it for the class?”
  3. Ask students to compare and contrast different approaches and then summarize what you hear. Students should understand what works and what doesn’t work (and why), which methods are more efficient, and how models are different. It is critical that teachers elicit, value, and celebrate approaches that are different but still arrive at the correct solution.
View evidence behind this recommendation

IES Recommendations

Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.

Evidence:
Strong

Source: IES Practice Guide: Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools

Interventions should include instruction on solving word problems that is based on common underlying structures

Evidence:
Strong

Source: IES Practice Guide: Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools

Teach number and operations using a developmental progression.

Evidence:
Moderate

Source: IES Practice Guide: Teaching Math to Young Children

Step 2: Give Students Strategies and Models

  1. Use a process chart to guide students when presenting them with new problems. Teachers should focus on how each step in the process supports better access to the problem. For example, reading the problem a second time with annotations helps students sort out the core information from the background noise. Visualizing a story can be a powerful strategy that helps students create a picture or diagram of the problem. Estimating or approximating an answer helps students decide if they’re on the right track.
    Possible problem-solving process
    • Read the problem, and then reread it and highlight key words and numbers.
    • Draw a picture of the situation that the problem presents. It may be helpful to first visualize a story or imagine a movie scene.
    • Determine the goal of the problem.
    • Establish a strategy or write an equation to represent the picture. Estimate an answer, if possible.
    • Solve the problem and check the reasonableness of your answer.
    • Explain your solution method.
  2. Create a gallery walk of student solutions to help them evaluate and expand their repertoire of appropriate models. Gallery walks allow for public discussion and easy comparisons of solutions to the same problem. Technology tools, such as Thinking Blocks, can also expand their repertoire with virtual models.
  3. Encourage students to embrace mistakes and errors, correct them as necessary, and move on with confidence. Note that it is rare to complete a problem from start to finish without a mistake or misstep (see UDL Checkpoint 3.2: Highlight patterns, critical features, big ideas, and relationships).
View evidence behind this recommendation

IES Recommendations

Intervention materials should include opportunities for students to work with visual representations of mathematical ideas and interventionists should be proficient in the use of visual representations of mathematical ideas.

Evidence:
Moderate

Source: IES Practice Guide: Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools

Help students recognize that fractions are numbers and that they expand the number system beyond whole numbers. Use number lines as a central representational tool in teaching this and other fraction concepts from the early grades onward.

Evidence:
Moderate

Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review.

Evidence:
Strong

Source: IES Practice Guide: Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools

Help students understand why procedures for computations with fractions make sense.

Evidence:
Moderate

Source: IES Practice Guide: Developing Effective Fractions Instruction for Kindergarten Through 8th Grade

Step 3: Provide Ongoing Formative Assessment

  1. Check in with students to ask, “Can you explain to me what you are doing here (pointing to a student’s work)?” to reveal whether or not students are on the right track and if additional guidance is needed.
  2. When students use pictures, diagrams, charts, expressions, and equations as part of the problem-solving process, it is very helpful to ask questions such as, “How does that diagram relate to the situation in the problem?” or “Can you explain to me why you think that is a good mathematical expression to use for this problem?” (See UDL Checkpoint 3.3: Guide information processing, visualization, and manipulation.)
  3. Mathematics should be a sense-making process. We don’t really know whether or not it makes sense until we see student work and hear student explanations. The formative assessment question, “Does that make sense to you?” is a powerful strategy for supporting learning.
    Supporting a sense-making process
    • Do not allow students to simply respond “yes” or “no.” Probe to understand the degree to which the mathematics makes sense to them. Elicit more detailed responses, prompting students by asking, “Why does it make sense?” or “Exactly what doesn’t make sense?”
    • • Make the sense-making process explicit when teaching students problem-solving strategies.
    • Keep the focus on student thinking and understanding. Ask students, “Does this make sense?” when they have solved a problem. Eventually, students should be expected to do this for themselves before finishing a problem.
View evidence behind this recommendation

IES Recommendations

Instruction during the intervention should be explicit and systematic. This includes providing models of proficient problem solving, verbalization of thought processes, guided practice, corrective feedback, and frequent cumulative review

Evidence:
Strong

Source: IES Practice Guide: Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools

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