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Math Language, Vocabulary, & Story Problems: A Conversation with Dr. Sarah Powell

At Made for Math, we’re passionate about making math accessible, meaningful, and even fun for students who face unique challenges in their learning journey. That’s why we’re thrilled to share a special conversation featuring our founder and CEO, Adrianne Meldrum, alongside Operations Manager Heather Brand, as they sit down with Dr. Sarah Powell, an inspiring leader in the field of math intervention.

Meet Sarah Powell

Dr. Sarah R. Powell is an Associate Professor in the Department of Special Education at the University of Texas at Austin, where she dedicates her work to improving math outcomes for students with learning difficulties. With a focus on research-driven strategies, Dr. Powell has been instrumental in developing and testing interventions that address critical aspects of math education, including peer tutoring, word-problem solving, math writing, and understanding the symbols and vocabulary within mathematics.

One of the key takeaways from Dr. Powell’s research is the importance of making math concepts more accessible to all learners, especially those who struggle with traditional teaching methods. By focusing on peer tutoring and word-problem solving, she has found innovative ways to enhance student engagement and comprehension.

Dr. Powell also emphasizes the role of language in math learning. Her work highlights how understanding the symbols and vocabulary within mathematics can make a significant difference in a student’s ability to grasp and apply concepts.

The Language of Mathematics

According to Dr. Powell, math language encompasses much more than words and numbers. It includes all the ways students interact with mathematics:

  • Visuals like bar models, number lines, and graphic organizers.
  • Tools such as manipulatives and virtual aids.
  • These components help students communicate and engage with mathematical concepts, but one critical aspect that often requires extra focus is math vocabulary.

    The Role of Math Vocabulary

    Dr. Powell emphasizes that math vocabulary is foundational for students to fully participate in the classroom. With hundreds of terms to master at each grade level, understanding this vocabulary can be a game-changer. However, many challenges come with teaching these terms:

    1. Unfamiliar Words: Many math terms, like “numerator” or “denominator,” are rarely spoken outside of school settings, making them new concepts for students.
    2. Multiple Meanings: Some words students recognize from everyday life—like “base”—have completely different meanings in math, which can lead to confusion.
    3. Language Barriers: For multilingual learners, understanding math vocabulary requires learning it in both English and their home language.
    4. Learning Differences: For students with dyslexia, dyscalculia, etc. math vocabulary can feel like an entirely new language to decode.

    These challenges are amplified for students with dyslexia, dyscalculia, or speech and language difficulties, making targeted intervention vital.

    Because math language isn’t commonly used at home, it needs to be explicitly taught and reinforced in the classroom or during tutoring sessions. Dr. Powell highlights the importance of consistent practice to help students grasp these terms and their meanings.

    Strategies for Supporting Students with Math Vocabulary

     
    Dr. Powell and her colleague Liz Stevens from the University of Kansas are conducting research to identify the most effective ways to teach math vocabulary. Here are some strategies they’re exploring:

    1. Concept Maps
    A concept map is a one-page tool that helps students break down a math term. It includes:

  • The term and a student-friendly definition.
  • Visuals and explanations that illustrate the term’s meaning.
  • Related language (e.g., for “numerator,” terms like “denominator,” “fraction,” and “equal parts”).
  • These maps help students connect math vocabulary to broader concepts and related terms, ensuring a deeper understanding.

    2. Interactive Games and Activities
    Practice is key to learning math vocabulary. Some engaging activities Dr. Powell and her team use include:

  • Guess My Number: A flexible game where students practice vocabulary and higher-level concepts. For example, they might ask, “Does your number have an exponent?” This question challenges them to understand what numbers with exponents look like while using key vocabulary.
  • Memory Matching: Students match terms with definitions, visuals, or examples.
  • Repetition Through Play: Games encourage students to revisit terms and reinforce their understanding in a fun, low-pressure way.
  •  
    3. Explicit Teaching with Repetition
    Teachers explicitly introduce terms with tools like concept maps, followed by repeated practice through games and activities. This approach ensures students don’t just hear the term—they interact with it in multiple ways.

    Math Language in Story Problems

    Let’s dive into the importance of schemas in helping students understand and solve word problems

    What are Schemas?

    Schemas represent the underlying ways students interpret mathematical operations like addition, subtraction, multiplication, and division. Decades of research have shown that a strong understanding of these operations lays the foundation for success in solving word problems.

    For example, addition can be understood in different ways:
     

  • Part-Part-Whole: Thinking of addition as combining parts to create a total. For instance, “Four blue cubes and three red cubes make seven cubes in total.”
  • Adding-On: Starting with a quantity and adding more to it. For example, “I have four blue cars. If I add three more, how many cars will I have?”
  •  

    These basic interpretations connect directly to the types of word problems students encounter. For instance:

  • Part-Part-Whole: “Four boys and three girls are playing on the playground. How many children are there in total?”
  • Adding-On: “Sally has four apples. She picks three more. How many apples does she have now?”
     

    Schemas help students understand the structure behind word problems, making it easier for them to identify the appropriate operation to solve the problem. This connection starts early—even in activities where teachers might not explicitly focus on word problems.

    Dr. Powell explains that hands-on tools, virtual manipulatives, or even everyday examples can support schema-building. For instance, using colored cubes to combine quantities or role-playing scenarios with toy cars provides students with the groundwork for later more formal word problem-solving.

  • Story Problem Strategies & Resources

    Word problems are a staple of math education, and yet they remain one of the most challenging aspects for students. Dr. Sarah Powell shared some fascinating insights about the work her team has been doing to help students overcome these challenges through innovative interventions like Pirate Math Equation Quest.

    Dr. Powell noted a concerning trend: across the United States, most students struggle to meet minimum proficiency levels in math, with word problems being a significant barrier. These questions test not just computational skills but also a student’s ability to translate real-world scenarios into mathematical equations and schemas.

    For example:
    “Adrianne and Heather have 10 pets. If Adrianne has 6, how many does Heather have?”

    This problem might seem simple, but it requires students to understand the part-part-whole schema and express it as an equation:
    6 + __ = 10

    If students cannot generate or solve this equation, they’ll struggle to solve the word problem itself.

    Dr. Powell’s team adapted and expanded a Vanderbilt University intervention called Pirate Math to help students navigate these challenges. Through their research, they developed Pirate Math Equation Quest., which teaches students to identify the schema behind a word problem,
    represent the problem using equations, and use equations to arrive at a solution.

    Check out these YouTube videos to see Sarah break down the schemas with hand gestures: Word Problem Instruction

    From Single-Step to Multi-Step Problems

    As students progress from grade three to grade four, the complexity of word problems increases significantly. Dr. Powell’s latest research focuses on helping students tackle multi-step problems, which often involve multiple schemas.

    Take this example:
    “A store has 5 shelves of toys with 8 toys on each shelf. If they sell 12 toys, how many are left?”

    To solve it, students must:

    1. Use an equal groups schema to calculate the total number of toys: 5 × 8 = 40

    2. Apply a subtraction schema to find how many remain after 12 are sold: 40 – 12 = 28

    Helping students approach problems like these requires explicit instruction, practice, and tools to break the problems into manageable steps.

    Dr. Powell’s research shows that these interventions significantly improve student outcomes. By focusing on schemas, equations, and step-by-step reasoning, students gain confidence and develop skills to tackle even the most daunting word problems.

    Gestures as Learning Anchors

    Dr. Powell emphasizes that pairing verbal explanations with specific hand gestures helps students focus on the type of word problem they’re solving. These gestures serve as a physical representation of the problem’s schema, making abstract concepts more tangible and easier to remember.

    For example, when reading a word problem, teachers might ask:

    • “Is this a total problem?” while bringing their hands together to symbolize combining parts into a whole.
    • “Is this a difference problem?” while showing a separation gesture with their hands to indicate comparing amounts.
    • “Is this a change problem?” while moving their hands up or down to reflect an increase or decrease.

      Students quickly adopt these gestures, often using them to indicate the schema without even speaking. This silent communication reinforces their understanding and helps them visualize the problem structure.

      Breaking Down the Process

      Dr. Powell’s team has developed a structured approach for introducing gestures and schemas into problem-solving:

      1. Read the Problem Together: Many students skip reading word problems and jump straight into calculations. Dr. Powell encourages students to read the problem aloud, either independently or with an adult, to understand the context.
      2. Discuss the Story: Ask questions like, “What’s going on in this story?” or “Is this about pets, sharks, or money?” Identifying the narrative helps students connect the math to real-world situations.
      3. Focus on the Schema: Using gestures, teachers ask targeted questions to determine the type of problem: total, difference, change, equal groups, or sets.
      4. Solve the Problem: Once the schema is identified, students can represent the problem using equations and proceed to solve it.

      Why Gestures Work
      Gestures provide a multisensory learning experience that enhances memory and comprehension. They act as a visual que, especially beneficial for students who struggle with language processing or have learning differences like dyslexia or dyscalculia.

      At Made for Math, we recognize the importance of connecting physical movement with math instruction. Incorporating gestures and schemas into lessons allows students to engage actively, fostering both confidence and comprehension.

      When it comes to solving word problems, Dr. Sarah Powell emphasizes that success hinges on two powerful tools: attack strategies and a focus on schemas. These research-backed methods offer a structured approach to breaking down even the most complex problems.

      What are Attack Strategies?

      Attack strategies provide students with a step-by-step roadmap for tackling word problems. These strategies guide students through the problem-solving process, helping them focus on what to do first, second, and beyond.

      Dr. Powell highlighted several popular strategies:

      1. SOLVE: An acronym that stands for:

    • Study the problem
    • Organize the information
    • Line up a plan
    • Verify the plan
    • Examine the answer2. UPS Check: The strategy Dr. Powell uses most often. It prompts students to:
    • Understand the problem
    • Plan how to solve it
    • Solve the problem
    • Check their workAttack strategies are like a game plan, giving students a clear sense of direction when they feel overwhelmed or unsure where to start.

      An attack strategy alone can help students navigate a problem, but combining it with a schema focus deepens their understanding of the mathematical structure behind the word problem.

      Schemas help students categorize problems into familiar types. Dr. Powell suggests using questions and gestures to identify these schemas:

    • Total problems: Are parts put together for a total?
    • Difference problems: Are amounts compared for a difference?
    • Change problems: Does one amount increase or decrease to a new amount?
    • Equal group problems: Are there groups with an equal number in each?
    • Set problems: Is a set compared multiple times?
    • By identifying the schema, students can better determine the appropriate operation and approach to solving the problem.

    How to Implement This in Your Classroom

     

    To bring these strategies to life:
    1. Teach an attack strategy: Start with a simple, structured approach like UPS Check to help students organize their thinking.
    2. Introduce schemas early: Use questions, gestures, and visual aids to help students identify the type of problem they’re solving.
    3. Practice both together: Create activities and games that encourage students to use both the attack strategy and schemas in tandem.

    If you’re looking for practical, free resources to enhance your teaching, check out Sarah’s Math Spiral website.

    Dr. Powell highlighted several popular strategies, including UPS Check and SOLVE, but at Made for Math, we’ve developed our own approach, ROMANS, to better meet the needs of students with learning differences.

    Made for Math’s ROMANS Strategy

    ROMANS is a step-by-step process that adds intentional scaffolding for students who benefit from more guidance:

    • R: Reading and Highlighting – Carefully read the problem and highlight key information.
    • O: Organize – Identify what you know and what the problem is asking for.
    • M: Make an Equation – Write out the equation that matches the problem.
    • A: Answer and Label – Solve the equation and label the answer correctly.
    • N: Need to Check – Review the solution to ensure it makes sense.
    • S: Sentence – Break down the language of the sentence. Who and what is the question actually asking about. Adrianne’s pets or Heather’s pets?
       

      We find that ROMANS provides the additional structure and a breakdown for students with dyslexia, dyscalculia, or ADHD.

      Advancing Special Education: The PhD Program at UT Austin

      For anyone looking to make a difference in the field of special education and math, Sarah’s doctoral programs at UT Austin offer a comprehensive and supportive pathway to becoming a leader in the field.

    Connect with Dr. Sarah Powell

    If you’re interested in learning more about Sarah’s work or have questions about how to implement the strategies discussed in this post, you can reach out to her directly:

  • Email: srpowell@utexas.edu
  • Social Media: @sarahpowellphd
  • With her extensive knowledge and commitment to improving math education for all students, Sarah Powell is an invaluable resource for anyone in the education field. Reach out today to learn more about her work and how you can incorporate these strategies into your classroom!

    💡 Is multisensory math right for you and your family?

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    MFM Authors

    Jennie Miller

    Jennie Miller

    Marketing Assistant

    is our Marketing Assistant and content creator here at Made for Math. Jennie loves being part of a company that is working to make mathematics accessible to children with dyscalculia.