Episode 26 - The Language of Math with Paul Riccomini, PhD

Episode Summary

All READers are invited to take a journey in mathematics with Penn State professor and The WI faculty member, Paul Riccomini, PhD. Dr. Riccomini and Danielle discuss the language of math with the underlying principle – if kids don’t understand the language of instruction, they’re not going to be able to learn to their potential. Dr. Riccomini explains certain markers of why children may experience challenges in math, when difficulties persist, and scaffolds and instructional practices to support struggling mathematicians. At the end of the episode, Dr. Riccomini answers “crowdsource” questions from adults READers including how parents/ guardians can support kids at home, and he takes on the curiosity of school-aged students by answering their top questions. Dr. Riccomini invites all listeners into a math class to listen closely for the importance of its numbers AND its mathematical language.

Top READ Bookmarks
Each episode, host Danielle Scorrano identifies key takeaways or “READ bookmarks.” 

1. The Language of Math

Math has its own markers of complex language such as vocabulary and symbol notations.

"If kids don't understand the language of instruction, they're not going to be able to learn whatever we're trying to teach. And that is true for the language of math."

Takeaways for instruction:

  • Vocabulary plays a central role in math, especially when solving word problems.
  • Prioritize and explicitly teach vocabulary terms in context
  • Be mindful of multiple meaning terms, like “product” in multiplication. Read more about the complex nature of math vocabulary in a 2015 article here.
  • Check state education websites and resources for curriculum related lists of key terms by grade.

"When I focus on vocabulary words, a lot of times the vocabulary word is an access point. In other words, the kid can't access the content if they don't know the terminology."

2. The Importance of Data and Error Analysis

"The nature of content in math pretty much guarantees at some point, children are going to struggle."

Takeaways for instruction:

  • At some point, all students will struggle with math, but some children, especially those with learning disabilities, may struggle for a longer time based on their challenges.
  • Math errors are predictable. Research shows that students tend to make math errors across four or five different clusters.
  • Error analysis is more than examining student scores on assessments and consists of analyzing student processes and mistakes for a small cluster of students over a period of time.

3. When Children Persistently Struggle in Math

When children struggle in math, it tends to occur across a continuous time frame and can be identified across important developmental milestones.

"In kindergarten, we can begin to identify kids that are going to struggle in third grade because of some skills that they have not developed in math." 

Some children may understand whole numbers but then struggle with rational numbers and fractions, typically around third or fourth grade. These challenges can later predict difficulty with more complex math like algebra.

"[Proficiency in] sixth grade math tends to be a key predictor for high school graduation."

4. Examples of Instructional Supports for Young Mathematicians

"In math, you have to match the strategy, scaffold, or practice to what you are trying to support."

  • Graphic organizers, like the Frayer Model, support vocabulary instruction in math.
  • Scaffolding problem solving to target student needs in vocabulary and language.
  • Worked out solutions to show students the process to problem solving.

"There's this emerging body of research that is suggesting that giving kids fully solved problems can be an intermediate bridge from the teacher model to the students solving the problem on their own."

  • Incremental practice to build fluency.
  • Interleaving of skills and concepts, spaced practice, test retrieval, and free recall with feedback to promote retention

5. Supporting math students at home through

  • Increased communication between teachers and parents/guardians on the learning progression in math (i.e. how students are expected to learn and show their mathematical thinking)

"Math has not changed. Place value is still place value. What is different is the learning progression."

  • Provided worked out solutions and answers for parents/ guardians to review work and support students who may have immediate questions
  • Encouragement for students to self-advocate to teachers
  • Mindful awareness that adult views toward math influence a child’s perception. Research shows that a parent or teacher view and actions (whether explicit or implicit) toward math will shape how their child approaches the subject- especially during times of challenge!

"Kids are not born hating math or having anxiety towards math."

  • Proactive, intentional supports and scaffolds early to mitigate challenges.

"If you constantly experienced failure in any subject or any activity you will eventually learn to not like it and then avoid it."


Follow Paul Riccomini, PhD on TwitterPaul Riccomini, PhD at Penn State University Sign up to learn more about upcoming workshops taught by Dr. Riccomini

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READ Podcast is produced by The Windward School and The Windward Institute. READ is hosted by Danielle Scorrano.

About READ: READ, the Research Education ADvocacy Podcast connects you with prominent researchers, thought leaders, and educators who share their work, insights, and expertise about current research and best practices in fields of education and child development.
Note: All information and insights shared demonstrate the expertise and views of our guests.