Do They Really Understand the Math: Marian Small on the Fresh Ideas for Teaching podcast

How can we be sure students understand the math concepts we are teaching?

How can we ensure that students are not simply copying what we show them, to get correct answers?

When students can demonstrate true understanding, they are better able to transfer and apply their knowledge.

In this episode of Fresh Ideas for Teaching podcast, we asked Marian Small, an internationally renowned mathematics educator, MathUP Classroom author, and professional learning consultant, “What Does Math Understanding Look Like?”

Get your notepads ready to listen to Dr. Marian Small as she shares practical tips, questioning techniques, and strategies to promote mathematical reasoning and uncover true student understanding in the K–12 math classroom.

Among other professional learning books, Marian Small has recently published Do They Really Understand? which is the perfect companion to this episode.

Find the episode here .

Encouraging Peer Interaction for Deeper Learning Language learners thrive when they have the chance to talk about content, make personal connections, and work together. Collaborative learning encourages both the development of social skills and the deepening of content knowledge.

How it works:

Structured Peer Discussions: Teachers can provide opportunities for students to engage in structured discussions about social studies topics, allowing them to connect historical events to their own lives. These conversations build not only an understanding of the content but also academic language. Group Activities: Group activities allow multilingual learners to collaborate with peers, practice using the language in a supportive environment, and gain exposure to different perspectives. Whether it’s working on a project together or solving a problem as a team, students are able to practice language skills and strengthen their grasp of social studies concepts. Language Transference: Through peer discussions, students also practice language transference, where they connect new terms or concepts in the target language to similar words or ideas in their home language. This process enhances comprehension and language retention.

By creating opportunities for multilingual learners to engage with their peers, teachers can create a classroom environment that fosters both academic growth and language development.

The Power of Graphic Organizers: Supporting Multilingual Learners Visually Graphic organizers are essential tools for multilingual learners as they help students visually organize their thoughts, make connections between concepts, and process complex information. These tools are especially valuable when learners are processing both new social studies content and a second language.

Best Practices:

Select the Right Type of Organizer: Use graphic organizers that match the learning task. For example, a Venn diagram is great for comparing historical events, while a timeline is effective for sequencing events. These organizers provide visual clarity, helping students focus on relationships between ideas. Incorporate First-Language Support: Encourage students to first label key ideas or terms in their home language before transitioning to the target language. This strategy reinforces comprehension and helps students draw on their existing linguistic knowledge. Collaborative Organizing: Have students work together to complete graphic organizers. This not only allows for peer support but also provides an opportunity for verbal interaction, further reinforcing language acquisition and content understanding. Use It as a Learning Tool, Not Just a Task: Encourage students to revisit and refine their graphic organizers as they learn more. This iterative process helps deepen their understanding and creates a visual record of their growing knowledge. Graphic organizers are an indispensable tool for making social studies content accessible, especially for multilingual learners who benefit from visual representations of complex ideas.

Empowering Multilingual Learners to Succeed in Social Studies Supporting multilingual learners in the social studies classroom requires intentional, research-based strategies that address both language development and content mastery.

By integrating multimodal learning, providing first-language support, offering targeted scaffolding, fostering peer interaction, and using graphic organizers, teachers can ensure that multilingual learners have the tools and resources they need to succeed.

With these strategies in place, students can engage with social studies in Spanish and other languages, building both their language and academic skills in tandem. Through thoughtful, strategic support, we can help multilingual learners thrive in the social studies classroom and beyond.

Before You Go … BLOG: Inquiry-Based Learning Is Essential to the Social Studies Classroom BLOG: Strategies for Differentiated Instruction in the Spanish Classroom UPCOMING WEBINAR: Using Authentic Resources to Build Communication and Culture

Do They Really Understand the Math: Marian Small on the Fresh Ideas for Teaching podcast

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