A sense of belonging supports psychological safety and increases students’ engagement, participation, and persistence.
Make the first introduction to establish accessibility and invite student connection.
Introduce yourself and key course features in your syllabus and online course materials. This example and additional ideas are shared in the UDL Syllabus.
Use “Getting to Know You” surveys to connect students’ experiences to course content.
Use surveys and other strategies for getting to know your students.
Review your pre-course survey with guidance for effective surveys.
Connecting content to students’ prior knowledge and values increase relevance, engagement, persistence, and transfer of disciplinary concepts.
A math teacher professor shares Innovative ways of teaching math help students better understand. Find one new strategy to try that will engage students and their interests.
Investigate and choose one of these Five ways to motivate students to learn math effectively
Meaningful choices increase autonomy, reduce barriers, and support motivation and engagement.
Students' varied backgrounds and experiences with math can be supported by flexible: lesson formats, assessments
Joy and curiosity in mathematics support positive engagement, persistence, and conceptual understanding.
Cultivate joy through curiosity-driven Questioning and Problem solving. This module provides samples to reflect on.
Inquiry-focused prompts encourage investigation and justification, supporting deeper sense-making.
Problem strings (Wieman et al., 2021) are sequences of related problems that gradually build conceptual understanding by guiding students to notice patterns, relationships, and underlying structures. This approach encourages reasoning over rote procedures and helps students make connections across problems. Examples include algebra sequences (Harris, 2017), precalculus sets, and “Open Middle” problems in algebra, statistics, probability, and calculus.
Thin slicing (Liljedahl, 2020) involves giving students a small, carefully chosen portion of a problem or example that reveals the essential mathematical structure. This scaffold focuses on key concepts while minimizing cognitive overload, fostering sense-making, exploration, and multiple solution strategies. Crowd-sourced curricular task spreadsheets provide rich collections of tasks designed for problem strings and thin slicing in diverse contexts.
Harris, P. W. (2017). Advanced Algebra Problem Strings. Kendall Hunt.
Liljedahl, P. (2020). Building Thinking Classrooms in Mathematics: 14 Teaching Practices for Enhancing Learning, Grades K-12. Corwin.
Wieman, R., Freedman, L., Albright, P., Nolen, D., & Onda, J. (2021). From notes to strings. Mathematics Teacher: Learning and Teaching PK-12, 114(12): 956–963. https://doi.org/10.5951/MTLT.2020.0331