Developing and Enhancing Mathematical Thinking for PreK–5 Learners

December 15, 2025

Three students standing in front of a poster titled “Measurement Thinking Poster.” The poster includes sections on measurement concepts and strategies, with colorful graphics. The setting includes a classroom with a recycling bin and a door.

Developing and Enhancing Mathematical Thinking for PreK–5 Learners Math Through Discovery: A Constructivist Pathway for PreK–5 Classrooms

Vermont State University’s Education Department recently hosted an inspiring event highlighting the culmination of a semester-long project, in which our students designed instructional posters that integrate the essential components of high-quality mathematics teaching for early childhood and elementary learners.

A colorful educational poster titled “Thinking Algebraically! Grades 1–2–3” by Adrienne, Maya, & Emerson. The poster includes sections such as Non-Negotiable Standards, History Snapshot, Triple-E Mini Model, Key Milestones in Early Algebraic Thinking, Mini Lesson, Big Idea, Problem Solving Corner, Quick Rubric, Exit Ticket, and Manipulatives. Graphics include books, lightbulbs, and playful icons.
A classroom setting with multiple students gathered around tables and standing near walls. The room has bookshelves, posters, and a door with educational materials displayed. A bright orange plush animal is on one of the tables next to laptops and water bottles. The environment appears collaborative and informal.
An educational poster titled “Integrating Algebraic Thinking Into 2nd Through 3rd Grade” by Ms. Tallmadge & Ms. Lee. The poster features sections such as Math History Snapshot, Problem Solving Corner, Standards Alignment, Big Ideas, Manipulatives, Exit Ticket, Assessment, Teacher Moves and Look-Fors, and Vocabulary. It includes colorful icons like a brain, math symbols, and cubes, with strategies for teaching algebraic concepts.
Two students standing in front of a bulletin board displaying a poster titled “Integrating Algebraic Thinking Into 2nd Through 3rd Grade.” The poster includes math history, problem-solving strategies, and standards alignment.
Three students standing near a wall-mounted poster titled “Thinking Algebraically!”. The poster contains sections on standards, history, and problem-solving strategies. The students appear to be engaged in discussion about the content.
Two students standing in front of a wall-mounted poster titled “Geometry.” The poster features colorful shapes and diagrams explaining geometric concepts. One student is holding a piece of paper.
Three students standing in front of a poster titled “Measurement Thinking Poster.” The poster includes sections on measurement concepts and strategies, with colorful graphics. The setting includes a classroom with a recycling bin and a door.
A colorful educational poster titled “Integrating Counting & Cardinality: PreK – Kindergarten – First Grade” by Ev and Morgan. The poster includes sections labeled History, Non-Negotiable Standard, Mini Activity, Math Pedagogy, Exit Ticket, Technology, Conclusion, and References. Visual elements include illustrations of fruits, a camera icon, and playful graphics. The content emphasizes counting strategies, CCSSM alignment, and developmentally appropriate practices.
A classroom scene where students are seated at tables while two individuals present posters on the wall. The posters include colorful educational content related to mathematics. A bright orange plush animal is visible on a table, along with notebooks and drinks.
A group photo of students standing and kneeling in two rows inside a classroom. Behind them, educational posters are displayed on the wall, including one labeled “Geometry.” The setting includes a door and bulletin board.

Key elements featured in the posters include:

  • Mathematical History: Stories and figures that shaped early mathematical thought
  • CCSSM Alignment: PreK–5 content and practice standards
  • Problem Solving and Reasoning: Rich tasks that strengthen conceptual understanding
  • Mathematical Thinking Models: Structure, pattern, representation, and inquiry
  • Developmentally Appropriate Practice
  • Creativity and Storytelling: Visuals designed for PreK–5 classrooms

Our pre-service educators have worked hard to blend mathematics, pedagogy, and child-centered design. Their posters illustrate meaningful ways to help young children think mathematically, not simply compute, and to support early numeracy development through engaging, research-based instructional choices.