Three learning trajectories and their connections show how to promote vertical coherence in PK–12 mathematics education.
Jere Confrey, Meetal Shah, and Alan Maloney
Matt B. Roscoe
Symmetric dot patterns are a particularly powerful object for investigation, providing opportunities for foundational learning across PK–5. We found that second-grade students naturally used repeated addends to count symmetric dot patterns created using the new software TileFarm.
Sarah B. Bush, Karen S. Karp, Jennifer Nadler, and Katie Gibbons
By examining ratios in paintings and using a free educational app, students can size up artists' use of proportional reasoning in their creations.
A cartoon exploring a problem about order of operations is coupled with a full-page activity sheet.
Kami M. Dupree
Abandon mnemonics and make stronger connections between the operations and properties of arithmetic.
Samuel Otten and Andrew Otten
Students make strategic choices–and justify them–to solve a system of two linear equations.
Nicole Panorkou and Alan P. Maloney
Develop fifth-grade students' early expression of pattern relationships through instructional tasks.
Use popular culture to draw students' attention to mathematical topics.
Core content provides opportunities to focus on the structure of mathematical theory, proof, and anticipation of subsequent topics.
Sonalee Bhattacharyya, Nama Namakshi, Christina Zunker, Hiroko K. Warshauer, and Max Warshauer
This activity engages students in problem solving while exploring key concepts of number theory, such as divisibility and divisibility tests, place value, fractions, and scale factors.