The way Frogger hops around, kind of reminds me of this picture:
This is one of Cathy Fosnot’s math trajectory diagrams. The general premise is that the bottom concepts on the trajectory (e.g., one-to-one tagging, counting, subitizing, magnitude, etc.) are the building blocks of addition and subtraction. In a Frogger-like fashion, learners can jump from concept to concept in an upward direction. If a teacher can identify where a student is on the trajectory, then s/he can craft appropriate baby-steps for student learning.
A lot of the work we do in our board is grounded in three Ministry of Education documents:
All three advocate for teachers to use learning goals and success criteria in teaching. They’re backed by huge bodies of research that say if you want students to learn, then they need to have clear goals for their learning and a series of steps to get them to those goals.
Learning trajectories seem to fit naturally into the work that we’re doing in Ontario. They are research-informed baby-steps. They are thought-out paths towards learning goals. They are maps that help learners navigate the busy streets and murky waters of the Ontario Math Curriculum.