“Independence and a mental curiosity…powerfully fostered from the very beginning.”

“Nor is there the least fear that your child will become dependent upon the rods. The very opposite is the case, for they enable him to gain independence and a mental curiosity that are the marks of the truly mathematical mind—and this is powerfully fostered from the very beginning.”

—Caleb Gattegno in Now Johnny Can Do Arithmetic: A Handbook on the Use of Colored Rods

“Some students construct ideas quite well with little guidance…other students need more direct guidance.”

“To genuinely understand mathematical ideas, students must construct these ideas for themselves as they intentionally try to make sense of situations; their success in constructing the meaning of new mathematical ideas is determined by their preexisting knowledge and types of reasoning and by their commitment to making personal sense of those ideas….Some students construct ideas quite well with little guidance other than well-chosen sequences of problems; other students need more direct guidance, sometimes in the form of explicit description.”

— Michael Battista in Reasoning and Sense Making in the Mathematics Classroom