ABSTRACT
Teachers’ knowledge of learning progressions is important in their understanding of the articulation of essential core concepts and processes in each domain within and across grade levels so that their students develop a deeper, broader, and more sophisticated understanding of the “big ideas” of mathematics. The other progression dealing with measurement data, which focuses on students’ development of different types of graphs and line plots to represent specific units of measurement, leads to the students’ understanding of statistical variability, chance processes and probability models, correlations, and an expanded array of functions at the middle and high school levels. Cross-grade-level clusters of standards provide greater clarity for incorporating more depth and complexity in problems and in ways of compacting the standards for gifted and advanced students. Afterschool or summer programs provide students with opportunities to work in an authentic context, such as in a laboratory, on a team with other researchers, and/or with mathematicians at the university level.
