Very nicely said Karen. Unfortunately, I think perhaps high stakes testing has a part in the decisions made by well intentioned educators to superficially "cover" a list of math topics like probability at each grade level. I've worked in districts where kindergartners and first graders are doing the same problems that are appearing on the fourth grade test, only with smaller numbers. We do have to be careful to choose appropriate experiences and to focus on the math that makes the most sense for children at different ages.
I think the modular format of Investigations allows teachers to develop a pacing schedule of core units that meet their particular standards. Some times units from one grade are moved to another grade. I've worked with groups that have chosen to move at least one Investigation from the probability unit Beyond Never and Always from 5th grade to 4th grade because their district, state standards and assessments expect students in 4th grade to have these experiences. Another fifth grade group decided to start the year with Seeing Solids and Silhouettes (from 4th grade) because they believed it coordinated with experiences they had in their science curriculum and also prepared the students for the writing portion of their state test (that happens to be in 5th grade in this particular state).
ONGOING PRACTICE It is impossible to have a core unit for every content area every year. Teacher can however provide ongoing practice of ideas like probability through daily routines / ten minute math experiences and homework. There are opportunities within core units where we can discuss other math topics -- like probability. There are also times in other curriculum area where students can apply some of what they've learned in mathematics. We need to find ways to assure students that continue to apply and practice mathematical ideas, even if it's not a core experience for that particular school year.
The bottom line is we have to look at the needs of the students at hand first (regardless of state standards and testing pressures), then we can make intelligent choices about core units (experiences) that expose students to in-depth mathematical learning. It's imperative for teachers and administrators to have cross grade level discussions to decide core mathematical ideas and the choose core units of study and ongoing practice experiences at each grade level. Adjustments will be made over the years.
