September 7th, the first day of school. Students clutter the hallways with fresh books, markers, clothes, and (happy or otherwise), fresh faces. Teachers prepare to greet a brand new class- excited by the prospect of change and eager learning. But how much do we really know about these students as learners? About how they have developed? Do we know that Johnny never fully trusted the ten frame? Or how Shelia counts 147 pieces of candy one-by one? Or how Ezra got lost around the purpose of the distributive property?
Besides a diagnostic exam, a note from parents, a student reflection, or (if lucky) some feedback from past teachers, we know very little about where each of these students is on the landscape of learning mathematics. And that is dangerous.
It is not about blaming the teachers students had previously; “I can’t believe they never taught you multiplication”, and it’s not about pawning unprepared learners off onto the teachers after us. It is about moving each student forward, and, in order to do that, it is imperative that we have a strong understanding of where he or she is going.
To develop this understanding, we need to be more collaborative. As teachers, it is common to plan on our own, often at home or during our lunch break. If we are fortunate, we work with colleagues that are willing to share ideas and work together. However, working collaboratively within our own school is not enough. The work that we do to truly understand the development of mathematics in students must involve teachers and learners from kindergarten to twelfth grade.
The CCSS show a progression of content. Often, the extensions of a 6th grade problem are the expectation of a 7th grade problem. Many teachers have a solid understanding of the content in the grade below them and the grade above them, but that is not helpful if a student is functioning three years below grade level. We cannot expect that all students develop at the same pace, and yet we are surprised when a student struggles in a way for which we haven’t planned. In order to help these students, we need to sit with teachers of all grade levels and explore the development and progression of mathematical ideas. If it isn’t possible to meet and explore with teachers of other levels, work with other teachers to explore different levels of content. Use the standards to initiate discussion and look for connections. Use websites (like Matific) to explore the different problems and games students are using in different grades. It is essential that we, as teachers, become familiar with the learning path of our students.
Elizabeth Masalsky is a 6th, 7th, and 8th grade mathematics teacher at Battery Park City School in Manhattan. She has a post-baccalaureate in mathematics from Brandeis University and her master’s in secondary math education from Bard College. Elizabeth is a Math for America Master Teacher and continues her professional development through workshops with Math for America, Metamorphosis and Math in the City.