Vertical Math Teams in your School
We’ve often created opportunities for math teachers to converse with grade alike partners, but to facilitate setting curricular priorities and supporting strong math achievement in our schools, we need math teachers to have conversations with the entire math team, up and down the grades, in order to get a sense of the flow of outcomes up through the years. In truth, this team already exists, and we are all players, whether we’ve recognized it or not.
Understanding where an outcome is going, or what future learning depends on its mastery, helps teachers prioritize topics and also to make those connections to past and future learning. Those connections to math concepts already taught or coming in the future are pivotal to advancing a strong mathematics program. Similarly, when introducing a new topic, it is extremely beneficial for a teacher to understand where the students are in that progression of understanding, what vocabulary and skill has been taught to date, what models have been used, and what to expect of the level of understanding of students.
We know that mathematical understanding is logical and sequential; ideas are built on concepts that are already learned. We know that the development math understanding is fluid and connected as a student studies math from K-12. But do our students know it? Or do they feel that each grade is new learning and discreet content? Sometimes we have to help them remember the connection.
Middle years and elementary teachers can help us understand how math concepts develop. How are these understandings built? High School teachers can explain the secondary goal of the strand. What will students ultimately need to be able to do with this skill/concept?
The centre of this conversation is not teachers but curriculum. What are students learning and when? What are the gaps in curriculum and how can we address them? What does it look like at each grade level? How do I support my colleagues that teach the grades before me and the grades above? Recognize that each grade has its own challenges, children are at different stages developmentally, and our system imposes artificial “grade level” expectations on what is simply a continuum of learning and development that evolves differently for every child.
“By promoting communication among educators about curriculum [outcomes] and instructional strategies, Vertical Teams foster the development of an educational community committed to improving student performance. This community then creates a continuum of learning among classes and across grade levels, and also reduces the redundancy and reteaching of content across grade levels and courses. This process can enable teachers to encourage students to apply previously gained skills and knowledge to new and more challenging material. Increased coordination can also help counselors, administrators, teachers, and students to develop a clearer vision of how the curriculum unfolds, enhancing their ability to understand its objectives.”
-The College Board, (2006). New York
Vertical teams of teachers look through the continuum of learning of math outcomes and decide what the non-negotiable learnings are. What are the things I need the teacher of the grade prior to really drive home to students? What are the promises I make to the next teacher? Does this mean we don’t teach all outcomes? Well, it might mean we don’t teach them all with the same depth (this is where UbD planning comes in). We will identify those concepts that are essential to our program and work collectively toward proficiency there.
What vocabulary have they been using? Symbols? What models have they seen? What connections have been made for students? How can I strengthen them?What level of proficiency is expected? What does practice look like at earlier grades? Future grades? To what do I go back when students aren’t getting the high school portion of this concept? How did curriculum at other grades introduce this topic? How can I best reach learners that don’t think like I do? What prior models can I draw on? what worked for this student last year? What does the next teacher really need my students to be able to do?
Having a clear understanding of who is teaching what, and when, in terms of agreed upon core curriculum areas, also helps keep the responsibility for learning where it belongs, with the learner! We will know what students have been taught, and that missing skills are because of their difficulties or choices, and not (as students sometimes like to suggest!) that they weren’t taught the concept.
We know there is no more time for regular meetings! But a couple collaborative opportunities to start, and some ongoing understanding and practices (maybe a common area to post things) will make a huge difference to our learners.
- Take a Big Picture view of curriculum
- Focus on student understanding across curriculum
- Focus on assessment
- Focus on difficult concepts to teach or to learn
- Reveal and deal with student misconceptions
- Enhance vocabulary coordination across curriculum
- Enhance notation consistency