The status quo in Mississippi is not always pretty. We know that ours is a state where there are still deep economic and racial divisions; where predicted health and financial outcomes for children—particularly African-American children—are grim; and where it is particularly difficult for those born at the bottom of the economic ladder to make their way to the top.
In a world shaped by “big data” and technology and money, we seem to be moving further, rather than closer, to a solution to these concerns. While we as teachers can be lifelong allies to our students, for better or worse it will fall to the students to find a way to transform the world.
Making that transformation will require our students to be mathematical thinkers. They’ll need to cut through the noise of data and statistics to find the truth beneath. They’ll need to find and explain logical solutions to deep problems, and push back against solutions that rest on faulty logic. They’ll need to model their world with numbers and symbols so that they can find ways to fix it.
As such, it’s essential that our students:
|Display mathematical fluency:||Possess mathematical agency:|
This year, the biggest gift we can give to our students is the gift of mathematical thinking. As a result of our teaching, our students must:
- Tackle unfamiliar problems with comfort and expertise, analyzing what mathematical concepts apply to a given problem and explaining (verbally or in writing) their solution strategy and why it makes sense.
- Own their learning, taking responsibility for the majority of the thinking and talking during class time.
While it is a year of transition, and our students are under pressure to perform on soon-to-be-out-of-date state tests while still being prepared for the new PARCC assessments, these outcomes will mean our students can perform on whatever tests are put in front of them. As such, we expect to see measurable gains in student performance including:
- Significantly improved performance on major benchmarkable multiple-choice assessments, including the SATP, MCT2, and ACT.
- 40% gap closure on state assessments
- 3 points of growth on the ACT
- 80% mastery of content on regionally created assessments when other metrics are not available
- Mastery of Common Core-aligned performance tasks
- Average score of 3.0, using our regional rubric.
For too long, math classrooms have not been places that pursue these kinds of outcomes for students. Instead, most classrooms approach math as simply a set of skills—or sometimes just a set of steps—that will allow students to jump through hoops and pass tests.
The arrival of Common Core may change this. The PARCC assessments that our students will take next year will demand that students operate with the kind of fluency and agency that will prepare them as leaders. Unfortunately, there has been little guidance from schools about how we as teachers should approach these tests.
Given this, we must act as the vanguard of math teachers in Mississippi. We must find (and share) methods that prepare our students for these rigorous assessments—and develop our students as the thinkers and leaders they need to be.
Doing so will require much of us, including:
- A commitment to teaching as leadership, wherein we think about what our students need not just for the test in our year, but what they will need in five years, ten years, or even fifteen years—and how we as teachers can provide those things now.
- A deep love of math as a subject area, and commitment to the fact that teaching math, as it is defined above, is the greatest gift we can give our students. (See below for the key beliefs and core components of teaching math.)
- A deep love of our students and communities, and the creation of sustainable, meaningful relationships therein.
- A willingness to be adaptive leaders, who will experiment and innovate and find ways to learn from both success and failure.
- Collaboration with one another, and with other math teachers around the world, in an “open source” or “gift economy” system in which share and build off one another’s work.
Core Components of Math Instruction
- Learning builds on what students know
- Students actively make connections between new content and their existing knowledge, concrete applications, and/or other mathematical topics as appropriate.
- Incorporate real and meaningful discourse
- Students construct and communicate viable arguments and critique the reasoning of others in ways that demonstrate precision and reasoning. They also reflect on their work and their learning process, pose questions, and initiate mathematical discussion orally and in writing.
- Support for all learners with grade-level content.
- Students identify where and how they need help and are eager to advocate for the support they need, which may include additional practice or relearning prerequisite concepts. Teachers provide accommodations and modifications while ensuring ALL students are ultimately “on the hook” for ALL content.
- Increase mathematical agency.
- Students own their learning, demonstrating confidence and pride in their work. They believe success in math is worth the effort because they are fascinated by how relatively simple mathematical concepts can lead to fundamental understandings of how our world works, and they recognize that math opens many pathways to opportunity. Thus, they’re willing to take risks and persevere through obstacles.
- Allow flexible engagement with problems.
- Students investigate complex and interesting questions, identifying patterns, structures, and repetition. As problem-finders and problem-solvers, they develop and test hypotheses for approaching given and self-generated questions. In doing so, they make their thinking explicit, communicate their understanding, reflect on processes and results, reason abstractly and quantitatively, and use math to model common applications.
Key beliefs of math teachers:
- Students learn through exploration, challenge, and dialogue.
- Real learning happens when we think deeply. That kind of deep thought is encouraged through communication and exploration.
- My students can think logically, and are able to solve problems if they are set up clearly and concretely.
- All students are sense-makers. They may not know the prescribed ways of solving a problem, but they all have ways of thinking mathematically.
- Math is based on concrete principles made abstract.
- Math uses symbols and logic to describe relationships. Even the number “2” is an abstract thing—but we can make it concrete by thinking about 2 apples, 2 houses, 2 people, etc.
- Math is a body of knowledge, not a checklist of skills.
- Deeply understanding math requires being able to see the connections between various ideas, and move back and forth between representations. When we reduce math to just a list of different kinds of problems students should be able to complete, we’re taking away their chance to make connections.
- Math is beautiful, useful, and exciting.
- We don’t just teach this because it’s a class, and there are tests align to it. The process of abstracting the world allows us to make fascinating, even beautiful, conclusions about the world.