Pedagogy for the Mathematics Classroom 

Math classrooms today are filled with students with a diverse set of abilities, needs, preferences, and experiences. Teachers face the challenging task of providing instruction to this diverse group with limited time and resources, often resulting in some students being engaged more than others. With mathematics being a significant predictor of educational success and career growth it's important to take action so students are not left behind. MathTrack recognizes how daunting this task is to educators and recommends several strategies to help sustainably reach every student. 

• Adaptive curriculum can make it easier to assign unique tasks to each student. Using online curriculum also comes with the benefit of increasing the amount of data teachers can easily access, enabling them to respond quicker to student needs and make adjustments. IXL and Mathspace are both examples of adaptive mathematics curriculum. 
• Incorporating student choice is a great way to respond to student needs by allowing the student to advocate for themselves organically. When a teacher provides a controlled set of choices to students they can ensure students have access to quality instruction, while still allowing for students to have options. One way to do this is through the MathTrack Compass method.
• Low floor, high ceiling lessons make it possible to engage students in one activity that is both accessible to struggling students, and interesting for excelling students. Youcubed, which is supported by the Stanford Graduate school of Education, is a great place to find these kinds of activities.

Being prepared to teach with a differentiated set of definitions, visuals, and manipulatives is a key part Grasp the Meaning, the first component of the GROWTH framework

Students rely on their teacher to be productive in the classroom, but they cannot rely on an adult keeping them motivated forever. In adulthood they will be expected to manage their own time and responsibilities, tasks that are quite complicated in reality, and we don't learn these skills on our own. When we promote self-directed learning in the classroom we provide space for students to learn how to manage their own learning in a supportive environment, and there are ways to gradually release students to this type of responsibility in a way that is developmentally appropriate.

The BEAR worksheet is one example of a tool that MathTrack developed to guide students to work through independent learning. It provides a framework for helping students tackle math problems while also practicing the kinds of soft skills that drive autonomous learning. These skills include:

• Breaking down a problem into smaller components
• Visual communication
• Using a variety of different resources
• Self-reflection

When students are empowered to work independently and productively, teachers can concentrate on other priorities, resulting in a more efficient and harmonious classroom environment.

Growth mindset, a term coined by Carol Dweck, has become a powerful tool in education because of it's ability to positively impact student performance across many topics. At MathTrack we aim to help teachers manage productive classrooms, but these spaces can also be enjoyable. Through modeling, language, and classroom practices we can nurture students to become resilient and joyful learners, and growth mindset helps us achieve this.

• Modeling looks like teachers embodying growth mindset themselves, such as embracing their own mistakes in front of students.
• Language plays a crucial role in fostering a growth mindset. By emphasizing progress over accomplishment and consistently praising effort, we can aid students in developing a growth mindset.
• Classroom practices such as grading policies can nudge students to value their progress and pursue growth.  

Schools are uniquely complex and highly regulated spaces that involve a diverse range of individuals, resources and responsibilities. The kinds of challenges present in education require solutions that are appropriate to this level of complexity and this is where MathTrack applies the Cynefin framework. Frequent changes to school schedules, school-wide initiatives, and other distractions can be disruptive to the learning process, but they are also inevitable. It's important for teachers to have routines that are appropriate for an unpredictable complex environment, which means they must be adaptable and collaborative. 

The MathTrack 5-day sequence is an example of one such routine. It has predictable elements with built in flexibility that makes adjusting to new situations and challenges easier for the teacher. Incorporating regular Do Nows and Exit Tickets is an excellent method to maintain predictable student expectations, while allowing flexibility to adapt their use each day. Tools like SMART goals are also a way to individualize expectations in a consistent but flexible way.

Mathematics-for-teaching is a unique approach to mathematics that is significantly different from how we think about mathematics for general use in everyday life. The GROWTH framework was developed by MathTrack to train educators on the nuanced work of teaching mathematics and it has guided the development of the pedagogical techniques outlined above. You can read more about the GROWTH framework here, but here are some examples for how Mathtrack pedagogical techniques support the implementation of GROWTH.

• Collecting and growing our definitions of math concepts is a core practice of G, Grasp the Meaning. This supports the implementation of differentiated instruction and the Compass method where teachers provide multiple options for students to learn from.
• Preparing students to make mathematical connections is possible when we Reveal the Horizon of math concepts. Routines like Do Nows and Exit tickets make it possible to engage students around pre-requisite and future topics easily.
• Growth mindset can help students Observe the Implications of mathematics. When we open our minds to new ways of thinking, and disconnect our past mathematics performance from our ability to learn, we can help students realize the beauty of mathematics.
• Students are more motivated to be self-directed learners when they are truly engaged in the classroom. To really get students engaged we can utilize storytelling, which goes beyond just demonstrating how a math concept is used in the real world today. When we Weave Together Concepts we explore the historical context for a mathematics skill, which can help students see why it was developed in the first place.
• The techniques that will be most impactful in a classroom are going to depend on the needs of your students and the resources in your school. Teaching with Peers involves collaborating with other teachers and parents to learn from each other on how to best respond to student needs. We can also encourage this collaboration between students with peer to peer learning.
• To be a data-driven educator you need to Hear your Students. Practices that get student thinking out loud, or documenting their thoughts generates data for the teacher to respond to.