Academic support to help students use numbers flexibly and efficiently, and to find joy and comfort in math.

I believe that a strong foundation of elementary and middle school math is important for life. I also know that when students don't feel confident in that math foundation, it can quickly lead to rigid thoughts like, "I'm bad at math." While my job is to teach math concepts, equally important to me is to help students see that when they put in the effort, they will make progress, and that like everything else, much can be gained from having an open mind and growth mindset.

My goal is to help students learn to use numbers flexibly and efficiently. To that aim, I teach and review strategies for understanding how numbers work with no time stress and no rote memorization.

How we work together

Models, strategy, and visualization

I primarily use models, strategy, and visualization for understanding the concepts I teach, from learning to add whole numbers “up” to Algebra. We use models to see how the numbers come together and break apart, creating a deep understanding and flexibility with the way numbers work. Those of us who were born in the 1970s or 1980s were taught standard algorithms, which focus more on memorizing routines ( like “carry the 1”) than on understanding how the numbers work together. Educational research in teaching mathematics has shown that learning concepts through modeling, strategies, and visualization is more effective for math literacy. These methods allow students to understand and put context to what they are doing and why the answer makes sense. As students practice with and understand how the numbers work together, we move from physical models and diagrams to conceptual thinking, keeping efficiency, accuracy, and flexibility in thinking at the forefront.

Concepts and Progressions

The typical system of education is difficult, particularly in how concepts are linked to standards and grade levels. While I understand why and how schools use state standards and specific curriculum, during one-on-one work it’s much easier to work with concepts as a progression of ideas with students. In this way we stay with certain concepts with students until they are efficient and flexible and can take that understanding to the next idea. For example:

A student who comes to me sharing that they “don’t get fractions,” in 5th or 6th grade either hasn’t been taught how to use models to add, subtract, multiply, or divide fractions or (more often) needs more strategies and practice for being efficient with multiplying and dividing whole numbers. Likely their class had to “move on” before the student was ready. My work with this student would be to go back to a concept that is a building block for fraction work and practice there before diving into fraction models. Another benefit of working this way is the student sees and feels what they know and gains confidence.

High Leverage Concepts

While I take my lead from students’ interest, there are “high leverage concepts” that are both necessary for life and a foundation for what comes next in school. These are the concepts I focus on because they build upon each other, unlike others (like learning to tell time) which can be learned without much previous knowledge. In my work with students we focus on concepts such as:

Multiplying and dividing numbers within 100, then 1000,
adding, subtracting, multiplying, and dividing fractions, and equivalent decimals and percentages,
using fractions and ratios to solve word problems (for example, scaling a baking recipe),
solving equations with variables, and
understanding linear relationships.