Mathematics
Developmentally sequenced math instruction from a preschooler's first number sense to AP Calculus, built to prevent the gaps that make algebra hard later.
How you'll see progress
Parents receive a written summary after every session; I make both qualitative observations and track measurable assessment data. Students old enough to make sense of their own data see it too. Reviewing your own progress builds the metacognitive and self-reflection habits that executive function depends on.
Learning progressions
Math is relentlessly cumulative. Gaps from years past don't stay in that grade; they continue showing up in advanced topics. Students above grade 3 take a diagnostic assessment to pinpoint existing learning gaps. My instruction is preventative by design: we build foundational skills early enough to prevent gaps from forming, before a later course can expose them. Every plan also includes spiral review, so students revisit earlier topics at a progressively deeper level.
I also introduce Number Talks: short routines where a student solves a math problem in multiple different ways and compares them. That builds procedural fluency and strategic competence at the same time, while reinforcing conceptual knowledge and adaptive reasoning. Working one-on-one, a student produces as many approaches as they can, and I supply the ones they didn't arrive at, so the comparison still happens. Read more about the five strands of mathematical proficiency below.
Why Algebra 1 is the pivot point
About half of students start Algebra 1 already knowing only a third of the concepts and skills the course requires; they rarely reach grade-level performance afterward.
of eighth graders were enrolled in Algebra 1 or above in 2024, and most of those were already the highest-performing students.
This is why I build algebraic foundations years before a student reaches Algebra 1.
Preschool-Grade 3: Learning Trajectories
Instruction follows the Learning Trajectories established by Drs. Sarama and Clements, which map the natural developmental progressions of mathematical reasoning and pair them with activities that help children reach the next skill in the sequence.
How that works
- Number sense: Recognizing how many objects are there without counting one by one, comparing quantities, and knowing where a number sits relative to others.
- Concrete-representational-abstract: Each student learns a concept with physical objects first, then with drawings and diagrams, then with written symbols. I make connections between the three explicit so a child doesn't need to infer.
Grades 4-8: Building Algebraic Foundations Early
I begin building algebraic foundations years in advance through targeted pathways, with extensive focus on fractions and proportional reasoning, the primary reason students struggle in algebra.
Why fractions
Fractions seemingly break the rules children spent three years learning. With whole numbers, a bigger number is a bigger amount and multiplying makes things larger. This isn't true with fractions, so a student who uses the same whole-number logic gets a reasonable-looking wrong answer and doesn't see the problem.
This matters well beyond fourth grade, because a fraction is also a division, a ratio, and a point on a number line, and understanding this is essential to algebra. Proportional reasoning, which is scaling a quantity up or down and knowing what stays fixed, is a similar idea, and it turns up in slope, in rates, and in most of chemistry and physics.
High School: Closing Gaps, Building Proficiency
Because so many high school and college students still struggle with algebra, I continue to address the missing key predecessor skills outlined by TNTP's Unlocking Algebra to accelerate conceptual understanding. This same foundation extends to the math section of other aptitude and entrance exams (including trade and apprenticeship exams) through problem-solving strategy.
Course-level support
I support the core math sequence and advanced courses. Advanced coursework depends on strategic competence and adaptive reasoning: working out what an unfamiliar problem is actually asking, choosing an approach, and being able to justify why it holds. Those are two of the five strands described below.
For AP and IB courses, I teach the content, not the exam. I don't offer dedicated test-taking strategies for AP or IB assessments; what I do is make sure a student fully understands the material those exams cover.
Course names vary by district
Washington districts don't all use the same name for the same math. What one district calls Integrated Math 2 covers much of what another splits between Geometry and Algebra 2. If your student's course title isn't listed here, ask me first; the underlying content usually correlates with something I already teach.
Core sequence
- Algebra 1
- Geometry
- Algebra 2
- Pre-Calculus
- AP Calculus AB/BC
- AP Statistics
- IB Mathematics: Analysis and Approaches
- IB Mathematics: Applications and Interpretation
Washington course names also covered
- Modern Algebra 2
- Integrated Math 1 / 2 / 3
- Modeling Our World with Mathematics (MOWWM)
- Quantitative Reasoning
The five interconnected strands of math proficiency
Students who struggle in math are usually competent in one strand, but don't have enough exposure to others. These strands are intertwined, so improving one strand will strengthen all the others. Select a strand to read more.
This work looks much the same at every grade level: taking a word problem apart to find what it is actually asking, recognizing which type of problem it is, choosing an efficient method, and managing timing pressure through emotion regulation, which is executive function work as much as it is math. Memorized tricks have a shelf life: a rule that works on one problem type doesn't apply to a different one, and a student who only has the memorized rule doesn't know why.
Knowing why a procedure works. A student with conceptual understanding can explain what dividing by a fraction actually does, connect a graph to its equation, and recognize when an answer is unreasonable.
Carrying out algorithms accurately, efficiently, and flexibly. Fluency frees up working memory: a student who isn't spending effort on arithmetic has attention left for the actual problem. For the same reason, I teach students to write out every step, an executive function externalization strategy applied directly to the math. This way, there are less numbers and steps to forget, and when something does go wrong, students can locate the exact step where they made a mistake.
Formulating and solving problems that don't come pre-labeled. This is the strand word problems actually test: using vocabulary to identify which procedures to apply and how to do this while maximizing efficiency.
Thinking logically about relationships, justifying an answer, and explaining a line of reasoning. It's the difference between getting a result and being able to defend it.
Seeing math as sensible, useful, and worth the effort — and seeing yourself as someone capable of doing it. This is the strand most damaged by years of struggle, and the one that makes the other four possible.
Ready to talk about your student's math goals?
Book a free consultation and we'll figure out where to start.