Start with a real question
A document, dataset, mechanism, or surprising result gives the maths a job. Students should know what they are trying to find out before anyone hands them a procedure.
Teaching at Primoris Academy
Use the maths. Make the call. Explain yourself.
I teach mathematics, financial literacy, and data science to students in grades 5 through 12. A right answer gets us through the door. Then I want to hear why it fits, what it assumes, and what would make the student change their mind.
At Primoris Academy , placement follows readiness rather than birthday. That leaves room to move quickly, pause, or circle back without turning pace into a ranking.
Teaching philosophy
See it first. Name it when the name helps.
I bring in the notation when it starts to earn its keep: first notice the pattern, then give it a name we can use. Precision matters, but it lands better after a student has something real to be precise about.
Show the working so we can poke at it
A sketch, table, graph, equation, spreadsheet, or bit of code makes the thinking visible. Then we can ask what works, what changed, and where it might break.
Try to break it, then use it again
Change a condition, find a counterexample, or take the method somewhere unfamiliar. That is when a remembered procedure starts becoming an understood idea.
What this looks like in class
A car offer beats a lonely page of loan formulas.
Suppose two fictional dealers advertise the same car. One offers a cash rebate and a higher interest rate; the other offers no rebate and cheaper financing. Students first read the terms and decide what information is missing. Then they build a spreadsheet that separates purchase price, principal, monthly payment, and total cost.
The answer is not “Dealer A” or “Dealer B.” Students vary the down payment, loan length, and outside interest rate until they can state the conditions under which each offer is better. The formula matters because it lets them make a defensible decision and revise it.
Read the offers→Build the model→Change an assumption→Defend the decision
Two influences
What I carry from studying in France and teaching in America.
Neither country has one teaching style. These are simply the habits I encountered and now try to combine.
From my French education
Build the architecture of the subject.
- Definitions and notation should be exact enough to support later ideas.
- A problem belongs to a larger mathematical structure, not a bag of tricks.
- Proof and counterexample are tools for finding the boundary of a claim.
From teaching in America
Let students investigate and make.
- Begin with a question students can understand and evidence they can handle.
- Invite discussion, conjecture, and more than one representation.
- Use experiments, projects, data, spreadsheets, and code when they make an idea testable.
The combination I want: students encounter an idea, make a conjecture, formalize it, try to break it, and then use it independently.
Current courses
What I teach now. What I am building next.
These courses use 45-minute, problem-first classes and generally have no homework. The outlines change as students show me which explanations click, which problems start a good argument, and which carefully prepared lesson needs to go back to the garage.
01
Readiness-based placement
Core Mathematics
Pre-Algebra · Algebra I · Geometry · Algebra II/Trigonometry · Precalculus · Calculus
No mathematical conveyor belt.
What students study
Alongside the labs, I'll teach the familiar maths sequence from Pre-Algebra through Calculus. The topics are common; the route through them is personal. Placement follows what a student is ready to understand, not the age printed on a class list.
How the pace works
Some eight-year-olds may be ready to begin Algebra. Another student may need more time to make fractions, negative numbers, or proportional reasoning truly solid. Neither student is winning or failing a race. Each needs a next step that is challenging enough to matter and supported enough to attempt.
Find the starting point→Teach and practise→Check, revisit, or move on
Adaptive does not mean alone. I still teach, ask questions, choose problems, and give feedback. Students are free to advance at their own pace, with support and permission to slow down when an idea needs another pass.
02
Typical audience: middle and high school
Financial Decision Lab
Personal finance · consumer mathematics · decision modeling
Read the terms. Build the model. Decide what would change your mind.
What students actually do
Students inspect fictional pay statements, credit offers, insurance policies, loan terms, and investment claims. They build transparent spreadsheet models, compare choices on the same basis, change assumptions, and write a conditional recommendation.
Nine-unit progression
- Money, Decisions, and the EconomyScarcity, trade-offs, incentives, and opportunity cost
- Work, Pay, and Financial ClaimsPay statements, taxes, benefits, and evidence
- Banking, Budgets, and ResilienceCash flow, bank accounts, fees, and emergency funds
- Credit Cards and Consumer CreditAPR, minimum payments, fees, and credit reports
- Loans, Transportation, and HousingAmortization, total cost, financing, and rent-versus-buy models
- Insurance, Risk, and Consumer ProtectionProbability, premiums, deductibles, and coverage
- Financial Markets and InvestingRisk, return, diversification, and compound growth
- Retirement and Long-Term PlanningTime value of money, inflation, and withdrawal assumptions
- Behavior, Evidence, and an Integrated PlanBias, sensitivity testing, and conditional recommendations
Representative problem: Compare a cash rebate with discounted financing, then identify the purchase price, down payment, and interest-rate combinations that reverse the decision. All cases are fictional; students never disclose family finances or receive individualized financial advice.
03
Typical starting audience: grades 7–8
Data Science Lab
Data literacy · statistics · visualization · introductory machine learning
Turn a table of records into a claim someone else can inspect.
What students actually do
Students ask what one row represents, repair inconsistent records, compare charts, calculate rates and conditional proportions, and test small classifiers and clustering rules. Code appears when the dataset or repetition becomes too large to inspect comfortably by hand.
Nine-unit progression
- A Picture Can Change a DecisionData visualization, scale, area, and misleading charts
- Data Has to Mean the Same ThingData cleaning, types, units, missing values, and consistent categories
- Same Numbers, Different WorldsDistributions, averages, sampling, and context
- Can a Flower Teach a Computer?Features, classification, and training and test data
- Patterns on a MapClustering, distance, and coordinate geometry
- When a Pattern ReversesConditional proportions and Simpson's paradox
- From Boundaries to Language ModelsDecision boundaries, vectors, and prediction
- Conversational Systems, Retrieval, and AgentsLanguage models, retrieval, tool use, and evidence paths
- Find the Signal: A Reproducible CapstoneQuestion design, analysis, validation, and communication
Representative problem: Two charts contain the same values but use different scales and areas. Students determine why they lead readers toward different conclusions, then redesign the display and state what the data still cannot prove.
04
For students ready to model with Python
Data Science with Python
Python · applied statistics · optimization · machine learning
Rebuild small versions of systems students normally see as black boxes.
What students actually do
Students work in Google Colab to simulate motion, estimate uncertain quantities, fit models, optimize functions, and validate predictions. Later units reconstruct recommendation systems, neural networks, and language systems from simpler mathematical parts.
Course progression
- Python Foundations in Google ColabVariables, functions, arrays, tables, and plotsoptional bridge
- Data, Models, and MotionSimulation, graphs, rates of change, and model assumptions
- Finding CeresNumerical search, measurement error, and orbital modeling
- Chance, Randomization, and EvidenceProbability, simulation, sampling, and hypothesis tests
- Modeling Change from Noisy DataRegression, residuals, uncertainty, and validation
- Optimization: How Models LearnLoss functions, gradients, and parameter fitting
- Decisions Under UncertaintyExpected value, Monte Carlo simulation, and risk
- Taste as GeometryVectors, similarity, and recommendation systems
- Hidden Axes in DataPrincipal components and dimensionality reduction
- Neural Networks as Composed FunctionsLayers, activations, gradients, and backpropagation
- Language SystemsTokens, embeddings, attention, and generation
- Capstone: Predicting Bike DemandData cleaning, feature engineering, prediction, and model evaluation
Representative problem: Build a simple recommendation system by representing preferences as coordinates, then test where “nearby taste” works, where it fails, and how a popularity-heavy dataset changes the result.
New Jersey standards
Standards set requirements. A course still needs a reason to exist.
The courses draw on New Jersey's mathematical practices and financial-literacy expectations, but they organize standards around longer investigations rather than presenting them as isolated objectives.
What remains aligned
- Make sense of problems and persevere.
- Reason abstractly and quantitatively.
- Construct arguments and critique reasoning.
- Model with mathematics, use tools strategically, and attend to precision.
- Connect financial knowledge to informed decisions and long-term consequences.
What the courses add
- Several standards are used together inside one sustained problem.
- Students read documents and work with realistic-sized records.
- Every model is paired with a changed assumption, failure case, or counterexample.
- Students leave an inspectable trail: annotated source, formula, spreadsheet, code, or written decision.
New Jersey requires at least 2.5 credits in financial, economic, business, and entrepreneurial literacy and permits several ways for students to meet that requirement. Financial Decision Lab is a deeper classroom sequence, not a claim of state endorsement or a substitute for a district's formal standards review.
A growing library
Classroom materials, published when they are ready.
This site is still being built. Over time, I plan to add selected lesson plans, student-facing investigations, spreadsheets, notebooks, reading notes, and reflections on what worked in class.
I would rather publish one complete, tested activity than a large folder of polished-looking material with no classroom evidence. Until the resources are here, the course outlines above show the direction of the work.
Planned formats: printable investigations · spreadsheets · Colab notebooks · teaching notes