Teaching Philosophy
“I’m Not a Math Person”
From the Blog
Throughout the school year, I make it a consistent priority to evaluate what is working and what isn’t. After a lesson, an activity, or a difficult conversation with a student, I ask myself: did that land the way I intended? What would I do differently? This isn’t a formal process — it’s a habit. And it’s one that makes me meaningfully better at my job over time.
The same practice that makes teachers better can make students better too. When students take the time to reflect on their learning experiences, they gain something that passive studying rarely provides: genuine insight into their own thinking. Why did I get that problem wrong? What did I actually understand going into that test? What would I do differently to prepare next time? These questions, asked honestly, are worth more than an extra hour of re-reading notes.
This is part of why my test retake process requires a written reflection as part of the application — because understanding what happened on the original test is essential to doing better on the next one. Reflection converts a frustrating experience into a learning opportunity, and by developing this habit, students become better equipped to tackle challenges, set goals, and move toward their potential. 🎵
My classes are built around carefully designed, discovery-based worksheets. Rather than presenting students with a formula or procedure and asking them to practice it, these worksheets guide students to explore new ideas using what they already know — to reason their way toward understanding before being told the answer.
This approach is sometimes called generative learning, and in many ways it is the antithesis of lecture. Lecture is a passive experience. Discovery-based learning requires active engagement. You can’t fake your way through figuring something out.
When students are actively working — connecting ideas, testing conjectures, reasoning through problems — they build understanding that goes deeper than memorized steps. They don’t just know what to do; they understand why it works. The “desirable difficulty effect” from cognitive science confirms it: when learning requires effort, memory is stronger. Discovery-based worksheets also create natural opportunities for mathematical conversation, and while students work, the teacher moves through the classroom providing individualized support that a lecture simply doesn’t allow for.
To make sure everyone finishes in the same place, each lesson closes with a summary that connects what students discovered to the formal mathematical concepts those discoveries represent. Discovery first. Clarity after. That’s the rhythm of learning in this classroom. 🎵
When a student turns in a test and quietly tells me they think they did badly, I don’t pull out a red pen. I tell them: “It’s going to be okay. Let’s plan for a retake.” The difference in that moment is immediate and visible. Instead of dread building up over the next few days, there’s hope.
All students may retake any test once for a replacement grade, but a retake is a structured learning experience, not just a do-over. To apply, students must complete: Test Corrections (go back through every missed problem and work it correctly), a Study Plan (what will you do differently?), and a Written Reflection (what happened during the original test, and what did you learn from it?). This process ensures the retake is never just a lucky second shot.
A retake gives students a genuine second chance to understand material they initially struggled with. It keeps students engaged rather than mentally checking out. It builds accountability — students can’t passively wait; they have to reflect, plan, and do the work. And it acknowledges that life happens: one hard day shouldn’t follow a student for the rest of the semester.
If you’re a fellow educator thinking about implementing a retake policy, feel free to reach out. 🎵
Math, at its core, is a language. It has vocabulary, grammar, notation, and conventions — and like any language, using it well requires precision, clarity, and practice. I believe that learning to communicate mathematically doesn’t just make you better at math. It makes you a better communicator, full stop.
In a math class, communication shows up through notation (writing symbols correctly), showing work (providing clear supporting evidence), using precise vocabulary, verbal articulation, and written reasoning that makes logic transparent. Each of these is a form of communication that I actively assess and develop.
When students write out their reasoning step by step, they’re developing the ability to explain a complex process in an accessible, logical way. Students who can articulate their thought processes clearly are better equipped to collaborate, to persuade, and to lead — and those outcomes start with something as simple as writing down each step and meaning it. 🎵
Instead of learning something once and moving on forever, students in my classes revisit important ideas and skills throughout the year. They see concepts again — in new contexts, from new angles, at greater depth — until those ideas become genuinely durable. Mathematics is perhaps the most naturally spiral-friendly subject there is, because new ideas are almost always built on earlier ones.
Seeing a concept multiple times and in different ways helps students develop a more complete, flexible understanding. The “spacing effect” from cognitive science confirms this: distributing practice over time leads to dramatically better retention than massed practice in a single block. And there’s something powerful about returning to a concept that once felt impossible and finding that it now feels manageable — each of those moments builds confidence and reinforces the belief that growth is real.
Spiraling shows up in my classes through cumulative reviews, comprehensive final exams, and what I call Blasts From the Past — problems that bring back earlier material during current units. All of these are intentional. They’re the mechanism by which learning becomes permanent. 🎵
Project-based learning has an almost uncanny ability to capture student interest in a way that traditional lessons often can’t match. A well-designed project doesn’t just present a task — it builds intrigue. There’s a mystery to solve, a challenge to beat, or a competition to win. The stakes feel real, and that changes how students show up.
PBL creates natural opportunities for students to connect ideas that they might otherwise experience as isolated. Working through a complex, multi-step project requires drawing on knowledge from multiple topics at once. This is also where collaboration becomes meaningful — when a task genuinely benefits from multiple perspectives, students aren’t just sitting next to each other, they’re actually thinking together.
PBL develops communication, organization, collaboration, and creativity — the skills that employers talk about and colleges look for. It also allows student voice and choice, so when a project allows students to express their findings in their own way, it becomes genuinely theirs. That ownership changes the quality of the work and the depth of engagement in ways I’ve seen again and again. 🎵
Grading is one of the most consequential things a teacher does — and also one of the most imperfect. Traditional point-deduction systems are so familiar that they’re rarely questioned, but they carry some significant hidden costs. That’s why I use a rubric system called INAME.
Instead of subtracting points for mistakes, each question is evaluated against a scale of understanding. The five levels are:
INAME also lets me assess skills beyond content knowledge: clear communication of ideas, correct notation and vocabulary, and evidence provided to support reasoning. These aren’t just math skills — they’re thinking skills that matter in every discipline. 🎵
Walk into most Algebra 2 classrooms on the day logarithms are introduced, and you’ll find a familiar scene: a board full of rules, a worksheet full of problems, and a room full of students wondering why any of this matters. The rules are learned, the problems are solved, and then — too often — most of it is forgotten by the time the test arrives.
The Mathematical Murder Mystery project was built to change that entirely. Instead of a worksheet, students get a crime to solve. Instead of practice problems, they get suspects, alibis, evidence, and financial motives. And instead of applying logarithmic and exponential rules in the abstract, they apply them to find out who committed a murder.
The premise is this: a beloved math teacher has been found dead in his classroom. Security camera footage identifies four suspects — each of whom claims to have been somewhere else, doing something else, at the time of the crime. Every suspect has a mathematically verifiable alibi. And every suspect has a financial motive.
Students are assigned the role of investigator. Their job is to examine the evidence, scrutinize the alibis, analyze the financial data, and use mathematics to determine who is telling the truth — and who is lying.
This is where the project earns its place in an Algebra 2 or Pre-Calculus curriculum. Every alibi requires a different application of exponential or logarithmic reasoning. One suspect claims to have been monitoring a radioactive decay experiment — and the half-life formula tells investigators whether the timing of his story holds up. Another claims to have been brewing coffee in the faculty lounge, and Newton’s Law of Cooling is the tool that either confirms or contradicts her account. A third suspect was working with bacteria under a microscope, and exponential growth equations determine when that bacterial count could have reached the observed level. The fourth involves cooling metal in a welding shop — again, Newton’s Law.
The financial motives layer in another dimension: compound interest, continuous compounding, exponential appreciation, and real estate math give students a reason to care about each suspect’s story beyond just the alibi. Who stood to gain the most from this crime? That answer requires math too.
To estimate the time of death, students apply Newton’s Law of Cooling to the body temperature data recorded by the first responders. This is not a plug-and-chug problem — students must set up the equation, solve for the rate constant, and work backwards to find when the body was at a normal living temperature. Getting the time of death right is essential, because it determines which alibis are even possible.
The Polonium-218 evidence adds another layer. A trace amount of a radioactive substance was found in a blood sample taken from the victim. Using the known half-life of Polonium-218, students work backwards to determine how much was present at the time of death — and whether the amount is consistent with poisoning.
Students submit either a completed investigative case report or a formal criminal complaint — a legal document accusing a specific suspect with mathematical justification. The assignment requires them to do more than just identify the killer; they must explain their reasoning clearly, show their calculations, and make a coherent, evidence-based argument. Mathematical communication is built directly into the assessment.
The project also asks students to create a visual timeline of events and a graph comparing the financial motives of the suspects — making data visualization a natural part of the process rather than an add-on.
The Murder Mystery works because it gives students a reason to care. The math is not a series of practice problems — it is evidence. Getting the half-life calculation wrong means accusing the wrong person. Misapplying Newton’s Law means the timeline falls apart. Students feel the stakes, and those stakes produce a quality of engagement that is genuinely difficult to manufacture through traditional instruction.
It also surfaces misconceptions in a way that worksheets rarely do. When a student’s alibi analysis produces an impossible timestamp, they have to go back and find their error — not because the teacher told them to, but because the answer doesn’t make sense in context. That kind of self-correction is one of the most valuable things mathematics education can develop.
The Mathematical Murder Mystery is available in the DJ Mathematics store on TeachersPayTeachers. If your students are studying logarithmic and exponential functions — in Algebra 2, Pre-Calculus, or even AP Calculus — this project is designed to be the unit they remember long after the course is over. 🎧
When I tell someone at a dinner party that I’m a math teacher, I’ve learned to brace myself. Almost without fail, the response is some version of: “I can’t do math.” or “I’m not a math person.” These statements are delivered casually, almost as a badge of honor — and I find it genuinely disheartening. Not because math is my subject, but because of what these labels cost the people who carry them.
Think about how rarely you hear the equivalent in other subjects. Math has a unique ability to make people feel fundamentally broken — as if not immediately grasping a concept means something permanent and shameful about who they are. Part of it is the nature of math itself — it’s sequential, and gaps compound over time. Another part is cultural: we’ve normalized mathematical helplessness in a way we’d never accept for reading or writing.
These powerful emotions — shame, anxiety, defeat — lead to disengagement. And disengagement leads to a self-fulfilling prophecy: the person who decides they’re “not a math person” stops trying, falls further behind, and eventually has evidence to support the label they put on themselves years ago.
Mathematical literacy is no longer just a school subject — it’s a tool for participating meaningfully in the world. Data and its algorithms influence mortgages, job opportunities, college admissions, the criminal justice system, and what information you see online. We need a population that is comfortable questioning data, and that kind of thinking starts in a math classroom.
If you’re a student reading this who has been telling yourself that story — consider this an invitation to try a different one. 🎵