Field notes
Short posts from the classroom, spanning AP Physics 1, Physics C Mechanics, Physics C E&M, AP Physics 2, AP Chemistry, AP Biology, AP Precalculus, AP Calculus, AP Statistics, and SAT Math. The misconceptions students actually bring in, what their wrong answers reveal, and how the diagnostic is built to drill them out.
10 field notes
Action-reaction "cancel out": why the third law looks like it predicts zero net force
The phrase "equal and opposite" sounds exactly like the phrase used to describe forces that cancel. Until students are forced to ask which object each force acts on, the third law looks like a contradiction.
Read noteConserving the spin rate: when angular velocity feels conserved but angular momentum is
No force means constant velocity. Students carry that straight into rotation as no torque means constant spin rate, which is almost right. The conserved quantity is not the spin rate you can see; it is the product of spin rate and rotational inertia, and the difference shows up the instant the shape changes.
Read noteCentripetal as an extra force: the FBD entry that doesn't exist
The textbook introduces centripetal force as a force law with a formula, in the same paragraph format as gravity and friction. Students draw it as a fifth arrow on the FBD, alongside the real forces. Then the radial equation has too much in it.
Read noteEnergy "used up": where the motion actually goes when an object stops
Every student can recite that energy is conserved. Then a block slides to a halt and they say its energy is gone. The recitation and the reflex live in separate compartments, and only the reflex shows up on problems.
Read noteMass vs. weight: the kg-vs-N gap that breaks every dynamics problem
Everyday English uses one word for two physical quantities. Until a problem leaves Earth's surface or asks for an FBD label, the conflation costs nothing. Then it costs everything.
Read noteMomentum is not energy: why students rank kinetic energy by momentum and conserve the wrong one
Both numbers say "how much motion." Both grow with mass and speed. Both come with a conservation law, taught a week apart. So students fuse them into one quantity and use whichever law is in front of them to answer whatever question is asked.
Read notePosition, distance, displacement: three words, three meanings, constant trouble
In English, they're synonyms. In physics, they aren't, and that gap shows up every time a problem has a turnaround, a sign convention, or a runner who finishes where they started.
Read noteSlope vs. area on v-t graphs: whichever the eye reaches first
Velocity-time graphs encode three quantities: instantaneous velocity, acceleration via slope, and displacement via area. Students read whichever one is most visually salient on the graph in front of them, regardless of which one the question is asking for.
Read noteThe lever arm: why torque is not just force times distance
The first dozen torque problems use forces that point straight across the wrench, so distance times force gives the right answer and the angle never matters. Then a force comes in at a slant, and the cached rule quietly drops the part that does the turning.
Read noteVelocity vs. acceleration: the Unit 1 trap that hides all year
It looks like a kinematics problem. It's actually a vector-category problem, and if it doesn't get cleared by the end of week two, every later unit pays for it.
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The constant-α equations, used anyway: the kinematic formulas that outlive the assumption behind them
Four equations get memorised in the first month of any mechanics course and never carry their precondition with them. In a calculus-based course, the precondition is the whole content of the topic.
Read noteForce is the negative slope of U: not the height of the curve, and not the positive slope either
A potential energy curve is one of the densest pictures in the course. Students read the wrong feature off it, and the two most common wrong readings are the height and the unsigned slope.
Read noteSHM acceleration treated as constant: the one motion in the course where every kinematic formula is illegal
Simple harmonic motion is defined by an acceleration that changes at every instant. It arrives after a year of problems in which acceleration did not change at all.
Read noteKinetic energy as a property of the object: the number that changes when you change who is watching
Mass is the same for every observer. Charge is the same for every observer. Kinetic energy is not, and nothing in the way we introduce it suggests otherwise.
Read noteCenter of mass as geometric center: the middle of the shape, regardless of where the mass actually is
For a uniform symmetric object the center of mass really is at the geometric center. That coincidence covers most of what students have seen, and it hides the definition completely.
Read noteCushioning read as shrinking the impulse: the airbag does not reduce the momentum change, and that is the whole point
Every student can tell you an airbag helps. Ask what quantity it changes and most will say it reduces the impact, which is a word doing the work of three different physical quantities.
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Which quantity is held fixed: a capacitor still connected to a battery behaves nothing like an isolated one
Pull the plates apart with the battery attached and the charge changes. Disconnect it first and the voltage changes instead. Students memorize one chain of consequences and apply it to both situations.
Read noteThe distance is a variable inside the integral: it changes from one piece of charge to the next
Setting up the field of a charged rod means writing the contribution of one piece and integrating. Students treat the distance to that piece as a constant, pull it outside, and are left integrating the charge alone — which is the point-charge answer wearing an integral sign.
Read noteOne time constant is not one third of the job: exponentials lose a fixed fraction, not a fixed amount
After one time constant a discharging capacitor retains 37% of its charge. Students scale that linearly and conclude it is empty after about three, or that it reaches zero at some finite time at all.
Read noteThe field is the derivative of the potential, not the potential divided by the distance
Dividing the potential by the distance is true for parallel plates because the field is uniform there. Students learn it in that context and apply it to point charges, where the field is the derivative of the potential and the two answers disagree.
Read noteLenz's law opposes the change in flux, not the field: a decreasing flux induces a current that helps
Students shorten Lenz's law to “the induced current opposes the magnetic field.” Half the problems have a decreasing flux, where the induced current points the same way as the field it is maintaining.
Read noteThe magnetic force does no work on a free charge: it turns the velocity and never changes its magnitude
A force perpendicular to the velocity at every instant contributes nothing to the work integral. Students see a strong force and a curved path and conclude the particle must be gaining energy.
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Adding a resistor in parallel lowers the total resistance: a new branch is a new path, not a new obstacle
More resistors sounds like more resistance. In parallel it is the reverse, and the equivalent resistance is smaller than the smallest branch — a result students reliably assume they have computed wrong.
Read noteBrighter light does not free electrons: below the threshold frequency, more photons is more of the wrong photon
Intensity sets how many photons arrive, and frequency sets how much energy each one carries. One electron absorbs one photon, so a brighter beam of low-frequency light ejects nothing at all.
Read noteThe medium sets the wave speed: raising the frequency shortens the wavelength and changes nothing else
Students read the wave equation as a formula where the right side determines the left. For a wave in a given medium it is the other way round: the speed is fixed, and frequency and wavelength trade off against each other.
Read noteThe magnetic force is perpendicular to the field: every electric intuition points the wrong way here
In an electric field the force on a positive charge points along the field. Students carry that straight into magnetism, where the force is perpendicular to the field and to the velocity both.
Read notePotential is not potential energy: one describes the location, the other needs a charge to be there
Electric potential is a property of a point in space, measured in volts. Potential energy exists only once a charge occupies that point, and it is measured in joules. The names differ by one word and the quantities differ by a factor of the charge.
Read noteTemperature is an average, not a total: a bathtub holds more energy than a cup and is not hotter
Temperature measures the average translational kinetic energy per particle. Students read it as how much thermal energy a sample has, so doubling the amount of substance doubles the temperature.
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Ionic as all-or-nothing: the bond that never finishes transferring its electron
Students learn ionic and covalent as two boxes. The CED asks them to treat bonding as a continuum. The box model answers most questions correctly right up until one asks them to rank.
Read noteEquilibrium means stopped: why “nothing is happening” survives every definition you give it
Every student can recite that equilibrium is dynamic. Ask what the molecules are doing and a large fraction will tell you the reaction is over. The words and the model are stored separately.
Read noteHeat equals temperature: the substance model that survives every thermochemistry unit
Heat is energy in transit and temperature is a measure of average kinetic energy. Students carry a single fused quantity called hotness, and it answers most questions correctly until one separates mass from intensity.
Read noteEntropy misread as disorder: the tidy-room analogy that stops working the first time a liquid freezes
We hand students the messy-bedroom picture because it is memorable. It is memorable, and it gives the wrong sign on some of the most common processes in the course.
Read noteWeak treated as fully ionized: why a 0.10 M weak acid is not a 0.10 M solution of hydrogen ions
Strong acids are taught first and their arithmetic is trivial: concentration in, pH out. That habit is fully formed by the time weak acids arrive, and the equilibrium is the only thing standing between the two.
Read noteOrders copied from coefficients: why the balanced equation cannot tell you the rate law
Equilibrium constant expressions really are built from coefficients. Rate laws really are not. The two look alike on the page, arrive two units apart, and only one of them can be read off the equation.
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Individuals do not evolve: the giraffe did not stretch, and the population did not decide
Students can define natural selection and still explain every specific case by having organisms change themselves. The definition and the explanation are stored in different places, and only one of them gets used.
Read noteEnzymes do not change ΔG: the catalyst lowers the hill, not the destination
An enzyme changes how fast a reaction gets there. It does not change where there is. Students merge the two, and the merged version explains catalysis perfectly well until a question asks about equilibrium.
Read noteEnergy flows, matter cycles: the one sentence that fixes half of ecosystem thinking
Carbon atoms go around and around. Energy makes one pass and leaves as heat. Students draw both as loops because the food web diagram has arrows and the arrows look like a circuit.
Read noteEvery cell has the same genes: what differs is which ones are switched on
A neuron and a liver cell carry identical genomes. Students reason that different cells doing different jobs must contain different instructions, which is a sensible inference and the wrong one.
Read noteProbability has no memory: three girls already does not make a boy more likely
A 3:1 ratio describes what happens over many offspring. Students read it as a quota that each family has to fill, and then expect the next child to make up the shortfall.
Read noteEquilibrium means motion stops: net movement of zero is not the same as no movement
Once concentrations equalise, students stop the molecules. The particles keep crossing in both directions forever, and the reason they must is the same reason diffusion happened in the first place.
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Additive versus multiplicative growth: adding the same amount and multiplying by the same factor are different worlds
Linear thinking is the most successful habit a student brings to precalculus. Exponential behaviour is the first place it fails badly, and the failure is invisible over short intervals.
Read noteInverse does not mean reciprocal: f−1(x) and 1/f(x) share a notation and nothing else
We use a superscript −1 for two unrelated ideas and expect students to tell them apart from context. Many of them cannot, and the notation gives them no help.
Read noteTrig functions are not linear: sin(a + b) is not sin a + sin b, and sin 2x is not 2 sin x
The angle sum identities exist precisely because the obvious thing is false. Students who never registered that reach for the obvious thing anyway.
Read noteThe graph is not a picture of the situation: a rising line is not a hill, and the runner is not going uphill
A graph of height against time and a photograph of the path look alike and mean different things. Students who read the first as the second get a coherent, confident, wrong answer.
Read notePeriod, frequency, and b: the number inside the function is none of the three things students think it is
In y = a sin(b(x − h)) + k, three of the four parameters do roughly what students expect. The one inside does the opposite, and it does it reciprocally.
Read noteA vector's magnitude is not the sum of its components: 3 east and 4 north is 5, and never 7
Components are written next to each other in a bracket, they are both numbers, and adding them is the obvious move. It is also the linearity overgeneralisation, arriving one last time before calculus.
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The limit is not the function value: where the function is heading, not where it arrives
For continuous functions the limit and the value agree, which covers every function students met before calculus. The definition is built entirely around the cases where they do not.
Read noteContinuous does not mean differentiable: you can draw it without lifting the pen and still have no tangent line
Differentiability implies continuity. Students remember that there is an implication between the two and reconstruct it in whichever direction the question needs.
Read noteThe inner derivative: the factor students leave behind, and the one the exam counts on
The chain rule is not hard to state and not hard to apply. It is hard to notice, and the error is almost always a failure of recognition rather than of technique.
Read noteA critical point is not an extremum: f′(c) = 0 is a candidate, not a verdict
Setting the derivative to zero finds the places worth checking. Students treat finding them as having answered the question, and y = x3 is waiting at the origin.
Read noteSigned area versus total area: the integral can be zero while the region is not empty
The integral was introduced as the area under a curve, and for a positive function that is exactly what it is. Below the axis it counts negatively, and the phrase students learned first stops being true.
Read noteThe nth term test cannot prove convergence: terms going to zero is necessary and nowhere near sufficient
The test is stated as a test for divergence and students use it in both directions. One direction is a theorem and the other is false, with the harmonic series as the standing counterexample.
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What the 95 refers to: the method over many samples, not this one interval and not 95% of the data
Once an interval is computed, the parameter either is in it or is not. The 95% describes how often the procedure captures the parameter, and students attach it to the interval in front of them instead.
Read noteCorrelation and causation: a strong r measures how tightly the points follow a line and nothing about why
Every student can recite that correlation does not imply causation. Asked to write a conclusion from an observational study with a correlation of 0.92, a large share of them will write a causal one anyway.
Read noteMutually exclusive is not independent: disjoint events are the most dependent events there are
Both terms sound like they mean “unrelated,” so students use them interchangeably. If two events cannot both happen, then one happening tells you everything about the other, which is the opposite of independence.
Read noteThe p-value is not the probability the null is true: it assumes the null and asks about the data
A p-value is computed by taking the null hypothesis as given. Students reverse the conditional and report it as a probability about the hypothesis, which is the one thing it cannot be.
Read notePaired or two-sample: the design decides the procedure, and two columns of numbers look identical either way
Before and after measurements on the same subjects are one sample of differences. Students see two columns, count two groups, and reach for the two-sample procedure.
Read noteSkew is named for the tail: the long thin side, not the tall crowded one
A right-skewed distribution has most of its data on the left. Students look at where the data is, call that the direction, and get the answer backward every time.
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Powers do not distribute over sums: the single most productive wrong rule in algebra
Multiplication distributes over addition, and it is the first rule students learn that lets them break a problem into pieces. Everything else then looks like it should distribute too.
Read noteThe equals sign is not an operator: it is a claim that two things are the same, not an instruction to compute
For most of primary school the equals sign meant “write the answer here.” Algebra needs it to mean “these two expressions have the same value,” and the switch is rarely made explicit.
Read noteDoubling the sides does not double the area: the scale factor applies to lengths, and its square applies to areas
Scale a figure by 3 and its area scales by 9. Students scale everything by 3, because a scale factor sounds like a single number that applies to the whole figure.
Read noteThe mean moves, the median does not: one billionaire changes the average income and not the typical one
Both are called measures of center, both get computed in the same lesson, and students file them as two routes to the same number. Then a question adds one extreme value and the two answers separate.
Read noteTrig ratios from the wrong sides: opposite and adjacent are relative to the angle, not to the page
SOH-CAH-TOA is a reliable mnemonic for a student who can identify the sides. The identification is the actual skill, and the mnemonic says nothing about it.
Read noteStopping at the solved variable: the test asks for 2x + 1, and x is sitting right there looking finished
This is not a gap in mathematics. It is a gap between finishing the algebra and finishing the question, and the answer choices are built to catch students in it.
Read noteComing next
What field notes are
These aren't a blog about teaching. They're a focused log of misconceptions seen in working classrooms across ten courses, written with other teachers in mind. Each note follows the same shape: the mistake, why it makes sense to the student, the correction, a sample item, what each wrong answer reveals, and where the platform handles it.
If a misconception you see in your room isn't here yet, the email's on the teacher page. Send it over.