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The Gauth Blog: Study Guides and Math Advice

Longer pieces, reviewed by working teachers, on how to actually get better at this.

AI and academic integrityWhere the line sits between learning with AI and handing in work that isn't yours, what integrity policies say, and a four-question self-test.Studying for math testsRetrieval practice, spaced repetition, and error logs: the study methods with evidence behind them, and why re-reading notes only feels productive.Common algebra mistakesThe twelve errors that show up most often in marked work, each shown wrong then right, with the underlying misconception named and corrected.Showing your workHow markers actually allocate method marks, why a bare correct answer scores badly, and what a full-credit solution looks like line by line.Checking your workSubstitution, estimation, units, symmetry, limiting cases, and reverse operations: six checks shown catching real errors rather than confirming them.Reading word problemsA repeatable five-step framework for decoding word problems, with the phrase-to-operator table and six worked examples of increasing nastiness.Solving quadraticsFour methods, a decision tree for choosing between them, and a derivation of the quadratic formula by completing the square that you can follow.Choosing an integration methodA decision tree for choosing an integration technique, a worked example down every branch, and the dead ends worth backing out of early.Calculus prerequisitesThe specific algebra and trig that calculus assumes you already have, with a diagnostic that maps each gap to the guide that closes it.Math anxietyWhat research says about math anxiety, the working-memory mechanism that makes it feel like inability, and a practical routine for reducing it.Function transformationsShifts, stretches, and reflections derived from one principle so you never memorise the table again, including why f(x-3) moves to the right.Best AI math solversThe same ten problems put through Gauth, Photomath, Symbolab, Mathway, Wolfram Alpha, ChatGPT, and Socratic, scored on correctness and working.

What we write about

Three kinds of thing. Method pieces that work a technique end to end, like solving any quadratic or choosing an integration technique. Study pieces grounded in research rather than folklore — retrieval practice and spaced repetition genuinely work, and re-reading your notes genuinely does not, however productive it feels. And honest pieces about using AI for schoolwork, including where the line sits.

A note on the hardest one to write: math anxiety is treated here as a working-memory problem with evidence behind the interventions, not a pep talk. If maths has felt impossible since a specific bad year, that piece is probably the most useful thing on this site for you, and it is worth reading before any of the method guides.

Everything is written by a mathematician and reviewed by a practising secondary teacher who marks exams, which is why the pieces on showing your work talk about how method marks are actually allocated rather than how people assume they are.

Start somewhere

Concept guidesShorter, method-focused explanations.Subject solversGet your own problem worked out.Academic integrityWhere we think the line sits.How accurate is it?An honest account of the limits.

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