Mathematics rewards practice with purpose: spaced revision, plenty of self-testing, making notes, checking with feedback, and calm, consistent routines. Below you’ll find exactly how to do this at different stages of school. The Big Three for All Learners Space it out Short, regular sessions beat last-minute marathons. Plan 20–40 minute slots across the week and revisit topics before you forget them. This is known as the spacing effect (Cepeda et al., 2008). Retrieve, don’t just reread Close the book and try to solve or recall from memory. Use past questions, quick quizzes, and “write-from-memory” summaries. Retrieval practice strengthens long-term learning, especially when you check your answers (Roediger & Butler, 2011). Think about your thinking Teach learners to plan, monitor, and evaluate how they study. Simple questions like, “What will I practise today? How will I know I’ve improved?” turn revision from passive to purposeful (EEF, 2018). Primary School (Grades 4–7) Goals Build number sense and fluency (times tables, fractions, decimals). Understand why methods work, not just how to perform them. Study Rhythm Mon/Wed/Fri: 20 min mixed practice (across old and new topics). Tue/Thu: 20 min facts fluency (typically something like time tables or fractions) Weekend: 25–30 min “Teach-Back” session: learner explains one concept aloud (e.g. “How do we find a common denominator?”). High School (Grades 8–12) Goals Strengthen algebraic fluency, geometry, trigonometry, statistics, and calculus. Build exam stamina and the ability to select appropriate methods. Exam Preparation Plan Weeks –4 to –3: Cover all topics and create a spaced schedule. Weeks –3 to –2: Attempt past-paper sections; very important to check with detailed memos. Prepare an error log of frequent mistakes. Weeks –2 to –1: Interleave topics and focus more on challenging topics (e.g., trig, functions, geometry). Final Week: Short, focused recall sessions from your “error log.” The Value of Writing Your Own Notes and Step-by-Step Summaries One of the most effective yet overlooked study habits is summarising key procedures in your own words . Mathematics is full of repeatable processes: simplifying fractions, expanding algebraic expressions, finding derivatives using first principles, or completing the square in a quadratic equation. Writing out the steps helps learners form mental blueprints they can rely on in tests. Why this works Research shows that encoding information through writing and explaining strengthens understanding and recall (Dunlosky et al., 2013; MIT Teaching + Learning Lab, 2020). When learners create their own step-by-step summaries: They engage in sense-making, not just copying. They uncover misconceptions early. They connect formulas with reasoning (“why does this step come next?”). They create a quick reference guide for revision. Examples: Simplifying fractions: Find common factors → Divide numerator and denominator → Check if it can simplify further. Completing the square: Divide so that x squared stands on its own →Take the constant term to the right-hand side →Add half of the coefficient of x squared to both sides → Factorise the left-hand side to form a perfect square → Simplify and solve for x. Visualisation and Trigonometry Trigonometry can be tricky until you visualise how angles behave on the Cartesian plane . Remember: in trigonometry, angles are measured from the positive x-axis , moving anticlockwise for positive angles and clockwise for negative ones. (See the labelled diagram above, showing where each trigonometric ratio is positive or negative, including the reduction formulae.) Using StudyChamp Resources Effectively StudyChamp’s detailed memos and step-by-step worked examples make maths study easier: Compare your solution to the memo. Highlight key reasoning steps. Add the process to your “Maths Procedures Notebook”. By exam time, that notebook becomes your own personalised study guide: practical, and written in your own words. References Cepeda, N. J., et al. (2008). Spacing effects in learning: A temporal ridgeline of optimal retention. Psychological Science, 19(11). Dunlosky, J., et al. (2013). Improving Students’ Learning With Effective Learning Techniques. Psychological Science in the Public Interest. Education Endowment Foundation (EEF). Metacognition and Self-Regulated Learning Guidance Report. Roediger, H. L., & Butler, A. C. (2011). The critical role of retrieval practice in long-term retention. Trends in Cognitive Sciences, 15(1). MIT Teaching + Learning Lab. (2020). Note-Taking and Sense-Making Strategies. Massachusetts Institute of Technology.
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