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The Cerebral Roadmap
A student's mathematical development.
Maths isn't a random collection of topics. It's a structured journey where each stage builds on the last — not just in content, but in how a student learns to think.
The Cerebral Roadmap maps the thinking skills a student builds at each stage, from Secondary 1 through to O-Level.
Secondary 1
Thinking Skills
- Learn the "grammar" of algebraCommon struggle: loses marks due to poor presentation
- Translate given information into mathematical expressionsCommon struggle: stuck whenever facing a word problem
- Package a word problem as an algebraic equation with the idea of equivalenceCommon struggle: attempts primary school heuristics, e.g. unchanged total, rather than using algebra
- Develop strong visualisation habits for algebraic manipulationCommon struggle: solves equations slowly without confidence
Secondary 2
Thinking Skills
- Understand algebraic expressions as transformable objects to equivalent formsCommon struggle: misinterprets question instructions
- Develop a firm foundation of arithmetic of algebraic expressionsCommon struggle: loses marks whenever algebra is involved
- Apply higher-level processes when working within more complex systemsCommon struggle: accurate only when solving easy questions
- Grasp the derivation of formulaeCommon struggle: memorises formulae by rote learning
From Secondary 3, the journey splits into two tracks
E-Math Track
Secondary 3 · E-Math
Thinking Skills
- Recognise patterns within diagrams that prompt the use of particular conceptsCommon struggle: inconsistent at solving geometry related topics
- Develop rigorous mathematical proofs with logic flowCommon struggle: loses marks for any explanation or proving questions
- Strategise the use of varied concepts to solve a cross-topic problemCommon struggle: easily overwhelmed by long demanding questions
Secondary 4 · E-Math
Thinking Skills
- Create a diagram as a tool to visualise a problemCommon struggle: lacks structure in workings
- Perceive fractional multiplication as a tool to scale mathematical objectsCommon struggle: stuck when any ratio or proportion is involved
A-Math Track
Secondary 3 · A-Math
Thinking Skills
- Formulate an equation or inequality based on criteria associated with mathematical phenomenaCommon struggle: unable to recognise question types
- Simplify any equation or inequality to a general form as a prerequisite to apply a standard processCommon struggle: manipulates expression or equations aimlessly
- Choose the most efficient approach to a problemCommon struggle: lacks time in exams
Secondary 4 · A-Math
Thinking Skills
- Manage their own mental processes in learning by using clear visualisation and self-talkCommon struggle: lacks flow and momentum when executing step-by-step processes
- Juggle multiple interconnected mathematical ideas at onceCommon struggle: unable to brainstorm a problem
- Plan larger steps to solve a complex problem while understanding the processes and skills needed within each stepCommon struggle: lacks foresight on where their working will lead
See where your child fits on the map.
The Cerebral Journey with Keith develops students holistically rather than the usual topical teaching. If your child feels lost or left behind, it is most likely a nagging pain-point waiting to be resolved.
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