What a 13+ Maths tutor may diagnose
Current ISEB Mathematics aims cover far more than topic recall. They include fluency, investigative thinking, problem solving, reasoning, selecting appropriate methods, logical working, making connections and learning from mistakes. England’s Key Stage 3 programme provides similar supporting context through fluency, reasoning and problem solving, although individual UK schools and assessment types differ.
A useful diagnostic separates missing knowledge from weak fluency, poor method choice, calculator judgement, timing, accuracy or confidence. It should follow the actual paper rather than assume every KS3 topic is relevant. For example, the current ISEB table allows Pythagoras at Additional but not Core, while trigonometry is not examined at either level.
- Traffic-light confidence across each confirmed content strand.
- Separate knowledge gaps from method choice, calculator judgement, timing and accuracy.
- Use unfamiliar multi-step problems to test reasoning rather than chapter recall alone.
- Record recurring errors and choose a small number of high-impact priorities.
- Number and calculation
- Integers, fractions, decimals, factors, powers, percentages, units, rounding and approximation. Diagnose mental and non-calculator fluency as well as sensible calculator use.
- Algebra
- Notation, substitution, expressions, equations, coordinates, linear graphs and sequences, with selected Additional extensions. Diagnose symbol sense, logical working and transfer.
- Ratio, proportion and rates
- Ratios, percentage change, scale, direct proportion, speed and unit pricing. Diagnose model choice, representation and reasonableness.
- Geometry and measures
- Perimeter, area, angles, polygons, transformations, congruence, circles and volumes. Diagnose diagram reading, units and assessment-specific limits.
- Probability and statistics
- Probability, averages and spread, tables, charts and scatter graphs. Diagnose interpretation, communication and supported conclusions.