Using fingers
Finger counting is widely use to introduce numbers up to 10, to develop counting skills and to form an association with a number to a physical quantity. However, around year 3, it can become less effective:
Drawbacks:
- Inaccuracy
- Slow development of mental math
- Limited range of numbers
- Hinders abstract thinking and visualisation
- Slows calculations
- Encourages one-by-one counting
Alternative methods like tally marks help with numbers over 10, but (according to research) don’t significantly improve speed or accuracy.
Why Mental Maths Matters
Early development of mental math improves speed, accuracy, number sense, and cognitive load capacity – tasks that initially felt difficult become easier with practice.
Foundation vs. Formula
Many think of maths as a collection of intimidating symbols – but it basically consists of two parts:
Foundation
- Arithmetic (addition, subtraction, etc.)
- Number theory (integers, rationals, reals)
- Algebra (variables, equations)
- Geometry (shapes, spatial reasoning)
Early arithmetic is essential – it underpins more advanced topics like algebra and geometry when taught visually.
Formulas
- BIDMAS
- Fraction opertations
- Area, volume, Pythagoras, integrals, etc.
These rules/formulas proliferate as topics get more complex, but require a foundation to be meaningful.
Procedural vs. Conceptual Understanding
- Procedural: Follow steps (e.g., subtracting by borrowing)
- Conceptual: Deep understanding (e.g., using cubes to show borrowing).
Best outcomes come from combining both: procedural skills support quick, accurate answers, while conceptual understanding fosters flexibility.
From KS1 to KS4
Success in modern maths depends on balancing procedural and conceptual understanding, plus strong foundational number sense. This balance helps manage cognitive load – working memory needs support when solving complex problems.
Example Comparison:
Q1. 5 + 9 = ?
Q2. 24 x 17 = ?
Q2 demands more working memory, but recalling the 17x table reduces load.
Learning by repetition (common in traditional systems) builds procedural memory but can be time-intensive, and may not scale well when topics multiply. In contrast, strong foundations enable conceptual learning supported by targeted practice.
Many educators believe that if complex topics are learned fr
Benefit of “frames” (5s and 10s):
- Promotes fast mental arithmetic
- Reduces working memory load
- Visualises abstract concepts (fractions, ratios,algebra, etc.)
- Improves speed and accuracy in tests