Mathematical misconceptions and difficulties#
See also: teaching-mathematics
A list of various types of mathematical misconceptions, grouped into two categories
- Mathematical - related largely to understanding mathematical concepts.
- Pedagogical - arising due to the way mathematics is taught.
Mathematical#
Pedagogical#
Assessment for common misunderstandings#
Collection of diagnostic tasks to reveal student thinking around key aspects of Number. Some may be useful for assessment-for-learning diagnostics
| By end of | Big Idea | Indicated by |
|---|---|---|
| Prep/K | Trusting the Count | Access to flexible mental objects for the numbers to ten based on part-part-whole knowledge derived from subitising and counting |
| Year 2 | Place-value | Capacity to recognise and work with place-value units and view larger numbers as counts of these units rather than collections of ones. Appreciates structure in terms of ’10 of these is 1 of those’ |
| Year 4 | Multiplicative Thinking | Initial Ideas – Works with multiple representations of multiplication and division (e.g., the ‘for each’, ‘times as many’ and ‘area’ ideas). Moving to factor-factor-product idea, efficient strategies for multiplication facts |
| Year 6 | Equi-partitioning | Uses partitioning strategies to construct line and areas models for fractions and decimals, uses representations to compare, order and locate fractions and decimals on number lines, recognise that numbers can be divided to create new numbers, solves simple problems involving fractions |
| Year 8 | Proportional Reasoning | Ability to recognise and work with an extended range of concepts for multiplication and division including rate, ratio, percent, solves problems involving intensive quantities and proportional relationships |
| Year 10 | Generalising | Capacity to recognise and represent patterns and relationships in multiple ways including symbolic expressions, devise and apply general rules and properties |