In the last two posts I made suggestions for differentiating instruction in maths class. In this final post for now on the topic of differentiation, I present a third approach. Unlike the other two, which were whole-class suggestions for differentiating instruction, this one requires particular knowledge of individual students and obstacles and strengths to learning that they possess.

For these ideas I acknowledge the work of Amy Brodesky, who has done work on teaching mathematics to learners with disabilities, and her colleagues at EDC. In particular this paper is worth reading.

Brodesky’s idea is that learning and doing maths requires key skills and these skills can be categorised under eight headings:

- Conceptual processing (e.g. identifying and extending patterns)
- Language (e.g. reading a word problem)
- Visual-spatial processing (e.g. working with 2-d and 3-d representations)
- Organisation (e.g. collecting and recording data)
- Memory (e.g. remembering number facts; remembering the steps of a mathematical procedure)
- Attention (e.g. focusing on the details in a maths problem)
- Psycho-social (e.g. working with a partner or in a group)
- Fine-motor skills (e.g. drawing geometric figures)

Some children may be good at paying attention and at remembering facts, whereas they may have difficulty with language or with their fine motor skills. Most students will have strengths and weaknesses in some areas and a teacher’s job in differentiating instruction is to build on a student’s strengths and to help compensate for the student’s weaknesses. This approach also draws on the research of David Rose and his colleagues at CAST.

If a child has been diagnosed with a specific learning disability or condition (such as dyslexia, autism spectrum disorders, adhd, etc.), a teacher will usually know or be able to find out the particular strengths that a pupil with that condition will have.

Let’s take an example. Imagine that you have a child in your third class who has been diagnosed as having dyslexia. Although the specific difficulties of each child with a condition such as dyslexia can vary, some patterns do occur. These are listed below and beside them are strategies that you can incorporate into your teaching to support the child with dyslexia in learning maths.

Possible learner strengths |
Possible learner difficulties |
Possible teacher responses |

Estimation | ||

Subitising | ||

Place value | ||

Language comprehension impairment | Use vocabulary that is familiar to the studentExplain new vocabulary carefullyMonitor and vary the level of text learners are expected to read in mathematics problemsHighlight words that have different meanings in different contexts (e.g. third, prime, factor) | |

Counting speed is slower than in other learners | Provide more time in table and other maths tests to allow students to use strategies when they can’t recall number facts | |

Memory problems | Give short instructionsRecap at end of lesson and revisit topics frequentlyMonitor early work on new topics carefully so that incorrect strategies are not practised.Use concrete materials (including fingers or pictures) | |

Number fact recall | Teach strategies to use when a child forgets number facts | |

Phonological (speech sounds) processing | Exaggerate difference between words that sound similar (e.g. ten and tenth; fifteen and fifty) | |

Difficulty with decimal places | Highlight the decimal point (possibly by using a different colour for it) | |

Directional confusion in writing digits and doing algorithms | Work on the concepts first and on recording later | |

Omissions of digits and numbers | Encourage learners to compare answers to estimates |

Much of the specific work in the table in relation to students having dyslexia and doing maths is based on research by Helland and AsbjØrnsen (2004), Simmons & Singleton (2007), Miles, Haslum and Wheeler (2001), and on the book by Chinn and Ashcroft (1998), *Mathematics for Dyslexics: A Teaching Handbook*.

Thanks so much for the 3 articles. They make so much more practical sense that the mantra “everybody should … , some should … , a few can”. This is “real” content – again thanks.

While I find the idea of playing to individual strengths of the child so appealing I just wonder how much experience would I need to identify of a pupil to be able put this into practice. As a TUT (totally unqualified teacher!) it seems unrealistic to expect to have this level of perceptiveness of thirty students.

I know there are aspects that sound wrong but are there any empirical tools that can be used to highlight such strengths and weaknesses?