Mathematics and Homeschooling

Mathematics. Homeschooling. An Overview.

Steve Chinn                                        www.stevechinn.co.uk

In these difficult times for educating children, I thought I’d write down a few ideas and some advice from my experiences of teaching maths for many decades, lecturing and training teachers in over 30 countries, writing books and creating resources.

This could be a good time to consolidate knowledge and concepts, maybe yours as well as those of your children. Maybe this is an opportunity for learners to reflect instead of coping with busy, rushed curricula.

I’d be surprised if many of you don’t think, ‘It was different in my day!’. That is very likely, but basic maths is still basic maths. Methods and procedures come into fashion and slip way again. The maths is still about the same principles.

Homeschooling is a chance to make learning more about sharing than telling. A chance to make this a two-way process. An opportunity to discuss and explore understanding. And to use understanding to support memory.

Maths is very developmental, so this is a chance to go back to the basics. It’s like building a wall. You need good foundations. You don’t want there to be too many bricks missing. As I mentioned, maths tends to motor on without checking that the understanding is there. And, even at my great age, I still learn things about maths and teaching maths.

Learners.

Maths is maths and learners are learners, but they are so very inter-connected. I’ve been working on a new book, ‘How to Teach Maths as it is to Learners as they are.’ Sort of a culmination of all those years learning about learners and how to teach them as effectively as I can.

So, know your learner and how he/she learns - and what might stop them from learning. In all my years of teaching I have never met a ‘perfect’ learner. Sadly, my students never met a perfect teacher, at least not in my classroom.

Learners are a heterogeneous bunch. Maths requires a constellation of abilities, so remember that,

‘Nothing works for everyone.’  And

‘Most things will work for someone.’ And

Beware the quick cure/solution.

Some evidence about learning.

These are from experts that I rate. Details can be found in my ‘Trouble with Maths’ and ‘Mathematics for Dyslexics and Dyscalculics’ books

‘Children who start behind generally stay behind.’ 

‘Students come to the classroom with preconceptions about how the world works. If their initial understanding is not engaged, they may fail to grasp the new concepts and information that they are taught, or they may learn them for the purposes of a test, but then revert to their preconceptions outside the classroom.  

‘Errors made in the initial stages of a pupil’s contact with the various processes tend to become fixed. Initial errors persist and repeat themselves even after periods of apparently full mastery.’  

‘The programmes with greatest effect were strategy-based methods.’

‘The highest effects accrued when teachers provided feedback data or recommendations to their students.‘ (The genuinely expressed question here is, ‘How did you do that?’)

These times are a good opportunity to identify misconceptions and address them in a way that inhibits the wrong learning and replaces it with correct learning. Teaching is a multi-faceted skill.

Some of the learner factors to consider when teaching.

Effective communication is the key alongside giving your learners experiences of meaningful success.

There is a constellation of learning factors. Some key factors are:

Long term memory for mathematical facts and procedures.

Adequate short term and working memories.

Speed of processing (often exacerbated by the culture of doing maths quickly).

Anxiety (maybe I’ll post a separate piece on this if you ask).

The symbols, vocabulary and language of maths.

Sequences, forward and backwards.

Generalising and patterns.

I now have a pretty poor short-term-memory. For me it’s an age thing. If you fail to recall information, such as basic instructions, they’re gone. Short term memory does not store information. So, when my wife says. ‘I’ve told you that three times!’ I say, ‘Three more might do it!’ A low capacity short term memory is an issue for some young learners. It’s easy to adjust your communication to deal with the initial barrier to communication.

The teaching ethos.

Create an empathetic teaching and communicating style. This implies an active awareness and consequent acknowledgement and adjustment to the learning strengths and dif?culties of learners, such as short term memory.   

Have a responsive ?exibility in the way you teach and share. Try to have a repertoire of resources and strategies which respond to the individual, and often changing, needs of the learner.

A source of teaching ideas and specially constructed worksheets:    www.mathsexplained.co.uk