Move it, draw it, think it, talk it……
Start small and grow thinking.
Start small and grow thinking.
This collection of statements passed by my Twitter window recently, extracted by Prof Rob Coe of Durham Uni, from a Harvard study by David Blazar. http://cepr.harvard.edu/files/cepr/files/blazar_2015_effective_teaching_in_elementary_mathematics_eer.pdf
A couple of months ago, I was asked to lead a training session on feedback in mathematics. I spent some time reflecting on the practicalities of this before accepting, as I could see a number of potential pitfalls and blocks, dependent on the school and individual thinking and working methods.
In the end, I decided to take as a central theme talking maths. This would allow me to explore presentational ideas as well as interactive elements of a lesson.
All thinking about teaching and learning comes back to the learner and the teacher understanding or their needs at a particular point in time, with regard to the specifics of the next steps in teaching. This knowledge should build on their previous experiences, with an overview of prior attainment, both of which will determine the means of sharing the new ideas, links with the prior learning, but also to consider the need to explain and model the new information in the light of individual needs. This modelling might be through concrete apparatus, visual diagrammatic representation or oral modelling, if the learners have secure internal models, which they can manipulate.
It would be interesting to know when the concrete apparatus is withdrawn from the teacher explanation repertoire, as this can be seen as only useful for SEN children, yet, used effectively, can enable even more able learners to make connections through very clear visual manipulation. This was made clear in the training session when I demonstrated the use of Dienes base 10 material to explore place value and four rules with decimals.
How do you know what a child is thinking unless you ask them directly to explain something?
We have become used to Talk for Writing, so why not Talk for Maths? If teachers and children engage in learning dialogue, the teacher can get a better view of how the children are thinking and the learners might become more secure in their willingness to have a go, especially when facing novel situations. We also talk of it being ok to make mistakes, especially in the context of Growth Mindset thinking. I would suggest that an openness to dialogue underpins GM, in that a child should be able to share insecurities and to be able to talk through a resolution. Learning to think and talk is an important stage in being able to do so internally, from the scaffolds developed through discussion and manipulation.
Language is key. Using the correct vocabulary and ensuring that children do so, underpins a mutual understanding, and may require interpretation and linkages to a broad range of synonymous language, to ensure all understand. In my opinion, it is fine for a learner to ask for a reminder. Asking supports Teacher Assessment, in that it might demonstrate a level of insecurity, which needs to be addressed to avoid this getting greater.
Asking a child to explain the steps they would take to solve an equation offers an opportunity for writing instructions, or reportage, but also links with a “Show your working” approach, which I would also advocate. Either way, I’d be looking to have as much information as possible available to review outcomes in the round. It is very easy to see maths as producing right or wrong answers.
Talking the steps and showing your working, with apparatus, written models and written methods, would, for me underpin any investigative approach to understanding a child who may be expressing difficulty.
This should be a teacher level activity, so that any remediation needed, perhaps in the hands of a Teaching Assistant, can be focused to the real needs, rather than assumption. The mathematical thinking of the TA needs to be considered, so that “short cuts” and alternative methods are not deployed to make it seem as if the child is getting it right, when they have underlying issues.
Children should be supported in their confidence throughout, encouraging effort, exploring alternative scaffolds and materials as needed, removing these when they are beginning to show confidence. It is also important to demonstrate the links between the scaffolds, eg number lines, number squares, Numicon, Dienes, so that they can select if need arises.
Using the analogy of teacher as storyteller, it is important that children are told the story in such a way that they can see the storyline and the developing detail, as it gets progressively harder. Activity should be accompanied by modelling, in a form that supports each learner’s needs. Articulation, from both teacher and learners should be a high priority, as this provides the insights that guide teacher decisions. Just marking the books can often give false information.
Keep talking mathematically, across all subjects, so that it is clear to learners where it can be used and applied. They must learn that maths is all around us, from an early age. Everything can be counted or measured in some form.
Linked posts
Maths everywhere
Show maths, talk maths, draw maths, image maths.
Investigating mathematically
More maths Activities
Quick (one minute) data
The answer is twelve?
Story maths?
In the end, I decided to take as a central theme talking maths. This would allow me to explore presentational ideas as well as interactive elements of a lesson.
All thinking about teaching and learning comes back to the learner and the teacher understanding or their needs at a particular point in time, with regard to the specifics of the next steps in teaching. This knowledge should build on their previous experiences, with an overview of prior attainment, both of which will determine the means of sharing the new ideas, links with the prior learning, but also to consider the need to explain and model the new information in the light of individual needs. This modelling might be through concrete apparatus, visual diagrammatic representation or oral modelling, if the learners have secure internal models, which they can manipulate.
It would be interesting to know when the concrete apparatus is withdrawn from the teacher explanation repertoire, as this can be seen as only useful for SEN children, yet, used effectively, can enable even more able learners to make connections through very clear visual manipulation. This was made clear in the training session when I demonstrated the use of Dienes base 10 material to explore place value and four rules with decimals.
How do you know what a child is thinking unless you ask them directly to explain something?
We have become used to Talk for Writing, so why not Talk for Maths? If teachers and children engage in learning dialogue, the teacher can get a better view of how the children are thinking and the learners might become more secure in their willingness to have a go, especially when facing novel situations. We also talk of it being ok to make mistakes, especially in the context of Growth Mindset thinking. I would suggest that an openness to dialogue underpins GM, in that a child should be able to share insecurities and to be able to talk through a resolution. Learning to think and talk is an important stage in being able to do so internally, from the scaffolds developed through discussion and manipulation.
Language is key. Using the correct vocabulary and ensuring that children do so, underpins a mutual understanding, and may require interpretation and linkages to a broad range of synonymous language, to ensure all understand. In my opinion, it is fine for a learner to ask for a reminder. Asking supports Teacher Assessment, in that it might demonstrate a level of insecurity, which needs to be addressed to avoid this getting greater.
Asking a child to explain the steps they would take to solve an equation offers an opportunity for writing instructions, or reportage, but also links with a “Show your working” approach, which I would also advocate. Either way, I’d be looking to have as much information as possible available to review outcomes in the round. It is very easy to see maths as producing right or wrong answers.
Talking the steps and showing your working, with apparatus, written models and written methods, would, for me underpin any investigative approach to understanding a child who may be expressing difficulty.
This should be a teacher level activity, so that any remediation needed, perhaps in the hands of a Teaching Assistant, can be focused to the real needs, rather than assumption. The mathematical thinking of the TA needs to be considered, so that “short cuts” and alternative methods are not deployed to make it seem as if the child is getting it right, when they have underlying issues.
Children should be supported in their confidence throughout, encouraging effort, exploring alternative scaffolds and materials as needed, removing these when they are beginning to show confidence. It is also important to demonstrate the links between the scaffolds, eg number lines, number squares, Numicon, Dienes, so that they can select if need arises.
Using the analogy of teacher as storyteller, it is important that children are told the story in such a way that they can see the storyline and the developing detail, as it gets progressively harder. Activity should be accompanied by modelling, in a form that supports each learner’s needs. Articulation, from both teacher and learners should be a high priority, as this provides the insights that guide teacher decisions. Just marking the books can often give false information.
Keep talking mathematically, across all subjects, so that it is clear to learners where it can be used and applied. They must learn that maths is all around us, from an early age. Everything can be counted or measured in some form.
Linked posts
Maths everywhere
Show maths, talk maths, draw maths, image maths.
Investigating mathematically
More maths Activities
Quick (one minute) data
The answer is twelve?
Story maths?
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