Using pre-teaching methods to create access to challenging age-appropriate maths concepts

Context “In line with the curricula of many high performing jurisdictions, the National Curriculum emphasises the importance of all pupils mastering the content taught each year and discourages the acceleration of pupils into content from subsequent years.” NCETM Teaching for Mastery

Context The essential idea behind mastery is that all children need a deep understanding of the mathematics they are learning so that: future mathematical learning is built on solid foundations which do not need to be re-taught; there is no need for separate catch-up programmes due to some children falling behind; children who, under other teaching approaches, can often fall a long way behind, are better able to keep up with their peers, so that gaps in attainment are narrowed whilst the attainment of all is raised. NCETM Teaching for Mastery

Mastery approaches to mathematics and the new national curriculum - NCETM “The intention of these approaches is to provide all children with full access to the curriculum, enabling them to achieve confidence and competence – ‘mastery’ – in mathematics, rather than many failing to develop the maths skills they need for the future…Taking a mastery approach, differentiation occurs in the support and intervention provided to different pupils, not in the topics taught, particularly at earlier stages.”

What stops children having enough time to learn? Learning for Mastery – Bloom 1968 “…Carroll’s (1963) view that aptitude is the amount of time required by the learner to attain mastery of a learning task. Implicit in this formulation is the assumption that, given enough time, all students can conceivably attain mastery of a learning task. If Carroll is right, then learning mastery is theoretically available to all, if we can find the means for helping each student.’’ What stops children having enough time to learn?

Pre-teaching Previous research project Article: “Remediation is often a terrible way to help kids catch up. Pre-teaching is more effective and more fun.” Minkel 2015

Student Responsibility Complex instruction Roles Multi Dimensionality Assigning Competence Student Responsibility adapted from Boaler 2015

Assigning Competence Read: Page 9 – Status Problems and Treatment Page 12 – Assigning Competence to Low-Status Students

Assigning competence “Teachers can assign competence to any student but it is especially important and effective to focus attention on low- status students. Cohen and Lotan found that status interventions boosted the participation of low-status students, while not suppressing the contributions of high- status students.’’ Mathematical Mindsets Boaler 2016  

Assigning Competence “Cohen (1994)…recommends that if student feedback is to address status issues, it must be public, intellectual, specific and relevant to the group task. The public dimension is important, as other students learn that the student offered the idea; the intellectual dimension ensures that the feedback is an aspect of mathematical work; and the specific dimension means that students know exactly what the teacher is praising.” Mathematical Mindsets Boaler 2016

Research question How can we support all children to access age-appropriate mathematics and be active and influential participants in maths lessons through effective use of pre-teaching and assigning competence?

Research focus different structures for pre-teaching (time/frequency/who etc.) different content for pre-teaching (what do the children need extra time for?) how to assign competence in maths lessons, linked to the pre-teach Think of the children you work with – what might be the focus for a pre-teach? Why?

Pre-teaching focus Run through the mathematics in the coming lesson; Address an identified misconception; Focus on and rehearse pre-requisite skills and understanding Introduce the children to a new concept Practise and make sense of key mathematical vocabulary; Activate relevant prior knowledge; Practise reasoning and explaining mathematical thinking; Explore questions that will be asked in the main lesson; Explore a new resource; Explore connections between, symbols, images, contexts and language; Engage in real-life, practical experiences or contexts that are relevant to them; Teach a game; Discuss how the working wall can help them; When they have been absent; …

Pre-teaching Accessing the mathematics in the lesson: Introducing new mathematics and new contexts Rehearsing prior learning Allowing confusion to happen

Y2 session Finding easy ways to add three numbers - using number bonds for ten 5 + 8 + 5 9 + 6 + 1 7 + 9 + 1 5 + 8 + 2 Make up your own number sentence where noticing something helps you to solve it.

To assign competence Notice something that a focus child has said or done and draw attention to it; Deliberately target questions, when the answers or explanations have been rehearsed in pre- teaching sessions; Ask a child to model how a resource demonstrates the mathematics; Add work to the working wall and explain how it is useful; Video children in the pre-teaching session and use it in the whole class lesson; Ask a child to teach a game to the whole class or a group; Ask a child to help another child to understand …

Y6 session Use reasoning rather than automatically using a formal method - multiplying a four-digit number by a two-digit number under twenty. Provide four calculations and ask: Which would you do first? Which do not need a formal method? Can you write a multiplication that does need a formal method?

Pre-teach 4640 x 15 5618 x 11 7979 x 10 2000 x 15 How might you do these? Which would you do first? Why? Which do not need a formal method?

Class lesson I wonder… x 15 x 11 x 10 …if you were multiplying a number by these multipliers…which one would you choose first? Why?

I wonder… 6220 x 15 9797 x 11 6816 x 10 4000 x 15 Which calculations do not need a formal method? What help is knowing the rules of multiplying by ten? Could you create a calculation which needs a formal method?

Reflections – pupils “Before I had the pre-teach I felt I was entering lessons half-asleep but now I feel I am wide awake.” “It’s a bit like cheating”

Reflections - pupil “I hate maths, it’s boring… It’s not boring when there’s been a pre-teach. If there hasn’t, it’s boring because I don’t know what I’m doing.”

Reflections – teachers about learners “So much time is wasted at the beginning of a lesson if a child starts behind. When other children have a better understanding of a concept, they immediately start making progress. One child spoke of feeling muddled while everyone else knew what they were doing. It strikes me that the gap is widened at the very beginning of lessons, before teacher intervention, because the playing field isn’t level for children with shaky prior knowledge.”

Reflections – teachers about learners A fairly small amount of pre-teaching can have a noticeable and long lasting impact (children had a 10 min pre teach for one-off fraction lesson in spring term 1 and remembered language and context in spring term 2) A short sequence of pre-teaching can develop confidence over a longer period Pre-teaching has more immediate and greater impact than catch-up Children’s self-esteem has improved greatly

Reflections – teachers about learners Children have felt more confident during maths lessons, happier to have a go without fear of failure and become vocal during lessons. Some children just need a quick input to allow them to approach the lesson with confidence. Giving them a slight input before others has ensured that I spend less time with them in the classroom which again increases their confidence. The impact has been extraordinary. The three children who have made the most progress this year have been the three focus children who have experience more pre-teaching than others.

Contact details Helen Edginton helen.edginton@babcockinternational.com Carolyn Wreghitt carolyn.wreghitt@babcockinternational.com Website: https://www.babcock-education.co.uk/ldp/primarymaths Facebook: www.facebook.com/babcockldpprimarymaths   Twitter: @BabcockLDPmaths Pinterest: https://uk.pinterest.com/babcockldpmaths/