Teaching for Mastery EMMA GALE AND SAM HICKMAN-SMITH TEACHING FOR - - PowerPoint PPT Presentation
Teaching for Mastery EMMA GALE AND SAM HICKMAN-SMITH TEACHING FOR MASTERY SPECIALISTS Aims To have a collective understanding of what mastery is To dispel myths surrounding TfM To demonstrate TfM lessons To explore leadership priorities
EMMA GALE AND SAM HICKMAN-SMITH TEACHING FOR MASTERY SPECIALISTS
To have a collective understanding of what mastery is To dispel myths surrounding TfM To demonstrate TfM lessons To explore leadership priorities
9:30am Collective Understanding – What is Mastery? Myths of Mastery 10:30 Break 10:50 Demonstration Lessons TRG style questions Potential Feedback 12:45 Lunch 1:30pm Whole school Implementation 3:00pm Questions 3:30pm Close
Brand new to mastery Working with many schools advising on mastery approaches
What are you hoping to get out of today?
A collective understanding of TfM princip nciples les To dispel el myths hs surrounding TfM To explore the 5 big ideas eas plus greater eater depth pth and support
(keep up not catch up) To demonstrate a TfM lesso son To explore lea eadership dership priorities and next xt steps ps
teaching maths, both have the same aim—to help pupils, over time, acquire mastery of the subject.
Pupils? Teachers? Support Staff? Parents? Governors? Management Team? Who is the biggest challenge to get on board?
example driving a car
Statement Sort Use the statements on your table to discuss what the key aspects of a mastery approach/curriculum are
(NAMA, 2015)
Let’s talk about the: ‘Effective teaching of mathematics’ (Th This is wil ill l be appli plicable cable to all ll sc school hools s at any stage ge of the heir ir journe rney.) y.)
Is this a group? Or is it concept and condition dependent?
“Ability labelling shapes teachers’ attitudes towards children and limits their expectations for some children’s learning. Tea eache hers rs vary ry their eir teac aching hing and nd respond
fere rentl ntly towards ards children viewed as ‘bright’, ‘average’ or ‘less able’ ” (e.g.
Rosenthal and Jacobson 1968; Jackson 1964; Keddie 1971; Croll and Moses 1985; Good and Brophy 1991; Hacker et al 1991; Suknandan and Lee 1998).
Also see Hart, S, Dixon A, Drummond MJ and McIntyre D (2004) Learning Without
ts, Open University Press (“A book that could change the world.” Prof. Tim Brighouse)
the ‘traditional’ way we differentiate i.e. putting the children into ability grouped tables and providing easier work for the less able and more challenging ‘extension’ work for the more able has ‘a very negative effect on mathematical attainment’ ‘one of the root causes for our low position in international comparisons’.
It damages the less able by fostering a negative mindset that they are no good at maths in practice it results in the less able children being given a ‘reduced curriculum’. it damage ages the more able le because it encourages children to rush ahead or can ‘involve unfocused investigative work’ labelling the child as ‘able’ creates a fixe xed minds ndset et so the child believes that they should find maths ‘easy’ and becomes unwilling to tackle demanding tasks for fear of failure.
C-P-A Expose Mathematical Structure Provide access and challenge Teacher-Pupil Talk Pupil-Pupil talk Developing Reasoning Skills
Precise mathematical language Stem Sentences Generalisations Definitions
A gap fill to support children in working with fractions. Transferrable Mathematically true Precise Language
“To find a half lf we divid vide e by 2, to find a ……we divide by…….” When we divid ide by 2 we find a half lf, when we divide by…..we find a ……..”
Mathematically true A structure of their own Should be used during the applic plication ation stage of a lesson Brid idge ge the concret rete/ e/pictorial pictorial to the abstract stract Tasks should prom
te disco cove very To be discov covered ered rather ther than an told ld Enab able le us to be fluent ent & effic icient ient- we do less s mat aths hs!
“The deno enominat minator
ny equal l parts rts there are in the whole le.” (Impor porta tant every ryon
e in school
nd uses these consis iste tent ntly.) ly.)
Efficiency - Accuracy - Flexibility
value system
In the late 1970s, mathematics teaching in China came across big
slightly changed
variation, they did not know what to do.
unconnected.
Conceptual Procedural
the concept
recognise it in any context
what it isn’t
from different angles – then we will know what it really looks like!
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2
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Boaler, Jo. (2016) Mathematical Mindsets a b c a
Boaler, Jo. (2016) Mathematical Mindsets
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Take e a squar uare e and nd fold ld it it in into 4 t to sho how w
The whole is divided into __ equal parts and ____ of those parts is shaded.
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Non Conceptual Variation The red part is , True or False?
× √ ×
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6
What is the concept, what is not the concept?
Use the stem sentence to help you decide.
Non Conceptual Variation What do you notice about these images ?
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4
1
4
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× × × √
Conceptual Variation What it is (positive) Standard Non- standard What it is not (negative)
The aim of variation is to develop a deep understanding of the concept. An important teaching method ... It intends to illustrate the essential features by demonstrating different forms of visual materials and instances or highlight the essence of a concept by varying the nonessential features. It aims at understanding the essence of object and forming a scientific concept by putting away the non-essential features
(M Gu 1999)
relationship (not just the procedure)
example to the next
problem to work out the next
Providing Textbook Supports for Teaching Math Akihik hiko
kaha hashi shi https: s://p //prezi.com
/s1nv nvam1gll gllv9 v9/p /prov
ng-textbook book-su suppor
hing ng-math/
Set A 120 – 90 235 – 180 502 – 397 122 – 92 119 – 89 237 – 182 Set B 120 – 90 122 – 92 119 – 89 235 – 180 237 – 182 502 – 397
Variation: What is it? ‘A well-designed sequence of tasks invites learners to reflect on the effect of their actions so that they recognize key relationships’ Teaching with Procedural Variation: A Chinese Way of Promoting Deep Understanding of Mathematics
Mun Yee Lai http://www.cimt.org.uk/journal/lai.pdf How do we do this? ‘Influencing the way children think through what we keep the same and what we change’ Debbie Morgan
Procedural Variation the questions that are asked are important… Providing the
mathematical thinking
Support deep learning by providing rich experience rather than superficial contact Provide the necessary consolidation (in familiar and unfamiliar situations) to embed and sustain learning Focus on conceptual relationships and make connections between ideas Support pupils’ ability to reason and to generalise
Shooting from all over the court or refining through making connections to previous shots.
journey through the mathematics.
and making connections The smaller the distance from the existing knowledge and the new learning, the greater the success (Gu, 1994).
Inclusion is essential but it must be thought about in a different way to allow ALL children an equality of access to quality teaching and learning in mathematics.
Differentiation should therefore be about how the teacher helps all pupils in the class to understand new concepts and
representations (like the Singaporean model of concrete- pictorial-abstract) may be different for different groups of pupils, or pupils might move from one to the next with more
as is creating an environment in which pupils are unafraid to grapple with the mathematics. Challenge comes through more complex problem solving, not a rush to new mathematical
and/or structures through carefully selected exercises or
Teaching the whole class together Small steps approach Precise use of mathematical language Speaking in full sentences Opportunities for children to go deeper Analysis of strategies Discussion Conceptual variation Useful context Link to relevant life-experience Key facts
Procedural variation Small focus Misconceptions at the forefront Review at the start of lessons Opportunities to make connections Generalisation found and used Colour-coding C-P-A Maths not ‘clouding’ learning
A helpful order for implementation: Mindsets – common language, clear vision, clear expectation Keep up and not catch up sessions Number Facts Coherence Representation and Structure Mathematical Thinking Fluency Variation
Benefi fits: ts:
Challenge allenges: s:
children
Maths Mentors
Supporting staff with the sequence of teaching Longer time teaching key topics Whole class teaching Small steps approach to lesson planning – reduce distance between old and new learning SKE Lesson Crafting Teach with low number Beware of the Golden Cloak Tasks and resources are used appropriately by the teacher Assessment of pupils’ strengths and weaknesses informs choice of task and how these address misconceptions Tasks build conceptual knowledge in tandem with procedural knowledge
An expectation that all children reach the abstract phase Structures used to expose structure and not help get to answer Contexts used to support understanding Key resources purchased/dusted off! (double sided counter, tens frames, Cuisenaire)
How will you get a whole school, consistent approach to the use of language? Do staff understand the importance of repetition? Is reasoning understood as linking calculations, identifying non-examples, solving questions through use of structure (not
Is handwriting taught in the writing lesson? Spelling? Reading? How can extra fluency sessions be provided to children?
The hardest to implement Which resources could help them? Text books NCETM professional development spines White Rose Nrich None used exclusively, just like we wouldn’t teach reading with one reading programme!
How do the expectations on marking and writing plans support teachers in enabling them to spend time redesigning their lessons? Lesson design is key.
Show us your sparkle Flamingo challenge Zoom Variation
Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content (DfE, 2013).
Audit Professional Dialogue Whole school planning Knowledge of what comes before and after to prevent mathematical untruths! NCETM – subject knowledge section Well timed ‘Mastery’ inputs from maths lead
Autumn PPM Coverage vs. progress Depth of understanding Diagnostic assessment identifies specific difficulties and whether interventions are appropriate How assessment informs planning Use of specific and clear feedback Teacher knowledge of misconceptions and how to address them How does the assessment system provided support teachers is spending more time on key topics?
Regular release Regular input Demonstration lessons Keep ahead A voice in the school (SMT) Team teaching Planning support Coaching TIME and Money (RAP)
Whole school planning support Focus year groups Team teaching Bi-weekly monitoring Lesson study Talent shifting TRGs Constant drip feeding (at least a staff meeting every 2 weeks) Demonstration lessons
Learning Together Parent Workshops Parents’ evening stand Newsletter updates Coffee Morning Number Facts Cards Fluency updates
Myth Buster!
Increased monitoring for: Training Needs Consistency Research Learning Evaluating Whole School Feedback No link to performance management in the 1st year
What has changed in lesson observations? Prerequisites in place Ping Pong Introduction Worked Examples Less examples Language Active adults C-P-A Repetition Pace Concept driven – no maths clouding the learning
Feedback Policy Impact All adults
Working walls (no longer laminated and up all year!) Classroom layout Groupings
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Sussex Maths Hub NCETM