EMMA GALE AND SAM HICKMAN-SMITH TEACHING FOR

Teaching for MasteryEMMA GALE AND SAM HICKMAN-SMITHTEACHING FOR MASTERY SPECIALISTS

AimsTo have a collective understanding of what mastery isTo dispel myths surrounding TfMTo demonstrate TfM lessonsTo explore leadership priorities

aCollective Understanding –What is Mastery?Myths of MasteryBreakDemonstration LessonsTRG style questionsPotential FeedbackLunchWhole school ImplementationQuestionsClose

Post – it note questionsQuestions?

Where are you now?Brand newto masteryWorkingwith manyschoolsadvising onmasteryapproachesWhat are you hoping to get out of today?

Teaching for Mastery and theShanghai Exchange Programme

Evidence basedpractice at a local,national and globallevel:

Aims of the morning:A collective understanding of TfM principlesTo dispel myths surrounding TfMTo explore the 5 big ideas plus greater depth and support(keep up not catch up)To demonstrate a TfM lessonTo explore leadership priorities and next steps

Collective understanding Mastery is something that we want pupils to acquire. So a ‘mastery maths curriculum’, or ‘mastery approaches’ toteaching maths, both have the same aim—to help pupils, overtime, acquire mastery of the subject. That’s why we use the phrase ‘teaching for mastery.’ NCETM

What is the mindset in theschools you visit?Pupils?Teachers?Support Staff?Parents?Governors?Management Team?Who is the biggest challenge to get on board?

What does it mean tomaster something? I know how to do it It becomes automatic and I don’t need to think about it- forexample driving a car I’m really good at doing it – painting a room, or a picture I can show someone else how to do it.

Mastery Means Statement SortUse the statements on your table to discuss what the keyaspects of a mastery approach/curriculum are

5 Myths of Mastery One single definition No differentiation Special Curriculum Repetitive Practice Text Books(NAMA, 2015)

Five Big QualityIdeas – FirstTeachingTeaching?for Mastery

Let’s talk about the:‘Effective teaching of mathematics’(This will be applicable to all schools atany stage of their journey.)

New terminology: don’t assumeeveryone speaks your language.Prior attainmentRapid graspers andStruggling learnersIs this a group? Or is it concept and condition dependent?

A Mind-Set Shift:“Ability labelling shapes teachers’ attitudes towards childrenand limits their expectations for some children’s learning.Teachers vary their teaching and respond differently towardschildren viewed as ‘bright’, ‘average’ or ‘less able’ ” (e.g.Rosenthal and Jacobson 1968; Jackson 1964; Keddie 1971; Croll and Moses1985; 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 Limits, Open UniversityPress (“A book that could change the world.” Prof. Tim Brighouse)

Charlie Stripp(Director NCTEM)the ‘traditional’ way we differentiate i.e. putting the childreninto ability grouped tables and providing easier work for theless able and more challenging ‘extension’ work for the moreable has ‘a very negative effect on mathematical attainment’‘one of the root causes for our low position in internationalcomparisons’.

Charlie Stripp claims:It damages the less able by fostering a negative mindset that theyare no good at mathsin practice it results in the less able children being given a‘reduced curriculum’.it damages the more able because it encourages children to rushahead or can ‘involve unfocused investigative work’labelling the child as ‘able’ creates a fixed mindset so the childbelieves that they should find maths ‘easy’ and becomes unwillingto tackle demanding tasks for fear of failure.

Representation and Structure

Key Structures Part – Part – Whole Tens Frames Bar Model Language

Representation and StructureC-P-AExpose Mathematical StructureProvide access and challengeTeacher-Pupil TalkPupil-Pupil talkDeveloping Reasoning Skills

LanguagePrecise mathematical languageStem SentencesGeneralisationsDefinitions

What is a Stem Sentence?A gap fill to support children in working with fractions.TransferrableMathematically truePrecise Language

Examples of stem sentences “To find a half we divide by 2, to find a we divide by .”When we divide by 2 we find a half, when we divide by .we find a .”

What is a Generalisation?Mathematically trueA structure of their ownShould be used during the application stage of a lessonBridge the concrete/pictorial to the abstractTasks should promote discoveryTo be discovered rather than toldEnable us to be fluent & efficient- we do less maths!

Example of a generalisation “The denominator tells us how manyequal parts there are in the whole.”(Important everyone in school owns and uses these consistently.)

FluencyEfficiency- Accuracy-Flexibility Deep understanding of low number Composition of numbers to 10 Repertoire of facts to draw upon Solid knowledge of 10 and 0 and their relevance in the placevalue system Clear understanding of the 4 operations Relationships between operations Variety of calculation methods Solid understanding of equality

Mathematical Thinking Highlighting relationshipsPattern spottingReasoningConcept/non-conceptLanguage

VariationIn the late 1970s, mathematics teaching in China came across bigchallenges. Regarding students’ mastery of mathematics: Understanding of mathematical concept was ambiguous and vague. Pupils could not identify the mathematics when its context wasslightly changed When pupils encountered mathematical problems with slightvariation, they did not know what to do. What they had learned in mathematics was inflexible andunconnected.

2 strandsConceptualProcedural

Conceptual Variation Varying the representation to extract the essence ofthe concept Supporting the generalisation of a concept, torecognise it in any context Drawing out the structure of a concept – what it is andwhat it isn’t To find out what something is, we need to look at itfrom different angles – then we will know what it reallylooks like! What’s the same and what’s different?

Conceptual Variation1212

Describe an Elephant

According to your descriptioncould this be an elephant?

Concept vs. non-concept

Non-standard examples ofan elephant

Standard and non-standardaabcBoaler, Jo. (2016) Mathematical Mindsets

Over half of eight year olds did not seethese as examples of a right angle,triangle, square or parallel linesBoaler, Jo. (2016) Mathematical Mindsets

Take a square and fold it into 4 to show14

How do you know it’s a quarter?The whole is divided into equalparts and of those parts isshaded.Stem Sentence Example

Non Conceptual VariationThe red part is 15, True or False? What is the concept, what is not the concept? 16Use the stem sentence to help youdecide.

Non Conceptual VariationWhat do you notice about these images ?11114534 14

Conceptual VariationStandardConceptualVariationWhat it is(positive)What it is not(negative)Nonstandard

Conceptual VariationThe aim of variation is to develop a deepunderstanding of the concept. An importantteaching method . It intends to illustrate theessential features by demonstrating differentforms of visual materials and instances orhighlight the essence of a concept by varyingthe nonessential features.It aims at understanding the essence of objectand forming a scientific concept by puttingaway the non-essential features(M Gu 1999)

Procedural Variation Procedural variation occurs within the processof doing mathematics. Provides the opportunity to focus on therelationship (not just the procedure) Small steps are made with slight variation There is a connection as you move from oneexample to the next Make connections between problems, using oneproblem to work out the next Recognition of connections needs to be taught

DifferentmethodsProviding Textbook Supports for Teaching Math Akihiko textbook-supports-for-teaching-math/

Procedural VariationWhich of these do you think is abetter example?Set A120 – 90235 – 180502 – 397122 – 92119 – 89237 – 182Set B120 – 90122 – 92119 – 89235 – 180237 – 182502 – 397

What do you notice aboutthe calculations below?

Rounding Example

VariationVariation: What is it?‘A well-designed sequence of tasks invites learners toreflect on the effect of their actions so that they recognizekey relationships’Teaching with Procedural Variation: A Chinese Way ofPromoting Deep Understanding of MathematicsMun Yee Lai http://www.cimt.org.uk/journal/lai.pdf How do we do this? ‘Influencing the way children thinkthrough what we keep the same and what we change’ Debbie Morgan

Procedural VariationProcedural Variationthe questions that are asked are important Providing theopportunity:- for practice (intelligent rather than mechanical); -to focus on relationships, not just the procedure;-- to make connections between problems;- to use one problem to work out the next;- to create other examples of their own.-The questions that are asked are important as they developmathematical thinking

BenefitsSupport deep learning by providing rich experience ratherthan superficial contactProvide the necessary consolidation (in familiar andunfamiliar situations) to embed and sustain learningFocus on conceptual relationships and make connectionsbetween ideasSupport pupils’ ability to reason and to generalise

What makes good practice?Shooting from all over the court or refining through makingconnections to previous shots.

Coherence A comprehensive, detailed conceptualjourney through the mathematics. A focus on mathematical relationshipsand making connectionsThe smaller the distance from the existingknowledge and the new learning, thegreater the success (Gu, 1994).

Whole Class TeachingInclusion is essential but it must bethought about in a different way toallow ALL children an equality of accessto quality teaching and learning inmathematics.

Ping-Pong

We don’t differentiate anymore!

OfstedDifferentiation should therefore be about how the teacherhelps all pupils in the class to understand new concepts andtechniques. The blend of practical apparatus, images andrepresentations (like the Singaporean model of concretepictorial-abstract) may be different for different groups ofpupils, or pupils might move from one to the next with moreor less speed than their classmates. Skilful questioning is key,as is creating an environment in which pupils are unafraid tograpple with the mathematics. Challenge comes through morecomplex problem solving, not a rush to new mathematicalcontent. Good consolidation revisits underpinning ideasand/or structures through carefully selected exercises oractivities. Mastery calls this ‘intelligent practice’.

Break!

A Year 5 Lesson

A Year 2 Lesson

Teaching for Mastery

Features of a lesson:Teaching the whole class togetherProcedural variationSmall steps approachSmall focusPrecise use of mathematical languageMisconceptions at the forefrontSpeaking in full sentencesOpportunities for children to go deeperAnalysis of strategiesDiscussionReview at the start of lessonsOpportunities to make connectionsGeneralisation found and usedConceptual variationColour-codingUseful contextC-P-ALink to relevant life-experienceMaths not ‘clouding’ learningKey facts

Lunch

A Leader’s View

Action PlanningA helpful order for implementation:Mindsets – common language, clear vision, clear expectationKeep up and not catch up sessionsNumber FactsCoherenceRepresentation and StructureMathematical ThinkingFluencyVariation

Keep up, not catch upBenefits: Live assessment Quick intervention Provided by an expert Closing the gap instantly Available to all learners Less marking Effective use of teacher time Perceptions of intervention Data – Target groups Pre-teach Greater depthChallenges: Timetabling Staffing Repeated use by samechildrenMaths Mentors