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
Agenda Agenda 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
Post – it note questions Questions?
Where are you now? Working Brand new with many to mastery schools advising on mastery approaches What are you hoping to get out of today?
Teaching for Mastery and the Shanghai Exchange Programme
Ev Evid idenc ence e ba base sed d pr prac actic tice e at a l at a loc ocal, al, na nati tion onal al an and gl d glob obal al le leve vel: l:
Aims of the morning: 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 ort (keep up not catch up) To demonstrate a TfM lesso son To explore lea eadership dership priorities and next xt steps ps
Collective understanding • Mastery is something that we want pupils to acquire. • So a ‘mastery maths curriculum’, or ‘mastery approaches’ to teaching maths, both have the same aim — to help pupils, over time, acquire mastery of the subject. • That’s why we use the phrase ‘teaching for mastery.’ NCETM
What is the mindset in the schools you visit? Pupils? Teachers? Support Staff? Parents? Governors? Management Team? Who is the biggest challenge to get on board?
What does it mean to master something? • I know how to do it • It becomes automatic and I don’t need to think about it - for example 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 Sort Use the statements on your table to discuss what the key aspects 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 Ideas – Teaching for Mastery Quality First Teaching?
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.)
New terminology : don’t assume everyone speaks your language. Pr Prior or at atta tainment nment Rapi pid d gr grasp sper ers s and nd Str truggli uggling ng lea earn rners ers Is this a group? Or is it concept and condition dependent?
A Mind-Set Shift: “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 ond diffe 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 out Limits ts, Open University Press (“A book that could change the world.” Prof. Tim Brighouse)
Charlie Stripp (Director NCTEM) 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’.
Charlie Stripp claims: 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.
Representation and Structure
Key Structures • Part – Part – Whole • Tens Frames • Bar Model • Language
Representation and Structure C-P-A Expose Mathematical Structure Provide access and challenge Teacher-Pupil Talk Pupil-Pupil talk Developing Reasoning Skills
Language Precise mathematical language Stem Sentences Generalisations Definitions
What is a Stem Sentence? A gap fill to support children in working with fractions. Transferrable Mathematically true Precise Language
Examples of stem sentences… “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 ……..”
What is a Generalisation? 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 omote 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!
Example of a generalisation… “The deno enominat minator or tells us how many ny equal l parts rts there are in the whole le .” (Impor porta tant every ryon one e in school ol owns and nd uses these consis iste tent ntly.) ly.)
Fluency Efficiency - 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 place value system • Clear understanding of the 4 operations • Relationships between operations • Variety of calculation methods • Solid understanding of equality
Mathematical Thinking • Highlighting relationships • Pattern spotting • Reasoning • Concept/non-concept • Language
Variation In the late 1970s, mathematics teaching in China came across big challenges. Regarding students’ mastery of mathematics: • Understanding of mathematical concept was ambiguous and vague. • Pupils could not identify the mathematics when its context was slightly changed • When pupils encountered mathematical problems with slight variation, they did not know what to do. What they had learned in mathematics was inflexible and • unconnected.
2 strands Conceptual Procedural
Conceptual Variation • Varying the representation to extract the essence of the concept Supporting the generalisation of a concept, to • recognise it in any context Drawing out the structure of a concept – what it is and • what it isn’t • To find out what something is, we need to look at it from different angles – then we will know what it really looks like! What’s the same and what’s different? •
Conceptual Variation 1 1 2 2
Describe an Elephant
According to your description could this be an elephant?
Concept vs. non-concept
Non-standard examples of an elephant
Standard and non-standard a a b c Boaler, Jo. (2016) Mathematical Mindsets
Over half of eight year olds did not see these as examples of a right angle, triangle, square or parallel lines Boaler, Jo. (2016) Mathematical Mindsets
1 Take e a squar uare e and nd fold ld it it in into 4 t to sho how w 4
How do you know it’s a quarter? The whole is divided into __ equal parts and ____ of those parts is shaded. Stem Sentence Example
Non Conceptual Variation 1 The red part is , True or False? 5 × × √ 1 What is the concept, what is not the concept? 6 Use the stem sentence to help you decide.
Non Conceptual Variation What do you notice about these images ? 1 1 1 1 4 5 3 4 √ × × × 1 4
Conceptual Variation Standard What it is (positive) Non- Conceptual standard Variation What it is not (negative)
Conceptual Variation 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)
Procedural Variation • Procedural variation occurs within the process of doing mathematics. • Provides the opportunity to focus on the relationship (not just the procedure) • Small steps are made with slight variation • There is a connection as you move from one example to the next • Make connections between problems, using one problem to work out the next • Recognition of connections needs to be taught
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