The Primary Mathematics Teaching for Mastery Specialist Teacher Programme Kim Mitchell Lead Practitioner Bramham /Shadwell Federation Gail Lee Headteacher Boroughbridge Primary School

Session Outcomes Understand the role of the mastery specialist What is mastery? What is depth of learning? How can we plan for mastery learning? Experience a ‘taste’ of a TRG

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 of Mathematics is more….. Deep and sustainable learning The ability to build on something that has already been sufficiently mastered The ability to reason about a concept and make connections Conceptual and procedural fluency

5 Big Ideas If you were to select five big ideas that teachers should focus on to develop teaching for mastery, what would they be?

Mathematical Thinking Teaching for Mastery Number Facts Table Facts Making Connections Procedural Conceptual Chains of Reasoning Access Pattern Representation & Structure Mathematical Thinking Fluency Variation Coherence Small steps are easier to take

What is Depth?

Is this what happens when learning is superficial with no understanding? www.youtube.com/watch?v=MS2aEfbEi7s

Solve the following  + 17 = 15 + 24 99 –  = 90 – 59 Consider the strategies you used? This illustrates how a conceptual method rather than a procedural method can lead to a quicker answers. Whilst procedures are important, they do not stand alone but need to be underpinned by conceptual understanding.

Attention to Structure We observe that children from quite early ages are able to appreciate structure to a greater extent than some authors have imagined. Initiating students to appreciate structure implies, of course, that their appreciation of it needs to be cultivated in order to deepen and to become more mature. John Mason Appreciating structure for all

Drawing attention to structure in KS1 Making Comparisons

Drawing attention to structure

Working Systematically

Developing Depth/Simplicity/Clarity 7 2 5 7 1.9 5.1 7.4 C 1.7 5.7 a b

What is Depth Factual and Procedural Fluency Conceptual Fluency Reasoning Sustained learning Connected Learning Simplicity and Clarity

How is depth achieved? Longer time on topics Intelligent practice (variation) Detail in exploring the concept – all aspects exposed and linked) (conceptual variation) Small steps Questioning and activities develop reasoning and make connections

Mastery Lesson 5 Big Ideas Observation Sheet

Mathematical Thinking Teaching for Mastery Number Facts Table Facts Making Connections Procedural Conceptual Chains of Reasoning Access Pattern Representation & Structure Mathematical Thinking Fluency Variation Coherence Small steps are easier to take

Letting Go! but then reining back in

Representation and Structure Mathematical tools should be seen as supports for learning. But using tools as supports does not happen automatically. Students must construct meaning for them. This requires more than watching demonstrations; it requires working with tools over extended periods of time, trying them out, and watching what happens. Meaning does not reside in tools; it is constructed by students as they use tools (p. 10). .(Hiebert 1997) Cited in Russell (May, 2000). Developing Computational Fluency with Whole Numbers in the Elementary Grades http://investigations.terc.edu/library/bookpapers/comp_fluency.cfm

Variation A key idea that is applied in East Asian countries that enhances mathematics learning

Fluency Efficiency Accuracy Flexibility Fluidity

Mathematical Thinking It is central to mathematics learning; the glue that both develops and holds mathematics learning together It involves: Looking for pattern and relationships Logical Reasoning Making Connections

Coherence It is important to present small connected steps both within individual lessons and running across groups of lessons

Working Collaboratively A significant element of teacher professional development happens when teachers work collaboratively together. This is common in other high performing Countries External expertise also has a role to play

TRG member A member of my TRG in Leeds will now talk briefly about how Mastery and the 5 big ideas are beginning to embed in her school