Updating the Mathematics and Statistics Learning Area: What could this look like? NZAMT16 Workshop 2019 Jane McChesney

Overview Dilemmas for curriculum information Clarity – of terminology and format Coherence – between different sources of curriculum information Focus 1 – content examples from number and algebra Focus on clarity and progression Focus 2 – mathematical processes and related approaches Focus on clarity and other approaches Focus 3 – review and looking ahead

Some curriculum issues 1. There are multiple sources of curriculum information for teachers that serve as a ‘proxy’ for the curriculum, and this can be very confusing and time wasting The primary sector has many of these NDP (Number Framework) PacT – the NMSSA KAMSi – Plus other sources of ‘big ideas’ 2. Levels 4 and 5 are problematic – in NZC, these encompass a relatively large content base and many students seem to slow in their learning for Years 7-10 3. What has happened to ‘problem solving’? Mathematical Processes was a strand in the previous MiNZC but not subsumed into the Key competencies or content ‘stem’ statement.

Focus 1 –from number and algebra This activity is aimed at Levels 4 and 5 And includes examples of curriculum content from different countries. (written as statements for student learning) For the topics of number or algebra (choose one) Which statements do you prefer and why? – choose as many or as few as you like, give reasons for your choices There are blank pieces of paper for you to write your own or to combine What would be the order of learning that you would suggest? And what might be missing in terms of a progression or trajectory of learning> Please record the numbers of each statement on the A4 piece of paper, and any other info

The number examples From 1, 13 the NZC (New Zealand Curriculum) 3 MiNZC (the previous mathematics curriculum Levels 1 to 8) 2, 6, 12 Australian Curriculum for Mathematics (2012) 4, 9, 10 Common Core Mathematics (USA) 5,11,14 NMSSA

The algebra examples From 1, 5, 10 the NZC (New Zealand Curriculum) 14 MiNZC (the previous mathematics curriculum Levels 1 to 8) 3, 9, 12 Australian Curriculum for Mathematics (2012) 2, 6, 13 Common Core Mathematics (USA) 4, 11 NMSSA

Mathematical thinking A key influence has been five strands of mathematical proficiencies (Kilpatrick et al, 2001) Conceptual understanding, Procedural fluency, Strategic competence, Adaptive reasoning, and Productive disposition, Taken up by the most recent Australian Curriculum as four proficiency strands Understanding, Fluency, Problem Solving, and Reasoning And the Common Core (USA) as eight Standards for Mathematical Practice The Mathematical Practices encapsulate the five processes of problem solving, reasoning and proof, communication, representation, and connections, as well as three of the mathematical proficiencies as above

Standards/ Mathematical Practices (USA) The Mathematical Practices encapsulate the five processes of 1. Make sense of problems and persevere in solving them (problem solving) 2. Reason abstractly and quantitatively (reasoning and proof) 3. Construct viable arguments and critique the reasoning of others (communication) 4. Model with mathematics (representation) 5. Use appropriate tools strategically (connections) Proficiencies 6. Attend to precision 7. Look for and make use of structure 8. Look for and express regularity in repeated reasoning

Focus 2 This activity is based on extracts from three sources The Australian Curriculum Proficiency strands The US Common Core xxxx And MiNZC (previous curriculum) In pairs decide and indicate which of the statements could be useful information for teachers in an official curriculum? And what are your reasons for your choices? What is missing? Or repetitive? How could the curriculum information about mathematical thinking be usefully presented to teachers? What would work for your school context?

More sources of information: Key competencies: How does your school/department/Learning Area currently include the Key Competencies in you school programme/syllabus? What are the strengths and limitations of embedding Key Competencies? How might the following be included or recognised in an updated mathematics curriculum? Key competencies, Capabilities Big ideas Other formats?

Mathematics/Australian Curriculum References Mathematics/Australian Curriculum https://www.australiancurriculum.edu.au/f-10-curriculum/mathematics To the Proficiency and content information for Years 6 to 9 (AU) https://www.australiancurriculum.edu.au/f-10- curriculum/mathematics/?year=11757&year=11758&year=11759&year=11760 Common Core Mathematics - Standards for Mathematical Practice http://www.corestandards.org/Math/Practice/ McChesney, J. (2017). Searching the New Zealand curriculum landscape for clarity and coherence: Some tensions in Mathematics and Statistics. Curriculum Matters, 13, 117-130.