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The Curriculum Project: Directions and Issues Vince Wright The University of Waikato Who me? Outline • • • • • Background to the development Structure of curriculum Issues Sources of enlightenment Where to? Curriculum Stocktake 1989 1991 1993 1992-97 1996 1997 1999 Tomorrow’s Schools Achievement Initiative Curriculum Framework Curriculum Statements Pause for completion of statements 2 year phase in Stocktake begins Stocktake Report • Essential skills modified from eight groupings to five essential skills and attitudes: creative and innovative thinking participation and contribution to communities relating to others reflecting on learning developing self-knowledge making meaning from information “The broad and flexible nature of the achievement objectives should be maintained, but they should be revised to ensure that they: • Reflect the purposes of the curricula • Are critical for all students; and • Better reflect the future focused curriculum themes of social cohesion, citizenship, education for a sustainable future, multi-cultural and bicultural awareness, enterprise and innovation and critical literacy” Teacher self-assessment of Content Knowledge Knowledge rated as good or satisfactory Rated as needing more content knowledge 90.1% 7.9% Key Competency Groupings • Thinking (critically, creatively, logically) • Relating and participating • Belonging and contributing • Managing self • Making meaning (multi-literacies, using language, movement, symbols, technologies) Mathematics Curriculum National Curriculum Key Competencies Each ELA: Essence statement and achievement objectives. Teacher resource material “2nd Tier” What does curriculum mean? Intended - What national curricula say. Planned - What schools/teachers plan to teach. Delivered - What is taught to students. Learned - What is learned by students Issue 1: School Based Curriculum Development At what level do we expect teachers, schools, and their communities to invent or interpret the curriculum? “The most striking feature of the school experiences of students in most other countries (than USA) whose test performance is very high, is that of a common, coherent, and challenging curriculum through 8th grade.” - William H. Schmidt USA research co-ordinator for TIMSS TIMSS 20022003 Year 5 Relative Strengths Year 5 Number Year 9 Patterns and Relationships Measurement Geometry Data NB: Time allocated Number Patterns and Relationships Measurement Geometry Data Are these items assessing what we think is important? Who is the audience? Students? Parents? Teachers? Audience “Primarily teachers but bearing in mind a much wider audience. The present New Zealand curriculum framework document was recognised as a document that communicated to a wide audience.” Essence Statement • What is mathematics and statistics? • Why does it deserve its place in the curriculum? Mathematician Someone who turns coffee into theorems. Statistician Someone with their head in an oven and their feet in a refrigerator who says, “On average I feel just fine.” Mathematics is the exploration and use of patterns and relationships in quantities, space and time. • Abstract structures that help us to describe, classify, organise and model our world •Symbolism that facilitates both communication between people and their thought processes •Methods of proof that involve making initial assumptions and deriving new results from them Statistics is the exploration and use of patterns and relationships in data. • Investigates phenomena which seldom can be interpreted with absolute certainty • Ways of classifying and presenting data that facilitates the recognition of relationships as well as displaying the relationships • Has variation and distribution as central ideas in considering similarity and difference • Used extensively in the media to validate assertions NB: Brenda and Dave Why teach Mathematics and Statistics? • Real world utility • Informed citizenship • “Gatekeeper” for future study and occupations • Ways of thinking that empower individuals to solve problems and model their world • Creative challenge and enjoyment Mathematical processes • To be integrated and not left as a separate strand • Will be represented as a stem applying to all AO’s at all levels • Will also be represented through active verbs in the AO’s • May be different to statistical processes • May contribute to a synthesised list of processes aligned to the key competencies Levels- a given! Where do we set the levels? Year Two Level One Stage Advanced Counting Percentage 62% Four Two Early Additive Part-whole 67% Six Three Advanced Additive 50% Eight Four Advanced Multiplicative 45% Ten Five Advanced Prop ? Ten Five Advanced Proportional ????? Level 6: Number Use strategies based on transforming quantities and units to solve problems involving scaling, approximation, betweeness (continuity), infinity, and lack of closure. A cricket ball covers 20 metres in 0.6 seconds. What speed is that in kilometres per hour? Issue 2:What kind of knowledge do we want our students to learn? Issue 3: Progressions vs “Mess-iness” Learning trajectories Learning as networking Capturing ideas as “objects” NB: Brown and Askew Stages as broad progressions Strand Structure Geometry and Measurement Number and Algebra Statistics Threads (Key ideas) Number and Algebra Geometry and Measurement Statistics The Key Ideas Statistics Strand Potential change: focus on variation and distribution at all levels • Statistical Thinking (Investigations) • Statistical Literacy (Interpreting reports) • Probability (Probability) Number and Algebra Big Ideas Potential change: focus on generalisation at all levels ( and all strands) • Number Knowledge (Exploring) • Number Strategies (Computation and estimation) • Patterns and Relationships • Equations and expressions Geometry and Measurement • Spatial properties (Shapes and solids) • Transformations (Reflection, rotation, etc.) • Direction and Movement • Measurement of physical attributes • Time and rate In a range of meaningful contexts students will learn to: Number and Algebra Strand Number Strategies Use simple additive strategies to solve problems involving whole numbers, and fractions. Number Knowledge Know forward and backward counting sequences with whole numbers to 1000, doubles, and groupings with tens. Equations and Expressions Record and interpret simple additive strategies represented by words, diagrams (pictures), and symbols. Patterns and Relationships Generalise that counting the number of objects in a set tells how many (cardinality). Use systematic counting strategies to find the number of objects that make up sequential patterns. Level Two Geometry and Measurement Strand Measurement Create and use measurement units sensible for a task, including grouping units to simplify counting. Time and Rates Develop ways to measure time intervals in order to compare the duration of events. Shape and Space Classify 2 and 3 dimensional objects by visual features noting similarities and differences. Image and draw shapes. Position and Orientation Create and use simple maps to show position and direction. Describe different views and pathways from a given location on a map. Transformation Predict the results of slides, flips, turns, and enlargements on objects. Number and Algebra Geometry and Measurement Statistics Statistics Strand Statistical Investigation (thinking) To answer questions, gather appropriate data in categories. Compare categories within datasets, and use data displays to highlight patterns and variations. Statistical Literacy Compare the features of category data displays with statements made about the data. Probability Recognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events. Issue 4: What if we don’t know the progressions? Link to the number framework stages: For example: What is the area of this rectangle? Sources of inspiration Assessment research projects, e.g. Exemplars, PAT development, NEMP. For example: Year 8 students are given a Jaffa packet and told to draw the net with measurements to the nearest centimetre. 4 sides, 2 ends, 3 gluing flaps, 4 small flaps appropriately proportioned… 10 (8) As above, except not including 4 small flaps 7 (11) 4 sides and 2 ends, appropriately proportioned 30 (34) Basic idea correct but significant distortions 27 (18) More inspiration Research since 1992… For example: Probability ideas: • Variability • Independence • Distribution • Sample space (possible outcomes) What do these students think about…? • • • • Variability Independence Distribution Sample space Issue 4: Can do’s vs can’t do’s Level One What we say: With simple chance events, systematically record trialing. What we want to say: Uses subjective criteria to assess likelihood. Level Two What we say: Recognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events. What we want to include: Does not recognise variability and places too much faith on small samples. Progressions Level One With simple chance events, systematically record trialing. Level Two Recognise apparent equal likelihood, impossibility and certainty from trialing of simple chance events. Level Three Predict trailing results from lists, diagrams, or visual models of all the outcomes. Compare the trial data with predictions, acknowledging that samples vary. Find all the possible outcomes for simple independent and conditional events. Describe the probability of outcomes using simple fractions, and recognise when the variation from a trial sample is reasonable or unreasonable. Level Four What if we don’t know? Spatial Reasoning- Van Hieles’ Levels: Pre-recognition Unable to identify shapes or image them, and recognises only a few characteristics when classifying. Visual Recognises shapes by visual comparison with other similar shapes rather than by identifying properties. Descriptive/Analytic Classifies shapes by their properties. Abstract Relational Classifies shapes hierarchically by their properties. Deduces that one property implies another. Formal Deduction Operates logically on statements about geometric shapes, solve problems and prove new results from statements. Resort to the wisdom of practice… and hope nobody asks this! Where to…? We will be successful with the mathematics curriculum revision when… • Teachers recognise the good parts of the ‘old’ in the ‘new’. • The changes transparently signal critical improvements that will better prepare our students for tomorrow’s world. May the future be better than this…