leading the australian curriculum: mathematics presented by linda spicer martine thurkle

Leading the Australian Curriculum: Mathematics

Presented by

Linda Spicer

Martine Thurkle

Celine Bellve

Australian Curriculum

Introduction

• Welcome


Geraldton Numeracy StrategyImplementation Plan for Australian Curriculum Mathematics

Sem 1 2012

Sem 2 2012

Sem 12013

Sem 22013

Sem 12014

•Number and Place Value N&A•Fractions Decimals up to Yr 6 N&A•Real Numbers Yr 7+ N&A•Data Representation and Interpretation S&P

•Geometric Reasoning Yr 3+ M&G•Pythagoras & Trigonometry Yr 9+ M&G•Chance S&P

•Using units of Measurement M&G•Shape M&G•Location and Transformation M&G

•Money and Financial Matters N&A•Patterns and Algebra N&A•Linear and non-linear relationships Yr 7+ N&A


TASK

• Order your containers

• Explain your findings. How do you know?

• Record your findings


TASK - Discussion

• What maths did you use?


Purpose of Today’s PL

• Examine structure and content for Measurement and Geometry using the Australian Curriculum.

• Familiarise ourselves with First Steps in Mathematics in order to facilitate and support learning activities.

• Explore the mathematics during hands on activities.

• Realise and identify opportunities for rich learning within the maths lessons.


Australian Curriculum in Mathematics

• The curriculum focuses on developing increasingly sophisticated and refined mathematical understanding, fluency, logical reasoning, analytical thought and problem-solving skills. These capabilities enable students to respond to familiar and unfamiliar situations by employing mathematical strategies to make informed decisions and solve problems efficiently.


Planning Cycle


Planning Cycle

• What are you/your school using at present to support this planning cycle?

• Is it successful? Why/Why not?


MEASUREMENT AND GEOMETRY


Measurement and Geometry

• Measurement and Geometry are presented together to emphasise their relationship to each other, enhancing their practical relevance.

• Students develop an increasingly sophisticated understanding of size, shape, relative position and movement of 2D figures in the plane and 3D objects in space.

• They investigate properties and apply their understanding of them to define, compare and construct figures and objects. They learn to develop geometric arguments.

• They make meaningful measurements of quantities, choosing appropriate metric units of measurement. They build an understanding of the connections between units and measurement and calculations.


Quiz


Structure of Measurement & Geometry

The Australian Curriculum v 4.2 Mathematics Foundation to Year 10 Curriculum

http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=3#level=5

http://www.australiancurriculum.edu.au/Mathematics/Curriculum/F-10?layout=3#level=5


Measurement & Geometry - What has changed?F • indirect comparison not only direct

•Tell time to hour

Year

1

•Doesn’t specify content related to estimation (throughout) because estimation is not mathematics it describes the application of mathematics

•Comparisons of mass not included now until Year 2

•Tell time to half hour

•Emphasis on giving and following (verbal) direction rather than representing

Year

2

•Comparisons of mass using balance scales is introduced

•Using uniform units to measure to prepare for metric units in Year 3

•Emphasis on 2D shapes and 3D objects

•Area not introduced until Year 4 (previously in Year 2)

•Tell time to quarter hour

•Introduce half and quarter turn angles

Year

3

•Introduction/Emphasis on using familiar metric units of length, mass and capacity

•Tell time to the minute (was only to quarter hour)

•Identify angles as measures of turn and identify angles in every day situations


Year

4

•Focus on reading graduated scales on a range of measuring instruments, including thermometer (linked to explicit teaching of metric units)

•Measurement of area and volume are introduced using grid paper and centicubes respectively

•Use am and pm notation and solve simple time problems (duration)

•Introducing angles in relation to right angles (greater than, less than)

Year

5

•Making choices of appropriate metric units relevant to measurement

•Using a protractor

•Compare 12 and 24 hour time systems and convert between them

•Introduce grid reference system to describe location

Year

6

•Cartesian co-ordinate system is introduced using all four quadrants

•Connect decimal representation to the metric system

•Convert common units of length, mass and capacity and solve problems

•Connect volume and capacity and their units of measurement

•Investigating angles on a straight line, at a point and vertically opposite – use results to find unknown angles

Year

7

•Identify corresponding, alternate and co-interior angles when 2 parallel straight lines are crossed by a transversal

•Reasoning involving parallel lines, classifying triangles, and properties of angles in triangles, parallelograms and quadrilaterals

Measurement & Geometry - What has changed?


First Steps Links

• ..\Australian Curriculum with SKILLS updated Sept. 2012\Year 3 Australian Curriculum Revised SKILLS updated Sept. 2012.doc


First Steps and AC Links

3 Books;

– Measurement: Understand Units & Direct Measure

– Measurement: Indirect Measure & Estimate

– Space: Represent Location, Represent Shape, Represent Transformation, Reason Geometrically


First Steps and AC Links• Understand Units – decide what needs to be measured by selecting what attributes

to measure and what units to use.

• Direct Measure – carry out measurement of length, volume, mass, area time and angle to needed levels of accuracy.

• Indirect Measure – select, interpret and combine measurements, measurement relationships and formulae to determine other measures indirectly.

• Estimate – make sensible direct and indirect estimates of quantities and be alert to the reasonableness of measurements and results.

• Represent Spatial Ideas – visualise, draw and model shapes, locations and arrangements and predict and show the effect of transformations on them

• Reason Geometrically – reason about shapes, transformations and arrangements to solve problems and justify solutions.

First Steps Mathematics


First Steps Key Understandings

The KU are the corner stone for the Fist Steps in Mathematics series.

The Key Understandings:

• Describe the mathematical ideas which students need to know in order to achieve the outcome

• Explain how these mathematical ideas relate to the levels of achievement for the mathematics outcomes

• Suggest what experiences teachers should plan for students so they achieve the outcome

• Provide a basis for the recognition and assessment of what students already know and still need to know in order to progress

• Provide content and pedagogic advice to assist with planning


First Steps other features• Diagnostic Map

– Shows key indicators of developmental learning

• Learning Activities – 3 Levels

– To develop the mathematical ideas of the KU

• Sample Lessons

– Illustrate how teachers can focus students’ attention on the mathematics during the learning activity

• ‘Did You Know?’ Sections

– highlights common understandings and misconceptions

• Background Notes

– Supplement the information provided in the KU. They are designed to help teachers develop a more in-depth knowledge of what is required for students to achieve.


Morning Tea


TASK - Ferris Wheel

• Solve with a partner

• Scootle – Home

– Improve

– Student tasks –online testing

– Online chats


Rich Tasks

Provide opportunities;

• To probe beyond eliciting the ‘correct answer’.

• For assessment, analysis and future planning

• To moderate within like year groups

• To extend


Working mathematically is emphasised in the Australian Curriculum for mathematics through the proficiency strands.

The proficiency strands are:

– Understanding,

– Fluency,

– Problem Solving, and

– Reasoning.

They describe how content is explored or developed, and the actions that students engage in when learning the content. They provide the language to build in the developmental aspects of the learning of mathematics and have been incorporated into the content descriptions of the three content strands

Proficiency Strands


• Refers to a student’s grasp of fundamental mathematical ideas

Students who learn with understanding have less to learn because they see common patterns in superficially different situations.

– (Kilpatrick and Swafford p. 10).

– Eg. Yr 3 ……identifying environmental symmetry.

UnderstandingUnderstanding


• Having the skill to perform procedures efficiently, accurately and flexibly

Includes:

– choosing appropriate methods and approximations

– recognising robust ways of answering questions

– recalling factual knowledge and concepts readily

– regularly using facts

– manipulating expressions and equations to find solutions

• Requires opportunities to practise the skills which need to be come permanent so that students can use them efficiently, accurately and flexibly.

• Also requires understanding so that procedures make sense and can therefore be used flexibly.

– Eg. Yr 7 ……calculating areas of shapes and volumes of prisms.

FluencyFluency


•Formulating problems mathematically and devising strategies to solve them using concepts and procedures appropriately

Includes:

-Making choices, interpreting, formulating, modelling and investigating problem situations and communicating solutions effectively.

-Familiar and unfamiliar situations

-Verifying that answers are reasonable

-Designing investigations

– Eg. Yr F ……sorting objects.

Problem Solving


Logical thought and action.

Includes:

• analysing proving, evaluating, explaining, justifying

and generalising

• adapting the known to the unknown

• proving something is true or false

• transferring learning from one context to another

– Eg. Yr 6 ……explaining the transformation of one shape into another.

Reasoning


TASK

• Highlight measurement and geometry content within the proficiences.


TASK – What proficiency is being assessed?

From the selection of problem cards – work with a partner to identify:

1. What strand does the task relate to?

2. What sub-strand does the task relate to?

3. What year level would the task be appropriate for? Why?

4. What proficiency/proficiencies are being assessed?

5. Does the problem constitute a ‘rich task’-why/why not?


Numeracy or Mathematics?

numeracy ≠ mathematics

Numeracy encompasses the knowledge, skills, behaviours and dispositions that students need to use mathematics in a wide range of situations.


LUNCH


The Polygon Song


More Activities…1. Making an Angle Wheel

Use 2 different coloured circles. Fold both circles to find the radii. Cut along the radii of both circles. Push circles together to make the angle wheel.

The underneath circle can be rotated slowly through the ‘on top’ circle to demonstrate an ever-increasing angle being created. Acute, obtuse or reflex?

2. Hexagons

By combining 2 pattern blocks at a time, create a collection of hexagons.

How many in a given time? Consider flip, turn etc.

3. Tessellations

Use pattern blocks to find out which shapes will tessellate. Which shapes will? Why?

How do you make a tessellation from an irregular shape? Start with a regular shape and turn.


What makes a good Assessment Task?• Open ended

• Inform teaching and planning cycle

• Opportunity for a range of info and learning

• Feedback to students

• Achievable but challenging

• Relevant to students - context

• Motivating

• Easy to administer and record

• Able to be differentiated

• Clear focus

• Displaying proficiencies

• Accessible and inclusive


Diagnostic Tasks for Measurement and Geometry

• Diagnostic Tasks provide analysis and diagnosis, at point of error. They are designed specifically, to provide teaching focus for:

– individual students (partial concepts, misconceptions)

– teaching content-deciding on the maths needed to move students on.

• They help to make judgments about students’ existing understanding of mathematical concepts. The tasks can be administered to individual students, small groups or a whole class.

• Diagnostic Tasks relate directly to Key Understandings and teaching content within First Steps.

• GNS – Reference http://geraldtonnumeracystrategy.edublogs.org/


General Capabilities


Using Digital TechnologiesGeneral Capabilities - Information & Communication Technology

• Students develop ICT capability when they investigate, create and communicate mathematical ideas and concepts using fast, automated, interactive and multimodal technologies.

• They employ their ICT capability to perform calculations, draw graphs, collect, manage, analyse and interpret data; share and exchange information and ideas and investigate and model concepts and relationships.

• Digital technologies, such as spreadsheets, dynamic geometry software and computer algebra software, can engage students and promote understanding of key concepts.


Mathematics Digital Resources

• Mathematical ideas have evolved across all cultures over thousands of years, and are constantly developing. Digital technologies are facilitating this expansion of ideas and providing access to new tools for continuing mathematical exploration and invention.

• Scootle provides digital resources for teachers and students. Many of the resources in Scootle match the Australian Curriculum content descriptions.

• Scootle Tour


Australian Curriculum Glossary

Australian Curriculum Glossary

Online Dictionary http://www.amathsdictionaryforkids.com/dictionary.html

Australian Mathematical Sciences Institute on SCOOTLE AMSI


Metric Units and Calibrated Scales

• KU 7&8 in UU refer to standard units in the metric system pg. 11

• KU 3 &4 in DM refer to the instrument we use and calibrated scales pg.93

• Relationship between units pg.78

Sample Lesson 4 pg. 88

Did You Know? pg. 90


Questions and Answers

• Review and Reflection

• Where to from here?

• Obligation - School Commitment


Thank you for attending

leading the australian curriculum: mathematics presented by linda spicer martine thurkle

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