Key Teacher in NumeracyDay 4

The Four Winds PrayerBuilding Positive Partnerships with Parents

Looking deeply into Space, Measurement, Chance and Data

Statistics and Probability

OrChance and Data

Why is Chance and Data important?

Informed citizens need to be numerate in data and chance and need to know

how to decipher and make sense out of information that is presented in

newspapers, medical reports, consumer reports and environmental studies.

Shaughenessy, 2002

People numerate in Chance and Data

• Recognise and understand the part chance plays in everyday life

• Recognise and interpret estimates of chance events

• Judge the quality and appropriateness of data collection

• Understand and use common methods of summarising and displaying data

• Make and question judgements based upon data presented

• Make predictions based upon data presented

The language of Chance

Working in a group of 6 or more people, rank the chance statements on your table from least possible to

most possible.

Be prepared to explain and justify your decisions!

After Morning Tea please meet on the grassed area where

the playground equipment is behind the car park.

Establishing Positive

Relationships with Parents

Reasons to run a Parent Evening

Parents often had less than positive experiences with maths when they were at school and are anxious to avoid this for their children.

This anxiety can often be expressed in ways which are problematical and difficult to deal with when you have a class waiting for your attention or feel outside your comfort zone.

Organisation

Set a time when most parents will be available to attend.

Perhaps have the children make the invitations.

Arrange tables and chairs, tea and coffee. Make it relaxed.

Organise some child care.

Practicalities

Have lots of photographs of children doing maths.

Start with a general introduction then break into groups as for tabloid sports.

Teachers volunteer to lead short sessions (10 minutes is plenty) on an activity they particularly enjoy and feel comfortable doing. Make sure there are ample copies of each activity, and sufficient materials.

Beware!

There is a temptation to ask if there are any questions but this is not a blood sport!

There will be opportunities for people to ask questions as they move around the ‘stations’.

Be prepared to pass any difficult questions over to the leadership team.

Suggestions for topics in introduction

How maths is taught todayUse of calculators

Mental ComputationEmphasis on Problem Solving

Less emphasis on written work

Recent changes in mathematics teaching

• Emphasis on problem solving, explaining, Emphasis on problem solving, explaining, reasoning and justifyingreasoning and justifying

• Learning by doing, talking, drawing and Learning by doing, talking, drawing and writingwriting

• Decreased emphasis on formal written Decreased emphasis on formal written methodsmethods

• The Australian Curriculum has four The Australian Curriculum has four Proficiency Strands – reasoning, fluency, Proficiency Strands – reasoning, fluency, understanding and problem solvingunderstanding and problem solving

They enhance children’s understanding

• Listening to children

• Valuing their methods of solving problems

• Praising their efforts

• Using appropriate prompts – enabling and extending – so they may begin work

What are your memories of school maths?

Heavenly? Or Horrible? Couldn’t wait to get there”? Or

Couldn’t wait to get away? What do you want for your child?

What differences have you noticed through your recent experiences with your own children?

Why are things different today?What do teachers want for the children they

teach?

Maths teaching - then and now.• Many people came through school when mathematics consisted

of a collection of facts and skills to be memorized or mastered by a relatively homogeneous group of students taught using a lecture approach.

• Now teachers are called on to teach new, more challenging mathematics to a very diverse audience using active learning approaches designed to develop understanding.

• A constructivist approach.

• Teaching for understanding - real understanding and the ability of students to make connections and use, and build upon, their knowledge.

Types of calculations used in everyday life

200 volunteers recorded all computations over a 24-hour period

• 84.6% involved some form of mental, written (11.1%), calculator use (6.8%), or other objects (19.6%)

• Almost 60% required only an estimate

• 24.9% involved time and 22.9% involved shopping

• 47.9% inside the home, shops (18%), cars (9.1%), entertainment (4.6%)

• 45.7% involved addition, 42.5% subtraction.

(Northcote & McIntosh, 1999, APMC, 4(1), 19-21)

How do teachers support children’s learning in mathematics?

• Building understanding• Making connections• Fostering fluency • Encouraging generalisations• Using multiple representations• Explaining• Building upon prior knowledge

Calculator Task – Number Buddies

• You need a partner, a calculator, a piece of paper and a pen/pencil.

• Work in pairs, with one calculator.• One person puts a two digit number into the

calculator.• The other person has to enter another

number so that it will sum to 100• Keep a record of your sums.• Discuss strategies.

Why develop estimation skills?

• Estimation is important in everyday life.• It is is an integral part of number sense.• Focused estimation tasks will help to create a

culture in the primary classroom where maths is supposed to make sense

• Estimation needs to be seen as a valuable strategy choice

• Students will begin to talk about “Is it reasonable ?” when doing exact calculations.

Supporting your child and the school

CommunicationBeing positive about schools and teachersDoing fun everyday maths activities as a

family (e.g., when playing games, cooking, travelling, shopping, etc.)

Asking your child’s teacher: “What can I do to help?”

What can you do?

• Think about what you already do.

• Praise effort and try not to criticise errors.

• People learn largely by working things out for themselves. Ask your children, “how would you work that out?”

• In maths situations involving the family, give children time to think and time to answer before telling them what to do.

Measurement

Measurement…has its roots, both historically and in individual

development, in significant everyday activity. Thus it can develop in the

earliest years from children’s experiences….Further, it spans and

connects mathematics and other sciences and thus can ideally integrate subject matter area.

Clements, 2003

People numerate in Measurement -

• Use the language of measurement appropriate to the task

• Choose and use measuring tools and instruments appropriate to the task

• Use estimation techniques• Use measurement techniques to solve

problems• Recognise that some measures are obtained

by combining two or more other measures

Measurement

Measurement involves comparing an amount of the attribute to be measured with a quantity of that attribute chosen as a unit in order to provide a number.

…a process that allows people to quantify the world.

`Teaching Primary Mathematics Booker, Bond, Sparrow and Swan

From the research

Learning sequence for measurement

• Identifying the attribute

• Comparing and ordering

• Non-standard units

• Standard units

• Applications

Measurement Language

• Comparative statements – shorter, taller etc• Confusion between volume (the amount of

space taken up by an object) and capacity (the amount it can hold)

• Discussion builds students’ conceptual and procedural knowledge of measurement and gives teachers valuable information for reporting and planning next steps. (Principles and Standards for School Mathematics, 2000)

Historical aspects of measurement

Hands to measure horses?Calendar (why is October the tenth month

when octo means eight?)A yard or a yardstickThe metric system – metron (Gk to

measure)Leagues and fathomsRods

Metric Prefixes

• Milli one thousandth

• Centi one hundredth

• Kilo a thousand

• Mega a million

Geometric Measures

• Length – 1D concept related to direction and line. Includes length, width, depth, thickness, nearness of objects, perimeters.

• Area – 2D concept related to the region enclosed by a plane shape. The use of formulae to calculate areas of common shapes is the appropriate final stage of the learning sequence.

• Volume and capacity – 3D concept

Common physical measures

• Mass – the measure of the inertia of an object. Mass may not be proportionate to volume. (Weight is the force gravity exerts on an object)

• Time- includes duration, sequence and order in time, clock face reading

• Temperature

Common physical measures ctd

Money and value• value of coins and notes• recognise the coins and notes• count money• know that cents require two-digit numeration

(Calculators truncate the final zero)• know that dollars require full numeration

system (no spacing)• rounding money amounts

Some Measurement activities to try

Piggy Bank Coins Game

Make a Skeleton

TIME Loop

Travel to the Moon

Space

GEOMETRY – ‘earth measuring’.

‘The overall aim of geometry teaching in the primary school, along with the development of a positive attitude, interest and enjoyment, is to equip children to use spatial ideas and

knowledge to complete practical tasks and solve a wide range of everyday

practical problems.’Booker, Bond, Sparrow and Swan Teaching Primary Mathematics

Spatial Sense and Spatial Reasoning

Spatial sense – children’s awareness of themselves in relation to people and objects around them (visual geometry).

Spatial reasoning – the ability to ‘see’, inspect and reflect on spatial objects, images, relationships and transformations.

People who are numerate in Space

• Recognise and describe common shapes• Use shapes appropriate to the task• Choose and use appropriate equipment for a

particular purpose• Recognise and interpret the conventions of

visual representation• Use spatial techniques to solve problems

Visual Geometry

• Informal• Using space, shape and form at a

personal level (eg designing a garden)• Could be interpreting a map, rearranging

objects, sketching a picture, playing with blocks, doing a jigsaw, using tangram pieces or pattern blocks

• Language tends to be natural and informal

Formal Geometry

• Objective• Language and representation is more

accurate• Highly structured and much less intuitive• Theorems and facts can be proven• Prerequisite for engineering, science,

technology

Language

• Language helps children to communicate their ideas and knowledge to others

• Helps them to develop and connect meanings and relationships

• Beware of putting so much emphasis on the development of geometric language that meaning is lost

• Language builds connected ideas

Language can be confusing!

• Two Irishmen were standing at the base of a flagpole looking up.• A blonde walked by and asked them what they were doing.• Paddy replied, "We're supposed to be finding the height of this

flagpole, but we don't have a ladder."The blonde took out an adjustable spanner from her bag, loosened a few bolts and laid the flagpole down.

• She got a tape measure out of her pocket, took a few measurements, and announced that it was 18 feet 6 inches.

• Then she walked off.

• Mick said to Paddy, "Isn't that just typically like a blonde! We need the height and she gives us the length."

Words out of context

• Regular and irregular

• Right and left angles

• Decagon, pentagon etc but what about quadrilateral and triangle?

• Trapezium and trapezoid?

• Similar and congruent?

Three Fundamental Strands

• Shape and structure – the 2 and 3D objects and the relationships between shape, structure and function

• Transformation and symmetry – changes of position, orientation, size and shape and symmetries in shapes and arrangements

• Location and arrangement – the representation of position and arrangement including the use of coordinates.

Map Activity

Work with a partner.

Use your photocopied map to first locate the Catholic Education Office and note its coordinates.

Write some instructions for your partner to find another location on the map. Give directions but not the coordinates.

Swap and see how clear your directions were!

Working with shape and space

Visualising spatial arrangements Communicating orally and in writing Drawing and making models Thinking logically Applying geometrical concepts and

knowledgeIn your table groups suggest a few activities you

might use to develop each of these aspects.

Federation Square in Melbourne

• Triangles are based on a 2x1 rectangle cut in half diagonally.

• Explore how you can make bigger triangles using 2, 3, 4 or 5 of them – it is the only one that works with 5. A special case.

• Draw a triangle. A hexagon. Discuss.

Take a Kindy square

• Take a kindy square, Fold it in half diagonally and cut it.

• With two triangles how many different shapes can you make (join on a whole side)

• Use four triangles – now how many different shapes can you make with a join on a whole side?

• With four triangles how many shapes can you make which join on one side, must meet at a corner but sides may be different lengths. Have you found them all? How do you know?

Incorporate these into your planning

Research recommends incorporating opportunities to:

• Explore and investigate• Experience a variety of activities• See a range of sizes and orientations of

shapes• Use a wide range of materials• Describe activities and relationships• Build new connections and develop new ways

of thinking

Quadrilateral Sort

Cut out all of the quadrilaterals on the sheet.

Sort them into groups.Now work with a partner. Can you work

out what their criteria for sorting was?Can they work out what your criteria

was?

Try some Space activities

PentominoesAngle LoopsTangrams

Angle MachinesMatchstick Puzzles

4 by 4 grid on the floorSoma Cubes

Mira

Where to from here?

• What do we hope to achieve with CC?• How will we organise the Networks?• Who will host the meeting in second

term?• How will the Agenda be decided?• What content will be included?• What roles need to allocated?

Review of 2010 – set goals for 2011

Reflection – in your Journals jot down your thoughts on this year in regard to your classroom teaching and your role as KTN. Consider both challenges and successes.

Goal Setting – formulate and then write your goals for the next year. Think about Personal Goals, teaching Goals, your goals as a KTN.