Welcome Who am I? Robyn Holder X3447 rholder@aes.ac.in Parent - - PowerPoint PPT Presentation

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Welcome Who am I? Robyn Holder X3447 rholder@aes.ac.in Parent - - PowerPoint PPT Presentation

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Welcome Who am I? Robyn Holder X3447 rholder@aes.ac.in Parent Workshops this Year September 22, 2011 Erma Anderson parent workshop video available for check out in library 10/12/2011 October 12 and 17, 2011 Workshop with

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  • Who am I?

Robyn Holder X3447 rholder@aes.ac.in

Welcome

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Parent Workshops this Year

  • September 22, 2011 – Erma Anderson parent workshop –

video available for check out in library

  • October 12 and 17, 2011– Workshop with Robyn Holder
  • November 4th, 2011 – morning coffee ‐ Math / Tech Home

Learning

  • February 2nd, 2012 – Erma parent workshop (focus TBD by

December)

  • March ? – Workshop with Robyn Holder
  • April 12, 2012 – morning coffee ‐ Math / Tech workshop on

summer learning

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Resources

  • A Maths dictionary for kids (and parents)
  • http://www.amathsdictionaryforkids.com/dictionary.html
  • National Library of Virtual Manipulatives
  • Games and manipulatives like the ones we will use today
  • AES Glossary of terms
  • I am working on that for you
  • In the mean time take a look at:

http://www.australiancurriculum.edu.au/Mathematics/Additiona l‐glossary‐information

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Let’s Think…

  • Who loves reading?
  • Who loves math?
  • Who really understands and can make

sense of what they read?

  • Who really understands and can make

sense of math?

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I can read this…

Once upon a time a tawndy rapsig named Gub found a tix of pertollic asquees. So chortlich was he with his discovery that he murtled a handful to show Kon, a cagwitzpat. “Pagoo!” cried Kon. “With these you could treeple a frange!”. “No,” smiled Gub, “I think I’ll just paible a catwicine.”

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5 York Adult Assessment

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But do I understand?

  • NO!
  • Reading is decoding and

comprehension.

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I can do this algorithm…

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365 ‐ 187 178

5 1 2 1

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But do I understand?

  • Not necessarily…

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8 Many students appear to know more than they actually do because they are able to give the correct response or perform a calculation correctly by relying

  • n rules they do not understand (Thomas, 1996; Steinle & Stacey, 1998).

A project funded under the Australian Government’s Numeracy Research and Development Initiative and conducted by the Association of Independent Schools of South Australia

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We must teach children to understand math!

In the ES we believe:

  • all students can learn math and strive to make sense of

math.

  • students are active learners who construct their own

understanding.

  • math is most meaningful when it is authentic and

connected to the real world and everyday life.

  • math understanding progresses from concrete, to

representational, to abstract.

  • number sense is the foundation of math learning.

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Our Standards

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Guiding Question

  • How does number sense develop?

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What is Number Sense?

  • "[Number sense] is an awareness and

understanding about what numbers are, their relationships, their magnitude, the relative effect of operating on numbers, including the use of mental mathematics and estimation“

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12 Fennell and Landis’ (1994) cited Parrish,2010

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What do we know?

Number Sense develops gradually

  • Children must spend time:
  • exploring numbers
  • visualizing numbers in a variety of contexts
  • Finding relationships between numbers (not

limited by traditional algorithms)

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13 Howden, 1989 cited, Erma Anderson

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How does Number Sense Develop?

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14 Step 15 Fact Families Multiplication and Division Step 14 Develop better multiplication strategies Step 13 Early fraction ideas with models Step 12 Early division ideas Step 11 Renaming three digit whole numbers Step 10 Skip Counting Step 9 Fact Families Step 8 Patterns in the Hundreds Charts Step 7 Compensation Step 6 Conservation of numbers Step 5 Counting on Step 4 Complements of Ten Step 3 Subitising Step 2 One to One Correspondence Step 1 Rote Counting

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At School

We keep moving students up the number sense ladder:

  • One to one correspondence
  • Subitising
  • Your turn to try
  • Complements of ten

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15 1 2 3

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At School

  • Counting on
  • Conservation of Number
  • video

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3 4 5

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At School

  • Compensation
  • When working with numbers you can take an amount from one

set and add it to another set and the TOTAL will not change.

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To help children…

  • Ask children to estimate*
  • Always ask – is your answer reasonable? Does

it make sense?

  • Discuss which number is biggest*
  • Play games like guess my number using an

empty number line.

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?

100

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What is Place Value?

Understanding that:

  • Sets of ten can be perceived as a single unit (unitizing:

research shows this develops toward the end of G1)

  • The position of digits in numbers determine what they

represent

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19 (Van de Walle, 2006)

Hundreds Tens

  • nes

3 2 5

This is a place value chart.

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What do we Know?

The ability to understand and to use place value is crucial to understanding mathematics.

  • Children must spend time:
  • Counting objects and placing them in groups of tens
  • Connecting what has been done with concrete

manipulatives to visual representations and then to numbers

  • putting numbers together and taking them apart in

a wide variety of ways

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20 Australian Government’s Numeracy Research and Development Initiative and US Common Core Clarification documents

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At School

  • Helping children understand how objects can be

grouped by tens and counted

  • Helping children understand that ten can be

thought of as one group of ten or ten individual items

  • Emphasize how numbers can be broken apart
  • Model for children how breaking numbers apart

can help them to compute

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How can you break apart…

47

  • 4 ten and 7 ones (40+7 = 47) *
  • 3 tens and 17 ones (30+17 = 47)
  • 2 tens and 27 ones (20+27 = 47)
  • 1 ten and 37 ones (10+37 = 47)
  • 47 ones (47 = 47)
  • * We refer to this as expanded notation

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In KG children work on 11‐19

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In KG children work on 11‐19

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18 = 10 + 8 18 is one group of ten and 8 “ones”.

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In G1 children work on 11‐99

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In G1 children work on 11‐99

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18 = 10 + 8 18 is one “ten” and 8 “ones”.

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In G2 children work on 100‐1000

325

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325 = 300 + 20 + 5 325 is 3 “hundreds”, 2 “tens” and 5 “ones”.

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To help children

Always refer to the digits in a number by what they represent

  • 395
  • The digit 3 represents 300 or 3 groups of a

hundred

  • The digit 9 represents 90 or 9 groups of ten
  • The digit 5 represents 5 or 5 ones

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Guiding Question

  • How does conceptual

understanding of calculation develop?

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What is Conceptual Understanding?

  • Literacy is the ability to apply and use

mathematical knowledge, skills and practices, in flexible and adaptive ways.

(Willoughby, 2000)

  • Understanding is the key to remembering

what is learned and being able to use it

  • flexibly. (Hiebert, in Lester & Charles, 2004)

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10/17/2011

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Parent Session AISCH

The Bridge to Understanding

Concrete

“DOING” Stage

Repr presentation esentation “SEEING” Stage Abstract

“SYMBOLIC” Stage

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Building Mathematical Concepts

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Concrete

Manipulatives

Pictorial

Representation

Abstract Symbols

I I I I I I I I

4 + 4 = 8 2 x 4 = 8

Significant time must be spent working with concrete materials and constructing pictorial representations in order for abstract symbol and

  • perational understanding to occur.
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Let’s represent 24

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24

pictorial Expanded notation Place value chart written 20 + 4 = 24 10 + 14 = 24 2(10) + 4(1) = 24 Tens Ones 2 4

Twenty‐four

  • II. . . .
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To help children with computation

Ask your child questions

  • How did you know that?
  • Explain to me what you are doing.
  • What were you thinking about when you did

that?

  • Does that make sense?
  • Can you teach me what you are doing?
  • I’m confused… (and point out where – but

don’t say that is wrong – but see if your child can find his or her own mistakes)

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Thank you

  • You are invited to stay and ask questions.
  • Feel free to write questions on a post‐it

and stick it to the charts in the back of the room

  • I will read all of these and they will help us

as we plan forward for future parent workshops

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