Junior School

Junior School Computer Room 30 Computers - IWB

It is an understatement to say that Learning is enhanced through the use of technology.

In mathematics we use technology for:

• games and drills to aid instant recall of facts

• practice in computation

• explaining geometrical and measurement principles

using the vast resources of the Internet and commercially produced educational software

“The integration of technology across the curriculum has become a major priority for educational

authorities and schools over the last decade;

this is more recently seen as essential for giving young people the understanding and skills necessary

to compete in an ever expanding, knowledge-hungry world.” (John Raiti)

It's about Culture: How to Really Integrate ICT

Australian Teacher Magazine Article

http://icttaskforce.edna.edu.au/icttaskforce/Jahia/home/inspired

A new personal computer for all students Yrs 9 -12

“However, this alone will not encourage teachers to use the new technology in the most productive way.”

(John Raiti)

Now more than ever, are teachers and students challenged to use existing ICT programs for

discovery and mathematical insights.

Australia’s New Government Computers for Students

Australian Secondary Schools Computer Fund

http://icttaskforce.edna.edu.au/icttaskforce/Jahia/home/inspired

Our aim is :• to get young minds excited about making their own -------- discoveries in mathematics and

• to encourage students to tell us about these -------- discoveries

The Spreadsheet

is an excellent tool for doing this

+ An Interactive Whiteboard

= A Winning Combination

“Mathematics is a tool with which God created the Universe.”

Galileo Galilei 1564 - 1642

Spreadsheets are now more available to 12 year olds.

You might ask “Why 12 year olds?”

If you’ve ever had a problem with your TV remote or DVD player, as the saying goes, “Ask a 12 year old.”

They’ll fix it for you!

Numbers can seem ordinary at first but …

What interesting patterns we can find in them!

Then they become more fascinating to students.

Getting young minds excited about their discoveries in Mathematics is what we are about.

How to do this?

Pythagoras concluded that there are only

Four Important Areas of Mathematics

The Quadrivium of Mathematics

Discrete Continuous

The AppliedThe Absolute The Static The Moving

Arithmetic

4 + 2 = 6

Music Geometry Astronomy

This is the focus of our presentation today using spreadsheets

Even though spreadsheets have not been used much

resources for them have been available for quite some time.

Two excellent books are:

Switched on Maths - Spreadsheets in Maths

Dr Ann Williams – Griffith University in Brisbane

“The power of spreadsheets lies in their capacity to take the students beyond what they can achieve within the normal classroom with

pencil and paper.”

Spreadsheets permit the exploration of relationships, thus presenting opportunities

for higher order thinking skills.

Bloom’s TaxonomyBloom’s Taxonomy

• Developed by Benjamin Bloom in the 1950’s as a means of Developed by Benjamin Bloom in the 1950’s as a means of expressing qualitatively different kinds of thinking:expressing qualitatively different kinds of thinking:

• RememberingRemembering,, UnderstandingUnderstanding,, ApplyingApplying, , AnalysingAnalysing, , EvaluatingEvaluating and and CreatingCreating..

• Lorin Anderson (former student of Bloom) revised the Lorin Anderson (former student of Bloom) revised the taxonomy in the 1990’s and made a number of changes. taxonomy in the 1990’s and made a number of changes.

• Note that in this presentation, I am using the Anderson’s Note that in this presentation, I am using the Anderson’s terms, but Bloom’s original order.terms, but Bloom’s original order.

Evaluating Justifying a decision or course of actionJustifying a decision or course of action

Checking, hypothesising, critiquing, experimenting, judgingChecking, hypothesising, critiquing, experimenting, judging

CreatingGenerating new ideas, products, or ways of viewing thingsGenerating new ideas, products, or ways of viewing thingsDesigning, constructing, planning, producing, inventing.Designing, constructing, planning, producing, inventing.

   Analysing

Breaking information into parts to explore understandings and relationshipsBreaking information into parts to explore understandings and relationshipsComparing, organising, deconstructing, interrogating, findingComparing, organising, deconstructing, interrogating, finding

  Applying

Using information in another familiar situationUsing information in another familiar situationImplementing, carrying out, using, executingImplementing, carrying out, using, executing

  Understanding

Explaining ideas or conceptsExplaining ideas or conceptsInterpreting, summarising, paraphrasing, classifying, explainingInterpreting, summarising, paraphrasing, classifying, explaining

  Remembering

Recalling informationRecalling informationRecognising, listing, describing, retrieving, naming, findingRecognising, listing, describing, retrieving, naming, finding

  

BLOOM’S TAXONOMY

Higher Order Thinking Skills

Lower Order Thinking Skills

Spreadsheets are under-utilised in Mathematics

Our 12 year olds have very limited knowledge

Writing of formulas is new to them

In 2008 we upgraded to Microsoft Office 2007

It has a very different menu system to 2003 version

First task: Teach the new screen features of Excel

We did this using the Interactive Whiteboard

Title BarQuick Access toolbarOffice Button

Title BarQuick Access toolbarOffice Button

Brackets ofX

+

20

9

26

36

8

3

11

3

20

9

26

36

8

3

11

3

L4

M5

K3

M6

M5

M3

M4

= B6 - B5653

= B6 - B5

Spreadsheets do the computational hard work while

students concentrate on exploring and discovering.

1. Click on A1 and drag to cell O12. Drag down to row 253. Use ‘page’ colour to colour the whole page.4. Use a text box to make the heading “Number Patterns”5. In B8 type ‘Number’, C8 type ‘2x table’, C9, 3x table etc 6. In B9 type 1. Click on the corner and drag down to B107. Click on the + sign and highlight the ‘Fill series’8. Drag down to number 15.9. In C9 type ‘ = B9*210.Drag the corner down 15.11.Repeat for all the other tables.12.Highlight C9 to M9 and click on the ∑ symbol13.Repeat for all the rows14.At C24 type sum and drag the cell across to O2415.Do the same for all the columns down

Instructions for the Product Chart

Number 2x Table 3x Table 4x table 5 x table 6x table 7x table 8x table 9x table 10x table 11x table 12 x table Sum1 2 3 4 5 6 7 8 9 10 11 12 772 4 6 8 10 12 14 16 18 20 22 24 1543 6 9 12 15 18 21 24 27 30 33 36 2314 8 12 16 20 24 28 32 36 40 44 48 3085 10 15 20 25 30 35 40 45 50 55 60 3856 12 18 24 30 36 42 48 54 60 66 72 4627 14 21 28 35 42 49 56 63 70 77 84 5398 16 24 32 40 48 56 64 72 80 88 96 6169 18 27 36 45 54 63 72 81 90 99 108 693

10 20 30 40 50 60 70 80 90 100 110 120 77011 22 33 44 55 66 77 88 99 110 121 132 84712 24 36 48 60 72 84 96 108 120 132 144 92413 26 39 52 65 78 91 104 117 130 143 156 100114 28 42 56 70 84 98 112 126 140 154 168 107815 30 45 60 75 90 105 120 135 150 165 180 1155

sum sum sum sum sum sum sum sum sum sum sum sum240 360 480 600 720 840 960 1080 1200 1320 1440 sum

Number Patterns

Draw lines to show patterns

The best teachers are The best teachers are those who equip those who equip students to THINK for students to THINK for themselves.themselves.

Powerful learning does Powerful learning does not occur by accident, not occur by accident,

it is usually the result it is usually the result of an effective learning of an effective learning situation created by a situation created by a skilful teacher.skilful teacher.

(Joyce & Showers, 1991)(Joyce & Showers, 1991)

Questions

• Do the work responses of the students demonstrate a deep understanding of the concepts or Ideas?

• Does classroom talk lead to sustained conversational dialogue between student and teacher and between student and student to enhance understanding of the topic at hand?

• Is the lesson connected to a focus on identifying and solving real world problems?

Better a thousand days Better a thousand days of diligent study, of diligent study, is one day with a great is one day with a great

teacher. teacher. (Japanese Proverb)(Japanese Proverb)