technology in science & math instruction presented by yasumasa shigenaga, kara johnson, kathie...

TECHNOLOGY IN SCIENCE & MATH INSTRUCTION

Presented by

Yasumasa Shigenaga, Kara Johnson, Kathie Kehl

Introduction

"We should all be concerned about the future because we will have to spend the rest of our lives there." Charles Francis Kettering, Seed for Thought, 1949

The use of technology in math and science instruction enables:

Accuracy of diagrams, illustrations Display animations and movements Enhances interest and motivation Nurtures autonomy in learning Changes outcomes more easily Saves time and prevents mistakes

Cautions & Constraints

Classroom Management Time Constraints Technical Difficulties Monitoring use and abuse Monetary Technical Support Availability Adequate Teacher Training

Technology in High School Science

Technology integrated into the high school classroom Authentic learning experiences

Edutopia.org Compare text to technology

Studio Daily Cell video

Technology in Elementary Science Water Cycle

Diagrams/animations: EPA.gov Earthguide.ucsd.edu Sweetwater.org

Animals Video: National Geographic Kids

Values of a, b & c in quadratic functions and their graphs

Lesson plan prepared by Mr. Katsuhisa Tomoda(math teacher at Osaka Kyoiku University Ikeda High

School; http://www.criced.tsukuba.ac.jp/grapes/)

In the quadratic function y=ax2+bx+c, what relationship exists between the values of a, b & c and the shape of the graph?

Value of a and the graph

In the quadratic function y=ax2+bx+c,how does the value of a influence the shape of the graph?

#2

x

y

O

Value of a and the graph (cont.)

When you change the value of a in y=ax2+bx+c,

the width and the direction of the graph changes. Therefore, the value of a signifies the width and the direction of the graph.

x

y

Oa = 0.5

a = 1

a = 2

a = 0.5

a = 1

a = 2

Value of c and the graph

In the quadratic function y=ax2+bx+c,how does the value of c influence the shape of the graph?

#4

-1 1 2 3 x

-2

-1

1

2

y

O

Value c of and the graph (cont.)

When you change the value of c in

y=ax2+bx+c,

the graph moves upward or downward without changing its shape.

The value of c signifies the y intercept.

-1 1 2 3 x

-2

-1

1

2

y

O

c = 2

c = 1

c = 0

c = 1

c = 2

Value of b and the graph

In the quadratic function y=ax2+bx+c,how does the value of b influence the shape of the graph?

#6

-2 -1 1 2 x

-2

-1

1

2

y

O

Value of b and the graph (cont.)

When you change the value of b in

y=ax2+bx+c,

it is not entirely clear what the value b signifies.

-2 -1 1 2 x

-2

-1

1

2

y

O

Value of b and the graph (cont.)

In y=ax2+bx+c,

let’s find a property that does not change even when the values of a and c are changed.

#8-2 -1 1 2 x

-1

1

2

3

y

O

Value of b and the graph (cont.)

When you change the value of a in

y=ax2+bx+c,

the graph always touches a straight line.

Let’s examine the relationship of this line and the quadratic function.

#9

-2 -1 1 2 x

-1

1

2

3

y

O

Value of b and the graph (cont.)

When you substitute 0 for a in

y=ax2+bx+c,

the straight line

y=bx+c is obtained.

Therefore, the value b signifies the slope of the tangential line on the y axis.

-2 -1 1 2 x

-1

1

2

3

y

O

a = 2a = 1

a = 4

a = 4

a =

a = 2

a = 1

y = b x + c

MathType 6

Compatible with Vista/XP/Macs Compatible with Word (2007 & older) Free for 30 days

and then it reverts to MathType Lite—with Equation Editor, fonts, & symbols

$97 ($57 academic) http://www.dessci.com/en/products/

mathtype/default.htm

MathType 6

Features and Benefits Fonts, symbols, templates Ingrates tabs and toolbars in many

applications (including Word, Powerpoint, and Excel)

Can add equations into virtually any application

Quick and automatic reformatting of equations

WebEQ

Interactive math on webpages Compatible with Windows (XP and older,

not Vista) and Macs Free for 30 days $495 ($99 academic) http://www.dessci.com/en/products/

webeq/

WebEQ

Editor for creating equations Publisher—can create:

an entire HTML page MathML Images Applet tags

Interactive WebEQ controls: Input, viewer, graph, evaluate

WebEQ

Drawbacks: Needs MathPlayer, WebEQ Viewer Control,

or Java installed to display MathML Not compatible with Vista Not intuitive (although there is a solutions

& examples section)

Technology in Science Instruction

Web Resources Collaborative Online Projects http://www.ciese.org/collabprojs.htmlScience News for Kids http://www.sciencenewsforkids.org/Internet into the curriculum http://www.cyberbee.com/intclass.htmlHistory of Science & Technology http://www.fi.edu/learn/sci-tech/ABC News Science & Technology http://abcnews.go.com/Technology/

Technology in Math Instruction

Enchanted Learning: http://www.enchantedlearning.comIlluminations: http://illuminations.nctm.org/Interactive: http://www.shodor.org/interactivate/activities/Grapes: http://www.osaka-kyoiku.ac.jp/~tomodak/grapes/ Online applications that appear particularly interesting:Mars Earth Orbit: http://illuminations.nctm.org/ActivityDetail.aspx?ID=119Grapes: http://www.osaka-kyoiku.ac.jp/~tomodak/grapes/