DES –TIME 2006 Hildegard Urban-Woldron EXPLORING MATHEMATICS AND PHYSICS CONCEPTS Using TI graphing calculators in conjunction with Vernier Sensors Dr

DES –TIME 2006 Hildegard Urban-Woldron

EXPLORING MATHEMATICS AND PHYSICS CONCEPTS

Using TI graphing calculators in conjunction with Vernier Sensors

Dr. Hildegard Urban-Woldron

T³ Österreich


2DES –TIME 2006 Hildegard Urban-Woldron

• INTRODUCTION

• RESEARCH QUESTIONS AND THEIR METHODICAL

BASIS

• TASKS AND PRACTICAL EXPERIENCES IN THE

CLASSROOM

• EVALUATION, ASSESSMENT AND DISCUSSION



• APPS - powerful technological tools

• explore, discover and extend mathematical ideas

• GC - IT-platform

– Vernier sensors for collecting various data

– GC for analyzing and building models

• impact of new technologies

INTRODUCTION


• software tools - students’ mathematical thinking

• educational potential of connecting Mathematics and

Physics

• effects of analyzing real world data

• ask own questions and explore them

• gain insight into the individual student’s perspective

RESEARCH QUESTIONS AND THEIR METHODICAL BASIS


• Students’ behaviour in the learning environment

• analyze the data both algebraically and graphically -

associate these relationships with mathematical

functions

• Do the offered tasks support reactive, active or pro-

active learning?

• The impact of the teacher’s behaviour on the learning

efficiency of the student

RESEARCH QUESTIONS AND THEIR METHODICAL BASIS


• EASYTEMP, EASYLINK, CBR 2

– in combination with the GC

– offer a learning environment for

– experimenting, modelling, analyzing and visualizing real world data

• Students are asked

– to explore the situations

– make conjectures and

– finally prove them

TASKS AND PRACTICAL EXPERIENCES IN THE CLASSROOM


• measure the movement of the ball

• describe it as a function of time

• and derive the gravity law

• time-distance graphs are parabolic functions

• The maximum height decreases from bounce to

bounce

ACTIVITY 1: THE BOUNCING BALL

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• highest speed of the ball

• acceleration during falling

• model to describe the height of the ball for a particular bounce

• total distance of the ball

• velocity change as the ball rises and falls

• What affects the shape of the graph of both the height and the velocity?









ACTIVITY 2: AIR UNDER PRESSURE – BOYLE’S LAW




• What kind of relationship exists between volume and pressure?– A quadratic function (parabola as graph)? – An exponential function?– A power function or a hyperbolic function?



for 20 ml the pressure was almost 102 kPa

.constVp



ACTIVITY 3: NEWTON’S LAW OF COOLING

What determines the cooling process?



?






Newton’s law of cooling

tkR eTTT 0

tR aTTT 0or

Students try to fit the temperature functions above to the actually measured curve by adjusting the parameters k and a.



• Has the starting temperature of the hot water any impact on the

value obtained for a?

• What could you do to your experimental apparatus to decrease

the value of k in another run? What quantity does k measure?

• If your starting temperature difference is cut in half, does it take

half as long to get 1°C above room temperature? Why or why not

does it take half as long?

Extensions – research questions



• simple questions motivated

– to a rich discourse and activity in the classroom

– and further exploration

• lessons involved multiple stages of investigation

– prediction, testing, rejection or extension of hypotheses

– discovering and exploring the underlying mathematics

– making generalizations and proving results

EVALUATION, ASSESSMENT AND DISCUSSION


• technology in the classroom especially supports the active, self-controlled and self-motivated student

• challenge for the teacher – embed technology tools in the general syllabus

– and into the class room

– substantial change in the learning process

– active, individual construction of knowledge

– guidance - room for individual exploration

EVALUATION, ASSESSMENT AND DISCUSSION

Documents

DES –TIME 2006 Hildegard Urban-Woldron EXPLORING MATHEMATICS AND PHYSICS CONCEPTS Using TI graphing calculators in conjunction with Vernier Sensors Dr