crossing a new the border - rfdzrfdz.ph-noe.ac.at/.../pineau_flores_gomes_chavez.pdf · crossing a...
TRANSCRIPT
L’HOSPITAL’SWEIGHTPROBLEMCrossing a new the Border
…into MexicoK AT H L E EN P I N EAUÉ c o l e d e t e c h n o l o g i e s u p é r i e u r e
H OM E R O F L O R E SU n i v e r s i d a d N a c i o n a l A u t ó n om a d e M é x i c o
F R AN C E C A R ONU n i v e r s i t é d e M o n t r é a l
AD R I A N A G ÓM E ZU n i v e r s i d a d N a c i o n a l A u t ó n om a d e M é x i c o
X O C H I T L C H ÁV E ZU n i v e r s i d a d N a c i o n a l A u t ó n om a d e M é x i c o
Outline
� Theoriginalweightproblem� Theactivity� ItsadaptationanduseinMexico� Observations� Conclusions
From Bernouilli to L’Hospital
To introduce differential calculus…
The activity and its variations
� Initiallyenvisionedforhighschool÷Hands-onactivity÷Synthesisofknowledge
� DesignedforthetransitioncourseatÉTS(engineeringschool)÷Byphysicslecturer,mathlecturer,andmatheducator÷Reviewofsecondarymathematics(trig),leadingtocalculus÷ Introductiontomodelling
� Reusedatthecollegelevel÷ Inbothpre-universityandtechnicalprograms
� Shortenedandusedinhighschool(Montreal&Mexico)
� Teamsof2or3� Eachteamhad
¡ itsownapparatus¡ measuringinstruments¡ symboliccalculators(TINspire – CAS)
@ÉTS
Overview of the (whole) Activity
1. Exploration2. Constructing Equations
3. Verification
4. Prediction
5. Validation6. Revisiting intuitions
Variation for Mexico
2. Constructing Equations3. Verification
CCH, UNAM & IPN • bachillerato: 15 to 17 year-olds• groups of about 25 students, • in 2nd or 4th semesters• 2 or 3 teachers participated in the activity each time
Teamsof3to5students2apparatuswithmeasuringtapesEachteamhaditsowncalculator(phone,…)
CCH – SurIPN
Solution AnalysingInterpretingValidating
Math.Model
Mathematising
Knownmodels
DataCollection
Problem
Realmodel
The Modelling Cycle (adapted from Blum & al., 2002)
StructuringSimplifyng
A certain situation
PurposeInterest
Doing themathematics
Math.results
Solution AnalysingInterpretingValidating
Math.Model
Mathematising
Knownmodels
DataCollection
Problem
Realmodel
The Modelling Cycle (adapted from Blum & al., 2002)
StructuringSimplifyng
A certain situation
PurposeInterest
Doing themathematics
Math.results
Where do the differences, between the quantities that were measured and those that were calculated, come from?
“las medidas son una predicción y lo calculado es exacto”
The Student’s Perspective
The Student’s Perspective
What Iliked What Ididn’tlike• Theory put in practice. Application
in real life. • Manipulation. Concrete, visual.
Interactive. • History.• Different approach than physics.• Learning Guide. Progressive
approach.• Possibility to review and
understand, to validate and self-correct.
• Team dynamics.• Visiting teacher. More than one
teacher during the activity.
• Measuring.• Time constraints.• Team dynamics.
My team didn’t cooperate. My team didn’t communicate enough.
• My profs at CCH do not usually have us do this type of activity.
• Formulas were difficult to find.
The Student’s Perspective
WhatIlearned What remains unclear
• Relationships between variables, between side lengths and angles.
• That we can validate our work mathematically.
• Trigonometric functions. Pythagoras’ theorem. The cosine property.
• To find formulas and to measure.• To substitute in order to find values.• To think(due to the difficulty of finding formulas.)
• Reviewed themes from math and physics.
• Properties of sine and cosinefunctions.
• Why there are differences between what is measured and what is calculated.
Observations
� Acknowledgethatthemodelisasimplified(imperfect)representationofarealsituation;todiscussassumptions,limitations,…
� Valueotherdisciplinestorevisitassumptions.
“When we deduce or find a formula and apply it, we can see if the formula is correct or not.”
Observations
Scaffolding¡Physical– structureoftheactivity– iskey
÷toempowering students÷toavoid theirstraying toofarawayfromcoursecontent
¡Natural– teamwork(Vigosky)÷empowersstudents÷empowersprofstodevelopandtryactivities
¡Technologyasscaffolding
Conclusions
� ModellingwouldbenefitfromInstitutionalisation� Institutionalisationwouldbenefitfrommodelling
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