Math, Science and Technology

GOAL Presentation

Christie Brown, MELS-SSCA: Christie.brown@mels.gouv.qc.ca

February 2009

MELS, QEP, 2007. p.11

Connections to the QEP

What is a Competency?

• A competency is defined as the ability to act effectively by mobilizing (using) a range of resources.

• MELS, p. 17, 2006

MELS, QEP, 2007. p.25

Weightings of the Competencies:

Competency % Competency %

Seeks Answers or Solutions to S&T problems

40% Solves a Situational Problem

30%

Uses knowledge of science and tech.

40% Uses Mathematical Reasoning

45%

Communicates using scientific language

20% Communicates using mathematical language

25%

Science Programs

General Education Path and Applied Education

Path

OPTION 2555-3066 credits

(150 hours)

555-4044 credits(100 hrs)

557-3066 credits

(150 hours)

557-4066 credits(150 hrs)

558-4044 credits(100 hrs)OPTION

558-4022 cr

(50 hrs)OPT

Cycle One Secondary III Secondary IV Secondary V

Physics4 credits(100 hrs)

Chemistry4 credits(100 hrs)

SCIENCE & TECHNOLOGY (S&T) OPTION

OPTION 1

APPLIED SCIENCE AND TECHNOLOGY (AST)

BRIDGE

Same for all

students

Approved documents are expected in Winter 2009.

Minimum to Graduate

Required to enter Pre-U SCIENCES

in CEGEP

Exams 2008-9

Competency 1: - identical App or GenScientific Method: May – June (end April)Design process: May – June (end April)

Competency 2: An example exam (Due to arrive “now?”) General Path – 3 hours on June 15th

Applied Path – 3 hours on June 15th

Physical Science 416 – this is the last year June 15th 2009.

Key scheduling points

Strongly suggested to keep same teacher with the same students for both the core course as well as the option course.

Students can not take the core course in one path (say General) and the option course of another path (say Applied)

Competency 1

This competency is identical in both paths.

This competency is developed through activities which force students to use either the scientific method or the design method.

Seeks answers or solutions to scientific or technological problems

Difference from Cycle 1?Cycle 1 said: “Chooses an investigation

or design scenario”

Competency 2Makes the most of his/her knowledge of science and technology

General Path: Grade 10

-Focuses on ISSUES analysis

Issues:- Climate Change- Deforestation- Energy Challenge- Drinking Water

MELS. General QEP, 2007. p. 46-53

Applied Path: Grade 10

-Focuses on the analysis of technical applications.

Examples of Technologies:- Medical- Transportation- Agricultural- Information and Communication

MELS. Applied QEP, 2007. p. 24

Note: The forms of analysis are the same 10 ways seen in Cycle 1.

Technology Oriented

GENERAL PATH

APPLIED PATH

Technology Oriented

Competency 3Communicates in the languages used in science and technology

This competency is identical in both paths.

In order to know whether the student has understood something - be it a concept, a skill, or a method – they must communicate this to us in an observable way…

Earth & Material Space World

Living Technological

World World

(Ecology)

Year 2 – General Path

Biogeochem

ical

cyclesClim

ate

Zone

Lithosphere

Hydrosphere

Phy

sica

l P

rope

rtie

s of

so

lutio

ns

Che

mic

al

Cha

nges

Organiza

tion

of Matte

r

Electricity and

Electromagnetism

Transformation ofEnergy

Dyn

amic

s of

Eco

syst

ems:

Electrical Engineering

Mechanical Engineering

Materials

Carbon cycle

Nitrogen C

ycle

Factors that influence the

distribution of biomes

Marine B

iomes

Terrestrial biom

es

Minerals

Soil profile

Permafrost

Energy resources

Catchment area; Oceanic Circulation

Glacier and ice floe; Salinity

Energy resources

Density, biological cycles

Troph

ic re

latio

nshi

ps;

Prim

ary

prod

uctiv

ity;

Mat

erial

and

Ene

rgy

flow;

Chem

ical r

ecyc

ling

Power supply; Conduction, insulation,

and protection.ControlTransformation of energy

(electricity and light, heat, vibration, magnetism)

Characteristics of linking of mechanical parts

Guiding controls

Construction and characteristics of motion

Transmission systems (friction gears; pulleys

And belt; gear assembly; sprocket wheels and chain;

wheel and Worm gear) Speed Changes

Construction and characteristics of transformation systems

(screw gear system, connecting rods, cranks, slides, rotating

Slider crank mechanism, rack and pinion drive, cams

Constraints

(deflection, shearing)

Characteristics of m

echanical

Properties;

Types of properties (plastics,

Thermoplastics,

thermosetting plastics

Ceram

ics, composites

Modification of properties

Degradation, protection

Law of conservation of energyEnergy efficiency

Distinction between heat and energy

Electricity: (Electrical charge; static electricity

Ohm’s law; Electrical circuits

Relation ship between power and

electrical energy)

Electromagnetism: (forces of attraction and

Repulsion; Magnetic field of a live wire)

Rutherford-B

ohr Model

Lewis Notatio

n

Combu

stio

n, p

hoto

synt

hesis

and

resp

iratio

n

Acid-b

ase

neut

raliz

atio

n re

actio

n;

Balan

cing

simpl

e ch

emica

l equ

atio

ns

Law o

f con

serv

atio

n of

mas

s

Con

cent

ratio

n (p

pm)

Ele

ctro

lyte

s; p

H s

cale

; E

lect

roly

tic d

isso

ciat

ion

Ions

; E

lect

rical

con

duct

ivity

Study of Populations

Dynamics of

Communities

Biodiversity

Disturbances

Atmosphere

Greenhouse Effect; Atmospheric circulation

Air mass; Cyclone and anticyclone

Energy resources

Space

Solar energy flowEarth-Moon system(Gravitational effect) Climate Change; Deforestation

Drinking Water; Energy Challenge

Earth & Material Space World

Technological

World

Year 2 – Applied Path

Lithosphere

Hydrosphere

For

ce a

nd m

otio

n

Chemical

Changes

Electrici

ty

Electromagnetism

Transformation ofEnergy

Manufacturing

Electrical Engineering

Materials

Mechanical Engineering

Minerals

Energy resources

Catchm

ent area;

Energy resources

DisturbancesTrophic RelationshipsPrimary ProductivityMaterial and energy flowChemical RecyclingFactors that influence the Distribution of biomesEcosystems

Power supply; Conduction, insulation,

and protection (resistance and coding,

Printed circuit).

Typical Controls (unipolar, bipolar, unidirectional

Bidirectional)

Transformation of energy

(electricity and light, heat, vibration, magnetism)

Other functions (condenser, diode, transistor,

Solid state relay

Constraints (deflection, shearing)

Characteristics of mechanical properties

Heat treatments

Types and properties:

Plastics (thermoplastics, therm

osetting, plastics)

Ceramics

Composites

Modification of properties (degradation,

protection)

Adhesion and friction of partsLinking of mechanical parts (freedom of movement)

Guiding controlsConstruction and characteristics of motion,

Transmission systems (friction gears, pulleys and belt,Gear assembly, sprocket wheels and chain,

wheel and worm gear)Speed changes, resisting torque, engine torqueConstruction and characteristics of motion:

Transformation systems (screw gear system, connecting rodsCranks, slides, rotating slider crank mechanism,

Rack and pinion drive, cams, eccentrics)

Law of conservation of energyEnergy efficiency

Distinction between heat and energy

Electromagnetism: (forces of attraction and

Repulsion; Magnetic field of a live wire)

Magnetic field of a solenoid

Electromagnetic induction

Electricity

: (Electric

al charge; s

tatic electric

ity

Ohm’s law; E

lectrica

l circ

uits

Relation ship betw

een power and

electrical e

nergy)Com

busti

on, o

xidat

ion

For

ce;

Typ

es o

f fo

rces

Equ

ilibr

ium

of

two

forc

esR

elat

ions

hip

betw

een

cons

tant

sp

eed,

dis

tanc

e an

d tim

eM

ass

and

Wei

ght

Dynamics ofEcosystems

Atm

osphere

Air m

ass; Cyclone and anticyclone

Energy resources

Space

Solar energy flow

Earth-Moon system

(Gravitational effect)

LivingWorld

Flui

ds

Arc

him

edes

Prin

cipl

eP

asca

l’s L

awB

erno

ulli’

s P

rinci

ple

GraphicalLanguage:

Multiview orthogonal projection(general drawing)

Functional dimensioningDevelopments (prism, cylinder, pyramid, cone)

Standards and representations(diagrams and symbols)

Manufacturing:

Characteristics of drilling, tapping, threading,

And bending

Measurement and Inspection:

Direct measurement (vernier calliper)

Control, shape, and position (plane

Section, angle)

Technologies: Medical, Information, Agricultural,

Automotive

Food Production

Residual Materials

Approved Version

Food Production

Residual Materials

Approved

Version

Math Programs

Cycle 2 Mathematics Paths

Secondary 3Secondary 3 Secondary 4Secondary 4 Secondary 5Secondary 5

Common Program

150 Hours

Cultural (CST)(100 hours – 4 credits)

Technical(150 hours – 6 credits)

Scientific(150 hours – 6 credits)

Cultural (CST)(100 hours – 4 credits)

Technical

(150 hours – 6 credits)

Scientific

(150 hours – 6 credits)

Mathematics at the Secondary LevelGeneral and Applied paths

Cultural, Social and Technical

Technical and Scientific

Science

FirstYear

563 100

Second Year

563 212

First Year563 306

Second Year

564 406

Third Year564 506

Second Year

563 404

Third Year563 504

Second Year

565 406

Third Year565 506

Cycle One Cycle Two

20052005 20062006 20072007 20082008 20092009

100 h100 h 100 h100 h

150 h150 h 150 h150 h

150 h150 h 150 h150 h

150 h150 h150 h150 h150 h150 h

Key scheduling points TS and S are equivalent in the eyes of

CEGEP pathways. There are bridging possibilities between

CST and TS between Sec 4 and Sec 5 that are under discussion.

Students should not switch between the CST and the Science math path.

Competency-based Program

Three Competencies in Mathematics Solves a Situational Problem Uses Mathematical Reasoning Communicates using Mathematical Language

Each Competency contains: Evaluation Criteria Developmental Profile End-of-Cycle Competency scale

(not available yet for Year 2)

Mathematics Competency One

Share&

Reflect

Decode Plan&

Model

Solve

Validate

Solves a Situational Problem

Mathematics Competency Two

TEXTMake

ConjecturesUse

Knowledge

Identifies and analyzes the

situation using a variety

of strategies

Uses Mathematical Reasoning

Construct

Proofs

Uses learned concepts and algorithms to

solve situation

Presents the solution using

a formal procedure

Mathematics Competency Three

Communicates Using Mathematical Language

ProducingMessages

UsingPrecision& Rigor

InterpretingMessages

UsingMultipleModels

Elements of a Learning and Evaluation Situation

A situation is made up of the following elements:

A context linked to a problem A complex task or set of tasks Learning activities linked to knowledge

BUT ALSO…it should: Be consistent with the aims of the QEP Be based on students’ interests and offers

challenges within their reach Demonstrate the usefulness of knowledge

Characteristics of COMPLEX TASKS

Called SITUATIONAL PROBLEMS in Math. All Situational Problems have the following characteristics:

Calls for all elements of a competency Key Features, Evaluation Criteria, Pedagogical Context, etc…

Presents a problem that students have not previously solved

Requires an elaborate production Students may use different strategies and create

different production (solutions) Evaluated along the criteria outlined for that

competency Evaluation is transparent and is adapted to the time of

year and to students’ prior learning

Characteristics of LEARNING ACTIVITIES

In order to solve learning activities students need to mobilize a series of resources. This calls for them to develop and use:

Factual Knowledge: Facts, concepts, rules Procedural Knowledge: Methods, steps, procedures Conditional Knowledge: Strategies, transferred knowledge

Learning Activities are used to develop and evaluate for Competency 2 & 3 C2: Uses Mathematical Reasoning Application Questions C3: Communicates Mathematically Communication Questions

Knowledge-based activities in Mathematics can include: Activities to assimilate a concept, process, rule, formula, theorem, etc…

These focus on a specific algorithm or procedure to be assimilated. Training activities that may vary in difficulty.

These are the more traditional textbook “exercises” that all Math teachers are familiar with.

Activities used to structure knowledge by creating links Summaries, concept maps, charts, diagrams, etc…

C2: Application Questions

Situations involving APPLICATION: Students are asked to choose and apply the appropriate mathematical

concepts and to present a procedure that clearly demonstrates their reasoning.

Here the focus is not necessarily a problem-solving process but more one in which the student can demonstrate certain skills or understandings related to the situation.

Situations involving VALIDATION: Students are asked to justify a statement, check a result or procedure,

take a position, provide a critical assessment or convince, using mathematical arguments.

Usually this requires clear and organized thinking from the student.

Situations involving CONJECTURE: Students use inductive reasoning, based on observation,

manipulation, simulation or a series of examples, to make a proposition or a conjecture.

The goal in this case is generalization.

C3: Communication Questions

Situations involving communication focus specifically on: The interpretation of a message, or The production of a message

It is also possible to develop and evaluate this competency by using Situational Problems or Application Questions designed to assess the first two competencies.

Pre-requisites for CEGEP, Fall 2010