Math, Science and Technology
GOAL Presentation
Christie Brown, MELS-SSCA: [email protected]
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 40% Solves a
30%
Solutions to S&T
Situational
problems
Problem
Uses knowledge of 40% Uses Mathematical 45%
science and tech.
Reasoning
Communicates
20% Communicates
25%
using scientific
using
language
mathematical
language
Science Programs
General Education Path and
Applied Education Path
Cycle One
Secondary III
Secondary IV
SCIENCE & TECHNOLOGY (S&T)
Same
for all
students
555-306
555-404
6 credits
4 credits
Minimum (100 hrs)
(150 hours)
to Graduate
557-306
6 credits
(150 hours)
557-406
6 credits
(150 hrs)
APPLIED SCIENCE AND
TECHNOLOGY (AST)
Secondary V
OPTION
558-404
4 credits
OPTION 1 OPTION 2
to enter
(100Required
hrs)
Physics Chemistry
Pre-U SCIENCES
OPTION
4 credits 4 credits
in (100
CEGEP
hrs) (100 hrs)
558-402
2 cr
Approved documents are expected in
Winter 2009.
(50 hrs)
OPT
BRIDGE
Exams 2008-9
 Competency 1: - identical App or Gen
Scientific 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
Seeks answers or solutions to
scientific or technological problems
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.
Difference from Cycle 1?
Cycle 1 said: “Chooses an investigation
or design scenario”
Competency 2
Makes the most of his/her knowledge of
science and technology
General Path: Grade 10
Applied Path: Grade 10
-Focuses on ISSUES analysis
-Focuses on the analysis of
technical applications.
Issues:
- Climate Change
- Deforestation
- Energy Challenge
- Drinking Water
MELS. General QEP, 2007. p. 46-53
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
Technology Oriented
APPLIED PATH
Competency 3
Communicates 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…
Year 2 – General Path
Earth &
Space
Solar energy flow
Earth-Moon system
(Gravitational effect)
Density, biological cycles
Study of
Populations
Material
World
Climate Change; Deforestation
Drinking Water; Energy Challenge
Electrical
Engineering
Living
Technological
World
(Ecology)
Transformation of
Energy
World
Law of conservation of energy
Energy efficiency
Distinction between heat and energy
Year 2 – Applied Path
Earth &
Material
Space
World
Living
World Technologies: Medical,
Multiview orthogonal projection
Graphical
(general drawing)
Language:
Functional dimensioning
Developments (prism, cylinder, pyramid, cone)
Standards and representations
(diagrams and symbols)
Information, Agricultural,
Automotive
Law of conservation of energy
Energy efficiency
Transformation of
Distinction between heat and energy
Energy
Electrical
Engineering
Technological
World
Mechanical
Engineering
Adhesion and friction of parts
Linking of mechanical parts (freedom of movement)
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, resisting torque, engine torque
Construction and characteristics of motion:
Transformation systems (screw gear system, connecting rods
Cranks, slides, rotating slider crank mechanism,
Rack and pinion drive, cams, eccentrics)
Approved Version
Food
Production
Residual
Materials
Approved
Version
Food
Production
Residual
Materials
Math Programs
Cycle 2 Mathematics Paths
Secondary 3
Common
Program
150 Hours
Secondary 4
Secondary 5
Cultural (CST)
Cultural (CST)
(100 hours – 4 credits)
(100 hours – 4 credits)
Technical
Technical
(150 hours – 6 credits)
(150 hours – 6 credits)
Scientific
Scientific
(150 hours – 6 credits)
(150 hours – 6 credits)
Mathematics at the Secondary Level
General and Applied paths
Cycle One
Cycle Two
Cultural, Social and
Technical
Second Year
563 404
Third Year
563 504
100 h
100 h
Technical and Scientific
First
Year
563 100
Second
Year
563 212
First Year
563 306
150 h
150 h
150 h
2005
2006
2007
Second
Year
564 406
Third Year
564 506
150 h
150 h
Science
Second
Year
565 406
Third Year
565 506
150 h
150 h
2008
2009
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
Plan
&
Model
Decode
Share
&
Reflect
Solves a Situational
Problem
Solve
Validate
Mathematics Competency Two
Uses Mathematical Reasoning
TEXT
Identifies and
analyzes the
situation using
a variety
of strategies
Uses learned
concepts and
algorithms to
solve situation
Presents the
solution using
a formal
procedure
Mathematics Competency Three
Communicates Using Mathematical Language
Producing
Messages
Interpreting
Messages
Using
Precision
& Rigor
Using
Multiple
Models
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:
Procedural Knowledge:
Conditional Knowledge:
Facts, concepts, rules
Methods, steps, procedures
Strategies, transferred knowledge
 Learning Activities are used to develop and evaluate for Competency 2 &
3


C2: Uses Mathematical Reasoning
C3: Communicates Mathematically


Application Questions
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
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