There are 4 strands in the course with the overall expectations (big ideas) in each strand:
There are also process expectations :
So instead of an exam I have asked my students to do the following:
In
preparation for your final interview you are required to supply your teacher
with 12 artifacts (one for each overall expectation-I combined two of them). Each one should be done
on a separate page (one only).
The
artifact should address the overall curriculum expectation and the process
expectation(s) that is (are) tagged to it.
The
artifact can be a homework question, an activity, an explanation, a diagram
with comments, ……. really anything that would demonstrate your understanding of
that curriculum expectation.
You
should consider the following questions when choosing and presenting your
artifacts:
- Why your artifact demonstrates
the curriculum expectation? or Why
did you choose it?
- In what ways does the artifact
show what you have learned or understand? or In what ways does the artifact show your growth of
learning?
- You chose the piece: What would
you like me to look at or pay attention to?
All
artifacts must be tagged (with stickies or highlights or markers or……)
indicating evidence of the appropriate process expectations.
You should consider the following questions
when tagging the evidence of the appropriate process expectations:
- Am I explaining why this tag
demonstrates the process expectation? or
Why did you choose it?
- In what ways does the tag show what you have learned or understand the process expectation? or In what ways does the tag show your growth of learning?
The Table looked like this:
Curriculum
Expectation
|
Process
Expectation(s)
|
Strand: CHARACTERISTICS
OF FUNCTIONS
|
|
F1:Demonstrate an understanding of average and instantaneous rate of
change, and determine, numerically and graphically, and interpret the average
rate of change of a function over a given interval and the instantaneous rate
of change of a function at a given point
|
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
Selects and uses
tools and strategies to solve a problem
|
F2:Determine functions that result from the addition, subtraction,
multiplication, and division of two functions and from the composition of two
functions, describe some properties of the resulting functions, and solve
related problems
|
CONNECTING
Connects
mathematical ideas to the context
REPRESENTING
Creates reasonable
models to represent the problem (scale model, diagram, numbers, formulas,
words)
|
F3:Compare the characteristics of functions, and solve problems by
modelling and reasoning with functions, including problems with solutions
that are not accessible by standard algebraic techniques
|
REPRESENTING
Creates reasonable
models to represent the problem (scale model, diagram, numbers, formulas,
words)
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
Selects and uses
tools and strategies to solve a problem
|
Strand: EXPONENTIAL AND LOGARITHMIC FUNCTIONS
|
|
EL1:Demonstrate an understanding of the relationship between exponential
expressions and logarithmic expressions, evaluate logarithms, and apply the
laws of logarithms to simplify expressions
|
PROBLEM SOLVING / REASONING / PROVING
Uses critical
thinking to solve a problem
REFLECTING
Reflects on the
processes used to solve the problem and reasonableness of answers
|
EL2:Identify and describe some key features of the graphs of logarithmic
functions, make connections among the numeric, graphical, and algebraic
representations of logarithmic functions, and solve related problems
graphically
|
CONNECTING
Connects
mathematical ideas to the context
REPRESENTING
Creates reasonable
models to represent the problem (scale model, diagram, numbers, formulas,
words)
|
EL3:Solve exponential and simple logarithmic equations in one variable
algebraically, including those in problems arising from real-world
applications
|
CONNECTING
Connects
mathematical ideas to the context
REFLECTING
Reflects on the
processes used to solve the problem and reasonableness of answers
|
Strand: POLYNOMIAL
AND RATIONAL FUNCTIONS
|
|
PR1:Identify and describe some key features of polynomial functions, and
make connections between the numeric, graphical, and algebraic
representations of polynomial functions
|
REPRESENTING
Creates reasonable
models to represent the problem (scale model, diagram, numbers, formulas,
words)
COMMUNICATING
Expressing and
organizing thinking
Using mathematical
vocabulary
|
PR2:Identify and describe
some key features of the graphs of rational functions, and represent rational
functions graphically
|
COMMUNICATING
Expressing and
organizing thinking
Using mathematical
vocabulary
|
PR3:Solve problems involving
polynomial and simple rational equations graphically and algebraically; demonstrate an understanding of solving
polynomial and simple rational inequalities
|
CONNECTING
Connects
mathematical ideas to the context
PROBLEM SOLVING / REASONING / PROVING
Uses critical
thinking to solve a problem
|
Strand: TRIGONOMETRIC
FUNCTIONS
|
|
T1:Demonstrate an
understanding of the meaning and application of radian measure
|
COMMUNICATING
Expressing and
organizing thinking
Using mathematical
vocabulary
|
T2:Make connections between
trigonometric ratios and the graphical and algebraic representations of the
corresponding trigonometric functions and between trigonometric functions and
their reciprocals, and use these connections to solve problems
|
CONNECTING
Connects
mathematical ideas to the context
REPRESENTING
Creates reasonable
models to represent the problem (scale model, diagram, numbers, formulas,
words)
|
T3:Solve
problems involving trigonometric equations and prove trigonometric identities
|
SELECTING TOOLS AND COMPUTATIONAL STRATEGIES
Selects and uses
tools and strategies to solve a problem
PROBLEM SOLVING / REASONING / PROVING
Uses critical thinking
to solve a problem
|
Ok MTBOS-here is what I am looking for.
What do you honestly think?
Advantages? Disadvantages?
A special thanks to Sandra Herbst - whom I heard speak on Monday November 25th.
She inspired this!
Awesome as an exam! I did something similar but as a portfolio. But the idea was the same - a focus on the mathematical processes. Students were able to submit evidence throughout their learning to demonstrate that they have achieved the process expectations. There were some physical artifacts, but also some electronic documents as well (with pictures). I did it as an ongoing assessment, but I think the way that you're doing it as a substitute for exam is great!
ReplyDeleteWhat do the students think? When can they submit the artifacts?
Something that I did with the portfolio was that students could combine expectations if it's a problem that involved multiple ones. Maybe that's harder to do with the MHF4U expectations though?
Thanks for sharing!
Hey Jimmy, the students are submitting the artifacts on the last day of the course. They then tell me what strand(s) (two max) they want to focus on during the interview. Interviews take place on exam day 8-3. They can totally combine expectations. I am just bringing the artifacts to the interview as a starting point. Should be an interesting two days (as I have two sections). I'll let you know how it goes.
ReplyDeleteAlex, this looks awesome--I definitely want to try this sometime in the future.
ReplyDeleteA few questions:
(1) Have students practiced oral exams/interviews with you before? I could see this as a disadvantage for some students who might be intimidated by a teacher and who would do much better submitting something like a recording of themselves presenting the material or answering your questions (using something like Doceri).
(2) What about students copying each other's work and submitting that to you? How do you check for this when you might have a high number of submissions?
(3) How much time will you give (have you given) your students to complete this assignment?
If possible, I'd love to see examples of students' submissions after the assignment. I'd be scared to do this as a final just because the quality of work could vary and the open-endedness of it could be intimidating to students if you haven't done something like that before. However, if you provide them with examples, I find you often get 40 variations of your example instead of the wide-open creativity that'd be possible otherwise. Let us know how it goes!
Hi Jonathan,
DeleteThanks for the interest.
1) This is my first crack at this. Students do a midterm interview with me but it is only about how things are going.
2) Copying could be an issue. Students will only interview on two strands max. It is about learning the expectations in the course. I intend to focus on the process expectations in the interview.
3) Students will be given 5 full periods to work on their "stuff". Students received the details about this on December 15th and the interview is the last week of January.
I will blog about the experience and include student samples. It should be interesting.