Transcript: Math 9 In-Service - Session #1 | Jun 15, 1999

The opening slate pops up with a countdown timer from 5 seconds and the title “TVO’s Virtual Classroom. Get connected.”
The “V” in “Virtual” is a tick, the “A” in “classroom” is an at sign with an extended loop that turns into a power cord with a plug at the end, and the first “O” in “classroom” is a spinning globe.
Mister C sits in the studio. He’s in his fifties, with a dark beard and wavy black hair. He’s wearing glasses, a white shirt, a black tie and a blue suit jacket.

Stewart says WELCOME TO THE
VIRTUAL CLASSROOM.
I'M STEWART CRAVEN, AND I
HAVE A GUEST, JUDY CROMPTON.

Judy sits next to Stewart. She’s in her forties with short greyish hair. She’s wearing glasses a pale blue jacket and a white shirt.

He continues TODAY WE ARE GOING TO
BEGIN TWO IN-SERVICE
SESSIONS ABOUT THE GRADE
NINE MATHEMATICS CURRICULUM.
FIRST OF ALL, I'D LIKE TO SPEAK
ABOUT JUDY, MY SIDEKICK HERE.
I'VE KNOWN JUDY FOR
A NUMBER OF YEARS.
SHE'S HAD A BIG PART
IN THIS NEW CURRICULUM.
FACT IS, SHE WAS THE PROJECT
MANAGER FOR THE WRITING OF
THE SECONDARY SCHOOL
MATHEMATICS CURRICULUM.
AND IN THAT CAPACITY,
SHE KNOWS HER STUFF.
OR AT LEAST SHE BETTER
KNOW HER STUFF, ANYWAY.

She laughs.

He continues WHAT I'M GOING TO DO IS ASK
YOU, FIRST AND FOREMOST,
WHERE DID THIS WHOLE
THING COME FROM?
HOW DID IT EVOLVE IN
THE LAST LITTLE WHILE?

Stewart WELL, THE MINISTRY OF
EDUCATION AND TRAINING TO
WRITE THE CURRICULUM FOR
SECONDARY SCHOOL ISSUED
TENDERS, INVITING QUALIFIED
GROUPS TO MAKE BIDS ON THE
WRITING OF THE
VARIOUS DISCIPLINES.
THE ONTARIO ASSOCIATION FOR
MATH EDUCATION, AND THE
ONTARIO MATH COORDINATORS
ASSOCIATION MET WITH THE
FIELDS INSTITUTE TO EXPLORE
THE POSSIBILITY OF MAKING A
BID, AND WE ACTUALLY DID DO
THAT IN CONJUNCTION WITH OTHER
PROVINCIAL MATH ORGANIZATIONS.
WE WERE FORTUNATE
TO WIN THE BID.
PULLED TOGETHER AN EXCELLENT
TEAM OF ONTARIO MATHEMATICS
EDUCATORS AT ALL LEVELS, ALONG
WITH A PANEL OF ADVISORS,
INCLUDING PEOPLE FROM BUSINESS
AND INDUSTRY, AND BETWEEN
MAY OF LAST YEAR AND DECEMBER
OF LAST YEAR, WE WROTE
THE CURRICULUM.
I WAS JUST GOING TO ADD THE
CURRICULUM ALSO WENT THROUGH
A SERIES OF FEEDBACK PANELS.

He says RIGHT, OF COURSE.

Judy continues AND THAT PULLED ADDITIONAL
ONTARIO EDUCATORS IN.

Stewart says WELL, YOU KNOW, IT'S A
BIG, NEW PIECE OF WORK.
CAN YOU TELL ME THE VERY
ESSENCE OF THE GRADE
NINE CURRICULUM?
WHAT IS THE HEART OF IT?

Judy says WELL, MY FEELING IS THE HEART
OF THE GRADE NINE CURRICULUM IS
INQUIRY, AS REPRESENTED
IN THE RELATIONSHIP STRAND.
THAT PARTICULAR STRAND
DESCRIBES THE PROCESS OF
INQUIRY AS AN OBJECT OF
LEARNING IN MATHEMATICS, BUT
IT IS ALSO A WAY OF CREATING
CONTEXT FOR OTHER LEARNING
WITHIN THE SUBJECT, AND FOR
WEAVING TOGETHER THE VARIOUS
STRANDS OF THE COURSE.

He says AS IT TURNS OUT, WE HAVE A
LITTLE BIT OF VIDEO FOOTAGE.
WE'VE BEEN OUT TO ABOUT THREE
OR FOUR CLASSES IN THE LAST
COUPLE OF WEEKS TO GET SAMPLES
OF THE KINDS OF THINGS THAT WE
HOPE WILL HAPPEN IN CLASSROOMS
ACROSS ONTARIO IN SEPTEMBER.
SO THE FIRST PLACE WE WENT
TO WAS LEASIDE HIGH SCHOOL
IN EAST YORK.
THE TEACHER IS LUCY BURSTON.
AND SHE IS DOING AN ACTIVITY
CALLED THE BOUNCING BALL.
HERE IT IS.

A clip plays.

Lucy stands in a classroom. She’s in her mid-forties with short curly brown hair. She’s wearing glasses and a blue patterned dress over dark trousers.

Lucy says NOW, IF I TAKE THIS BALL,
OR ANY BALL, AND I DROP IT,
WHAT IS GOING TO HAPPEN?
IT'S GOING TO BOUNCE BACK UP.
ALL RIGHT, CAN YOU TELL ME
SOMETHING ABOUT THE MANNER
IN WHICH IT IS GOING
TO BOUNCE BACK UP?

A male student says PROBABLY STRAIGHT UP.

Lucy says PROBABLY STRAIGHT UP.
OKAY.
WHAT ELSE MIGHT HAPPEN?

A female student says IT'S NOT GOING TO GET
AS HIGH WHEN IT BOUNCES.

Lucy says OKAY.
AND WHAT YOU ARE GOING TO BE
DOING, LET ME JUST DESCRIBE
IT FOR YOU.
IS YOU ARE GOING TO
BE TAKING A RULER.
THERE IS MASKING TAPE TO
FASTEN IT TO THE WALL FOR YOU
IN A COUPLE OF MINUTES, WHEN
YOU ACTUALLY GET TO DO THIS.
BUT YOU ARE GOING TO BE
MEASURING WHAT ACTUALLY
HAPPENS WHEN YOU DROP THE
BALL, WHAT THE ACTUAL
BOUNCE BACK IS.
YOU ARE GOING TO NEED TO
MEASURE THE BOUNCE BACK,
ALL RIGHT?
SO YOU ARE GOING TO DROP AND
MEASURE THE BOUNCE BACK.
ONE OF OUR EXERCISES, OF
COURSE IS GOING TO BE, AS WE
ARE CONDUCTING THIS EXPERIMENT,
IS TO KEEP TRACK OF OUR DATA.
AND WHAT ARE SOME WAYS THAT
WE CAN KEEP TRACK OF DATA?

A male adolescent says RECORD IT ON A
TABLE OR A CHART.

Lucy says OKAY, SO WE NEED TO
KNOW THE TYPE OF BALL.
AND OF COURSE I NEED
LONGER LINES HERE.
WE'LL JUST DO
THEM FREE HAND.
TRIAL, THREE, FOUR.
NO, WE SAID THREE.
SAY 53 HERE.
WHAT ACTUAL NUMBER DO YOU
THINK WOULD BE REPRESENTATIVE
OF THE BOUNCE BACK HEIGHT?

A female adolescent says YOU COULD TAKE THE THREE
TRIALS AND AVERAGE THEM TO
FIND THE MOST COMMON
HEIGHT IT WOULD BE.

Lucy says WHAT WE'RE GOING TO DO
THEN IS TAKE WHAT WE CALL
A MEAN AVERAGE.
WHICH IS WE ARE GOING TO ADD
THE THREE NUMBERS UP, DIVIDE
BY THREE, AND THAT SHOULD GIVE
US A PRETTY GOOD IDEA OF A
GOOD NUMBER TO USE FOR
THE BOUNCE BACK HEIGHT.
SO THE FOURTH COLUMN WE WILL
USE HERE IS THE MEAN AVERAGE.

[general chatter]

A girl with shot hair says YOU SAW 37?

A blond female student says 44.

A blond male student drops a ball.

A brunette student says THAT WAS 18.

Lucy says OKAY, WHEN YOU ARE DONE
COLLECTING YOUR DATA,
WHAT I WOULD LIKE YOU TO
DO IS TO SUMMARIZE YOUR DATA
ON A GRAPH, OKAY?
SO WHAT WE ARE LOOKING FOR IS
THE RELATIONSHIP BETWEEN THE
DROP HEIGHT AND THE
BOUNCE BACK HEIGHT.
SO COULD I JUST GET YOU TO
STEP OVER FOR A SECOND?
SO ON A SET OF AXES, YOU ARE
GOING TO HAVE A HORIZONTAL
AXIS, AND A VERTICAL AXIS.
WHICH ONE DO YOU THINK
YOU'RE GOING TO PUT
ON EACH OF THE AXIS?

A female student with curly hair says THE DROP HEIGHT ALONG THE
BOTTOM BECAUSE IT'S CONSISTENT.

Lucy says THE DROP HEIGHT, OKAY.
AND WHAT WILL YOU HAVE
ALONG THE VERTICAL?

The female student with curly hair says THE HEIGHT.

Judy says LET'S CALL IT BOUNCE
HEIGHT AVERAGE.

The female student with curly hair says YOU JUST WANT US TO PUT
THE AVERAGE ON THERE?

Judy writes down the answers on the blackboard.

Judy says YEAH, JUST THE AVERAGE.
BECAUSE EACH DROP HEIGHT IS
GOING TO HAVE ONE NUMBER TO
REPRESENT WHAT THE
BOUNCE BACK HEIGHT WAS.

A male student wearing glasses says ALL THE POINTS
ARE PRETTY CLOSE.

A girl with her hair tied-up says SO IS THAT GOOD?

The male student wearing glasses COULD GO DOWN A BIT MORE.
I GUESS IT'S FINE.

Judy says WHEN YOU DID YOUR GRAPHS, YOU
FOLLOWED ALL THE PROTOCOL.
YOU DID VERY GOOD GRAPHS WITH
NICE UNITS MARKED, AND NICELY
EVENLY SPACED, ETC. AND I
HEARD A LOT OF TERMS LIKE THE
LINE OF BEST FIT, WHICH WAS
NICE TO HEAR, THAT A LOT OF
YOU HAD ALREADY BEEN EXPOSED TO
THAT IDEA OF LINE OF BEST FIT.
COULD SOMEBODY DESCRIBE FOR ME
WHAT A LINE OF BEST FIT IS?

A male student wearing a blue shirt says JUST SO THERE IS PRETTY MUCH
AN EVEN AMOUNT OF POINTS ON
EITHER SIDE OF THE LINE.

Judy says OKAY, THAT'S GOOD.

A female student with short hair says I JUST WANTED TO SAY NOT ALL
THE POINTS HAVE TO BE ON THE
LINE FOR IT TO BE
A LINE OF BEST FIT.

Judy says OKAY, AND IN FACT AT TIMES,
DEPENDING ON THE SCATTERING OF
THE POINTS, AND THE NUMBER OF
POINTS, THE LINE MAY NOT HIT
ANY OF THE POINTS.
BUT YOU WANT THE LINE THAT
FITS BEST, SO IT'S GOT ROUGHLY
THE SAME NUMBER OF POINTS
ON EITHER SIDE, AS GREG
MENTIONED BEFORE.
NOW, WHAT WE'D LIKE YOU TO DO
NEXT IS TO TAKE THE RESULTS
YOU HAVE AND JOIN FORCES WITH
ONE OR TWO OTHER GROUPS.
SO, BASICALLY, THE CLASS IS
GOING TO DIVIDE IN HALF.
SO LET'S SAY, ONE, TWO, THREE
AT THE BACK OF THE ROOM, AND
THEN THESE TWO GROUPS, AND
WHAT I'D LIKE YOU TO DO IS
SHARE THE RESULTS THAT YOU GOT.
SO I WANT YOU TO
LOOK FOR COMPARISONS.
WHAT'S THE SAME ABOUT THE
KINDS OF RESULTS YOU GOT,
AND WHAT IS DIFFERENT?
SO IF YOU WILL FOR EACH OF
YOUR GROUPS, TAKE ONE OF THESE
HALF SHEETS OF TRANSPARENCY,
AND A MARKER PEN, AND GIVE US
YOUR RESULTS AGAIN.
IF WE ARE GOING TO COMPARE
THEM, WHAT'S GOING TO HAVE TO
BE TRUE ABOUT THE UNITS WE
USE ON BOTH OF THE AXES?
SAME INCREMENTS.
OKAY, SO KEEPING THAT IN MIND,
LET'S GET TOGETHER WITH
OUR GROUPS.
AND LET'S SAY WE
SPEND FIVE MINUTES.

[general chatter]

The clip ends.

Stewart says WHAT YOU SAW THERE IS PERHAPS
SOMETHING THAT LOOKS LIKE WHAT'S
GOING ON IN YOUR CLASSROOM
RIGHT NOW, PERHAPS NOT.
WHAT I WOULD LIKE TO DO RIGHT
NOW IS TO INVITE YOU TO PHONE
IN, AND MAKE COMMENTS
ABOUT WHAT YOU SAW.
THAT IS TO SAY, WHAT WAS THE
SAME, WHAT'S DIFFERENT, WHAT
ASPECTS OF THIS ARE PROBABLY
I'D SAY MORE EXPLORATORY THAN
PERHAPS THINGS THAT YOU'VE
DONE IN THE PAST, ETC.
SO THE WAY TO
PHONE IN IS THIS.
YOU HAVE THE PHONE IN FRONT
OF YOU, YOU PRESS POUND 9.
POUND 9 TO PHONE IN.
AND IT TAKES A FEW SECONDS TO
GET CONNECTED, SO BEAR WITH US.
WHEN YOU ARE DONE YOUR CALL,
MAKE SURE YOU HANG UP THE PHONE.
PLEASE COME ON,
PHONE IN.
I KNOW THERE ARE A
FEW PEOPLE OUT THERE.
I ACTUALLY THINK TOM'S IN THE
AUDIENCE, AND I'M CERTAIN
HE COULD PHONE IN AND AT
LEAST MAKE A COMMENT.
OKAY, WELL, WHAT DO YOU --
WHAT WOULD YOU SAY ARE THE
KINDS OF DIFFERENCES THAT
MIGHT BE BETWEEN WHAT WAS
GOING ON IN THAT CLASSROOM,
AND WHAT WE MIGHT HAVE DONE
EVEN A COUPLE OF YEARS AGO?

Judy says WELL, FOR ONE THING, STUDENTS
WERE WORKING IN GROUPS.
THEY WERE NOT SITTING IN ROWS,
FOLLOWING A LESSON, OR TRYING
EXAMPLES AND SO ON.
THEY WERE ACTING... WORKING
MORE INDEPENDENTLY.
THE TEACHER WAS GUIDING
INDIVIDUAL GROUPS AS THEY
MOVED, PERHAPS AT DIFFERENT
PACES, THROUGH THE ACTIVITY.
SO IT'S VERY MUCH A DIFFERENT
KIND OFTEN CLASSROOM MANAGEMENT.

Stewart says NOW, HERE'S A QUESTION I SEE
WE ARE GOING TO CONNECT TO
SOMEBODY FROM
SAINT MARK'S SCHOOL.
AND WHEN WE GET CONNECTED,
WHAT I WOULD LIKE YOU TO DO
WHEN THE PHONE FINALLY
CONNECTS, I'D LIKE YOU TO
INTRODUCE YOURSELF
AND GO AHEAD.

Bailey says THANK YOU.
HELLO.
BAILEY CARLTON FROM SAINT
JOSEPH'S HIGH SCHOOL IN
RENFREW.
IN THE MODEL LESSON WE JUST
SAW, WHAT PROPORTION OF THE
TIME WAS SPENT ON BEHALF
OF THE STUDENTS ACTUALLY
MEASURING AND
RECORDING THEIR DATA?

Stewart says I WAS IN THE CLASSROOM AND
WATCHED THE ENTIRE PROCEDURE.
I WOULD SAY IN THIS PARTICULAR
ONE, IT WAS A 75-MINUTE
PERIOD, AND YOU'VE GOT TO
REMEMBER WHEN TV CREWS ARE IN
THERE, IT'S NOT QUITE AS
SMOOTH AS ALL THAT, BUT I
WOULD SAY IT WAS ABOUT A THIRD
OF THE TIME, CLOSE TO A THIRD
OF THE TIME.
DOES THAT SURPRISE
YOU OR NOT?

Bailey says NO, THAT DOESN'T
SURPRISE ME AT ALL.
IT WOULD SEEM THAT WITH
AN INQUIRY-BASED MODEL OF
LEARNING, YOU WOULD HAVE TO
BUDGET A LOT MORE TIME FOR THE
IMPLEMENTATION OF THE LESSON
THAN FOR ANYTHING ELSE
IN THE CLASSROOM, IN FACT.

Stewart says RIGHT.

Bailey says THANK YOU VERY MUCH.
I WAS WONDERING HOW
LONG IT DID TAKE.

Stewart says THAT WOULD BE
A FAIR ESTIMATE.
ABOUT A THIRD OF THE TIME.
ARE THERE ANY OTHER
QUESTIONS OUT THERE?
AGAIN, IT'S VERY
EASY TO PHONE IN.
POUND 9 IS THE
WAY YOU DO IT.
JOIN IN THE CONVERSATION.

Judy says IF A THIRD OF THE TIME WAS ON
DATA GATHERING, HOW WAS THE
REST OF THE TIME SPENT?

Stewart says I WOULD SAY THE SET-UP, IF
YOU WANT TO CALL THE SET-UP,
WOULD BE ABOUT A THIRD
OF THE TIME, AS WELL.
THAT IS THE WHOLE --
DESCRIBING THE PROCEDURE,
DISTRIBUTING THE EQUIPMENT,
SO ON AND SO FORTH.
NOW, WHAT I WILL SAY
UNEQUIVOCALLY, THIS LESSON WAS
NOT DONE WHEN WE LEFT THERE.
IN FACT, THE TEACHER KNEW FULL
WELL RIGHT AT THE END OF THE
PERIOD WHERE THEY WERE
REGROUPING, THAT IN FACT THEY
WERE GOING TO HAVE TO REGROUP
THE FOLLOWING DAY, COMPLETE
THAT PART OF THE TASK, THEN
BRING THE WHOLE SET OF
STUDENTS BACK TOGETHER AGAIN
TO DISCUSS THE RESULTS AS AN
ENTIRE GROUP.
NOW, THERE MAY HAVE BEEN
ANOTHER ASSIGNMENT ATTACHED
TO IT AT THAT POINT BUT,
NONETHELESS, THIS IS NOT
REALLY A ONE-PERIOD CLASS
YOU WERE SEEING THERE.
IT REALLY WOULD HAVE
REPRESENTED A COUPLE.

Judy says NOW, EACH GROUP GATHERED ITS
DATA, PROBABLY GOT ITS GRAPH
DONE DURING THE PERIOD?

Stewart says YEAH, THEY GOT THE INITIAL
GRAPH DONE FOR THEIR ONE BALL.

Judy says RIGHT.
SO THEY WERE BEGINNING
TO LOOK AT WHETHER
THERE IS A RELATIONSHIP.
RIGHT AT THE END OF THE CLIP,
THE TEACHER WAS ASKING THEM
TO COMPARE RESULTS
WITH OTHER GROUPS.

Stewart says THAT'S RIGHT.
THAT WAS RIGHT AT THE
END OF THE PERIOD.

Judy says SO THE NEXT DAY THEN THERE
WOULD BE SOME DISCUSSION
AND REFLECTION ABOUT
HOW THEY COMPARED.

Stewart says ABSOLUTELY.
AND AS I SAY, THERE WOULD
HAVE HAD TO HAVE BEEN MORE,
PROBABLY AN ASSIGNMENT
EVENTUALLY ATTACHED TO THAT,
AND FURTHER INVESTIGATION
OF THE SKILLS.
WE HAVE A CALL.
CAN YOU INTRODUCE
YOURSELF, PLEASE?

Cyril says YEAH, HI.
IT'S CYRIL BUTLER CALLING
FROM SAINT MARK'S HIGH SCHOOL
IN OTTAWA.

Stewart says GREAT.
GLAD TO HAVE YOU ONBOARD.
WHAT'S YOUR QUESTION?

Cyril says THE QUESTION IS JUST AGAIN
GETTING BACK TO THE FIRST
QUESTION ABOUT TIME.
IT SEEMS WITH THE AMOUNT OF
MATERIAL THAT'S BEING PUSHED
DOWN AND PACKED INTO THE GRADE
NINE CURRICULUM, IT'S JUST
A QUESTION ABOUT WHETHER THE
TECHNOLOGY ASPECT AND THE
TIME IT TAKES TO IMPLEMENT
THIS SORT OF LESSON IS GOING
TO ALLOW US ENOUGH TIME TO
ACTUALLY GET ALL THE MATERIAL
ACROSS THAT WE'RE
BEING ASKED TO TEACH.

Stewart says YOU WANT TO ANSWER THAT, THEN
MAYBE I CAN ADD SOMETHING.

Judy says IT'S A QUESTION THAT IS A
CONCERN FOR A LOT OF TEACHERS.
AND THE WAY I WOULD ANSWER IT
IS TO THINK ABOUT HOW OFTEN
I WOULD DO ACTIVITIES OF THE
SORT WE SAW IN THE VIDEO.
IT'S NOT SOMETHING YOU WOULD
NECESSARILY DO EVERY DAY.
YOU WOULD USE ACTIVITIES
FOR PARTICULAR REASONS, TO
IDENTIFY A RELATIONSHIP YOU
WANT TO USE IN A PARTICULAR
MANNER PERHAPS TO INTRODUCE
LINEAR RELATIONSHIPS
IN ANALYTIC GEOMETRY.
YOU MIGHT USE AN ACTIVITY TO
SET A CONTEXT FOR SOME KIND
OF PROBLEM SOLVING
OR SKILL EXTENSION.
SO YOU WOULD USE THEM
FOR APPROPRIATE REASONS
AT KEY POINTS.

Stewart says ONE OF THE THINGS I WOULD ADD
IS, IN FACT, IT'S INTERESTING
TO LOOK AT THE OTHER LESSONS
WE DID IN THIS SERIES.
WE DID LESSONS WHERE THERE
WAS MORE TECHNOLOGY INVOLVED.
THE KIDS HAD THEIR OWN
CALCULATOR, SO THEY COULD HAVE
DONE SOME CALCULATIONS
WITH THOSE.
HOWEVER, THE DATA GATHERING
AND THE EFFICIENCY OF IT
MAY CHANGE WHEN YOU SEE
OTHER KINDS OF LESSONS.
SO TECHNOLOGY, IN A SENSE, MAY
ACTUALLY MAKE THIS WHOLE KIND
OF INQUIRY PROCESS, AT LEAST
IN SOME CASES, MORE EFFICIENT.
AND NEXT WEEK ON THE 17th,
WE'RE REALLY GOING TO
CONCENTRATE ON THOSE ASPECTS.

Judy says THE OTHER INTERESTING THING
ABOUT WHAT YOU ARE SAYING,
STEWART, IS YOU CAN STILL
ACCOMPLISH THE EXPECTATIONS
AROUND INQUIRY WITHOUT USING
GRAPHING TECHNOLOGY AND SO ON.
THE USE OF GRAPHING
TECHNOLOGY IS VERY, VERY
POWERFUL, AND TAKES YOU IN
NEW DIRECTIONS, BUT INQUIRY
ITSELF CAN BE
ACCOMPLISHED WITHOUT IT.

Stewart says THAT'S GREAT.
WE'VE HAD A COUPLE OF QUESTIONS,
AND THAT'S REALLY FINE.
WHAT I INVITE YOU TO DO OVER
THE COURSE OF THIS ENTIRE
SHOW IS WHEN YOU SEE SOMETHING
YOU'D LIKE TO COMMENT ON
OR ASK, PLEASE, POP IN.
BUT RIGHT NOW, WE'RE GOING
TO TAKE A LOOK AT A FEW
QUOTATIONS THAT MIGHT BE...
WELL, REPRESENTATIVE OF THE
KINDS OF THINGS THAT ARE
PART OF THIS NEW CURRICULUM.
SO LET'S RUN THE
FIRST SET OF SLIDES.

A slate appears under the title “Communication.” It reads “Opportunities should be provided for students to engage in writing activities in which they explore their own perceptions of mathematical concepts and report on their attempts to apply mathematics to problem solving.”

The slate changes to “Experiential Approaches. Both the review of previously encountered concepts and the development of new ones should take place through approaches that relate abstraction to manipulative materials or to real-life situations.”

The slate changes to “Applications. Whenever possible, skills and concepts should be related, from the beginning, to their applications. Applications shall be interspersed throughout the program, rather than developed in isolation. An effort should be made to relate the mathematics program to programs in other subject areas.”

The slate changes to “Technology. The use of computers should change the quantity and type of interactions in the classroom and encourage co-operative learning. Alternative strategies for teaching and learning mathematics using the computer should be explored.”

The slate changes to “Modeling. The process of problem solving using mathematics inevitably involves the choice or creation of a mathematical model. As a problem becomes more complex, the selection of an appropriate mathematical model becomes more crucial.”

He continues THESE ARE PHENOMENALLY
STRONG STATEMENTS.
Holding a workbook, I WENT THROUGH THIS, WHICH
IS THE 1999, AND TO BE QUITE
HONEST, I DIDN'T SEE THEM.
WHERE DID THEY COME FROM?

Judy says WELL, INTERESTING YOU
SHOULD ASK THAT, STEWART.
THEY ARE STATEMENTS THAT
CERTAINLY REFLECT THE
PHILOSOPHY OF THE '99
GUIDELINE, BUT THEY COME
FROM THE '85 GUIDELINES.
THEY'RE FOUND IN THE FIRST
23 PAGES OF THAT DOCUMENT.
AND THE AUTHORS OF THAT
DOCUMENT WERE CERTAINLY
FARSIGHTED IN THE
PLANNING THAT THEY DID.

Stewart says I MUST ADMIT THAT I PROBABLY
DIDN'T READ THOSE FIRST 23
PAGES NEARLY CLOSELY ENOUGH.

Judy says WELL, I THINK A LOT OF US
READ THEM AND WERE VERY
IMPRESSED WITH THEM, BUT THEN
TURNED TO THE CONTENT SECTION
AT THE BACK AND
FOCUSSED ON THAT.

Stewart says RIGHT.
WELL, LET'S LOOK AT THE
PARALLELS IN THIS NEW 1999
CURRICULUM GUIDELINE BECAUSE
I THINK YOU'LL BE SURPRISED
AT JUST HOW CLOSE
THEY REALLY ARE.
LET'S GO WITH THE
NEXT SET OF SLIDES:

A slate appears under the title “Echoes in the 1999 Guidelines. Communication.” It reads “In all strands and all courses, expectations are included that require of students the clear and concise communication of reasoning or of findings.”

The slate changes to “Experiential Approaches. The philosophy of the Grade 9 course reflects the belief that students learn when they have initial opportunities to explore through hands on experiences, followed by careful guidance into an understanding of the abstract mathematics involved.”

The slate changes to “Applications. This curriculum embeds the learning of mathematics in the solving of problems based on real-life situations. Skill acquisition is an important part of the program; skills are embedded in the contexts provided.”

The slate changes to “Technology. The development of sophisticated yet easily used calculators and computers is changing the role of procedure and technique in mathematics… This curriculum integrates appropriate technologies.”

The slate changes to “Modeling. The inquiry process is assumed as a major strategy that underlies teaching and learning at all levels and all grades. An important stage in the inquiry process is that of mathematical modeling.”

He continues THESE ARE SO VERY,
VERY CLOSE TOGETHER.
WHAT ARE THE REAL DIFFERENCES
BETWEEN THE 1985 AND THE
1999 GUIDELINES?

Judy says THERE ARE TWO DIFFERENCES
THAT I SEE, STEWART.
ONE IS THAT IN THE '85
GUIDELINES ALL OF THE
STATEMENTS WERE IN THE UP
FRONT MATERIAL, THEY WERE NOT
A PART OF THE
CONTENT OBJECTIVES.
IN THE '99 GUIDELINES, THE
STATEMENTS ARE IN THE FRONT,
BUT THEY ARE ALSO EMBEDDED
IN THE EXPECTATIONS THAT
STUDENTS WILL ACHIEVE.
THAT IS A SIGNIFICANT
DIFFERENCE.
THE OTHER VERY INTERESTING
DIFFERENCE IS TECHNOLOGY.
THE ARCHITECTS OF THE '85
GUIDELINES FORESAW THE
IMPORTANCE OF COMPUTER
TECHNOLOGY, BUT DID NOT HAVE
IT AT THAT POINT.
WHEREAS RIGHT NOW, WE
HAVE RIGHT IN FRONT OF US
TECHNOLOGY THAT WILL ALLOW US
TO ACCOMPLISH MANY DIFFERENT
KINDS OF APPLICATIONS.

Stewart says THE 1999 CURRICULUM IS GOING
TO ASK TEACHERS TO WORK
DIFFERENTLY IN THE CLASSROOM.
I THINK ALL TEACHERS ARE
WONDERING WHAT KIND OF
SUPPORTS WILL BE AVAILABLE
TO THEM OVER THE NEXT LITTLE
WHILE TO HELP THEM OUT?

Judy says ONE WONDERFUL SUPPORT THAT'S
AVAILABLE RIGHT NOW IS
COURSE PROFILES.
THEY ARE AVAILABLE ON
THE ONTARIO CURRICULUM
CLEARINGHOUSE WEBSITE.
COURSE PROFILES HAVE BEEN
WRITTEN FOR EACH SUBJECT,
BOTH ACADEMIC AND APPLIED IN
MATHEMATICS, AND TWO SETS OF
COURSE PROFILES WERE WRITTEN.
ONE SET BY A PARTNERSHIP
OF CATHOLIC SCHOOL BOARDS
AND A SET BY A PARTNERSHIP
OF PUBLIC SCHOOL BOARDS.
IN ALL CASES, THE PROFILES
WERE WRITTEN BY TEACHERS
FOR TEACHERS.
THEY CONTAIN AN
OVERVIEW OF THE COURSE.
THEY ALSO CONTAIN DESCRIPTIONS
OF UNITS, AND EACH UNIT IS
BROKEN DOWN INTO ACTIVITIES
THAT ARE FULLY DESCRIBED.
WHAT IS UP ON THE OCC WEBSITE
RIGHT NOW IS ABOUT 40 PERCENT
OF THE FINAL COURSE PROFILE.
AND THAT INCLUDES THE COURSE
OVERVIEW, AND ABOUT 40 PERCENT
OF THE UNIT WORK.
IT SHOULD BE AVAILABLE IN
BOARDS IN PRINTED FORM
PROBABLY BY THE MIDDLE OF MAY.
THE FINAL 60 PERCENT SHOULD BE
AVAILABLE TOWARD THE END OF
THE SUMMER.

Stewart says ONE OF THE THINGS I SAW AS I
WAS LOOKING THROUGH A NUMBER
OF THE EXPECTATIONS IN THE
1999 CURRICULUM IS A STATEMENT
LIKE THIS ONE RIGHT HERE.

A blue piece of paper reads “The Curriculum embeds the learning of mathematics in the solving of problems base on real-life situations.”

He continues NOW,
EMBEDS

- CAN YOU
ELABORATE A LITTLE BIT MORE
ON WHAT THAT REALLY MEANS?

Judy says I MENTIONED AT THE BEGINNING
OF OUR DISCUSSION THAT I SEE
INQUIRY AS BEING CENTRAL
TO THIS CURRICULUM.

They appear in a small window at the right bottom of the screen.

She continues AND THE RELATIONSHIP STRAND IS
AN INTEGRATOR TO ALL OF THE
OTHER STANDS OF THE COURSE.
IF YOU TAKE A LOOK AT THE
ACTIVITY WE JUST SAW IN VIDEO,
THE BOUNCING BALL ACTIVITY,
A TEACHER CAN GO A LOT OF
DIFFERENT WAYS
WITH THAT ACTIVITY.
FOR INSTANCE, IF STUDENTS
ARE ASKED TO COME UP WITH A
FORMULA TO REPRESENT THE LINE
OF BEST FIT THEY ARRIVE AT,
TO DO THAT, THEY ARE PROBABLY
GOING TO HAVE TO LOOK AT
RATIOS OF BOUNCE HEIGHT TO
DROP HEIGHT, AND FROM THERE
DETERMINE WHAT IS THE
MULTIPLYING FACTOR.
AND THAT OPENS A CONTEXT FOR
DISCUSSION OF SKILLS AND RATIO.
SO WHAT I WOULD BE TEMPTED
TO DO AS A TEACHER IS, UPON
COMPLETION OF THE INQUIRY
ACTIVITY, AND EXTENSION AND SO
ON, I WOULD TALK ABOUT HOW
IMPORTANT THE USE OF RATIO WAS
IN DETERMINING THE FORMULA.
HOW POWERFUL RATIO IS AS A
COMPARER, AND THEN GO INTO
AN EXPLORATION OF STUDENT
SKILLS WITH RATIO.

He says YOU SAY EXPLORATION
OF STUDENT SKILLS.
WELL, WHAT DO YOU MEAN
BY EXPLORING SKILLS?

She says WELL, STUDENTS WHO COME INTO
GRADE NINE WILL PROBABLY
PRESENT QUITE A VARIATION IN
TERMS OF THEIR SKILL LEVELS.
AND RATHER THAN ASK EVERY
STUDENT TO RELEARN THE SAME
THINGS, IT WOULD PROBABLY
BE WORTHWHILE SPENDING
SOME TIME DIAGNOSING.
GETTING A SENSE OF WHICH
STUDENTS ALREADY HAVE SKILLS
AT THE LEVEL OF THE
EXPECTATION AND WHICH
STUDENTS NEED SOME
ADDITIONAL WORK.
FOR THOSE STUDENTS WHO NEED
ADDITIONAL WORK, THEN DIRECT
TEACHING MAY BE CALLED FOR,
ALONG WITH DRILL AND PRACTICE.
FOR STUDENTS WHO ALREADY
HAVE THE SKILLS, EXTENSION OR
ENRICHMENT ACTIVITIES
WOULD BE APPROPRIATE.
SO IT'S A MATTER OF TARGETING
THEIR NEED AND MEETING IT.

He says I THINK AT THIS POINT WE'VE
JUST COVERED A WHOLE BUNCH OF
MATERIAL HERE.
WE'VE TALKED ABOUT
EMBEDDING SKILLS.
WE'VE TALKED ABOUT THE
DIFFERENT THINGS YOU FIND IN
THE 1999 GUIDELINE THAT YOU
ALSO FIND IN 1985, REFERRING
TO TECHNOLOGY, REFERRING
TO COMMUNICATION.
THIS IS AN IDEAL MOMENT,
AGAIN, THIS IS A FORUM.
WE WOULD REALLY, REALLY LIKE
TO HEAR YOUR QUESTIONS, TO
CLARIFY CERTAIN ASPECTS, TO
ELABORATE, WHATEVER YOU WOULD
LIKE TO HEAR.
SO AGAIN, I WOULD REALLY URGE
YOU TO PHONE IN DURING THIS
LITTLE SEGMENT RIGHT NOW.
REMEMBER, THE WAY
TO DO IT IS POUND 9.
AND IT TAKES A MOMENT OR TWO
TO GET CONNECTED, BUT IT
DOESN'T TAKE TOO LONG, AND
THEN WE CAN SORT OF TRY TO
ANSWER AS BEST WE CAN.
WE CAN SORT OF BARREL ALONG
HERE, BUT I WOULD LOVE TO TAKE
A LITTLE BIT OF A BREAK
AND HEAR YOUR COMMENTS
AND QUESTIONS.
OKAY, WELL, I GUESS WHAT WE'RE
GOING TO DO IS JUST KEEP GOING.
AND IF WE DO GET A CALL,
PLEASE POP IN ANY TIME.
I REALLY DO MEAN THAT.
BECAUSE I THINK AS MUCH AS
ANYTHING, TALKING HEADS IS
BAD ENOUGH, WHEN IT'S NOT
A CONVERSATION, YOU KNOW
HOW IT IS.
I SEE THAT WE HAVE
A CALL COMING IN.

Judy says GOOD.

He continues SO IN A MOMENT OR TWO
WE'LL GET CONNECTED.
WHEN YOU ARE CONNECTED, PLEASE
INTRODUCE YOURSELF AND GO
AHEAD WITH YOUR
COMMENT OR QUESTION.

A man says FROM SIMCOE.

He says YES, GO AHEAD.

The man says IN ALL THE DISCUSSION ABOUT
APPLICATIONS BEING THE FOCUS
FOR MATHEMATICS, IT SEEMS
TO ME WE'RE IN A DANGER OF
CREATING A COURSE LIKE
PHYSICS, AND SO ON.
I ALWAYS THOUGHT OF
MATHEMATICS AS BEING THE
GENERAL OVERVIEW OF
LOGICAL THINKING.
IS THERE ANYTHING IN THIS
PROGRAM THAT ALLOWS STUDENTS
AND TEACHERS TO EXPLORE JUST
MATHEMATICS FOR THE ENJOYMENT
OF MATHEMATICS, RATHER THAN
ALWAYS PUTTING IT INTO
AN APPLICATION?

Stewart says DID YOU HEAR
THE END OF THAT?

Judy says YES, I DID HEAR
THE END OF IT.
AND MY ANSWER TO
THAT WOULD BE YES.
IF YOU LOOK AT THE ANALYTIC
GEOMETRY STRAND, IT RELATES TO
THE RELATIONSHIP STRAND IN
THAT IT IS THE ABSTRACTION OF
THE CONCRETE WORK THAT OCCURS
IN EXPLORING RELATIONSHIPS.
AND WITHIN THAT STRAND, THERE
IS QUITE A LOT OF OPPORTUNITY
FOR MULTI STEP PROBLEM SOLVING
INVOLVING EQUATIONS OF
STRAIGHT LINES.
IF YOU GO INTO THE MEASUREMENT
AND GEOMETRY STRAND, IN
THERE, AS WELL, THERE ARE
OPPORTUNITIES TO EXPLORE
RELATIONSHIPS
WITHIN MEASUREMENT.
FOR INSTANCE, THE RELATIONSHIP
BETWEEN VOLUME AND SURFACE
AREA OF A THREE
DIMENSIONAL OBJECT.
IN THE GEOMETRY SECTION, THE
EXPECTATIONS INVOLVE EXPLORING
RELATIONSHIPS AMONG
PROPERTIES OF PLAIN FIGURES.
SO THERE ARE MANY
OPPORTUNITIES TO EXPLORE THE
MATHEMATICS, AS WELL AS
LINKING IT TO OTHER THINGS.

Stewart says SOMETHING I WOULD ADD, TOO,
IS THERE IS OFTEN THE TERM
AUTHENTIC TYPES OF ACTIVITIES,
AUTHENTIC MATHEMATICS.
AUTHENTIC DOESN'T ALWAYS MEAN
IT'S AN APPLICATION THAT IS
USED IN A REAL-LIFE SITUATION,
LIKE AS A CARPENTER MIGHT,
FOR INSTANCE.
BUT IT'S ALSO ABOUT
THE MATHEMATICS THAT
MATHEMATICIANS DO.
SO THAT IS A REALLY
AUTHENTIC TASK, AS WELL.
AND THAT'S ANOTHER PLACE.
AND IF I RECALL CORRECTLY, THE
WORD ABSTRACTION DEFINITELY
DID APPEAR IN THE
CURRICULUM GUIDELINE.
SO THERE HAS TO BE SOME
SENSE OF THAT ABSTRACTION.
I THINK THE KEY TO THE
APPLICATIONS IS THAT, YES, YOU
INTRODUCE THEM AS YOU GO ALONG,
AND IT'S AN IMPORTANT THING.
IT'S IMPORTANT BECAUSE I
THINK IT'S A MOTIVATOR.
WE HAVE ANOTHER CALL.
THANK YOU VERY
MUCH FOR THAT CALL.
THAT WAS WONDERFUL.
AND I HOPE THAT GIVES
YOU A DECENT ANSWER.

Toni says HI, THIS IS TONI LANGOLSIC
FROM SAINT MARK HIGH SCHOOL
IN MANOTICK.
I JUST WONDERED, WE'RE DOING
A LOT OF WORK TO HELP THE
TEACHERS IN THIS CURRICULUM,
BUT ARE THE STUDENTS GOING TO
BE READY FOR THIS SORT OF
CHANGE IN THE CLASSROOM?
STUDENTS FROM THE ELEMENTARY
SCHOOL SYSTEM, WILL THEY HAVE
HAD EXPERIENCE, AND WILL THE
CURRICULUM HAVE BEEN COMPACTED
ENOUGH SO THAT WHEN THEY DO
COME TO US IN GRADE NINE,
THEY WILL BE PREPARED
FOR THE EXPECTATIONS?
BECAUSE RIGHT NOW, THE WAY I
SEE IT, LOOKING AT THE WORK
HABITS OF STUDENTS IN GRADE
NINE, AND ALSO THE LEVEL OF
KNOWLEDGE AND SKILLS,
THERE'S A LOT LACKING THERE.
AND WHEN YOU ARE DOING THESE
SORTS OF ACTIVITIES, YOU
REALLY NEED TO HAVE THEM ALL
FOCUSSED SO WE KNOW WHERE
WE'RE GOING WITH THEM.

Judy says THANK YOU FOR THE QUESTION.
I'LL ANSWER IT IN TWO PARTS.
ONE IS THE READINESS OF
STUDENTS WITH REGARD TO
EXPECTATIONS, AND THE OTHER
PART WE'LL DEAL WITH, THE
RELATIVE PHILOSOPHIES OF THE
ELEMENTARY CURRICULUM VERSUS
THE SECONDARY CURRICULUM.
BEGINNING WITH READINESS
OF STUDENTS, IN TERMS OF
EXPECTATIONS, THE GRADE ONE
TO EIGHT MATH CURRICULUM WAS
INTRODUCED ABOUT TWO
YEARS AGO, I THINK.
IS THAT CORRECT, STEWART?
IS IT TWO OR THREE?

Stewart says I THINK IT'S TWO.

Judy continues TWO.
AND IT WAS INTRODUCED IN
ALL EIGHT GRADES AT ONCE.
SO THERE CERTAINLY HAS NOT
YET BEEN ENOUGH TIME FOR THE
ENTIRE CURRICULUM TO BE
IMPLEMENTED FOR STUDENTS TO
WORK THEIR WAY THROUGH
ALL THE NEW EXPECTATIONS.
SO I WOULD EXPECT FOR THE NEXT
TWO OR THREE YEARS, WE WILL
FIND OURSELVES IN A TRANSITION
SITUATION IN WHICH WE MAY SPEND
MORE TIME ON NUMERIC SKILLS
IN GRADE NINE THAN WE WILL
IN THE FUTURE.
GRADUALLY, STUDENTS WILL COME
IN HAVING ACHIEVED THE MANY
NUMERICAL EXPECTATIONS
THAT ARE FOUND IN THE
ONE-TO-EIGHT CURRICULUM.
AND WE CAN THEN ADJUST WHAT WE
DO IN GRADE NINE ACCORDINGLY.
IN TERMS OF PHILOSOPHY AND
RECOMMENDED PEDAGOGY AND SO
ON IN THE TWO CURRICULA,
THEY ARE IN SYNC.
IT'S THE SAME PHILOSOPHY RIGHT
THE WAY THROUGH GRADE NINE.
AND THAT IS A BELIEF THAT
STUDENTS LEARN EFFECTIVELY
WHEN THEY HAVE OPPORTUNITIES
TO BE INVOLVED IN HANDS-ON
ACTIVITIES, TO HAVE CONCRETE
EXPERIENCES BEFORE MOVING
TO ABSTRACTIONS.

Stewart says I THINK THAT
PARALLEL IS CRITICAL.
I DO THINK IT IS
GOING TO TAKE TIME.
I DO THINK, THOUGH, WHEN YOU
SEE THE TAPES FROM THE TWO OR
THREE CLASSES NEXT WEEK, WHAT
YOU WILL SEE IS THAT EVEN THOUGH
THOSE KIDS MAY NOT HAVE HAD
THE SOLID FOUNDATION WE REALLY
WANTED, ARE ACTUALLY ALREADY
DOING THESE TYPES OF ACTIVITIES.
AND THE KEY IS, I THINK,
REALLY, COME BACK TO
MOTIVATION AGAIN.
THEY ENJOY THAT TYPE OF CLASS.
AND I THINK YOU WILL SEE THE
TEACHERS COMMENT ON THAT
AS WELL.
BY THE WAY, ONE OF THE THINGS
WE WILL BE ADDING JUST IN A
FEW MOMENTS HERE, IS WE DID
INTERVIEW FOUR TEACHERS WHO
ARE ACTUALLY DOING THESE TYPES
OF CLASSES AND ACTIVITIES.
AND I THINK YOU'LL BE
SURPRISED AT THEIR ENTHUSIASM
ABOUT HOW IT DOES WORK.
AND I THINK THIS IS A GOOD
OMEN, I HOPE, ANYWAY.
OKAY, WELL, I THINK ON THAT
NOTE, WE'LL KIND OF MOVE ALONG
A LITTLE BIT TO ANOTHER REALLY
RATHER CRITICAL ASPECT OF
THIS WHOLE -- THERE'S GOING
TO BE A CHANGE IN ASSESSMENT.

Judy nods.

He continues AND ASSESSMENT IS GOING TO
BECOME A BIGGER AND BIGGER
ISSUE, I THINK, IN HIGH SCHOOL
BECAUSE THERE ARE DEFINITELY
SOME BIG CHANGES COMING.
FOR INSTANCE, I THINK IN
THE PAST, WHAT WE WERE MOST
CONCERNED ABOUT WERE
CONCEPT AND PROCEDURE.
DID THE STUDENT
UNDERSTAND THE CONCEPT?
COULD THEY DO THE PROCEDURE?
BUT WE LEFT OUT SOME
PRETTY MAJOR PIECES.
CAN YOU DESCRIBE
SOME OF THOSE PIECES?

Judy says WELL, THE WHOLE AREA
OF THINKING, INQUIRY,
PROBLEM SOLVING.
WE ALL MAKE A REAL EFFORT TO
DO THAT IN OUR CLASSROOMS,
BUT IT MAY NOT BE AN
AREA THAT WE HAVE ASSESSED
AS FULLY AS WE MIGHT.
THE AREA OF COMMUNICATION AND
APPLICATION ARE TWO OTHER AREAS.
AND I THINK STEWART IS ABOUT
TO BRING UP THE ACHIEVEMENT
CHART FROM THE CURRICULUM
POLICY DOCUMENT.

He shows a blue document that displays five columns.

Stewart says NOW, THIS IS NOT A REALLY
GOOD PICTURE OF IT, ALTHOUGH
IT'S PAGE 39 IN
YOUR CURRICULUM.
AND WHAT ITS SET-UP IS, THIS
ACHIEVEMENT CHART FOR GRADE
NINE AND TEN, HAS
CATEGORIES AND LEVELS.
AND WHAT WE'RE GOING TO DO
IS TAKE A CLOSER LOOK AT THE
CATEGORIES, THEN JUDY IS GOING
TO DESCRIBE THE LEVELS FOR
ONE OF THOSE CATEGORIES.
SO WE'LL BRING UP SOME SLIDES
HERE TO BEGIN TO LOOK AT THIS
SOMEWHAT MORE CLOSELY.
FIRST OF ALL, THE FIRST
CATEGORY IS KNOWLEDGE
AND UNDERSTANDING.

A slate appears on screen under the title “Achievement Chart. Grade 9-10. Categories.” It reads “Understanding of concepts. Performing algorithms.”

The slate changes to “Thinking/Inquiry/Problem Solving. Reasoning. Applying the steps of inquiry/problem solving.”

The slate changes to “Communication. Communicating reasoning orally, in writing, and graphically. Use of mathematical language, symbols, visuals and conventions.”

The slate changes to “Application. Applying concepts and procedures relating to familiar and unfamiliar settings.”

Judy says WE'RE GOING TO GO NOW GO ON
AND LOOK AT ONE PARTICULAR
LEVEL OF THE
ACHIEVEMENT CHART.
ONE PARTICULAR CATEGORY, RATHER
THE APPLICATION CATEGORY.
AND EXAMINE THE FOUR LEVELS
FOUND IN THAT CATEGORY.
AS WE WALK THROUGH THEM,
LOOK FOR THE GROWTH THAT GOES
FROM CATEGORY TO CATEGORY.
SO, FIRST OF ALL,
APPLICATION LEVEL 1:

The slate changes to “Applies concepts and procedures to solve simple problems relating to familiar situations.”

The slate changes to “Application. Level number 2. Applies concepts and procedures to solve simple problems of some complexity relating to familiar situations.”

The slate changes to “Application. Level number 3. Applies concepts and procedures to solve complex problems relating to familiar situations; recognized major mathematical concepts and procedures relating to unfamiliar situations.”

The slate changes to “Application. Level number 4. Applies concepts and procedures to solve complex problems relating to familiar and unfamiliar settings.”

Stewart says EXACTLY WHAT IS THE
SIGNIFICANCE OF THIS WHOLE
CHART IN TERMS OF WHAT
WE DO AS TEACHERS?

Judy says WELL, WHAT I FIND TO BE THE
MOST SIGNIFICANT THING IS
THE FOUR CATEGORIES.
I THINK MOST OF US AS TEACHERS
DO A REALLY GOOD JOB OF
ASSESSING KNOWLEDGE,
UNDERSTANDING, PROCEDURES.
BUT AS YOU MENTIONED, THIS
CHART GOES MUCH BEYOND THAT.
IT LOOKS AT THE UNDERLYING
PROCESSES OF MATHEMATICS
THAT ARE MOST IMPORTANT.
THINKING, INQUIRY, PROBLEM
SOLVING, ALONG WITH KNOWLEDGE
AND UNDERSTANDING, ALONG WITH
COMMUNICATION AND APPLICATION.
AND I THINK THAT'S ONE OF
THE MAJOR CHALLENGES FOR A
TEACHER IS TO ASSESS THEIR
OWN PRACTICE AND ASK THE
QUESTION IN THE OPPORTUNITIES
THAT I GIVE TO STUDENTS IN
THE CLASSROOM, HOW WELL DO I
REFLECT ALL THESE CATEGORIES.

Stewart says RIGHT.
I THINK AT THIS POINT, AGAIN,
THIS IS A VERY, VERY LARGE
ISSUE, AND PERHAPS IT HASN'T
BEEN ADDRESSED TERRIBLY FULLY
YET IN THE ROLL-OUT OF THE
SECONDARY SCHOOL REFORM
IN A GENERAL SENSE.
THIS IS A GREAT TIME TO
AGAIN PHONE IN AND ASK SOME
QUESTIONS FOR CLARIFICATION
PURPOSES OR WHATEVER BECAUSE
I THINK THIS CHALLENGE IS ONE
THAT I THINK IS GOING TO BE
VERY DIFFICULT FOR
HIGH SCHOOL TEACHERS.
WHAT WE HAVE TO KEEP IN MIND
IS ELEMENTARY SCHOOL TEACHERS
ARE DOING THIS OR TRYING
TO DO THIS RIGHT NOW.
AND THEY ARE STRUGGLING.
BUT THEY'RE COMING ALONG.
AND I THINK IN DUE TIME, YOU
WILL SEE QUITE A DIFFERENCE
IN THE WAY THEY ASSESS, AND
THEREFORE THE WAY KIDS
UNDERSTAND
ASSESSMENT, AS WELL.
AGAIN, A GOOD
TIME TO PHONE IN.
POUND 9, YOU KNOW HOW
TO DO IT NOW.
YOU'RE GETTING
USED TO THIS.
PLEASE CALL IN AND TAKE
ADVANTAGE OF JUDY'S EXPERTISE.

Judy says STEWART, I THINK ONE OF THE
REALLY IMPORTANT THINGS TO
REMEMBER ABOUT THIS
ACHIEVEMENT CHART IS IT'S A
GRADUAL GROWTH FOR TEACHERS
IN LEARNING HOW TO USE THIS
STYLE OF ASSESSMENT.
AND I WOULD START BY LOOKING
AT WHAT IS HAPPENING
IN THE CLASSROOM.
ARE THERE OPPORTUNITIES
FOR THINKING, INQUIRY AND
PROBLEM SOLVING?
AND AS YOU TRY THOSE
ACTIVITIES, YOU ARE THEN TAKEN
INTO LOOKING AT OTHER
ASSESSMENT TOOLS.
THE STANDARD MARKING SCHEME IS
PROBABLY NOT APPROPRIATE FOR
ASSESSING COMMUNICATION,
FOR INSTANCE.
AND WHAT OTHER
TOOLS WILL WORK.

Stewart says THERE YOU ARE GETTING INTO
THE IDEA OF RUBRICS,
I PRESUME, AND THAT
KIND OF THING?

Judy says YEAH, POSSIBLY RUBRICS, MAYBE
A VERSION OF OBSERVATION
OF STUDENTS.
THERE'S QUITE A
RANGE OF THINGS.

Stewart says I UNDERSTAND IN THE PROFILES,
AS WELL, THAT THERE'S QUITE A
DEPARTURE IN TERMS OF THE
FINAL ASSESSMENT AND EVALUATION
OF THE STUDENTS AT
THE END OF THE COURSE.
CAN YOU DESCRIBE WHAT THE
PUBLIC PROFILE MIGHT HAVE DONE
WITH THAT?

Judy says YES, THE PUBLIC PROFILE HAS
SET ASIDE ABOUT, I THINK,
15 PERIODS, OR 15 HOURS,
FOR A FINAL ASSESSMENT.
AND PART OF IT IS A FINAL
EXAMINATION WITH A REVIEW,
AS WE ARE ACCUSTOMED TO DOING,
BUT THE OTHER PART OF IT IS A
SERIES OF PERFORMANCE TASKS
IN WHICH STUDENTS HAVE
OPPORTUNITIES TO DEMONSTRATE
THEIR SKILLS AND UNDERSTANDING
OF INQUIRY, AND COMMUNICATION
AND APPLICATION.
AND IT'S A WONDERFUL FUND
OF PERFORMANCE TASKS AND
ACTIVITIES THAT TEACHERS
MIGHT DRAW UPON.
THEY MAY NOT BE READY
IMMEDIATELY TO UNDERTAKE
ANYTHING QUITE THAT EXTENSIVE,
BUT THE WHOLE CONCEPT OF
BLENDING A PERFORMANCE TASK
WITH AN EXAMINATION IS A
VERY IMPORTANT NEW
DIRECTION FOR US.

Stewart says ACTUALLY, THAT
SOUNDS EXCITING.
WE DO HAVE A CALL.
AT LEAST FROM THE
SCHOOL SAINT MARK'S.
I'M NOT SURE WHERE
THE TEACHER IS FROM.
GO AHEAD AND
INTRODUCE YOURSELF.

Toni says HI, IT'S TONI LANGOLSIC AGAIN,
FROM SAINT MARK HIGH SCHOOL.
I'M PARTICULARLY, I GUESS,
CONCERNED REGARDING THAT
LEVEL FOUR AND TESTING
STUDENTS AT THAT LEVEL.
BECAUSE I FIND NOWADAYS, EVEN
WITH NORMAL TESTS, WHEN WE DO
HAVE A TRUE PROBLEM SOLVING
QUESTION, STUDENTS FIND, IT'S
DIFFICULT FOR MANY OF THEM,
AND THEY WOULD OBVIOUSLY
RATHER SEE QUESTIONS THAT ARE
SIMILAR TO WHAT THEY'VE DONE
IN THE HOMEWORK, ETC. SEE
THAT LEVEL FOUR AS THOSE TRUE
PROBLEM SOLVING QUESTIONS.
THE TYPE WHERE THEY'VE LEARNED
THE SKILLS, BUT NOW THEY HAVE
TO PUT THEM TOGETHER
IN A DIFFERENT WAY.
WOULD YOU AGREE WITH THAT IN
TERMS OF TESTING THAT SKILL IN
THAT PARTICULAR AREA, APART
FROM DOING TASKS IN CLASS THAT
SHOW THAT LEVEL FOUR THINKING?

Judy says I WOULD CERTAINLY AGREE THAT
BEING ABLE TO DEMONSTRATE
LEVEL FOUR ACHIEVEMENT
REQUIRES THAT THE ACTIVITY
ALLOW IT TO HAPPEN.
WHEN YOU LOOK AT MOST TESTS OF
SKILLS, THEY USUALLY ARE NOT
LEVEL FOUR KINDS OF QUESTIONS
ON IT, OR QUESTIONS THAT
WOULD ALLOW DEMONSTRATION OF
LEVEL FOUR UNDERSTANDING.
AND THAT'S ONE OF THE REASONS
FOR GETTING INTO PERFORMANCE
TASKS, WHICH DO INVOLVE MORE
INDEPENDENT WORK ON THE PART
OF THE STUDENT.
WHICH DO INVOLVE MORE OPEN
REASONING, WHICH ARE FAR MORE
OPEN FOR STUDENTS TO GO IN A
VARIETY OF DIRECTIONS, AND
REALLY DEMONSTRATE WHAT
THEY ARE ABLE TO DO.
NOT ONLY WOULD THAT BE A PART
OF ASSESSMENT, BUT IT MUST
ALSO BE A PART OF WHAT HAPPENS
IN THE CLASSROOM, AND IN
HOMEWORK, SO THE STUDENT
ACTUALLY HAS A CHANCE TO
PRACTICE THAT, AND TO
EXPERIENCE IT BEFORE
THEY ARE ASSESSED ON IT.

Stewart says I WOULD ALSO ADD TO DO WITH
LEVEL FOUR, THAT IT'S NOT
LEVEL FOUR JUST
IN ONE CATEGORY.
SOME STUDENTS ARE VERY
EFFECTIVE, FOR INSTANCE, AT
COMMUNICATING, AND SO
EFFECTIVE THAT THEY CAN
ACTUALLY ATTAIN A LEVEL
FOUR, BUT MAYBE HAVING MORE
DIFFICULTY WITH THE CONCEPTUAL
PART, AND MAYBE NOT ACHIEVE
AT THE SAME LEVEL.
THIS IS ONE OF THE GREAT
DIFFICULTIES WITH THIS.
YOU ARE ACTUALLY DOING A
BIT OF A BALANCING ACT.
YOU ARE LOOKING AT A STUDENT
IN A NUMBER OF DIFFERENT FACETS.
AND IN SOME OF THOSE FACETS
THEY MAY BE PERFORMING WELL
ABOVE GRADE LEVEL, OR AT GRADE
LEVEL, AND SOME OTHER FACETS
THEY MAY NOT BE.
HEREIN IS THE DIFFICULTY.
AND THIS IS QUITE A DEPARTURE,
I THINK, ALL BY ITSELF.

Judy says YES, IT IS.
AND AGAIN, I WOULD RECOMMEND
THAT TEACHERS HAVE A LOOK AT
THE COURSE PROFILES.
BOTH THE PUBLIC CONSORTIUM
AND CATHOLIC CONSORTIUM, THEY
BOTH HAVE BLENDED PERFORMANCE
TASK WITH FINAL EXAMINATION,
SO THERE ARE OPPORTUNITIES
FOR DEMONSTRATION OF LEVEL
FOUR IN THE PERFORMANCE TASK,
BUT ALSO IN THE EXAMINATION
THERE ARE QUESTIONS INCLUDED
THERE THAT ALLOW THE STUDENT
TO DEMONSTRATE THAT
LEVEL FOUR PERFORMANCE.

Stewart says I DON'T WANT TO PUT YOU ON
THE SPOT, BUT I THINK THAT THE
MINISTRY IS GOING TO WORK ON
EXEMPLARS FOR GRADE NINE.

Judy says THAT'S CORRECT.

Stewart continues AND I THINK, IN FACT, THIS
IS GOING TO HELP A LOT.
BECAUSE YOU KNOW, I THINK
IT IS UNCLEAR IN MY MIND
WHAT A LEVEL FOUR
PERFORMANCE REALLY IS.
AND I THINK WE NEED SAMPLES
OF STUDENT WORK DISTRIBUTED
TO ALL TEACHERS.
AND THE EXEMPLARS PROJECT IS
PROBABLY GOING TO DO JUST THAT,
WHICH WILL HELP US UNDERSTAND
WHAT A LEVEL FOUR REALLY MEANS.
I THINK YOU MIGHT BE
A BIT SURPRISED, TOO.

Judy says I AGREE.
AND I THINK THE RESULTS OF
THAT EXEMPLARS PROJECT WILL BE
VERY HELPFUL TO US.

Stewart says WELL, I DON'T SEE ANY -- OH,
THERE'S A QUESTION COMING IN,
SO I WON'T POP OFF
ONTO SOMETHING ELSE.
AND I THINK IT'S ALSO COMING
FROM St. MARK'S SCHOOL,
AS WELL, IN THE OTTAWA AREA.
AND WE'LL BE CONNECTED IN
JUST A HALF A SECOND OR SO.
GO AHEAD, AND YOUR NAME IS?

Tom says IT'S TOM FROM OTTAWA.
HELLO, JUDY AND STEWART.

Stewart laughs.

Judy says HI, TOM.

Stewart says I KNEW YOU'D CALL SOMETIME.

Tom says I'M GOING TO READ A SENTENCE
FROM THE PROGRAM PLANNING AND
ASSESSMENT THAT PROBABLY WILL
BE ON A LOT OF PEOPLE'S MINDS.
IT SAYS, UNTIL THESE MATERIALS

REFERRING TO SOME
MATERIALS TO SUPPORT
ASSESSMENT, ARE PROVIDED,
TEACHERS MAY CONTINUE
TO FOLLOW THEIR CURRENT
ASSESSMENT AND
EVALUATION PRACTICES.
I JUST WONDERED IF YOU COULD
COMMENT ON THAT, JUDY.

Judy says THE INTENT OF THAT STATEMENT
IS TO ALLOW TEACHERS TIME TO
BEGIN WORKING WITH THE NEW
CURRICULUM, AND THE COURSE
PROFILES THAT GIVE THEM GOOD
EXAMPLES OF PERFORMANCE
ASSESSMENT.
SINCE THE EXEMPLARS ARE NOT
YET AVAILABLE, IT DIDN'T SEEM
FAIR TO ASK TEACHERS TO BEGIN
ASSESSING COMPLETELY FROM THE
ACHIEVEMENT CHART UNTIL THEY
DO HAVE GOOD EXAMPLES OF
PERFORMANCE AT
EACH OF THE LEVELS.
SO IT'S AN OPPORTUNITY FOR
TEACHERS TO GROW WITH THIS
NEW DIRECTION.

Stewart says DOES THAT ANSWER
YOUR QUESTION, TOM?
OH, HE'S GONE.
OKAY.
WELL, BYE, TOM.
YOU KNOW, IN A MORE HOLISTIC,
LOOKING AT ASSESSMENT, AT THE
INQUIRY MODEL, THE WHOLE
BUSINESS, I WOULD SAY THIS
WOULD BE KIND OF OVERWHELMING
TO MOST TEACHERS.
I REALLY FEEL THAT MYSELF.
WHAT DO YOU THINK A TEACHER
SHOULD DO TO GET STARTED?

Judy says WELL, THERE'S NO QUESTION
THERE ARE A LOT OF NEW THREADS
AS A RESULT OF
THIS CURRICULUM.
YOU HAVE NAMED ASSESSMENT,
INQUIRY, AND OF COURSE
INQUIRY INVOLVES CHANGES
IN CLASSROOM MANAGEMENT.
TECHNOLOGY IS ANOTHER
MAJOR NEW DIRECTION.
MY ADVICE TO TEACHERS IS TO
SELECT SOMETHING THAT IS NEW
AND START WORKING ON IT.
FOR INSTANCE, IT MAY BE
THAT FOR THIS COMING YEAR,
THE FOCUS OF YOUR EFFORTS WILL
BE AT TRYING TO INCLUDE MORE
ACTIVITIES OF AN
INQUIRY NATURE.
AND TRYING TO IMBED SKILLS
WITHIN THOSE ACTIVITIES.
AND IF THAT'S WHAT YOU WORK
ON NEXT YEAR, I WOULD SAY
THAT IS A MAJOR STEP.
A TEACHER MAY FIND HE OR SHE
IS GRADUALLY MORE COMFORTABLE
WITH INTEGRATING TECHNOLOGY
INTO THOSE, AS MORE EXAMPLES
OF THE USE OF TECHNOLOGY
BECOME AVAILABLE.
SO I GUESS MY ADVICE WOULD BE,
GET STARTED, ALLOW YOURSELF
TO GROW, MAKE A
CONSTANT EFFORT AT IT.
TALK WITH COLLEAGUES.
GO TO WHATEVER IN-SERVICE IS
AVAILABLE TO YOU, AND JUST
KEEP ON WORKING WITH IT.

Stewart says I SEE WE HAVE ANOTHER
CALL COMING IN, SO AS SOON
AS WE ARE CONNECTED,
WE WILL GO AHEAD.
GO AHEAD.

Anne says HI.
IT'S ANNE CURRIE FROM
IMMACULATA HIGH SCHOOL
IN OTTAWA.
I UNDERSTAND EVERYTHING YOU
ARE SAYING, AND IT'S MAKING
MUCH MORE SENSE TO ME
AT THIS POINT IN TIME.
THE ACTIVITIES, I WAS UNDER
THE IMPRESSION THE WHOLE
COURSE WAS GOING TO BE THAT.
SO IT'S MAKING MORE SENSE NOW
TO ME THAT WE ARE GOING TO
SUPPLEMENT WITH ACTIVITIES
AT THIS STAGE OF THE GAME.
NOW, I HAVE, I
GUESS, TWO QUESTIONS.
NUMBER ONE, HAVE YOU WORKED
WITH THE UNIVERSITIES TO SEE,
ARE WE GOING TO HAVE THESE
KIDS READY FOR UNIVERSITY WITH
THOSE CALCULATORS, ETC. DO
THEY USE THOSE CALCULATORS AT
UNIVERSITY, OR SHOULD WE
BE PUTTING MORE FOCUS
ON COMPUTERS?
AND MY SECOND QUESTION IS,
DO WE HAVE A BOOK AVAILABLE?
ARE WE GOING TO
GET A TEXTBOOK?
WE'RE MID-MAY NOW.
THIS IS BEGINNING
IN SEPTEMBER.
IS A TEXTBOOK COMING OUT FOR
US SO WE CAN ACTUALLY SEE
HANDS-ON WHAT'S HAPPENING?

Judy says OKAY, THE FIRST QUESTION
ABOUT TECHNOLOGY.
THE DIFFERENCE BETWEEN
CALCULATORS AND COMPUTERS,
IT'S A VERY FINE LINE.
FOR INSTANCE, A GRAPHING
CALCULATOR WILL DO VIRTUALLY
EVERYTHING THAT GRAPHING
SOFTWARE ON A COMPUTER WILL DO.
THE DIFFERENCE BEING IT'S HAND
HELD, THE DISPLAY IS SMALLER,
BUT ONE ADVANTAGE TO A
MATH TEACHER IS GRAPHING
CALCULATORS USUALLY ARE IN THE
MATH DEPARTMENT, SO YOU HAVE
CONTROL OVER THEM, AND
YOU HAVE MORE ACCESS AND
FLEXIBILITY IN THEIR USE.
THE ADVANTAGE OF COMPUTERS IS
IT'S A LARGER COLOUR DISPLAY.
IT'S MORE GRAPHICALLY
APPEALING, AND SO ON.
AND, IN FACT, THERE MAY BE SOME
SOFTWARE NOT AVAILABLE ON
GRAPHING CALCULATORS,
OR VICE VERSA.
IN TERMS OF UNIVERSITIES,
WHEN WE GO TO THE LEVEL OF
PROFESSIONAL MATHEMATICIANS,
THEY MAKE USE OF TECHNOLOGY
ALL OF THE TIME.
I GUESS OUR QUESTION
IS ABOUT FIRST YEAR.
WHAT HAPPENS IN FIRST YEAR
MATHEMATICS PROGRAMS?
AND FROM WHAT I'VE BEEN
ABLE TO TELL, THERE IS NO
CONSISTENT ANSWER THERE.
IT VARIES FROM
SCHOOL TO SCHOOL.
IN THE SENIOR DIVISION,
IN GRADES 11, 12 OF THE
CURRICULUM, WHICH ARE STILL
IN VALIDATION, THAT IS A
QUESTION WE ARE DEALING
WITH VERY CAREFULLY.
WE WANT TO BE SURE THAT OUR
STUDENTS ARE PREPARED WELL FOR
WHATEVER THEY ARE GOING TO
MEET IN FIRST YEAR UNIVERSITY.
BUT WE ALSO WANT THEM TO BE
CONVERSANT WITH THE MOST
RECENT TECHNOLOGIES, THAT
ALLOW THEM TO WORK WITH MORE
ENGAGING, MORE
CHALLENGING PROBLEMS.
SO WE'RE WALKING A FINE LINE,
AND WE ARE STILL DEVELOPING
OUR APPROACH AROUND
THE SENIOR DIVISION.

Stewart says YES, VERY MUCH SO.
WHAT I THINK WE'LL DO AT THIS
POINT IS WE'RE GOING TO DO A
REALLY QUICK BOUNCE BACK TO
LOOK AT THAT ACTIVITY ONE MORE
TIME AS A BIT OF A REMINDER
ABOUT WHAT THAT ACTIVITY WAS
ALL ABOUT.
BECAUSE IT WAS A LONG TIME
AGO NOW THAT WE ACTUALLY
LOOKED AT IT.
SO WE ARE GOING TO WATCH ABOUT
20 SECONDS OF IT, AND THEN WE
ARE GOING TO FINISH OUT ON A
COUPLE MORE NOTES, AND TAKE
SOME MORE QUESTIONS, AND THAT
SHOULD BE JUST ABOUT IT.
GO AHEAD WITH THAT
LAST 20 SECOND, PLEASE.

The clip plays again.

[general chatter]

A student says DOES THAT LOOK
STRAIGHT TO YOU?

A girl with shot hair says YOU SAW 37?

A blond female student says 44.

A blond male student drops a ball.

A brunette student says THAT WAS 18.

Lucy says OKAY, WHEN YOU ARE...

The clip ends.

Stewart says THAT'S A BIT OF A REMINDER.
I SEE WE'VE GOT A CALLER FROM
ASSUMPTION, AND WE'LL TAKE
THAT CALL AND GO
ON FROM THERE.
GO AHEAD, AND
INTRODUCE YOURSELF.

Pina says HELLO, MY NAME IS PINA DE
CLEMENTE FROM ASSUMPTION
HIGH SCHOOL IN BURLINGTON.
I JUST NEED A LITTLE BIT OF
HELP WITH CONCRETE EXAMPLES.
EVEN THOUGH YOU DON'T HAVE
THE STUDENT EXEMPLARS TO
DEMONSTRATE LEVEL FOUR
THINKING, CAN YOU NOT PROVIDE
A SPECIFIC EXAMPLE OF HOW
YOU WOULD TEST LEVEL
FOUR THINKING?

Stewart says I MIGHT JUMP IN ON
THIS ONE IN A SENSE.
THERE ARE ALL KINDS OF
ACTIVITIES THAT ARE OPEN ENDED.
AND ONE OF THE ACTIVITIES --
I WISH I HAD IT WITH ME NOW,
THAT YOU'VE ASKED THE
QUESTION -- THAT I ASK STUDENTS
IN GRADE SEVEN AND EIGHT,
AND ACTUALLY IS A WONDERFUL
LITTLE PROJECT EQUALLY SO IN
GRADE NINE, WHERE YOU SIMPLY
ASK A QUESTION LIKE, YOU HAVE
TRIANGLES WHICH HAVE INTEGRAL
LENGTHS -- OR I SHOULD
SAY INTEGRAL PERIMETERS.
SO A PERIMETER OF SAY 12.
YOU ASK THE STUDENT TO FIND
ALL THE POSSIBILITIES YOU CAN
FIND OF LENGTHS OF SIDES THAT
WOULD MAKE A TRIANGLE WITH A
PERIMETER OF 12, BUT OF
COURSE THE SIDES ALSO HAVE
TO HAVE INTEGRAL LENGTH.
AS IT TURNS OUT, IF YOU DO A
WHOLE INVESTIGATION WHEN YOU
START WITH A PERIMETER OF
THREE AND MOVE ON UP AS FAR AS
YOU WANT, THIS IS THE KIND OF
THING WHERE IT TAKES A LOT OF
WORK ON BEHALF OF THE STUDENTS
TO ORGANIZE THEIR INFORMATION,
AND THEN EVENTUALLY
DRAW CONCLUSIONS.
NOW, THERE ARE A LOT OF
DIFFERENT LEVELS OF ACTUAL
PERFORMANCE IN THAT.
MAYBE AT LEVEL ONE, THEY ARE
JUST BEGINNING TO GET AN
UNDERSTANDING OF
THE TRIANGLES.
PERHAPS THEY DON'T EVEN
QUITE UNDERSTAND THE
TRIANGLE INEQUALITY.
SO THEY'LL GIVE A TRIANGLE,
FOR INSTANCE, A GOOD EXAMPLE
MIGHT BE A TRIANGLE WITH
SIDES ONE, FOUR, AND FIVE.
OR ONE, THREE, AND FIVE, WHICH
IS AN IMPOSSIBLE TRIANGLE.
THEN YOU MOVE ALONG THROUGH
THE LEVELS UNTIL YOU GET TO
THE STUDENT WHO NOT ONLY
UNDERSTANDS WHAT MAKE UP A
TRIANGLE AND LIST THEM ALL
VERY CAREFULLY AND VERY
ACCURATELY, BUT ALSO GETS TO
THE POINT WHERE THEY CAN BEGIN
TO ANALYZE THEIR RESULTS IN
SOME WAY, SHAPE OR FORM, IN
TERMS OF SEEING EITHER A
PASTERN, OR THE EXISTENCE OF
A PATTERN, OR SOMETHING
ELSE ALONG THAT LINE.
IT'S A WHOLE CONTINUUM.
SO WE NEED TO ASK MORE
QUESTIONS WHICH ALLOW FOR
MANY LEVELS OF ANSWERS.

Judy says YES, EXACTLY.
HERE'S ANOTHER EXAMPLE THAT WE
HAVE USED IN OUR GRADE NINE
THE LAST COUPLE OF YEARS.
IT INVOLVES
APPLICATIONS OF PERCENT.
SO THERE'S A VARIETY OF THEM.
TIPS, SALES TAX,
COMMISSION, AND SO ON.
AND WHAT WE ASK STUDENTS TO DO
IS WRITE A STORY, AND WITHIN
THE STORY, THEY HAVE TO
REFLECT ALL OF THE DIFFERENT
APPLICATIONS OF PERCENT.
AND WE USUALLY TIE IN SOME
RATIO AND RATE AS WELL.
AND IT'S AMAZING THE
DIFFERENCES YOU SEE IN THAT
KINDS OF THING.

Stewart says I SEE WE HAVE ANOTHER CALL.
GO AHEAD AND
INTRODUCE YOURSELF.

Karen says HELLO, KAREN BRUSSO FROM
SAINT PETER'S HIGH SCHOOL IN --
WHERE AM I?
ORLEANS.
A LOT OF US HAVE HAD A LOT OF
EXPERIENCE IN TRANSITIONS AND
DOING A LOT OF GROUP WORK,
AND ONE OF THE CONCERNS OF THE
TEACHER IS HOW CAN WE ENSURE
THAT STUDENTS DO THEIR OWN
WORK AND DEMONSTRATE THEY
UNDERSTAND THE CONCEPTS AND
DON'T DEPEND ON THEIR FELLOW
STUDENTS FOR SUCCESS?

Stewart says GO AHEAD, JUDY.

Judy smiles and says RIGHT.
THERE'S NO QUESTION THAT'S A
PROBLEM THAT REMAINS WITH US.
AND THERE ARE A
VARIETY OF TECHNIQUES.
ONE THAT I'VE USED, IF IT'S
A GROUP ACTIVITY, I WILL ASK
THAT EVERY STUDENT PREPARE THE
WRITTEN REPORT, AND EITHER
HAVE THEM ALL HAND THEM
IN, OR RANDOMLY SELECT ONE.
SO THAT WAY EVERY STUDENT
HAS TO BE PREPARED.
HAVE YOU USED
OTHER TECHNIQUES?

Stewart says WELL, I THINK
THERE'S TWO THINGS.
I MEAN, THERE'S THE
ACTIVITY ITSELF THAT
CAN BE COOPERATIVE.
BUT EVENTUALLY AN ASSESSMENT
CAN BE BASED ON THE ACTIVITY
ITSELF WHICH ASKS FOR
INDIVIDUAL PERFORMANCE, AS WELL.
SO THERE ARE A NUMBER
OF SITUATIONS HERE.
THE OTHER THING IS, IN
COOPERATIVE GROUP WORK, WE'RE
LOOKING AT OTHER CATEGORIES,
AS WELL, PERHAPS.
AND MAYBE WE'RE NOT LOOKING
FOR THE PROCEDURAL KNOWLEDGE,
OR THE CONCEPT KNOWLEDGE, SO
MUCH AS MAYBE THE COMMUNICATION
AND ABILITY TO ACTUALLY GET
SOME PROBLEM SOLVING DONE
AS A GROUP.
SO IT DEPENDS UPON EXACTLY
WHAT YOU ARE ASSESSING WHEN
YOU ARE DOING A
COOPERATIVE SMALL GROUP.
I THINK ALSO, ONE THING I HAVE
DONE, AND THIS IS SOMETHING I
LIKE DOING EXCEPT THAT IT'S
TIME CONSUMING, AND YOU CAN'T
DO IT FREQUENTLY.
THAT'S WHERE, IN FACT, THE
STUDENTS HAVE DONE A GROUP
PROJECT, AND I INTERVIEW EACH
STUDENT INDIVIDUALLY FOR FIVE
MINUTES, PROBABLY DURING A
LUNCH PERIOD, OR AFTER SCHOOL,
OR SOMETHING LIKE THAT, WHERE
THEY ACTUALLY HAVE TO SIT
DOWN IN FRONT OF ME AND
ACTUALLY EXPLAIN ORALLY
EXACTLY WHAT THEY UNDERSTOOD
AND WHAT THEY LEARNED.
AND THAT CLARIFIES
MANY, MANY PROBLEMS.

Judy says NOW, COULD YOU DO A VARIATION
ON THAT AND ACROSS A SET OF
ACTIVITIES, YOU WOULD GET
TO EVERY STUDENT, BUT NOT
NECESSARILY INTERVIEW EVERY
STUDENT EVERY ACTIVITY.

Stewart says THAT'S RIGHT.
THAT WOULD BE A GOOD
VARIATION, AS WELL.
NOW, WE DID RUN THAT
LITTLE PIECE OF TAPE.
AND ONE OF THE REASONS WE RAN
IT WAS TO ASK, IN THAT KIND
OF ACTIVITY, WHAT CATEGORIES
COULD WE HAVE ASSESSED?
WE CAN ASK YOU, IF YOU
WOULD LIKE TO OFFER.
DO YOU THINK WE WOULD BE ABLE
TO ASSESS MAYBE ONE CATEGORY,
TWO, OR PERHAPS ALL FOUR?
WHAT DO YOU THINK?

Judy says YOU'RE ASKING ME, OR ARE YOU
ASKING THE FOLKS AT HOME?

She laughs.

Stewart says WELL, I'M ASKING THE FOLKS
OUT THERE, BUT, YOU KNOW,
IT'S LATE IN THE DAY, SO
I'M GOING TO ASK YOU.

She says ALL RIGHTY.
I WOULD ASSUME THE TEACHER
WOULD ASK FOR A WRITTEN REPORT.
SO THERE'S AN OPPORTUNITY
THERE TO LOOK AT
COMMUNICATION, TO
LOOK AT REASONING.
DURING THE ACTUAL WORK ON THE
ACTIVITY IN CLASS, THROUGH
OBSERVATION, YOU CAN GET A
LOOK AT HOW THE STUDENT IS
MANAGING THE WHOLE ACTIVITY,
WHETHER THEY'VE UNDERSTOOD THE
PROBLEM, WHETHER THEY ARE ABLE
TO PLAN A REASONABLE APPROACH
TO IT, WHETHER THEY CONSIDER
REPRESENTIVITY IN THE DESIGN
OF THEIR EXPERIMENT.
FOR INSTANCE, THE TEACHER IN
THE VIDEO CLIP ASKED THEM TO
TAKE THREE MEASUREMENTS AND
THEN FIND THE AVERAGE OF THEM.
SO THROUGH OBSERVATION, YOU
CAN SOMETIMES GET A LOT
OF INFORMATION.
BUT I THINK THE WRITTEN REPORT
WOULD GIVE YOU A GOOD LOOK
AT COMMUNICATION, AND AT
REASONING, AND THE WHOLE
INQUIRY PROCESS.

Stewart says THAT'S GREAT.
NOW, WHAT WE ARE GOING TO
DO AT THIS POINT IS RUN A
LITTLE VIDEO PIECE WITH THREE
DIFFERENT TEACHERS COMMENTING
ON THE ASSESSMENT THEY SEE
IN THIS PARTICULAR ONE.

Judy says GOOD.

Stewart says LET'S SEE IT.

A clip plays.

John Kennedy sits in a library. He’s in his mid-thirties, clean-shaven with short combed hair. He’s wearing a checked shirt and a blue patterned tie.

John says IN ASSESSING THIS KIND OF AN
ACTIVITY, CERTAINLY YOU DO
HAVE TO USE DIFFERENT
TECHNIQUES, IN THAT NOT ONLY
ARE WE SIMPLY TRYING TO TEACH
THE KIDS SPECIFIC SKILLS AND
COMPUTATIONAL SKILLS, IT'S THE
WHOLE PROCESS OF COMING UP
WITH A QUESTION, COMING UP
WITH HYPOTHESES, TESTING THEM,
ANALYZING DATA,
DRAWING CONCLUSIONS.
SO IN THAT FULL CIRCLE, YOU
WANT TO BE OBSERVING THE
STUDENTS AND HAVE SOME IDEAS
OF THE EXPECTATIONS AND THE
KIND OF THINGS YOU
WANT TO SEE FROM THEM.
SO IF YOU HAVE SPECIFIC
LEARNING OUTCOMES IN ADVANCE,
SO YOU CAN THEN OBSERVE THE
KIDS WHILE THEY ARE ACTUALLY
WORKING, AND ASSESS THEM IN
THAT FORMAT, THOSE ARE THE
KINDS OF THINGS YOU HAVE TO
DO A LITTLE BIT DIFFERENTLY
THAN WHAT WE DO NOW.
AND THEN, OF COURSE, DOWN THE
ROAD, YOU WILL ALSO HAVE A
TRADITIONAL PENCIL AND PAPER
KIND OF EVALUATIONS AS WELL.

Lucy says THERE WAS A LOT
GOING ON IN THE ROOM.
I WOULD BE WALKING AROUND
OBSERVING HOW THEY WORK IN
GROUPS, HOW THEY COMMUNICATE.
ARE THEY USING
MATHEMATICAL TERMS?
ARE THEY COLLABORATIVE
IN THEIR APPROACH?
YOU'RE LOOKING FOR, DO THEY
GIVE UP BECAUSE BEING ABLE TO
STAY WITH A MATHEMATICAL
PROBLEM IS 90 PERCENT OF
GETTING THERE.
SO YOU ARE LOOKING FOR THEIR
DETERMINATION TO PURSUE TO THE
END WHAT THE ANSWER TO A
PARTICULAR QUESTION IS, OR THE
CONCLUSION OF AN EXERCISE.
SO I'D BE LOOKING FOR
PERSONALITY TRAITS LIKE
DETERMINATION, TASK
COMMITMENT, THOSE KINDS
OF THINGS.
AND THAT'S THROUGH
OBSERVATION.
IN THEIR WRITTEN WORK, I'D
BE LOOKING FOR HOW WELL
THEY HAD UNDERSTOOD
MATHEMATICAL CONCEPTS.
HOW CLEARLY DO THEY PRESENT
WHAT THEY HAVE DONE.
DO THEY USE GOOD APPROPRIATE
MATHEMATICAL LANGUAGE.
CAN THEY TAKE WHAT THEY'VE
LEARNED HERE AND USE IT IN A
DIFFERENT SITUATION
THAT'S SIMILAR?
ARE THEY ABLE TO DO THAT?
AND THAT CAN BE DONE BY GIVING
THEM A DIFFERENT EXERCISE.
SENDING THEM OUT TO TRY
A DIFFERENT EXPERIMENT.
IT CAN CERTAINLY EVEN BE DONE
IN VERY TRADITIONAL WAYS WITH
A TEST ON SLOPE, ALTHOUGH
IDEALLY, YOU'D REALLY WANT TO
SEND THEM OUT TO RUN ANOTHER
EXPERIMENT OF THEIR CHOICE,
AND BRING YOU BACK
RESULTS FROM THAT.

Myrna Ingles appears. She is in her late forties and has short blond hair and bangs. She’s wearing a bright blue cardigan with floral motifs.

Myrna says WHEN ASSESSING AN ACTIVITY
LIKE THIS, IT'S GOING TO
DEPEND A LITTLE BIT ON WHAT
PART OF THE SEMESTER YOU'VE
USED IT.
IF THE KIDS HAVE WORKED WITH
THE TECHNOLOGY BEFORE, OR
LOOKED AT RELATIONSHIPS
BEFORE, YOU MIGHT ASSESS IN A
MORE FORMAL WAY.
IF YOU ARE JUST INTRODUCING
THE UNIT ON RELATIONSHIPS, OR
IF YOU ARE JUST STARTING TO
USE TECHNOLOGY, PROBABLY JUST
OBSERVATION WOULD BE
YOUR BEST WAY TO DO IT.
LISTEN TO WHAT THE KIDS SAY,
WATCH WHAT THEY ARE DOING,
GIVE SUGGESTIONS WHERE YOU
SEE THAT CORRECTIONS WOULD
BE APPROPRIATE.
IF YOU'VE WORKED WITH THESE
MATERIALS QUITE A BIT BEFORE,
IT WOULD BE HANDY TO SAY I'M
GOING TO ASSESS MORE FORMALLY
WHAT SOME OF THE
STUDENTS ARE DOING.
YOU WON'T HAVE TIME TO ASSESS
EVERYBODY ALL AT ONCE, SO YOU
PICK A SMALL GROUP OF STUDENTS
AND SET YOURSELF OUT A RUBRIC
OF DIFFERENT THINGS YOU'D LOOK
FOR, AND LOOK FOR THE RANGE
OF RESPONSES YOU MIGHT GET.

The clip ends.

Stewart says WELL, WE'RE BACK.
AND WE'RE REALLY AT THE
VERY END OF THIS PROGRAM.
SO WHAT WE'RE ASKING FOR,
THIS IS THE QUESTION
AND ANSWER SESSION.
AS IF WE HAVEN'T ANSWERED ANY
QUESTIONS UP TO THIS POINT,
OR TRIED TO ANYWAY.
SO THIS IS YOUR LAST
OPPORTUNITY THIS WEEK
TO GIVE US A CALL.
NEXT WEEK ON THE 17th, IT IS
AN ENTIRELY DIFFERENT PROGRAM.
UNFORTUNATELY, I WON'T
HAVE JUDY WITH ME.
I WILL HAVE A GENTLEMAN
NAMED VINCE DELISI.
AND HE IS VERY KNOWLEDGEABLE
WHEN IT COMES TO USING
TECHNOLOGY IN THE CLASSROOM.
AND WE WILL ADDRESS A FEW OF
THE OTHER ISSUES DURING THAT
PROGRAM THAT WE HAVE NOT
CERTAINLY ADDRESSED THIS TIME.
I SEE WE HAVE A QUESTION.
AND COULD YOU INTRODUCE
YOURSELF, PLEASE?

Karen says HELLO, KAREN BRUSSO FROM
SAINT PETER'S HIGH SCHOOL.
THERE'S A CONCERN OVER
HERE ABOUT CLASS SIZE.
NOW, THE VIDEO THAT WE SAW
SEEMED TO INDICATE THERE WERE
ABOUT 15 STUDENTS
IN THE CLASSROOM.
AT THIS POINT, CLASS SIZES
SEEM TO BE INCREASING.
I JUST THINK IT'S A
CONSIDERATION FOR PEOPLE WHO
ARE PUTTING TOGETHER THESE
ACTIVITIES TO CONSIDER THAT
THE CLASS SIZE SEEMS TO BE
INCREASING, AND HOW ARE WE
GOING TO DEAL WITH THAT AND
STILL DO THESE OBSERVATIONS
THAT SEEM TO BE SO IMPORTANT
FOR THE NEW CURRICULUM?

Stewart says QUICK RESPONSE ON THAT ONE.
YES, YOU'RE RIGHT, THAT
PARTICULAR CLASS WAS
QUITE SMALL.
THE OTHER TWO CLASSES THAT
WE DID IN UNIONVILLE --
OR I DIDN'T MENTION WHO THE
SPEAKERS WERE, AND I'LL
MENTION THAT IN JUST A MOMENT,
BUT IN UNIONVILLE, THE CLASS
WAS PROBABLY ABOUT 24, AND THE
CLASS THAT WE DID AT MARSHALL
MCLUHAN WAS ABOUT 24 OR 25.
AND, IN FACT, WHEN WE
WENT TO THE THIRD SCHOOL,
MARC GARNEAU, THE CLASS
SIZE WAS AT LEAST 30.
SO I GUESS WHAT I'M SAYING
THERE IS WE'VE ACTUALLY TRIED
THIS IN CLASSES THAT
ARE DEFINITELY LARGER.
I THINK THE CHALLENGES ARE
A LITTLE BIT DIFFERENT,
AND I WOULD CERTAINLY AGREE.
BUT WHILE I'M ON THAT NOTE,
THE FIRST SPEAKER, BY THE
WAY, WAS JOHN KENNEDY
FROM UNIONVILLE.
THE SECOND SPEAKER WAS LUCY
BURSTON, WHO YOU HAD SEEN AT
LEASIDE IN THE
CLASSROOM BEFORE.
AND THE THIRD SPEAKER IS
MYRNA INGLES, AND SHE'S ALSO
AT UNIONVILLE.
AND I BELIEVE SHE HAD
SOMETHING TO DO WITH THIS
CURRICULUM, DIDN'T SHE?

Judy says YES, MYRNA WAS ONE OF OUR LEAD
WRITERS IN THE CURRICULUM.

Stewart says AND SHE'S A TEACHER, IN
THE CLASSROOM RIGHT NOW.

Judy says THAT'S RIGHT.

Stewart says AND I THINK THAT'S IMPORTANT
TO REALLY, REALLY HIGHLIGHT.
AGAIN, WE'LL GIVE YOU ONE
LAST OPPORTUNITY TO PHONE IN.

Judy says JUST BEFORE YOU DO THAT,
I'D LIKE TO ADDRESS KAREN'S
QUESTION ABOUT HOW DO
YOU MANAGE ASSESSMENT BY
OBSERVATION WITH A CLASS OF
OVER 30, AND I THINK MYRNA
MADE A REFERENCE TO THE FACT
THAT YOU DON'T TRY TO ASSESS
EVERYTHING WITH
EVERYONE EVERY DAY.
WHAT YOU WOULD DO IS SELECT
A CRITERION, SELECT A SMALL
NUMBER OF STUDENTS, AND
THAT'S ALL YOU'D DO
FOR ONE PARTICULAR DAY.
BUT ACROSS THE COURSE, AND
ACROSS MANY ACTIVITIES,
YOU WOULD HAVE AN OPPORTUNITY
TO SEE ALL STUDENTS
IN A VARIETY OF CRITERIA.

Stewart says THAT'S GREAT.
WELL, I DON'T SEE
ANY MORE CALLS.
I AM VERY, VERY PLEASED
THAT YOU JOINED US TODAY.
I'M VERY PLEASED WE DID
GET SOME REPARTEE GOING.

Judy says ME, TOO.

Stewart says IT WAS PLEASANT
TO HEAR FROM YOU.
I REALLY HOPE YOU COME BACK
3:45, MAY 17th, FOR THE SECOND
PART OF THIS VERY
SHORT SERIES.
AND I HOPE IT'S BEEN
REALLY WORTHWHILE FOR YOU.
THANK YOU VERY MUCH, JUDY.
IT'S BEEN A
PLEASURE HAVING YOU.

They shake hands.

She says BEEN A PLEASURE,
THANK YOU, STEWART.

Stewart concludes AND WE'LL SEE YOU.
SAME TIME NEXT WEEK.
BYE-BYE.

Judy says BYE.

The slate changes to “See you next week. Same time (3:45 Monday, May 17), same place! Grade 9 Mathematics. The New Curriculum Part 2.”

Watch: Math 9 In-Service - Session #1