GECDSB Mathematics Learning Teams (MLT) Session #1
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Transcript of GECDSB Mathematics Learning Teams (MLT) Session #1
AGENDA
MATHVISIONWhatdoesitmeantobegoodatmath?Burningquestions
EARLYMATHLEARNINGCountingandQuantity
JUNIORandINTERMEDIATE MATHArraysandAreasModels
PEDAGOGICALSYSTEMSPlanningaTask
LEADINGMATHINYOURSCHOOLTheroleoftheschoolmathlearning team
TODAY’S LEARNING
Weare:• Extending ourunderstanding oftheGECDSB:
Mathematics VisionandMathematical Proficiencies
• Building anunderstanding ofnumbersense conceptsfromK-10
• Developing anunderstanding ofPedagogical Systems
• Planning amath task
• Learning toleadmath inourschools
MathPedagogy
MathContent
Leadership&
ProfessionalCapital
THE MATHEMATICS JOURNEY• Mathematics journey isunlikemanyothers• Itisnot animplementation ofaprogramorprocess• Itisthe enaction ofthe GECDSBVision
The Work: Ambitious and Necessary
Enact the Vision
“The GECDSB provides mathematics education that engages and empowers students through collaboration, communication, inquiry,
critical thinking and problem-solving, to support each student’s learning and nurture a positive attitude towards mathematics.”
Table Talk…Why is this work both ambitious and necessary?
SCHOOL MATH TEAM
Clicktoaddtext
Session1 OctoberSession2 NovemberSession3 JanuarySession 4 & 5 FebruaryandMarchSession6 April
TableTalk...Whatistherole(possible role)oftheschoolmathteamatyourschool?
Wherearesomeprofessional learningspacesinyourschool?
What does it mean to be good at math?
Enjoy learning mathDevelop persistence and tenacityLearn to use math to solve problemsDevelop logic and reasoning skillsSee the value for mathematics in their worldLearn their facts and mathematical proceduresUnderstand the ‘whys’ of math
GECDSB: A Vision for MathematicsStrategic Competence
Procedural Fluency
Conceptual Understanding
Adaptive Reasoning
Productive Disposition
This is a vision for mathematics that is both ambitious and necessary.
Math Task Force Data
What does it mean to be good at math?
Math as a functional skillMath as applied to a professionMath as a way of thinking and seeing the world
Math Vision: Understanding Proficiency
StrategicCompetenceProceduralFluencyConceptualUnderstandingAdaptiveReasoningProductiveDisposition
Jigsaw: ReadChapter4
Math Task
Clicktoaddtext
HowCloseto100?Instructionscanbefoundathttps://www.youcubed.org/task/how-to-close-100/
Math Task: Consolidation
Howdoyouseethismathtaskconnectedtothedevelopmentof
mathematicalproficiency?
Isthereareaparticularmathematicalproficiencythatcouldbestrengthened throughthistask?
Doesthischangeyourdefinitionofwhatitmeanstobegoodatmath?
The Work: Guided By Our Questions
We have many questions about mathematics education.
Table Talk…
With the learners at your table, brainstorm some of the
questions you have or your staff may have about mathematics education.
Share them with the larger group.
Early MathematicsIn2007,itwasfound thatmathematicsskillsamongchildreninKindergartenwerethebestpredictoroflaterschoolachievement,regardlessofgenderorsocio-economicstatus(Duncanetal.,2007). Kindergarten Program, 2016
CriticalQuestionHowcaneducators takeadvantageofthemathematicalknowledgeandexperiencethatchildrenhave?
CriticalUnderstandingThepresencealoneofmathematicsinplayisinsufficient forrichlearning tooccurIntentional,purposeful teacherinteractionsarenecessarytoensure thatmathematicallearning ismaximizedduringplay.
Early Mathematics
Aseducatorswemustconstantlyaskourselves:
Whythislearning,forthisstudent,atthistime?
Early Mathematics
Whatmathematical skillsdoyouthinkouryounglearnersneed?
NumberSense• Counting• QuantityRelationshipsGeometryandMeasurement
arefoundationalskillsthatmustbeinplacetosupportallfuturemathlearning.
Counting and Quantity
Conservation
One-to-oneCorrespondence
Cardinality
StableOrder
OrderIrrelevance
Abstraction
MovementisMagnitude
Subitizing
Unitizing
Case Study
• Whatprinciplesofquantityandcountingdoesthechildunderstand?
• Whatmightbethenextstep(s)forlearningforthischild?
Countingand
Quantity
Stable-Order Order Irrelevance
Conservation
One-to-One Correspondence
Abstraction
Movement is MagnitudeSubitizing
Unitizing
Cardinality
Stable-OrderThe list of words used to count must be in a repeatable order.
This “stable list” must be at least as long as the number of items to be counted.
12
3
45
6
7 8 9 10
ConservationUnderstanding that the count for a set group of objectsstays the same no matter whether they are spread out or close together.
7 8 9 101 23 4
5 6
ConservationUnderstanding that the count for a set group of objectsstays the same no matter whether they are spread out or close together.
7 8 9 101
23 4
5
6
… the quantity of five large things is the same count as a quantity of five small things or a mixed group of five small and large things.
Abstraction…we can count any collection of objects, whether tangible or not.
1 23 4
51 2 3 4 5
Understanding that each object being counted must be given one count and only one count. It is useful in the early stages for children to actually tag each item being counted and to move an it out of the way as it is counted.
One-to-One Correspondence
123
4
5
Understanding that the last count of a group of objects represents how many are in the group. A child who recounts when asked how many candies are in the set that they just counted, has not understood the cardinality principle.
Cardinality
1 2 3 4 5 6
The ability to 'see' a small amount of objects and know how many there are without counting.
Subitizing
“5”
Understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going up/down by.
Movement is Magnitude
1 2 3
Understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going up/down by.
Movement is Magnitude
1 2 3 4
Understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going up/down by.
Movement is Magnitude
1 2 3 4 5
Understanding that as you move up the counting sequence (or forwards), the quantity increases by one and as you move down (or backwards), the quantity decreases by one or whatever quantity you are going up/down by.
Movement is Magnitude
1 2 3 4
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
1 0
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
1 9
Understanding that in our base ten system objects are grouped into tens once the count exceeds 9 (and into tens of tens when it exceeds 99) and that this is indicated by a 1 in the tens place of a number.
Unitizing
tens ones
2 0
PROCEDURAL FLUENCY
STRATEGIC COMPETENCE
ADAPTIVE REASONING
PRODUCTIVE DISPOSITION
CONCEPTUAL UNDERSTANDING
kylep.ca/gecdsbvision
Math Proficiencies
PRODUCTIVE DISPOSITION
Ability to formulate, represent & solve mathematical problems using an effective strategy
STRATEGIC COMPETENCE
PROCEDURAL FLUENCY
Understanding and using a variety of mathematical procedures
ADAPTIVE REASONINGCapacity for logical thought, reflection,
explanation, and justification
Inclination to see mathematics as useful and valuable.
Ability to understand mathematical concepts, operations, and relationships
CONCEPTUAL UNDERSTANDING
5 x 6“5 groups of 6”
= ?
1
11
11
1 1 1 1 1 1
1 1 1 11 11 1 1 11 11 1 1 11 11 1 1 11 11 1 1 11 1
612182430
1 1 11 1 11 1 1
111
1 1 1 1
1111
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 16
1 1 11 1 11 1 1
111
1 1 1 1
1111
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 1664
1 1 11 1 11 1 1
111
1 1 1 1
1111
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 16 16 1664 square-units
1 1 11 1 11 1 1
111
1 1 1 1
1111
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
What’s the Area of the Pool?
16 161 1 11 1 11 1 1
1 1 11 1 11 1 1
1 1 11 1 11 1 1
1 1 11 1 11 1 1
1 1 11 1 11 1 1
111
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
64 square-units
“Spatial thinking, or reasoning, involves the location and movement of objects and
ourselves, either mentally or physically, in space. It is not a
single ability or process but actually refers to a considerable number of
concepts, tools and processes.”
(National Research Council, 2006)
“The relation between spatial ability and mathematics is so
well established that it no longer makes sense to ask whether
they are related…”
“…moreover, spatial thinking was a better predictor of
mathematics success than either verbal or mathematical skills.”
Activities to Develop Geometric and Spatial Thinking
visualizing diagramming
designing(Davis, Okamoto & Whiteley, 2015)
orientinglocating
perspective taking
slidingrotating
reflecting
modelingexploring symmetry
composing
decomposingscaling
map-making
@MathletePearcewww.tapintoteenminds.com
6 x 7=
5
5 25
2
10
1
5 x 5 5 x 2 1 x 5 1 x 2+ + +
= 25 10 5 2+ + +
5 2
5 x 14 = ?“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
5 x 14 = ?“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
5 x 14 = ?“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
5 x 14 =“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
x 105
5 x 14 =“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
+x 105 x 45
5 x 14 =“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
+x 105 x 45
5 x 14 =“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 1
1 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1
+(105 )45
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
10
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
101010
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
10101010
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010101010
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010101010
1 1 1 1
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010101010
1 1 1 11 1 1 1
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010101010
1 1 1 11 1 1 11 1 1 1
5 x 14 = ?“5 groups of 14”
“5 groups of 10 plus 5 groups of 4”or
1 1 1 1
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
11111
1010101010
1 1 1 11 1 1 11 1 1 11 1 1 1
1 1 1 1
5 x 14 = ?“5 groups of 14”
11111
1 1 1 1 1 1 1 1 1 1 1 1 1 110
5
“5 groups of 10 plus 5 groups of 4”or
11111
1010101010
1 1 1 11 1 1 11 1 1 11 1 1 11 1 1 1
4 x 12 = ?“4 groups of 12”
“4 groups of 10 plus 4 groups of 2”or
1 1
1111
1 1 1 1 1 1 1 1 1 1 1 110
1111
4 x 12 = ?“4 groups of 12”
“4 groups of 10 plus 4 groups of 2”or
1 1
1111
1 1 1 1 1 1 1 1 1 1 1 110
1111
1 1101 1101 1101 110
@MathletePearcewww.tapintoteenminds.com
13 x 14 = ?1 110 1 1
10
1
1
1
100 10 10 10 10
10
10
10
1 1 1 1
1 1 1 1
1 1 1 1
@MathletePearcewww.tapintoteenminds.com
13 x 14 = 1821 110 1 1
10
1
1
1
100 10 10 10 10
10
10
10
1 1 1 1
1 1 1 1
1 1 1 1
@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
10
10
1 1 1 1 1
1 1 1 1 1
12 x 15 = ?
@MathletePearcewww.tapintoteenminds.com
1 110 1 1 1
10
1
1
100 10 10 10 10 10
10
10
1 1 1 1 1
1 1 1 1 1
12 x 15 = 180
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
(6 x 20)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
(20 x 2)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
(20 x 20)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
400 (20 x 20)
The “Standard” Algorithm
22x
26
1
04421 3
+
275
Arrays & Area Models
A “Conceptual“ Algorithm
22x
26
12 (6 x 2)
120 (6 x 20)
40 (20 x 2)
400 (20 x 20)
572
+
The “Standard” Algorithm
22x
26
1
04421 3
+
275
9 x 12 = ?“9 groups of 12” 1
11111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
? ?
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
?
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
?
?
?
?
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12 = ?
111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
“9 groups of 12”
“5 groups of 10plus
4 groups of 2”
or
9 x 12
= (5 + 4)(10 + 2)
9 x 12
111111111
1 1 1 1 1 1 1 1 1 1 1 110 2
5
4
50
40
10
8
= (5 + 4)(10 + 2)
= (5 + 4)(10 + 2)
First
Outside
InsideLast
“FOIL”
Concreteness Fading
1 2 3Enactive
Concrete
Iconic
Visual
Symbolic
Abstract
22x
26
1
04004
21 3
+
275
PROCEDURAL FLUENCY
STRATEGIC COMPETENCE
ADAPTIVE REASONING
PRODUCTIVE DISPOSITION
CONCEPTUAL UNDERSTANDING
kylep.ca/gecdsbvision
Math Proficiencies
PRODUCTIVE DISPOSITION
Ability to formulate, represent & solve mathematical problems using an effective strategy
STRATEGIC COMPETENCE
PROCEDURAL FLUENCY
Understanding and using a variety of mathematical procedures
ADAPTIVE REASONINGCapacity for logical thought, reflection,
explanation, and justification
Inclination to see mathematics as useful and valuable.
Ability to understand mathematical concepts, operations, and relationships
CONCEPTUAL UNDERSTANDING
In Math ClassTable Talk…What would we see, hear and feel in an exemplary math class?
Write one idea per sticky note.
Identify the groups with a heading/theme/category.
Pedagogical System
Non-threateningClassroom
Environment
InstructionalTask
ToolsandRepresentations
ClassroomDiscourse
In Math Class
Table Talk…
Fold the chart paper into quarters to reflect the 4 aspects of the pedagogical system.
Do your ideas fit/match these categories?
What other ideas can you add?
InstructionalTask
Non-threateningClassroom
Environment
Tools andRepresentations
ClassroomDiscourse
Pedagogical System: Understanding Task
What is a Math Task?Any problem or set of problems that focuses students' attention on a particular mathematical idea and/or provides an opportunity to develop or use a particular mathematical habit of mind.
High or Low Cognitive DemandThe cognitive demand of a task is the level of cognitive engagement needed to complete the task (Stein et al. 2009).
A task by itself is not rich;it is what we do with the task and how it connects to the pedagogical
system that makes it rich.
Understanding Task
Bump It UpBumpupataskasanAssessment forLearning•UsetheTaskCardsatyourtable
•Grade,Topic,OverallExpectationandaTask
•UsetheMathematicsCurriculumandfindthespecificexpectations
• Re-writethetask
Task: Assessment for Learning
TomSchimmer’s (GradingFromtheInsideOut,2016)premiseisthatallassessmentpracticesshouldbeputthroughtwofilters:
1.Isitaccurate?2.Doesitpromoteconfidence/optimisminstudents?
“Schoolisnolongeraboutthecompletionofaseriesofactivities,butratherthepursuitofproficiencyasasetofoutcomesthatstudentsachievethroughtheinstructional experience”
UnderstandingMathTasksGrade2Topic: Counting
OverallExpectations: read,represent, compare,andorderwholenumbers to100,anduseconcretematerials torepresent fractions andmoneyamounts to100¢
SpecificExpectation(s): countforwardby1’s,2’s,5’s,10’s,and25’sto200,usingnumber lines andhundredscharts,starting frommultiples of1,2,5,and10(e.g.,countby5’sfrom15;countby25’sfrom125)
TaskCountby2s
Task: Assessment for Learning
Whatwasyourtask?
Whatdidyounoticeabout thecurriculum?
What/Howcanthetaskbemodified, refined,extended tosupport ALLstudents?CCoonnssiiddeerr- studentswithpersistent learningchallenges- students identified asgifted
Howcouldyouusethis learning toleadmath learning inyourschool?
Understanding Task: Consolidation
UnderstandingMathTasks
If you deny students the opportunity toengage in this activity – to pose their ownproblems, to make their own conjectures anddiscoveries, to be wrong, to be creativelyfrustrated, to have an inspiration, to cobbletogether their own explanations and proofs –you deny them mathematics itself.
Paul Lockhart, A Mathematician’s Lament, 2009
Mathematics Learning
UnderstandingMathTasks
Quotationsaboutmathematicsbymathematicians.• Choose1thatconnectswithyourthinking• Explainyourchoiceandyourthinking
BuildingConfidenceinourNextBestMove…Whatisyournextbestmove?
Leading Math Learning in Our Schools
Bringstudentworkbased onamathematics task.ConsiderCurriculum expectationAssessment forLearning
Wewillanalyzethetaskinthecontext ofpedagogical system.
For Next Time…