confucius say: tell me and i will forget; show me and i may not remember;
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Teaching. Wisdom. Confucius say: Tell me and I will forget; show me and I may not remember; involve me and I will understand. or. ????. Problem. What?. Problem Solving. Why?. So if problem solving could be said to assist in the construction of these networks of understanding,. - PowerPoint PPT PresentationTRANSCRIPT
Confucius say:
Tell me and I will forget; show me and I may not remember;
involve me and I will understand.
Wisdom
SENSES Intelligence SHORT-TERM LONG-TERM Type MEMORY MEMORY
SMELL
SOUND
TOUCH
SIGHT
TASTE
SENSES Intelligence SHORT-TERM LONG-TERM Type MEMORY MEMORY
SMELL
SOUND
TOUCH
SIGHT
TASTE
VISUAL
AUDITORY
KINETIC
INTRA-PERSONAL
INTER-PERSONAL
MUSICAL
LOGICAL-MATH
SENSES Intelligence SHORT-TERM LONG-TERM Type MEMORY MEMORY
SMELL
SOUND
TOUCH
SIGHT
TASTE
V I S UA L
A UD I TO R Y
K I NETI C
INTRA-PERS ONAL
INTER-PERS ONAL
M US I C A L
LOGICAL-MATH
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SENSES Intelligence SHORT-TERM LONG-TERM Type MEMORY MEMORY
SMELL
SOUND
TOUCH
SIGHT
TASTE
VISUAL
AUDITORY
KINETIC
INTRA-PERSONAL
INTER-PERSONAL
MUSICAL
LOGICAL-MATH
or
????
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SENSES Intelligence SHORT-TERM LONG-TERM Type MEMORY MEMORY
SMELL
SOUND
TOUCH
SIGHT
TASTE
VISUAL
AUDITORY
KINETIC
INTRA-PERSONAL
INTER-PERSONAL
MUSICAL
LOGICAL-MATH
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chunk-4chunk-3
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So if problem solving could be said to assist in the construction
of these networks of understanding,
Table 1: Percentage of the Grade Devoted to Problem Solving in Alberta
Level Exam QuestionType
NumberofProblemSolvingQuestions
TotalNumber ofQuestions
ValueofExam
Percentage ofValue ofExam onProblemSolving
HighSchool inAlberta
January2002 C30Diploma
Multiplechoice,numericalresponse,and fulldevelopment
16 58 100 34%
Chem101midterm
3 5 43 49%Universityof Alberta
Chem102 finalexam
Fulldevelopment
9 12 92 54%
Table 2: Percentage of the Grade Devoted to Problem Solving in Quebec
Level Exam QuestionType
Number ofProblemSolvingQuestions
TotalNumber ofQuestions
ValueofExam
Percentageof Value ofExam onProblemSolving
June 2002MEQComplementary
exam
13 25 100 52%HighSchool inQuebec,Chem534 January 2002
exam atQuebec HighSchool
Multiplechoice andfulldevelopment 11 22 100 36%
ChemistryNYA 6 15 150 38%
CEGEPinQuebec Chemistry
NYB
Fulldevelopment
9 12 150 59%
You need 3 lbs of mushrooms to makea special dish. Mushrooms cost $2.64a kilogram. You have been told thatthere are 2.2 lb in one kilogram. Howmuch money should you take to thestore to buy the mushrooms?
Given: Mushrooms @ $2.64/kg mushrooms2.2 lb/kg3.0 lb of mushrooms
Objective: $
Pathway:
$
?
Given: Mushrooms @ $2.64/kg mushrooms2.2 lb/kg3.0 lb of mushrooms
Objective: $
Pathway:
?
$ kgmushrooms
$2.64/kg
Given: Mushrooms @ $2.64/kg mushrooms2.2 lb/kg3.0 lb of mushrooms
Objective: $
Pathway:
2.2 lb/kg$2.64/kg
$lb mus hrooms
= 3 .0k g
m u s h ro o m s
Answer:
$3.60 mushrooms kg
$2.64
mushrooms lb 2.2
mushrooms kg 1mushrooms lb 3.0$
A chemical analysis requires 2.00 L of 0.150 mol/L AgNO3. Whatmass of silver nitrate solid is required to prepare this solution?
Objective: m (AgNO3) in g
Given: 2.00L of solution L
AgNOmol 0.150 3
m =g Ag NO s
Pathway:
?
A chemical analysis requires 2.00 L of 0.150 mol/L AgNO3/ Whatmass of silver nitrate solid is required to prepare this solution?
Objective: m (AgNO3) in g
Given: 2.00L of solution L
AgNOmol 0.150 3
m =g Ag NO s
molAgNO 3
Pathway:
mol
g 169.98?
A chemical analysis requires 2.00 L of 0.150 mol/L AgNO3/ Whatmass of silver nitrate solid is required to prepare this solution?
Objective: m (AgNO3) in g
Given: 2.00L of solution L
AgNOmol 0.150 3
m =g Ag NO s
molAgNO 3
L s olution=2 .0 0
Pathway:
mol
g 169.98
L
mol 0.150
Answer:
3
3
333 AgNOg 51.0
AgNOmol
AgNOg 169.88
solution L
AgNOmol 0.150solution L 2.00(AgNO m )
A chemical analysis requires 2.00 L of 0.150 mol/L AgNO3/ Whatmass of silver nitrate solid is required to prepare this solution?
Objective: m (AgNO3) in g
Given: 2.00L of solution L
AgNOmol 0.150 3
m =g Ag NO s
molAgNO 3
L s olution=2 .0 0
Pathway:
mol
g 169.98
L
mol 0.150
Answer:
S M EL L
V I S UA L
S O UND
TO UC H
S I G H T
S E N S E S In tellig en ce S H O R T -T E R M L O N G -T E R M T y p e M E M O R Y M E M O R Y
A UD I TO R Y
K I NETI C
N otes for reviiew
1 . . . . . . .2 . . . . . . .3 . . . . . . .4 . . . . . . . .
E X TE R N A L M E M O R Y( P A P E R !!!)
TA S TEINTRA-
PERS ONAL
INTER-PERS ONAL
M US I C A L
LOGICAL-MATH
1. Reasoning begins with the Objective.
2. Each step represents a direct relationship.
3. When the pathway reaches information that is known,the pathway is complete.
4. When the pathway reaches the unattainable, theproblem solver must return to a previous objective,eliminating the branch under construction.
Exam #1, Question #2
0
0.2
0.4
0.6
0.8
1
0 5 10Grade
Fra
ctio
n <
/= G
rade
-Pathway
+Pathway
A plot of the fraction of students who obtained a grade less thanor equal to the grade on the x-axis, for those students who usedPathways (pink) and those who did not (blue)
21
21
nn
nnDL
2-2L2eP
Komogorov-Smirnov
where D is the maximum difference between the groups
and P is the probability that the two groups are identical
Exam #1, Question #2
0
0.2
0.4
0.6
0.8
1
0 5 10Grade
Fra
ctio
n <
/= G
rade
-Pathway
+Pathway
An example of a graph for which P that the two groups areidentical is very small:
Exam #2 Question 4
0
0.2
0.4
0.6
0.8
1
0 2 4 6 8 10Grade
Fra
ctio
n <
/= G
rade
-Pathway
+Pathway
An example of a graph for which the P that the two groups areidentical is NOT small:
Table 1. Pathway Use, Grades and Probabilities for the “Harder” Problems
Class-Test-Question
Pathway Use(out of 3) Grade (out of 10) Probability that the groupsare identical
C1-T1-Q1 1.94 5.9 <0.01C1-T1-Q2 0.91 3.3 0.02C1-T1-Q4 0.97 5.3 0.01C2-T1-Q1 2.35 7.2 <0.01C1-T2-Q1 1.41 5.4 <0.01C1-T2-Q2 0.94 4.4 <0.01C1-T2-Q5 0.29 1.2 0.06C2-T2-Q1 1.96 5.6 <0.01C2-T2-Q2 1.96 6.6 0.04C2-T2-Q5 1.26 4.2 <0.01C1-T3-Q1 2.11 7.4 <0.01C1-T3-Q2 1.50 6.8 <0.01C1-T3-Q3 2.00 5.8 <0.01C2-T3-Q2 1.81 6.9 0.01Average 1.4 +/- 0.6 5 +/- 2 0.01
Table 2. Pathway Use, Grades and Probabilities for the “Easier” Problems
Class-Test-Question Pathway Use(out of 3)
Grade (out of 10) Probability that thegroups are identical
C1-T1-Q3 0.24 5.7 0.97C2-T1-Q2 1.70 6.1 0.41C2-T1-Q3 0.04 4.0 >1C2-T1-Q4 1.13 6.9 0.20C1-T2-Q3 0.18 8.6 >1C1-T2-Q4 0.76 9.4 >1C2-T2-Q4 1.87 9.4 >1C1-T3-Q4 1.50 8.1 0.54C1-T3-Q5 2.24 7.4 >1C2-T3-Q1 2.80 8.6 0.30C2-T3-Q3 2.42 8.2 >1C2-T3-Q4 2.05 8.6 >1C2-T3-Q5 2.48 8.1 >1Average 1.5 +/- 0.9 8 +/- 2 >1
Pathway use vs exam number(difficult questions)
0
1
2
1 2 3Exam #
U=n
2/n1
Pathway use vs exam number(easier questions)
0
5
10
1 2 3Exam#
U=
n2/n
1
Pathway Use Over the Semester
Pathway Use in Test 1 vs HS grade
R2 = 5E-05
0
1
2
3
70 80 90 100
High School Grade
Pat
hway
Use
Correlation between Pathway Use and High School Grades
Pathway Use in Test 2 vs HS Grade
R2 = 0.0237
0
1
2
3
70 80 90 100
High School Grade
Pat
hway
use
Pathway Use in Test 3 vs HS Grade
R2 = 0.0026
0
1
2
3
70 80 90 100
High School Grade
Pat
hway
use
Correlation between Pathway Use and High School Gradesfor tests 2 and 3
In Alberta: there is a clear gap, that nobody owns, betweensecondary and university levels.
In Quebec, is there a gap? By the numbers, no.But do we not also find that students have notdeveloped independence in novel problem-solvingsituations?
Objective: to develop independence in student resolution ofnovel problems
Given: the education system as it exists in Quebec
Pathway:
Objective: to develop independence in student resolution ofnovel problems
Given: the education system as it exists in Quebec
Pathway:
Inde pe nde nc e inno ve l pro ble m s
Wh ere can w eb es t d ev elop
th is ?
G o o d c o nc e ptua lk no w le dg e
H ig h S c ho o lc la s s e s
C E G E P c la s s e s
P a thw a y M e tho d
!!!
The End(?)