Suzanne White Brahmia Department of Physics University of - - PowerPoint PPT Presentation
Yale University CTL Helmsley STEM EducaAon Series December 2014 Suzanne White Brahmia Department of Physics University of Washington 11/17/17 1 Collabora've Principal Inves'gators Andrew Boudreaux; Western Washington University Stephen
Yale University CTL Helmsley STEM EducaAon Series December 2014
11/17/17 1
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This work is supported by NSF DUE-1045227, NSF DUE-1045231, NSF DUE-1045250
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hUp://juni.osfc.ac.uk/Extension/level_2_extension/Science/lesson1/ equaLon_triangles.asp
“There are many occasions when you have to use an equaAon in Science, parAcularly in Physics. The EquaAon Triangles are a way in which you can easily learn to use and rearrange equaAons, even if you are not confident in your Maths.”
“There are many occasions when you have to use an equaAon in Science, parAcularly in Physics. The EquaAon Triangles are a way in which you can easily learn to use and rearrange equaAons, even if you are not confident in your Maths.”
hUp://juni.osfc.ac.uk/Extension/level_2_extension/Science/lesson1/ equaLon_triangles.asp
(from CLASS, 2006, 42 statement survey)
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Consider the following statement about Winnie the Pooh’s dream: “There are three Ames as many heffalumps as woozles.” A correct equaLon to represent this statement, using h for the number of heffalumps and w for the number
Consider the following statement about Winnie the Pooh’s dream: “There are three Ames as many heffalumps as woozles.” A correct equaLon to represent this statement, using h for the number of heffalumps and w for the number
Reversal Correct
Consider the following statement about Winnie the Pooh’s dream: “There are three Ames as many heffalumps as woozles.” A correct equaLon to represent this statement, using h for the number of heffalumps and w for the number
Reversal Correct 4% 37% 3% 47% 9%
Nmatched=685
Consider the following statement about Winnie the Pooh’s dream: “There are three Ames as many heffalumps as woozles.” A correct equaLon to represent this statement, using h for the number of heffalumps and w for the number
Reversal Correct 4% 37% 3% 47% 9% 3% 37% 2% 49% 9% σpooled=1.8% p-value = 0.8418
Nmatched=685
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Bartholomew is making rice pudding using his grandmother’s
pints of milk and 0.5 cups of rice. Bartholomew looks in his refrigerator and sees he has one pint of milk. Given that he wants to use all of the milk, which of the following expressions will help Bartholomew figure out how many cups of rice he should use?
0.5/0.75 0.75/0.5 0.5 x 0.75 (0.5 + 1) x 0.75 none of these
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Bartholomew is making rice pudding using his grandmother’s
pints of milk and 0.5 cups of rice. Bartholomew looks in his refrigerator and sees he has one pint of milk. Given that he wants to use all of the milk, which of the following expressions will help Bartholomew figure out how many cups of rice he should use?
0.5/0.75 0.75/0.5 0.5 x 0.75 (0.5 + 1) x 0.75 none of these
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change 65/+9 42/+9
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change 65/+9 42/+9 Math Reasoning % pre/ change 51/+4 43/-2 2.3/4.4
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change 65/+9 42/+9 Math Reasoning % pre/ change 51/+4 43/-2 2.3/4.4 CLASS Problem Solving (Gen) % pre/change 71/-2 62/-10 CLASS Personal Interest % pre/change 73/0 65/-9
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change 65 42 Math Reasoning % pre/ change 51 43 2.3/4.4 CLASS Problem Solving (Gen) % pre/change 71 62 CLASS Personal Interest % pre/change 73 65
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change +9 +9 Math Reasoning % pre/ change +4
2.3/4.4 CLASS Problem Solving (Gen) % pre/change
CLASS Personal Interest % pre/change
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Top 20%
(nsample=98)
The rest (nsample=363) Effect size SAT_M 710 670 11.4 FCI % pre/change 65/+9 42/+9 Math Reasoning % pre/ change 51/+4 43/-2 2.3/4.4 CLASS Problem Solving (Gen) % pre/change 71/-2 62/-10 CLASS Personal Interest % pre/change 73/0 65/-9 Average of the Median MHI High School Q 0.9*Q
p-value < .02
5.5
MHI Quin'le Socioeconomic Status Schoolwork culture 2nd Working class Work is evaluated for obedience to procedure. Students learn to imitate the teacher in math class. 3rd-4th Middle class Work is gedng the right answer. CreaLve acLviLes are
are given some choice in math on which of two procedures to use to get an answer. 4th-5th Affluent professional Work is a creaLve acLvity carried out independently. The products of work should show individuality. Students gather data and use it to learn about mathemaLcal processes. Top 1% ExecuLve elite Work is developing one’s intellectual powers; students invent ways to measure and calculate in math class.
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MHI Quin'le Socioeconomic Status Schoolwork culture 2nd Working class Work is evaluated for obedience to procedure. Students learn to imitate the teacher in math class. 3rd-4th Middle class Work is geXng the right answer. CreaLve acLviLes are occasional, for fun but not part of learning. Students are given some choice in math on which of two procedures to use to get an answer. 4th-5th Affluent professional Work is a crea've ac'vity carried out independently. The products of work should show individuality. Students gather data and use it to learn about mathemaLcal processes. Top 1% ExecuLve elite Work is developing one’s intellectual powers; students invent ways to measure and calculate in math class.
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0% 5% 10% 2001 2005 2009 Physics Black Physics Hispanic Biology black Biology Hispanic Chemistry black Chemistry Hispanic
*NaLonal Science FoundaLon’s NaLonal Center for Science and Engineering StaLsLcs
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0% 5% 10% 2001 2005 2009 Physics Black Physics Hispanic Biology black Biology Hispanic Chemistry black Chemistry Hispanic
*NaLonal Science FoundaLon’s NaLonal Center for Science and Engineering StaLsLcs
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Slide courtesy of Michael Marder
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Slide courtesy of Michael Marder
On the surface, this seems like a problem with prior math
than math in math. Teaching the mathemaAcal habits of mind that are characterisAc of physics thinking should be a major goal of physics instrucAon at all levels. Physics – flexible and generaLve mathemaLcs in context Math – axiomaLc reasoning in the absence of context
On the surface, this seems like a problem with prior math
than math in math. Teaching the mathemaAcal habits of mind that are characterisAc of physics thinking should be a major goal of physics instrucAon at all levels. Physics – flexible and generaLve mathemaLcs in context Math – axiomaLc reasoning in the absence of context
On the surface, this seems like a problem with prior math
than math in math. Teaching the mathemaAcal habits of mind that are characterisAc of physics thinking should be a major goal of physics instrucAon at all levels. Physics – flexible and generaLve mathemaLcs in context Math – axiomaLc reasoning in the absence of context
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(Gray and Tall 1994)
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(Gray and Tall 1994)
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(Gray and Tall 1994)
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comparison
(Gray and Tall 1994)
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accumulaAon comparison
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² Seeking invariance is at the heart of learning (Gibson & Gibson , 1955). ² Many students don’t spontaneously consider invariance when quanLfying nature in school (Simon&Blume, 1994).
² Tuminaro (2004): Students who do not expect conceptual knowledge of mathemaLcs to connect to physics problems do not engage in sense making when calculaLng. ² Brahmia & Boudreaux (2016): Students errors can be traced to a failure to disLnguish products from factors when reasoning about physics quanLLes.
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² Seeking invariance is at the heart of learning (Gibson & Gibson , 1955). ² Many students don’t spontaneously consider invariance when quanLfying nature in school (Simon&Blume, 1994).
² Tuminaro (2004): Students who do not expect conceptual knowledge of mathemaLcs to connect to physics problems do not engage in sense making when calculaLng. ² Brahmia & Boudreaux (2016): Students errors can be traced to a failure to disLnguish products from factors when reasoning about physics quanLLes.
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² Seeking invariance is at the heart of learning (Gibson & Gibson , 1955). ² Many students don’t spontaneously consider invariance when quanLfying nature in school (Simon&Blume, 1994).
² Tuminaro (2004): Students who do not expect conceptual knowledge of mathemaLcs to connect to physics problems do not engage in sense making when calculaLng. ² Brahmia & Boudreaux (2016): Students errors can be traced to a failure to disLnguish products from factors when reasoning about physics quanLLes.
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² Seeking invariance is at the heart of learning (Gibson & Gibson , 1955). ² Many students don’t spontaneously consider invariance when quanLfying nature in school (Simon&Blume, 1994).
² Tuminaro (2004): Students who do not expect conceptual knowledge of mathemaLcs to connect to physics problems do not engage in sense making when calculaLng. ² Brahmia & Boudreaux (2016): Students errors can be traced to a failure to disLnguish products from factors when reasoning about physics quanLLes.
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Your task this Lme is to come up with a fastness index for cars with dripping oil. All the cars drip oil once a second
Start
C A D E F B
Start Start Start Start Start
This task is a liFle harder than before. A company always makes its cars go the same fastness. We will not tell you how many companies there are. You have to decide which cars are from the same company. They may look different!
Conceptual understanding
representations Connection to the physics world Physically meaningful reasoning in introductory physics
double scope arithmeAc reasoning blend, in which two disLnct domains of thinking are merged to form a new cogniLve space opLmally suited for producLve work
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Starting Resources math procedures (disconnected) capacity to respond to prompts to calculate (rigid response) disconnected definitions of some physics concepts Coordinated set of Resources Proceptual understanding of mathematics flexibilty in mathematizing capacity to invent or imagine inventing physical quantities
Invention Tasks
(quantification and symbolizing)
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QF: Identify quantifable features
AC: Arithmetically construct index CC: Compare across contrasting cases for invariance Harel’s necessity principle Socioconstructivist framework MU: Make meaning
NC: Evaluate in new context
CM: Clarify Mission-
To make mathematical choices to generate a useful quantity Collaborative productive failure R C : R u l e s a n d c
s t r a i n t s i m p
e d b y t h e i n v e n t i
6mph 35mph 25mph 15mph 5mph 55mph 40mph 25mph 10mph 34mph 24mph 14mph 4mph 57mph 42mph 27mph 12mph 9mph 3mph Car A Car B Car C Car D Car E
These cars all drip oil once every second. Invent a speeding-up index that allows you to rank the cars in terms of how quickly they speed up.
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(Steele & Aronson 1995)
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(Steele & Aronson 1995)
(Bandura 1997, Sawtelle 2011)
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Error bars represent the standard error.
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EAP I (Underprepared) AP I (Mainstream) # of students ~120 ~700 Mean SAT 610 680 % URM 40% 12% % female 30% 21% Median MHI
district 0.7*Q
p-value<.000000001
Q
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EAP I (Underprepared) AP I (Mainstream) # of students ~120 ~700 Mean SAT 610 680 % URM 40% 12% % female 30% 21% Median MHI
district 0.7*Q Q
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Force Concept Inventory; σmean: EAP I (n=135) 1.4%(pre), 1.5%(post); AP I (n=757) 0.8%(pre), 0.8%(post)
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sin−1 H 8 # $ % & ' ( sin−1 8 H # $ % & ' (
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sin−1 H 8 # $ % & ' ( sin−1 8 H # $ % & ' (
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10 20 30 40 50 60 70 80 90 100 Underprepared Mainstream
pre post
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10 20 30 40 50 60 70 80 90 100 Underprepared Mainstream
pre post
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0.2 0.4 0.6 0.8 1
APIhigh APIlow EAPIlow
(full year)
pre post
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0.2 0.4 0.6 0.8 1
APIhigh APIlow EAPIlow
(full year)
pre post
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50# 55# 60# 65# 70# 75# 80#
0.8# 1# 1.2# 1.4# 1.6# 1.8# 2# 2.2#
%"that"agree"with"experts"
CLASS"Problem"Solving"9General" APIHi#
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50# 55# 60# 65# 70# 75# 80#
0.8# 1# 1.2# 1.4# 1.6# 1.8# 2# 2.2#
%"that"agree"with"experts"
CLASS"Problem"Solving"9General" APIHi# APILow#
SES:
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50# 55# 60# 65# 70# 75# 80#
0.8# 1# 1.2# 1.4# 1.6# 1.8# 2# 2.2#
%"that"agree"with"experts"
CLASS"Problem"Solving"9General" APIHi# APILow# EAPILow#
SES:
101
pre$ post$
50# 55# 60# 65# 70# 75# 80#
0.8# 1# 1.2# 1.4# 1.6# 1.8# 2# 2.2#
Percentage)agree)with)experts)
CLASS)Personal)Interest) APIHi#
SES:
102
post% pre%
50# 55# 60# 65# 70# 75# 80#
0.8# 1# 1.2# 1.4# 1.6# 1.8# 2# 2.2#
Percentage)agree)with)experts)
CLASS)Personal)Interest) APIHi# APILow#
SES:
103
SES:
104
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