The effect of educational environment on representational

competence in introductory physics

Patrick Kohl and Noah Patrick Kohl and Noah FinkelsteinFinkelstein

University of Colorado at University of Colorado at BoulderBoulder

OutlineOutline Review of research questions and Review of research questions and

original studyoriginal study Performance data from additional Performance data from additional

studiesstudies Analysis of representational content Analysis of representational content

of course environments of course environments ConclusionsConclusions

IntroductionIntroduction Original study investigated:Original study investigated:

Effect of problem representation on Effect of problem representation on student performance (student student performance (student representational competence)representational competence)

Effect of providing students with a Effect of providing students with a choice of problem representation choice of problem representation (student meta-representational (student meta-representational competence)competence)

IntroductionIntroduction Student performance was strongly Student performance was strongly

affected by representationaffected by representation Effect of representation choice was Effect of representation choice was

strong and either positive or negativestrong and either positive or negative

Research questionsResearch questions Can we explain the choice/control Can we explain the choice/control

splits?splits? Will these effects be present in other Will these effects be present in other

courses?courses? Why or why not?Why or why not?

Study methodsStudy methods Four question pre-recitation homework Four question pre-recitation homework

Verbal, mathematical, graphical, pictorial Verbal, mathematical, graphical, pictorial question formatsquestion formats

One question recitation quiz in one of four One question recitation quiz in one of four formatsformats

Half receive format at random, half chooseHalf receive format at random, half choose Study covered two topic areas in each of Study covered two topic areas in each of

Phys 2020 (Trad), 2010 (Reform), 2020 Phys 2020 (Trad), 2010 (Reform), 2020 (Reform)(Reform)

Atomic phys. quizzes, pictorial & Atomic phys. quizzes, pictorial & verbalverbal Spectroscopy Problem -- Pictorial Format

The Balmer series of spectral lines is shown below, as seen through a spectrometer: Now suppose we are in a world where electric charges are weaker, so the electron is not held as tightly by the nucleus and the ionization energy is 13 eV instead of 13.6 eV. Choose the picture that best represents what the new spectrum would look like.

Spectroscopy Problem -- Verbal Format Consider the Balmer series of spectral lines from hydrogen gas. Now suppose we are in a world where electric charges are weaker, so the electron is not held as tightly by the nucleus. This means that the ionization energy for the electron will be smaller. What will happen to the Balmer lines that we see? A) The spectral lines will remain the same.

Choice/control splitsChoice/control splitsQuiz SubjectQuiz Subject VerbVerb

alalMathMath GraphicGraphic

alalPictorialPictorial

2020 Diffraction 2020 Diffraction (T)(T)

-- -- 0.040.04 0.030.03

2020 2020 SpectroscopySpectroscopy

0.0020.002 0.0000.00011

0.00040.0004 0.0010.0012010 Springs (R)2010 Springs (R) -- 0.090.09 -- 0.070.072010 Pendulums2010 Pendulums -- -- -- --2020 Diffraction 2020 Diffraction (R)(R)

-- 0.060.06 -- --

2020 2020 SpectroscopySpectroscopy

-- -- -- --

Choice/Control splitsChoice/Control splits Effect of instruction appears to be Effect of instruction appears to be

strongstrong Hypothesis: Reform style using Hypothesis: Reform style using

broader selection of representation broader selection of representation imparts broader representational skill imparts broader representational skill sets, reducing splitssets, reducing splits

Is analysis of lectures and exams Is analysis of lectures and exams consistent?consistent?

Study methodsStudy methods Videotaped several lectures from Videotaped several lectures from

each class, analyzed in terms of each class, analyzed in terms of representation userepresentation use

Compared representation use on Compared representation use on class examsclass exams

Conducted problem-solving Conducted problem-solving interviews in 2010 (Reform) and interviews in 2010 (Reform) and 2020 (Reform) sections2020 (Reform) sections

ExamsExams Means by which students are held Means by which students are held

responsible for representation useresponsible for representation use

Each exam sub-problem has its Each exam sub-problem has its representational content assessedrepresentational content assessed

We tally fraction of points possible We tally fraction of points possible associated with each representationassociated with each representation

Averaged exam contentAveraged exam content

0.000.100.200.300.400.500.600.700.800.901.00

201 Reform 202 Reform 202 Trad

Verbal

Math

Graphical

Pictorial

Multiple

Course analysisCourse analysis Both reform-style used more Both reform-style used more

representations in a more integrated representations in a more integrated wayway

Could plausibly account for quiz Could plausibly account for quiz performance dataperformance data

Course also included other Course also included other components: recitation, lab, components: recitation, lab, homeworks homeworks

ConclusionsConclusions Both micro- and macro-level sources Both micro- and macro-level sources

of performance variationof performance variation Students have fairly robust opinions of their own Students have fairly robust opinions of their own

representational competencerepresentational competence Opinions are cross-context; skills are not necessarilyOpinions are cross-context; skills are not necessarily

Pervasive use of different/multiple representations in Pervasive use of different/multiple representations in instruction can have a noticeable effect on student skillsinstruction can have a noticeable effect on student skills

AcknowledgementsAcknowledgements This work was supported in part by This work was supported in part by

an NSF Graduate Fellowship and by an NSF Graduate Fellowship and by Colorado PhysTEC. Colorado PhysTEC.

Special thanks to the PER group at Special thanks to the PER group at CU-Boulder and to Drs. Beale, CU-Boulder and to Drs. Beale, Munsat, and Peterson. Munsat, and Peterson.

Performance data – traditional Performance data – traditional 2020 2020

VerbalVerbal MathMath GraphGraph

ChoiceChoice 35% 35% (N=17)(N=17)

37% 37% (N=57)(N=57)

4% 4% (N=26)(N=26)

ControControll

24% 24% (N=17)(N=17)

56% 56% (N=18)(N=18)

25% 25% (N=16)(N=16)p = 0.04p = 0.04

PictorialPictorial

82% 82% (N=72)(N=72)58% 58% (N=19)(N=19)p = 0.03p = 0.03

Wave optics quizWave optics quiz

ChoiceChoice 81% 81% (N=21)(N=21)

90% 90% (N=42)(N=42)

96% 96% (N=28)(N=28)

ControControll

32% 32% (N=19)(N=19)p = 0.002p = 0.002

13% 13% (N=15)(N=15)p < p < 0.00010.0001

53% 53% (N=17)(N=17)p = p = 0.00040.0004

39% 39% (N=58)(N=58)83% 83% (N=18)(N=18)p = p = 0.00120.0012

Atomic physics quizAtomic physics quiz