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Meltzer Department of Physics and Astronomy Iowa State University 4N!!LMWhat Affects Learning Gains?X Normalized Learning Gain [Hake s g ] is a widely used measure of conceptual learning. [g=(posttest-pretest)/(100%-pretest)] g is not correlated with pretest scores. g is virtually invariant among traditional instructors. g is correlated with instructional method (higher g found for Interactive Engagement methods). ____________________________________________ Many studies assert that correlations exist between students performance in physics and various preinstruction parameters (e.g., mathematical skill, reasoning ability, etc.) Is it possible that such a correlation might also be reflected in learning gains as measured by g on the FCI, CSE, or similar conceptual diagnostic instruments? l!@( -! !`-! - !'"!9.ZA>]KD ; nWhat if there are Hidden Variables Correlated with g?$85 If g is correlated with any precourse measure (such as mathematical ability), this would have to be taken into account when comparing learning-gain data. It is usually assumed that [pretest score + instructional method] together determine posttest score. However, if precourse measures are correlated with g, then: other hidden variables besides pretest score would be required to fully characterize a student s preinstruction mental state-function. could no longer assume that, e.g., equal FCI pretest scores necessarily imply equal posttest scores for courses taught with identical instructional methods. !!`22-&+# > SummaryThere is significant evidence that precourse measures may be correlated with students individual learning gains (even normalized gains). Purely quantitative skills may be (indirectly) related to conceptual learning ability. Patterns of wrong answer choices may provide evidence of students initial knowledge state (and of their probable learning gains in a course). u Ku# HaDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?ba$ Probably not. More likely, performance on a math skills test is related to other relevant parameters. (Reasoning ability? Learning rate? Motivation?) :!UPpX Previous Studies on Factors Influencing Students Achievement in PhysicsIH$ More than a dozen studies report that mathematical knowledge is significantly correlated with students grades. Several studies suggest that logical reasoning ability is an independent factor as well. However: These studies almost all use traditional, quantitative end-of-chapter problems as their performance criterion. All of these studies focus on students scores on course exams, which are not necessarily the same (nor even necessarily correlated) with how much the student actually learned in the course. < !(<0 <&Q" 4j<&Guiding Themes of This WorkTResearch has shown that success on traditional problems is not necessarily indicative of students conceptual knowledge. Students who perform well on exams may have learned little, and students who have lower exam scores may have learned much (if they started with little or no previous knowledge). Here we report investigations of factors related to learning gains, as measured by pre/posttests of conceptual understanding. b+ <! < <+>;:Could a Math Skills Pretest be a Predictor of Performance?~H.T. Hudson and others have found significant correlation between performance on math skills pretest and student performance on traditional, quantitative exams. Here we examine possible correlation with learning gain on a qualitative, conceptual diagnostic test (CSE). Previous study by Hake et al. (1994): Students with high learning gains on FCI scored 19% higher (than low gainers) on math skills test taken when entering university. Fall 98 data sample: 59 students enrolled in second semester of non-calculus general physics course; 63% female. Math pretest taken within previous 18 months (before taking first semester course). <! d;/4p1Learning Gains vs. Math Pretest Scores[Fall 98] *2'$ !hLearning Gains vs. Wrong Answer Pretest[Fall 98] *5* $ t Wrong Answer Pretest for High and Low Gainers[Fall 98] 6;/ t Wrong Answer Pretest for High and Low Gainers[Fall 97] 6;/ 6Math Pretest Score for High and Low Gainers[Fall 98] 67+ x Wrong Answer Pretest for High and Low Gainers[Spring 98] 6=/ How Can We Search for Possible Hidden Variables in Initial Knowledge State?N FM$Study relationship between learning gains and: ACT Math score (two samples) Math Skills Pretest (algebra & trig) (one sample) Pattern of wrong answers on conceptual diagnostic pretest (three samples)|/!h<2 K. &=Diagnostic InstrumentsConceptual Survey of Electricity (23-item abridged version), by Hieggelke, Maloney, O Kuma, and Van Heuvelen. It contains qualitative questions and answers, virtually no quantitative calculations. Given both as pretest and posttest. Diagnostic Math Skills Test (38 items) by H.T. Hudson. Algebraic manipulations, simultaneous equations, word problems, trigonometry, graphical calculations, unit conversions, exponential notation. Not a mathematical reasoning test. Given as pretest only.r <!#4P@ { pAnalysis of Wrong Answer Pattern on Conceptual Pretestt Wrong Answers on 11 (out of 23) items on CSE pretest analyzed; Certain specific answer options are identified as favored (though incorrect), perhaps representing transitional states of knowledge. Percentage of favored options selected is assigned as WA score. (Correctly answered questions are ignored.) ; <;k ` ̙33` ` ff3333f` 333MMM` f` f` 3>?" dd@,|?" dd@ " @ ` n?" dd@ @@``PR @ ` `p>>c( 6 P T Click to edit Master title style! ! 0D RClick to edit Master text styles Second level Third level Fourth level Fifth level! 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What Affects Learning Gains?8What if there are Hidden Variables Correlated with g?IPrevious Studies on Factors Influencing Students Achievement in PhysicsGuiding Themes of This WorkNHow Can We Search for Possible Hidden Variables in Initial Knowledge State?;Could a Math Skills Pretest be a Predictor of Performance?Diagnostic Instruments2Learning Gains vs. Math Pretest Scores [Fall 98] 7Math Pretest Score for High and Low Gainers [Fall 98] bDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?5Learning Gains vs. Wrong Answer Pretest [Fall 98] ;Wrong Answer Pretest for High and Low Gainers [Fall 98] ;Wrong Answer Pretest for High and Low Gainers [Fall 97] =Wrong Answer Pretest for High and Low Gainers [Sposoft Word Document0U bDocument Word.Document.80.Microsoft Word Document0^bDocument Word.Document.80.Microsoft Word Document0` bDocument Word.Document.80.Mikx4NȥZmo[p75gCsA4] `!d Y-6}$49翿H:GںlaƊ]b=|CTnqD`Zq$-a[X?FcMV@Y`'.c9GnF$}.QE E zfa1%)1L%j,uJ#@v0N:^{%W!GĔGLqCq 0%76y{{GK\fǹiU%Vk.T>uLjOymSOŏl"wYN,-e@{u >ZޯW#59Uk^2L_Ly+mCBRZlYg8MWP%\# {1%%bt5&[ncՁW䉾H:&HPEVGuz{ gM|5Z!jkػvTFx/cwegeny/ʙ ^TXh簭b??o5w-od5wkmYf$\G>Bso=ah1jvH:]=z5, =+FCu.{T4=|mkMY.+Wa7cwiv§0jbhIhʚ*;O}o<|jvВKLCzQ&Oi^\ :'L'٧Q/o=wBS ܕd@y=H1C4{>_ўtttHJU0z`Aκ%(|iM~h^xC<QS._ko.{#s.Document.80.Microsoft Word Document0IbDocument Word.Document.80.Microsoft Word Document0U bDocument Word.Document.80.Microsoft Word Document0^bDocument Word.Document.80.Microsoft Word Document0` bDocument Word.Document.80.Microsoft Word Document0bDocument Word.Document.80.Microsoft Word Document/0LDArial0Hb b b,b0PbPb0"" @n?" dd@ @@``P< o2$Uj:ȝvH2$V(wcB`*H2$_ـB`?#2$];J:7'+2$$dg%2$C.G%*ܜEqkc$@g4MdMd\b0Tb Bpppp@?%]5Are there Hidden Variables in Students Initial Knowledge State Which Correlate with Learning Gains?hg$N David E. Meltzer Department of Physics and Astronomy Iowa State University 4N!!LMWhat Affects Learning Gains?X Normalized Learning Gain [Hake s g ] is a widely used measure of conceptual learning. [g=(posttest-pretest)/(100%-pretest)] g is not correlated with pretest scores. g is virtually invariant among traditional instructors. g is correlated with instructional method (higher g found for Interactive Engagement methods). ____________________________________________ Many studies assert that correlations exist between students performance in physics and various preinstruction parameters (e.g., mathematical skill, reasoning ability, etc.) Is it possible that such a correlation might also be reflected in learning gains as measured by g on the FCI, CSE, or similar conceptual diagnostic instruments? l!@( -! !`-! - !'"!9.ZA>]KD ; nWhat if there are Hidden Variables Correlated with g?$85 If g is correlated with any precourse measure (such as mathematical ability), this would have to be taken into account when comparing learning-gain data. It is usually assumed that [pretest score + instructional method] together determine posttest score. However, if precourse measures are correlated with g, then: other hidden variables besides pretest score would be required to fully characterize a student s preinstruction mental state-function. could no longer assume that, e.g., equal FCI pretest scores necessarily imply equal posttest scores for courses taught with identical instructional methods. !!`22-&+# > SummaryThere is significant evidence that precourse measures may be correlated with students individual learning gains (even normalized gains). Purely quantitative skills may be (indirectly) related to conceptual learning ability. Patterns of wrong answer choices may provide evidence of students initial knowledge state (and of their probable learning gains in a course). u Ku# HaDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?ba$ Probably not. More likely, performance on a math skills test is related to other relevant parameters. (Reasoning ability? Learning rate? Motivation?) :!UPpX Previous Studies on Factors Influencing Students Achievement in PhysicsIH$ More than a dozen studies report that mathematical knowledge is significantly correlated with students grades. Several studies suggest that logical reasoning ability is an independent factor as well. However: These studies almost all use traditional, quantitative end-of-chapter problems as their performance criterion. All of these studies focus on students scores on course exams, which are not necessarily the same (nor even necessarily correlated) with how much the student actually learned in the course. < !(<0 <&Q" 4j<&Guiding Themes of This WorkTResearch has shown that success on traditional problems is not necessarily indicative of students conceptual knowledge. Students who perform well on exams may have learned licrosoft Word Document0bDocument Word.Document.80.Microsoft Word Document/0LDArial: 0Pbtbb4b 0XbXb 0"" @n?" dd@ @@``P< o2$Uj:ȝvH2$V(wcB`*H2$_ـB`?#2$];J:7'+2$$dg%2$C.G%*ܜEqkc$@g4>d>ddb 0\bppp@?%5Are there Hidden Variables in Students Initial Knowledge State Which Correlate with Learning Gains?hg$PowerPoint Document+,D՜.+,(hp|DocumentSummaryInformation 8j#Title _PID_GUIDAN{CE5D9922-9911-11D2-96ED-9925392B142D}î0CE #sq0ВRւz(1Tb\?SώW_";/z!Gt{qbcdýG&!:$ss훭N2߲CDs|$hUkb\/1pX yԘ%r|8{r-WUٔ% d gEΎ] %gT5ϓxѢ~s>fY㵺r+߶9upF?PVvƦRg|u>qxOV&yz|ѢW4v(hI]1z o[nQ1Bu( vkQ> g;@np6Cڝ`g 1vg#fv"[~#`~Bq/Ѳ?az</#߶m2|un :C6jʼ+!fƏgಈXJ]sxceVa7˨ B͋x{ 壯*Lz 7 7Lu]eʪv:qpvW>O~ 2 2Ϲlb9}o|iO=#Tx؞sXʠwDU8"Cy-i-6LhmF[H{L35CK\,5vu)vsJ7}Xo4,w+2C˲}gT(M{{HDįQ:T0@ZΚ(vIA";掷'o:Y[~w?!`!_ـB`?P2ؖTvxWkY?sgWcӦ,ch+.+huW+(Y@H("(&}]i)Hν3N&&u!qΉq ;`fNZ5ZN۹ޱ>BIoU<3^C=))ix&c߷bDocument Word.Document.80.Microsoft Word Document0IbDocument Word.Document.80.Microsoft Word Document0U bDocument Word.Document.80.Microsoft Word Document0^bDocument Word.Document.80.Microsoft Word Document0` bDocument Word.Document.80.Microsoft Word Document0bDocument Word.Document.80.Microsoft Word Document/0LDArial0Hb b b,b0PbPb0"" @n?" dd@ @@``P< o2$Uj:ȝvH2$V(wcB`*H2$k `TLK䎐\Rb2$];J:7'+2$$dg%2$C.G%*ܜEqkc$@g4MdMd\b0Tb Bppp@?%]5Are there Hidden Variables in Students Initial Knowledge State Which Correlate with Learning Gains?hg$N David E. Meltzer Department of Physics and Astronomy Iowa State University 4N!!LMWhat Affects Learning Gains?X Normalized Learning Gain [Hake s g ] is a widely used measure of conceptual learning. [g=(posttest-pretest)/(100%-pretest)] g is not correlated with pretest scores. g is virtually invariant among traditional instructors. g is correlated with instructional method (higher g found for Interactive Engagement methods). ____________________________________________ Many studies assert that correlations exist between students performance in physics and various preinstruction parameters (e.g., mathematical skill, reasoning ability, etc.) Is it possible that such a correlation might also be reflected in learning gains as measured by g on the FCI, CSE, or similar conceptual diagnostic instruments? l!@( -! !`-! - !'"!9.ZA>]KD ; nWhat if there are Hidden Variables Correlated with g?$85 If g is correlated with any precourse measure (such as mathematical ability), this would have to be taken into account when comparing learning-gain data. It is usually assumed that [pretest score + instructional method] together determine posttest score. However, if precourse measures are correlated with g, then: other hidden variables besides pretest score would be required to fully characterize a student s preinstruction mental state-function. could no longer assume that, e.g., equal FCI pretest scores necessarily imply equal posttest scores for courses taught with identical instructional methods. !!`22-&+# > SummaryThere is significant evidence that precourse measures may be correlated with students individual learning gains (even normalized gains). Purely quantitative skills may be (indirectly) related to conceptual learning ability. Patterns of wrong answer choices may provide evidence of students initial knowledge state (and of their probable learning gains in a course). u Ku# HaDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?ba$ Probably not. More likely, performance on a math skills test is related to other relevant parameters. (Reasoning ability? Learning rate? Motivation?) :!UPpX Previous Studies on Factors Influencing Students Achievement in PhysicsIH$ More than a dozen studies report that mathematical knowledge is significantly correlated with students grades. Several studies suggest that logical reasoning ability is an independent factor as well. However: These studies almost all use traditional, quantitative end-of-chapter problems as their performance criterion. All of these studies focus on students scores on course exams, which are not necessarily the same (nor even necessarily correlated) with how much the student actually learned in the course. < !(<0 <&Q" 4j<&Guiding Themes of This WorkTResearch has shown that success on traditional problems is not necessarily indicative of students conceptual knowledge. Students who perform well on exams may have learned little, and students who have lower exam scores may have learned much (if they started with little or no previous knowledge). Here we report investigations of factors related to learning gains, as measured by pre/posttests of conceptual understanding. b+ <! < <+>;:Could a Math Skills Pretest be a Predictor of Performance?~H.T. Hudson and others have found significant correlation between performance on math skills pretest and student performance on traditional, quantitative exams. Here we examine possible correlation with learning gain on a qualitative, conceptual diagnostic test (CSE). Previous study by Hake et al. (1994): Students with high learning gains on FCI scored 19% higher (than low gainers) on math skills test taken when entering university. Fall 98 data sample: 59 students enrolled in second semester of non-calculus general physics course; 63% female. Math pretest taken within previous 18 months (before taking first semester course). <! d;/4p1Learning Gains vs. Math Pretest Scores[Fall 98] *2'$ !hLearning Gains vs. Wrong Answer Pretest[Fall 98] *5* $ t Wrong Answer Pretest for High and Low Gainers[Fall 98] 6;/ t Wrong Answer Pretest for High and Low Gainers[Fall 97] 6;/ 6Math Pretest Score for High and Low Gainers[Fall 98] 67+ x Wrong Answer Pretest for High and Low Gainers[Spring 98] 6=/ How Can We Search for Possible Hidden Variables in Initial Knowledge State?N FM$Study relationship between learning gains and: ACT Math score (two samples) Math Skills Pretest (algebra & trig) (one sample) Pattern of wrong answers on conceptual diagnostic pretest (three samples)|/!h<2 K. &=Diagnostic InstrumentsConceptual Survey of Electricity (23-item abridged version), by Hieggelke, Maloney, O Kuma, and Van Heuvelen. It contains qualitative questions and answers, virtually no quantitative calculations. Given both as pretest and posttest. Diagnostic Math Skills Test (38 items) by H.T. Hudson. Algebraic manipulations, simultaneous equations, word problems, trigonometry, graphical calculations, unit conversions, exponential notation. Not a mathematical reasoning test. Given as pretest only.r <!#4P@ { pAnalysis of Wrong Answer Pattern on Conceptual Pretestt Wrong Answers on 11 (out of 23) items on CSE pretest analyzed; Certain specific answer options are identified as favored (though incorrect), perhaps representing transitional states of knowledge. Percentage of favored options selected is assigned as WA score. (Correctly answered questions are ignored.) ; <;k 4( r SD# 0 6A`?q`H 0h ? ̙33 ^x\ pT>gKHYGX)`3 !Utcmu:S S:mXZ;PB{۽?awޜw=s=/FC.M"F3 ( 2UlooCg `g*GHB`ppb%1L)ұ0p8X3Nu% 8 888U=F[\Iv-_c^6N)aC)KbCC6^+Vi -Vj: V>)Yy'mh #cT)_s?}Dg_&2`5qit`x9p+Yc#Ƈ heKw>5]-u;cO-Z4'uĹ҉˟a`,c&לw*|On#\y!ߥ3GD`WHv3(jH}Ln흱-űxg&,i)Ґ'-^VU6^Sr0bӤS"(f3Er#:8`/"p͆+N`EG?-Fԅ}t:z2 9겨g+v"l ˍ Mw[طfҜ㽏Q!ǤʹЇG*f\r\Dzk1ѷf &dI.0/ӗJ':HT?, `O1VhWF=]fP3wFF*="5۷)}`OP0mflTvOgI٢+S%$Z ܖQNw/,Ϣ\ )WXc N=ʱإWU!Q[>gZ;][enE"FVx'!A$M_@mOঢ়"&9~d(}]Ed*~C^!?&3R8H RJ0=潽sy3"=}g+XO\V]<<r1Fk0#\*;T>DsR^j8N3REy5U-UUyBn9(t݅`4`NSZ db%v\1gd&TA>:+QCDjh}}]'QϮ8]'.YKu~6S0U6u}-+|EKbݱ-:!|]&΅2р#c 4["k#USEi9O|;Jh*+k]]5UzH*EXt2S['Z矖Ӫ{Ԟ)zoQ{lڳ$ǐ_l8jmBncƗLҭ^Q%ZLv&TԅfZnkQP&vd˿%=?SDNM.%8m2nO(!)AMzXA!b}ԇÕ5uD[ury\Ș<]5u" d?[*b5|IeJ}UP 3*Jͤ Lգ-ؖ[wtGSdt6EGIѣnТ}41f24i*wdXg2θ0^oP!䟛 f3W-W|,pd̥z]MקoG%VR;}LRSZn쌍)0et;H ޢѺޢUܑaJh;YdEǙ 4D83p5CP$:TǤFZ HDP+7CHuu*#K=zB,wJ/Ц٪MY7ڴVQE0'KsZеxm"LbltdSjJ[7Y`c(sHt8R^z5SP!3%vjNXef;OTPb>X[m//EG|kةEjp)1 G"~/1+Sϯ{ʪޕ/.|5bVE/I\W|jض[6uCHxwDځUȩ~В&-8eMr=ג?QaS*? x)SU|7|ǔa&Niz2՚S6ӧ̿RjϷΠ:Ca֭R^z;|3Uϩʟގw)߀TŁg;(b#OۏZ%ց@/Jy|X[ˡ Gr)Z7=YRI$9ԓTLiu\>LcǦZ߾*p[ p"XW[m["C7o1gFpp<'gN{GO}gzΣ.:z2bނ) b _pT_>s pF|}R]:ɖ88L4<8[/SY6)Gz?zz杌e>'oi2~>}}KhM{ߞ5no0PO}b8St`%{O^釂4y/e\/Jܿǃ$vqݪ$ߋxdoG"%*Q+JC~_VVάY\j̮3l-\`os ;:Could a Math Skills Pretest be a Predictor of Performance?~H.T. Hudson and others have found significant correlation between performance on math skills pretest and student performance on traditional, quantitative exams. Here we examine possible correlation with learning gain on a qualitative, conceptual diagnostic test (CSE). Previous study by Hake et al. (1994): Students with high learning gains on FCI scored 19% higher (than low gainers) on math skills test taken when entering university. Fall 98 data sample: 59 students enrolled in second semester of non-calculus general physics course; 63% female. Math pretest taken within previous 18 months (before taking first semester course). <! d;/4p1Learning Gains vs. Math Pretest Scores[Fall 98] *2'$ !hLearning Gains vs. Wrong Answer Pretest[Fall 98] *5* $ t Wrong Answer Pretest for High and Low Gainers[Fall 98] 6;/ t Wrong Answer Pretest for High and Low Gainers[Fall 97] 6;/ 6Math Pretest Score for High and Low Gainers[Fall 98] 67+ x Wrong Answer Pretest for High and Low Gainers[Spring 98] 6=/ How Can We Search for Possible Hidden Variables in Initial Knowledge State?N FM$Study relationship between learning gains and: ACT Math score (two samples) Math Skills Pretest (algebra & trig) (one sample) Pattern of wrong answers on conceptual diagnostic pretest (three samples)|/!h<2 K. &=Diagnostic InstrumentsConceptual Survey of Electricity (23-item abridged version), by Hieggelke, Maloney, O Kuma, and Van Heuvelen. It contains qualitative questions and answers, virtually no quantitative calculations. Given both as pretest and posttest. Diagnostic Math Skills Test (38 items) by H.T. Hudson. Algebraic manipulations, simultaneous equations, word problems, trigonometry, graphical calculations, unit conversions, exponential notation. Not a mathematical reasoning test. Given as pretest only.r <!#4P@ { pAnalysis of Wrong Answer Pattern on Conceptual Pretestt Wrong Answers on 11 (out of 23) items on CSE pretest analyzed; Certain specific answer options are identified as favored (though incorrect), perhaps representing transitional states of knowledge. Percentage of favored options selected is assigned as WA score. (Correctly answered questions are ignored.) ; <;k 4( r SD# 0 6A`?q`H 0h ? ̙331 Nx[ lUW{-AW/[ Axcj5l6#n9ECEbtHԩuUl 9eCb8=|u{ӏ=YoG҅TDr_Hӎ8QpjCvn"p+4Kd`x8 7G ʿ \A%K-V.I;\ϼ<B>$oͯ>/c=Q|RyQD.DPfmu^Ӑ?ɱo"q8xy˿OQ;.n6aiad<ٞL$vMdMlߕs ,Hl;:so iLe"fNG<9QZ)*1Rv[F2"܍īV1";1*6"h~ie[d|KhytY ^R~gXg\0k _dpUT(*%P:b"ɊĩP:)ga]"Va,-|9Z=j=k;av;IԄtL A~l@loT<d}9ށFE|]54}rⶺ }cuCS_1NHz>,pa:B퇟:7ͣXy/ctzEzZH5ƵyXI/w,DI:o8]j5ww1}58`ڕ\IݴȜx~N]>4D-.e|r\F+]_gwe/KQӨMoNU.`MC^4.l1Ul팎W _6.mGU h|W44>tX>C` 7[ K?w3YN3Y1Xkr}1z{Ǉ^:w^~zGWRJV-נ4HȢce%3WkF0ؖMLWjM+ȘnmVdJ-mqjUNTpf0.* $x_~+qWyq*.ǘ&81 :X3W3 }@dU_ʭY/{+ang_`OB(GϟDθ5VΏFgYs+Gc0|W)YMdu;q;v=owӘ4xu%694JƸWޱTuhRб7 fs}_ =tqq!K[Rw~ 8GOd 1xe*Vv!C5Đ[U톼giui%ϲ{`ӈRēȆR.Qbq8qXϽpSBlo}unPSCCCCCCCCCCCCCJ _߾~ |}O`(d~Kg}m7=ngIxo}$&yJ4vvҠȃT^LTJƞT_<4=JVf2f;ilm_ݺSk\K+i5Qn¯EV"*Y3Eo=b4sB4XTrT =;p0CFb=( 0bDocument Word.Document.80.Microsoft Word Document0IbDocument Word.Document.80.MicrRoot EntrydO)@D- ggPictures'Current User<PSummaryInformationn8D(ummaryInformationHkmhj !"@$%&'()*+,-./0123456789:;=ABCDEFHIJKring 98] 9Analysis of Wrong Answer Pattern on Conceptual PretestSummaryFonts UsedDesign TemplateEmbedded OLE Servers Slide Titles Slide Titles(_dDavid E. MeltzerDavid E. Meltzer87B-11D2-96ED-9925392B142D}(_㋄David E. MeltzerDavid E. !"#$%&'()*+,-./0123456789:;<=>?@ABCDEFGHIJKLMNOPQRSTUVWXYZ[\]^_`abcdefgilnopqrstuvwxyz{|}~earning. [g=(posttest-pretest)/(100%-pretest)] g is not correlated with pretest scores. g is virtually invariant among traditional instructors. g is correlated with instructional method (higher g found for Interactive Engagement methods). ____________________________________________ Many studies assert that correlations exist between students performance in physics and various preinstruction parameters (e.g., mathematical skill, reasoning ability, etc.) Is it possible that such a correlation might also be reflected in learning gains as measured by g on the FCI, CSE, or similar conceptual diagnostic instruments? l!@( -! !`-! - !'"!9.ZA>]KD ; nWhat if there are Hidden Variables Correlated with g?$85 If g is correlated with any precourse measure (such as mathematical ability), this would have to be taken into account when comparing learning-gain data. It is usually assumed that [pretest score + instructional method] together determine posttest score. However, if precourse measures are correlated with g, then: other hidden variables besides pretest score would be required to fully characterize a student s preinstruction mental state-function. could no longer assume that, e.g., equal FCI pretest scores necessarily imply equal posttest scores for courses taught with identical instructional methods. !!`22-&+# > SummaryThere is significant evidence that precourse measures may be correlated with students individual learning gains (even normalized gains). Purely quantitative skills may be (indirectly) related to conceptual learning ability. Patterns of wrong answer choices may provide evidence of students initial knowledge state (and of their probable learning gains in a course). u Ku# HaDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?ba$ Probably not. More likely, performance on a math skills test is related to other relevant parameters. (Reasoning ability? Learning rate? Motivation?) :!UPpX Previous Studies on Factors Influencing Students Achievement in PhysicsIH$ More than a dozen studies report that mathematical knowledge is significantly correlated with students grades. Several studies suggest that logical reasoning ability is an independent factor as well. However: These studies almost all use traditional, quantitative end-of-chapter problems as their performance criterion. All of these studies focus on students scores on course exams, which are not necessarily the same (nor even necessarily correlated) with how much the student actually learned in the course. < !(<0 <&Q" 4j<&Guiding Themes of This WorkTResearch has shown that success on traditional problems is not necessarily indicative of students conceptual knowledge. Students who perform well on exams may have learned little, and students who have lower exam scores may have learned much (if they started with little or no previous knowledge). Here we report investigations of factors related to learning gains, as measured by pre/posttests of conceptual understanding. b+ <! < <+>;:Could a Math Skills Pretest be a Predictor of Performance?~H.T. Hudson and others have found significant correlation between performance on math skills pretest and student performance on traditional, quantitative exams. Here we examine possible correlation with learning gain on a qualitative, conceptual diagnostic test (CSE). Previous study by Hake et al. (1994): Students with high learning gains on FCI scored 19% higher (than low gainers) on math skills test taken when entering university. Fall 98 data sample: 59 students enrolled in second semester of non-calculus general physics course; 63% female. Math pretest taken within previous 18 months (before taking first semester course). <! d;/4p1Learning Gains vs. Math Pretest Scores[Fall 98] *2'$ !hLearning Gains vs. Wrong Answer Pretest[Fall 98] *5* $ t Wrong Answer Pretest for High and Low Gainers[Fall 98] 6;/ t Wrong Answer Pretest for High and Low Gainers[Fall 97] 6;/ 6Math Pretest Score for High and Low Gainers[Fall 98] 67+ x Wrong Answer Pretest for High and Low Gainers[Spring 98] 6=/ How Can We Search for Possible Hidden Variables in Initial Knowledge State?N FM$Study relationship between learning gains and: ACT Math score (two samples) Math Skills Pretest (algebra & trig) (one sample) Pattern of wrong answers on conceptual diagnostic pretest (three samples)|/!h<2 K. &=Diagnostic InstrumentsConceptual Survey of Electricity (23-item abridged version), by Hieggelke, Maloney, O Kuma, and Van Heuvelen. It contains qualitative questions and answers, virtually no quantitative calculations. Given both as pretest and posttest. Diagnostic Math Skills Test (38 items) by H.T. Hudson. Algebraic manipulations, simultaneous equations, word problems, trigonometry, graphical calculations, unit conversions, exponential notation. Not a mathematical reasoning test. Given as pretest only.r <!#4P@ { pAnalysis of Wrong Answer Pattern on Conceptual Pretestt Wrong Answers on 11 (out of 23) items on CSE pretest analyzed; Certain specific answer options are identified as favored (though incorrect), perhaps representing transitional states of knowledge. Percentage of favored options selected is assigned as WA score. (Correctly answered questions are ignored.) ; <;k rF_F{b>( Document Word.Document.80.Microsoft Word Document0IDocument W .@"Arialw@ ƏIwIw0- .$2 PAAPT Winter Meetingt . .2 )eJanuary 12, 1999 . .$2 FZAnaheim, Californiat Meltzerord.Document.80.Microsoft Word Document0U Document Word.Document.80.Microsoft Word Document0^Document Word.Document.80.Microsoft Word Document0` Document Word.Document.80.Microsoft Word Document0Document Word.Document.80.Microsoft Word Document/0LDArialpLv0( 0$" `. @n?" dd@ @@``P9 o2$Uj:ȝvH2$V(wcB`*H2$_ـB`?#2$];J:7'+2$$dg%2$C.G%*ܜEqkc$@g4=d=dv0ppp@uʚ;2Nʚ;<4!d!d{ 0<4dddd{ 0<4BdBd{ 0:2___PPT9/0?%5Are there Hidden Variables in Students Initial Knowledge State Which Correlate with Learning Gains?hg$ David E. Meltzer Department of Physics and Astronomy Iowa State University AAPT Winter Meeting January 12, 1999 Anaheim, California^M!!9!( L8What Affects Learning Gains?X Normalized Learning Gain [Hake s g ] is a widely used measure of conceptual learning. [g=(posttest-pretest)/(100%-pretest)] g is not correlated with pretest scores. g is virtually invariant among traditional instructors. g is correlated with instructional method (higher g found for Interactive Engagement methods). ____________________________________________ Many studies assert that correlations exist between students performance in physics and various preinstruction parameters (e.g., mathematical skill, reasoning ability, etc.) Is it possible that such a correlation might also be reflected in learning gains as measured by g on the FCI, CSE, or similar conceptual diagnostic instruments? n!@( -! !`-! - !'"!9.ZA ,]K nWhat if there are Hidden Variables Correlated with g?$85 If g is correlated with any precourse measure (such as mathematical ability), this would have to be taken into account when comparing learning-gain data. It is usually assumed that [pretest score + instructional method] together determine posttest score. However, if precourse measures are correlated with g, then: other hidden variables besides pretest score would be required to fully characterize a student s preinstruction mental state-function. could no longer assume that, e.g., equal FCI pretest scores necessarily imply equal posttest scores for courses taught with identical instructional methods. !!`22-&+# > Previous Studies on Factors Influencing Students Achievement in PhysicsIH$ More than a dozen studies report that mathematical knowledge is significantly correlated with students grades. Several studies suggest that logical reasoning ability is an independent factor as well. However: These studies almost all use traditional, quantitative end-of-chapter problems as their performance criterion. All of these studies focus on students scores on course exams, which are not necessarily the same (nor even necessarily correlated) with how much the student actually learned in the course. < !(<0 <&Q" 4j<& Guiding Themes of This WorkTResearch has shown that success on traditional problems is not necessarily indicative of students conceptual knowledge. Students who perform well on exams may have learned little, and students who have lower exam scores may have learned much (if they started with little or no previous knowledge). Here we report investigations of factors related to learning gains, as measured by pre/posttests of conceptual understanding. b+ <! < <+>;How Can We Search for Possible Hidden Variables in Initial Knowledge State?N FM$Study relationship between learning gains and: ACT Math score (two samples) Math Skills Pretest (algebra & trig) (one sample) Pattern of wrong answers on conceptual diagnostic pretest (three samples)|/!h<2 K. &=:Could a Math Skills Pretest be a Predictor of Performance?~H.T. Hudson and others have found significant correlation between performance on math skills pretest and student performance on traditional, quantitative exams. Here we examine possible correlation with learning gain on a qualitative, conceptual diagnostic test (CSE). Previous study by Hake et al. (1994): Students with high learning gains on FCI scored 19% higher (than low gainers) on math skills test taken when entering university. Fall 98 data sample: 59 students enrolled in second semester of non-calculus general physics course; 63% female. Math pretest taken within previous 18 months (before taking first semester course). <! d;/4pDiagnostic InstrumentsConceptual Survey of Electricity (23-item abridged version), by Hieggelke, Maloney, O Kuma, and Van Heuvelen. It contains qualitative questions and answers, virtually no quantitative calculations. Given both as pretest and posttest. Diagnostic Math Skills Test (38 items) by H.T. Hudson. Algebraic manipulations, simultaneous equations, word problems, trigonometry, graphical calculations, unit conversions, exponential notation. Not a mathematical reasoning test. Given as pretest only.v <! # 4P@ { 1Learning Gains vs. Math Pretest Scores[Fall 98] *2'$ 6Math Pretest Score for High and Low Gainers[Fall 98] 67+ aDoes this imply that improving algebraic skills will lead to increased conceptual learning gains?ba$ Probably not. More likely, performance on a math skills test is related to other relevant parameters. (Reasoning ability? Learning rate? Motivation?) :!UPpXhLearning Gains vs. Wrong Answer Pretest[Fall 98] *5* t Wrong Answer Pretest for High and Low Gainers[Fall 98] 6;/ t Wrong Answer Pretest for High and Low Gainers[Fall 97] 6;/ x Wrong Answer Pretest for High and Low Gainers[Spring 98] 6=/ pAnalysis of Wrong Answer Pattern on Conceptual Pretestt Wrong Answers on 11 (out of 23) items on CSE pretest analyzed; Certain specific answer options are identified as favored (though incorrect), perhaps representing transitional states of knowledge. Percentage of favored options selected is assigned as WA score. (Correctly answered questions are ignored.) ; <;SummaryThere is significant evidence that precourse measures may be correlated with students individual learning gains (even normalized gains). Purely quantitative skills may be (indirectly) related to conceptual learning ability. Patterns of wrong answer choices may provide evidence of students initial knowledge state (and of their probable learning gains in a course). u Ku# Hr TT .--"System 0-&TNPP &0