by
Michael Svec,Ph.D.
Furman University
One of the first topics taught in a traditional introductoryhigh-school or college physics course is motion, including theconcepts of position, velocity and acceleration. Graphs of objectsin motion are frequently used since they offer a valuable alternativeto verbal and algebraic description of motion by offering studentsanother way of manipulating the developing concepts (Arons, 1990).Graphs are the best summary of a functional relationship. Manyteachers consider the use of graphs in a laboratory setting tobe of critical importance for reinforcing graphing skills anddeveloping an understanding of many topics in physics, especiallymotion.
If graphs are to be a valuable tool for students, then we mustknow the level of the students' graphing ability. Studies haveidentified difficulties with such graphing abilities. Studentshave difficulties making connections among graphs of differentvariables, physical concepts and the real world, and they oftenperceive graphs as just a picture (Linn, Layman, & Nachmias,1987; McDermott, Rosenquist, & van Zee, 1987).
Laboratory activities which focus on graphing more than thetraditional labs are valuable in the investigation of studentuse of graphs. Microcomputer-based labs (MBL), provide immediatelyavailable, computer-drawn graphs of objects in motion. MBL iscentered around a sonic ranger which measures the distance toan object and creates a distance-versus-time line graph of theobject's motion in real-time. Learners can move and see the graphof their motion on the computer screen respond to their motion.When compared to traditional physics labs, the MBL places muchmore emphasis on reading and making graphs. The computer labsprovide an excellent tool to explore the connection between graphingskills and learning science concepts.
Whether the students are in middle school, high school, orcollege, MBL has demonstrated the ability to improve their understandingof science concepts and cognitive skills such as observation andprediction (Brasell, 1987a; Thornton & Sokoloff, 1990; Friedler,Nachmias, & Linn, 1990). Students can connect abstract conceptswith concrete, kinesthetic experiences. The ability of the computersto display the data graphically is cited as one of the reasonswhy MBL is so effective.
MBL materials appear to improve students' graphing skills (Linn,Layman & Nachmias, 1987; Mokros & Tinker, 1987; Brasell,1987b). MBL activities seem to help students overcome difficultieswith discrimination of slope and height, changes in slope andheight, and matching narrative with graph features. This is particularlytrue of motion labs which involve the student physically movingand creating a graph.
As cited above, MBL and its use of graphs have been shown toimprove content knowledge specific to graphing problems and graphingskills. This investigation further explores the relationship betweenlearning the content and graphing interpretation skills, and whetheror not students can apply the new content knowledge to new problemswhich do not use line graphs. Two types of motion content knowledgewere defined: 1) content knowledge restricted to graphing problems,and 2) more general content knowledge including word, math andpicture problems. The definition of graphing skills was narrowedto interpretation skills such as calculating and interpretingslopes, and changes in slope, which are required to read motionline graphs.
Methods
Research Questions
Because the use of graphs to help students learn content hasimportant classroom implications, it is important to documentwhat the students are learning when using MBL labs and how theyare learning those topics. The purpose of this study was to examinethe relative effectiveness of the traditional lab method and theMBL for engendering conceptual change in students and to investigatestudents' ability to interpret and use graphs to help them betterlearn the kinematic concepts and to apply this understanding ofthose concepts to new non-graphic problems.
This study seeks to assess the conceptual change in the students'general graphing interpretation skills, specific kinematic graphingskills and conceptual understanding of motion as indicated byachievement on the Graphing Interpretation Skills Test (GIST)and Motion Content Test (MCT). In addition, the results from theinstruments will be used to investigate students' abilities tointerpret and use graphs to better learn the kinematics conceptsand to apply this understanding of those concepts to new problems.The research questions to be explored are presented below.
Research Question 1 (RQ1) was assessed using the scores onthe Graphing Interpretation Skills Test (GIST). Questions fromthe Motion Content Test (MCT) which involve interpreting motiongraphs were used to answer RQ2, while the remaining MCT questionshelped answer RQ3. Assessment included an analysis of the overallmeans and item analysis of specifically designed questions containingdistractors which identified difficulties. To further frame theoriginal research questions and guide the item analysis, answerswere sought to specific hypothesis. By identifying the difficulties,it was possible to provide a richer interpretation of the overallmeans.
Instruments
The GIST contained 11 multiple-choice items. Three of the itemswere adapted from the Test of Graphing in Science (TOGS) by McKenzieand Padilla (1986). The remaining items were written by the investigatorto match the specific interpretation skills. Distracters weredeveloped and were based on previously identified misconceptionsand difficulties. In a field test, the graphing interpretationskills test (GIST) had a KR-20 reliability of 0.97.
The MCT was constructed from several sources and consistedof two types of problems, those which focused on kinematic graphsand those which focused on more traditional non-graphing motionquestions. Multiple-choice items on kinematics graphing were adaptedfrom tests by Thornton and Sokoloff (1990) and written by theauthor in consultation with course instructors. Non-graphing motionitems were adapted from the Mechanics Diagnostic Test (Halloun& Hestenes, 1985a), and the Force Concept Inventory (Hestenes,Wells & Swackhamer, 1992). Additional items were developedby the investigator based on the pilot study. The motion contenttest (MCT) had an KR-20 reliability of 0.98 as a pre- and post-testin a field test.
Both GIST and MCT were field tested in a pilot study conductedin the Fall of 1993 and reported in Svec (1994). The field studyinvolved 133 students enrolled in a physics for elementary teacherscourse and 420 students enrolled in a general physics course. The motion content test (MCT) had an KR-20 reliability coefficientof 0.98 as a pre- and post-test for both populations. On thegraphing interpretation skills test (GIST), the KR-20 reliabilitywas 0.97. In the study and the pilot study both instruments hadKR-20 reliabilities above 0.90. Test having KR-20 reliabilitiesgreater than 0.70 are generally considered to be reliable forgroup measurements.
The validity of the instruments was constructed based on the results. Individual test questions were used to identify misconceptionsand difficulties which were identified in other studies usingsimilar multiple-choice tests and descriptive studies. Contentvalidity was established by having two physicists and one physicslab instructor review the test and answers. Only one item onthe MCT and two items on the GIST were identified as being potentiallyconfusing leaving 95% of the items appropriate. In addition,since many of the items were taken from published tests designedfor college students, from previous tests given in the courseand by the researcher for college students, the appropriatenessof the items for the grade level is seen as high. The resultsbetween pilot study and final study were consistent with thesame misconceptions and difficulties being documented in approximatelythe same percentages. The items on the MCT test accurately representthe topics covered in both the courses.
Design
The nonequivalent control-group design (Campbell & Stanley,1963) was selected. The students in one undergraduate introductoryphysics class, Physical Science for Elementary Teachers (Q202),used the MBL laboratories and served as the treatment group. Anotherundergraduate introductory physics class, General Physics(P201), employed more traditional motion laboratories and functionedas the control group. The two courses are separate from each otherand are taken by different student populations. The dependentvariable will be student achievement on a motion test and a graphinginterpretation skills test. The content of the lectures and laboratoryactivities was documented to identify differences in instructionwhich may affect the variables.
Sample
The samples consist of students enrolled in two general-levelundergraduate physics courses. The two courses were offered attwo different large Midwestern universities located in the samestate. The courses included lecture and laboratory and were requiredin their majors. A pilot study was conducted in the Fall of 1993(author, 1995) and the final data were gathered in the Springsemester of 1994.
The treatment course was Physical Science for ElementaryTeachers (Q202) which is required to be taken by elementaryeducation majors. The course is three credit hours and involvestwo 50-minute lectures and one three-hour lab each week. No textbookwas used.
The control course was General Physics (P201). The courseis taken mainly by premed, life and health science majors. Thecourse focuses on mechanics and waves and is the first half ofa 1 year sequence. The class consists of one 2 1/2-hour lecture,one discussion section and one 2-hour lab for five credits. Thecourse text book was Physics, Principles with Applications(Giancoli, 1991).
The treatment group is 83% female while the control group ismore evenly mixed with 53% of the students being female. Whilethere are gender differences between the two groups, they areof the same ethnicity, predominantly Caucasian. Both populationshad similar number of high school credits in science. Q202 studentsdid take slightly more math in high school and 46% had physicsin high school compared to 28% of the P201 students. The P201students did complete more science course in college
Data Analysis
Test means and standard deviations for GIST, and the two subscales of the MCT were determined. The effect size is a statisticfor quantitatively describing how well the average student whoreceives the intervention performed relative to the average studentwho did not receive the intervention. Effect sizes are commonlyused in meta-analysis but its use in educational research is becomingmore popular. It is a useful statistic for assessing the practicalsignificance of research results (Borg & Gall, 1989).
Since both groups come from different samples, the change frompre-test to post-test was used instead of the actual raw scoresthemselves to determine if significant change has occurred. Theeffect size of the changes for the control group and the treatmentgroup was calculated using the raw score gains, which resultfrom subtracting the pre-test mean score from the post-test meanscore. The standard deviation of the control group on the post-testwas used as the denominator. The effect size is calculated usingthe following equation:
E.S. = (Xtreatment post-Xtreatment pre) - (Xcontrol post-Xcontrol pre)
scontrol post
Where X represents the raw score mean and s is the standard deviation.The effect size will help answer the questions as to whether MBL'sgraphic presentation improve students' ability to interpret avariety of line graphs and whether MBL improves students' conceptualunderstanding of velocity and acceleration.
To further answer the three research questions and to providedata, individual item analysis was employed. The Statistical AnalysisSystem (SAS) was used to construct matrices which displayed thefrequency of students' responses on two different questions oron both the pre- and post-test. For each hypothesis, matricesof appropriate items were constructed to answer the hypothesis.
With the matrix method, it is possible to document whetherstudents' difficulties or misconceptions are consistent acrossquestions and whether there is a relationship between difficultiesand misconceptions identified in one question and the way in whichstudents answered another question. For the purposes of evaluatingthe effect of MBL material, this method of data presentation issuperior to the simple presentation of students' percentages selectinga specific multiple-choice answer on the pre- and post-test. Thematrix method allows the strength of the students' understandingof a concept to be evaluated.
The results from a matrix were classified into one of threecategories: thorough understanding, partial understanding andno evidence for understanding. When comparing two similar questions,the students who answer both questions correctly were classifiedas having a thorough understanding. Students who answer one ofthe questions correctly but answer the second question incorrectlywere classified as having a partial understanding. Students whomiss both questions demonstrate no evidence for understanding.
A sample matrix is illustrated in Figure 1. The column representthe possible choices for Q19 while the rows represent the responsesfor Q14. Question 19 involved calculating the slope of a lineon a generic graph and Question 14 had the students determiningthe slope of a specific line on a graph of mass versus volume.The total for the column shows how many students selected thatoption for the question. Within the matrix are boxes which containthe data on how students responded on both questions. The numberin the box is the frequency, which is a total number of studentswho selected the corresponding question options.
The results of the matrix in Figure 1 are interpreted belowas an example. The correct answer, shown in bold on the matrix,is B for Q19 and C for Q14. Sixty-four of the 134 students, or48%, answered both questions correctly and have demonstrated athorough understanding of the concept tested in the two questions.This corresponds to the frequency on the matrix. Of the 90 studentswho answered Q14 correctly, 71% (64 of the 90) of those studentsalso answered Q19 correctly. Eighty-two students answered Q19correctly, of those, 78% (64 of the 82) were also successful andanswered Q14 correctly. Students who answer one of the questionscorrectly but answer the second question incorrectly have a partialunderstanding. Of the 90 students who answered Q14 correctly,26 of the students missed Q19. These 26 along with the 18 studentswho answered Q19 correctly and Q14 incorrectly comprise thosestudents who have a partial understanding. They account for 33%of the students. For the 19% of the students who miss both questionsthere is no evidence they have an understanding of the conceptor ability.
Figure 1: Example of a Matrix Produced by SAS
| Q | Frequency | Question 19 | |||||
| A | B | C | D | J | Row Total | ||
| A | 6 | 8 | 0 | 0 | 9 | 23 | |
| B | 2 | 6 | 2 | 1 | 2 | 13 | |
| C | 9 | 64 | 8 | 4 | 5 | 90 | |
| D | 0 | 4 | 2 | 1 | 0 | 7 | |
| J | 0 | 0 | 0 | 0 | 1 | 1 | |
| Column Total | 17 | 82 | 12 | 6 | 17 | N=134 | |
The data are from the Q202 Spring 1994 pre-test. The correctresponses are shown in bold and the interpretation of the responsesappears in the text. Based on the above matrix and additionalmatrices for Q202 post-test, P201 pre-test and P201 post-test,the Table 1 was constructed and is characteristic of the tablesused in the study.
Table 1: Summary of matrix Q14 and Q19
(in percent)
| Pre-test | Post-test | ||||||
| Course | thorough | partial | none | thorough | partial | none | |
| Q202 | 48 | 33 | 19 | 65 | 23 | 12 | |
| P201 | 58 | 31 | 11 | 76 | 16 | 8 | |
The matrix methods help answer each individual hypothesis.The results from each hypothesis and the effect size results willbe used in the final analysis to find detailed answers to threeresearch questions.
Results and Analysis
Graphing Interpretation Skills
The calculated effect size using the gains in the raw scoreswas 0.78, which is an effect size of medium strength. The controlgroup's initial score was higher than the treatment group's butafter instruction, the control group's score did not change. Thetreatment's score improved and, on the post-test, exceeded thecontrol group's score. MBL was successful at improving the Q202students' graphing interpretation abilities. Traditional instructionon motion did not improve P201 students' graphing skills. Theraw score means, standard deviations (s) for the means and thenumber of students (N) who took the instruments are summarizedin Table 2. To further address research question 1, five hypothesiswere developed for item analysis. Results from GIST were usedin the item analysis and following discussion.
Table 2: Pre- and Post-test results for theGIST
| Pre-test | Post-test | ||||||
| Course | mean | s | N | mean | s | N | |
| Q202 | 7.9 | 1.6 | 138 | 9.1 | 1.6 | 136 | |
| P201 | 8.6 | 2.0 | 64 | 8.4 | 1.8 | 34 | |
The maximum score on the GIST is 12.
MBL will improve students' ability to read and interpretcurves.
Students in both groups and on both the pre-test and post-testdemonstrated they could successfully read and interpret graphs.Four questions from GIST were used in the analysis. In both courses,86-97% of the students answered the four questions correctly.MBL did not improve the students' ability to read and interpretcurves since they already possessed that ability.
MBL will improve students' ability to calculate the slopeof a curve.
Students demonstrated they could calculate the slope of a line,but had difficulty with the concept of zero-slope. Three itemsassessed students' ability and two matrices were constructed.Both groups improved slightly on the post-test, but when includingthe zero-slope concept, Q202 Physical Science students showedimprovement whereas the P201 General Physics students did not.The treatment group appeared to have more conceptual change occurring.In the end, about 50% of students in both groups could calculatethe slope and understand the zero-slope. The calculations canbe successfully performed by the student without the student fullyunderstanding what graphically corresponds to a zero slope andwhat are the implications of dividing numbers by zero.
MBL will improve students' ability to qualitatively interpretthe slope of a curve.
Two items, used to construct a matrix, addressed the qualitativeinterpretation of slopes. The first question required the studentsto recognize that the slope of the line on a mass-versus-volumegraph was the density and that the more steep the curve, the moredense the metal. The students were told that the density was theratio of mass divided by volume. The second question involveda more complicated curve of the mean temperature versus month.Approximately half of the students on the pre-test demonstrateda thorough command of qualitatively interpreting the slope. Post-testresults showed the treatment improving and the control group stayingthe same. The results are shown in table 3. MBL improved students'ability to qualitatively interpret the slope.
Table 3: Summary of matrix measuring student'sability to interpret slope
(in percent)
| Pre-test | Post-test | ||||||
| Course | thorough | partial | none | thorough | partial | none | |
| Q202 | 51 | 43 | 6 | 67 | 30 | 3 | |
| P201 | 55 | 37 | 8 | 47 | 42 | 11 | |
MBL will improve students' ability to qualitatively interpretthe change in slope of a curve.
Students in both courses performed poorly on both the pre- andpost-test. Two items were used to evaluate student knowledge.Q202 improved after intervention while P201 did not. Even afterinstruction, less than 30% in both courses demonstrated a thoroughunderstanding of the change in slope. MBL did improve the students'ability to qualitatively interpret the change in slope with 23%of the Q202 students improving their understanding to thorough.
MBL will improve students' ability to interrelate the resultsof two or more graphs.
One question was used to assess how students related data on twoseparate graphs. The ability of interrelating the results of twographs again showed P201 students not improving after instructionand Q202 students making slight improvements. These improvementsbrought the Q202 students up to the same level as the P201 students.The most frequent error made by students was not reading the scaleson the graph; instead they use the relative heights of curvesto determine magnitudes. MBL only slightly improved the students'ability to interrelate the results on two graphs.
RQ1. Does MBL's graphic presentation improve students' abilityto interpret a variety of line graphs?
The computation of the effect size demonstrated the treatmenthad a practical effect on the students. This was born out in theitem analysis. The Q202 students typically had initial scoreslower than the P201 students, but MBL labs lead to improvementswhich brought the Q202 students to the same level of achievementas the P201 students. P201 students typically did not change in
their understanding. Students using MBL made improvements, butthe change was small. Since graphing interpretation was neverovertly taught in either class, any improvement would be the resultof using the skills in laboratory. Improvements are the resultsof students applying what they learned in a different contextto new situations. MBL did improve the students' ability to interpreta variety of line graphs.
Motion Graphs
The calculated effect size using the gains in the raw scoreswas 1.71, which is a large effect. There were 34 items which assessedthe students' ability to interpret motion graphs. The Q202 students'pre-test mean was lower than the P201 students by 8%. Post-testresults showed Q202 students making large gains and exceedingby almost 20% the P201 students, who made only a slight improvement.MBL was most successful at improving the students' ability tointerpret motion graphs. The raw mean scores are summarized inTable 4. To address research question 2, six testable hypothesiswere developed for item analysis. Results from the graphing portionof the MCT were used in the item analysis and following discussion.
Table 4: Results for the Motion Content Test;Graphing Items
| Pre-test | Post-test | ||||||
| Course | mean | s | N | mean | s | N | |
| Q202 | 11.5 | 3.8 | 138 | 24.4 | 6.1 | 136 | |
| P201 | 14.2 | 4.5 | 64 | 17.7 | 5.5 | 34 | |
The maximum score on the graphing portion of theMCT was 34.
MBL will improve students' ability to determine the directionof motion from a motion graph.
Students started off not understanding how to interpret directionfrom motion graphs. Nine questions were used in the assessmentand four matrices were constructed. The control group was moresuccessful with distance-graphs on the pre-test, but with velocityand acceleration-time graphs, both group's performances were nearlythe same. The students had more difficulty with motion towardthe origin than motion away from the origin. A large number ofthe students, 20% of the Q202 and 34% of the P201 students, selectedthe distance analog on a pre-test matrix. Figure 2 illustratesone questions used in the matrix which revealed the students alternativeconception. Acceleration graphs were the most difficult to interpret.Post-test results show dramatic improvement in the treatment group.The treatment group scores all surpassed the control groups, withsometimes 30% more of the Q202 students than P201 having a thoroughunderstanding of the direction. The control group scores did improve,but the gain was small compared to the treatment groups gains.MBL significantly improved the students' ability to determinethe direction of motion from a motion graph.
Figure 2: Sample answers to Q52 illustratingthe distance-analog
MBL will improve students' ability to determine the magnitudeof velocity from a motion graph.
Responses from five questions were used. Pre-test resultsshowed 25% of the students used height of curve as the criteriafor determining the magnitude of the velocity from a distance-graph.
Both groups improved on the post-test, but Q202 made a more significant
gain and surpassed the P201 students. In both groups about 78%
of the students were able to defrmine the magnitude of the velocity
by calculating the slope after instruction. The same was true
of determining the magnitude from a velocity-time graph. On the
post-test, most of the P201 students continued to assume the sign
on the graph indicated magnitude and not direction. MBL improved
the students' ability to determine the magnitude of velocity from
a motion graph.
MBL will improve students' ability to determine the magnitude
of acceleration from a motion graph.
Determining the magnitude of the acceleration was a more difficult
task for the students than determining the velocity. Three test
questions were used. Q202 students demonstrated more difficulties
on the pre-test than P201 students. They made sign errors more
often and based their answers on their beliefs and not the available
data. Terminology also played a role, students were more successful
when the phrase "change in velocity" was used instead
of acceleration. The treatment group again made larger gains on
the post-test than the control group. These gains helped approximately
the same percentage of Q202 students as P201 reach a thorough
understanding. MBL improved the students' ability to determine
the magnitude of acceleration from motion graphs.
MBL will improve the students' ability to qualitatively
interpret distance-time graph curves.
The ability of students to interpret distance-time graphs was
assessed using a series of six questions. P201 students were more
successful in interpreting distance-time graphs on the pre-test.
On the post-test the treatment group surpassed the P201 students,
with typically 20% more students having a thorough understanding
on any one question. Common difficulties on the pre-test included
not being able to determine direction, interpreting velocity,
and interpreting acceleration from distance-time graphs. Post-test
results showed 90% of the Q202 students had a thorough understanding
of distance-time graphs. The results for six of the seven questions
are shown in table 5. MBL significantly improved the students'
ability to qualitatively interpret distance-time graphs.
Table 5: Percentage of students responding
correctly to distance-time graphing questions
(in percent)
|
Pre test |
Post test |
|||
| Question | Q202 | P201 | Q202 | P201 |
| Q31 | 65 | 67 | 88 | 73 |
| Q32 | 36 | 76 | 95 | 76 |
| Q33 | 23 | 51 | 94 | 71 |
| Q34 | 60 | 87 | 95 | 73 |
| Q35 | 52 | 65 | 90 | 84 |
| Q36 | 55 | 81 | 90 | 63 |
MBL will improve the students' ability to qualitatively
interpret velocity-time graph curves.
Students ability was evaluated using a series of seven questions.
Initially, both populations of students answered velocity-time
graphs questions in similar fashions and approximately the same
percentages having partial and thorough understandings. The most
common error involved using position criteria when interpreting
velocity-time graphs as shown in table 6. Post-test results showed
a significant improvement in the Q202 scores with approximately
80% of the students having a thorough understanding of velocity-time
graphs. P201 students also made gains, typically improving by
20% or more. MBL significantly improved the students' ability
to qualitatively interpret velocity-time graphs.
Table 6: Percentage of students responding
with distance analog
(in percent)
|
Pre-test |
Post-test |
|||
| Question | Q202 | P201 | Q202 | P201 |
| Q52 | 46 | 51 | 11 | 23 |
| Q53 | 45 | 46 | 9 | 13 |
| Q54 | 23 | 37 | 3 | 15 |
| Q56 | 33 | 40 | 8 | 34 |
| Q57 | 18 | 29 | 13 | 15 |
MBL will improve the students' ability to qualitatively
interpret acceleration-time graph curves.
Both populations of students did poorly on acceleration-time graphs
with less than 10% having a thorough understanding on the pre-test.
Five questions were used in the assessment. Students used velocity-graph
criteria to solve acceleration graph questions. Approximately
half of the students selected a velocity analog, and another 20%
selected a distance analog. The errors were further complicated
by a lack of understanding of sign and an inability to interpret
"speeding up at a steady rate." Post-test results demonstrated
little improvement for the control group but more significant
improvement for the treatment. Less than 15% of the P201 students
had a thorough understanding compared to approximately 57% of
the Q202 students. MBL significantly improved the students' ability
to qualitatively interpret acceleration-time graphs.
RQ2. Does MBL's graphic presentation improve students' ability
to interpret distance-time graphs, velocity-time graphs and acceleration-time
graphs?
The effect size shows MBL made the largest impact on students'
ability to interpret motion graphs. This is an expected result
since the treatment group spent much of its lab time working with
motion graphs. The item analysis further enforces the gains made
by the treatment group. Both groups had similar difficulties,
and the treatment was more effective at addressing the difficulties
and overcoming the problems. MBL significantly improved the students'
ability to interpret distance-time, velocity-time and acceleration-time
graphs.
Conceptual Understanding of Motion
The calculated effect size using the gains in the raw scores
was 0.88. The control group's initial raw score mean was higher
than the treatment group's and did improve slightly on the post-test.
The treatment's score improved more significantly on the post-test.
MBL was successful at improving the students' conceptual understanding
of motion as measured by non-graphing questions. The raw score
means, standard deviations (s) of the means and number of students
(N) are summarized in Table 7. To further address research question
3, four testable hypothesis were developed for item analysis.
Results from the non-graphing portion of the MCT were used in
the item analysis and following discussion..
Table 7: Test Results for the Motion Content Test; Non-graphing
| Pre-test | Post-test | ||||||
| Course | mean | s | N | mean | s | N | |
| Q202 | 9.8 | 2.4 | 138 | 13.6 | 3.7 | 136 | |
| P201 | 13.4 | 3.9 | 64 | 14.3 | 3.3 | 34 | |
The maximum score on the non-graphing MCT test is 22.
MBL will improve students' ability to differentiate between
position and velocity.
If students' understanding of position and velocity are undifferentiated,
then it should be possible to detect their confusion by analysis
of a matrix of questions 43 and 44. The results are shown in table
8 and the question in shown in figure 3. P201 students did significantly
better on the pre-test being able to differentiate between position
and velocity. On the pre-test, 27% of the Q202 used a distance-analog
to answer both questions. Q202 students did make significant gains
on the post-test, but P201 students still had a more thorough
understanding and fewer of the students used a distance-analog
on both the pre-test and the post-test. The significant improvement
by the Q202 students demonstrated that MBL does improve the students'
ability to differentiate between position and velocity.
Table 8: Summary of matrix of question 43 and
44
(in percent)
|
Pre-test |
Post-test |
||||||||
| Course | thorough | partial | none | analog | thorough | partial | none | analog | |
| Q202 | 42 | 16 | 42 | 27 | 71 | 7 | 22 | 12 | |
| P201 | 69 | 18 | 13 | 8 | 76 | 5 | 19 | 4 | |
Figure 3: Question 43 and 44
The number which characterizes the ball's velocity
when:
| 43. the ball travels downward____ | a. gets larger |
| 44. the ball travels upward ____ | b. is constant and equal to zero |
| c. is constant and not equal to zero | |
| d. gets smaller |
MBL will improve students' ability to differentiate between
velocity and acceleration.
A matrix of question 43 by 45 and question 49 by 50 detected students'
understanding of velocity and acceleration. The Q202 students
more likely to confuse velocity and acceleration. The difference
might be due to the P201 lecture bias. The instructor's lecture
before the pre-test included some of the topics covered on the
pre-test. Approximately 70% of the Q202 students used velocity
criteria to answer acceleration questions. Post-test results show
no change for P201 students and sizable gains for the Q202 students.
Even with the large gains for the Q202 students on the post-test,
over 20% more of the P201 students had a thorough understanding
of the concepts. Acceleration is the most difficult concept for
the students; even after instruction, less than 60% of the students
in either class have a thorough understanding of the concept.
MBL did improve the students' ability to differentiate between
velocity and acceleration.
MBL will improve students' ability to solve simple quantitative
problems.
Two simple quantitative problems were presented. Q202 students
were more capable at answering simple quantitative questions prior
to instruction than P201 students. After instruction, both groups
improved with P201 slightly improving more, which is to be expected
from a course which emphasized quantitative understanding. Instruction
in both cases improved ability to solve quantitative problems.
MBL improved the students' ability to solve simple quantitative
problems, but similar gains were also achieved with traditional
instruction.
MBL will improve students' ability to solve picture problems.
Questions 60 and 65 and a matrix of questions 59 and 64 were used
in the assessment. Figure 4 is the illustration for questions
59 and 60. Question 59 and 64 asked the same question: when do
the balls have the same speed, for two different pictures. The
students on the pre-test were not successful with picture problems,
with less than 30% in either class demonstrating a thorough understanding.
The post-test results showed approximately equal gains for both
groups. MBL did improve the students' ability to solve picture
problems, but the same gain was also achieved from traditional
instruction.
Figure 4: Example of picture problem, Q59 and Q60.
Two balls A and B move at constant speeds on separate tracks. Positions occupied by the two balls at the same time are indicated in the figure below by identical numbers. The balls are moving to the right. Starting points are not shown.
RQ3. Does MBL's graphic presentation improve students' conceptual
understanding of velocity and acceleration?
The effect size demonstrated the treatment had a practical affect
on the students. The treatment students made gains in their abilities
to differentiate between concepts and in their ability to solve
quantitative and picture problems. The gains they made were typically
larger than the gains made by the control group although more
P201 students started and finished with a thorough understanding
of the topics. The Q202 students learned the content within the
context of motion graphs and were able to apply it to non-graphing
problems. The P201 students were not able to apply their knowledge
to graphing problems. Through out the MCT and GIST, the Q202 group
appears to be making more conceptual changes than the P201 students.
MBL improved the students' conceptual understanding of velocity
and acceleration.
Discussion and Conclusion
This study sought to explore what the students were learning and how well they mastered those concepts. In addition, the study sought to identify what the students knew prior to instruction. Knowing what the students bring to the classroom helps the instructor better address the students' knowledge and elicit conceptual change, bringing the students' beliefs closer to the accepted scientific explanations.
The results on the Graphing Interpretation Skills Test and Motion Content Test indicated significant differences between a traditional laboratory and microcomputer-based laboratory. MBL was more effective at engendering conceptual change in students. The results were determined by computing effect sizes and by item analysis. The multiple-choice instruments had high reliability and the use of gain scores corrects for the initial differences in the two student populations.
The students in both groups entered the study being able to read and interpret a variety of line graphs. Understanding the change of slope remained the most difficult skill for the students, which is not unexpected since they probably have never had to interpret this before. Only about one-half of the students were able to calculate a slope and interpret a zero-slope curve. This is a disappointing result for such a basic graphing skill. The ability to work with the slope is a significant skill for the students to master in order to facilitate interpreting motion graphs. Instructors can not assume the students will completely understand how to calculate and interpret the slope. MBL provides an excellent medium for helping students develop a more thorough understanding of how to calculate the slope and how to interpret its meaning. Activities which involved slope should be built into the motion labs so that the students will gain experience with the skill. Students should be expected to understand how to determine the slope and how to apply this specifically to motion after instruction.
Students will probably have never experienced motion graphs prior to using MBL labs. When they first encounter these graphs, they can rely on either their graphing interpretation skills or their own preconceptions. It appears that students resort to their own preconceptions before they attempt to use their graphing interpretation skills to determine an answer. This might be the result of a multiple-choice test in the study, a format which is typically used to measure the students' ability to memorize facts. The students might also choose the answer which requires the least amount of effort. On a test where time is a limiting factor, it is more likely the student will resort to memorized facts or their own preconceptions than to take the time and figure out an answer. These limitations influence the pre-test motion graph results and would yield scores which are lower than the students' actual abilities.
The biggest difficulty encountered by the students was interpreting the direction of motion from a motion graph. This affects their success in interpreting the results of all motion graphs. Students find motion toward the origin especially difficult. Perhaps motion away from the origin is easier for the students because the reference point is also the location where the motion began. The students do not have to change their reference frame. On a distance-time graph, the motion away is an additive process with increasing distance from the same spot where the motion began. This may be easier for the students than moving toward the origin, involving distances from the origin getting smaller even though you are getting further from the starting point. Motion toward requires the students to change their frame of reference which is a difficult task without prior experience. MBL labs must provide the students with experiences predicting and interpreting direction on a variety of motion graphs. As demonstrated by the successful Q202 laboratories, experiences should include motion away from the origin to provide the students with an anchoring concept, something they are familiar and successful with. An understanding of motion toward the origin can be built upon their understanding of motion away from the origin.
Beyond determining direction, the students often confused types of graphs, perhaps reflecting their confusion of the associated concepts. In addition, the students must have an opportunity to explore the differences and the relationships among the various motion graphs. They need to create distance-time, velocity-time and acceleration-time graphs of the same motion and discuss the differences between the graphs. As the students learn to differentiate between the graphs, they will begin to develop a more precise definition of the concepts and will be able to better differentiate the concepts. Numerous examples are needed in order to provide the student with sufficient experience and examples.
The dominant preconception the students bring to the classroom is undifferentiated understandings of the concepts of position, velocity and acceleration. Scientists have precise definitions of these concepts which they can apply to numerous situations. Students have had a variety of experiences in which they have built up their understanding of the concepts. Since they probably have never had a formal course in physics, their understanding consists of overlapping, misinterpreted pseudo-definitions which may work in a few specific instances but are not generalizable. Formal instruction will hopefully provide the students with a scheme for understanding their experiences and narrowing their definitions of the concepts. MBL provides an excellent environment in which to address the students' preconceptions. The students can test their own theories and the proposed scientific theory with quick, easily understood graphs.
Challenging the students' understanding does not guarantee that conceptual change will occur. When faced with a discrepancy, students can change their own beliefs, rationalize the data away or they can become apathetic. Indeed, in lab, students would ask the instructor if they "should write down the correct answer or what the graph said," thereby attempting to rationalize away the data and maintain their current beliefs. While MBL is a powerful tool for conceptual change, it must be accompanied by other factors which will encourage the students to challenge their beliefs and to begin to change their own concepts. Factors might include motivation, interest and relevancy for the student. Identifying those factors will be a significant research topic to pursue.
The study showed that the Q202 students learned more about graphing interpretation skills, more about motion graphs and more about conceptual understanding of motion, than did the P201 students. That learning was made possible by the effective use of MBL activities. While the P201 students spent less time on motion, it can and should be argued that if the students would gain as much as the Q202 students, then it would be to their advantage to devote more time to the basic concepts. Q202 took advantage of the learning environment and instructional possibilities made possible by MBL. As demonstrated by the Q202 lab materials, to effectively use that time, MBL activities designed to elicit conceptual change should be incorporated into introductory physics courses.
Bibliography
Arons, Arnold B. (1990). A Guide to Introductory Physics Teaching. New York: John Wiley.
Borg, W. R. and M. D. Gall. (1989). Educational Research: An Introduction. (5th ed.). New York: Longman.
Brasell, H. (1987a). Effectiveness of a microcomputer-based laboratory in learning distance and velocity graphs. Dissertation Abstracts International. 48, 2591.
Brasell, H. (1987b). The effects of real-time laboratory graphing on learning graphic representation of distance and velocity. Journal of Research in Science Teaching. 24 (4) 385-395.
Campbell, D. T. and J. C. Stanley. (1963) Experimental and quasi-experimental design for research. Boston: Houghton Mifflin Co.
Clement, J. (1982) Students' preconceptions in introductory mechanics. American Journal of Physics. 50 (1) 66-71.
Friedler Y., Nachmias R., & Linn, M.C. (1990). Learning scientific reasoning skills in microcomputer based laboratories. Journal of Research in Science Teaching. 27 (2) 173-191.
Giancoli, D. C. (1991) Physics: Principles with applications. (3rd ed.). Englewood New Jersey: Prentice Hall.
Halloun I. and D. Hestenes. (1985a). The initial knowledge state of college physics students. American Journal of Physics. 53, 1043-1055.
Halloun I. and D. Hestenes. (1985b). Common-sense concepts about motion. American Journal of Physics. 53 1056-1065.
Hestenes D., M. Wells and G. Swackhamer. (1992, March). Force concept inventory. Physics Teachers. 30 (3), 141-158.
Linn, M.C., Layman, J., & Nachmias, R. (1987). Cognitive consequences of microcomputer-based laboratories: Graphing skill development. Contemporary Educational Psychology. 12 (3) 244-253.
McDermott, L.C., M.L. Rosenquist and E.H. van Zee. (1987). Student difficulties in connecting graphs and physics: Examples from kinematics. American Journal of Physics. 55 (6) 503-513.
McKenzie, D. L. and M. J. Padilla. (1986). The construction and validation of the Test of Graphing in Science (TOGS). Journal of Research in Science Teaching. 23, 571-579.
Mokros, J.R., & Tinker, R.F. (1987). The impact of micro-computer based labs on children's ability to interpret graphs. Journal of Research in Science Teaching. 24 (4) 369-383.
Svec, M. T., W. J. Boone, and C. Olmer. (1995). Changes in a Preservice Elementary Teachers Physics Course. Journal of Science Teacher Education. (2) 79-88.
Thornton, R.K. & Sokoloff, D.R.. (1990). Learning motion concepts using real-time microcomputer-based laboratory tools. American Journal of Physics. 58 (9) 858-867.
About the author . . .
Michael Svec, Ph.D., is an Assistant Professor of Science Education in the Department of Education at Furman University, 3300 Poinsett Highway, Greenville SC, 29613-1134, FAX (864) 294-3341, michael.svec@furman.edu.