Learning Concepts First – A Course Structure with Improved ... - arXiv

Learning Concepts First – A Course Structure with Improved Educational Outcomes in the Short, Medium, and Long Terms (Especially for Minority Groups Underrepresented in Physics) D. J. Webb, Dept. of Physics, University of California, Davis, CA Abstract - An active learning physics course (treatment) was re-organized in an attempt to increase students’ problem solving abilities. This re-organized course covered all of the relevant concepts in the first 6 weeks with the final 4 weeks spent in practice at solving complicated problems (those requiring students to use higher order cognitive abilities). A second active learning course (control) was taught in the same quarter by the same instructor using the same curricular materials but covering material in the standard (chapter-by-chapter) order. After accounting for incoming student characteristics, students from the treatment course scored significantly better than the control for two outcome measures: i) the final exam and ii) their immediately subsequent physics course. More importantly, students from minority groups who are underrepresented in physics had final exam scores as well as class grades that were indistinguishable from the rest of their class if and only if they were in the treatment class. Finally, many of the students in this cohort took a Concepts First course in their third quarter of introductory physics. The students who took at least one Concepts First course are found to be have significantly higher rates of graduation with a STEM major than those students from this cohort who did not take a Concepts First course.

Introduction Devising solutions/explanations for complicated problems is arguably1 the most important skill that experts possess and that novices seek to learn. Research2,3 has shown that an expert’s large and wellstructured knowledge in the field of their expertise allows them to see deep conceptual issues and patterns in complicated situations rather than the surface features that are sometimes the only details apparent to a novice. It is in this sense that an expert “sees” a different problem than a novice and has a much better chance of solving it4. Although students are only taking their first steps toward expertise, this specific idea of expertise in problem solving suggests that it might be useful to structure a classroom experience so that students do not work on learning to solve complicated problems until after their initial efforts in understanding all of the applicable conceptual issues. If a physics teacher structures a course in this way, will their students’ abilities to solve physics problems improve more than they do with the usual curricular organization5,6? An experiment along these lines was carried out a few years ago in introductory physics here at UC Davis and is discussed in this paper. Method In a recent spring quarter UC Davis offered four lecture sections, Sections 1 through 4, of Physics 9A (classical mechanics). A student in Physics 9A has three hours of lecture, one hour of discussion section, and 2.5 hours of laboratory each week. The textbook and the laboratory experiments for all four sections were exactly the same but the lectures, discussion sections, and homework are under the control of the instructor assigned to teach that section. The material in Section 1 was organized so that students worked to learn the classical ideas connecting forces and motion (mostly Newtonian mechanics of point-like objects and/or rigid bodies) over the first 6 weeks of the 10 week quarter and then used the final 4 weeks to apply those principles to solve the analytically (and algebraically) complicated physical problems that physicist prize. This course used active learning techniques so this treatment group will be called “Active Learning Plus Concepts First” (AL&CF). The other three sections learned ideas at the same time as calculations over the entire 10 weeks of the quarter. Section 2 was also taught using active learning techniques and so will be called “Active Learning Only” (ALOnly). Sections 1 (AL&CF) and 2 (ALOnly) were both taught by the author and had identical homework problems7, discussion section problems/questions, lab problems, and lecture questions8. These two sections were active learning classes in that there were peer-peer discussions happening in both the lecture (in answering clicker questions) and in the one-hour per week discussion section (where attendance was required) and there were conceptual questions on midterm exams. At this point I should note that I will be using a somewhat strict definition of the term “Active Learning” by

including only classes where the lecturer involves the students in peer-peer discussions on conceptual issues9 and where the exams include one or more questions that are primarily conceptual. Sections 1 and 2 are the focus of this paper but some of the data will necessarily involve students from the other Sections 3 and 4 so we should note that the instructors in the other two sections historically received significantly higher student evaluations than the instructor in Sections 1 and 2 but that Sections 3 and 4 were not active learning classes (i.e. NoAL courses) in that neither used active learning techniques in lecture or discussion although Section 3 did include some conceptual questions on exams. In Winter Quarter following the original experiment this cohort of students took Physics 9C, a course which covers electricity and magnetism (including electric circuits). The author taught one of the four sections of 9C and ordered the course in the same way as the treatment course of 9A (for electricity and magnetism the complicated two and three dimensional integrations were among the problems dealt with in the last 4 weeks). In addition, another of the four instructors (one who always runs an active learning course) was recruited to organize his course in the same way; 6 weeks of conceptual learning followed by 4 weeks of calculations. Thus, the original cohort (made up of all 4 lecture sections) of 9A students had many who had experienced an AL&CF class and some who had taken two AL&CF classes, some who had ALOnly but no AL&CF (there were ALOnly courses in 9B during the intervening quarter also), and the rest had only NoAL classes. There was no controlled study during this quarter but since the original experiment was done almost 4 years ago there is now graduation data available for this cohort of students. The students had no knowledge of how any of the sections would be taught when they enrolled. In addition, each class was completely full and almost no students could switch sections after they heard how the class would be taught so, although this is not a randomized trial, student selection issues related to the course structure are probably negligible even though student selection regarding instructor is likely. Table I shows a number of measurements of student academic skills and attitudes as they enter the course (the errors shown are standard deviations showing the breadth of the distributions). The American Physical Society10 notes that women and a set of minority groups (the variable UndRpMns11 includes African Americans, Native Americans, and Hispanic Americans) are underrepresented in physics so this paper will discuss results for women and the group of students (self-identifying as) belonging to one of these underrepresented minority groups along with the entire class. FCI refers to the Force Concept Inventory12 which is a 30-question multiple-choice survey of the student’s understanding of forces, motion, and their Newtonian relationship. This survey was given to all students at the beginning of the quarter (pretest) and again (posttest) in the 8th week of the 10-week

quarter at least 3 weeks after every section had finished working on the Newtonian physics of pointlike objects. We take the pretest (FCIpre) to be a measure of the initial Newtonian understandings that the students bring to the class. CLASS refers to the Colorado Learning Attitudes about Science Survey13 which was given both at the beginning of the course (pre) and at the end of the course (post) but was only given to the two sections that are the main focus of this paper. The CLASS questions have 5-point Likert-scale answers. Each question is scored as either the same as expert would answer (favorable), neutral, or opposite to how an expert would answer (unfavorable). To produce a single score14, we use the fraction of favorable answers minus the fraction of unfavorable answers so a higher score is associated with a more expert-like attitude/epistemology. A student’s GPA is their UC Davis GPA at the beginning of the quarter and we take this to be a measure of their general academic ability. A student’s IntrMathZ is the average of their grades (grouped by the quarter the course was given and then converted to z-scores) in the introductory calculus courses completed by the end of the spring quarter15 in which they took the courses described in this paper. “Semesters Physics” refers to the number of semesters of previous physics classroom experience and was self-reported by the students.

Table I – Five incoming measures for these three course-types. Sections 3 and 4 (NoAL with about 330 students in the Class, about 90 Females, and about 50 UndRpMn, each of these depending slightly on the specific measurement) are grouped together. Section 1 (AL&CF) has about 155 in the Class, about 38 Females, and about 18 UndRpMns and Section 2 (ALOnly) has about 160 in the Class, about 40 Females, and about 20 UndRpMns. Shown are distribution averages with standard deviations for the five incoming measures of student abilities or learning attitudes. Lecture 1 (AL&CF) 2 (ALOnly) 3&4 (No AL)

Group Class UndRpMns Females Class UndRpMns Females Class UndRpMns Females

GPA 2.96 ± 0.57 2.69 ± 0.60 3.03 ± 0.56 2.96 ± 0.52 2.70 ± 0.37 3.01 ± 0.55 3.11 ± 0.58 2.70 ± 0.63 3.12 ± 0.51

IntrMathZ 0.17 ± 0.69 -0.12 ± 0.73 0.21 ± 0.67 0.11 ± 0.67 -0.11 ± 0.49 0.19 ± 0.76 0.40 ± 0.67 0.03 ± 0.68 0.38 ± 0.62

FCIpre 16.1 ± 7.0 15.6 ± 5.7 12.0 ± 6.5 16.3 ± 6.4 14.2 ± 5.6 13.1 ± 6.0 15.5 ± 6.8 13.7 ± 6.4 12.1 ± 6.0

Semesters Physics 1.9 ± 1.0 2.0 ± 0.8 1.6 ± 1.0 1.9 ± 1.2 1.7 ± 1.0 1.5 ± 1.1 1.8 ± 1.2 1.6 ± 1.0 1.7 ± 1.2

CLASSpre 0.47 ± 0.22 0.52 ± 0.17 0.42 ± 0.24 0.46 ± 0.23 0.47 ± 0.22 0.42 ± 0.21

Results We have three main immediate outcome measures: the final exam, the FCI given in 8th week of the class to all four lecture sections, and the CLASS given the 9th week of the class only to Sections 1 and

2. First we’ll briefly point out that the CLASS survey showed no significant differences between Sections 1 and 2. The two sections had similar CLASSpre scores that were not appreciably changed by the course. We will deal with FCI gains after discussing the final exam scores. A. Final Exam Each of the four sections took the same final exam at the same time (the final exam is printed at the end of this paper). This exam was written by the two instructors from sections 3 and 4 with additional help from a third instructor who often teaches this course. The instructor in Sections 1 and 2 had no input on the final and did not see it until all instruction (including review sessions) had ended. There were eight problems on the final exam and they had equal value. For Sections 1 and 2 together, each final exam problem was graded a single grader. The instructor from Section 3 supervised the grading. To assess the value of the particular curriculum organization of Section 1 (treatment group is AL&CF class), we will control for the effects of 1) general academic skill using incoming GPA, 2) mathematical ability using introductory math scores, 3) previous understanding of Newtonian mechanics using FCI pre, 4) previous physics experience using Semesters of Physics, and 5) attitudes toward learning physics using the CLASS. We calculate the final exam z-scores using the average and standard deviation for the entire group of students from all four lecture sections. Because we have three very different groups, we build a specific predictive model for each group and only use covariates 1) through 5) when they either increase R2 by at least 0.01 or have a p-value < 0.1. Of course we always include a categorical lecture variable (AL&CF = 1 for Section 1 and 0 for Section 2) to decide whether the treatment or control section performed better16. The coefficient of this lecture variable will be an approximate effect size for the treatment. Thus, a generic model looks like 𝐹𝑖𝑛𝑎𝑙𝐸𝑥𝑎𝑚𝑍 = 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 + 𝛽!"# 𝐺𝑃𝐴 + 𝛽!"#$%&#!! 𝐼𝑛𝑡𝑟𝑀𝑎𝑡ℎ𝑍 + ⋯ + 𝛽!"&!" 𝐴𝐿&𝐶𝐹 where βAL&CF is the coefficient we will use to decide the results of the AL&CF class. We can deal with the results for Female students simply by saying that the treatment effect size for Females on almost all the measures we examine have the same sign as for the whole class but are generally slightly smaller and this, together with the smaller sample size, leads to most of these measures not reaching the standard, p < 0.05, often used to determine significance. In fact, every identifiable group with enough statistical power (this includes Males, Chinese Americans, and East Indian Americans as well as Females) showed effects with the same sign as those for the whole class and some of those results reached statistical significance. From this point on the groups we show analysis for and discuss are i) the entire class and ii) the minority groups who are underrepresented in

physics. For the final exam these results are shown in Table II. One sees that the students who had AL&CF performed better, than those who had ALOnly, for both groups. Both of these results reached the p < 0.05 level that is often used as a standard for identifying a result as “significant”. Because zscores were used for the final exam, these coefficients are reasonable approximations for the effect size of the treatment for the respective group. A survey17 of effect sizes in education experiments shows that an average size effect for a whole class education experiment is about 0.18 ± 0.41. For this reason, we would describe the effect of AL&CF for the whole class as a medium size positive effect and the effect of AL&CF for the underrepresented minorities group as a large positive effect.

Table II – Modeling the final exam z-score. The table shows the model coefficient for the treatmentcontrol variable (as well as listing the covariates from the model), its t-statistic, the resulting p-value, and the adjusted R2 for the total model. The set of covariates available are 1) GPA, 2) IntrMathZ, 3) FCIpre, 4) Semesters Physics, and 5) CLASSpre and the one used in the final model are listed in parentheses below the lecture coefficient. Group

N

All students

268

βAL&CF = increase of Final Exam z-score for AL&CF course (covariates) 0.18

t-statistic

p-value

adj. R2

2.35

0.019

0.60

3.94

< 0.001

0.64

(1,2,3,4,5)

UndRpMns

35 (17 in AL&CF)

0.92 (2,3,5)

B. Conceptual Gains Regarding conceptual learning, we analyze results of the (30 question) FCI by computing a normalized gain for each student as follows: 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 − 𝐹𝐶𝐼 𝑝𝑟𝑒 30 − 𝐹𝐶𝐼 𝑝𝑟𝑒 𝑑𝑟𝑜𝑝 𝑆𝑡𝑢𝑑𝑒𝑛𝑡 𝑙𝑒𝑣𝑒𝑙 𝐹𝐶𝐼 𝑔𝑎𝑖𝑛 = 0 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 − 𝐹𝐶𝐼 𝑝𝑟𝑒 𝐹𝐶𝐼 𝑝𝑟𝑒

𝑖𝑓 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 > 𝐹𝐶𝐼 𝑝𝑟𝑒 𝑖𝑓 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 = 𝐹𝐶𝐼 𝑝𝑟𝑒 = 30 𝑜𝑟 0 𝑖𝑓 0 < 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 = 𝐹𝐶𝐼 𝑝𝑟𝑒 < 30 𝑖𝑓 𝐹𝐶𝐼 𝑝𝑜𝑠𝑡 < 𝐹𝐶𝐼 𝑝𝑟𝑒

We compute an average gain for each section by averaging these student level gains. The results are shown in Table III for each of the groups we have been discussing. As is almost always found18,

classes where active learning techniques are used (Sections I and II) have higher gains on conceptual surveys than the standard lecture type of class. The only statistically significant differences are between AL&CF and NoAL for the entire Class (p < 0.0001, t-statistic = 5.4) and for UndRpMns (p = 0.0003, t-statistic = 3.8).

Lecture

Table III – Average gain on Force Concept Inventory (FCI) for each group in each course-type along with the relevant standard errors.

1 (AL&CF) 2 (ALOnly) 3&4 (No AL)

Group Class UndRpMns Females Class UndRpMns Females Class UndRpMns Females

Avg. FCI gain 0.42 ± 0.02 0.47 ± 0.07 0.31 ± 0.05 0.37 ± 0.03 0.32 ± 0.06 0.32 ± 0.05 0.26 ± 0.02 0.19 ± 0.04 0.22 ± 0.03

C. Transfer Next we describe how this cohort of students performed in their next introductory physics class, Physics 9B, which most of them took in the Fall quarter following the Spring quarter in which they took 9A. The author had nothing to do with any of the teaching or grading in any of these 9B courses. Physics 9B includes a diverse set of topics including waves, optics, and thermodynamics so there is very little overlap between concepts in 9A and those in 9B. For this reason, an effect on 9B grades should be considered a transferred effect. We compare 9B z-grades (calculated separately for each particular lecture section of 9B) using the same set of pre-9A covariates to model the transfer effects of the “concepts first” teaching. The results are shown in Table IV. Again, all of the individual groups with large enough statistical power show AL&CF students performing better than ALOnly students and the whole class comparison reaches p < 0.05 level of significance with a medium size effect.

Table IV – Modeling the z-grade of the introductory physics course taken after the experiment. The table shows the model coefficient for the treatment-control variable (as well as listing the covariates from the model), its t-statistic, the resulting p-value, and the adjusted R2 for the total model. The set of possible covariates are the same as for Table II and the ones actually used in the particular model are listed in parentheses below the lecture coefficient. Group

N

All students

275

αAL&CF = Increase of Physics 9B z-grade for AL&CF (covariates) 0.22

t-statistic

p-value

2.33

0.021

adj. R2 0.36

0.61

0.545

0.42

(1,2)

UndRpMns

33 (16 in AL&CF)

0.14 (1)

D. Course Grades for Minority Groups Who are Under-Represented in Physics It is particularly interesting that one finds no significant grade gap19 between students from minority groups who are underrepresented in physics and the rest of the class in the AL&CF course although there are significant (between 0.5 and 1 standard deviation) grade gaps for the ALOnly and NoAL courses. We use z-grades for all 4 sections and use a t-test for each section to measure the grade gap (GradeGap = CourseGradeUndRpMns – CourseGradeRestOfClass) between underrepresented minority groups and the rest of the class. We find GradeGap = -0.08 ± 0.24 (t-test gives p = 0.75) for AL&CF, GradeGap = -0.88 ± 0.22 (t-test gives p = 0.0001) for ALOnly, and GradeGap = -0.60 ± 0.14 (t-test gives p = 0.0025) for NoAL. For Females, a grade gap is present for AL&CF, ALOnly, as well as NoAL classes unless we use FCI scores to control for initial understanding of Newtonian physics, after which there are no statistically significant gender grade gaps in any of these course types. E. STEM Major Retention As discussed earlier, many of the students in the cohort that began introductory physics during the quarter of the experiments took an AL&CF course during the third quarter of their introductory physics series. Since the original experiment was done almost 4 years ago there is now graduation data available on this cohort of students (normal graduation would have been 2.25 years after taking 9C and, to date, the data include students who graduated within 2.75 years of taking 9C). We have identified the majors of the students who have graduated as either STEM majors or non-STEM majors and can find the ratio of the odds of graduation in STEM for a student who has taken at least one “concepts first” introductory physics class to the odds of a student without any “concepts first” class graduating in a STEM major. We use logistic regression to control for student level differences in the various relevant covariates in the way that we have previously done. Table IV shows this odds ratio for the entire cohort and also for UndRpMns group of students. We find that the members of this cohort who took at least one AL&CF course are 70% more likely to graduate with a STEM major than those who did not have an AL&CF course. Also notable is that the students from underrepresented minority groups are over two and a half times more likely to graduate with a STEM major if they took an AL&CF course than if they did not take such a course. In each of these two cases we also found that taking 2 AL&CF courses had a positive effect (on top of the positive effect of taking one AL&CF course) but this extra amount was not statistically significant so we left that variable out of the final models.

Table IV – Modeling the ratio of the odds of graduation (within 2.75 years after taking 9C) with a STEM major for students who took at least one “concepts first” course to the odds of graduation for students who took no “concepts first” course. The table shows this model odds ratio (as well as listing the significant covariates), its z-statistic, the resulting p-value, and the pseudo R2 for the total model. The set of covariates tested are 1) GPA, 2) IntroMath, and 3) FCIpre and the ones used are listed in parentheses below the odds ratio. Group

N

All students

654

UndRpMns

90 (39 in treatment)

odds ratio of STEM major graduation for students taking at least one AL&CF course (covariates) 1.72 (1) 2.68 (1,3)

z- statistic

p-value

pseudo-R2

2.86

0.004

0.12

2.04

0.041

0.14

Finally, a model variable for those students who took ALOnly courses but didn’t take an AL&CF course was included in the above model. That variable changed the STEM graduation odds by 0.95 (p = 0.86) so the increases in STEM graduation rates seem to be associated with the concepts-first organization of a course. F. Other Outcome Measures Two other outcome measures were considered, examined, and found to not differentiate between the treatment and control classes. First, student grades in an engineering course that covers statics (i.e. Newtonian mechanics of rigid bodies which are not accelerating) were examined. This course was taken by many of this cohort of students either in the Fall quarter, the Winter quarter, or the Spring quarter following their Spring quarter intro physics experience. The students in the treatment group had slightly higher scores in this course than the control group but the gap decreased when the course was taken later (Winter or Spring rather than Fall) and in no case reached statistical significance. As opposed to Physics 9B, this statics course is not a course that is primarily about new concepts but mostly about new computational details involved in using only a single basic concept. The other outcome examined was average grade in upper division STEM courses. For each of the identifiable groups, this measure was statistically independent of whether the students took a concepts first course or not.

Discussion Changing classroom education is probably most commonly thought of as either revising curricular materials (textual and/or online pieces), modifying the structure of the learning environment (introduce peer-peer active learning), or even changing teachers. The experiment described in this paper suggests a type of change quite different from those just listed, indeed every effort was made to keep the treatment and control course identical in all of the ways just named. Nevertheless, even though one might have thought that the changes were small we find that the treatment resulted, on balance, in significantly better outcomes and, as far as we know, no worse outcomes. In addition, the results for minority groups underrepresented in physics were so strikingly positive that these students are at parity with the rest of their class. Developing this sort of course organization largely involves dividing the desired learning outcomes using a grouping suggested by ideas from Bloom’s taxonomy20. One would first pick the learning outcomes that are characterized as belonging to the higher Bloom’s levels of analyzing, evaluating, and creating (and maybe even the most complicated kinds of applying). These are the tasks that students would be working on in the final 40% of the course. During the first 60% of the course21, active learning activities should be devised to help students work, with all of the concepts of the course, at the Bloom’s levels of remembering, understanding, and (the simpler) applying levels. Acknowledgements The author thanks Wendell Potter, Emily West, and the rest of the UC Davis PER group for useful discussion and comments.

(a) A truck is accelerated in the forward direction ground | ground on the truck’s tire | none of the a

Appendix

(b) A rough surface can exert a(n) ( normal | tange force.

(c) Many of the great rivers in the world have a ten equator. Over time as they carry sediment toward 9A Final Exam (given to all 4 sections of course offered that quarter) will ( increase | decrease | not change ) .

[1] Circle the answer that correctly completes the sentence correctly. (d) For the graph of the potential energy of a parti the greatest speed the potential a) A truck is accelerated in the forward direction by the force of the (truck’s tire on the ground | ground onwhere the truck’s tire | energy grap none of the above ) none of the above ). b) A rough surface can exert a(n) ( normal | tangential | all of the above | none of the above) force. (e) For an object in circular motion ( centripetal | t c) Many of the great rivers in the world have a tendency to flow from the pole towards the equator. Over time as they above ) acceleration will change the direction of th carry sediment towards the equator, the length of the earth’s day will ( increase | decrease | not change ) . d) For the graph of the potential energy of a particle as a function of x, the particle will have the greatest speed where theto the figure below Statements (f) through (h) refer potential energy graph is ( maximum | steepest | 0 | minimum | none of the above ) a function of time. Circle all the times that comple Physics 9A, section A | all of the Final Exam e) For an object in circular motion ( centripetal | tangential above | none Name:____________________ of June 13, 2012 Last 4 digits of ID:_____________ the above ) acceleration will change the direction of the velocity vector. Statements f) through h) refer to the figure to the right, which shows the position of [3] The figure below shows the potential energy U(x) as a function of the position x. an object as a function of time. Circle all the times that complete the statement correctly (a) Mark the positions where the force is zero. f) The total force acting on the positive at ( t1of| tthe t5 ). (b) object What is the direction 2 | tforce 3 | t4 | at sectionatA x = object 4 m?9A, g) The total force acting onPhysics the is negative ( t1 | t2 | t3 | t4Final | t5 ). Exam Name:____________________ June 13, 2012 Last 4 digits of ID:_____________ h) The total force acting on the object is zero ( t1 | t2 | t3 | t4 | t5 ).

(f) The forceroll acting onthe the object is positive [2] A 90,000 kg jet has two[2] engines whichkgproduce a constant thrust of produce 110,000 N each during thetotal takeoff along jet has two engines which (c)AIf90,000 an object moving in this potential energy a constant thrust of 110,000 N each runway. The takeoff speed is 210 takeoff km/hr. Neglect airthe and rolling The during runway. has a the total energyroll of 5along Joules, mark the turning (g) The total force acting on the object is negative resistance, and assume the engine thrust is parallel to the runway. takeoff speed is 210 km/hr. Neglect air and points of its motion. rolling resistance, andtotal assume theisengine thrust The runway is slightly inclined at θ=1°. the (d) Assuming energy 5 J, estimate (h) The total force acting on the object is zero ( t1 Physics 9A, section A Final Exam Name:____________________ is parallel to the runway. The runway is a) Determine the length s ofthe theobject’s runway kinetic requiredenergy first for an uphill at points June 13, 2012 = 1°. Last 4 digits of ID:_____________ x =B,- 3inclined m and x at= 2! m. takeoff direction from Aslightly to Constants: (a) Determine the length s of the runway required first for an uphill takeoff direction from A b) and second determine the[3] length s for a downhill takeoff direction from B to A. 2 G = 6.67 ! 10"11 N g = 9.8 of m/sthe =position 32 ft/s 2x. to B, The figure below shows the potential energy U(x) as a function (a) Mark the positions where the force is zero. [3] The figure to the right shows the potential energy U(x) a function of (b) What is the direction of theasforce at the position x. x = 4 m? a) Mark the positions where the force is zero. b) What is the direction of the force at x = 4 m? c) If an object moving in this[4]potential hasstands a totalupenergy of 5kgJoules, A 50 kgenergy woman in an 80 canoe 5.00 m long. She walks from a point A (c)itsIfmotion. an object moving in this potential energy mark the turning points of which is 1.00 m from one end to a point B which is 1.00 m from the other end. If you ignore has a total energy of 5 Joules, mark the turning to motion of the canoe in the water, d) Assuming the total energyresistance is 5 J, estimate the object’s kinetic energy at how far does the canoe move during this points of its motion. process? points x = - 3 m and x = 2(d) m. Assuming the total energy is 5 J, estimate the object’s kinetic energy at points x = - 3 m and x = 2 m. [4] A 50 kg woman stands up in an 80 kg canoe 5.00 m long. She walks from a point A which is 1.00 m from one end to a point B which is 1.00 m from the other end. If you ignore resistance to motion of the canoe in the water, how far does the canoe move during this process? (b) and second determine the length s for a downhill takeoff direction from B to A. [5] A children’s merry-go-round consists of a thin disk of mass 2m and radius r0. It is initially spinning with angular speed ω0. There is a thin girl of[4] mass at the outer SheShe walks along a radial path Am 50standing kg woman stands upedge in anof80the kgmerry-go-round. canoe 5.00 m long. walks from a point A to the which is 1.00 m from one end to a point B which is 1.00 m from the other end. If you ignore center of the merry-go-round. 2 to motion of the canoe in themoment water, how far does canoe this a) Explain what happens to resistance the girl-merry-go-round system. The of inertia of athe disk is I =move ½ Mrduring b) What is the final angular process? speed of the merry-go-round?

Page 1 of 7

June 13, 2012

Last 4 digits of ID:_____________

2 [6] The moment of inertia of a solid sphere is I s = mr 2 . The moment of inertia of a ring is 5 2 I r =mr . A disk and a ring with equal mass (m) and equal radii, r, both roll up an inclined start the2 same linear velocity, v, for the center [6] The moment of inertia ofplane. a solidThey sphere is Iwith S =2mr /5. The moment of inertia of a ring is of Physics mass. 2 section Ir = mr . A disk and a ring with equal9A, mass (m) andAequal radii, r,Final both Exam roll up anName:____________________ (a) Clearly explain which will go higher. 13, 2012 4 digits of ID:_____________ inclined plane. They start June with the same linear velocity, v, for the center Last of mass. a) Clearly explain which will go higher. [7] An art object of nonuniform composition is suspended horizontally from the b) Use conservation of energy to determine the maximum vertical height, hd , the disk and ceiling by two wires at its ends. The object is of length L, and its center of mass is L/4 the maximum vertical height, hr the ring will reach.

from its left end. The wire at its right end makes a 30° angle with the horizontal and has a 100 N tension. Determine the object’s weight and the tension in the other wire.

[7] An art object of nonuniform composition is suspended horizontally from the ceiling by two wires at its ends. The object is of length L, and its center of mass is L/4 from its left end. The wire at its right end makes a 30° angle with andof has a 100to N determine tension. the maximum vertical height, h , the disk and the (b) the Usehorizontal conservation energy d Determine the object’s weight and the tension in the other wire. maximum vertical height, h the ring will reach. r,

[8] The density of a typical asteroid is 2.5 x 103 kg/m3. This is important, for you’re intent on finding the largest heavenly body on which you can stand and launch a rock into a low circular orbit by hand, and your best throw is only 40 m/s. a) Assuming a spherical asteroid (not a very realistic assumption), what is the radius of the asteroid you desire? (Note: “low orbit” means the minimum possible radius. The volume of a sphere is 4πR3/3.) b) If you threw the rock instead straight up, would it go forever, and if not, how high would it go? Assume the radius is for the asteroid in part a).

References 1

C. Bereiter and M. Scardamalia, Surpassing Ourselves: An Inquiry into the Nature and Implications of Expertise (Open Court Publishing, Chicago, IL, 1993).

2

W. G. Chase and H. A. Simon, “Perception in chess,” Cognitive psychology, 4, 55-81 (1973).

3

M. T. H. Chi, P. J. Feltovich and R. Glaser, “Categorization and representation of physics problems by experts and novices,” Cognitive science, 5, 121-152 (1981).

4

D. P. Maloney, "An Overview of Physics Education Research on Problem Solving," in Getting Started in PER, edited by C. Henderson and K. A. Harper (American Association of Physics Teachers, College Park, MD, 2011), Reviews in PER Vol. 2, .

5

For a course organized somewhat like the one in this paper, see A. Van Heuvelen, “Overview, case study physics,” American Journal of Physics, 59, 898-907 (1991).

6

For a middle school version of a concepts first course see M. Perry, “Learning and transfer: Instructional conditions and conceptual change,” Cognitive Development, 6, 449-468, (1991). Pageused 5 of for 7 about 80% of homework and the The online homework service, MasteringPhysics, was other 20% of homework had solutions/graphs/diagrams/descriptions written down and turned in for grading. MasteringPhysics includes the conceptual questions, simple one-step problems, and tutorial problems that were used in the first 6 weeks of the course as well as more complicated problems used in the final 4 weeks of the course.

7

8

All curricular materials as well as the scheduling of these for the two different classes are available Page 6 of 7 online at ?

9

E. Mazur, Peer Instruction (Upper Saddle River, NJ: Prentice Hall, 1997).

10 APS website regarding underrepresented groups in physics is https://www.aps.org/programs/minorities/index.cfm 11

We include both Mexican/Mexican American as well as Latino/Latina under the more general category Hispanic American. We find that Hispanic Americans made up 84% of underrepresented students in the cohort who took Physics 9A this particular quarter and African Americans made up 11% of this group.

12

D. Hestenes, M. Wells, and G. Swackhamer, “Force concept inventory,” The Physics Teacher, 30, 141-158 (1992).

13

Adams, W. K., Perkins, K. K., Dubson, M., Finkelstein, N. D., & Wieman, C. E. (2004). “The design and validation of the Colorado Learning Attitudes about Science Survey”, Proceedings of the 2004 Physics Education Research Conference, 790, 45–48, (2004).

14

One could use the individual scores, favorable and unfavorable, or even use the various subcomponents of the CLASS as independent covariates. The decision to use a single variable was done to keep the analysis as simple as possible. We haven’t tried using all possible CLASS variables as covariates but, generally, have found that using more of these independent covariates can decrease treatment p-values (and even increase some effect sizes) but does not substantially change this paper’s conclusions and so is unnecessary.

15

Math scores received in Spring quarter are used simply to give us more data in this average.

16

The distribution of the final exam scores that end up being left out of the fit (40 student scores for AL&CF and 33 for ALOnly) because we are missing at least one piece of data from each is statistically indistinguishable (t-test gives p = 0.2 for AL&CF and p = 0.7 for ALOnly) from the data that we include.

17

M. W. Lipsey, K. Puzio, C. Yun, M. A. Hebert, K. Steinka-Fry, et al. “Translating the statistical representation of the effects of education interventions into more readily interpretable forms.” Washington, DC: National Center for Special Education Research, Institute of Education Sciences, US Department of Education; 2012. NCSER 2013-3000.

18

R. R. Hake, “Interactive-engagement versus traditional methods: A six-thousand-student survey of mechanics test data for introductory physics courses,” American Journal of Physics, 66, 64-74 (1998).

19

Not surprisingly, final exam grades for underrepresented minority groups are similarly statistically indistinguishable from the rest of the class if and only if the course is AL&CF. 20 D. R. Krathwohl, “A Revision of Bloom's Taxonomy: An Overview”, Theory Into Practice, 41, 212218 (2002). 21

In the two years following this experiment the author has taught a “watered down” version (8 weeks of concepts and 2 weeks of problem solving) of this Concepts First 9A class. The results show that the transfer effects are still present (to be published) but that the grade-gap for underrepresented groups is about !! (rather than the !! in the present paper) of the grade-gap for the standard lecture sections. It may be that the problem solving time needs to be large enough (i.e. 4 weeks rather than 2) to be important to the students and to not overlap their final exam preparation time.