Enhancing mechanics learning through cognitively

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Enhancing mechanics learning through cognitively appropriate instruction Fernando Espinoza Department of Middle and High School Education1 , Lehman College, The City University of New York, 250 Bedford Park Boulevard West, Bronx, NY 10468, USA E-mail: [email protected]

Abstract The unquestionably central role of physics in the development of scientific literacy is undermined by its perceived difficulty. An investigation of high school students’ use of the concepts of momentum and force suggests that, in the case of mechanics, the reason for physics’ unpopularity and image as a ‘hard’ subject is largely due to an incompatibility between the way it is taught in the standard model and students’ cognitive representations. An analysis of high school students’ understanding and use of force and momentum strongly implies that conservation laws should precede dynamics and kinematics in the physics curriculum due to the cognitive precedence of momentum over force. This conclusion is based on two findings: (a) students performed better at momentum than at force in pre-instructional activities; (b) an inversion in the order of introduction of topics shows that covering momentum before force is superior to the standard approach in enhancing students’ understanding of mechanics. The study therefore provides a pedagogical rationale for physics instruction that is consistent with current learning theory.

Introduction Research in physics education during the last 40 years has concentrated on instruction emphasizing problem solving as the principal measure of student understanding [1]. A number of researchers have investigated students’ understanding of mechanics. Among the findings are the following: (a) Students entertain Newtonian and nonNewtonian views of force simultaneously; the dominant view is determined by the 1 Data were gathered at Archbishop Molloy High School, 83–53 Manton Street, Briarwood, NY 11435, USA.

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circumstances of the situation. The nonNewtonian view is one of proportionality of the force to the velocity of the object instead of the acceleration, and having a direction along that of the object’s motion. (b) There is a conflict between the students’ intuitive preconceptions about motion and Newton’s second law of motion. (c) Students rationalize their non-Newtonian beliefs very skillfully. (d) The translations between verbal problems and algebraic equations present such difficulties for students that they resort to memorization of procedures of calculation rather than an understanding of the situation.

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(e) The interpretation of student knowledge is constrained by the context of the situation, and by the concepts or models used during instruction, resulting in an incompatibility between the material being presented and the students’ views [2–7]. Other studies have found that the initial ‘common sense’ knowledge of students presents a significant detrimental effect on the learning of formal physics. The instruction must take these misconceptions into account, analyse their origin and invent ways to change them. Misconceptions that students have reveal patterns that are not idiosyncratic; they tend to be applied haphazardly to a variety of situations, and so more detailed descriptions of students’ beliefs are necessary as part of a major instructional effort that goes beyond the conventional teaching of Newtonian mechanics. These studies provide evidence that students’ understanding of mechanics and dynamics is of a ‘paradoxical’ nature [8–10]. The paradox consists of the ability to manipulate algorithms and carry out complicated mathematical steps in solving a problem, while at the same time displaying a deep misunderstanding of the basic concepts underlying the algorithms [11]. In addition, the lack of reorganization of physics courses for over 50 years, and the abstract and didactic nature of the presentation contribute to the difficulties many students have when attempting to learn the material; this prompted Paul Hurd in ‘The Case Against High School Physics’ to argue that, of all the courses in high school, physics related the least to everyday living [12]. The relevance of everyday phenomena encountered by students to their learning of physics is that, while the content of the typical physics course may show some slight variations, the bulk of the material concerns mechanics [13]. Having non-inquiry laboratory tasks where the emphasis is on obtaining the correct answer, rather than in developing an appreciation for scientific thinking, hinders the benefit of such activities since they have produced no appreciable cognitive gains [6, 14, 15]. A particular difficulty in incorporating students’ cognitive reality of many everyday phenomena into the learning of physics can be seen in a survey of current textbooks. Their approach reveals a similar order of presentation at both the high school and 182

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college levels. The concept of force is invariably introduced before that of momentum; the order of introduction of the main topics in mechanics is: (i) Kinematics and motion; (ii) Dynamics and forces; (iii) Conservation laws (momentum, energy). This sequence of introduction seems odd given the documented familiarity of some concepts for students, and their persistent misconceptions and difficulties in grasping more abstract ideas [16]. According to current learning theory, schemata used by students to incorporate new information provide motivation to learn when the context encompasses familiar situations [17]. This is consistent with a good deal of science education research emphasizing fairly recent findings in cognitive science [18–22]. It must be recognized that some concepts necessary to grasp the laws of motion such as frictionless surfaces, net external forces, acceleration etc, are just not part of the students’ concrete experiences. It has been pointed out that the difficulties for students in learning physics arise because “there is a jarring disparity between the courses that introduce students to the subject of physics and those ideas and activities that comprise the practice of physics” [23]. A reassessment of the order of introduction of some concepts in mechanics is mirrored by the recommendation that what is needed in physics instruction is a fresh formulation and a restructuring of the knowledge relevant to mechanics that is more in keeping with the cognitive realities of most students [24].

Methodology I engaged a population consisting of three groups of high school students: 269 enrolled in a physics course and two subgroups—one of 70 students who had the traditional instruction sequence of force before momentum, and another of 66 students who were instructed in momentum before force. The first group undertook a series of penciland-paper activities with some items testing for an understanding of force and others for an understanding of momentum; the activities were administered on the first day of classes to test the students’ pre-instructional understanding of these concepts. The two other groups were assigned the control and experimental instructional treatments, March 2004

Enhancing mechanics learning through cognitively appropriate instruction

B A

C

Figure 1. A projectile is fired from a cannon. Illustrate (by drawing an arrow) at the respective points A, B and C the direction of its momentum, and the force acting on the projectile. Ignore the effects of air resistance.

one group (I) with force before momentum and the other (II) in the reverse order. Following coverage of these topics, and before studying two-dimensional motion, both groups were given an activity where they were asked to draw the directions of the momentum and the force on a projectile fired from the ground, at various points along the path as illustrated in figure 1. The activities contained some situations used by other researchers but redesigned to avoid responses prompted by the wording of the question or by the choices given as possible answers [8, 25].

Table 1. Results of performance on pre-instructional activities for physics students on the first day of classes (n = 269).

Results

velocity and its vertical component. The third choice (c) suggests that the students think the projectile gradually loses momentum until gravity brings it down, consistent with findings among students about beliefs similar to ‘impetus’ theories in the past [26]. Figure 3 shows the percentages of choices for the force on the projectile; there was a proliferation of answers, with group I including 12 different choices, and group II seven different choices. All the choices from group II appear in the figure, whereas only 85% of those from group I are included. Choice (a) shows that 37% of students from group I confuse momentum with force, or associate an impulsive force with the motion of the projectile consistent with reported misconceptions; this is nearly double the number from group II. Choice (b) shows that more students from group II drew the correct direction for the force; choices (d), (f ) and (g) can be interpreted as students experiencing a gradual conceptual change toward the scientifically correct view of the motion; however, this is only

The results of the first set of activities to determine students’ pre-instructional understanding of force and momentum are summarized in table 1. The mean percentage of correct answers for the force activities was 38% whereas for the momentum 2 activities it was 51%. A chi-square test χ(6 df) = 33.15, p < 0.001, yields a statistically significant difference between the two means; the physics students possess a better command of momentum than of force prior to formal physics instruction. The results of the projectile activity are illustrated in figures 2 and 3. Figure 2 shows the percentages drawn to represent the momentum of the projectile at points A, B and C. The average results are quite consistent between the two groups and they represent over 90% of all responses. The majority of responses indicate the proper answer to the direction of the momentum in choice (a); choice (b) shows that these students think the projectile has no momentum at the highest point by virtue of not having a velocity, thus demonstrating confusion between the total March 2004

Activity

Force (%)

Momentum (%)

1 2 3 4 5 6 7

45 54 50 47 55 9 9

56 36 83 57 61 51 16

Average

38

51

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(a) 69% (I), 64% (II)

(b) 15% (I), 17% (II)

(c) 8% (I), 8% (II)

Figure 2. Percentages drawn for the momentum of the projectile; no arrow indicates zero value at that point. Slightly over 90% of the responses are represented for both groups.

experienced by 14% of those from group I, whereas 41%, nearly three times the number from group II, display this feature.

Conclusion The results from table 1 confirm findings made about elementary school students [27]. High school students also possess a more intuitive concept of momentum than of force. The significance of the results from figures 2 and 3 can be summarized as follows: • There is no statistical significance to the percentages of answers from both groups in the momentum activity; this supports the findings from the first set of activities. The pre-instructional cognitive awareness of momentum tends to average out performance due to its intuitiveness for students, regardless of the instructional method. 184

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• The number of misconceptions in dealing with force is greatly reduced by the sequence of instruction being momentum before force. • Covering momentum before force increases the performance of students when dealing with force, compared with those exposed to traditional instruction of force before momentum. • Students benefit in undergoing conceptual change toward the proper understanding of the force acting on the projectile by more than three times when the instruction exposes them to momentum before force. • The proliferation of views about momentum increases by 33% for students undergoing the traditional sequence of instruction compared with those exposed to momentum before force; it increases by 42% for views about force, which is particularly significant in light of the documented findings on misconceptions about force. The findings of this study are consistent with other studies where the fruitfulness of momentum in building a concept of force has been shown [28], and provide pedagogical support for the suggestion that the order of introduction in mechanics of force and momentum could well be reversed [21]. While there have been several attempts at the college level to introduce momentum before force, they are based on reasons other than the cognitive precedence of one concept over the other in students’ preconceptions of physical phenomena. The sources of these attempts are not published articles but textbooks. Weidner and Sells [29] based their approach of introducing momentum before force on the following reasons: 1. linear momentum and its conservation emerge in a simple way from elementary experiments; 2. the concept of force and Newton’s second and third laws easily follow once momentum is clear; 3. conservation of momentum provides details about collisions without having to know in detail the forces acting between the colliding objects; 4. force is a subordinate concept to momentum in modern physics. These reasons are based on a sophisticated understanding of mechanics that includes the March 2004


(a) 37% (I), 19% (II)

(b) 17% (I), 25% (II)

(c) 11% (I), 3% (II)

(d) 9% (I), 14% (II)

(e) 6% (I), 12% (II)

( f ) 3% (I), 12% (II)

(g) 2% (I), 15% (II)

Figure 3. Percentages drawn illustrating the force on the projectile; no arrow indicates zero value at that point. The responses for group II are all represented, whereas those shown for group I represent about 85% of the responses.

mathematical precedence of momentum over force in a calculus-based approach, as well as knowledge of the dynamics of atomic and subatomic particles. The text does not completely rearrange the topics since it first covers the law of inertia (Newton’s first law), followed by momentum, and eventually by Newton’s second and third laws. Reichert [30] emphasizes the use of differential equations instead of memorizing the algebraic kinematical equations; he points out the advantage of using differential as opposed to integral equaMarch 2004

tions. Conservation laws are given precedence by the introduction of conservation principles as fundamental laws of nature. This text begins with variable forces as interactions; energy as a scalar and momentum as a vector are introduced as the approximations of the relativistic expressions for low velocities. Moore [31] also begins with conservation laws and acknowledges that these are better understood than Newton’s laws by students; the derivation of conservation laws from Newton’s PHYSICS EDUCATION

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laws involves taking integrals, whereas the derivation of Newton’s laws from the conservation laws involves taking derivatives. The latter is obviously much easier for students just beginning their study of calculus. Of these three sources Moore is the only one that shows an awareness of the research findings on student learning; the reason is that this text came out of the efforts of the Physics in Context model of the Introductory University Physics Project (IUPP) supported by the National Science Foundation during 1987–1995. All these sources concern the calculus-based undergraduate physics level; their recommendations follow pedagogical arguments largely based on the mathematical representation of mechanics. The findings in this study by contrast are based on the demonstrated cognitive precedence of momentum over force in high school students’ pre-instructional understanding of these concepts, thus providing an independent but complementary rationale for the efforts made to teach momentum first at the undergraduate level. Since those efforts address a selective student population that would use such textbooks, their impact is limited by their scope. Instructional reform based on learning theory could potentially have a much wider reach since it deals with a larger student population. This study provides evidence for teaching momentum before force at the pre-college level where it is perhaps most significant in enhancing the importance of physics in the development of scientific literacy; using pedagogically appropriate instruction based on learning theory is useful in developing a theoretical framework for physics education reform rather than relying on a series of unrelated efforts. Received 20 June 2003 PII: S0031-9120(04)64990-2 DOI: 10.1088/0031-9120/39/2/007

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[23] Rigden J S 1988 The spirit of reform is needed in physics Phys. Educ. 23 197 [24] Gamble R 1989 Force Phys. Educ. 24 79–82 [25] Hamilton D J 1994 Use of interviews to compare ninth- and tenth-graders’ preinstructional knowledge with medieval impetus theories Ed D Dissertation Teachers College, Columbia University [26] McCloskey M, Caramazza A and Green B 1980 Curvilinear motion in the absence of external forces Science 210 1139 [27] Raven R J 1967–68 The development of the concept of momentum in primary school children J. Res. Sci. Teach. 5 216–33 [28] Thijs G D 1992 Evaluation of an introductory course on ‘force’ considering students’ preconceptions Sci. Educ. 76 (2) 155–74

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[29] Weidner R T and Sells R L 1965 Elementary Classical Physics (New York: Allyn & Bacon) [30] Reichert J F 1991 A Modern Introduction to Mechanics (Englewood Cliffs, NJ: Prentice Hall) [31] Moore T 2002 Six Ideas that Shaped Physics (New York: WCB/McGraw-Hill) Fernando Espinoza is an Assistant Professor of Science Education at Lehman College, City University of New York, USA. He holds a Doctorate in Science Education from Columbia University. He has taught physics, earth science, and physical science at high school and college levels for over 20 years.

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