Article pubs.acs.org/jchemeduc
Investigation of Absolute and Relative Scaling Conceptions of Students in Introductory College Chemistry Courses Karrie Gerlach,† Jaclyn Trate,‡ Anja Blecking,‡ Peter Geissinger,‡ and Kristen Murphy‡,* †
Brookfield Academy, Brookfield, Wisconsin 53045, United States Department of Chemistry and Biochemistry, University of WisconsinMilwaukee, Milwaukee, Wisconsin 53201, United States
‡
S Supporting Information *
ABSTRACT: Scale as a theme in science instruction is not a new idea. As early as the mid-1980s, scale was identified as an important component of a student’s overall science literacy. However, the study of scale and the scale literacy of students in varying levels of education have received less attention than other science-literacy components. Foremost into the foray of students’ scale literacy has been the research by Gail Jones and co-workers, who have been studying students in middle and high school, in-service teachers, and experts in their respective fields. However, the scale literacy of students in undergraduate college chemistry courses is unknown. One should not assume that students in introductory chemistry courses have an appropriate and developed conception of scale, particularly down to the relevant size realms for chemistry. The research presented here investigates the relative and absolute scaling conceptions of students in introductory chemistry courses. KEYWORDS: First-Year Undergraduate/General, Chemical Education Research, Testing/Assessment FEATURE: Chemical Education Research
■
■
INTRODUCTION
LITERATURE REVIEW For undergraduate students in general chemistry, thinking about matter on a level that is orders of magnitude below the resolution afforded by the human eye (i.e., below 0.1 mm) is often a new and challenging concept. In addition to the expectation that students develop an abstract understanding of a different-scale world, there is also an expectation for students to bridge the visible world to this “new” particle world. Conception of scale or simply put, “scale literacy”, is integral for students to be able to connect these worlds. Although the development of scale literacy involves the application of many skills, a working knowledge of scale literacy is often demonstrated through relative (comparing sizes) and absolute (understanding actual sizes) scaling activities. Out of a number of studies focused on assessing scale literacy, the most notable research by Tretter, Jones, Andre, Negishi, and Minogue7,8 looked at the absolute and relative scaling abilities of students from elementary to the graduate level. When students at various K−12 levels were compared to “experts” (doctoral students in science education or in astrophysics and nanoscience) on their understanding of scale, the experts only ranked at the 60th and 30th percent accuracy level in fitting an object with its size (within 1 order of magnitude) at the nanoscale (10−9 m) and microscale (10−6 m) levels, respectively.8 K−12 students performed at or below the 20th percent accuracy level for both sizes. This research showed that cultivation of students’ understanding of scale, particularly
Recently, the National Research Council has released the framework for K−12 science education that includes seven crosscutting concepts.1 This framework guided the development of the new national science standards,2 the recently released Next Generation Science Standards.3 However, recommendations to approach science education by crosscutting concepts or themes are not new. In 1989, Bybee, Buchwald, Crissman, Heil, Kuerbis, Matsumoto, and McInerey presented frameworks for science instruction with nine “explanatory concepts”.4 Later, in Project 2061, the American Association for the Advancement of Science (AAAS) identified four common themes for science literacy in general.5,6 These themes or cross-cutting concepts pervade any science course, and scientifically literate students who have a working knowledge of these themes would be expected to be successful in science courses. Scale is a common theme across these various frameworks;1,4,6 however, unlike other common themes (such as models), scale is commonly omitted in formal instruction. Because there is a continuing and increasing need for scientists and engineers, aspects of technology and engineering are expected to be integrated more into science education.1,3 Additionally, because these scientists and engineers are expected to drive progress in nanotechnology and nanoscience, the need to have a better understanding and further-reaching conception of spatial scale becomes increasingly more important. © XXXX American Chemical Society and Division of Chemical Education, Inc.
A
dx.doi.org/10.1021/ed4004707 | J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
development of anchor points were most influential on their sense of scale. Those interviewed mentioned these anchor points or “quick mental benchmarks” as an easy reference as one moves through a spatial spectrum. The development of new anchor points represents a mechanism to differentiate between novices and experts in the development of scale literacy. For example, the use of one’s own body to make size references or comparisons is commonly used by both novices and experts and both groups demonstrate the ability to extend to approximately 3 orders of magnitude in scaling outside of this range without much difficulty. This was previously cited by AAAS, particularly in reference to scale and the ease with conceiving 1000 mm in 1 m or 1000 m in 1 km but having difficulty in understanding that 1,000,000 mm make up 1 km.5,6 Therefore, novices without a developed concept of scale over a broad range of sizes may be comfortable using only their bodies as a reference and have a developed understanding of ±3 orders of magnitude of size around this. Conversely, experts would have developed anchor points that differ from their own bodies that have allowed them to cultivate a developed understanding of scale surrounding that new anchor point. More generally, this same study examined a “trajectory of scale concept development” from novice to expert. This progression of scale concept development illustrates the skills a student will possess at different stages in gaining scale literacy. The authors noted that at the novice level, learners will have developed a number sense12 and a conceptual understanding of relative sizes.7,8 As learners progress to the experienced level, they develop visual spatial skills,13 an ability to visualize scales14 and apply conceptual anchors in scale estimation (as exemplified in the Jones, 2009 study) among others. An understanding of relative sizes that are relevant to the system of study depends on an ability to conceptualize the scale of that size. In the domain of chemistry, the development of visual spatial skills as well as the ability to understand and generate representations is of particular importance. This logically extends into understanding representations of the particulate nature of matter with vast areas of study dedicated to this research.15,16 Current efforts to enhance scale literacy include viewing successive images of increasing or decreasing magnifications as well as participating in experimentation utilizing instrumentation. In a study of middle-school students’ proportional reasoning skills and scale conception prior to and following the viewing of images over many orders of magnitude,17 it was found that scale accuracy on a “Scale Card Sorting” activity correlated with proportional reasoning skills and was enhanced through viewing the images.18 Proportional reasoning was cited as an important component of developing scale conception. Research into shifting students’ anchor point from themselves (their own bodies) to a very small unit (atom or molecule) used a two-step activity to enhance students’ conception of the nanoscale in both a relative and absolute sense.19 Following instruction on viruses in a biology class, high-school students had the opportunity to use an (remote) online controllable atomic force microscope (AFM), which provided both visual and tactile feedback through a joystick device.20 Assessment both prior to and following the use of the AFM indicated that students’ conception of the small scale was enhanced through the experiment. In another study by Jones and colleagues,21 novice (preservice) and experienced teachers performed the same activities as described above7,8 and an additional assessment
down to the nanometer size, needs to continue beyond their elementary and secondary education years. Activities, assessments, and interviews were used in this study to elucidate the scale conception of the participants. In one portion of the study, participants were given 31 objects of widely varying sizes (from galactic to subatomic) and asked to assign the objects by their absolute sizes to a set of size ranges.7 Additionally, the participants were asked to place 26 of the objects into groupings (based on size) and requested to order the objects by size in relation to one another. Finally, participants were interviewed on their experiences completing the activities and what skills they used to perform the tasks. From this portion of the study, conceptual scale boundaries as well as formative experiences (both in and out of school) for developing scaling conception were examined. The results of the study indicated that students begin to develop a concept of scale sometime between their middle-school and high-school years. However, all participants had difficulty with scaling activities related to very small objects. This was also evident in the size categories identified by the participants in the study. The less experienced the participant, the more likely they would have less differentiation between objects that are small, particularly those objects that are nonvisible.7 In other components of this study, scale conception related to the perception of scale along a size continuum to both the very large and very small was examined.8 The results indicated that participants in ninth grade and lower had a discontinuous perception of scale below 1 mm, believing spatial sizes to fall into discrete categories rather than a continuous spectrum. Participants in this group consistently named visible objects when prompted to give objects that would fall in a micrometer range or other nonvisible size range. These participants also were found to perform better when using their own bodies as a reference versus using the metric system. Comparatively, the 12th grade students and experts performed better using the metric system rather than their own bodies as a reference. Additionally, the experts who participated in the study and who have experience using instrumentation were able to draw upon these experiences to demonstrate a better understanding of size and scale in the nanoworld. As stated by Tretter et al. (in ref 8, p 1082), One aspect of experts’ experiences that emerged as particularly powerful for scale conceptions was the importance of experience, including the instruments used when working with different-scale worlds. Even within the expert group, those who had little experience at an extreme of scale expressed difficulty thinking at that scale. Finally, Tretter and Jones proposed a series of activities that facilitated the process of students connecting their perception of relative scale to their perception of absolute scale.9 One activity that was adapted from a previous activity10 had students using a clothesline or number line to place objects of various sizes, beginning with a linear scale and moving into a logarithmic scale. Although no results from this study were presented, an adaptation of the proposed activities was incorporated into the work presented here. More recently, professionals in various fields, including some from outside of the scientific domain, were interviewed about their current use of scale and their experiences leading to their current successes in their respective fields.11 Apart from formal educational experiences (learning about different scales and how to convert between units), these professionals most commonly reported that classroom experiences and the B
dx.doi.org/10.1021/ed4004707 | J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
called “Scale Anchoring Objects” (SAO) that looked for participants’ conceptual understanding at a variety of scales using objects to represent different size scales. As part of this, participants used their own bodies as a standard measurement. In the SAO assessment, both groups performed perfectly when working at the human scale; however, both groups’ accuracy decreased as they moved in both directions away from the human scale. This result was very similar to the results found in previous studies.7,8 In all studies, it was noted that previous experiences in and out of school played an essential role in their scaling abilities. In contrast to those described previously, very few studies have been conducted on undergraduate students’ conceptions of scale. A recent study of students in introductory engineering courses examined their understanding of size and scale by asking them to create a scale for placing small, nonvisible objects (i.e., atom, virus) and visible objects (i.e., football field).22 The results of the study were similar to those obtained by Jones in that students’ development of number sense and proportional reasoning varied widely. Students in general tended to be accurate within the human realm and became less accurate as they moved away from this region. The authors also noted that current instruction is not effective in helping students develop a sophisticated understanding of “size and scale” and confirmed the importance of formal education experiences as critical in their understanding of scale, much like the experts from Jones’s study had reported.11 Finally, the need to develop a student’s scale literacy would not be limited to understanding the very small or subsequently isolated to the domain of chemistry. The development of a student’s scale literacy outside the discipline of chemistry has been noted as an important component of a student’s overall science literacy.1,4,6 The centrality of students’ scale conceptions in all science disciplines, and the paucity of studies on the scale conception of undergraduate students require renewed attention. In particular, in this paper, the following research questions were investigated: (1) How do undergraduate students in introductory chemistry courses conceive boundaries of scale? (2) What is the relative scaling proficiency of undergraduate students in college introductory chemistry courses? (3) What is the absolute scaling proficiency of undergraduate students in college introductory chemistry courses?
■
convenience. In addition, a group of chemistry graduate students (students pursuing Ph.D. or M.S. degrees in traditional chemistry subdisciplines) made up the experienced group (N = 10). The research protocol is approved (IRB #09.047), and all included data are from students who consented via this protocol. Activities
The scale activity design was based on the interviews that were outlined by Tretter10 and Jones.7,8 Each activity was broken into four parts: (1) Bin Creation and Item Sort. (2) Item Ordering Within Bins. (3) Item Ordering With Measurements. (4) Item Ordering on a Number Line. The activities took place in two phases in which the format remained the same but the content of the activity was slightly altered to examine different aspects of scale conception, with the phases separated by approximately 2 weeks. The activities were also designed to offer no instruction to the students but rather present them with each task and record the results. At no time did the students receive the correct answers or any instruction to help them arrive at the correct answers. Therefore, students from the first phase of interviews were invited to participate in the second phase of interviews where the second phase was a unique and separate measurement. The number of participating students by phase and course are given in Table 1. Table 1. Number of Students Per Course and Per Phase Group in Study Preparatory Chemistry students General Chemistry I students Experienced students
Phase 1 (total)
Phase 2 (total)
Participated in both Phase 1 and Phase 2
14
10
10
32
21
21
10
5
5
In Part 1 (Bin Creation and Item Sort), students were instructed to create bins or categories that would allow them to organize 20 objects by a single dimension in length such as diameter or distance between two points. In the event of a student creating only bins with a fixed beginning and end, they were encouraged to leave the largest and smallest bins open on one end as a “catch-all”. In contrast to the activities designed by Jones,7,8 in this study, the participants were not provided with the objects prior to creating their bins as this prevented the bins from being biased due to cueing from a specific object. The participants were then given 20 cards (see Tables 2 and 3), which described items similar to the ones that Jones et al.7 used in their interviews. The sizes of these items covered a large portion of the spatial scale spectrum, both larger and smaller than human sized. At this point in the activity, the cards only had the description of the size such as “New York to Los Angeles” with no measurements given. If students questioned the meaning of an object name, clarification was provided without guidance (for example, if they asked which dimension of the textbook, this was provided as the length). There was certainly the possibility that students correctly knew that the description used for the object was generic and that there is a
METHODS
Overview
One-on-one activities were performed at a large public urban doctoral institution in the Midwest. The activities were performed while sitting at a table, and the entire activity was video and audio recorded and photos were taken of all responses. The recording of the activities was retained as a reference of the results of each component of the activity. The audio recording was not transcribed or used in the analysis of the results as the activities were designed to provide the results directly from the students’ actions and not from the students’ articulation of their actions. The scaling activities were conducted with students enrolled in preparatory chemistry (N = 14) or the first semester of a two-semester sequence of general chemistry (N = 32). These students are referred to by the course in which they were enrolled, or collectively, as “novices”. Students were requested during a regular lecture to participate voluntarily in the one-on-one studies at their C
dx.doi.org/10.1021/ed4004707 | J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
In Part 3 (Item Ordering With Measurements), new item cards were presented to the student with measurements and units along with the objects’ description. This was accomplished by having the two sets of cards, those with only the name of the object (for Parts 1 and 2) and those with the name and size of the object clipped together. For Part 3, the object card with only the name was removed by the interviewer revealing the object name and size card below. The students were asked to reflect on their ordering of the objects in their bins with the help of the new information and make any changes as desired. The units for the cards for phase 1 were chosen based on previous studies.7 For the most part, the units for the cards for phase 2 were chosen based on the results of phase 1, where students struggled with the absolute and relative scaling of the items. Phase 2 was designed to extricate the issues that surfaced with prefixed units and conversions between exponential and decimal notation. In Part 4 (Item Ordering on a Number Line), the same objects and information from the cards used in Part 3 (for example, New York to Los Angeles, 4800 km) but transferred onto a single-lined card with a point (for more precise placement) and a logarithmic number line were provided to the students. The logarithmic number line extended from −9 to 9 and also included a greater than and less than on both ends for those items that fell beyond those boundaries. If objects fell into the >9 or the
