Article pubs.acs.org/jchemeduc
Periodic Properties and Inquiry: Student Mental Models Observed during a Periodic Table Puzzle Activity Kathleen G. Larson,† George R. Long,*,‡ and Michael W. Briggs‡ †
Department of Psychology, Indiana University of Pennsylvania, Indiana, Pennsylvania 15705, United States Department of Chemistry, Indiana University of Pennsylvania, Indiana, Pennsylvania 15705, United States
‡
ABSTRACT: The mental models of both novice and advanced chemistry students were observed while the students performed a periodic table activity. The mental model framework seems to be an effective way of analyzing student behavior during learning activities. The analysis suggests that students do not recognize periodic trends through the examination of elemental data. Even simple relationships (e.g., the sequence of atomic mass values) proved important to novice understanding of the trends in the periodic table. The use of common heuristics for decision making, and well-known common errors associated with those heuristics independent of the students’ chemistry background, were also observed. KEYWORDS: Chemical Education Research, Inquiry-Based/Discovery Learning, Misconceptions/Discrepant Events, Periodicity/Periodic Table, Problem Solving/Decision Making FEATURE: Chemical Education Research
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students learn during an activity, we must consider both the important organizing features of the periodic table, as Criswell does, and students’ prior knowledge of the periodic table. Our objective in this study was to examine students’ mental models operative in performing a periodic table puzzle activity. The periodic table puzzle used in the study is available online.6 Examining learners’ mental models will provide information regarding how prior knowledge impacts activities designed to help students learn about the periodic table. From our perspective, this is the addition of new information to their mental models of the periodic table, which thus informs the future development of such activities. In general, these studies bring to light important cognitive aspects of student learning that may have an impact on how inquiry-based chemistry learning activities are structured. The fundamental goal of such studies is to allow the design of learning activities that rely less on a best-practices approach7 in favor of a more cognitivetheory-based design. A theoretical approach to learning activity design is more generalizable to various learning environments, and provides a much-needed foundation for pedagogical practice. Our view is that the results of this study can be applied by a practitioner to any activity intended to introduce students to the periodic table.
he periodic table is an iconic tool in chemistry, and its study is an essential part of any introductory chemistry course. Consequently, numerous approaches and methods have been proposed to help students learn the details of the organizational structure of the periodic table.1 Indeed, discussion continues regarding the best representations of the table;2 these often center on the educational impact of the organizational choice.3 Despite the questions raised in such discussions, one format of the periodic table is used in the vast majority of introductory level textbooks. Thus, it is important to determine the various ways students interact with this table, and those aspects of the table that effect their learning; that is, the construction of a mental model of the periodic table. The activity studied here is based on a well-known inquiry activity in which students independently explore elemental data to learn periodic trends with minimal instructor guidance.4 Criswell5 has done an analysis of the important concepts encountered by students seeking to understand the periodic table, and suggested a sequence of activities to enhance their learning. He points out several difficulties with inquiry-based activities in which students act as “Mendeleev for a day” and try to arrange unknown elements into the sequences found in the periodic table. Criswell points out that the arrangement of the periodic table by Mendeleev is but a small aspect of students’ conception of the periodic table. Today’s chemistry students look at elements very differently than Mendeleev, because properties and details of atomic structure, unavailable to Mendeleev, can inform students on the structure of the periodic table. The prior knowledge students bring to their study of the periodic table is variable. Thus, if we intend to describe how © 2012 American Chemical Society and Division of Chemical Education, Inc.
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THE MENTAL MODEL The concept of the mental models used in this work derives from work by Johnson-Laird,8 but has been refined to include Published: September 17, 2012 1491
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Table 1. Comparative Examples of How Process Skills Act as Sensemaking Processes Foraging Process SkillsOperating with Uncertainty Observing Measuring Inferring Predicting Formulating hypotheses
Using one’s senses to gather information about an object or event Using standard measures or estimations to describe specific dimensions of an object/event Formulating assumptions or possible explanations based upon observations Guessing the most likely outcome of a future event based upon a pattern of evidence Stating the proposed solutions or expected outcomes for experiments
Exploiting Process SkillsOperating with Certainty Classifying Organizing data in tables and graphs Formulating models Communicating Identifying causal relationships Identifying variables Characterizing variables
Grouping or ordering objects or events into categories based on characteristics or defined criteria Making data tables and graphs for data collected Recognizing patterns in data and making predictions based on these patterns. Using words, symbols, or graphics to describe an object, action or event Understanding cause and effect relationships Stating the changeable factors that can affect an experiment Describing relationships between variables
of decision processes. Clearly, decision making is an important part of any problem solving or inquiry activity; thus, it is the interaction of students’ prior knowledge and their decision making that allows the construction of new or more detailed mental models. Examples of well-known simple heuristics used in sensemaking include these: 1. Representativeness, or how much does A resemble B? Students predict that the chemical properties of an unknown element will be similar to the properties of a similar element. 2. Availability, or how easily is an event brought to mind? For example, a student’s prediction of a correct chemical mechanism will be based on those mechanisms most recently studied. 3. Adjustments f rom an anchor, or how is this problem like something I know? Often, students start a problem by reproducing something they already know, and then making adjustments. Simple heuristics are typically the sensemaking process used when a student lacks a starting point for an activity, that is, the student is dealing with uncertainty. This often occurs when a student has limited prior knowledge of a concept, or if the question is asked in an unfamiliar way. However, if significant information is available, either provided by an instructor, or available from a student’s prior knowledge, the sensemaking processes become more complex. For example, for a novice, the task of predicting elemental properties is accomplished using the heuristic of representativeness, while an individual with more information about the periodic table (i.e., greater prior knowledge) may rely on classification of the elements into families to accomplish the task. Thus, we divide sensemaking into two categories, processes that deal with uncertainty, termed “foraging”, and processes that operate with certainty, termed “exploiting” by Pirolli and Card.15 The simple heuristics fit the foraging category.
specific constituents. These constituents provide a method for defining the mental models of individuals, and allow detailed comparisons between study participants. This is in contrast to the generalized mental models referred to in conceptual change theory, in which there are no systematic structural constituents.9 Our current conceptualization of mental models is based on the work of Lesh et al.10 We have refined and expanded the original meanings of the proposed constituents used by Lesh et al., and added one additional constituent, the sensemaking process.11 The constituents of a mental model were characterized in detail in a previous article12 in this Journal. Briefly, we define the constituents in the following way. A referent is the symbol, label, or object (either mental or physical) used by a learner to construct and communicate knowledge. In this study, an example of a referent is the identity of a specific property (e.g., mass or electronegativity). Labels for locations on the periodic table are also referents, the p-block, for instance. A relation is the connection between referents. It is also the constituent that conveys hierarchy and direction between an individual referent and a set of referents. For instance, the relationship “mass increases as you go down the column” is a relation. Syntax is used to construct a mental model and afford the ordering of referents and their relations so that meaning can be assigned. For example, rules for writing chemical symbols, and the ordering of the atomic numbers on the periodic table are examples of syntax. A result is the consequence of applying syntax, or a sensemaking process to a set of referents or relations. During an activity, a participant may conclude “The electronegativity decreases as you go down group 17.” The result can then be used later to solve related problems. The sensemaking processes are the part of the mental model that acts on information, animates the available static constituents during problem solving, and drives the construction of new mental models. The term sensemaking was coined by Pirolli and Card12 in regard to processes used to analyze intelligence information. Here we generalize this concept, applying it to classroom activities. A fundamental sensemaking process may be a simple heuristic. Some of these heuristics are well-known, from fundamental studies on decision making reviewed by Tversky and Kahneman.13 Johnson-Laird14 has shown that the framework of the mental model is compatible with these descriptions
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RELATION TO PROCESS SKILLS AND INQUIRY BASED LEARNING One perspective of inquiry-based learning emphasizes process skills as an important component of the activity.16 The process skills are a defining feature of any cognitively based definition of inquiry learning.17 Significant overlap exists between what we see as complex sensemaking processes, and the “process skills” important for success with inquiry-based activities.18 Table 1 lists some of the process skills we view as corresponding to our 1492
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“sensemaking process” constituent, and classifies them as either foraging or exploiting. It is important to recognize that the distinction between foraging (working with unknowns) and exploiting (working with knowns) sometimes has more to do with the context of the activity than the details of the process. For instance, surely some overlap occurs with regard to the process used to predict something, and the process used in formulating models. However, in the case of predicting, the focus is on the result of the prediction, and the question involved is “Is there a pattern here?” When formulating a model, the focus is on extending what is known by building relationships between a known pattern and other knowledge. The questions involved with formulating a model are “What can I learn from this pattern?” or “What can I do with this pattern?” Thus, a learner is exploiting the pattern to gain new knowledge. The incorporation of these processes into our conception of a mental model, the connection of the processes to more fundamental decision making processes, and the link to other types of constituents (e.g., referents and relationships) provides a means to study the nature of the interaction between content knowledge and process during inquiry-based activities,19 and the impact of instruction on the development of process skills.20
and location based on these placements. This thought-revealing activity closely resembles the “have students be Mendeleev for a day”5 inquiry approach to introducing the periodic table, however it is important to note that our purpose was not to report on an actual activity, but to use the thought-revealing activity as a probe into students’ cognitive processes during study of the periodic table. Participants were first shown the color-coded periodic table and asked to describe periodic trends of five important properties, based on the color pattern observed (mass, density, ionization energy, electronegativity, and electron affinity). Participants were subsequently asked to solve four different puzzles of increasing difficulty, that is, increasing numbers of elements involved. In each puzzle, a section of the periodic table was removed, and the element symbols were left blank. Students had to place the elements in the correct position on the periodic table based only on the value of the property (represented by the color of the element block). Participants could change the property shown, which would change the color of an element block accordingly. The participants each completed two interviews. Participants were asked to talk aloud while doing this puzzle. The students’ voices and actions were recorded using Adobe Captivate software. During the first interview, three different problems were given in which sections of the periodic table were made blank: alkaline earth metals; row 3 elements; and the p-block elements. In the second interview, the participant repeated the problem with a blank pblock puzzle, and then worked on a puzzle in which the entire periodic table was blank. Both interviews required the participant to initially describe observed trends for the five different properties. The participants were six undergraduate students from Indiana University of Pennsylvania; they had varying levels of chemistry knowledge. Of the six participants, two were chemistry majors, Bob and Cassandra. (All student names used here are pseudonyms.) One student, Sally, had taken a general chemistry course in college. Annie, Ashley, and Hank last had a chemistry course in high school. Bob and Cassandra were senior-level students; the other participants were juniors. The participants’ chemistry background is shown in Table 2.
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METHOD The online periodic table puzzle6 requires that participants put the elements in sequence based on properties coded by color. The more difficult puzzles require information about relationships of the element properties in both the horizontal and vertical directions. An example of a simple puzzle is shown in Figure 1. Students choose properties and attempt to place
Table 2. Distribution of Participants by Chemistry Background Students’ Pseudonyms
Figure 1. Example of a simple periodic table puzzle.
Ashley Annie Hank Sally
colored element boxes in the correct position in the alkaline earths column of the table. Under the window for atomic radius is a mapping of values to colors for the property. Participants can change this selection to other properties in order to place each colored box in the correct position. The changes in color are a cue to the ordering of the elements with respect to their position on the periodic table. The colors play the role of a metaphor for a selected property and illustrate clearly the sequencing of values for that property. The larger the range of elements included in the puzzle, the more complex the sequencing required. In an inquiry mode in which the students would not know all of the relationships, an element block’s property-dependent color would provide a hint as to the appropriate placement of the element. The students are then expected to infer the relationships between property
Cassandra Bob
Previous Chemistry Coursesa High school chemistry High school chemistry High school chemistry One college-level general chemistry course Senior-level college chemistry courses Senior-level college chemistry courses
Category Novice Novice Novice Advanced Advanced Advanced
a
Senior-level means general, organic, inorganic, and physical chemistry courses.
When examining qualitative data, we determined participants’ mental models by identifying specific constituents in the participants’ words and actions. The various constituents provide an organized way to represent the participants’ thinking and learning process. Mental models, then, can be seen to evolve as new constituents are added, and less useful constituents are ignored. The use of well-defined constituents 1493
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even though detailed understanding of these properties was not available to the participant. Hank noted, “The noble gases and the second column and last column are completely blue”, observing similarities in properties. Additionally, understanding of color relationships and general knowledge of shapes and patterns seemed to be helpful, particularly for those participants with limited chemistry background. The novice participants sometimes go into great detail regarding the colors, and the shapes of patterns they saw on the table. For instance, while solving the p-block puzzle, Annie noticed that rows were different colors. After some trial and error she noted that for mass, “[T]he colors [in row 6] went from an orange [radon] to more of a gold, to a real really bright yellow.” This is a result, which she used to predict the colored element blocks that would go in row 5 and 6, though the result had no utility beyond solving this puzzle. She claimed, “[T]he next I think are going to be green, the next row”, which was correct. However, when she began to solve row 2 and 3, the colors depicting mass were more similar, and harder to discriminate. Annie stated, “[I]t looks like it could possibly be hard”, because both rows had blue colors. To solve the puzzle, Annie chose several different properties, and determined from the color distribution of the element blocks the property that she felt would allow her to locate the blocks. The property choices were based on the colors of the elements that need to be placed. She chose boiling point, “[B]ecause these greens match up,...it’s kind of a different color scale now.” She continued choosing properties to work with based on the discrimination she saw in the unplaced elements, and placed elements based on similarity of properties, noticing that nitrogen electron affinity was an “oddball” (this is of course a result that would require detailed background knowledge to explain). Clearly, Annie was obtaining results only applicable to the puzzle, but was demonstrating a fairly complex sensemaking process. Additionally, the names of the elements seemed to have significance for Annie, as she noted every element name that she successfully placed in the table.
allows a comparison between the domain-specific constituents and constituents used by the learner. The comparison provides important details concerning how a student is interacting with information, and a direct determination of the learner’s relevant prior knowledge. Our analysis seeks to identify these constituents within audio and video recordings of the participants’ activity in solving the periodic table puzzle.
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RESULTS AND DISCUSSION Participants were observed using several important referents and relationships while solving the periodic table puzzle. Far and away the most common and important relation used by the participants was the relationship between mass and location on the periodic table, namely, mass increases from top to bottom on the periodic table, and from left to right. For example, Cassandra noted, “As you go from left to right the masses get higher.” Bob also noted, “Mass increases left to right across the period.” Ashley also relied on the mass, remarking, “Now all that is left is blue and they all have a low mass level.” Hank observed the regular nature of the change in mass as he mentioned, “The mass one [property] was more linear.” Not only does the property provide significant discrimination between elements, the regularity of the change provides some discrimination both across the rows, and down the columns. In some instances, participants could use the mass property alone to complete significant portions of the puzzle. The advanced participants also relied on knowledge of specific groupings on the periodic tables. They consistently used referents describing areas on the table, such as the d-block, transition metals, nonmetals, noble gases, halogens, and so on. Such groupings provide some information about the connection between location and property. For example, Cassandra noted, “Electronegativity is greatest at fluorine, it decreases as you proceed from the upper right hand corner to the bottom left hand corner.” Knowledge of the relationship that halogens have high electronegativities and the noble gases do not helped some participants choose the correct location of the element blocks. In particular, Cassandra used a combination of electronegativity relationships, and atomic mass relationships to find the location of a number of element blocks. When asked, “Why did you pick electronegativity?”, Cassandra responded: Because I know how the trend looks, cause it kind of goes like this [gestures with the mouse indicating the electronegativity trend.] And then these are all the lighter elements they go in these two rows, and if I can just figure out the color sequencing.... The other advanced participant, Bob, also relied heavily on electronegativity. In fact, he pointed out several relationships dealing with electronegativity: Electronegativity increases from left to right across the period. Fluorine has a higher electronegativity because it has the greatest affinity for an electron. Hydrogen is green in the group 1 column because hydrogen still has a great affinity for an electron because it has an unfilled s orbital and it doesn’t experience shielding. Despite some inaccuracies in describing electronegativity, Bob clearly shows detailed prior knowledge of the concept through the many complex relationships, and applies this knowledge to the solution of the puzzle. Often certain general relationships are of great value in solving the periodic puzzle. In particular, knowledge of the general design of the periodic tablethat elements in the same columns would have certain similar propertieswas essential,
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OBSERVING THE SENSEMAKING PROCESS The puzzle software records both the time required to complete the puzzle and the number of incorrect element placements. While this has substantial limitations, and should not be viewed as an absolute metric, we can at least use these values as a relative characterization of the efficiency of the participant’s decision process. The values are useful in that they provide a general overview of how the participants performed on the puzzle. These data are summarized in Table 3. Bob, a senior chemistry major, had the most errors, but also showed the greatest improvement. The number of errors does not correlate with the amount of time spent on the puzzle, as Table 3. Comparative Quantitative Results for Selected Runs of the Periodic Table Activity, Solving the p-Block Elements
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Participants
Time to Completion for Trial 1, s
Number of Errors in Trial 1
Time to Completion for Trial 2, s
Number of Errors in Trial 2
Ashley Annie Hank Sally Cassandra Bob
650 289 277 860 278 334
37 35 34 21 31 114
565 304 239 398 316 254
57 103 72 12 12 43
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focused on the atomic mass property, because the regular color patterns associated with changes in mass could be more easily interpreted; other properties seemed confusing and almost random to the participants. Annie expressed this when she said, “density looks scary”, after she had selected the density property. She quickly chose another property. The novice participants recognized that different properties allowed local discrimination of elements, and would randomly change properties to fill in areas of the puzzle, but would usually return to the more regular changes observed with the atomic mass. It was clear that all students rejected a gross trialand-error method, but rather looked to increase the likelihood of a guess being correct. This partly explains the increase in the number of errors from the first to the second trials. Note that the time required decreased in the case of Ashley and Hank, and increased only slightly with Annie. Novice participants were not able to inductively construct the property relationships on the periodic table. It appears that the novice students were only able to recognize the simple relationships of mass and atomic number on the periodic table, and to notice the unique nature of the noble gases and fluorine regarding electronegativity. Hank best described this aspect of the strategy used by the novices, when he said, “[I]f I had more knowledge I might be able to make use of some of the other options of shading”; he concluded that using mass and atomic number was the best way to complete the puzzle, given his prior knowledge. Further, he described properties as being “grouped horizontally” (mass), and “grouped vertically” (ionization energy), so being able to predict this relationship would let him choose appropriate properties to solve the puzzle without as much trial and error. The sensemaking process of the novice participants showed some interesting variability. Hank seemed to demonstrate the most deliberate approach. As mentioned previously, he explicitly recognized information that he was missing, and the fact that he needed to rely on some trial and error to complete the puzzle. On the other hand, Annie had a less deliberate, more intuitive approach that relied on detailed perceptions of the color patterns observed. She stated: It goes orange, orange to almost like a gold color to yellow. The next are going to be green, the next row. I feel this is going to be bright green, I guess I was right [as she fills in the puzzle]. This is all only because of the color scale that is helping me. While she used the representativeness heuristic to choose colors, as well as using trial and error, she seemed to be able to use more complex information, looking for color patterns rather than individual color similarities. Further, she was quite willing to change her approach to solving the problem, and would work on different sections of the periodic table depending on success levels, and would change between each section depending on her success. Specifically, she would select mass to help her solve a few elements and then try another property before going back to mass. She recognized how mass was categorized by rows and referred to mass as being the “jackpot”: a term used when she recognized a local pattern. Further, Annie had a keen eye for distinguishing the colors, and used the most specific descriptive names when referring to the various colors. She recognized the need to be able to distinguish between elements, and would determine the utility of a particular property based on the number of different colors observed among the unplaced element blocks. It might be suggested that Annie had very well developed sensemaking
Sally showed the greatest average time to complete the puzzle. While these are not direct measures of success on the puzzle, it does tell us something about the general strategies used in each case. For example, a low number of errors reflect a process that did not rely on significant trial and error. The higher error rates suggest that a trial and error based strategy was used. Examination of the video captures of the students performing the activity support this assertion. Interestingly, Sally and Cassandra showed both the fewest average errors, and a significant decrease in the number of errors for trial 2. This suggests that they were able to improve the approach to solving the puzzle. In fact, Sally also showed a significant reduction in the amount of time required to complete the puzzle, a further indication that the method used to solve the puzzle was learned, and used nearly two months later (the time between interviews). Bob also had fewer errors the second time he performed the activity. A closer look at his strategy shows that during his first trial he chose electronegativity as the property to place the elements, and then ran into difficulty, and began guessing. During his second trial, he initially chose atomic number, stating, “I will pick, um, [pause] I guess I’ll go with atomic number...the way these pieces should be ordered with atomic number is the darkest blues should be the period 1.” Bob continued to complete the puzzle using only atomic number, which was a bit more effective than electronegativity, and required less guessing. Bob could predict which period the element block should go into, though he had some trouble distinguishing color shades. It is not clear from the data what led to this different choice of physical property, though we may speculate that frustration with the electronegativity property during the first trial might have influenced his choice. In both cases, Bob was unwilling to change properties while solving the puzzle. Three participants had more errors during their second run. This is consistent with an increased reliance on a type of trialand-error strategy. Qualitative data support this, as each of these participants directly indicated that certain placements of the blocks were made simply by guessing. For example, Hank chose the mass property, and explained, “It seems I can line these up, with horizontal lines, and, um, it seems to be working out through some trial and error.” So, by the second trial the novice students had determined that they needed to do more trial and error to explore the different properties. The increase in use of trial and error correlates with the level of chemistry background for each of the participants. This suggests that prior knowledge has a significant impact on the types of sensemaking processes used.21 Impact of Prior Chemistry Knowledge
The qualitative data were compared with respect to two groups: novice and advanced students (Table 2). The group memberships are chosen based on demographic data and general observations of puzzle solving strategies, as mentioned above. Keep in mind that the activity is designed to allow novice participants to infer periodic trends. It is the details of the strategy, and what is gleaned from the activity, that is important. Essentially, the sensemaking process used by novices was the well-known heuristic of “representativeness”.13 To choose where to put the element block, novice participants essentially compared colors, and assumed that elements with similar properties were near each other on the periodic table. Additionally, we observed that the novice participants often 1495
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Figure 2. Example of sensemaking process. Sally first organized the blocks by row using the mass property, and then selected electronegativity to determine the column.
Participants with Some Chemistry Prior Knowledge
processes when it comes to color discrimination, likely related to her experiences as an art student. It is important to note that Annie did try to relate chemistry knowledge to the colors of the elemental blocks. For example, when describing the trends under mass, she said, “Up at the top of the table where they are kind of a darker blue, it kind of seems like maybe they are cooler or maybe that means they are lighter.” When describing the trends under density she said, “I think the white in this one means they’re less dense.” These statements occurred during the first interview, by the second interview she stopped trying to relate colors, and the chemical properties, and just identified the general pattern of the colors. Ashley, on the other hand, worked more methodically, focusing on one region of the periodic table. In fact, when solving the most complex puzzle, Ashley began with the recognition of the high electronegativity of fluorine. She stated, “I placed that there because I remember from last time that only one of them had a high electronegativity” [on the puzzle, it is the only red block when the electronegativity property is selected]. From there she simply matched the colors of the nearest neighbors, occasionally choosing different properties. She explained, “I am still placing it anywhere there is the same color, and right now I am on the boiling point property, and trying all the blue.” Ashley’s unwillingness to deviate from a specific location on the periodic table is indicative of what Tversky and Kahneman13 called “insufficient adjustment from an anchor”, in which individuals’ expectation of change are much less than what is reasonable. This illustrates common impediments to success with the simplest sensemaking processes. Ashley would not venture far away from her anchor. Interestingly, it was possible to complete the puzzle this way, but resulted in significantly greater time required to complete the puzzle. These examples provide a striking model of the sensemaking processes observed among participants without much previous knowledge of the periodic table. One could speculate with regard to the degree that each of the novices would react to various forms of scaffolding for the activity; clearly, however, had this activity been intended to teach periodic trends to beginning students, the most effective scaffolding and preparation would likely be somewhat different for each participant. The observations also bring to light similarities and differences in the students’ sensemaking process. Hank was able to determine what information would be useful to complete the activity. Clearly, the variability in the sensemaking processes observed suggests that the sensemaking (i.e., process skills?) available to these students is not completely dependent on prior content knowledge.
Similar to the novice participants, the more advanced students used the property “mass” as an anchor in completing the puzzle; however, a better understanding of the organization of the periodic table allowed a more robust use of this property, namely, the understanding that the value of the mass wraps around the table, and allows the student to use other properties that complement the organization. For example, attending to the property mass easily allows the elements to be grouped by row, while other properties, such as electronegativity, allow better discrimination by column. Students with this knowledge were able to construct a multistep approach, in which elements were cataloged based on their mass, and then, by electronegativity or ionization energy. The multistep approach can be viewed as a complex sensemaking process requiring that participants anticipate the result of one property or another. This fits the “formulating models” process skill, in which the participant “exploits” a trend she has found in the data. Interestingly, the two participants who used this method, Cassandra and Sally, differed significantly in terms of chemistry background. From our observations, we can infer that Sally learned a method of solving the puzzle. Her second interview was almost two months later, yet when solving the p-block puzzle activity, she immediately chose mass and said, What I noticed before was that the color codes were across by rows, so I’m just going to match the row colors and kind of categorize them in the bottom [a work space below the periodic table] as I see them in the top [in the periodic table puzzle]. Once the blocks were categorized, she immediately switched the property to electronegativity, shown in Figure 2, and was able to quickly solve about two-thirds of the puzzle. Her initial trial of the puzzle took much longer, and while she grouped the elements by color before placing them, she ran through a series of different grouping choices before settling on the mass. This is perhaps the one example of inquiry learning observed in the study, where the unguided exploration of the elemental properties, with the goal of solving a puzzle, led to a greater understanding of the periodic table. Evidence from both the student’s words and actions, and from the decrease in time required for Sally to complete the puzzle from one trial to the next, suggests learning took place on the first trial of the activity. Examination of Sally’s first trial shows that she initially considered grouping the unidentified blocks by color, but experimented with several properties. She initially used electron affinity, and was trying to group the colors as columns. On the basis of her observations, she recognized that she must first group the elements with respect 1496
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Kahneman,13 “The internal consistency of a pattern of inputs is a major determinant of one’s confidence in predictions based on these inputs.” This consistency was generated by Bob’s somewhat-generalized knowledge of the relationships between the property of electronegativity, the element’s location on the periodic table, and the initial success of the placements. Bob’s knowledge of these relationships must not have included details of the electronegativities of the metalloids, which is not uncommon for undergraduates. Thus, we see evidence that a student’s previous knowledge, correct yet incomplete, had an impact on the nature of the sensemaking process employed to solve the problem of the periodic puzzle. This well-known limitation in the sensemaking process preempts the possibility that Bob would, through his inquiry, learn that the metalloids have similar electronegativities, and that perhaps other properties such as mass or density vary more among this group of elements: using those properties as well could have allowed him to complete the puzzle. The one instance of inquiry learning observed, the example of Sally noted above, could not be linked to any particular understanding of periodic trends. Instead this inquiry learning seems connected to the idea that the element groups (i.e., the columns) had similar properties, and that different relationships pertain between elements in a column and elements in a row. Additionally, to solve the puzzle, participants had to recognize that they must be able to discriminate between the various elements, which had to have significantly different properties (or colors). This second item is not really chemistry content knowledge at all, but rather a puzzle-solving skill (perhaps what some may call a process skill). In fact, Bob’s more advanced knowledge of the periodic table acted as a hindrance to the application of this skill. Cassandra used a complex sensemaking process to solve this puzzle, but she was not really seen to define new relationships; rather she was already aware of all the essential concepts needed to perform this task. This suggests that there may be a particular background level most amenable to inquiry learning, a prior knowledge level “sweet spot” of sorts, in which inquiry methods would be most effective. Of course, the as-yet-unknown size of this “sweet spot” and its relation to the nature of the activity has important implications for the use of inquiry-based activities. A second important implication of these results is that common heuristics used for decision making and the common errors associated with those heuristics seem to describe fairly accurately some sensemaking processes we have observed students use when they confront an unfamiliar puzzle. This was true independent of the students’ prior knowledge, although the prior knowledge, as evidenced by observation of static constituents, had a significant impact on how the sensemaking process was applied. Knowing possible common errors in decision-making heuristics is important for instructors wishing to apply inquiry-based methods because these heuristics may help define common trouble spots and suggest effective scaffolding methods.
to mass, and then use additional properties. This was retained and used during the second trial, and provides direct evidence of learning through inquiry. It is interesting to note that it was a process that Sally learned, and not specific facts or trends about the periodic table. While details of the periodic properties are inherent in the process she used, these details were not evident in her description of her solution. Essentially, she recognized that some properties categorized elements by row, while other by column. This is an important recognition, but not what is often expected of such activities. A third advanced participant, Bob, did not use such an approach (Figure 3). This participant provides an interesting
Figure 3. Another example of sensemaking process. Bob was able to complete this part of the p-block puzzle before he began to use trialand-error methods.
example of a student who has difficulty with solving the puzzle, despite demonstrating significant prior knowledge. While performing the initial stages of the activity, he demonstrated a complex mental model of the periodic table, based on the number of static constituents, referents and relationships, he used in describing trends on the table. This included relationships that linked ideas about atomic structure to the property, and explanation of how the properties changed with position on the table. However, when doing the more complex puzzles, Bob did not use a complex combination of properties (as observed with Sally, and Cassandra), but rather stuck stubbornly to a single property (in this case, electronegativity). Initially, electronegativity is an efficient property to select, as it provides some significant discrimination among elements, and allows someone with an understanding of the property to quickly place a number of elements in the correct locations (as was observed in this trial); thus, the sensemaking process was applied. In this instance, Bob is using classification, a sensemaking process that requires prior knowledge (operating with certainty). Nonetheless, the electronegativity property does not discriminate very well between the various metalloids, and so at some point a second property must be chosen to allow the elements to be discriminated and placed properly on the periodic table. Bob was unwilling to do this, even when reminded by the interviewer that he could select other properties. We see this behavior as a common error in the sensemaking process, similar to what was described by Tversky and Kahneman13 as the “illusion of validity”. This common error occurs when a person is overconfident in the ability of an observation’s to predict an outcome: in this example, the ability of the electronegativity property to predict an element’s location on the periodic table. According to Tversky and
For the Practitioner
On the basis of our results, we offer this synopsis for instructors interested in using active learning methods to introduce the periodic table to novice students. 1. The expectation that students will easily recognize periodic trends from elemental data seems to be overly optimistic; rather, our study suggests that even the organization of the periodic table with respect to mass 1497
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(10) Lesh, R.; Hoover, M.; Hole, B.; Kelly, A.; Post, T. Principles for Developing Thought-Revealing Activities for Students and Teachers. In Handbook of Research Design in Mathematics and Science Education; Kelly, A., Lesh, R., Eds.; Lawrence Erlbaum: Mahwah, NJ, 2000; pp 591−645. (11) Briggs, M. W. Models and Modeling as a Theory of Learning. In Theoretical Frameworks for Research in Chemistry/Science Education; Orgill, M. K., Bodner, G. M., Eds.; Prentice Hall: Upper Saddle River, NJ, 2007; Chapter 4. (12) Briggs, M .W.; Long, G. R.; Owens, K. Qualitative Assessment of Inquiry-Based Teaching Methods. J. Chem. Educ. 2011, 88 (8), 1034−1040. (13) Tversky, A.; Kahneman, D. Science 1974, 185, 1124−1131. (14) Johnson-Laird, P. N. Cognition 1994, 50, 189−209. (15) Pirolli, P.; Card, S. Psychol. Rev. 1999, 106 (4), 643−675. (16) Windschitl, M. What Is Inquiry? A Framework for Thinking about Authentic Scientific Practice in the Classroom. In Science as Inquiry in the Secondary Setting; Luft, J., Bell, R., Gess-Newsome, J., Eds.; NSTA Press: Arlington, VA, 2008. (17) Padilla, M. Research MattersTo the Science Teacher: The Science Process Skills (No. 9004, 1990). http://www.narst.org/ publications/research/skill.cfm (accessed Sept 2012). (18) Windschitl, M.; Buttemer, H. Am. Biol. Teach. 2000, 62 (5), 346−50. (19) Kind, V.; Taber, K. S. Science: Teaching School Subjects 11−19; Routledge: London, 2005. (20) Millar, R. Doing Science: Images of Science in Science Education; The Falmer Press: London, 1989. (21) Nelson, R. R. J. Econ. Behav. Org. 2008, 67, 78−89.
and atomic number may require some instructor scaffolding. 2. Students choose different strategies for completing an activity depending on their prior knowledge of the topic and their available sensemaking processes. Students with less-developed sensemaking processes need scaffolding specific to these process skills. For instance, in this periodic table example, some students may need to be told that properties providing a greater diversity of values will be more useful in positioning elements than properties that have values similar to adjacent elements. 3. The ability to use certain process skills does not seem to be correlated with prior knowledge, and in some cases, certain prior knowledge may hinder a student’s ability to complete an activity successfullystudent’s may overvalue the utility of certain knowledge in solving a problem. 4. Instructors should be aware of the common errors in decision-making heuristics and use them to provide effective scaffolding during active learning. Finally, by studying the development and application of students’ mental models during an open-ended learning activity, we hope to offer instructors a cognitive foundation to frame their interactions with students and to provide more information about effective scaffolding during active learning.
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AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We would like to thank Brian Reid for permission to use images of the periodic table puzzle, and the anonymous reviewers for their helpful comments. Funding for this research project has been provided by the National Science Foundation, Department of Undergraduate Education, Course Curriculum and Laboratory Improvement: 0736836.
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REFERENCES
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