Periodic Universe: A Teaching Model for Understanding the Periodic

Article Cite This: J. Chem. Educ. 2019, 96, 1367−1376

pubs.acs.org/jchemeduc

Periodic Universe: A Teaching Model for Understanding the Periodic Table of the Elements Matthias Bierenstiel*,† and Kathy Snow‡ †

Department of Chemistry, Cape Breton University, Sydney, Nova Scotia B1P 6L2, Canada Department of Education, Cape Breton University, Sydney, Nova Scotia B1P 6L2, Canada

‡

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S Supporting Information *

ABSTRACT: The Periodic Table of the Elements (PTE) is arguably one of the most central topics in chemistry. This article provides a critical review of current teaching practices of the PTE to high-school students and undergraduate university students. It also provides a new teaching model, the “periodic universe”, for understanding of the PTE through building on its foundational periodicity. Students learn through a guided re-creation of the PTE from simple periodic simulations and interdisciplinary processes. The periodic-universe teaching model directs students to conceptualize, rather than memorize, relationships between the elements by predicting patterns in progressively challenging simulated worlds. This mixed-method research project consists of both quantitative (n = 58) and qualitative (n = 15) responses from university undergraduate students, demonstrating the utility of inquiry-based learning of the PTE for novice chemistry students. Herein, we position the periodic-universe teaching model in the current educational literature of inquiry and interdisciplinary studies by outlining the function of the model and illustrating its effectiveness on the basis of empirical analysis with undergraduate students in a postsecondary-education setting. The results indicate that knowledge of the PTE increases after instruction with the model, and that nonchemistry-major students have increased engagement, understanding, and appreciation of the importance of periodicity to chemistry when presented with the periodic-universe teaching model. KEYWORDS: High School/Introductory Chemistry, Interdisciplinary/Multidisciplinary, Analogies/Transfer, Inquiry-Based/Discovery Learning, Testing/Assessment, Periodicity/Periodic Table

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understanding periodicity.5 Professional academic resources have begun to encourage an examination of periodicity with activities based on pattern recognition of element properties, the fundamental concept Mendeleev and Meyer used in the 19th century to create the first PTE. In 2005, Talanquer, mirroring Mendeleev’s work, engaged preservice science teachers through a simulation of periodicity known as “A Periodic Table for a Parallel Universe”.6 Talanquer’s model focused on discerning the impact of the simulation on prospective teachers’ pedagogical content knowledge (i.e., on their knowledge of how to teach). The aims of our teachingmodel research project, the “periodic universe”, differed from

INTRODUCTION The Periodic Table of the Elements (PTE) is arguably one of the most central topics in chemistry. Understanding the periodicity and hence the related predictability of elemental properties, on the basis of the similarities within a group and the variations along a period, is critical knowledge of the fundamental aspects of chemistry. However, instruction on the PTE, as the current education literature and introductory chemistry textbooks illustrate, is based predominantly on traditional historic perspectives coupled with quantumchemistry atomic theory (i.e., the Aufbau principle). This approach often requires students to memorize elements and their position on the PTE rather than to understand how the elements came to be positioned there.1−4 In a 2015 survey of 57 general chemistry textbooks, Brito et al. found that none described adequately the role atomic theory played in © 2019 American Chemical Society and Division of Chemical Education, Inc.

Received: September 12, 2018 Revised: May 20, 2019 Published: June 4, 2019 1367

DOI: 10.1021/acs.jchemed.8b00740 J. Chem. Educ. 2019, 96, 1367−1376

Journal of Chemical Education

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elements, facilitated by the development of pattern-recognition skills. Students are encouraged to find similar elements within their 3D models on the basis of the prescribed instructions for model creation (e.g., all noble gases use the same colored ball as a foundation). The physical manipulation and visualization allow students to begin understanding complex abstract concepts. The abstract nature of understanding elemental properties has led to innovation in the adoption of parallel metaphors not dissimilar to the mnemonic approach for concepts but allowing students to relate to chemical properties through stories or personalization of the rules. For example, instructors adopt a storyline approach to teaching 11 to 12 year old children the elements’ essential properties, which allows them to develop mental images for concepts of chemical change, bonding, and electrons.16 In this method, scientific theories replace a portion of the students’ misconceptions, although some students develop new misconceptions, and others are resistant to change.

those of Talanquer’s model insofar as we were interested in how teaching an understanding of the PTE impacts and engages undergraduate students. Our goal was to determine the efficacy of introducing the PTE through a series of simulations of periodicity in simplified, highly “periodic worlds”, which students then extrapolated to more complicated, less periodic worlds until they were able to predict the functions of the elements in our own world. As the complexity of research into the best practices of chemistry education cannot be understated, our periodic-universe-teaching-method pilot study aimed to pair academic improvement with holistic factors for a broad evaluation of the learning intervention.

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TEACHING THE PERIODIC TABLE OF THE ELEMENTS Salame et al.7 divides the cognitive elements of learning the PTE into two discrete skills: (i) conceptual understanding and (ii) application. Through evidence-based analysis of student testing, they identified a critical gap in knowing and applying chemical knowledge derived from the PTE. Addressing this gap is not a new challenge facing instructors of chemistry, according to Hoffmann and Hennessy;8 students often overlook the finer details of grouped elements’ periodicity in trying to predict reactivity. Furthermore, undergraduate students need to be encouraged to think critically about the PTE, as countless misconceptions developed through previous (mis)instruction can affect their learning in a postsecondary environment.7 Once students adopt false theories of chemistry, it can be difficult to challenge their thinking.9 Therefore, realworld approaches and transdisciplinary-learning designs have been adopted for the classroom to support bridging the gap between theory and practice.10,11

Inquiry-Based Learning of the Periodic Table of the Elements

A radical shift in the chemistry curriculum occurred in the 1960s,17 instigated by evidence from educational research respecting working-memory capacity, cognitive loading, and prelearning.17 Countries across Europe and North America began reorienting educational outcomes to reflect process rather than content-knowledge goals. Process orientation is at the heart of inquiry-based approaches to teaching the PTE. In 2006, a quantitative analysis of grade 10 students (n = 200) revealed, through test scores on knowledge and application, a significant improvement in understanding when educators adopted an inquirybased orientation: they asked students to make and evaluate predictions using the PTE instead of memorizing it.18 Another outcome of this study indicated that beyond academic improvement, students evidenced a positive attitudinal change toward chemistry.18 In 2012, Larsen et al. disseminated new technology adapted to create an online puzzle where students were challenged to order the elements of the periodic table based on their properties.19 Through color coding and trial and error, the students developed a strategy for organizing elements based on personally derived theories about grouping and ordering. Similar to Talanquer’s study,6 preservice teachers were encouraged to adopt an inquiry-based approach to pedagogical content knowledge: these instructors would ask students to derive a PTE or classification system for 12 elements from an “alien” universe on the basis of data from the aliens’ recordings of chemical properties. Most of the students identified increased interest in chemistry from this activity; they were also able to synthesize information that they may have previously held in isolation. A drawback to this approach was that novice learners found the exercise time-consuming and complicated, given the complexity of the provided information and the need to derive the rules for periodicity in addition to considering how to subsequently arrange the element table. After analyzing the concepts encountered by students seeking to understand the PTE, Criswell20 argued that derivation of the table is too complex to achieve in the curriculum’s usual time parameters (one or two lessons); he suggested a further refinement of the process through the use of an inquiry cycle (i.e., focus → exploration → reflection →

Traditional Approaches to Teaching the Periodic Table of the Elements

The traditional approach to teaching the PTE, even if chemistry instructors want to teach its underlying principles, often comprises lecture-style instruction and memorization of the elements and their properties. In this approach, the majority of the students simply memorize the lecture content by rote, a practice learned in high school and further fortified by standardized testing. One common strategy for memorization of content knowledge is based on the development in 2015 of a mnemonic helping students arrive at the electronic configurations of the elements built on previous visualizations (e.g., Yi’s orbital diagram or Hovland’s chessboard diagram).12 This may be considered an improvement over previous teaching models because it is based on the cognitive-load theory of breaking up information into discrete or more easily memorizable factors (i.e., chunking of information); however, it does not account for variability of true periodicity and will not function in all cases. Thus, students need to be independently taught exceptions to the mnemonic. Alternatively, educators use games for teaching the PTE (e.g., crossword puzzles or Bingo) to increase recall.13,14 Although the related preteaching encourages understanding of periodicity, the games themselves are akin to drills assessing recall capacity. They may produce content knowledge, but they do not elucidate the underlying principles. A third example of traditional teaching is 3D modeling: students create their own manipulatives, building elements and placing them in their correct locations on a periodic-table chart.15 This method is based on content acquisition and learning the features of the 1368



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Figure 1. World #1 ionization graphs showing periodicity of groups of four elements, with every fourth element, i.e., the noble element, being particularly stable.

model aims to build on previous work in relation to inquirybased learning and transdisciplinary approaches in order to present a simple inquiry that is relevant to novice chemistry students, one that does not ask them to recreate the laws of periodicity but rather to apply them to the standard IUPAC periodic table used today. Herein, we present an educational model for examining periodicity through the increasing complexity of problem-solving within a one- or two-lesson time frame. It was our hope in developing this method that it would not only help younger and less experienced undergraduate students achieve academic success but would also motivate and interest them. The research questions we examined in our pilot project were: how does the periodicuniverse teaching model affect novice undergraduate students’ knowledge of the PTE, and how does the understanding affect engagement toward chemistry?

application) that positions the derivation of the table over a prolonged time so the complexity of periodicity can be reiterated and reconceptualized. Transdisciplinary Concept Development for Deep Understanding

The review of the literature on teaching the PTE also revealed a lack of investigation into the impact of the cultural bias upon which the PTE is built.21 The Cartesian coordinates and the left-to-right sequence of increasing atomic numbers in the standard PTE are clearly based on Western languages, which are written from left to right. One can assume a flipped arrangement of the PTE if its pioneers had been Chinese or Japanese scientists, as those languages are written from top to bottom. Moreover, Swedish scientist Jöns Jacob Berzelius moved the representation of elements from symbols to capitalized, one- or two-letter abbreviations of the Latin alphabet. While cultural aspects and biases are not the major factors in understanding the PTE, they help in providing a critical perspective of the current standard PTE. Furthermore, there have been few attempts to include the historical context of culture on the design of the standard PTE that is adapted by IUPAC; rather, there have merely been a few pauses to discuss the history of Mendeleev and Meyer in particular, or the mid19th century more generally. Ben-Zvi and Genut argue that if teaching approached the possible changing form of the PTE, students would be more cognizant of the scientific thinking from which it was derived.22 In bringing together what is known about the best practices of teaching the PTE, the periodic-universe teaching model attempts to fill some of the gaps highlighted in the literature in relation to teaching and learning periodicity. The model attempts to move beyond memorization and drills, instead guiding students toward scientific thinking. Additionally, the

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DESIGN OF THE LEARNING INTERVENTION: THE “PERIODIC UNIVERSE” TEACHING MODEL The periodic-universe teaching model is built on the promotion of inquiry or problem-based learning skills and, less dominantly, on the role of culture on the development of scientific communication. The model asks students to participate in a series of simulations of progressively complex worlds through a facilitated inquiry into the development of a periodic table for each world. The principles of this method are based on simplified physical laws and rules, which become increasingly complex with each world. The goal is to teach for understanding, with the application of five basic rules: (1) Bohr’s atomic model (i.e., a positive nucleus is surrounded by negatively charged electrons) applies. (2) Coulomb’s law of electrostatic interactions of positive q ×q and negative particles applies, with E ∼ 1 2 2 (with qx r 1369



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being the charge and r being the distance between the charges). (3) Ionization energy (i.e., the energy that is required to remove one electron from an atom or ion, determined using Coulomb’s law) applies. (4) The chemical properties of an element depend on the number and arrangement of electrons around a nucleus. (5) The charge of the atom or ion is the atomic number of the element subtracted by the number of electrons present. Rather than being presented with the elements in the format of an ordered table a priori, students are initially given ionization-energy graphs and then asked to build a periodic table and predict how the elements will react with one another. This allows students to develop data-interpretation skills, rather than providing them with a periodic table as a fait accompli that they are expected to memorize. The lesson begins with students discovering the pattern of an ionization-energy graph with only few elements; it follows a repeating pattern that is easy to interpret (Figure 1). Students are presented with 20 elements of a hypothetical world that is highly periodic but follows the physical and chemical rules of our world. (For simplicity, the elements are labeled Aa, Ba, Ca, etc.) Students are then asked to develop an element table for this world that will reflect the properties of the ionizationenergy graphs (Figure 2). This exercise asks students to apply

5. Students are asked to identify the noble elements (i.e., the elements that are relatively unreactive because they are at a local maximum in ionization energy, as in rule 4). Instructors tell students that a relative maximum in ionization energy provides a relative stable state; thus, removal or addition of electrons is energetically unfavored. Further to that, instructors explain that other elements seek the noble electron configurations, as illustrated by the second and thirdionization-energy graphs for the +1 and +2 charged elements of Figure 1. An element that is positioned to the left of the noble element will have a −1 charge as it accepts one extra electron in order to achieve the isoelectronic (and stable) structure of a noble element (rule 5). Instructors explain that the principle of adding electrons to an atom or ion is called electron affinity, as opposed to ionization energy, which removes electrons. Although electron affinity has similar patterns, its impact is typically smaller than that of ionization energy. An element positioned to the right (i.e., the first element of the next row) will lose one electron to become an ion with a +1 charge and, again, gain the isoelectronic (and stable) structure of a noble element. Once students understand these five rules and how to apply these to a graph of ionization energies, the fun portion of the lesson begins: modeling a sample compound for the students, instructors ask students to make predictions about compounds. For example, the ionic compound formed by elements Ea and Ka is EaKa, whereas Fa and Ga generate FaGa2. Instructors model these samples specifically to illustrate oxidation states of +3 and −3 for group I and III elements, respectively, as a means to clarify the periodicity rules. The result of teaching the rules this way, using World #1, is that students must process information rather than rely on rote memorization. In addition, students build confidence in extracting information from a given periodic table. Once students are comfortable with the 20 elements of World #1, instructors provide them with the graphs of elements in Worlds #2 and #3, which increase to 24 elements (6 × 4 matrix) and 28 elements (7 × 4 matrix), respectively. Worlds #2 and #3 are limited to four rows each to allow for repeated practice with the structure from World #1 and not to get too unwieldy large (see the Supporting Information for details about Worlds #2 and #3). There is no change in the overall periodicity; similar to World #1, the ionization energies of all elements in a period will increase. The purpose of Worlds #2 and #3 is to provide, through ionization-graph interpretation and oxidation-state assignments, a repetition of concepts and increased practice. Again, for simplicity, instructors only provide students with the first ionization graph to arrange an element table. Second and third ionization energies, along with electron affinity, are only needed for the conceptual background of the oxidation states. The preferred stable oxidation state of any given element can now be obtained from the table. Instructors introduce World #4 after students have gained confidence with a balanced number of elements in each of the periods of the previous three worlds. In World #4, the overall pattern of an increase of first ionization energy within a period is kept, but the number of elements in a period increases incrementally (Figure 3). This 30-element world has an arrangement of 2 + 4 + 6 + 8 + 10 elements. It no longer allows for the creation of a simple a × b matrix as in the first three worlds. As before, instructors ask students to arrange the elements in a table and discuss their positionality and periodicity. Because World #4 presents a new conceptual

Figure 2. Periodic table of World #1 that correlates to the ionizationenergy graph of Figure 1. The concept of oxidation states is readily introduced.

rules 2 and 3 in their development of the table. In their process of creation, the students must address the removal of an electron and the generation of a positive ion. In “World #1”, the 20 elements can be arranged in a 4 × 5 matrix that is clearly visible and is directly linked to the ionization-energy graph of Figure 1. A 20-element world allows for a 4 × 5 matrix, which is less confusing for students than a 16-element universe (4 × 4 matrix) that presents an equal number of groups and periods. The matrices students create might read left-to-right, right-to-left, bottom-to-top, or top-to-bottom; it is at this point instructors can introduce the concept of cultural bias in reading and writing conventions and its impact on table design, as discussed earlier in this article. The next step is to increase the complexity of the simulation through the determination of oxidation states using rules 4 and 1370



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Figure 3. First ionization graph of World #4 with highlighted elements per period.

Figure 4. Visualization of four different table arrangements for World #4. Solid arrows indicate noble elements (oxidation state of 0), and dotted arrows indicate “alkali” elements (oxidation state of +1).

instruction gives rise to multiple “what if” questions and encourages students to make and test predictions, as well as to challenge each other. Instructors can reignite a discussion about cultural preferences because the representation of all four tables in Figure 4 is correct. The interpretation of the given table format will be different. For example, the V-shaped

problem to the students, they usually go silent for several minutes before beginning a loud discussion as they grapple with determining the new arrangement of the table. In some cases, the students will arrive at the solution independently, but often instructors need make shape suggestions: a staircase shape, a V-shape, or a pyramid shape (Figure 4). This 1371



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end of the row; +7 to reach the end of the previous row; and +5, which is the electron configuration of group II. For students these are valid answers, but instructors then explain that the high energetic cost of charge separations will make the high oxidation states less likely. For example, the group III elements (Ca, Ka, Sa, and Ab in Figure 6) have three potential stable oxidation states, such as +1, by being positioned to the right of group II; +3, by being positioned three spaces from group VIII; and also −5, by being positioned five spaces to the left of group VIII. The oxidation state of −5 is large compared with +1 and +3 and therefore less probable because of the large charge separation. The most dominant oxidation state in group V is −3. Oxidation states +3 and +5 are theoretically possible but less likely because of unfavorable energies and large charge separation for +5. Instructors outline that elements in group IV can have +2, +4, and −4 as oxidation states, which are all within reasonable energetic levels and more likely to occur. Instructors present a culminating activity in World #6, which represents our known world in a somewhat simplified firstionization-energy-graph arrangement (Figure 7) and its tabular

table (Figure 4d) has the arbitrary preference of having oxidation-state rules applied vertically along a group and thus coincides with the Eurocentric left-to-right and up-to-down reading pattern. The level of complexity is increased again with the final two worlds (#5 and #6). The focus of World #5 is to introduce the concept of multiple oxidation states (Figure 5). Similar to the

Figure 5. First ionization graph for World #5 for the introduction of multiple oxidation states.

early and highly periodic worlds previously examined, World #5 has 32 elements that can be arranged in an 8 × 4 matrix (Figure 6). The difference introduced here is that the second

Figure 7. First ionization graph for World #6, a simplified graph for earth (our known elements).

representation (Figure 8). It combines all the concepts provided to the students on the guided trip through increasingly complex world simulations. It is important to state that World #6 is a simplified expression of our world and does not incorporate ionization-energy trends, such as those for nitrogen and oxygen founded in Hund’s rule and within the transition-metal block. However, students can now begin to work with known elements and make predictions on the basis of their understanding of the foundations of chemistry and periodicity and the extraction of data from ionization graphs.

Figure 6. Periodic table and selected oxidation states for World #5. The less dominant oxidation states are in parentheses. The complete oxidation assessment is group I: +1, (−1), (−7); group II: (0), +2, (−6); group III: +1, +3, (−5); group IV: +2, +4, −4; group V: (+5), (+3), −3; group VI: (+6), (+4), −2; group VII: (+7), (+5), −1; and group VIII: 0, (+6), (+8), (−8).

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METHODS FOR EVALUATION OF EFFECTIVENESS OF THE “PERIODIC UNIVERSE” TEACHING METHOD The authors used the periodic-universe teaching model for many years with perceived success; thus, we attempted to validate personal perceptions through trials of the model with two distinct groups: science- and nonscience-engaged students. Our mixed-methods approach involved collecting both quantitative and qualitative data about the success of the teaching intervention. Quantitative evidence was gathered through the use of pre- and post-tests (see the Supporting Information) that examined student knowledge of common oxidation states, binary salt composition, and atomic radii. An

element of each row has a relatively high first ionization energy, which makes this electron configuration relatively stable. The stable electron configurations states are thus not only the configurations for the elements at the end of a row (i.e., the noble elements) but also the configurations for the elements in the second group. Any element can now have multiple stable oxidation states (i.e., they can be isoelectronic with group II and group VIII members). In theory, an element of group VII can have three oxidation states: −1 to reach the 1372



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Figure 8. Table for World #6.

students required to take a 1000-level introductory generalchemistry course for the science- or engineering-degree program. Because the vast majority of the students arrived from a number of the region’s different high schools, they possessed differing levels of chemistry knowledge and competencies. In an attempt to mitigate personal knowledge and anxiety in entering university, the trial was conducted midsemester with the hope that some leveling effect in relevant knowledge had occurred by that point. All students in a firstyear introductory chemistry course taught by one of the authors were subjected to the teaching method as part of the normal instruction of the course. Students were offered the opportunity to participate in the research study by allowing their pre- and post-test sets for the lesson to be analyzed for the purpose of research and publication. Students were informed their participation had no bearing on their course achievement; to ensure their anonymity from the professor and researcher, the results of the pre- and post-tests were not reviewed until after final term grades were submitted. In Student Group 1, 58 students agreed to participate by letting their pre- and post-tests be included for analysis. As all of these participants were self-selected science and engineering students in their first year of general science programming at the university, it was deemed their pre-existing interest and engagement in chemistry could not serve as a complete measure of how engaging and impactful this instruction method was. What follows is the recruitment and participant profile of Student Group 2. Participants in this group were students pursuing a Bachelor of Education degree. These students were asked in two separate classes (Elementary Science Methods and Secondary Science Methods) if they would like to participate in the research by attending a model lesson and giving qualitative feedback. Fifteen students agreed to participate. Of these students, eight were science majors (not chemistry) from their first undergraduate degree, and seven were not. Their backgrounds in science ranged as follows: only high-school chemistry and no science education at the postsecondary level (n = 1); some postsecondary science instruction but no chemistry (first-year biology and geology courses) (n = 5); first-year postsecondary chemistry and biology courses (n = 2); first-year postsecondary introductorychemistry and second-year organic-chemistry instruction (n = 6); and a minor in chemistry with a B.Sc. (biology) (n = 1).

additional question to examine students’ perceived self-efficacy was included, which asked them to rate their knowledge of the period table using a 7 point Likert scale, where 1 represented “very poor”, 7 represented “very well”, and 4 represented “neutral”. Both pre- and post-tests contained similar (but not identical) concept questions, none of which were directly copied from the learning-intervention examples. Qualitative evidence consisted of written feedback on an open-ended questionnaire that sought to determine students’ comfort level with science and chemistry generally and the impact of the teaching model on their comfort level. Two parallel versions of the questionnaire were used to account for the difference in students’ background education in science (see the Supporting Information). Prior to engaging student groups, ethical approval was obtained from the Research Ethics Board of the university where the testing was conducted. The trial period consisted of a 60 min instruction period for each student group using the periodic-universe teaching model and student participation in either the quantitative- or qualitative-data-collection procedure. Quantitative analysis comprised descriptive statistical analysis of pre- and post-test scores from the assessment instrument, whereas qualitative analysis consisted of coding student written narratives for themes using the methods for emergent thematic analysis as outlined by Saldana.23 There are critical limitations to the validity of the testing conducted, as is the case with most small-scale explorations of “best practices” for teaching, particularly when empirical methods are used. This was not a large-scale study; therefore, the total sample size was insufficient for statistical significance to be determined. Additionally, to ensure parity of education for all students, a control group adopting a traditional teaching approach was not incorporated. Finally, given the nonscience students’ anxiety about tests about chemistry, the quantitative method of pre- and post-testing was not adopted. Although the results in the following section cannot be presented as a definitive measure of success, the insights gained from this analysis offer value as a pilot examination of inquiry- and problem-based learning of the PTE.

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RESULTS AND ANALYSIS OF TESTING WITH SCIENCE AND NONSCIENCE POSTSECONDARY STUDENTS What follows is the recruitment and participant profile of Student Group 1. Participants in this group were first-year 1373



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Quantitative Analysis and Discussion of Student Group 1 Trial: First-Year General-Chemistry Students

In total, 58 students responded for the pre- and post-tests, and a histogram representation is provided in Figure 9. After the

Figure 10. Students’ perception of understanding of the periodic table from a 7 point scale (1, know very little, to 7, know very much) for both classes’ preassessment (triangle markers) and postassessment (square markers). The average went up from 3.97 to 4.92, which is significant with more than 2 standard deviations.

Figure 9. Frequency of marks from the preassessment (triangle markers) and postassessment (square markers), with n = 58 respondents and a maximum total mark score of 12 for three questions.

Qualitative Analysis and Discussion Student Group 2: Preservice Teachers

Three themes emerged from an analysis of the questionnaires, which consisted of 10 open-ended questions about students’ experience with the periodic-universe teaching model. Students reported a positive attitude to chemistry learning, a deeper understanding of the purpose and construction of the PTE, and an appreciation for the activity of learning chemistry when it is positioned in an inquiry-based and interdisciplinary approach to learning. With regard to students’ positive attitude to chemistry, all students used at least one of the following terms to describe their learning experience: “easy”, “simple”, and “thoroughly engaged”. This illustrates a sense of excitement and enjoyment in learning periodicity as presented. One postsecondary student stated: “I think it [the periodic-universe teaching model] is interesting [for me] to have a little story to it, it encouraged nonchemically minded students [to engage]”. All students, regardless of background, also claimed some form of deeper understanding of chemistry. Students described this as “discovery”, “thinking like scientists”, and thinking about “why things are the way they are”. Profoundly, one of the most chemically experienced participants stated, “I didn’t really know there was any pattern to the table so it [the periodicuniverse teaching model] made it easier to understand what is on it, now I know why”. Another participant with a chemistry education limited to high school stated, “I learned more in this workshop than I did in my entire grade 11 course”. Finally, in response to the questions about teaching and adoption of the periodic-universe teaching model, participants responded that the method lent itself superbly to interdisciplinary understandings of mathematics, because of the calculation of oxidation states needed to build the table, and scientific thinking through prediction and testing of predictions. They also indicated the model was effective because the stepwise approach reflected cognitive-loading theory, starting with simple analysis and moving to increasingly complex pattern deduction. Four of the 15 participants described these tasks specifically as “real science”, as opposed to theoretical and rotelearning patterns. One participant noted, “When I was in High School, it [the periodic table] was taught in a complicated waythis way, with diagrams [and analysis] was great. I

periodic-universe-teaching-method lesson, 75.8% of the students in this group achieved 10 or more points out of 12. A total of 34.5% of students achieved a perfect score (12/12). This contrasts markedly against the preassessment, where there was a much larger range in scores with an average of 7.5/12. For the preassessment, the median score was determined to be 9 with a standard deviation of 3.43, whereas the median for the postassessment was 11 with a standard deviation of 2.67. Without a control group, we cannot account for the impact of the teaching itself. However, the smaller range of response is illustrative of a leveling effect of the method on chemistry learning. Because of the small sample size of the pilot study, we cannot fully account for pre-existing knowledge. It was found that for 10 students, there was no change pre- and post-test. Of these 10 students, 8 scored 12/12 on both tests, indicating they entered the lesson with all of the prerequisite knowledge. Histographic analysis of the difference in the pre- and post-test scores of all individuals is illustrative of a positive value for improvement and a negative value for decline. The remaining 48 students increased their scores from pre- to post-test. As the pilot did not include a control group, the actual impact of the model compared with traditional teaching cannot be definitively determined. However, attitude toward learning and self-efficacy have been illustrated as important indicators for academic achievement. To measure attitude, we evaluated students’ response to a request that they rate their perceived confidence (Figure 10). These responses fell into a normal, bell-curve-like distribution, with the median score of 4 (neutral response) increasing a full point to 5 (somewhat confident). Examined individually, each student pre- and post-test increased by at least one, again indicating the method has a positive impact on students’ perceptions of efficacy, an important claim given first-year chemistry courses frequently leave students with reduced confidence in their ability to succeed.24,25 1374



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to interpret the world known as the PTE. From the analysis of quantitative and qualitative data of self-selected chemistry students and nonchemistry students, it was determined that the periodic-universe teaching method offers potential for improvement over conventional instruction of chemistry and that it deserves further in-depth examination and discussion. The periodic-universe teaching method should not replace current teaching models of the concepts surrounding the PTE; instead, it should be a short, constructive teaching unit that will help students reach an understanding of its underlying principles.

actually started to understand the periodic table.” Finally, in describing the current structure of the table in a cultural context, one student noted the importance of global thinking: “it gets you thinking about the table and why it is the way it is”. The success of the periodic-universe teaching model warrants further examination. Although of the 58 first-year students tested in Student Group 1, 48 showed improvement, we are unable to demonstrate that the teaching itself was the exclusive reason for student progress. A new test with a control group, accompanied by an examination of the impact of the method over time, would allow for stronger evidence of the model’s impact on student learning. The 10 students who did not improve had already achieved the top score on the pretest, indicating our testing method needs refinement to ensure that all students are challenged or reach a challenge point. Additionally, a larger-scale test with greater numbers of students would allow us to better evidence the differentiation of students’ knowledge before and after the teaching intervention. With all these limitations in place, we can nevertheless claim that the periodic-universe teaching method was not detrimental to learning, as the majority of the students progressed and improved their results. Furthermore, we have clear evidence that the method offers students an opportunity to improve their attitudes about and experience with chemistry concepts. The qualitative results presented from the predominantly nonscience students offered insight into the challenges they face in understanding periodicity and its role in chemistry and the development of the PTE. The periodic-universe teaching model was designed after extensive review of practice, with the aim of distancing students from rote memorization and application and encouraging them to “think like scientists” through inquiry and transdisciplinary examinations. Mathematics and graphical modeling were chosen as they were found to be best aligned with students’ learning needs; they also taught skills related to the actual challenge of the task at hand. Instead of beginning without rules and asking students to derive them, we attempted to simplify the process of discovery by focusing on the task (the arrangement) given the rules for periodicity, which allowed the task to be completed in a shorter period of time, which was an issue raised by previous examinations of “Mendeleev for a day” learning activities. The students’ responses indicate that we have found an appropriate balance of inquiry and simplicity; however, more testing of the teaching method is needed. Finally, we asked students to think about the impact of culture on the constructs we use to describe science. Although students did not address this in their qualitative comments, our observations indicate that this is an important aspect of critical thinking that will support chemical understanding over time.

Implications for Instruction

In the development of the teaching model, there were three key design principles that can offer insight to others who may wish to refine the model. 1. Simplicity: one discrete objective was selected as the basis of the inquiry, and students were given the tools to examine this objective. 2. Visual representations: the presented ionization-energy graphs, as well as the graphing of alternative tables in relation to the observation states, allowed students to more comprehensively understand the PTE (which itself is a visual representation). 3. Transdisciplinary approaches that authentically reflect Mendeleev’s work: the transdisciplinary lenses we selected deliberately aligned with the work of the task in order to avoid overcomplication of the process and to allow for deeper insight into “why things are the way they are”. The periodic-universe teaching model can also be used to challenge students’ conceptions and their understandings of the PTE. For example, a theoretical world where shielding decreases within a period (i.e., the most stable electron configuration is not at the end but at the beginning of a row) will have the noble elements at the beginning of the row. Also, Hund’s rule of stability of half-filled orbitals, as seen with nitrogen and oxygen in their first ionization energies, can be challenged in a simulated world that has an odd, rather than even, number of elements in a period.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00740. Example of PowerPoint slides from World #1 to World #8 for the presented periodic-universe teaching method; three examples (Worlds #9a−c) of advanced universes that have different first-ionization-energy graphs; survey instruments for quantitative analysis (pre- and postassessment tests); and open-ended, qualitative-feedback questionnaires (PDF)

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CONCLUSION In creating his original chemistry textbook, Mendeleev was concerned that chemistry students view the subject not simply as a huge collection of facts but rather as a set of laws with an interpretable order.26 It is interesting that in the common practice of teaching the PTE, which often involves memorization, this element of interpretation is sometimes neglected. Our educational research attempts to restore the importance of understanding the PTE; we aim to achieve this through simplified periodic-world simulations that allow both experienced and novice undergraduate students an opportunity to evaluate and query the creation of the visualization we use

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Matthias Bierenstiel: 0000-0002-8433-2664 Notes

The authors declare no competing financial interest. 1375



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Article

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ACKNOWLEDGMENTS The authors would like to thank the students of Cape Breton University for participating in this study. We also thank Patricia Betts, who assisted in conducting the quantitative method with B.Ed. students in her methodology courses for teachers, and Julie Sutherland, who proof-read and copyedited the manuscript.

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REFERENCES

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Periodic Universe: A Teaching Model for Understanding the Periodic

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