Chapter 14
Systems Thinking as a Vehicle To Introduce Additional Computational Thinking Skills in General Chemistry Downloaded via AUBURN UNIV on August 21, 2019 at 05:52:21 (UTC). See https://pubs.acs.org/sharingguidelines for options on how to legitimately share published articles.
Thomas Holme* Department of Chemistry, Iowa State University, 2415 Osborn St., Ames, Iowa 50011, United States *E-mail:
[email protected] Water chemistry is proposed as an example where incorporating systems thinking approach can improve mathematical reasoning for students in general chemistry. These advantages are gained with relatively modest mathematical manipulations, such as how does one compute the volume of a pollutant entering an ocean/gulf from a river. Students are accustomed to calculating volume using the familiar lenght x width x height formula; changing the demands on this idea, even modestly to account for river flow rates rather than a length, provides important opportunities for enhancing computational thinking.
Introduction General chemistry courses have long included important quantitative skills as key learning objectives. Carrying out quantitative tasks in chemistry is sufficiently important that a number of studies have established connections between math preparation and course performance in general chemistry (1–9). This level of importance for mathematical skills has a strong influence on the perceptions of both teachers and students in general chemistry. For example, instructors have noted concerns that context-based approaches to chemistry curricula may not provide students with the level of mathematical rigor needed for continued chemistry studies (10). Additional studies have found significant differences between male and female students in terms of liking mathematics and physical sciences (11), with secondary school-aged girls notably less interested in these subjects. These types of studies suggest that (a) connections between math and chemistry are important when developing a curriculum, and (b) there are factors that influence student impressions of the desirability of studying chemistry that may be connected to mathematics. In addition to these overall concerns, specific math-heavy topics within chemistry, such as kinetics, have been the subject of studies on the role of mathematics in student understanding (12). One feature of these studies is that they are largely focused on the role of math in the fundamental aspects of the quantitative description of chemistry. Researchers have identified numerous concerns with regard to student understanding © 2019 American Chemical Society
Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
of traditional mathematically related chemistry topics and the ability of students to utilize their math skills within the chemistry context (13, 14). With prior work suggesting that students struggle with math applications in the traditional topic curriculum of chemistry, how can chemistry educators respond to new demands that arise with curricular intervention? For example, the Next Generation Science Standards (NGSS) incorporate mathematics with skills that go beyond calculations and include computational thinking (15). While still important, it is not clear if the prior emphasis on skills such as algebraic manipulation of common expressions in chemistry (13) would be able to address this new push for computational thinking. In addition, the NGSS also notes the importance of systems models as a cross-cutting component of education across all of the sciences, including chemistry (16). Recent work in defining skills as represented in the NGSS identifies two concepts: computational thinking and systems thinking, which both present challenges to define (17–20), let alone incorporate in existing general chemistry curricula. For the purposes of discussions in this chapter, we will utilize the initial set of computational thinking skills identified by Weintrop et al. (20), to designate characteristics associated with computational thinking: 1. 2. 3. 4. 5. 6. 7. 8. 9. 10.
Ability to deal with open-ended problems Persistence in working through challenging problems Confidence in dealing with complexity Representing ideas in computationally meaningful ways Breaking down large problems into smaller problems Creating abstractions for aspects of a problem at hand Reframing a problem into a recognizable problem Assessing the strengths/weaknesses of a representation of data or representational system Generating algorithmic solutions Recognizing and addressing ambiguity in algorithms
It is clear that some aspects of the problem solving traditionally encountered in general chemistry classes touch on some of these skills. At the same time, there are aspects of this listing that tend to go beyond the “end-of-chapter” style exercises commonly found in the chemistry curriculum. Systems thinking also presents a challenge when identifying which definition is to be considered in a given context. Assaraf & Orion (21) have categorized many of the skills and abilities needed to understand the hydro-cycle system into eight categories. Because the specific example described in this chapter also touches on the biogeochemistry of water, the following set of categories represents a useful way to organize the definition of systems thinking for the present discussion: 1. 2. 3. 4.
The ability to identify the components of a system and the processes within the system The ability to identify dynamic relationships among the system components The ability to identify dynamics relationships within the system The ability to organize the systems’ components and processes within a framework of relationships 5. The ability to understand the cyclic nature of many systems 6. The ability to make generalizations 7. Understanding the hidden dimensions of the system 240 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
8. Thinking temporally, including retrospection and prediction To incorporate this set of attributes into a curriculum represents a relatively high level of instructional dedication to the importance of systems thinking. This chapter does not suggest that this high level is required in general chemistry, but rather that finding ways to connect more traditional chemistry topics to this type of reasoning is helpful not only for introducing the idea of systems thinking to students, but also in honing their knowledge of fundamental chemistry content and how it fits in with the bigger picture of science knowledge. In particular, we will argue that students are accustomed to thinking of chemistry content at what amounts to the laboratory scale. By asking questions about whether that is the correct boundary to consider, we can provide enhancements in terms of how well students learn the chemistry, how well they can use computational thinking, and how they can begin to approach systems thinking attributes. Ultimately, the longstanding challenges students have traditionally faced with mathematical reasoning in general chemistry might now include new challenges for computational and systems thinking. Therefore, the process by which traditional chemistry content coverage can be expanded now incorporates key components of systems thinking merits consideration. Another component of the NGSS that is relatable to system challenges lies in the cross-cutting concept of scale (22). In chemistry, the most commonly considered challenge related to scale has been how students understand the atomic/molecular scale (23). Nonetheless, the ability to apply fundamental chemical concepts to understand regional or global scale issues is also an important skill related to this crosscutting concept. Context and Systems Thinking The idea that presenting chemical ideas within real world contexts has been an active area of curriculum development for decades (10, 23–26). This prior work represents an important resource for enhancing systems thinking components in chemistry classes. For example, in biology the connections between contexts and more complete systems thinking have been studied (27). The idea of expanding previously considered concepts of context-based curricular ideas in chemistry with approaches that explicitly include the previously enumerated components of systems thinking appears to be worth considering. One important concept for establishing a rich context basis lies in establishing connections between chemistry and the needs of the earth and human society. One useful noteworthy context for the curricular concepts presented here is that of “planetary boundaries” (28, 29). This is the concept that there are aspects of the human/planet system that have, according to best scientific estimates, progressed past tipping points that would assure long-term sustainability. While there are several categories to explore in the description of planetary boundaries, the two with the most direct connection to the system thinking ideas presented here are “land system changes” and “biochemical flows”. It should be noted that prior work (21) on systems thinking has identified the latter as “biogeochemical” in nature, but because of the connection to the planetary boundary framework, this chapter will use the term biochemical flow for this concept. Land system change research currently tends to focus on rain forest changes in locations such as Amazonia (30), but the land use changes made centuries ago in North America can still provide important context and systems thinking perspectives today (31). Historical land use change has served as a valuable context for enhancing ideas around both sustainability and systems thinking in the first semester general chemistry course at Iowa State 241 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
University for several years. Like most of the Midwestern United States, a large fraction of the land in Iowa is planted with row crops each year. In 2017, over 23 million acres of corn and soybeans were planted in Iowa out of a total area of roughly 36 million acres. Prior to the large-scale settlement of the area by European immigrants to North America, this area was mostly tall-grass prairie. These land use changes have a direct impact on biochemical flows, and the combination of these factors provide an accessible way for students to apply water chemistry knowledge commonly taught in general chemistry to the understanding of larger scale challenges for earth and societal systems.
Water Chemistry Content Water chemistry is of sufficient importance for the understanding of chemistry that it commonly appears in several subjects of current general chemistry textbooks. Because the textbook is arguably the most influential artifact for content coverage in this (or almost any undergraduate chemistry) course, one way to assess the content coverage is to catalogue textbook coverage. We considered the coverage in nine relatively recent textbook editions (32–40) and found that the water chapter routinely follows the initial chapter on stoichiometry in traditional general chemistry textbooks. The information in Table 1 shows a remarkable level of similarity in coverage of fundamental concepts. It also shows relatively modest application coverage; this judgement is based on the observation that at least a section of the narrative has been dedicated to the application. Water comes up again in many of these textbooks, and while applications are possible there, the key point for the current discussion is that there is only a modest level of context-based motivation presented in most general chemistry textbooks when water chemistry is introduced. There are also four areas where calculations of some kind are included (as indicated by the shading of the rows with such mathematical content). Table 1. “Early” Water Chemistry Chapter Content
a Equilibrium ideas for water.
from seawater.
b Hard water.
c Ion exchange for hard water treatment.
d Obtaining metals
e Spectrophotometry to determine concentration.
The Opportunity for Systems Thinking Based on Water Chemistry The event that brought a sense of immediacy to the issue of water chemistry and water quality in central Iowa (where Iowa State is located) was a lawsuit filed by the Des Moines Water Works (DMWW) against upstream rural Iowa counties in response to the cost the DMWW incurred for 242 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
treating for nitrates (41). Because water treatment to create potable drinking water includes all of the reaction types commonly covered (see Table 1) in acid/base chemistry, precipitation, and ultimately redox chemistry, this topic seemed ideal to add context components related to systems thinking. Our method for incorporating systems thinking in this course is to ask the following questions: “When we consider this chemistry, is the boundary of what’s going on in a beaker in the laboratory too limiting? What if we expand the boundary of what we are considering?” These questions cause students to think about precipitation as a reaction that can do more than produce a (sometimes colorful) solid at the bottom of a test tube in the teaching laboratory. Asking these questions near the beginning of the coverage of water chemistry allows us to introduce the fundamental steps of water treatment: (1) screening; (2) particle removal including flocculation; (3) chlorination; (4) ozonation; and (5) fluoridation. We note concentration levels of nitrates in the Des Moines and Raccoon Rivers and their fluctuation levels throughout the year by graphically presenting the levels as reported by the Department of Natural Resources monitoring stations. Because the nitrate levels vary with weather conditions, they allow for emphasis on both dynamic components (systems thinking attribute [STA] #2) and temporal components (STA #8) because of the seasonality of the nitrate loading in rivers. This information can then be used as a topic for further discussion as new concepts are introduced about water chemistry. For example, once solubility rules have been introduced, we refer back to the conversation on flocculation in water treatment and how it uses precipitation. Students are then asked, without further direct instruction, “Why would nitrates be difficult to remove from drinking water?” as a clicker question. Looking over several semesters, the results are quite consistent with an example from a fall 2018 class shown in Figure 1. This conceptual connection provides a valuable basis upon which to build the treatment of nitrates in water sources, and incorporate numerical aspects of the problem as well.
Figure 1. Clicker question for students to make connections between solubility rules and water treatment processes prior to any direct instruction. The next new mathematical concept that this issue allows us to add to the topic of water chemistry is the concept of drinking water standards and the motivations behind them in terms of atrisk subpopulations (in this case, infants). A key reason that nitrates are regulated in drinking water lies in the potential for inducing methemoglobinemia, or blue-baby disease, which occurs when infants are exposed to levels of nitrates that are too high. With infants, careful consideration of toxicity 243 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
and the units for this important public health measure are required. The standard for nitrate is given as 10 mg/L or ppm Nitrate-nitrogen (42), which means the measure is being considered as a unit of nitrogen, the diatomic molecule. As soon as this standard is presented, there are two mathematical reasoning questions that present themselves. First, can students establish that mg/L is a unit that corresponds to ppm? Second, what does the nitrate-nitrogen concept imply, and how would this compare with other logical units? This type of learning exercise is connected to the computational thinking concepts noted earlier, in part because they require students to consider how a new idea (in this case, a mathematical unit) is related to an already familiar unit (in this case, computational thinking attribute [CTA] #7). The first task, allowing students to determine that mg/L is equivalent to ppm, requires the consideration of the density of water. Once the students are reminded that water is so close to 1 g/mL in density, they areable to work out the equivalence. The second component requires the students to reinforce their understanding of chemical formulas and the concept of mass percentage based on the formula (a task that has been covered prior to this chapter). With some prompting from an active learning assignment, students are able to determine the percentage of nitrogen in nitrate. We have noted that the charge on the ion does occasionally cause student concerns, and we have to remind them of the relative mass of electrons so they can feel comfortable leaving the additional mass of the “extra electron” out of the calculation. Once the students have determined the percentage of nitrogen, we note the similar total nitrate standard often used in Europe is 40 mg/L of nitrate. Using the percentage of nitrogen in nitrate results in this standard yields 22%, which seems to be off by a factor of two; this is addressed by the diatomic nature of nitrogen (N2). This set of activities introduces students to the importance of carefully considering concentration units. The vast majority of concentration-related problems introduced in general chemistry are based on the unit of molarity. This is, of course, quite practical from the perspective of connecting lecture and laboratory, but it becomes less all-encompassing when we ask the question that promotes greater awareness of systems thinking: “Are we considering the right boundary for the chemistry we are studying?” Incorporating concentration units within context-based practical applications serves the purpose of pushing the knowledge students gain outside of the comfortable box of information that is only used in the chemistry classroom or laboratory, where students tend to perceive molarity to be used. The extension of mathematical skills required is modest and generally within the coverage of ideas discussed in the course, but the tendency of students to compartmentalize their mathematical understanding can be addressed with even small changes to the math expectations for topics that are commonly taught in the curriculum. The potential for long-term gains associated with incorporating these conceptual and mathematical activities related to nitrates in the environment has been estimated to some degree as well. The course in which this idea has been introduced uses ACS Exams (43) for its final examination. This fact prevents us from providing a specific discussion of any items on the final exam. Nonetheless, in one semester where this context was employed for instruction, an ACS Exam that included an item where knowledge of nitrates would be helpful to correctly answer the question was used. Course-wide performance on this item was 21% better than national statistics for the same question, and this constituted the third highest positive differential in the entire test. This was accomplished with only about 20 additional minutes of instruction time. It is not possible to attribute this strong performance wholly to the contextualization of the concept of nitrates in the environment, but the strong positive effect is nonetheless tantalizing as an indicator of ways that gains from introducting mathematical extensions that promote awareness of systems thinking could be measured in future studies. 244 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
Stretching Mathematical and Estimation Skills with Systems Thinking There are constraints inherent in the delivery of chemistry in large lecture formats. When teaching over 700 students, most of whom need fundamental chemistry education for coursework in other disciplines in addition to subsequent advanced chemistry classes, the amount of time available for providing mathematical context through systems thinking is somewhat modest. Even within this learning environment at Iowa State, additional opportunities for mathematical education arise. For example, students who wish to take the general chemistry course as an honors course volunteer to sign up for extra activities, and in these small group sessions, it is possible to add content including systems thinking-related activities for water chemistry. The context used for these extra activities remains the same—the biochemical flow of nitrogen. The difference lies, once again, in expanding the boundary of what is considered in the context. In particular, rather than focusing on the need to treat water in a municipal water system close to home, we consider the creation of the “dead zone” 850 miles away in the waters of the Gulf of Mexico. The loading of both nitrogen and phosphorous into the waterways of the Midwest is largely responsible for this concern, which provides a large-scale example of how fundamental chemistry content can be connected to planetary boundaries. Estimates show that roughly 40% of the nutrient loading that is responsible for the dead zone originates in Iowa. We ask the students, “what would we need to do to investigate the accuracy of this statement?” This setup is, once again, capable of engaging both enhanced systems thinking and computational thinking. Initial brainstorming sessions from the students (captured on whiteboards) show how hard it is for them to confront the need to expand their fundamental knowledge to larger, context-based systems. Figure 2 shows the topics noted in these initial sessions discussing the question, “What things have you learned in chemistry that would help you address the question of whether or not this estimate is reasonable?”
Figure 2. Initial group brainstorm responses for what chemistry ideas might be needed to start to estimate the percentage of gulf nutrient loading that originates in Iowa. 245 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
While some strategies are mentioned by students immediately upon confronting this question, other strategies show the challenges faced in framing a problem as ill-defined as this one. Once the students had this initial reflection time, they were prompted with a more specific question from the discussion leader: “What would you want me to Google?” At that point, the groups began to coalesce around what was perceived to be the most productive approaches, most of which are associated with determining the volume of water. Thus, students begin with essentially a laundry list of water-related chemistry topics, but when prompted anew, they go beyond identifying components. They start to organize those components within a larger framework (STA #4), and because of the incorporation of inherently dynamic river flow, they adopt dynamic features as well (STA #2, STA #3). There was significant interest in trying to gauge water entering and exiting the area where Iowa rivers are. The students were essentially honing in on the idea that in order to determine the percentage, they needed to know the whole sample entering the gulf and also the amount originating from Iowa itself. Thus, they began to engage in the process of breaking down the larger problem into smaller ones (CTA #5). It was at this point that the groups hit an interesting snag. By selecting Memphis as a location to investigate, it took little time to determine the depth and width of the Mississippi River downstream from the confluence with the Missouri River. (In this case, the convenience of having a familiar, wellestablished location for model building became important.) Even so, the students struggled with how to determine the volume in this case. They found themselves stuck with the idea that volume equals a (length x width x depth), and they could not determine what “length” would work. While they did determine that using the flow rate x time could obtain the third dimension in this problem, it was apparent that there was discomfort associated with having to seemingly abandon a trusted mathematical formula. In terms of the computational thinking traits, this suggests moving toward an ability to deal with open-ended problems (CTA #1) and a persistence in working through challenging problems (CTA #2) where familiar algorithms no longer work. The next eye-opening aspect of their problem-solving arose from the magnitude of the water flow in a river as large as the Mississippi. When they ultimately found an estimate of the water volume leaving the river and entering the Gulf, they were hesitant to keep moving forward because the number seemed so large. This reaction suggests that the propensity to provide laboratory-scale exercises in general chemistry problem-solving examples carries a cost with it in terms of student comfort level (at least initially) with global-scale issues. It is ultimately the connection to global-scale issues that provides the clearest incorporation of systems thinking attributes within this topic. Students identify individual components (STA #1) in terms of concentration concepts (and even components of concentration), such as the idea that concentration includes “per unit of volume”. They note that in order to determine volume, they must abandon a comfortable static formula for a dynamic one that includes river flow rates (STA #2). The fact that students need information about the watershed both before and after it flows through Iowa to estimate the percentage of nitrates that originate there helps to establish a framework where they can repeatedly apply mathematical relationships (STA #4). In the time frame over which this problem was discussed, the students did not include factors such as interaction of nitrates with soil, but they recognized the importance of such issues. This type of reasoning represents a form of understanding hidden dimensions (STA #7), or at least the need to consider other dimensions. Finally, the scale of the problem, in this case the vast amount of water that flows within the Mississippi watershed, induces students to think about time frames (i.e., translating flow rates per min into annual nitrate loading). Because of the relative unfamiliarity of calculations at such a large scale, students also showed signs of retrospection and questioned their ability to predict information based on the models they were creating (STA #8). 246 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
In the end, these fairly strong students grew more comfortable with building models for this problem and applying computational reasoning to the issue at hand. This is reflected in comments provided in the end-of-exercise statements they submitted, which are summarized in Figure 3.
Figure 3. A sample of individual student responses about what they might need to include in a mathematical model that estimates the percentage of Gulf nutrient loading attributable to Iowa. These statements also reveal enhanced aspects of computational thinking. Attributes such as assessing strengths/weaknesses (CTA #8) is notable in the response from Student 1; representing ideas in computationally meaningful ways (CTA #4) is apparent in the way Student 2 phrased their response; and confidence in dealing with complexity (CTA #3) is shown in the response from Student 3 who includes a large number of factors that would need to be considered. These observations begin to exemplify how helping students connect fundamental chemistry concepts to large-scale systems-oriented global issues can enhance both the systems thinking awareness and computational thinking attributes. Despite initial challenges, these students began building models that extended their basic mathematical skills in important ways. The large, systems-based consideration quickly pushed them toward accepting ways to build approximate models to start understanding the problem. Several students noted that improvements would be needed subsequent to these initial efforts, but all of them noted the value of getting a sensible estimate from which to begin considering more global scale implications of chemistry. At the same time, they were able to identify specific skills, such as the concept of concentration multiplied by volume to obtain an amount of nitrates involved in this issue. This occurred, even as they struggled with how to obtain a volume when the “length” dimension was causing confusion.
Conclusions and Extrapolations While it is certainly true that this chapter represents a single observation of the possible utility of incorporating systems thinking approaches within general chemistry, the initial results are largely promising. Modest extrapolations of concepts (such as solubility) that are commonly taught in any general chemistry course show evidence that students can make connections to real-world applications, and such connections appear to enhance long-term retention of conceptual 247 Towns et al.; It’s Just Math: Research on Students’ Understanding of Chemistry and Mathematics ACS Symposium Series; American Chemical Society: Washington, DC, 2019.
understandings. Mathematical reasoning aspects can also be expanded, particularly in terms of introducing a wider variety of concentration units and using them in practical situations (in this case, exposure limits of potentially harmful compounds). With a smaller group (or more available time), the introduction of biochemical flow issues as a component of water chemistry presents several potentially useful expansions of the topic. Students can be encouraged to use mathematical reasoning to build models, starting with more approximate treatments, and identify ways to build in greater accuracy. The topic, particularly the role of transportation of chemicals in river ways, lends itself to pushing students to expand their numerical reasoning beyond resorting to familiar and comfortable equations. For example, determining the volume of water that flows from a river into a larger body (the Gulf of Mexico) presents students with the challenge of determining one of the three customary variables used for volume calculations. We have carried out similar exercises within other contexts, but not to the same extent as the ideas reported here. Thus, climate change and anthropogenic global warming have been used in the description of gases. We began this chapter discussing how to determine information about the composition of the atmosphere and global temperatures in “deep time” through ice-core data. This approach, starting with ice cores, leading naturally to the idea of beginning the treatment of gases with kinetic gas theory. This idea introduces gases in a sufficiently new way, such that a large fraction of the students in the class did not react with a perception that the topic of gases will be the same ideas they learned in secondary school. Starting with this realization has proven to be an effective motivational tool for many students. The key message lies in the idea that it is possible to consider mechanisms to include systems thinking and models in general chemistry in ways that enhance student engagement and learning. Surprising challenges emerge for students when approaching the mathematical component of this strategy. Because students may compartmentalize their mathematical skills as applied to chemistry problem-solving, identifying contexts where they can logically extend those ideas and enhance their computational thinking can be highly useful, given the context of expectations that have emerged from the NGSS. Water chemistry represents one example of these advantages, but a number of others seem reasonable to propose and will be the topic of future work.
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