The Development of Computational Thinking in a High School

Jul 31, 2017 - Computational thinking is a component of the Science and Engineering Practices in the Next Generation Science Standards, which were ado...
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The Development of Computational Thinking in a High School Chemistry Course Paul S. Matsumoto* and Jiankang Cao Galileo Academy of Science and Technology, San Francisco, California 94109, United States S Supporting Information *

ABSTRACT: Computational thinking is a component of the Science and Engineering Practices in the Next Generation Science Standards, which were adopted by some states. We describe the activities in a high school chemistry course that may develop students’ computational thinking skills by primarily using Excel, a widely available spreadsheet software. These activities were classified as (i) the use of simulation and modeling, (ii) experimental data analysis, (iii) coding or programming, (iv) algorithmic reasoning, and (v) statistics and probability. KEYWORDS: High School/Introductory Chemistry, Interdisciplinary/Multidisciplinary, Mathematics/Symbolic Mathematics, Computer-Based Learning

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Common Core mathematics standards9,10 explicitly refer to the use of a spreadsheet and computer algebra system. While both types of software can be used to develop students’ computational thinking skills, in this paper we will emphasize the use of Excel, a spreadsheet software, because of its wider availability, lower cost, and ease of use. Excel is used in many educational settings, e.g., college courses in business,11 engineering,12,13 biology,14 physics,15 and chemistry.16,17 While the use of spreadsheet software is a valuable skill, many entering college students do not have much experience with using such software,16,18,19 which may reflect the limited use of computer technology among high school teachers.20,21 Therefore, the use of a spreadsheet software in a high school chemistry course may benefit students enrolling in college. Physics teachers use technology more than chemistry teachers,22 but because there is a larger enrollment of students in chemistry than physics,23,24 chemistry teachers will have a larger impact on the number of students exposed to the use of a spreadsheet software in the classroom than physics teachers.

INTRODUCTION A component of the Next Generation Science Standards (NGSS)1,2 is the Science and Engineering Practices,3,4 which includes the use of mathematics and computational thinking.5−8 In this article, we describe potential activities in a high school chemistry course to develop students’ computational thinking skills. As the concept of computational thinking is relatively new, it will be the focus of this article. Figure 1 shows the relationship between the use of mathematics and computational thinking.6 Computational

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SIMULATION/MODELING This section describes the use of simulations to model a system, which may improve student learning.25,26 Furthermore, the NGSS science and engineering standards27 and the Common Core mathematics standards10 include the use of models. Mathematica28,29 and Excel can be used to build simulations to model the behavior of the system, and the remainder of this section describes the use of these software applications with an emphasis on using Excel. Excel was used to simulate a strong acid−strong base titration, as shown in Figure 2. The simulation presents the titration curve and an estimate of its derivative30 to find the equivalence point, which occurs at the inflection point. The

Figure 1. Venn diagram illustrating the relationship between the use of mathematics and computational thinking. Adapted with permission from ref 6. Copyright 2014 NSTA.

thinking involves, e.g., the use of simulation and programming and overlaps with the use of mathematics, e.g., modeling, analyzing data, and statistics. This paper will be organized into five sections: (i) simulation/modeling; (ii) analyzing experimental data; (iii) programming; (iv) algorithmic reasoning/ problem solving, and (v) statistics. While the NGSS do not explicitly refer to the use of a spreadsheet software or a computer algebra system, the © XXXX American Chemical Society and Division of Chemical Education, Inc.

Received: December 15, 2016 Revised: June 16, 2017

A

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[FeSCN2 +]e =

⎛ 1 ⎞⎫ 1 ⎡⎧ 3 + ⎢⎨[Fe ]0 + [SCN−]0 + ⎜ ⎟⎬ ⎝ K ⎠⎭ ⎩ 2 ⎢⎣ 2 ⎛⎧ ⎛ 1 ⎞⎫ 3+ − ⎜ ⎟ ⎜ ⎬ ⎨ − ⎜ [Fe ]0 + [SCN ]0 + ⎝ K ⎠⎭ ⎝⎩

⎞1/2 ⎤ − 4[Fe ]0 [SCN ]0 ⎟⎟ ⎥ ⎠ ⎦⎥ 3+

This equation was used in the Excel and Mathematica simulation shown in Figures 3 and 4. In the equilibrium simulation shown in Figure 3, there are sliders in the Excel and Mathematica simulations; sliders also appear in the titration simulation shown in Figure 2. The value of sliders29,33,30 is that they let students explore the effect of changing the values of parameters in the simulation, which leads to a deeper understanding of the behavior of the system. Figure 3 is a screenshot showing the implementation of the equation describing the system as a formula in the Excel-based simulation versus a command in the Mathematica-based simulation. The Excel-based formula is less elegant than the Mathematica command, since the Excel formula is in a single line and it has other formulas distributed among several cells, while the part of the Mathematica command (corresponding to the equation describing the reaction) is written in a more natural format, which makes the code much easier to understand. The Excel simulation requires the use of various options in the ribbon menu to generate the resulting graph, while the Mathematica command includes the code to generate the graph. The three graphs in Figure 4 correspond to three different sets of formulas, which were modified to account for the different units (i.e., molar, millimolar, and micromolar) in the simulation. From a developer (i.e., student) perspective, it might be easier to generate the graph using Excel rather than Mathematica, since the ribbon menu with various options in Excel could guide the developer during the process, while the developer has to know the syntax of the Mathematica language prior to generating the appropriate graph/plot using Mathematica. The results of the Excel simulation in Figure 4 show that the larger the concentration of the limiting reactant is, the smaller is the ratio of the concentration of the excess reactant to the concentration of the limiting reactant where the concentration of the product is approximately equal to the concentration of the limiting reactant. Identical results were obtained using the Mathematica simulation (not shown). To develop a more complicated simulation, Excel’s Visual Basic for Applications (VBA), a programming language,34,35 can be used to develop simulations. While articles about the use of VBA have appeared in this Journal,36−38 none of these articles are appropriate in a high school setting. Excel’s VBA feature was used to develop two simulations involving the generation of random numbers to simulate rolling multiple six- or 10-sided dice. A major benefit of using an Excel simulation of rolling many dice rather than using physical dice is the significant time savings in the generation and (partial) analysis of the data. A benefit of using VBA is to automate repetitive commands, which significantly reduces the amount of time for students to gather data for subsequent analysis. The VBA code is initiated when the user clicks on the command button(s).

Figure 2. Simulation of a strong acid−strong base titration using Excel. The formula to estimate the derivative is shown in the bottom panel. The values of the parameters in the simulation (shown to the left of the sliders) are the following: the volume of the acid is 50 mL, the concentration of the acid is 75 mM, and the concentration of the base is 250 mM. The equations used in the simulation were given in prior work.30,31

volume of the base at the equivalence point is used to calculate the concentration of the acid. A second simulation using Excel, shown in Figures 3 and 4, was to simulate the behavior of the chemical reaction Fe3 +(aq) + SCN−(aq) ⇄ FeSCN2 +(aq)

which was used to validate the assumption in a lab32 that the concentration of the product is equal to the concentration of the limiting reactant when the concentration of the excess reactant is much greater than the concentration of the limiting reactant. The basis of the simulation is that the equilibrium constant expression29,30 of the chemical equation is K= =

−

[FeSCN2 +]e [Fe3 +]e [SCN−]e [FeSCN2 +]e {[Fe3 +]0 − [FeSCN2 +]e }{[SCN−]0 − [FeSCN2 +]e }

and the concentration of the product is B

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Figure 3. Comparison of the coding in Excel (top panel) vs Mathematica (bottom panel) to simulate the behavior of the reaction Fe3+(aq) + SCN−(aq) ⇄ FeSCN2+(aq). To simplify the figure, only the graphical output for the Mathematica simulation is shown, while the Excel graphical output is shown in Figure 4. In both simulations, a graph of the product concentration, [FeSCN2+], as a function of the concentration of the “excess” reactant, [SCN−], is shown, and the value of the “limiting” reactant, [Fe3+], can be varied using the slider. The preceding terms referring to the excess and limiting reactants are relative, i.e., the excess reactant is not the “excess reactant” until its concentration is greater than the concentration of the “limiting reactant”. The blue line in the graph refers to [FeSCN2+], while the orange line refers to the concentration of the “limiting” reactant, [Fe3+], which was included to show that [FeSCN2+] approaches the concentration of the “limiting” reactant, [Fe3+], as the concentration of the “excess” reactant, [SCN−], increases.

“=(A1+A2+A3+A4)/4” to find the average of the values in cells A1 through A4). Figure 7 is an example of a histogram that shows the distribution of data from the simulation of rolling many dice shown in Figure 5. The histogram for a sample size of 1 (i.e., rolling one die) approximates the expected distribution for a uniform discrete probability distribution;39 the remaining histograms are consistent with the central limit theorem.39 In the classroom of one of us (P.S.M.), one of the major uses of Excel is the graphical analysis of experimental data, which involves generating a scatter plot that shows the relationship between two variables, followed by either a least-squares linear regression analysis or estimation of the value of the first derivative. The graphical analysis of laboratory data may involve a calibration curve, which describes the relationship between the aqueous concentration of a chemical and its absorbance. The specific laboratories using a calibration curve include a modified Beer’s law lab and a crystal violet (CV) kinetics lab. In the modified Beer’s law lab,40 the determination of the concentration of an unknown sample of copper(II) nitrate using Excel’s linear regression feature is compared with using graph paper to estimate the concentration of the chemical from a sketch of the best-fit line. In the CV kinetics lab,40 the calibration curve is used to transform the absorbance versus time data into the concentration of CV, [CV], as a function of time. In addition, the data are transformed using Excel’s

The purpose of the simulation shown in Figure 5 is to illustrate the validity of the central limit theorem,39 which states that the distribution of the mean can be described by a normal distribution. The motivation and context of this laboratory activity is that in subsequent laboratory activities, student groups would run duplicate or triplicate trials and share the mean of their data with the class for subsequent statistical data analysis using the t test or one-way analysis of variance (1ANOVA), which assumes the data comes from a normal distribution,39 thereby satisfying this assumption. The second simulation using VBA was to simulate the decay of a radioactive isotope by simulating rolling multiple dice. As in the preceding laboratory activity, the simulation could be done with physical dice, but using an Excel simulation generates the data much faster. In this simulation (shown in Figure 6), students repetitively select the “run” and “clear” command buttons and record the number of remaining dice (i.e., radioactive isotopes) in the simulation for subsequent data analysis.

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ANALYZING EXPERIMENTAL DATA

In Excel, graphs are called charts, and the difference between a f unction and a formula is that a function has a specific syntax while a formula has a code developed by the user (e.g., the function “=AVERAGE(A1:A4)” vs the formula C

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and y-intercept are used to estimate the number of moles of gas in the system and the volume of the tubing, respectively. The last example of a graphical analysis using Excel in a classroom of one of us (P.S.M.) is in a laboratory activity to determine (i) the concentration of an acid in a strong acid− strong base titration and (ii) the value of Ka for acetic acid on the basis of an analysis of the titration curve, where the equivalence point is estimated using a graph of the first derivative of the titration curve. Figure 2 is a simulation of a strong acid−strong base titration curve and a graph of the first derivative of the titration curve, which are similar to actual experimental results.

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PROGRAMMING In coding or programming activities, students write formulas or use Excel functions, but they do not write Excel VBA commands, since it is much easier to teach students to write a formula or use a function than to teach them VBA commands and there is minimal marginal benefit to students in using VBA commands in the context of analyzing their experimental data or developing a simulation. On the other hand, as mentioned in the earlier section on simulations, from a teacher’s perspective, using VBA in the development of a simulation is valuable. In Excel, cells can be referenced by their location with respect to the column and row. For example, a cell in column C and row 3 would be denoted as cell C3, and this label can be used in either a function or formula. To refer to a range of cells, one selects the range of cells using the mouse or names the first and last cell in the cell range. While using Excel’s name feature41 would make it easier to understand the code in Excel, because of the relatively simple nature of the coding and the simplicity of identifying a cell by its column and row, students are asked to use the latter convention. Laboratory data analysis using Excel’s formula feature is performed in three laboratories: (i) the acid−base titration lab, (ii) the CV kinetics lab, and (iii) the Boyle’s law lab. In the acid−base titration lab, an estimate of the derivative (see Figure 2 for the formula) is graphed to estimate the inflection point, which is then used to determine the concentration of the acid. In the CV kinetics lab, several data analysis tasks are undertaken. First, the absorbance is converted to the concentration of CV, [CV], using Beer’s law. Next, [CV] is transformed to (i) its reciprocal and (ii) its natural logarithm. Finally, Excel’s select, copy, and paste features are used to transform the remainder of the crystal violet data. For example, if the value of [CV] is in cell A1, then the formula for its reciprocal would be “=1/A1” and the formula for its natural logarithm would be “=LN(A1)”. Select, copy, and paste can then be used to generate the corresponding formulas for other values of [CV]. In the Boyle’s law lab, the value of the pressure in the syringe is transformed to its reciprocal (the formula is the same as in the CV kinetics lab), which is graphed as a function of the volume in the syringe. Students can generate a small part of the code for the VBAbased simulation examining the central limit theorem (see Figure 5), which involves the simulation of rolling many sixsided dice and calculating the average value for rolling multiple dice by using the Excel functions RANDBETWEEN() and AVERAGE(), respectively. In the radioactive decay simulation (Figure 6), students are asked to develop an Excel-based radioactive isotope decay simulation and, supported by prelab questions, to describe the

Figure 4. Excel simulation of the reaction Fe3+(aq) + SCN−(aq) ⇄ FeSCN2+(aq), where the value of the equilibrium constant is 200. Graphs of the product concentration, [FeSCN2+], as a function of the concentration of the “excess” reactant, [SCN−], are shown for different values of the concentration of the “limiting” reactant, [Fe3+]: 10 μM (top panel), 10 mM (middle panel), and 10 M (bottom panel). The preceding terms referring to the excess and limiting reactants are relative, i.e., the excess reactant is not the “excess reactant” until its concentration is greater than the concentration of the “limiting reactant”.

formula feature to obtain the reciprocal of [CV] and the natural logarithm of [CV]. Three scatter plots are used to determine whether the reaction follows zeroth-, first-, or second-order kinetics on the basis of which plot best fits the experimental data. These three scatter plots are (i) [CV] versus time, (ii) ln [CV] versus time, and (iii) 1/[CV] versus time, respectively. The fits are performed and judged using Excel’s trend line command and the R2 option. A laboratory activity using Excel’s linear regression feature that does not employ a calibration curve is a Boyle’s law lab31 involving a syringe connected to a pressure transducer with tubing. It is described by the equation P(Vsyringe + Vtubing) = nRT

Upon rearrangement, the equation becomes ⎛1⎞ Vsyringe = nRT ⎜ ⎟ − Vtubing ⎝P⎠

so a graph of Vsyringe on the vertical axis versus the reciprocal of the pressure on the horizontal axis generates a straight line with slope = nRT and y-intercept = −Vtubing. The values of the slope D

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Figure 5. Screenshot of an Excel simulation to (i) generate the values for rolling up to 64 six-sided dice; (ii) calculate the average values for rolling two, nine, 36, or 64 dice; and (iii) automatically repeat the simulation 120 times and record the output of the simulation for subsequent data analysis. This simulation has a single command button, entitled “run”, which triggers the VBA code to generate the output in the green region of the spreadsheet. The student uses the appropriate Excel functions to fill in the yellow cells (to generate a random number simulating a dice roll) and orange cells (to calculate the average) prior to running the simulation.

Figure 6. Screenshot of an Excel-based simulation of the decay of a radioactive isotope based on simulating rolling multiple six-sided or 10-sided dice, which simulate radioactive isotopes with different decay constants. This simulation has multiple command buttons, entitled “reset-6”, “reset-10”, “run”, and “clear”, which trigger specific VBA codes. The “reset-6” and “reset-10” command buttons set up simulations for six- and 10-sided dice, respectively; the “run” button generates a random number of radioactive isotopes to decay, while the clear button identifies the recently decayed radioactive isotopes and removes them from the simulation.

dice rolls, where the decay constant is the negative of the slope of the graph) for simulations in which multiple six-sided or 10sided dice are rolled. The use of dice with different numbers of sides simulates radioactive decay of isotopes with different halflives and decay constants. Lastly, students use the Mathematicabased unpaired t-test statistics program to compare the sixversus 10-sided dice simulation on the pooled class data for the half-life and the decay constant. The motivation for having students use these Excel functions and develop/write the formulas described previously reflects our goal to support the recent initiative to have students learn

Excel functions RANDBETWEEN(), COUNTIF(), and COUNTIFS() and their syntax. These functions can be used in the simulation, as shown by a series of increasingly complex Excel simulations of the process during the prelab session (see the Supporting Information). Such a prelab session provides a scaffold7 for students to develop a simulation to model radioactive decay, which is simulated by rolling multiple dice. Subsequently, students use Excel to analyze the output of their simulation to estimate the half-life (using a graph of the number of dice remaining vs the number of dice rolls and the definition of the half-life) and decay constant (using a graph of the natural logarithm of the number of dice remaining vs the number of E

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Figure 7. Histograms of the means for rolling n dice (n = 1, 2, 9, 36), with a total of 120 simulated trials. The horizontal axes are “bins” with a size of 0.5.

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computer programming concepts,7,8 which is a component of computational thinking.6

CONCLUDING REMARKS While this article refers to Excel, there are other spreadsheet software programs. For example, Google sheets45 and Google Apps Scripts46 may substitute for Excel and VBA, respectively. While Excel is a widely used software program, it is not free; Google Sheets is free,47 and has features similar to those of Excel as described in this article (except for sliders, but there is an easy workaround: users manually enter the output of the slider in a specific cell in the spreadsheet). Students seem to prefer Google Sheets over Excel because of its cost, so we generated a Google Sheet file to emulate the Excel file.48 Another motivation to develop the Google Sheet-based simulation is that school districts are increasingly adopting Google products rather than Microsoft products.47 Excel and Mathematica can both be used to develop simulations. However, we recommend the use of Excel for simple simulations and Mathematica for complex simulations. Hopefully, with the implementation of the Common Core mathematics standards, which encourages the use of spreadsheet software and a computer algebra system,9,10 students in the future will be entering their high school chemistry courses with prior experience of using such technological tools. Furthermore, chemistry and mathematics teachers could collaborate on the use of these spreadsheet/computer algebra software teaching tools to reinforce concepts taught in their respective courses. While this article focuses on the use of computational thinking, mathematics, and models, which is a part of the NGSS science and engineering practices, the remaining components in the science and engineering practices3 are involved in these activities. Specifically, these are (i) asking questions, (ii) planning and carrying out investigations, (iii) analyzing and interpreting data, (iv) constructing explanations, (v) engaging in argument from evidence, and (vi) communicating information. Therefore, the activities described in this article provide an opportunity for students to develop all of the skills described in the NGSS science and engineering practices. The NGSS assessments could involve simulations49 and animations. Although the use of animation is not mentioned in

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ALGORITHMIC REASONING/PROBLEM SOLVING An algorithm is a plan or outline that describes how a computer program solves a problem. One technique to express an algorithm is a flowchart.29 The preceding programming activities develop students’ algorithmic reasoning skills, which can be applied to other facets in a high school chemistry course, other classes, or in various life situations; that is, algorithmic reasoning skills is a subset of critical thinking skills, which have wide-ranging applications. Solving various chemistry problems involves developing algorithms. Some chemistry problems require students to integrate various chemistry concepts, in which case it would be beneficial to outline a plan to solve the problem. For example, a thermodynamics problem could integrate multiple chemistry concepts. An example of such a problem would be to determine the final temperature of 75 g of water at 21 °C by heating it through the combustion of 2.0 g of ethane and 5.0 g of oxygen.

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STATISTICS The use of statistics in analyzing chemistry laboratory data42 fulfills both the use of mathematics and computational thinking in the science and engineering practices3,4 in the NGSS. While Excel has several statistical functions, there are caveats;43 thus, we recommend another source for statistical analysis of chemistry laboratory data. In P.S.M.’s chemistry class, students have access to either Mathematica29 or Minitab,44 a statistics software. Mathematica is a computer algebra programing language software with statistics commands, and it was used to develop t-test and 1-ANOVA programs in which students use a dialogue box to enter the data rather than writing any code. A benefit of using a statistics software program is that the user interface is similar to Excel, so students’ familiarity with the user interface might make it easier for them to use a statistics software rather than Mathematica. However, Mathematica is a more versatile software because it can be used to develop simulations, which is not possible with statistics software. F

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https://peer.asee.org/using-a-concurrently-collaborative-spreadsheetto-improve-teamwork-and-chemical-engineering-problem-solving (accessed June 2017). (13) Oke, S. A. Spreadsheet Applications in Engineering Education: A Review. Int. J. Eng. Educ. 2002, 20 (6), 893−901. (14) Carlton, K.; Nicholls, M.; Ponsonby, D. Using Spreadsheets to Teach Aspects of Biology Involving Mathematical Models. J. Biol. Educ. 2004, 38 (4), 183−186. (15) C21: Physics Teaching for the 21st Century. Using spreadsheets. http://c21.phas.ubc.ca/article/using-spreadsheets (accessed June 2017). (16) Rubin, S. J.; Abrams, B. Teaching Fundamental Skills in Microsoft Excel to First-Year Students in Quantitative Analysis. J. Chem. Educ. 2015, 92, 1840−1845. (17) The Chemistry Hypermedia Project. Spreadsheet Simulations for Analytical and Physical Chemistry. http://www.tissuegroup.chem. vt.edu/chem-ed/simulations/spreadsheets.html (accessed June 2017). (18) Tesch, D.; Murphy, M.; Crable, E. Implementation of a Basic Computer Skills Assessment Mechanism for Incoming Freshmen. J. Inf. Syst. Educ. 2006, 4 (13), 3−11. (19) Schlotter, N. E. A Statistics Curriculum for the Undergraduate Chemistry Major. J. Chem. Educ. 2013, 90, 51−55. (20) Cuban, L.; Kirkpatrick, H.; Peck, C. High Access and Low Use of Technologies in High School Classrooms: Explaining an Apparent Paradox. Am. Educ. Res. J. 2001, 38, 813−834. (21) Gilakjani, A. P. Factors Contributing to Teacher’s Use of Computer Technology in the Classroom. Univers. J. Educ. Res. 2013, 1 (3), 262−267. (22) Waight, N.; Chiu, M. M.; Whitford, M. Factors that Influence Science Teachers’ Selection and Usage of Technolgies in High School Science Classrooms. J. Sci. Educ. Technol. 2014, 23, 668−681. (23) Walford, E. T. High School Chemistry: Preparation for college or preparation for life? J. Chem. Educ. 1983, 60, 1053−1055. (24) Sheppard, K.; Robbins, D. M. Physics Was Once First and Was Once for All. Phys. Teach. 2003, 41, 420−424. (25) Laxman, K.; Chin, Y. K. Impact of Simulations on the Mental Models of Students in the Online Learning of Science Concepts. J. School Educ. Technol. 2011, 7 (2), 1−12. (26) Why Teach with Simulations? http://serc.carleton.edu/sp/ library/simulations/why.html (accessed June 2017). (27) Science and Engineering Practices: Developing and Using Models. http://ngss.nsta.org/Practices.aspx?id=2 (accessed June 2017). (28) Wolfram Mathematica. https://www.wolfram.com/ mathematica/ (accessed June 2017). (29) Matsumoto, P. S. Exploring Interactive and Dynamic Simulations Using a Computer Algebra System in an Advanced Placement Chemistry Course. J. Chem. Educ. 2014, 91, 1326−1333. (30) Matsumoto, P. S.; Tong, G.; Lee, S.; Kam, B. The Use of Approximations in a High School Chemistry Course. J. Chem. Educ. 2009, 86 (7), 823−826. (31) Matsumoto, P. S.; Ring, J.; Zhu, J. L. The Use of Limits in an Advanced Placement Chemistry Course. J. Chem. Educ. 2007, 84 (10), 1655−1658. (32) Vernier. Computer 20: Chemical Equilibrium: Finding a constant, K c . http://www2.vernier.com/sample_labs/CWV-20COMP-equilibrium.pdf (accessed June 2017). (33) Raviolo, A. Using a Spreadsheet Scroll Bar To Solve Equilibrium Concentrations. J. Chem. Educ. 2012, 89, 1411−1415. (34) VBA Tutorial. https://www.tutorialspoint.com/vba/ (accessed June 2017). (35) VBA in ExcelEasy Excel Macros. http://www.excel-easy.com/ vba.html (accessed June 2017). (36) Kaess, M.; Easter, J.; Cohn, K. Visual Basic and Excel in Chemical Modeling. J. Chem. Educ. 1998, 75, 642−643. (37) Glasser, L. Dealing with Outliers: Robust, Resistant Regression. J. Chem. Educ. 2007, 84, 533−534. (38) Litofsky, J.; Viswanathan, R. Introduction to Computational Chemistry: Teaching Huckel Molecular Orbital Theory Using an Excel

this article, we believe that our simulations may prepare students for the NGSS assessment. Lastly, a potential impediment to developing students’ computational thinking skills would be an insufficient amount of time.7 However, the NGSS excludes a number of traditional chemistry concepts,50 so there might be sufficient time in the academic year to develop students’ computational thinking skills. While many of the activities described in this article have already been done in a high school chemistry course, other activities will be done in the future, when the school district revises the course to a NGSS chemistry course, as there is currently an insufficient amount of time to include all of the activities in this article.

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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.6b00973. Excel and Mathematica content mentioned in the article (ZIP) Description of the use of the various software programs mentioned in the article (PDF, DOCX)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Paul S. Matsumoto: 0000-0003-1880-6072 Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Next Generation Science Standards. http://www.nextgenscience. org/ (accessed June 2017). (2) NGSS@NSTA: STEM starts here. http://ngss.nsta.org/ (accessed June 2017). (3) Appendix FScience and Engineering Practices in the NGSS. http://www.nextgenscience.org/sites/default/files/ Appendix%20F%20%20Science%20and%20Engineering%20Practice s%20in%20the%20NGSS%20-%20FINAL%20060513.pdf (accessed June 2017). (4) Science and Engineering Practices. http://ngss.nsta.org/ PracticesFull.aspx (accessed Jun 2017). (5) Science and Engineering Practices: Using Mathematics and Computational Thinking. http://ngss.nsta.org/Practices.aspx?id=5 (accessed June 2017). (6) Sneider, C.; Stephenson, C.; Schafer, B.; Flick, L. Exploring the Science Framework and NGSS: Computational Thinking in the Science Classroom. Sci. Teach. 2014, 81 (5), 53−59. (7) Lee, I.; Martin, F.; Denner, J.; Coulter, B.; Allan, W.; Erickson, J.; Malyn-Smith, J.; Werner, L. Computational Thinking for Youth in Practice. ACM Inroads 2011, 2 (1), 32−37. (8) Paul, A. M. The Coding Revolution. Sci. Am. 2016, 315, 42−49. (9) Common Core State Standards Initiative. Standards for Mathematical Practice ≫ Use appropriate tools strategically. http:// www.corestandards.org/Math/Practice/MP5/ (accessed June 2017). (10) Common Core State Standards Initiative. High School: Modeling. http://www.corestandards.org/Math/Content/HSM/ (accessed June 2017). (11) Bell, P. C. Teaching Business Statistics with Microsoft Excel. INFORMS Trans. Educ. 2000, 1 (1), 18−26. (12) Silverstein, D. Using a Concurrently Collaborative Spreadsheet To Improve Teamwork and Chemical Engineering Problem Solving. G

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Journal of Chemical Education

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DOI: 10.1021/acs.jchemed.6b00973 J. Chem. Educ. XXXX, XXX, XXX−XXX