Evidence-Based Approaches to Improving Chemical Equilibrium Instruction

Evidence-Based Approaches to Improving Chemical Equilibrium Instruction

Jodi L. Davenport †, Gaea Leinhardt ‡, James Greeno ‡, Kenneth Koedinger §, David Klahr §, Michael Karabinos §, and David J. Yaron *§

† WestEd, Oakland, California 94612, United States

‡ University of Pittsburgh, Pittsburgh, Pennsylvania 15213, United States

§ Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, United States

J. Chem. Educ., 2014, 91 (10), pp 1517–1525

DOI: 10.1021/ed5002009

Publication Date (Web): September 19, 2014

Copyright © 2014 The American Chemical Society and Division of Chemical Education, Inc.

Supporting Information (18 pages): showed sample applications of the M & M strategy to various acid-base problems involving monoprotic acids and problems involving multi-protic problems.  An example was also shown for solubility equilibria problems.

Abstract: http://pubs.acs.org/doi/full/10.1021/ed5002009

In this article, the authors present instructional improvements for covering equilibrium concepts.  Part of the motivation is to ensure that conceptual learning is taking place along with quantitative mastery of equilibrium problems.  They present two evidence-based suggestions for improvement:

1)      Presenting the progress of a reaction more explicitly

2)      Using the majority and minority (M & M)  strategy to “frame both the qualitative and the quantitative analysis of equilibrium systems”

They describe these two instructional strategies, present the results of two studies supporting these strategies, and show an application of the M & M strategy to multiple reaction systems.

RECOMMENDATIONS FOR INSTRUCTION

RECOMMENDATION 1: Make the “Progress of Reaction” explicit

In this strategy, the authors suggest using molecular diagrams in addition to just showing reaction arrows to indicate shifts in the direction of the reaction (toward product, reactant, or no net shift):

RECOMMENDATION 2: Teach equilibrium problem using the M & M strategy

This strategy presents a more conceptual framing of the small-x strategy for reactions that have very large K or very small K values. 

In phase one, the size of K is used to identify the major species (any species with nonzero concentrations) and its concentration at equilibrium. Species that have zero concentrations are minor species.

In phase two, law of mass action (letting Q = K) is used to calculate the concentration of the minority species.  The usual 5% tolerance can be applied to check the answer (the authors use 10%).

Here is the example given in the paper for reactions with large K:

For reactions with small K, the opposite assumption can be used, letting K à0.  Alternatively, the large K strategy can be used for the reversed reaction (Krev = 1/K).

The improvement of the M & M strategy over the traditional straight-math calculation is a more explicit conceptualization of the chemical basis for the algebraic simplification, i.e. “qualitative reasoning regarding the position of equilibrium along the progress of reaction”.  It is based on the limiting reactant assumption with the calculation of the actual non-zero concentration of the limiting reactant as a refinement. The authors believe that this strategy improves upon the more algorithmic method of solving equilibrium concentrations using the small-x method.

In two studies, the author investigated some claims about the M & M strategy.

In Study 1, they posed the question “Do experts use the M&M reasoning when solving problems about equilibrium?” and sought to find about the difference between how experts and novice solve the same equilibrium problem. The experts were either chemistry faculty or graduate students; the novices were students that had completed two semesters of introductory chemistry in the previous year. Problem solving results were in the form of written solutions and recorded think aloud statements made by the participants as they were solving the problem.  Analysis of written solutions was coded for “progress of reaction” and “approximation”.  Analysis of verbal records was coded for state-based or reaction-based.

Results of Study 1 (taken verbatim from article): “On written solutions: more likely to integrate concepts with problem solving. All five of the experts correctly applied equilibrium values in the mass action formula, compared to less than half of the novices. In addition, experts were more likely to demonstrate M&M type reasoning as they more frequently used the approximation strategy during problem solving. All three professors used an approximation strategy, compared to no novices or graduate students.” Only 2 chemistry faculty got the correct answer, one made an arithmetic error, the 2 graduate students did not get the correct answer using the non-approximation method and no novice got the correct answer.  On Verbal Discussion: “The t test results revealed that experts made more state-based comments (M = 4.6) than novices (M = 2.1), t(1,13) = 2.2, p < 0.05, and experts made more reaction-based comments (M = 3.0) than novices (M = 0.7), t(1,13) = 3.2, p < 0.01.” In the Discussion section, the authors conclude that the results suggest that the experts use the M & M strategy when solving the problem. They also speculate that the failure of the novice students (who have passed with B grades) to solve the problem correctly point to a lack of conceptual understanding of the processes and knowledge based on remembering procedures and instructions.

Study 2 investigated the question “Is the M & M strategy learnable by students and does it improve problem-solving performance?”  The researchers collected two semesters of data from 310 students comparing the results for students who were taught the traditional small x method to solve a large K problem (control) and for students who were taught the M & M strategy (treatment).  The exam results were analyzed for three items: 1) whether students applied conceptual understanding by using equilibrium concentrations in the law of mass action formula, 2) whether approximation was used in the problem solving, and 3) whether they got the correct equilibrium concentrations.  A summary of results (taken verbatim): Significantly more students in the M&M semester used equilibrium values in the mass action formula (80%) than students in the control semester (63%), X2(1, N = 310) = 10.88, p < 0.001. Significantly more students in the M&M semester used an approximation strategy (92%) than students given the small-x instruction (24%), X2(1, N = 310) = 149.75, p < 0.001. Finally, 50% of students given M&M instruction found all correct concentrations at equilibrium, compared with only 17% of students in the small-x condition, X2(1, N = 310) = 36.03, p < 0.001. See Figure 6.

In the Discussion section, the authors have this to say about why the treatment students did better in all 3 regards: Phase 1 of the M&M strategy replaces this with a thought experiment that focuses attention on the chemical consequences of having a large K. The thought experiment asks “What would happen if K were not just large, but infinite?” This question helps the transition to phase 2, when we ask “What are the consequences of K only being large, as opposed to infinite?” The small-x approach may obscure this chemical reasoning by introducing unneeded algebraic complexity. In particular, the various algebraic approximations (for example, x is ignored when added or subtracted from a large number but not when multiplied by a large number) are difficult. This may distract students from the key chemical idea that a reaction with large K lies to the far right of the progress of reaction. In addition, students may attach significance to the sequence of actions in the small-x approach, and misinterpret the reaction as proceeding to completion and then relaxing back to an equilibrium state. Phrasing the M&M strategy as a thought experiment may prevent this misinterpretation.