Teaching Methods for Balancing Chemical Equations: An Inspection versus an Algebraic Approach

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Now, to systematically apply the rules imposed by inspection methodology (see Table 2 – Table 4):

Table 2. Rule 2 Balance the Metals (Except Hydrogen)

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Table 3. Rule 3 Balance the Nonmetals (Except Oxygen)

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Table 4. Rule 5 Balance Hydrogen

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Rewriting the chemical equation for the balanced condition imposed by the results of Table 2 – Table 4 gives the final solution for equation 1a:

(1a)

The second common teaching method involves applying linear algebra to solve for balanced chemical reactions with a system of equations ^[6]. Many students typically become frustrated with the inspection method, informally referred to as the trial-and-error method, when the student experiences a complication with applying it to more advanced problems that do not lend easily to an instantaneous or serendipitous solution ^[5]. Thus, the mathematical balancing method is more approachable than use of the novel inspection methodology ^[10]. The algebraic approach generally has six steps; the undetermined coefficient list, as discussed below, is depicted in Table 5 through 8.

1. Assign undetermined coefficients to each chemical species (e.g., a, b, . . . y, and z) of the unbalanced reaction.

2. Craft a list to track the solution of each undetermined coefficient.

3. Write a balanced condition for each element.

4. Set one of the undetermined coefficients to the value of 1.

5. Solve for each undetermined coefficient.

6. Simplify any factorial solutions through multiplication.

This method is grasped best through an example. As an example, balance the following chemical reaction illustrated with equation 2:

(2)

Applying Rule 1 to equation 2 gives rise to equation 2a:

(2a)

Applying Rule 2 also gives rise to Table 5 for the undetermined coefficients:

Table 5. Undetermined Coefficient List

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Appling Rule 3 gives the following algebraic representation of the balanced condition for each element:

(2b)

(2c)

(2d)

(2e)

(2f)

Likewise, application of Rule 3 gives rise to the follow solution the undetermined coefficients depicted in Table 6:

Table 6. Undetermined Coefficient List

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This instantaneously gives the solution set depicted in Table 7:

Table 7. Undetermined Coefficient List

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Then, solving for the reaming undetermined coefficients gives the following conditions:

(2g)

(2h)

(2i)

(2j)

(2k)

(2l)

Completing the undetermined coefficient list yields the following solution set as depicted in Table 8:

Table 8. Undetermined Coefficient List

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Thus, plugging the resolved coefficients back into Equation 2a gives the following balanced chemical reaction illustrated in equation 2m:

(2m)

The goal of this study to was determine which methodological approach to balancing chemical reaction was most effective when measured with a teacher made summative assessment.

2. Methodology

2.1. Sample

The sample was purposefully drawn from the author’s students enrolled in a chemistry courses at single suburban high school in the Southeast within a major U.S. metropolitan area. The sample was representative of the school district’s distribution in terms of student algebra I ability and consisted of 196 students, 47% of which were female, enrolled in eight separate chemistry classes (whole-class cohorts). In total across all cohorts, high performing algebra I skills accounted for 28.9% of the sample, 37.5% of the sample accounted for average algebra I skill ability, and 33.6% of the sample accounted for below average algebra I skill ability (as determined by FCAT2.0^® achievement levels). Similarly, the distribution of algebra I skill level abilities was analogous within the each of the eight whole-class cohorts.

2.2. Primary Instructional Practice

Four of the whole-class cohorts (49% of the sample) received two days of traditional direct instruction by the author and nine days of subsequent guided practice for balancing chemical reactions by inspection as previously described in Example 1. The direct instruction, facilitated by the author, occurred over the course of two 45-minute periods supplemented with guided practice for nine 45-minute periods over the course of nine school days. The nine days of guided practice were carried out with analogous practice problems similar to those in Table 9 (see equations A–E); this was done in order to focus on the conceptual skill development and sustainment at both the whole-group and individual learner levels. This pedagogy lends well to cooperative learning, which encourages problem solving and allows for a positive social support structure to enable learners to challenge misconceptions ^{[11, 12, 13, 14, 15]}. Specifically, each of the reactions in Equations A–E were modeled with direct instruction. Then, with instructor-facilitated, peer-supported guided practice, students completed 20 analogous problems over the course of four school days for one iteration of practice for each singular 45-minute period per day ^{[16, 17, 18]}. After four days of exercise with the sustainment problems, students were again exposed to the research problem set (Equations A–E) where solution resolution was supported by small peer groups and modeled by the instructor. The students then completed an additional 20 analogous problem sets over the course of four school days for one iteration of practice for each singular 45-minute period per day. At the end of the nine days of guided instruction, students were re-assessed with an instrument crafted specifically from Equations A–E.

Likewise, the remaining whole-class cohorts received traditional direct instruction, facilitated by the author, and sustained practice for algebraically balancing chemical reactions as previously described in Example 2 and conserved the teaching methodology previously discussed for the balance-by-inspection method. Again, the direct instruction method coupled with guided practice allowed for conceptual skill development and sustainment at both the whole-group and individual levels ^{[11, 12, 13, 14, 15]}. Moreover, this approach allowed for a cooperative learning environment that encouraged problem-solving and allowed for a positive social support structure to enable learners to challenge misconceptions ^{[11, 12, 13, 14, 15]}. Across all cohorts, all students were specifically exposed to the five research chemical reactions, as depicted in Table 9 (Equations A–E), during direct instruction, again after the fourth day of analogous practice, and once more on their summative assessment, which included the following (unbalanced) equations:

Table 9. Balancing Chemical Reaction Assessment Items

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2.3. Summative Assessment Validity and Reliability

Table 9 depicts the five items used for summative assessment of all students for concept mastery. A table of specifications was employed to determine the validity of the test items as they pertain to Florida Sunshine State Standards SC.912.P.8.8 and SC.912.P.8.9 for chemical reactions and the law of conservation of matter, respectively. To this end, three on-site chemistry content teachers, with an average 15 years of experience, evaluated each of the five items and unanimously concurred with the summative assessment’s item alignment with both of the content standards. Moreover, each content expert stated that the items were novel, representative, and appropriate for the secondary learner in a chemistry course of study.

The summative assessment, reported in Table 9, was initially pilot tested with a subset of representative students (n = 24) whom proceeded the research cohorts by one academic year. Cronbach’s alpha was calculated for the summative assessment from the pilot test data where: α = .813, demonstrating good internal test reliability, before fielding the assessment instrument with the research cohorts.

3. Results

Table 10 and Table 11 depict the percentage of correct responses to the summative assessment of the unbalanced chemical reactions for Equations A–E for both the balance-by-inspection and algebraic methods, respectively.

Table 10. Correctly Balanced Chemical Equations, Inspection Method, by Item Number (n = 97)

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Table 11 Correctly Balanced Chemical Equations, Algebraic Method, by Item Number (n = 99)

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