Students' Success at Answering Algorithmic Versus Conceptual Problems on Chemical Equilibrium
Amanda J. Schachtel, Brittany N. Christian and Dr. Ellen J. Yezierski, Department of Chemistry and Biochemistry
Results
Introduction
Chemistry educators have assumed implicitly that success in solving algorithmic equations indicates mastery of a chemical concept.1 Over the past quarter
century, chemistry education research has questioned this widespread assumption by comparing students success at answering algorithmic versus conceptual
problems. An algorithmic problem is one that can be solved using a memorized set of procedures, whereas a conceptual problem requires the student to work
from an understanding of the concept to the solution to the problem when no memorized procedure is likely to be known. Previous studies have been
conducted comparing conceptual learning versus problem solving in topics such as density, stoichiometry, ideal gas, and molarity.2 However, the topic of
chemical equilibrium has yet to be explored. Chemical Equilibrium is an important topic to study because it is an advanced and reoccurring topic in second
semester general chemistry
• Distribution curve of
students’ total scores
• Test of normality
• Test of internal
consistency
Research Question:
How does students’ success at answering algorithmic equilibrium problems compare to their success at answering conceptual problems of the same topic?
Methods
Setting and Sample
 Two College Chemistry II classes at Miami University
 One section for chemistry majors – small majors class (N = 38)
 One section containing a wide range of majors – large non-majors class (N = 63)
 A quiz was given during regularly scheduled class time within a few weeks of students’ examination over chemical equilibrium topics.
Anderson-Darling
Test of Normality
Quiz Contents
11-Item
Quiz
Cronbach’s Alpha
0.538
Internal Consistency6 Moderate
Conceptual
(5)
General
(1)
Equilibrium
Systems (2)
Le Chatelier’s
Principle (1)
Correlation of Items Large Non-Majors Class
2
Conducted with a Spearman’s Rho
Correlations is significant
at 0.01 level
Correlation is significant
at 0.05 level
Conceptual-based problem
Algorithmic-based problem
General question
11
Equilibrium
Systems (4)
6
1
10
8
9
3
4
7
Items used for the quiz were modified from several different resources.3, 4, 5
Example of an Algorithmic Question:
For questions 1-3 use the following system at equilibrium:
4NH3(g) + 5O2(g) ⇌ 4NO(g) + 6H2O(g)
Increases the concentration of NO
Decreases the concentration of NO
No effect on the concentration of NO
Not enough information given
2
6
1
10
8
9
3
4
7
11
Small Majors Class
5. The diagram represents the equilibrium state for the following reaction:
+2 ⇌2
The closed system, with a movable piston pictured above, undergoes an increase
in volume while the temperature remains constant. What will the system look like
after the change in volume when equilibrium is reestablished?
More reactants and products
More products
More reactants
No change
Data Collection
Consent forms were distributed according to approved IRB protocol. The 11-item instrument described above was used to assess students’ chemistry
content knowledge and success at answering both algorithmic versus conceptually based problems.
Data Cleanup
An Excel file was built in order to score all of the raw data collected from the 11-item quiz. Students without consent forms or who did not complete the
quiz in its entirety were deleted.
Data Analysis
Keeping the two classes separate, each student’s quiz was scored in Excel. The number of algorithmic, conceptual, and general questions correct was
calculated along with the mean and standard deviation for each of these categories. A series of descriptive and inferential statistical tests were conducted:
TOTAL SCORE ANALYSIS
• Histograms
Descriptive Test Statistics
• Test of Normality (Anderson-Darling)
Small Majors Class
Large Non-Majors class
• Internal Consistency (Cronbach’s Alpha)
Average Total Score (11)
6.7 ± 2.2
5.2 ± 2.4
ITEM ANALYSIS
Range (Max - Min)
11 to 2
10 to 1
• Difficulty
Average Algorithmic Score (5)
2.9 ± 1.2
2.4 ± 1.4
• Discrimination Index
Average Conceptual Score (5)
2.9 ± 1.4
2.2 ± 1.3
• Correlation (Spearman’s Rho)
Average General Score (1)
0.8 ± 0.4
0.6 ± 0.5
Discrimination
Example of an Conceptual Question:
a.
b.
c.
d.
5
∆H = −904.4kJ
2. How does increasing the volume of the system affect the concentration of NO?
a.
b.
c.
d.
p = 0.0064
Non-Normal
Cronbach’s Alpha
0.597
Internal Consistency6 Moderate
Correlation of Items Small Majors Class
5
Le Chatelier’s
Principle (3)
Anderson-Darling
Test of Normality
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
Large Non-Majors Class
8
2
4
9
10
1
11
6
5
3
7
0
0.2
0.4
0.6
0.8
1
• A plot of discrimination
versus difficulty shows
individual item performance
• Items above a 0.3
discrimination are said to
discriminate well7
• Items below 0.2 difficulty
are hard, whereas above 0.8
are easy7
Discrimination
Algorithmic
(5)
p = 0.0114
Non-Normal
Difficulty (% Correct)
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
5
8
10
3
1
11
9
7
4
0
0.2
0.4
6
2
0.6
0.8
1
Difficulty (% Correct)
Future Work
• Compare correlation between items for high preforming students and low preforming students
• Interview data for problem solving techniques of conceptual versus algorithmic problems
• Investigate classes with markedly different instructional methods than those previously studied
Discussion/Conclusion
Data collected from the quiz had good psychometric properties. This supports conclusions based on the data. Predicted differences between algorithmic
and conceptual items were not observed in the initial data. However, inter item correlations demonstrated student strengths and weaknesses in particular
sub concepts of chemical equilibrium.
Le Chatelier’s Principle when assessed with both a conceptual and algorithmic problem did not always result in a significant correlation. For example, item
5 and 2 dealing with changes in volume of an equilibrium system were significantly correlated (0.05 level) for the large non-majors class but not correlated
for the small majors class.
References
1Nakhleh,
M. B., and Mitchell, R. C. (1993). Concept learning versus problem solving: There is a difference. Journal of Chemical Education 70(3) p. 190-192.
2Cracolice, M. S., Deming, J. C., and Ehlert, B. (2008). Concept learning versus problem solving: A cognitive difference. Journal of Chemical Education 85(6) p. 873-878.
3LeMay, H., Brown, T., Bursten, B., Murphy, C., and Woodward, P. (2008). Chemistry: The central science. 11. Prentice Hall.
4Bauer, R., Birk, J. and Marks, P. (2007). The gaseous state. In a conceptual introduction to chemistry (316-361). New York, NY: McGraw-Hill.
5Birk, J. (Personal Communication November 2011). Test Bank CHM 113/115. Arizona State University.
6Pallant, J. (2007). SPSS Survival Manual (3rd ed.). New York, NY: Two Penn Plaza.
7Popham, W.J. (2005). Classroom Assessment: What teachers need to know (4th edition). Boston: Pearson.
Acknowledgments
Thank you to both chemistry instructors and their students for participating in my project!