Report Cite This: J. Chem. Educ. XXXX, XXX, XXX−XXX
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ConfChem Conference on Mathematics in Undergraduate Chemistry Instruction: The Chem-Math Project W. Cary Kilner* Chemistry Department, University of New Hampshire, Durham, New Hampshire 03824, United States
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S Supporting Information *
ABSTRACT: From 2005 to 2010, I conducted 80 min recitations for ∼20% of the general chemistry population who were identified and placed as underprepared or at-risk in the first semester, or who elected it as their assigned “group-learning experience” in the second semester. Action-research was used to determine the extent of mathematics remediation needed, the effectiveness of pedagogical techniques used, and the increase in students’ skills and confidence in course success as a result of our work together. Data for analysis included recorded student dialogue and individual interviews, survey data, students’ work on paper, and photos of group work on white-boards. This report summarizes paper 6 of the 8 invited papers to the ConfChem online conference on Mathematics in Undergraduate Chemistry Instruction, held from October 23 to November 27, 2017, and hosted by the ACS DivCHED Committee on Computers in Chemical Education (CCCE). KEYWORDS: High School/Introductory Chemistry, First-Year Undergraduate/General, Second-Year Undergraduate, Upper-Division Undergraduate, Continuing Education, Physical Chemistry, Inquiry-Based/Discovery Learning, Problem Solving/Decision Making, Testing/Assessment, Mathematics/Symbolic Mathematics
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INTRODUCTION The focus of this study was students’ lack of facility with basic arithmetic and algebra in solving chemistry exercises and problems. Previous research in high school had led me to postulate a distinction between formal-math as taught in mathematics classes, and chem-math as the specific mathematics skills used in the physical sciences combined with proportional-reasoning.1 Weaker students tend to think that “chemistry is all math” and are unduly intimidated. Data showed that students doing poorly on formal-math assessments often have an inherent proportional-reasoning ability that can lead to success if appropriately accessed. When chem-math is specifically addressed, requisite skills can be memorized and practiced, and students can be disabused of the apprehension of chemistry as formal-math that prevents them from attending to chemistry concepts. Thus, addressing the affective domain is important in building confidence that chemistry IS a learnable subject, leading students to doing hard work in the face of adversity and in seeking genuine understanding rather than memorizing for exams.2 To investigate the hypothesis that chem-math and formalmath constitute two distinct domains, that formal-math alone is not the primary barrier for underprepared students, and that good proportional-reasoning represents an ability to learn chemistry, I developed a structural equation model (SEM) with two latent variables: math-prep and chem-prep.3−5 I administered a chem-math quiz that included some proportional-reasoning exercises similar to those used on the TOLT and GALT tests. Formal-math was assessed via a calculus placement exam similar to SAT-Math.6,7 These two variables comprised math-prep. Chem-prep was assessed with some early chemistry applications similar to those found on the Toledo8 and California9 exams. To investigate students’ expectation of © XXXX American Chemical Society and Division of Chemical Education, Inc.
success in the course I included a Likert-scale survey requesting self-reported readiness, based upon high-school chemistry experience or lack thereof. I then linked math-prep and chem-prep to their final course grade (excluding the lab component). This SEM model could ultimately be used to estimate a final course grade and thus place at-risk students in chem-math recitations, rather than using a formal-math measure, typically the SAT-Math, as the lone indicator of future success.
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KEY FINDINGS AND DISCUSSION As part of the 2017 Fall ConfChem: Mathematics in Undergraduate Chemistry Instruction,10 this contribution was discussed online: the original paper and its discussion are provided in the Supporting Information. Readers suggested an initially reviewing general mathematics skills, or beginning with the needed mathematics upon first exposure and reviewing chem-math all at once, or introducing chemistry-related mathematics on a need-to-know basis. Any such review is best done via recitations led by a pedagogical-content expert, by a suitable graduate student, in a learning assistant program, or by use of the PLTL methodology.11,12 Some students need a stand-alone “prep-chem” course, run in tandem with lecture or in the preceding semester. Such an implementation must be made by survey of the specific needs of students and the time available for such an intervention. The most ill-prepared students need a separate introductory chemistry or physical science course to provide the missing conceptual fundamentals necessary for success in general chemistry. Students who need Received: February 5, 2018 Revised: May 25, 2018
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DOI: 10.1021/acs.jchemed.8b00075 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
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a separate course will often not elect it, and so must be diagnosed and assigned if they are to access such help. The recitation format has shown to be an effective way for capable but underprepared students to be integrated into the lecture course. It provides the small-group, cooperativelearning format in which an instructor can monitor class interactions; the mathematical strengths of students can contribute to their groups, and the weaknesses of each student can be identified and addressed. The recitation instructor would tailor chem-math instruction to the course syllabus to enable students to keep up with its fast-paced lectures. Recitation also provides a way to institute tested models such as POGIL, Modeling Instruction, and BSCS 5-E Instruction.13−15 Students’ misunderstanding of terminology can present a major obstacle to learning.16 This includes science nomenclature to which students are assumed to have been introduced, common English words that have specific chemistry applications, and important words and phrases from mathematics instruction that should be used when addressing chem-math procedures. Specifically asking students about the vocabulary their mathematics instructors have used can reveal misunderstandings, while conversations with mathematics teachers can inform the instructor about terminology commonly used in teaching fundamental mathematics skills. Detection of confusion when it arises is possible in the small class, whereas in the large lecture the instructor may be unable to recognize it and thus intervene. Multiple representations of chemical macroscopic and microscopic phenomena are useful for helping students understand the underlying mathematics.17,18 Particulate models enable students to see important proportional relationships.19 Presenting a common set of mechanics encourages students in setting up and solving exercises and problems properly so they are all doing their mathematics correctly, rather than using a variety of careless steps they may have brought from high school. Quality online sites for chem-math practice are available, such as the Khan Academy20 and chemreview.net with its accompanying text.21,22 These allow students to seek the specific help and practice they choose. ALEKS can be assigned as homework to ensure that students do their mathematics study in the correct sequence of topics, thus ensuring prerequisite fundamentals are in place.23
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REFERENCES
(1) Bodner, G. Action Research: Overcoming the Sports Mentality Approach to Assessment/Evaluation. University Chemistry Education 1999, 3 (1), 31−36. (2) Tobias, S. Overcoming Math Anxiety, 2nd ed.; W.W. Norton & Co.: New York, 1993. (3) Byrne, B. M. Structural Equation Modeling with AMOS; Basic Concepts, Applications, and Programming; Lawrence Erlbaum Associates: Mahwah, NJ, 2001. (4) Kline, R. B. Principles and Practice of Structural Equation Modeling, 3rd ed.; Guilford Press: New York, 2011. (5) Ullman, J. B. Structural Equation Modeling: Reviewing the Basics and Moving Forward. Journal of Personality Assessment 2006, 87 (1), 35−50. (6) Lewis, S. E.; Lewis, J. E. Predicting At-Risk Students in General Chemistry: Comparing Formal Thought to a General Achievement. Chem. Educ. Res. Pract. 2007, 8 (1), 32−51.. (7) Bunce, D. M.; Hutchinson, K. D. The Use of the GALT (Group Assessment of Logical Thinking) as a Predictor of Academic Success in College Chemistry. J. Chem. Educ. 1993, 70 (3), 183−187.. (8) WHAT is the TCPE (Toledo Chemistry Placement Exam)?. http://rheum4us.org/wp-content/uploads/2011/08/Toledo_ Chemistry_Placement_Exam.pdf (accessed May 2018). (9) The California Chemistry Diagnostic Test (CCDT)Assessment Services. https://pasadena.edu/admissions-and-aid/assessmentservices/chemistry-exam.php (accessed May 2018). (10) American Chemical Society, Division of Chemical Education, Committee on Computers in Chemical Education. 2017 Fall ConfChem: Mathematics in Undergraduate Chemistry Instruction. https://confchem.ccce.divched.org/2017FallConfChem (accessed May 2018). The Chem-Math Project paper and discussion are available at https://confchem.ccce.divched.org/content/ 2017fallconfchemp6 (accessed May 2018). (11) Learning Assistant Program, University of Colorado Boulder. https://laprogram.colorado.edu/ (accessed May 2018). (12) Gosser, D. K.; Roth, V. The Workshop Chemistry Project: Peer-Led Team Learning. J. Chem. Educ. 1998, 75, 185. (13) POGIL. https://pogil.org/contact-us/the-pogil-team/richard-smoog (accessed May 2018). (14) Modeling Instruction in High School Sciences. http:// modeling.asu.edu/modeling-HS.html (accessed May 2018). (15) 5-E Model for Teaching Inquiry Science. http://www. bioedonline.org/videos/supplemental-videos/5e-model-for-teachinginquiry-science/ (accessed May 2018). (16) Johnstone, A. H. Words That Matter in Science: A Report of a Research Exercise; The Royal Society of Chemistry: Great Britain, 1985. (17) Jensen, W. B. Logic, History, and the Chemistry Textbook. J. Chem. Educ. 1998, 75 (7), 679−687. (18) Johnstone, A. H. Modeling with Magnets: A Unified Approach to Chemistry Problem Solving. Science Teacher 1992, 59 (3), 58−63. (19) Sanger, M. J. Evaluating Students’ Conceptual Understanding of Balanced Equations and Stoichiometric Ratios Using a Particulate Drawing. J. Chem. Educ. 2005, 82 (1), 131−134. (20) Chemistry. https://www.khanacademy.org/science/chemistry (accessed May 2018). (21) Calculations in Chemistry. Problem-Solving Tutorials. http:// chemreview.net/ (accessed May 2018). (22) Dahm, D. J.; Nelson, E. A. Introduction to Chemistry Calculations; ChemReview Publishing, 2011. (23) ALEKS Course Products. https://www.aleks.com/about_ aleks/course_products (accessed May 2018).
ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available on the ACS Publications website at DOI: 10.1021/acs.jchemed.8b00075. Full text of the original paper with associated discussions
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Report
from the ConfChem Conference (PDF)
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
W. Cary Kilner: 0000-0002-3777-7695 Notes
The author declares no competing financial interest. B
DOI: 10.1021/acs.jchemed.8b00075 J. Chem. Educ. XXXX, XXX, XXX−XXX
