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2017 Fall ConfChem: Mathematics in Undergraduate Chemistry Instruction

Organizer(s): 
Cary Kilner and Eric Nelson

Chemistry is a quantitative science.  For college majors in the sciences and engineering, “general chemistry for science majors” is a required course that is expected to provide students with a foundation in solving scientific calculations: mathematics applied to measurements.  In recent years, many instructors have noted deficits in the background of growing numbers of students seeking to enroll in general chemistry.  In a 2012 survey of nations with highly developed economies, US 16 to 24 year olds had the lowest scores in “numeracy” among the 22 nations tested.

During this four-week conference, each week two papers will be posted for concurrent discussion.  Authors will discuss their interventions to improve student skills in the mathematics used in courses ranging from high school college-preparatory chemistry to college physical chemistry. As the conference organizers, we believe you will find ideas in each paper that can provide substantial “food for thought” in your work to help students learn.

For the two papers posted each week, Monday to Wednesday will be “reading/question days” when readers may question the authors on the content of their papers.  Thursday to Sunday will be “general discussion days” where readers and authors may originate comments and pose questions on issues related to the ideas broached in the papers.

Questions begin for the first two papers on Monday Oct 23th.  Discussion of the last two will end on Sunday, November 19.  Starting Monday, November 20 for one week (including Thanksgiving), comments may be submitted to this the main conference page in a final discussion and wrap-up.  If you have a question or comment on a paper after its week for discussion has passed, this will be the time to present it.  The conference will conclude on Monday, November 27.

Without registration, anyone may read the conference papers, questions, and comments.  However, to ask questions or post comments, you will need to register with CCCE via the instructions at the top left of this page. 

Because registration can take a day or two to activate, if you think you may want to submit questions or comments, we recommend you register as soon as possible.

Additional detail on the conduct of the conference is available at

https://confchem.ccce.divched.org/ConfChem-Newsletter%20Discussion%20Protocols

To begin, read a paper and its discussion by clicking on the title below.

Enjoy the conference!

-- Cary Kilner and Eric Nelson, Conference organizers

 

Conference Dates

Week Author Title
Week 1: Monday October 23 - Sunday October 29
Paper 1 Penn Estimation – An Empowering Skill for Students
Paper 2 Mason et. al. MUST-Know Pilot—Math Preparation Study from Texas
Week 2: Monday October 30 - Sunday November 5
Paper 3 Ranga Impact of Quick Review of Math Concepts
Paper 4 Leopold Strengthening Math Fluency through Calculator-Free Chemistry
Week 3: Monday November 6 - Sunday November 12
Paper 5 Craig Building Student Confidence With Chemistry Computation
Paper 6 Kilner The Chem-Math Project
Week 4: Monday November 13 - Sunday November 19
Paper 7 Shipman et. al. Applied Mathematics for Chemistry Majors
Paper 8 Nelson Addressing Math Deficits With Cognitive Science
Week 5: Monday Novenber 20 - Sunday November 27
ConfChem Wrap-Up

 

Conference Articles

Abstracts of Papers:

Estimation – An Empowering Skill for Students in Chemistry and Chemical Engineering

Lynn S. Penn

Abstract

Today’s students are from the generation that has always used calculators to compute the answers to problems.  This has rendered them with no means to estimate numerical answers and no way to recognize an unrealistic answer.   Lower-level undergraduate students are able to overcome these deficiencies by means of training in piece-by-piece execution of a complex algebraic computation.  By moving to fewer and fewer products and quotients in a single equation, an estimate of the final value of a complicated algebraic equation can be made readily; the students gain a sense of scale when they see that their estimates are within 10% of the exactly computed value.  At first, students resist this training, claiming that they will always have a calculator at hand.  This presentation addresses how to overcome student resistance and how to move step-wise through practice exercises to the goal of rapid and reliable estimation final values.

 

MUST-Know Pilot Study

Amy Petros, Rebecca Weber, Sue Broadway, Robyn Ford, Cynthia Powell, Kirk Hunter, Vickie Williamson, Deborah Walker, Blain Mamiya, Joselyn Del Pilar, G. Robert Shelton and Diana Mason

Abstract

Since 2007, the reported SAT (reading + math) scores for the state of Texas have steadily fallen from a high of 999 to an all-time low of 944. Solving this problem requires a multifaceted approach. For our part as instructors of a known gateway course, general chemistry, we chose to focus on the most fundamental crosscutting topic in STEM: arithmetic. Hence, the MUST Know (Mathematics: Underlying Skills and Thinking) study was conceived and implemented. General chemistry is widely considered a gateway course because students' success in general chemistry provides entry into several STEM and some non-STEM careers. Failure to succeed in general chemistry has been linked to students' mathematics fluency that other researchers have attributed to poor algebra skills. However, is it possible that this relationship should really be attributed to students' lack of "must-know" arithmetic skills? In Fall 2016-Spring 2017, a team of 11 chemical educators investigated the relationships between solving simple arithmetic problems and course grades for 2,127 students (60.3% female) enrolled in general chemistry I and II at six post-secondary institutions (3, large public research universities; 2 Hispanic Serving Institutions; and 1, 4-year private university) from varied geographic locations in the heart of the state of Texas overlaying 32,000 square miles. The arithmetic concepts evaluated for this study are introduced to most Texas students starting at the 4th-grade level. The selected concepts include multiplication, division, fractions, scientific notation, exponential notation, logarithms, square roots and balancing chemical equations. Results support that students, without the aid of a calculator, succeeded at the 40%-correct level (Chem I) and 60%-correct level (Chem II). Students' algebra skills might be a better predictor of overall success, but the initiator of the problem we posit starts with lack of automaticity and fluency with basic arithmetic skills. Correlations between final course grades and mathematics fluency ranged from 0.2-0.5 with the Hispanic-serving classes being among the weakest correlations and the research universities exhibiting the strongest. Building a strong profile of a successful general chemistry student is beginning to form from this continuing investigation. Future plans include implementation of High-Impact Practices (HIPs) to increase numeracy followed by dissemination of outcomes and expansion of the study to include other needed success-producing skills like logical thinking, spatial ability, and quantitative reasoning ability.

 

Impact of Quick Review of Math Concepts in General Chemistry Courses: Engaged Student Learning

Jayashree S. Ranga

Abstract

Math proficiency is a vital skill for mastering concepts in General Chemistry courses. In this article, the author discusses simple yet powerful, pedagogical interventions implemented in General Chemistry courses to assist students with math. (a) A quick review of math concepts essential for solving chemistry problems has led to positive learning experiences in General Chemistry courses. This includes topics such as rearranging equations, exponents, etc. (b) A major challenge in General Chemistry courses include improper use of calculators. A quick discussion emphasizing the importance of parentheses/various function keys on calculators has led to efficient problem solving sessions. (c) Problem-solving skills are one of the most important skills acquired in these courses. Students learn how to read a problem, identify the given content, and then proceed to solve the problem. To alleviate stress during the problem solving sessions, pedagogies such as pause method were explored.  Sample math review content, tips for using a calculator effectively, and problem solving strategies used in General Chemistry courses will be presented in this article.

 

Strengthening Students' Math Fluencies through Calculator-Free Chemistry Calculations

Doreen Geller Leopold

Abstract

In a previous study of students in second-semester general chemistry classes at the University of Minnesota, higher scores on a calculator-free Math Assessment, administered at the start of the semester, were found to correlate with higher grades in this course, despite the use of calculators during exams.1  The present paper describes some methods subsequently used to enhance students' math fluency through solving numerical problems using pencil-and-paper math, without the use of a calculator.  When doing such problems in class, the instructor can efficiently interleave reminders of basic algebraic methods to simplify expressions, to work with common and natural logs, and to estimate results to one or two significant figures.  Multiple-choice exams incorporating problems of this type, in which calculators were not allowed, were also administered.  It is hoped that these methods can help motivate students to gain greater intuitive and conceptual insight through solving quantitative chemistry problems, and to become more fluent in expressing science in the language of math.  Examples of such problems and their pencil-and-paper solution methods are presented in the areas of chemical equilibrium, acid-base reactions, buffers and titrations.  Students' evaluations of this pedagogical approach are also discussed.  Finally, we discuss some "broader impacts" of strengthening basic math skills, using as an example a suggested connection between some eligible voters' understanding of percentages and probabilities, and the outcome of the 2016 presidential election.

 

Building Student Confidence with Chemistry Computation

Peter R. Craig

Abstract

I work in a liberal arts college as a chemistry professor.  Not educated in the US, I have been welcomed into my adopted culture by being given the opportunity to teach that has allowed me to learn about a system I knew little about beforehand.  At the college level, chemistry can be portrayed as applied algebra.  In my experience algebra takes on a whole new level of difficulty and significance for students when the level they need to understand it underpins the comprehension of a subject it is a prerequisite for.  This appears to be exacerbated by the following factors: the lack of continuity of the offering of high school algebra and chemistry prior to entering college, the increased emphasis of attaining confidence at the cost of learning content at high school, and the numbers of students attaining access to college who don’t know how to study.  This paper looks at attempts to redevelop the robustness of students’ chemistry read-only memory (ROM) – their ability to identify and apply appropriate computational methods to solve problems without much thinking or hesitation.  With the confidence of a reliable ROM, students are better able to learn chemistry at college.

 

The Chem-Math Project

W. Cary Kilner

Abstract

Much national effort has been directed at the recruitment of STEM students. However, retention has become an equally important task, especially when many STEM students find the mathematics of chemistry a formidable barrier. In a five-year action-research study, the author has examined this problem closely from the students’ point of view. By anticipating and addressing a myriad of small issues, students’ skills and confidence can be built up and they can become proactive learners.

In this paper, the author shall present some direct quotes from students, along with examples of student work, to show how we may help students overcome their mathematics anxiety and become successful chemistry students. “Chem-math” represents a contradistinction from the “formal-math” to which these students are typically referring. In a chem-math recitation, we will review mathematics fundamentals, show how they are applied to chemistry, and clearly define all words and symbols they will use in their study. We will not allow any sloppiness in execution. Through such rigor we can set students on the road to the successful execution of chemistry exercises and problems.

 

Applied Mathematics for Chemistry Majors

Rachel Neville, Amber T. Krummel, Nancy E. Levinger, Patrick D. Shipman

Abstract

The math that chemistry students need is significant.  In physical chemistry, students need to be comfortable with ordinary and partial differential equations and linear operators. These topics are not traditionally taught in the calculus sequence that chemistry students are required to take at Colorado State University, thus mathematics can present a significant barrier to success in physical chemistry courses.  Through the collaboration of the mathematics and chemistry departments, Colorado State University has developed and implemented a two-semester sequence of courses, Applied Mathematics for Chemists (MfC), aimed specifically at providing exposure to the math necessary for chemistry students to succeed in physical chemistry.  The prerequisite for the sequence is a first semester of Calculus for Physical Scientists—that is, a working knowledge of derivatives, integrals and their relation through the Fundamental Theorem of Calculus.  MfC begins with a look at the Fundamental Theorem of Calculus that emphasizes a scientific realization that it provides, namely an understanding of physical phenomena in terms of an initial condition and the rate of change.  This introduces the first topic of MfC, namely first- and then second-order differential equations.  Working with differential equations at the start of the course allows for questions from chemistry to motivate the mathematics throughout the sequence.  Solving the differential equations naturally introduces students to another fundamental mathematical concept for physical chemistry, and another theme of the course, namely linear operators.  The flow of the course allows for topics traditional to second and third semesters of calculus, such as Taylor series and complex numbers, to be motivated by solving chemical problems and leads to some topics, such as Fourier series, which are not part of the standard calculus sequence.  Feedback from students who have taken MfC and then physical chemistry has been positive.

 

Addressing Math Deficits to Improve Chemistry Success

Eric A. Nelson

Abstract

The brain solves problems in structures termed “working memory.”  Between 2001 and 2010, cognitive experiments verified that at each step when solving a problem, working memory can hold only a few small elements of knowledge that are not well-memorized.  One implication of this limit is that students must rely almost exclusively on the application of memorized facts and algorithms when solving mathematical or scientific calculations. 

Unfortunately, since 1990, K-12 math standards in most U.S. states assumed that with access to calculators and computers, memorization in math could be de-emphasized.  As a result, many students have deficits in “automaticity” in the recall of math that is necessary for chemistry.  This paper will include evidence that if math fundamentals are moved into memory as preparation for a chemistry topic, student success in first-year chemistry improves substantially.

Comments

Hi All,
This is the second test of the ConfChem.  Hopefully this goes out to everyone, and has a link that brings you back to the conference homepage.  On Monday morning we will subscribe papers 1 and 2 to the list, and send out a message to the list, indicating the start of the discussions.  Please feel free to read the articles, but withhold making comments until the list is subscribed to the papers.  That way the authors can be available to respond. 

Hopefully this will be the last test email.

Cheers,
Bob

Bob Belford's picture

Hi All, 

Please pardon if this seems a bit in left field, but hopefully it is of relevance to the recent discussion that was carried on the ConfChem list, dealing with the preparation of instructors for the task of instruction.

When my students complain about varied and often contradictory theories I often tell them a story from my grad school days, and the importance of thinking and conditional knowledge. This was the story of a colleague who received his PhD in Russia in the immediate-post Stalin era. He explained to me that it was not “healthy” in the day’s of Stalin to be a scientist who believed in genes, and that there was actually an alternative theory called Lysenkoism, https://en.wikipedia.org/wiki/Lysenkoism.  (Please check it out if you are not familiar – it is an eye opener!)

The point at hand here is that Mendelian genetics were making their way back into the Russian universities when he was a student, and he not only had to know both theories, but guess on who was asking the question, and then determine which theory he should reply with. My point here is that part of the “task of instruction” is to get students to think, and not just parrot what the instructor knows, and things could be worse, a lot worse! 

Cheers,
​Bob