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MUST-Know Pilot—Math Preparation Study from Texas


Amy Petros1, Rebecca Weber1, Sue Broadway1, Robyn Ford1, Cynthia Powell2, Kirk Hunter3, Vickie Williamson4, Deborah Walker5, Blain Mamiya6, Joselyn Del Pilar7, G. Robert Shelton7 and Diana Mason1

1University of North Texas, Department of Chemistry, Denton, TX
2Abilene Christian University, Department of Chemistry and Biochemistry, Abilene, TX
3Texas State Technical College, Chemical Technology Department, Waco, TX
4Texas A&M University, Department of Chemistry, College Station, TX
5The University of Texas at Austin, Department of Chemistry, Austin, TX
6Texas State University, Department of Chemistry and Biochemistry, San Marcos, TX
7Texas A&M University-San Antonio, Department of Science and Mathematics, San Antonio, TX
1Retired, University of North Texas, Department of Chemistry, Denton, TX

10/26/17 to 11/01/17

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.


Declining numeracy in the U.S. is real and gaining concern. The curiosity for this investigation piqued when a co-author from the Naval Academy noticed that U.S. students were "calculator dependent" and had not received appropriate number-sense training in their K-12 studies (Hartman & Nelson, 2016). These authors offered a link to a quiz ( that the last author of this paper named the MUST (Math-up Skills Test), and subsequently employed it as part of a pilot study named the MUST-Know project initiating a statewide investigation.



Texas, we have a problem!

In general, college-ready Texas students are less prepared now than they have been over the last 30 years (Fig. 1).

Figure 1. SAT scores over 30 years (points 1-30) with demarcations indicating changes to state adopted curriculum standards. [Note when Science Director Comer resigned: point 21 (2007).]

Some of the justification of declining scores is attributed to the 2010-11 academic year (AY), when the Texas Education Association (TEA) funded free SAT exams. With lower-income students able to take the SAT, potentially additional weaker students may have contributed to the decline. In AY 2011-2012 and thereafter, some districts began offering SAT exams during the school day, thereby increasing the number of less motivated students (i.e., a get out of class free card!) that may have attracted a population who had not completed the suggested college-prep curriculum. Related to the graph in figure 1, separating Math SAT scores from SAT Reading + Math, a decline of 22 points occurred from 2010 to 2015 (504 to 482, respectively). However, on a positive note, there is a slight bump in AY 2012-2013, when the 4´4 curriculum was fully implemented. The Texas 4´4 program required all high school students to sit for four assessments in English, mathematics, science and social studies, and pass a minimum of three in each discipline in order to graduate. One can assume from this small upward movement that “when required” (i.e., when tested), students' understanding will improve. Since 2013, high-stakes testing is no longer required and SAT scores in Texas have plummeted.


Texas Curriculum Assessments

Texas has changed the state-adopted curriculum four times over the last 30 years. Each was accompanied by high-stakes assessments (estimated to cost about $1M each). TEA instituted a statewide testing program in 1979 for grades 3, 5 and 9. Prior to 1990, there was TABS (Texas Assessment of Basic Skills), and by 1986, TEA implemented TEAMS (Texas Educational Assessment of Minimum Skills) that when not passed students were not eligible to receive a high school diploma stemming from Governor White's "no pass, no play" policy. Curriculum was changed to TAAS (Texas Assessment of Academic Skills) in 1990 and then to TAKS (Texas Assessment of Knowledge and Skills) in 2003, with the latest version (2011-2012) becoming the STAAR (State of Texas Assessment of Academic Readiness) program that was dismissed by the current governor as a requirement for graduation. Now, from four science assessments being required for graduation there is only one required test in science (Biology STAAR) and poor performance no longer prevents a student from graduating. Another observation coinciding with the constant decline of SAT scores is the resignation of a dynamic TEA science director in 2007. Science Director Comer helped develop and promote the 4´4 curriculum as a strong advocate of advancing study in all sciences and recognizing the necessity of partnering with mathematics education.


Calculator Usage

Currently, Texas high school students only take one high-stakes science assessment and STAARs in Algebra I and II. The calculator policy states no calculators are permitted on STAARs in grades 3-7, but districts must ensure that each student has a graphing calculator to use on all STAARs starting with 8th-grade mathematics (both paper and online versions) and biology. For the biology assessment, there should be one calculator (four-function, scientific, or graphing) for every five students. Students may bring their own calculators with them to the assessments, but Internet capabilities must be disabled and calculation applications on smartphones are not allowed. [There was at one time a graduation proposal that student's score on end-of-course assessments would be 15% of their final grade for that course, but this was rejected almost as soon as it was suggested!] Beginning in May 2018, the grade 8 science STAAR will require students to have access to calculators with four-functions, scientific or graphing capability (TEA, 2017).

MUST [Mathematics: Underlying Skills and Thinking] Know Pilot Study

Demographics: Institutions

One strength brought to this investigation on what arithmetic-fluency levels are necessary to succeed in general chemistry lies in the team's differences. With variations in required institutional prerequisites, class sizes, instructors, textbooks, teaching methods, information and communication technology (ICT) tools, etc., the evaluations have produced similar results leading the team to a "value added" model that may contribute to curricular improvements.

Our research team consists of eight general chemistry instructors employed at six universities (three public research; two Hispanic Serving Institutions (HSIs); and one, four-year private) spread across 32,000 mi2, about 12% of the state. All faculty team members have acquired IRB approval for this research at each institution.

Abilene Christian University (ACU) is a small private university in west Texas. The student body is ethnically diverse; there are ~4,500 full-time enrollees with 63% of students listing Caucasian, while 37% are from underrepresented minority groups. Female students comprise 59% of the student population. Texas residents make up 86% of the student body.

Texas A&M University–San Antonio (TSA) was the first Texas A&M University System institution to be established in a major urban center in 2009. Currently enrolled are approximately 5,500 students. Both undergraduate and graduate-level classes are offered. The Fall 2016 semester marked A&M-SA’s first cohort of freshman and sophomore students. Of these students, 74% are first generation, 60% female, and nearly 83% identify as Hispanic or Latino recognizing A&M-SA as a HSI. Nearly 1 in 6 students are military connected.

Texas State University (TSU) founded in 1899 is the fourth largest public university in the state of Texas and 34th largest in nation with an enrollment of almost 40,000 students with over 34,000 classified as undergraduates. The university offers 98 bachelors degrees, 91 masters degrees, and 13 doctoral degrees, and is in the top 6 in graduation rates among the 38 public universities in Texas. The population includes 57.9% females, 10.7% African-American, 34.7% Hispanic, and 48.1% white with the remaining 6.6% being Native American, Asian/Pacific Islander, or Non-Resident Alien. This HSI ranks 14th in the nation for total number of bachelors degrees awarded to Hispanic students. The reported six-year graduation rate stands at 54% and the retention rate of returning freshmen is 77.4%.

Texas A&M University (A&M) opened its doors in 1876 as the state's largest and first public institution of higher learning. TAMU is among nation’s five largest universities with an enrollment of over 66,000 students. TAMU is one of only a few universities in the country to be designated a land grant, sea grant and space grant university, and is reported by the U.S. News & World Report as ranking second in the nation in the "Best Value Schools" category among public universities. Enrollment includes 52% male, with 58% white, 20% Hispanic, and 22% other ethnic groups (black, Asian, international, Native American, etc.). The university has more than 130 undergraduate degree programs, 170 masters degree programs, 93 doctoral programs and 5 first-professional degrees as options for study. The reported six-year graduation rate for the undergrads stands at 79.5%.

The University of Texas at Austin (UTX) is a Tier One research institute, the flagship campus of The University of Texas System, and second largest in the state. Enrollment of 51,000 students (40,000 undergraduates) represents all 50 states alongside 118 countries. Student demographics include a population of 51.5% female, 43.3% white, 20.0% Hispanic, 17.8% Asian, 3.9% black, 10.1% foreign, and less than 5% other or combination of these. UT strives to improve upon several accolades, including Forbes’ 17th Best Value School and Kiplinger’s #13 Best Value Public College. As one of the largest science colleges in the U.S., UT’s College of Natural Sciences includes over 13,000 undergraduates. Many of these students participate in groundbreaking, nationally recognized programs such as the Freshman Research Initiative (FRI) and Texas Interdisciplinary Program (TIP). UT currently reports a six-year graduation rate of 81.2% for undergraduates.

University of North Texas (UNT) established in 1890 is a four-year public R1 (Carnegie Classification) doctoral university with an enrollment over 38,000 students (fifth largest in the state), 31,000+ classified as undergraduates. For 21 years in a row, UNT has been named one of America's Best College BuysÒ with 16 programs (5 STEM areas) reported by the U.S. News & World Report as ranking in the Top 100. The reported ethnic makeup includes African-Americans (14.01%), Hispanics (22.12%), and white-non-Hispanics (48.41%) with the remaining 15.46% being Native American/Alaskan and Asian and Pacific Islanders or Non-Resident Alien. The reported six-year graduation rate for the 2008 UNT undergrads stands at 59.1%.

Demographics: Students

The research team investigated relationships between solving arithmetic problems appropriate for success in general chemistry and course grades of 2,127 students. The combined student population consists of 60.3% female and 85.4% freshmen and sophomores enrolled in general chemistry I and II (Chem I and Chem II) and engineering chemistry courses. Gathering data on the ethnicities within these classes proved problematic at different institutions given various IRB inclinations. However, we assume that the combined students' ethnicities mirror those of Texas given the wide geographic area involved.

Texas Student Profile 2015-2016 (2017 Texas Public Higher Education Almanac)

  • Debt level of bachelor-degreed graduates: State average = $31,186
  • Racial and ethnic distribution (majority minority state):
    42.5% white, 39.9% Hispanic, 11.4% African American, 6.1% other
  • Higher education enrollment:
    36.4% white, 36.0% Hispanic, 13.2% African American, 14.4% other
  • Students meeting college readiness benchmarks: 26%


MUST Instrument: Statistically valid and reliable

The instrument chosen to assess the arithmetic skills of general chemistry students in the pilot study was published in a report by Hartman and Nelson (2016). This instrument contains a total of 16 items, has two versions, and is named the MUST (Math-Up Skills Test). Both versions of the MUST were validated by two UNT mathematics professors. The MUSTs were statistically proven to be highly reliable (KR-21 = 0.821) and no statistical differences between versions were shown to exist. The two mathematics professors noted that the concepts covered by this instrument were not taught at the college level because they had been previously taught and assessed prior to post-secondary matriculation.

The MUST was given to students (n = 2,127) face-to-face during class without the use of a calculator (time limit of 12 min) followed by with use of a calculator (time limit of 12 min). Each correct answer earned 1.0 point and no points were awarded to an incorrect answer. Table 1 presents the grade level where the various topics on the MUST are introduced to Texas students and the means for each correctly answered question. The overall mean is X̄ = 7.36/16 = 46.0%.

Table 1. MUST questions (without use of calculator, 1.0 point each)



Level Introduced (typical grade)



multiplication of two, two-digit numbers

4th grade



exponential notation multiplication

algebra I (8th or 9th grades)



exponential notation multiplication

algebra I (8th or 9th grades)




6th grade



number raised to zero power

algebra I (8th or 9th grades)



exponential notation division

algebra I (8th or 9th grades)



exponential notation division

algebra I (8th or 9th grades)



convert fraction to decimal

6th grade



convert fraction to decimal

6th grade



solve for an unknown variable

algebra I (8th or 9th grades)



determine base-10 logarithm

algebra II (10th or 11th grades)



determine base-10 logarithm

algebra II (10th or 11th grades)



number in exponential notation squared

algebra I (8th or 9th grades)



square root of number in exponential notation

algebra I (8th or 9th grades)



balancing chemical equation

chemistry (10th or 11th grades)



balancing chemical equation

chemistry (10th or 11th grades)



As can be seen in Table 1, some of the topics are introduced as early as 4th grade and all have been presented to students prior to high school completion. The last two questions cover the topic of balancing equations, technically an exercise in counting, but not a required course for all high school graduates. Raising an integer to the zero power appears to be the most understood concept with base-10 logarithms being the least understood concept. A challenge to teaching general chemistry is presented when only 66% of the students assessed can multiply two, two-digits numbers (like, 87 ´ 69) correctly.


Data without student identifiers from each institution were sent to the research team leader (last author) for compilation. The data analyses to date include descriptive statistics, measures of reliability, correlations, and t-tests. As the database grows and the study continues, more statistical evaluations are planned such as Spearman rho correlations and ANOVAs to compare relationships between groups.

Combined data (n = 2,127) from this pilot study were evaluated, then separated by courses, by institution and semester, and re-evaluated. Some of the team members presented the MUST with demographic information and IRB consent forms on different days, some gave the MUST without a calculator and with a calculator on different days, and some students did not answer all the required demographic information requested reducing the population with complete data sets to n = 1,415 or 66.5% of the whole. However, for the purpose of this report, the larger population will be acknowledged most of the time.

One of the first observations made was how the scores on the MUST followed the same pattern across multiple classes at various institutions (Fig. 2). It is not that students at the various universities scored the same, but the up and down flow of the means of each question regardless of class (Chem I, II, Engineering), institution, semester (fall, spring) all appear to illustrate the same trends. The majority of these students were educated in Texas secondary schools, so it appears that many have garnered similar understandings.


Figure 2. Pattern produced by MUST scores across multiple settings. Y-axis: point value of 1.0 per question. X-axis: MUST question numbers.

By Student Success

The percentage of successful (grades of ABC) Chem I students (n = 482) is 66.1%, Chem II (n = 901) is 79.9%, and Engineering Chem (n = 32) is 68.8%. However, some of the successful students in the courses did poorly on the MUST and vice versa. The percentage of successful Chem I students who have a MUST score below the mean (i.e., MUST scores = 0-4) is 153/319 = 48.0%. The percentage of unsuccessful (grades of DF) Chem I students who have a MUST average below the mean (i.e., MUST scores = 0-4) is 119/163 = 73.0%, highlighting that a higher percentage of Chem I students with a low MUST score are unsuccessful students in this course. The percentage of successful Chem II students who have a MUST average below the mean (i.e., MUST scores = 0-8) is 280/720 = 38.9%, and the percentage of unsuccessful Chem II students who have a MUST average below the mean (i.e., MUST scores = 0-8) is 145/181 = 80.1%. Yes, students can be successful with low MUST scores and with above average MUST scores one is not guaranteed success, but the odds are better for success if a student has adequate arithmetic skill. If you are in Chem II, lacking MUST skills is even more pronounced with over 80% not being successful in the course when MUST scores are below average.

By Course

As reported in Table 2, students without the aid of a calculator and complete data sets (n = 1,415) succeeded at less than 30%-correct level in Chem I (4.53/16) and slightly more than the 50%-correct level in Chem II on the MUST (8.38/16) with the engineering class' MUST score falling between (7.63/16). With the use of a calculator, students performed better in Chem I and II with approximately 70% and 80% correct, respectively. However, the correlation to course grades without a calculator was higher than with a calculator, r = 0.451(Fig. 3) and r = 0.402, respectively. Even though correlations are low, the MUST was shown to be a consistent predictor of success despite existing variations between the classes; the combined data relationship between MUST scores and course grades appears to be linear (Figs. 3 & 4).


Table 2. MUST without calculators by class


Number of students (n = 1,415)

MUST mean (SD), max = 16
Course Average (SD)

Chemistry I

n = 482

4.53 (3.33)
74.16% (16.06)

 Chemistry II

n = 901

8.38 (4.41)
78.48% (15.84)

Engineering Chemistry

n = 32

7.63 (3.62)
71.53% (15.92)

Course Grade

MUST mean(SD)

MUST mean(SD)

      MUST mean(SD)


F: 0-59.4%

2.94 (2.50)

3.97 (3.57)

5.75 (5.50)

D: 59.5-69.4%

3.57 (2.95)

5.84 (3.78)

8.33 (4.46)

C: 69.5-79.4%

4.34 (2.97)

7.49 (4.14)

7.62 (3.69)

B: 79.5-89.4%

4.97 (3.46)

9.60 (3.77)

7.75 (2.05)

A: 89.5-100.0+%

6.73 (3.51)

10.71 (3.83)

10.00 (n/a)


Figure 3. Relationship between MUST (without calculator) and course grade. (Slope: m = 1.73)


Figure 4. Relationship between MUST (with calculator) and course grade. (Slope: m = 1.51)

Graphical representations of the data supporting Table 2 show the greater linear relationship of course grades to the MUST without the use of a calculator than to the MUST with a calculator especially in Chem I (Fig. 5). Students who used a calculator have a greater variance in success in Chem I as noted the percentage of students who did well on the MUST but not so well in the subsequent course. In Chem II (Fig. 6) both without and with the use of a calculator there appears to be less of a difference when compared to course grades.


Figure 5. CHEM I: MUST scores without and with the use of a calculator vs. grade.


Figure 6. CHEM II: MUST scores without and with the use of a calculator vs. grade.


By Institution and Semester

Table 3 separates data from the various institutions. The research universities in ranked order are UT Austin, A&M and UNT. Noting Chem II MUST scores of these universities in the spring semester, they are 11.41, 10.73 and 5.38, respectively. ACU is a private university in Abilene and performed very well on the MUST, and the two HSIs (TSU and TSA) reported the lowest MUST scores in both the fall and spring courses.


Table 3. Data without calculators by institution (n = 2,127)










































































By Gender and Classification

When general chemistry data, separated by semesters, were evaluated (Table 4), males outperformed females on the MUST without the use of a calculator (p < .05) in the fall, but not in the spring. As to course grades, no statistical difference was evident in the fall course averages, but in the spring, females statistically outperformed males.

Table 4. Combined data by gender (without calculator)





Spring 2017




















*p < .05 (males outperformed females on MUST in fall 2016 without a calculator; no difference in spring)

**p < .05 (females outperformed males in course averages without statistical difference on MUST)


No statistical differences were discovered between the various classifications (Table 5) where of interest is that freshmen distinguished themselves by bringing the highest MUST and course averages while students identified as juniors had both the lowest MUST and course averages.

Table 5. Combined data by classification (n = 2,127)


n (%)


Course Average (SD)


1197 (56.3%)

7.87 (4.30)

79.33 (13.96)


620 (29.1%)

7.08 (4.22)

76.94 (15.03)


238 (11.2%)

5.87 (4.03)

70.14 (18.29)


72 (3.4%)

6.07 (4.68)

72.51 (18.56)

Successful and unsuccessful male MUST scores were statistically higher (p < .05) than those of the females (Table 6). Course averages presented no statistical differences for successful or unsuccessful students of either gender. A slightly greater percentage of females were successful in the classes on the average than males even though they entered with lower MUST scores. It is possible that this observation is due to the nature of general chemistry curriculum in that algorithmic assessments are paired with conceptual understanding assessments and females improve their overall grades because final grades are not solely based on mathematics fluency.

Table 6. Successful female and male students (without calculator)


n (%)

MUST Average (SD)*

Course Average (SD)

Successful Females

989 (77.1%)

7.76 (4.00)

84.17 (8.39)

Unsuccessful Females

294 (22.9%)

4.28 (3.36)

56.70 (12.85)

Total Females


6.96 (4.13)

77.87 (15.01)

Successful Males

618 (73.2%)

8.94 (4.33

83.88 (8.37)

Unsuccessful Males

226 (26.8%)

5.25 (3.87)

56.72 (13.38)

Total Males


7.95 (4.51)

76.60 (15.61)

*p < .05 (Total males outperformed total females on MUST)



The average successful (course grades of ABC) general chemistry student based on pilot study data has the following profile: Chem I MUST score ≥ >32% correct and Chem II ≥ 58% correct. The team is in the process of building a more definable profile of what it takes to be a successful general chemistry student. In the fall 2017, an algebra-skills assessment is being added to the investigation, and the MUST (with calculator) is being eliminated. The demographic section has been expanded in order to give us more information about students' experiences so that those in danger of not succeeding may receive informed advising and hopefully avoid some of the noted attrition, and thereby grow the understanding of a successful general chemistry student.



2017 Texas Public Higher Education Almanac Chem13 News (September 2012). Why students fail in college.

De Vega, C. A.; McAnally-Salas, L. (2011). US-China Education Review, 1, 10.

Hartman, JudithAnn, and Nelson, Eric A. (2016). Automaticity in Computation and Student Success in Introductory Physical Science Courses. Cornell University Library. arXiv:1608.05006v2 [physics.ed-ph] Paper presented as part of Chemistry & Cognition: Support for Cognitive-Based First-Year Chemistry.

Technical Digest 2008-2009, Chapter 1: Historical Overview of Assessment in Texas (pp 1-8).

Texas Education Agency (TEA) Student Assessment Division. (2017). Updated calculator policy.

Texas Essential Knowledge and Skills (TEKS) Home Page. (accessed September 2017).

Texas CCRS. Website of the Texas Higher Education Coordinating Board, Texas College Readiness Standards. (accessed Sep 2017).

Tai, R. H.; Ward, R. B.; Sadler, P. M. (2006). High School Chemistry Content Background of Introductory College Chemistry Students and Its Association with College Chemistry Grades. Journal of Chemical Education, 83, 1703–1711. DOI: 10.1021/ed083p1703

Zeegers, P. L. M. (2001). A Learning-to-learn Program in a First-year Chemistry Class. Higher Education Research Development, 20, 35–52. DOI: 10.1080/07924360120043630


Supplemental Information for Discussion

For the past 25 years, academic statistics on college readiness have remained relatively constant (Tai, Ward, & Sadler, 2006; Chem 13 News, 1986 and 2012). On average, students take six years to complete a four-year college degree, and 30-60% of these students will require remedial coursework upon entering college (Tai, Ward, & Sadler, 2006). A more disturbing statistic is that roughly 30% of incoming first-year students consider terminating their academic studies entirely (Zeegers, 2001). Students have many challenges as they progress from secondary to postsecondary education. The failure of many freshmen comes from their inability to become proficient at time management, planned study time, a heavier reading load, no reminders of tests and homework, balancing work and play, and having to seek out help on their own (De Vega & McAnally-Salas, 2011).

College-Ready Students

"Why students fail in college" was published in Chem 13 News (September 2012), but originally published in October/November 1986 in Chem 13 News, pages 10-11.

Which of the following remain true today?

1.  Unprepared (or underprepared) to assume responsibility for their own learning.

2.  Time management skills are lacking.

3.  Lack of self-discipline needed to study effectively.

4.  Do not understand whether or not they comprehend the material needed.

5.  Lack of skills to find needed information or how to separate misleading or irrelevant information.

6.  Difficulty in synthesizing information from several sources.

7.  Failure to complete (and sometimes even begin) assignments.

8.  Failure to interpret tables, diagrams, graphs, mathematical expressions, and specialized languages such as chemical equations.

9.  Poor communication skills especially when attempting to express their own ideas.

10. Lack of originality needed to synthesize subject matter and draw conclusions.

      11. Writing is often poorly organized, grammatically incorrect and riddled with contradictions.

      12. Inability to evaluate facts, directions, or other information.

13. Lack flexibility when faced with a poor instructional environment to acquire useful knowledge on own.

      14. Meaning of memorized words remains unclear.

      15. Failure to understand logic behind the algorithms or rule.

16. Proportional reasoning is lacking at a level required to understanding most chemistry concepts and computations.

17. The logic inherent in mathematical and chemical language, spatial reasoning, mental constructs and how to think about chemical changes are at best in an immature stage.

      18. Inability to retrieve information "taught" from long-term memory.


Transition from high school to college

Coursework in high school chemistry and in general chemistry is aligned (Texas College and Career Readiness Standards, 2009). Future employers expect diligence, persistence, reliability, problem-solving skills, and logical thinking that can be promoted in chemistry courses. What is not in place is how to help student adjust to a set of new expectations, but we can help here, too! Maybe when implementing your latest high impact practices (HIPs) consider the following:

(1)  High school expectations are mainly effort based.

  • students who make below 70% on a test can retake it

  • make up work is required when there is an excused absence

  • extra credit is routinely available

  • attendance is required


(2)  Postsecondary level expectations are performance based.

  • students are not given opportunities for re-takes on tests
  • makeup work is not available (even though it is usually possible to drop one lab grade)
  • extra credit is not normally available
  • attendance is for the most part not a requirement, only encouraged



Good points! You mentioned you've "saved a good 60% of students...who would have failed GenChemI". How did you measure that? Math SAT scores?

Gregorius's picture

We tried to find some indicators for possible W or F grades in GenChem I. The best indicator at 90% certainty is failing the first exam in GenChem I. The next at 75% certainty is a Math SAT at lower than 580. So we preregister the low MSAT students into an alternative, one-year (instead of one semester) GenChem I . In the alternative program, we flip the classroom, intersperse group work with the flipped classroom discussion, have quizzes at least once a week. We also allow the students who were above the 580 MSAT cutoff but failed their first exam in the standard GenChem I the option to transfer into the alternative program. About 60% of the students who started or transfered into the alternative program passed the first semester of the alternative program, and nearly 100% pass the second semester. Nearly 100% of the students who make it through the year-long alternative program, pass GenChem II.

I can't tell (and I don't know how to evaluate) whether it is the alternative program or one (slow) semester of "seasoning" and adjusting to the college culture that helps these students, but I can say that switching from a standard textbook, lecture approach to a flipped classroom with Flash-based animations changed the success in the first semester of the alternative program from 40% to 60% (I have some published papers detailing this, if you're interested). Hence, my thinking that getting underperforming students to learn how to learn is more important than remediating the math.

How did you get the college to buy into the full-year 1st semester alternative Chemistry Course. I've suggested this idea before and I got some pretty major push back because it takes more credit hours on paper to complete the degree program.  Also how is the course broken down by topic? 

Dr. Janna Blum

Gregorius's picture

Several things had to fall into place before we could approach the administration for approval. The department had to agree that we had tried and instituted all sorts of modern teaching practices and these had only incremental effect on the pass/fail rates. The department also had attempted a one semester "science learning" course that ultimately failed as we realized that we couldn't change the way underachieving students studied or learned in one semester. We had to have faculty who were willing (even excited) to teach the planned one-year GenChem I; working with a classroom of 35-50 uninspired students (which ballooned to two sections) was going to be demoralizing and frustrating.

When we had those in place, convincing the administration was relatively easy since we had data that showed that a good portion of students who failed GenChem I actually left the college (we were viewed as one of the best premed schools in the area, and so the cost of going to our college was acceptable so long as they were in the premed program; if they couldn't be because of failing genChem, then they might as well go to the cheaper schools nearby). We also showed that students who succeeded in the alternative program could graduate in 4 years (by either taking GenChem II in the summer or in the Fall with OrgChem).

GenChem I and II traditionally followed the textbook sequence, with GenChem I covering about the first half of the textbook: so from measurements and units to solids (11 chapters). The alternative program just split the 11 chapters into two semesters. The first semester tackled measurements and units, foundations of chemistry, stoichiometry, reactions in solutions, and thermochemistry. The second semester tackled atomic theory, molecular (bond) theory, and states of matter. 

Greg –

In the last line of the "Math Skills" comment above, you suggest “less math” in general chemistry. Let me ask the following.

Don’t students take gen chem (instead of “chemistry and society”) because they seek to be science majors?

Don’t science departments require gen chem with the understanding that gen chem will teach chemistry calculations that lay the foundation for the calculations required in health fields, biological research, engineering?

Are not all science majors required to pass “science-major” chem AND physics? Doesn’t “less math” in chem simply set students up for failure in physics and/or later courses in science majors?

If a gen chem section has “less math,” what happens when students in that section who want to be chem majors arrive in physical chemistry?

Lack of K-12 preparation for the math of science is a real problem, but I don’t think “less math” in science-major chem is the answer.

-- rick nelson

Rick and Greg,

I think Rick has misunderstood Greg's point. I don't think Greg is saying that math is not needed in chemistry but rather that math is a tool that chemists use but not the chemistry iteself. Yes, some basic math is needed and students need to be facile with math, but chemistry is not math and learning chemistry cannot be measured solely by asking questions that do not get at conceptual understanding. It is very difficult to design such questions in a multiple-choice format so in the gen chem course I have been teaching at UW-Madison for the past 15 years or so we don't use M-C. It takes me, another faculty member, and 16 TAs about 6-7 hours to grade about 700 papers every time we give an exam, but we do know a lot more about what our students  understand (or don't understand) when the exam is over. However, I realize that not everyone has the time to do this much grading. We also provide online homework and conceptual tutorials on a weekly basis to keep students working continually and to provide them with formative feedback.

I was speaking with a physical chemistry colleague yesterday who bemoaned the fact that some of his students did not remember simple stuff from general chemistry so it seems unlikely to me that if, in gen chem, we de-emphasized math and emphasized understanding it would destroy students' ability to succeed in p. chem. There are some portions of the course I teach where students barely need to use a calculator during an exam because the questions have to do with molecular structure, polymers, biomolecules and other topics that do not require calculating an answer but rather reasoning based on knowledge gained in the course. There are other portions of the course where students need to calculate a result but even in those portions the exams are not purely calculating results--there are many questions that emphasized concepts over calculations.

On numerous occasions my students have told me that this chemistry course is where they learned how to study--because it was the first time they really had to study to succeed. I think that lesson in the first semester a student is in college is more important than either chemistry or math and we need to emphasize it more. I applaud Greg's approach and wish it were possible for more of us to adopt it.

Drs. Moore and Gregorius,

I think your position is that in teaching first-year chemistry, conceptual understanding is most important. Scientists who study how the brain reasons say: Whether conceptual understanding is important depends on which type of conceptual understanding you are talking about.

Science (and our experience) divide conceptual understanding into two distinct types. “Explicit” conceptual understanding is the ability of an expert in a field to explain why things work. A computer scientist can explain the hardware and software in my computer work.

“Implicit” (tacit, intuitive, unconscious) conceptual understanding is what we use outside our field of academic expertise to solve problems, and what we need to know about most related fields to solve problems. Chemists need to solve math problems intuitively, but don’t need the understanding of a mathematician.

Let’s take an example. Try this:

1. Solve for x: 3x – 2 = 25
2. Explain why you took the steps you did in the order you did.
3. Did you use commutative, or associative, or distributive properties?

College math-majors in their senior year need to be able to answer all 3 questions. Chemists can usually solve Part One in about 3 seconds. But if you are a chemist, the correct answer to Parts 3 and probably Part 2, is “Who cares? I don’t need to know that.”

And that’s the right answer. In chemistry, algebra is a tool we use by intuitive recall of what steps to take when. Our brain knows what to do, automatically applying the right steps effortlessly, even if we can’t explain why we do what we do. And what we need in our work, for the math component of chemistry problems, is simply the right answer, every time.

Every time you speak a sentence, you combine the 44 sounds of the English language at the rate of 5-10 sounds a second, correctly applying complex and precise rules for vocabulary, syntax, semantics, pronunciation, and morphology. Your brain knows the rules, or else you could not speak grammatically correct sentences in your dialect. But that implicit understanding is not part of your conscious ability to explain explicitly how and why speech works. The brain manages your behavior quite well in most cases, without your ability to explain why. That’s the nature of the brain humans have been dealt by evolution.

To understand conceptual understanding requires knowledge of neurons, axons, dendrites, synapses, long-term memory and working memory, and how the brain grows the wiring that is the physiological substance of conceptual understanding.

But our pressing question is: How much explicit and implicit understanding do students in first year chemistry need?

Scientists who study how the brain reasons say those students need primarily implicit understanding, because over 90% of the students in gen chem are not aiming to be chemistry majors. They need chemistry understanding the way chemists need math and computer understanding, as a tool to solve problems with chemistry and calculation content intuitively, but accurately, in their science and engineering majors.

But what position are you advocating? The scientists who study how the brain understands: Are they correct? In first-year gen chem, in your view, should our goal be that students have explicit or implicit understanding?

- - rick nelson

Gregorius's picture

Rick -

Excuse me if I get a bit didactic here, I'm really just trying to make my position clear.

Just as there is a philosophy of science, I'd like to think that all the of the science disciplines have some central conceit, a core philosophy. For example, I would say that the central philosophy of physics might be stated as: an effort to reduce phyiscal phenomena to an identifiable flow or transformation of energy and to obtain mathematical expressions of this flow/transformation. And if we agree with this, then physics instruction must always be related to following the energy, and the mathematical equations describing that flow of energy.

The central conceit of chemistry, if I may, is that we look at macroscopic phenomena and relate those to particulate structure and behavior. As chemists, we believe that practically every physical phenomenon can be explained from the perspective of what is happening at the particulate level. The color of flames? Electron excitation and decay. Need to strike a match to burn down a forest? Energy of activation, molecular transition structures. Relative boiling points? Intermolecular attractive forces, which are dependent on molecular structures. [And we don't lose sight of the fact that atoms and molecules are not physically "real" - that these are models.]

So, if we accept this philosophy of chemistry, then the focus of our instruction must be, refering to Johnstone here, the three learning domains: macroscopic phenomena, symbolic representation, and particulate conception - with an emphasis on how these three domains are always interacting in a chemistry professional's mind. Math does come in when we talk symbolic, but math is only a portion of that domain and symbolic representation is only one of three learning/thinking domains.

Yes, part of our duties as GenChem instructors is to prepare students for the higher disciplines, but I think we do a diservice to our students if we focus on math skills which is only a small section of the philosophy of chemistry, and only a small section of the three thinking domains of a chemist. If we want to develop good chemists from our students, we have to have them think in all three domains.

Gregorius asked, "How much math should be in GenChem?" I'd like to suggest a companion question, "When should math be introduced?" I first decided to write a textbook because I thought that starting introductory chemistry courses with unit analysis and chemical calculations may give students the wrong impression of what chemistry is and may discourage the more math-averse folks. My solution was to postpone the math. In the chemistry-first version of my book, units are introduced in Chapter 1, but unit analysis (dimensional analysis) is introduced in Chapter 8, immediately before mole calculations and chemical formulas (Chapter 9) and equation stoichiometry (Chapter 10). The math is still there; it's just postponed and clustered. The idea was to start with the concepts of chemistry with an emphasis on an early introduction of chemical changes. If you're interested you can see the table of contents and the text itself (and its tools) at

Mark Bishop

osrothen's picture


My approach is that math is introduced day one. I can appreciate alternatives, but I'll state my approach:

I taught the non-major large lecture section general chemistry course at Illinois State University for almost 30 years. As an interesting aside, students from the college of business were consistently my high grade students. Math and stoichiometry were part of this class from the day one class meeting.

Try this with general chemistry students on day one: Walk into class with a small basket containing 5 apples. Using all of your student excitement raising skills to elicit an enthusiastic mass response to your question ask, “If there were 4 more baskets on the lecture table filled exactly like this basket, how many apples would you see on the lecture table?” The enthusiastic answer was 25 from about 35,000 students during my teaching years. In answering this silly question, what did my students prove:

1) They had the arithmetic skills to use math to see unseeable things - in this case apples.
2) They were ready to see atoms in molecules just like John Dalton did in 1803.
3) They were ready for stoichiometry.

We are living in an age of adult science denial. Many intelligent Americans think science is about belief rather than a logical way of seeing and understanding. We must get back to teaching the methodology of this seeing and understanding to all chemistry students. The non-major chemical civics approach to chemistry that became popular in the 1970's drove me crazy. So I also wrote a textbook. I think all textbooks are written by malcontents!

“Seeing” and understanding atoms and molecules is fundamental to understanding chemistry. They can be “seen.” They are not beliefs, and to “see” them all that is necessary is a component of math that most adults understand intuitively.

Must this intuitive math skill be enhanced? Of course. And if it means we have to teach some math to do this, so be it. I have long suspected (I’m not a pedagogic researcher.) that my business college students had an advantage in chemistry because many business courses focused on understanding though numbers.

I'll go out on a limb here. We need to teach them some math. That's all there is to it. Inadequate prerequisite training complaining is ubiquitous among teachers, including me! So it goes, and we modify our teaching. I think most physical chemistry teachers have dealt with this for years. Are there any P-chem teachers who do not re-teach the calculus that they need for their course? Maybe a few.


Otis wrote, "We need to teach them some math." Please note that I wasn't necessarily arguing for less math (although I would certain do so for classes designed for non-science majors). I was just suggesting that we all might want to consider postponing the math for classes such as prep-chem and general chemistry for the reasons that I stated. I might also add that although the chemistry-first approach of my text was very popular with reviewers, it was not as popular with adopters, which is why I rearranged the same material to create the atoms-first version, which does the math early and often.

Clearly this problem of lack of numeracy affects most strongly the colleges and universities in USA.  The source of the problem is, of course, the school system, public or private, which perhaps makes a difference although I have not noticed such a distinction in the comments here.  The action required in those colleges and universities with respect to the students who enrol in general chemistry for whatever reason becomes hence remedial.  Even the oft-quoted specification of introduction of multiplication in the fourth year of school seems tardy on comparison with practice in other developed countries.  I wonder how it is possible for students to arrive at a USA college or university having nominally completed algebra, trigonometry, geometry and even some introductory calculus in school as a criterion for admission to an institution at tertiary level in scientific and technical programmes with so poor basic numeracy.  Perhaps the fault arises because courses at early levels in schools are called mathematics instead of arithmetic [satirical comment].  I can only suggest that the cure of the problem must be undertaken at the school level, such that, for admission to any programme involving science, technology, engineering and mathematics in any and all USA colleges and universities, an applicant must prove a sufficient competence in both arithmetic and basic mathematics -- algebra, trigonometry and geometry -- through a satisfactory score on a standard examination, effective beginning in 2022, for instance.  If the instructors of chemistry and other scientific and technical disciplines were able to impose such a criterion through the concerted action of administrations of their institutions, perhaps there might be sufficient impetus to improve the teaching of arithmetic and mathematics -- in quality and quantity -- in schools to alleviate this severe problem within the teaching careers of most present instructors.  Meanwhile, present instructors must try to cope with the present students, with whatever assistance and inspiration the contributors to this discussion can provide.

I can appreciate that my book Mathematics for Chemistry, which is freely available from or through the apprpriate links, would be useless in the face of the conditions to which the contributors to this conference are trying to respond. 

One of the contributors to this discussion mentioned trying to teach VSEPR and related topics in general chemistry.  It is facile to blame the students, or the schools that failed to prepare them properly for entrance to college or university, for their poor understanding of basic arithmetical and mathematical operations, but there is so much garbage in textbooks of general chemistry that is present there through market forces -- the instructors of chemistry choose and dictate the course textbooks, to which the authors respond by including the irrelevant nonsense, based not on understanding of ideas about electronic structure of molecules and materials but of ignorance -- "that sad benighted chemistry professoriate" of which Valiunis wrote [A. Valiunas, The man who thought of everything, The New Atlantis, No. 45, 60 - 98, 2015;].  The USA chemists should put their own houses in order before blaming other instructors, at the same or lower levels, for the arithmetical and mathematical deficiencies of the students who are the victims of a poorly organised system of general education.

If I might build off John Ogilvie's comment.

First, for those outside of the US it is difficult to understand the enormous range of tertiary educational institutions and the populations they serve.

Second, on line educational resources/textbooks if they are flexible enough offer a way of dealing with this.  Discussions can be nested to both test and direct students to the appropriate level of materials. Students could be allowed to level up when they have understood the materials or encouraged to step back down when there are clear problems (Aleks for example implements this strategy for evaluation)

Third, some OER, for example LibreTexts with which I am involved, allows instructors to purpose build texts to match their curricula using off the shelf chapters, etc. with a small investment of time.

I am certainly aware that the quality of tertiary educational institutions in USA has an enormous range.  USA has some of the best universities in the world, but most are far below that quality.  The participants in this conference are likely associated with institutions above the average, as they seek to improve the quality of the instruction of chemistry, which requires a mathematical component.  The problem of inadequate understanding of mathematics and its application to chemical systems is by no means confined to USA, but is a global concern, as one can verify by reading textbooks of mathematics for chemistry published in other countries, even though the problem might be more acute in USA because of that great diversity in the quality of schools in the preparation for tertiary education.

I quote below from Eric Nelson's contribution posted above.

"Let’s take an example. Try this:

1. Solve for x: 3x – 2 = 25
2. Explain why you took the steps you did in the order you did.
3. Did you use commutative, or associative, or distributive properties?"

The first step is a simple exercise in algebra, and Eric correctly stated that its solution is a prime requirement for a student of general chemistry.  Whether that student used a calculator or manual means to obtain the correct answer implies in either case perhaps some understanding of the algebra, the explanation of which in step 2 is somewhat irrelevant.  Although this conference is devoted to the mathematical competence of students, or their numeracy, I am equally aware of the prospective inadequacy of the communication of the student if he tried to respond to step 2.  Both numeracy and literacy are essential attributes of a liberal or technical education.  Even if an instructor of chemistry were not directly concerned that a student might lack an ability to present a literate response to step 2, it is important that examinations in chemistry require more than numerical answers or multiple-choice questions that fail to indicate the capability of a student to express a reasoned argument.  Such a literate component of instruction in mathematics for chemistry is essential; a graduate who is deemed fit to practise chemistry in some setting must possess both numeracy and literacy.

osrothen's picture


I’m probably being a bit touchy here, but we prefer to view our diverse tertiary institutions as differing in mission - not quality.

This touchiness on my part is germane to this discussion. Although most of my career was at the university level, I did spend several years teaching at the US junior college level. Math remediation for chemistry courses was MUCH more intense at the junior college level than it was at the university level. It even included one on one tutoring. Why? This was the junior college mission.

By the way, in most US states, our junior colleges are set up with transfer of chemistry (thorough organic) credit agreements with major universities.


Now that the “reader comment” period for Week One has started, may I offer two suggestions?

1. To readers:

The Texas Team paper offers a link to a copy of the MUST test. I’d suggest that readers t currently teaching first-year chemistry at any level might consider giving the test to your students (or a recitation representative sample thereof). A quiz “mid-semester,” after memory has been refreshed by use, may be a good measure of their “during semester” skills. Correlations between scores, course grades, and retention may be of interest.

Will your results be similar to those in Texas? Maybe not. From 1995 to 2014, like Texas, most states had K-12 “state math standard” mandatory testing that favored use of calculators over mental math. Some states, however, (including Minnesota and some New England states) had standards that encouraged “computational fluency.” Those states in international testing had high student numeracy test scores -- essentially tied with Japan, but our national average was far below Japan. Scores on the MUST in 2017 may depend on state requirements in 2007, when current first-year students were in third grade.

If you are teaching AP Chemistry -- or have a college section with many students who have had AP chemistry -- MUST scores may be very good. The AP Chem exam has two parts, and one does not allow calculators, so experienced AP instructors often emphasize “no-calculator” math.

Other factors, including review of math during chem, may affect outcomes as well. To be sure, try the experiment.

2. To the paper authors:

I hope you will publish these and subsequent results in one or more other venues.

My guess would be that half a million US students each year are “placed” into different levels of first-year college chem, and that most placement instruments include math with a calculator.

Your Figure 5 data offers support for past findings that to steer students into different first year chemistry levels, to select who needs the most help, the best instrument is a test of “simple chem math without a calculator.”

But a new discovery I think is your Figure 5 finding that “calculations with calculators” tended to identify as not needing help the students most at risk of “DFW” in first-semester gen chem. Chem departments (perhaps worldwide) are likely to appreciate being advised of your data.

Many chem departments are required to rely on “math placement tests” for chem placement (to minimize initial testing), but in my reading, I have found math instructors generally have the same concerns about numeracy that we do. With the Texas and/or your data, they may be willing to adjust a placement test given by the math department to include at least a separate section that reports scores in "math without a calculator."

-- rick nelson


You have certainly given us something to think about.  I really hope that the data from this fall support the data from fall 2016.  Getting similar data from different semesters at the same universities would be quite powerful in supporting your observations!  It is interesting that even the AP exams have parts where calculators are not used.  


We started offering the two-semester gen chem I about four years ago in response to high DFW rates in the one semester course. We offer both and target the lower range of Math ACT Students (23-25) for the two semester course. It’s not required so it doesn’t add to credit hours required for a degree. Since these students are at a high risk of failing the one semester course, it still may have taken them two semesters to get through it anyway but then they have a W or failing grade on their transcript. We do lose a fair number of students after the first semester of the slower paced course but they are often leaving with a better grade than they would have had if they had left after the traditional course. 

For content, they cover the same thing at half the speed so about 5 chapters in the first semester and 5 in the second. Our labs are separate courses, so they can take gen chem I lab during the second semester of the slower course.  I just looked at some data for these students comparing similar math ACT scores. All students end up together in gen chem II so we looked at DFW rates in gen chem II  for those who took the one semester gen chem I vs two-semester gen chem I. In each group of Math ACT scores, Students had higher success rates in gen chem II if they took gen chem I in two semesters. 

I like this approach! "It’s not required so it doesn’t add to credit hours required for a degree."  I'm wondering if Texas could think about developmental courses like this.  Degrees are limited to x h (I think, 138 h).  If you enroll for more than y hours, then you will have to pay out-of-state tuition, which is considerably more. What are the rules in other states?

We do not have a similar "penalty" for students taking extra hours at University of Kentucky.  Degree programs are limited to 120 hours (with some exceptions for programs to require up to 128 such as due to accreditation requirements).  Students are charged full time tuition for 12 hours/semester and above and are capped at 19 credit hours/semester but I can't even find that those taking more than 19 are even charged additional tuition.  My daughter's school (one of the regional state schools) charges additional tuition per credit hour above 16 hours/semester but at in-state rates.

While I know that this online conference is about undergraduate chemistry instruction, I was wondering if anyone knows of any similar work regarding factors affecting high school student achievment in a high school chemistry course.  In my school district, the high school graduation requirements are to fulfill the University of California admission requirements; so almost all sophomores take a high school chemistry course and almost all freshman in the district take algebra I.  The conceptual chemistry course was discontinued - probably to provide all students with a "rigorous" course.  I teach in a school district, where about half of the students qualify for the federal free / reduced lunch program and about a fourth of the students are English language learners.  The motivation for my inquiry is the relatively high number of students failing a high school chemistry course.

Paul –

My recommendation would be to adopt the rule I have seen many AP Chem teachers use: Teach the mental math skills (the AP test is in part “calculations with no calculators allowed), and never let the students use a calculator if it can be avoided.

The best source for lots of mental math practice materials may be to find some high school Algebra I and II books from before-1980, when calculators were generally not allowed in high school math, and math “automaticity” was taught effectively with lots of “distributed practice.” Until the 1980’s, these were math skills most students entering college science knew. Those skills are one important part of getting students ready for college science-major courses.

-- rick nelson

On this the last day of conference discussion of the Texas paper, here’s what I personally think I have found.
The Texas group went looking for a way to identify which students were most at risk of failure in gen chem, and what skill refresher could best better prepare them.

Science says the best predictor of student success in scientific calculations is “automaticity:” fluent recall and application of arithmetic and algebra fundamentals without a calculator. The Texas Figure 5 data say this is also a good early predictor of student grades in Gen Chem. This also suggests more basic arithmetic and algebra prep may raise grades.

The Texas data also say that a test of math that allows a calculator may well identify the wrong kids as needing the most help. If that is verified as a likely issue, it has major implications.

On the “help for some” solution:

Greg and Allison suggested another, probably even better, predictor of Gen Chem success: -- Grades on the first exam. I’ve seen the “transfer to an intense preparation course in the last 5 weeks” option also work well at another school. But it takes schedule flexibility --- and adds a semester to the gen chem sequence.

To avoid “adding a semester,” how would it work to offer a one-credit “math for the sciences” course that runs concurrently during first semester gen chem, and if schedules permit, on a faster schedule during the last 5-8 weeks of each semester?
Such a course could reduce the need for math review during chem courses. As an “option,” it would not increase graduation requirements.

Study after study (Wagner et. al, Tai et al., Leopold and Edgar, and more) has found that “math without a calculator” is the best predictor of gen chem success. New cognitive science predicts this result as well. Why not offer an optional review that increases math fluency?

Some students might need a two-credit calculations course, and others may need full 3-credit prep chem. But for many prospective physical science, pre-med, and engineering majors, I think a one-credit review might be a viable solution to the problems identified on the MUST test that are likely similar in most states.

The MUST test was incredibly easy (take a look), and the calculations are important, but the “no-calculator” scores that predict success were abysmal at every school. If scores in your population are similar, the one-credit concurrent "gaining math automaticity" course might be part of the solution.

-- rick nelson

As an author of a textbook Mathematics for Chemistry that employs advanced mathematical software (Maple) for the teaching, learning and implementation of mathematics in chemistry at a tertiary educational level, I wholeheartedly agree with Eric Nelson that pupils in schools should be able to undertake simple calculations without the use of calculators, whether simple or programmable involving use of parentheses or equivalent.  The design of my book is to teach the mathematical concepts and principles and the mechanisms to undertake calculations with that software, expecting that the students would derive sufficient understanding of those concepts or principles to implement a calculation without necessarily being able to explain the specific path of a particular calculation.  Any such application of calculator or computer at an advanced level requires a facility of mental calculation and estimate acquired before admission to a tertiary institution.  The best methods to ensure such an ability must be developed and implemented, which is the topic of this discussion.

Incidentally, a propos my preceding comment about literacy, according to BBC news online today, USA ranks 28 among 31 developed countries for adult literacy.  Literacy is, however, not a black or white decision; even those who might not be classified as functionally illiterate can struggle to express the meaning of a chemical calculation.  As chemical educators in every country and society, we must be aware of the necessity to ensure both sufficient numeracy and literacy in students of general chemistry and at any higher level.

I like the idea of a part-of-term course focused on math and topics related to chemistry success and we have discussed it here as an option.  I'm not sure it would be enough to help students recover their grade for the current semester if they have already been struggling in gen chem.  I think a lot of students think their math skills are fine because they got an A or B in high school calculus, but many of those students haven't had algebra in a few years.  It comes back to an issue of "they don't know what they don't know".  We identify many students who should be in the half-paced gen chem course sequence but will not take it for any number of reasons and then are surprised when they do poorly in Gen Chem I.  An 18-year old is convinced that if 1 in a 1000 students can succeed in gen chem I with weak math skills going in that they are the one and not the 999.  Maybe the bigger issue is convincing students of the reality of their skills and perhaps the MUST or similar assessment helps do this.


I just had a chance to take a look at the MUST that was linked to the paper.  Do students complain about a balancing question on this, since it is a topic for the class?

Is one of the versions in the linked MUST examples turned into the calculator version? 

I intend to try this with my Spring Chemical Principles I (Gen Chem I) classes.  Does administering both the calculator and non-calculator versions have value or is non-calculator sufficiently diagnostic?

(I can see the value of both for ChemEd research, but I am trying to assess the time committment)

This year we are focusing on the no-calculator version, as it better correlated with grades.


We ran our stats with and without the two questions on balancing.  The bottom line is that balancing is just an exercise in counting--a skills introduced very early in life--but it does in a way involve algebra skills. When we gave it to the mathematics professors for the purpose of validity, they had no problem balancing even though they commented that it had been years since they had done this. In light of our stats from last year, we left the balancing questions on this year's MUST. [As an aside, for some students, the balancing is the only thing they correctly answer!] 

We used two versions of the MUST (one had the first number as 87 and the other as 78). Each student got a 87 and a 78 version handed out upside down and then did the top one without a calculator followed by doing their next one (a different version) with a calculator. It seemed to work well. 

Our data support that the non-calculator version is more indicative of students' success. However, that was from our pilot study. This semester we kept the MUST and add the DAT (diagnostic algebra test) and did both without a calculator. It will be very interesting if the arithmetic skills over algebra skills have a higher correlation--more on this at a later time. 

Thank you one and all for all y'all's comments and insights.  Your suggestions have given us a lot to think about. 

Best wishes for continued success.  I'm looking forward to week #2!



Thank you for your response.  My concern is not the students in my ap chemistry class - it's the students in my regular chemistry class. 

At a first approximation, expect that the argument for the reasons why students struggled in a first year college chemistry class would apply in a high school chemistry class, but prefer arguments specifically for a high school regular chemistry course, since assume that there's a significant (?) difference in student populations; e.g. high school graduation requirment fillment versus college major requirements, where students somewhat self-select themselves in the later, but not in the former situation.


Just for the record, we are looking into high school chemistry course completion and how taking on-level, PAP and/or AP/IB chemistry makes a difference. We are also looking into current mathematics enrollment at the college/university level.  More on this next year!

Paul --

If they take Algebra I as 9th graders and chem as 10th graders, during 10th grade are they taking Algebra 2 or geometry?

I think that a college preparatory chem class is going to need topics involving exponents and logarithms that in my day were not practiced extensively until Algebra 2. So Algebra 2 and Chem needed to be concurrent and to some extent coordinated. But when or if these topics are ever practiced extensively in HS math under current California standards and district realities is a question I would think would need to be checked into. Way back when, Chem was taught in 11th grade to allow time for needed mastery of the math required for college prep chem.

But in any case, I'd say, whenever in intro chem courses, limit calculator use to cases where high precision is required.

-- rick nelson

I totally agree with concurrent enrollment in HS chem and alg 2.  It's a good match for both chemistry and mathematics--understanding would definitely improve.