Do your students know their “arithmetic facts” perfectly, without hesitation? Is it important that they do?
In our text Calculations In Chemistry, we included a review of math and algebra fundamentals — just before they were needed for chemistry topics. Working initially with students in engineering chemistry, compared to past semesters, success was pretty spectacular. But in subsequent experiments with “mostly bio-major” general chem and “prep for general chem,” though averages improved notably, more students struggled with quantitative problems than we thought should.
Our diagnostic testing found that strugglers tended to have trouble doing simple math “in their heads.” Searching the academic literature, we found:
- In chemistry education journals, others had observed a high correlation between “mental math” skills and general chemistry achievement.
- Cognitive science emphasized: Quantitative reasoning depends on quick, automatic recall of math facts.
- Math education journals noted that about 10 years ago, when current chemistry students were in 3rd grade, “math standards” in about 40 states required teachers to prepare students to use calculators on 3rd grade state math tests. As a result, many students had essentially never been required to “memorize their math facts.”
For students lacking math automaticity, cognitive research suggested that strengthening mental math would help more students succeed in courses in the quantitative sciences.
To assess and sharpen mental math at the start of chemistry:
- We have prepared a 15-minute quiz at www.ChemReview.Net/MentalMathAssessment.pdf that will identify students who need help in mental math.
- For students lacking fluency, we have written homework assignments that practice mental math, with an online quiz added to encourage practice completion. The activities in this Mental Math packet may be downloaded at www.ChemReview.Net/MentalMath.PDF
(click and check your PDF downloads).
Researchers say that if during a course, students are given a mix of calculator and “no calculator” problems that keep their mental math sharp, they will better understand quantitative examples and proportional reasoning.
In different populations, skills will vary, but the 15-minute quiz should tell you quickly which individual students will benefit from “Mental Math” homework.
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This is great stuff! As HS chemistry becomes more of a “required course for graduation,” basic preparation with “math facts” is essential. It is possible that many “real-life” connections between math/science are never made because learners cannot automatically “do” simple mental math. Way to Go Chem and Cognition Blog!
I never memorized “the times table”.. I don’t know if this “held me back”. So, possibly, not important.
I also often count on my fingers, tho I sometimes can use the trick of adding to one number and subtracting from the other to have a remembered addition or subtraction.
I did memorize 2^n; 0< n <13 in college, because that was before nuclear scalers of 10 were common.
But I have memorized simple diffs and integrals, as I use them often.
I usta joke I couldn't multiply numbers, but could find an integral in the complex plane using residuals.
bc had to ask his wife what x was in the captcha