12 – Help for Students in Mental Math

Do your students know their “times tables” 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, fluent 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 times tables.”

For students lacking math fluency, 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:

  1. We have prepared a 4-minute quiz  that will identify students who need help in math-fact recall.  We recommend it be given as early in chemistry as possible, preferably at the start of courses that prepare students for General/AP Chemistry.
  1. For students lacking fluency, we have written homework assignments that practice mental math, with an online quiz added to encourage practice completion.

The free “Mental Math Activity Packet” is at www.ChemReview.Net/MentalMath.pdf

In addition, posted at www.ChemReview.Net/WeekOneFiles.pdf  are over 50 pages of free homework tutorials on exponential notation and the metric system that can be used in first-year chemistry at all levels. Editable files are provided that quiz on calculations without a calculator.

Researchers say that if during a course, students are given a mix of calculator plus occasional “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 4-minute quiz should tell you quickly which individual students will benefit from the “math automaticity” homework and re-quiz.

Try the 4-minute quiz with your students — and the follow-up activities if needed. See if the cognitive research is correct in predicting that improving “automaticity in math fundamentals” will significantly increase success rates in chemistry.

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2 Responses

  1. Jason Just July 27, 2015 / 10:31 am

    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!

  2. bernard cleyet October 11, 2016 / 7:35 pm

    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

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