Tutor Lists Top 10 Math Skills To Cover During Closings
Back in early February when I began my first draft of this blog, COVID-19 seemed like another continent’s problem. With a working title of “When April Showers Don’t Bring May Flowers,” I’d intended to address the epidemic of anxiety that I’ve been seeing in many of the students I tutor. Six weeks later, the title and the theme still apply: now, more than ever, we all need to find ways to relax.
However, I’ve opted to address an issue with an easier immediate fix. Since so many parents across the world have essentially become a tutor now (even if students see their teachers online, you’re still the human in the room), I want to call your attention to something you may not know about your child – during a rare period where you may be in a unique position to do something about it. And while the first two sections of this newsletter may seem dire, the last section provides concrete, sequential actions you can take now to tutor your child, no matter their age or ability. (So, I encourage you to read the entire piece!)
The Problem: Basic Math
This winter, I served as a tutor to seven students in math: six for the SAT and one middle schooler in arithmetic. Two themes emerged quickly. These trends were so clear – and so alarming – that I thought them important to share.
Almost ALL students struggle with basic arithmetic facts, like addition and multiplication, without the use of a calculator. What does this look like? A sixteen-year-old counting out “six times seven” on her fingers – and coming up with 41. A different high school junior arriving at “45,” then “40,” and finally, “35” to the question “What’s 7 x 5?” Yet another student I tutor staring a “8 x 8” on a page, asking if she could use a calculator to compute the answer, and breaking into tears when she could not.
While the severity of this inability varies from student to student (and even from day to day for a single student), I have witnessed shocking arithmetic errors among all but two of the many students with whom I've worked as a tutor in the past several years. (And lest you think that the three examples I cited occurred in students who attend challenged high schools, think again. All three of these students attend elite, private schools, in three different states.)
This is how many of our children are learning subtraction. Image from understood.org, accessed March 18, 2020.
2. Many students do not understand basic arithmetical concepts and processes, such as what ratios and proportions are and how they work, or why when you add two negative numbers, you get a bigger negative number. Other common gaps in the students I tutor: long division; multiplying numbers with two or more digits; what fractions, decimals, and percents are; adding, subtracting, multiplying, and dividing fractions; converting among fractions, decimals, and percents.
Why These Trends Concern Me
These knowledge gaps are problematic for several reasons. First, a weak foundation in arithmetic makes it difficult to ascend to higher levels of mathematics. If you don’t have a solid command of multiples, for example, proportions and much of algebra never really make sense. You may be able to follow your teacher’s example while doing a certain type of problem, but you likely have no clue about what it is that you’re actually accomplishing – let alone about an alternative way to solve the problem. As a result, your grades in algebra probably never surpass the B- range because problems that require intellectual flexibility – i.e., true “problem solving” – are beyond your grasp.
Second (and least important, in my mind), without a firm mastery of arithmetic, you’re unlikely to achieve your full potential score on the ACT / SAT. That’s not because you’re getting arithmetic problems wrong. There aren’t any strictly arithmetic problems on these exams. However, fractions, ratios, division, and the rest appear throughout the standardized tests as minor steps in larger, more difficult problems. If you can’t compute 8x8 quickly and correctly in your head, how are you supposed to manage “ x3(x2-5)= - 4x. If x > 0, what is one possible solution to the equation above?”
Lastly and most importantly, when you can’t do math, you’re missing a crucial method of building your brain. Some of you know that I have a doctorate in U.S. History, an undergraduate degree from Harvard in Art History, speak four languages, and was a theater-band-visual arts kid (i.e., “nerd” :-)) in high school: I’m probably the least likely candidate to tout the importance of mathematics. I’ve spent my professional life reading books, writing, and teaching students how to write – another invaluable life skill. So, let’s be clear: I’m not advocating that every child take calculus. However, rudimentary algebra and geometry will strengthen your child’s analytical ability in ways that merely reading and writing alone cannot. So, even if you have a kid who’s determined to become a guitar-playing, Philosophy undergrad with a Ph.D. in Comparative Lit, get him to master arithmetic and then the basics of geometry and algebra.
This time-consuming method of multiplication - the method many of our children learned in school - slows them down on standardized tests and makes them more prone to errors. Image from understood.org, accessed March 18, 2020.
The “M.D.” Fix: Memorize & Drill
Here are three things I know: I believe that every child can “do” and understand math. I also believe that the errors and gaps of the students I tutor are not their fault. And, finally, I believe that you can be your child's math tutor. We’ve all heard the jokes about “new math”: as Chaucer wrote (albeit in different form), “Many a true word is spoken in jest.” I believe that current pedagogy caused serious flaws in our kids’ mathematical understanding and processing:
The good news is that the gaps are “fill-able” and the errors are preventable, in my opinion, through memorization – which requires repetition, a no-no in the current educational climate. I suggest that you quiz your kids verbally on the following facts – and quiz ‘em often. Just because they “learned” 8x7 correctly in third grade doesn’t mean they know it today. And don’t think that if they “learned” it today, that they’ll remember it tomorrow or a week from now. You underestimate the enormous amount of rote memorization that we were required to do as children if you believe that just a few quick check-ins will suffice.
Start at the top, working your way down the list. Try to “mix it up” (i.e., don’t quiz all the 2’s, then all the 3’s; rather ask “7x9” then “6x8”). When you find that your child is stuck, slow down and do some remediation ( tutor :-)) , using the list of resources that follows the list of concepts and skills.
List of Essential Arithmetic Skills (1-5 Before Middle School; 6-10 Before High School)
Addition: should be able to add up to any two-digit and one-digit number in their head; bigger numbers on paper
Subtraction: same as above
Multiplication: 10x10 table memorized; bigger numbers by hand; know the “perfect squares”
Division: same as above; should be able to do long division by hand
Fractions: what are they? be able to reduce, add, subtract, multiply, divide, and convert to / from decimals and percents
Decimals: what are they? be able to add, subtract, multiply, divide, and convert to / from fractions and percents
Percents: what are they? be able to convert to / from fractions and decimals; be able to find the percentage of another number (e.g., what’s 16% of 80?)
Ratio: what is it? what does it tell us?
Proportion: what is it? how do I set one up?
Negative numbers: adding, subtracting, multiplying, dividing – even with negative fractions/decimals.
Image by @monicomelty on Unsplash
Finally, embed Common Sense / Mathematical Thinking into each of these skills and processes. For example, if I don’t know how to find 16% of 80, but I know that 10% of 80 is 8, I should be able to reason that 16% of 80 is a bit more than 12, because one-half of 8, or the next 5% of 80, is 4, and 8 plus 4 is 12. Especially on multiple-choice tests like the Common Core and (most of) the SAT, using Common Sense / Mathematical Thinking can help students check a right answer and at least eliminate wildly wrong ones.
Make math relevant to daily life. If you’re making a recipe, for instance, show your children how fractions work in real life. (I’ve even used percent increase as a way to show the relevance of math to one student I tutor by referencing the increasing spread of the virus from day to day….)
Many students – especially those who have struggled with math in the past – will not engage in mathematical thinking on their own. But when prompted by a parent or tutor to use their common sense to validate (or invalidate) an answer, they can do it. Encourage them to use what they do know to figure out the right answer, even if it’s not the way they’re “supposed” to do a certain problem. This encouragement gives the rule-followers the permission they need to be intellectually flexible enough to reason their way out of a pickle.
List of Useful Resources
Khan Academy Free, online videos and accompanying worksheets
Math Refresher for Adults Clear and comprehensive workbook
Everything You Need to Ace MATH in One Big Fat Notebook Less comprehensive than the workbook above, but introduces basic geometry and algebra
Final Thoughts
I know that these are scary, trying times. Silver linings, like reconnecting with loved ones and with nature, can be found, if only we look (though we may need to squint!). Using just a tiny fraction of your newfound “together time” with your child to shore up their basic arithmetic will pay off not just in their math grades and test scores now, but also in how well their brain can reason and analyze throughout their lives. Now more than ever, we need to mold the next generation to think rationally: our future depends on it.
Wishing you and your families continued good health,
Dr. P.
What do you think? Post your comments below!
To read more articles like this, visit the Desk to Nest blog.
To receive the latest blog post in your inbox, click here.
To get answers to many questions about education, check out and SUBSCRIBE to my YouTube Channel.
To get YOUR OWN question answered in my next blog post or YouTube video, email it to me now.
Graphic by Dominique Padurano. Photos by Jessica Lewis and JESHOOTS on Unsplash.