My Daughter’s Number Nightmare
“Picture it,” as Sophia (of the late 80’s-early 90’s sitcom, The Golden Girls) would say. College Algebra, first semester Freshmen year, first day. Shiny new textbook, crisp new college-ruled notebook, graph paper tablet, engineering calculator, and a 12-pack of multi-colored 0.7 mm mechanical pencils. I’m ready to go!
Of course, I’ll have to figure out how to hide counting on my fingers when I add—or just use the calculator. So what if I’m a little rusty with my multiplication tables above 5’s; they’ll review. And, I’m sure they’ll go over fractions and decimals, because honestly, who remembers that stuff anyway? Surely, there’ll be just review for at least the first couple of weeks. I know I’m not the only one who changed schools a lot, or passed notes and shared homework from third grade on—instead of paying attention during math classes. That’s probably why I never was very good at long-division, and could never understand the first thing about percents, or ratios, and plotting graphs. Don’t even mention Roman numerals!
I wish late registration and the bookstore hadn’t taken so long. I’m only 15 minutes late, but the professor’s already scribbling out calculations all over the board with her dry-erase marker. I’ll just slip in the back.
Whoa! I’m copying as fast as I can, and I didn’t even hear that last question! I’m glad I’m back here, so, she won’t call on me. Ah, there it is: I’m caught up. That wasn’t so hard.
Wait! What was that last question? “What is the inverse operation used here?” What is the what? Inverse! What’s an inverse? Oh well. I’ll go over that in the first chapter of the book tonight. No problem.
Armed with that blissfully ignorant mantra, I fought off bouts of inner hysteria, that threatened to swallow me, at each bafflingly unfamiliar sentence that poured out of my professor’s mouth, like an alien tongue from Middle-earth in The Lord of the Rings, or the Valyrian spoken in Game of Thrones.
Rational? Integers? Linear? Non-linear? I contented myself with the nervous assurance that going over the first chapter of my shiny new math text, in the seclusion of my room, would clear up everything.
Second verse (worse than the first): “Picture it: College Algebra, second day.” (Completely indecipherable calculations—no wait—equations, are multiplying like a plague of locusts, scrawling out with lightening speed. They’re being rudely punctuated by rapid-fire questions, in that same alien tongue that everyone knows but me. Hands are shooting up all over the room, and more alien squawkings are coming from the dizzying sea of robotic, other-worldly A.I.’s seated all around me. My face is burning. Everyone can see my face turning bright red—I just know it! I’ve got to get out of here! When is that stupid bell going to ring? What is that language…Klingon? Na’vi?)
I never went back. At least, not that semester.
Now, repeat that nightmare—six times. Register. Drop. Register. Drop. And, “Why?” you might ask. Because some ancient idiot decided, way back in the dark ages (when people could actually multiply four-digit numbers by four digit numbers in their head), that everyone who finished the eighth grade and/ or graduated, should know how to solve equations for use in daily life. So, I had to pass Algebra, or I would never graduate from college, never earn a degree, even in my major, art (‘though I couldn’t imagine when an artist would ever need to find the square root of “x” to the 10th power).
Double Trouble, or is it Trouble Squared?
Now, fast forward, four and a half years: Senior year, last semester. Standing in the late registration line, with my mother along, so she could pay my registration fees with her credit card, until my student loan funds would arrive. She had met me on campus, after her doctor’s appointment.
“You’ll never guess what happened when I went to the math lab to get the dean’s approval to take two math classes the same semester. Right in front of everybody, he came right out and said he was giving his probationary approval, because he didn’t think I’d pass! I’ll show him!”
“It costs extra to take 21 hours. Are you sure you don’t want to wait and take Algebra by itself, in the summer, and just take the ‘Math for Elementary Teachers’ now?” (I’m sure we both secretly hoped the education course would go over elementary math concepts that my daughter had missed, to give her some hope of passing the algebra, however slim.) “If you wait, you’ll have time to get tutoring before you take it,” I suggested.
“No, Mom. I want to graduate in May!” my daughter insisted. “It’s already taken me ten years to get a four year education, because of your car accident, and then, my car accident. I just want to finally get this over with. They have tutors, and practice labs. I can do it!”
“OK,” I reluctantly agreed. But, I would have bet a fortune, that, not in a million light-years, could my honor-roll daughter ever pass college-level algebra—never mind score as high as she ended up doing. But, this is how it all came about, I swear.
* * * *
Right off the bat, my daughter showed up at the end of that first day, asking for my help in learning her multiplication tables. A former special education teacher of learning-challenged middle school and high schoolers, I had a few tricks for learning these foundational facts. I dug out the laminated math facts sheets and flash cards I’d purchased from Walmart and Books-a-Million years ago, and had my determined daughter make her own, hand-written copies.
We then went over each table, one by one, checking to see which facts she knew, and which she didn’t. She could count by 2’s, 5’s and 10’s, so we crossed those out. We also got to eliminate the matching facts in the remaining tables. For example, in the sevens table, which she was sure she didn’t know, 7 times 5 is exactly the same as 5 times 7, which she did know, even though she had to count by fives in her head, 5, 10, 15, 20, 25, 30, 35, flexing her fingers all the way up to the seventh.
The next thing I showed my daughter, to keep her from having to use her fingers anymore, was the dot patterns of dominoes. “Memorize the dot placement, from two to twelve, and you can tap your pencil using the dot patterns to keep track of where you are, and no one will ever know.”
She found that she also remembered the numbers times themselves, up to 6’s, so we crossed those out, too. By the time we had finished, those multiplication tables looked a lot more manageable, and she spent the first night memorizing them, and completing review assignments from the first chapter of her text. And, instead of complaining, as we all have, about having to do so many of the same type of problem, she welcomed the repetitive practice, as a way of retaining the facts and concepts.
From then on, my daughter began her amazing odyssey into the formerly formidable world of numbers. Day after day, she faithfully attended her classes—all 21 semester hours of them—then, dutifully went to math lab. She also took the initiative to hire a grad student tutor, and kept him busy with questions. At home, she’d complete all her assignments, including the Algebra homework, which might consist of the even-numbered problems in a section. But then, she also assigned herself the odd-numbered problems, to “drill the material into her head,” as she would put it. Each section included practice tests, which she took, and re-took, until she missed 10-20% or less.
As the the semester progressed, my daughter’s pace never let up. She relentlessly drove herself to conquer each new concept, memorizing formulas, and completing both assigned and unassigned problems. She would cram at night, then, review in the morning, before or between classes. And, gradually, the questions put to her tutor became more and more complex. Slowly, but surely, she began to score consistently in the 90th percentile on her practice tests. And, when the actual tests came, she was scoring in the 80′s and 90′s.
Finally, the day came for her final exam in Algebra. Since she had been reviewing concepts on a daily basis all semester, studying for the final was just more of the same. She knew from her test scores so far, that she was finally going to pass the dreaded Algebra course. She headed into the exam room nervous, but confidant. Then came the wait for grades to appear.
When the time came to pick up her progress report, she was ecstatic to see that she had not only passed the difficult course, but had earned a score she’d never dreamed possible. She called me from school to announce the news.
“Mom! I did it! I did it! I passed Algebra! And you’ll never guess what I got,” she teased. I expected to hear that she had passed, after all the hard work she’d put in. But, I was not prepared for her next announcement, although I had been praying for her success. “I got a “B”!
My amazing daughter had gone from adding numbers with her fingers, subtracting them upside-down, and 2 times 2 equals 4, to graphing and solving quadratic equations, and more, in a single semester!