Many parents would admit that they couldn’t sit down and pass an Algebra or Calculus test today, since they haven’t kept up with practice since high school or college. However, a recent graduate with good grades in math classes, heading into college, should probably be able to handle those same subjects, right?
Not according to a UC San Diego report.
Instead, the college is finding that students struggle with even basic elementary math, despite grades that would normally suggest mastery of skills.
Tutors’ observations in remedial math courses further suggest that some skills are being lost.
Math Skills, Calculator Skills, Reasoning Skills
Katherine Johnson and her fellow “human computers,” or “hidden figures,” famously joined NASA and performed the complex math required for space travel to begin. Today, those same calculations are done by machines, and a teenager who dreamed of working for NASA would need to develop the skills to work with those computers, perhaps more than the math skills.
This applies across most employment fields: for a cashier today, the skill to communicate a price change to the computerized cash register is more necessary than the skill to do that math herself; a tax preparer needs to understand a computer program more than she needs to be able to calculate percentages mentally; even a doctor or pharmacist will use a computer to calculate dosages rather than doing it with pen and paper.
That means that schools must teach students to find answers using calculators and computer programs — but it seems like the basic skills are being lost or forgotten, at least in some cases.
What Should Math Scores Mean?
Why are students who passed calculus landing in remedial math classes when they head to college? A group of tutors who worked with these students in their remedial classes shared their observations of the students’ skills and abilities.
One significant factor tutors noted was that some students seemed to have undiagnosed dyscalculia, which makes mathematical procedures more difficult. They also questioned how some of the students ever passed higher math courses, or even some lower ones, on their own strength, recognizing that some still lacked the skills taught in elementary math.
Another factor was that some students had not taken a math course in their senior year of high school, and so were entering college with over a year of no real practice.
However, a significant part of the problem may be with how high school math courses are taught and graded. Tutors observed that in high school, students had been walked through a problem, then immediately given practice work, whereas their college courses might not give a written assignment until a few days after the lesson. They also cited what they called a “plug and chug” method — essentially memorizing a formula for long enough to get through the homework and test.
The conclusion is that high schools seem to be giving students passing grades without those students achieving proficiency — they might pass the tests and complete the homework, whether through memorization, luck, using online programs to find answers, or other strategies, but they aren’t actually internalizing and learning the procedures.
How Can Parents, Teachers, & Students Address This?
We need to make sure our kids understand that math is important in careers and in life, and that it’s necessary to understand the “why” of mathematical procedures, not just how to plug them into a machine and get an answer.
From elementary school, we need to emphasize that there’s a reason we want to figure out what number goes in the blank, a reason we want to know what happens when we add or multiply these two numbers, and a reason we want to know the square root of a number. These aren’t just tasks that must be completed to get a good score on the test; they’re tools that we’ll eventually use to make sure we weren’t overcharged for the pizzas, or that we have the right number of tiles for the floor, or that we can make it home without stopping for gas.
We also need to make sure that students are achieving proficiency, not just memorizing a strategy for long enough to pass a test.
The Long-Term Solution
Ultimately, resolving this issue may require revisiting how we teach mathematics.
Students do need the skill set to use calculators and problem-solving programs. (Way back in 2001, I remember my Calculus teacher showing us how to write a program in our TI-83 calculators that would help us solve quadratic equations, and I still remember the song she taught us to ensure we wouldn’t forget the quadratic formula.)
They do need to know how to look a formula up if they’ve forgotten it, and using the many apps and websites that walk through the steps of the problem is an effective way to double-check their work and figure out where they’ve gone wrong. They do need to know how to communicate the issue to a machine when that’s required.
However, there may need to be a significant focus back on learning to carry out the basic operations and understanding why the math works. Most of all, there clearly needs to be a change in how math is graded, with a real focus on proficiency rather than simply the correct answers.