The year was 1991 – you may remember it. The Cosby Show was the most watched TV show and Duran Duran was topping the charts. Big hair reigned and so did shoulder pads, penny loafers, and Members Only jackets. Just thinking about the early ’90s brings a smile to my face, not only because of the pop culture memories, but also because it was the beginning of my career as a teacher in Fairfax County Public Schools.
I was teaching math to an engaged group of fourth graders who breezed through tough concepts such as place value to the billions, four-digit by three-digit multiplication, and even complex division. But their confidence in math came to a screeching halt when it came to — fractions. Yes, it was fractions that threw even the best students off kilter. They struggled to understand why 3/8 was smaller than 2/3. In their minds, it made no sense. They had been taught that the larger the number, the larger the value, but this concept wasn’t true when it came to fractions.
I tried the usual tactics of introducing attractive visuals such as pizzas, pies, and colorful charts. Some kids got it and some didn’t. The ones that didn’t fell even further behind when we went on to dividing and multiplying fractions. They could perform the operations by rote, but when the same calculation was put into a word problem, my students struggled to apply the correct operation. They were confused, and as a new teacher, I was at a loss as to how to help them.
The Problem with Fractions
Turns out the methodologies I had been taught in my undergraduate and graduate teacher education programs and the tips I learned from other teachers, weren’t necessarily the best, even though they were considered “best practice” at the time. In fact, the problem wasn’t isolated to my brightly-painted classroom at North Springfield Elementary School. The problem with fractions was nationwide.
In recent years, our government has funded new research on better ways to teach fractions. Research has shown that our old ways weren’t the most effective. Instead of relying on circle charts and graphs, students are learning fractions by utilizing number lines, paper models, and games. And before moving on to complex operations such as dividing fractions (who remembers the “invert the second fraction and then multiply” rule?), students gain a deeper understanding beforehand.
What the Research Says…
Why does this matter? New research shows that knowing how to place fractions on a number line in third grade is a far better predictor of a fourth grader’s math skills than calculation skill, ability to pay attention, and working memory. A recent study by Nancy Jordan at the University of Delaware, found that the effect doesn’t stop there; it lasts at least through elementary school.
My personal experience in teaching and tutoring hundreds of students over the last twenty years in Northern Virginia has been that those with little understanding of fractions, decimals, and percents in elementary school end up struggling with more complex subjects, such as algebra, later on. Often, being “good at math” in high school is not an inherent quality but a result of how well a student understood more basic concepts in elementary school.
So what’s a parent to do? Here are a few ideas:
Utilize online resources. One of my favorite games is called “Battleship Numberline” on BrainPOP.
Ask lots of questions during day-to-day activities, like cooking and grocery shopping. If a price is marked “40% off,” encourage your child to do the mental math to figure out the new price. When cooking, have your child do all the measuring.
Outside of fractions, there are three basic strategies that can be used in any math subject:
1. When you see that your child is struggling in math class, intervene right away; don’t wait. Math is the one subject that is completely cumulative. Get behind one week and it’s hard to catch up the next. Encourage your child to get extra help after school from the teacher or hire a math tutor to reinforce concepts and explain them in a more meaningful way. When students feel like they “can’t do math,” they can develop a negative attitude about the subject that can be life-long.
2. Be sure your student knows how to properly study. Over the years, I’ve had lots of kids say to me, “You either know math or you don’t. You can’t study for math.” This sentiment is entirely untrue. The best research-proven way to study is to create a practice test. How is this done? Students need to go back through their notes and write down problems that have already been solved correctly. They should also find example problems in their text book that have solutions provided and write those down on their practice test as well. By using a variety of sample problems, students create a practice test which will likely simulate their teacher’s version of the real exam.
3. Parse out time. Here’s a question for you: Is it better to study math for an hour the day before an exam or to study just 15 minutes per day for the four days leading to the test? If you guessed that it’s better to parse out time, you’re right. The reason is that sleep “lays down learning.” When a student studies just a little each day, the information is far more likely to be committed to long-term memory.
Whether you have a fourth grader studying fractions or a twelfth grader studying calculus, these researched-based strategies will make a significant difference on test day. I guarantee it!
Questions, comments, or suggestions for future blog posts? Let me know! And if I can help you secure a math tutor who can help your child boost his or her grade, drop me a line.
Wishing you the best on the road to math success,