Make It a Habit: Tips for Studying Math - Tips Study Mathematics Blog

Posted: 02 Dec 2014 07:44 AM PST

If it seems like math tests these days are harder than they used to be, that's probably because they are. In a recent national survey, 86% of responding math teachers said they believe the newly adopted common core standards are more rigorous than prior standards.

But a more difficult curriculum doesn't need to spell disaster for all (or any) students. Actually, adjusting to the revised common core standards can be quite simple and painless when students practice a few good studying habits.

Slow and Steady
Math isn't like other subjects that can be easily learned through late-night cramming or memorized with mnemonic devices. For most students, mathematical operations are disorienting, cumbersome, and unintuitive, and that makes it hard to process and retain large bits of unfamiliar material at once.

In other words, students won't get the hang of trigonometry by speed-reading the three chapters they missed while on vacation, but it is possible to gain some traction by making a habit (rather than a special occasion) of studying and absorbing the material bit by bit.

So start early
Keep up with the homework and show up to class with questions about confusing parts of the chapter. That way, there will be no need to cover and catch up on large amounts of material at once, which can be challenging for anybody in the math world.

Find Time Every Day
Don't be intimidated by the idea of finding time each day to study. It doesn't have to be an all-night commitment. Instead, plan a half-hour before bed for practice problems or take advantage of downtime on the bus, between classes, or elsewhere to review notes and reread key sections from the textbook.

Do the Math

Mental math is fine for students who have already mastered the material, but working it out in your head is not an effective way for anyone to learn or review new material. Students–even good ones– who convince themselves they know the steps without ever performing them on paper often regret it on test day when they don't get the answer they'd expected or struggle to remember key steps and operations.

Working out the problems not only reinforces the rules and orders of operations in students' minds but also develops a sort of "muscle memory" for mathematical problem-solving. And that, in turn, reduces the chances of panicking or drawing a blank when tests and exams roll around.

Adjusting to the revised common core standards has potential to be a road bump for any student of math, but with a bit of effort, students who make habits of these studying tips will find they're quickly up to speed and comfortable with the new material.

- Tips Study Mathematics

Posted: 01 Dec 2014 07:56 AM PST

When I first decided to homeschool, I asked for a lot of advice from experienced homeschoolers because I was nervous:

Would my son learn to read? How would he make friends? Could I trust my own ability to guide his learning?

The enthusiasm of other parents was encouraging. They told me of chemistry experiments and trips to paleontology museums. Their kids were learning voraciously, and the adults were having fun.

Until it came to math.

"Oh, we just give them some Saxon worksheets," was the most common response to my request for advice on a math program, and the distaste was palpable. Probe a little deeper, and parents told me more:

"I hate math." "I can't add." "I'm horrible at math." For them, math had become the same thing it had been to them as children: something to endure.

Confession: I love math. I want my children to enjoy it, too, and to see a future in it as accessible as becoming a motorcycle mechanic, English professor, farmer, or corporate lawyer.

I also can't add. But math isn't about being good at adding, and an inability to add doesn't mean you can't teach your kids mathematics.

Finding what works

In her book What's Math Got To Do With It? detailing findings from longitudinal studies on math education, Stanford professor Jo Boaler notes that Americans are familiar with two kinds of math: "the strange and boring subject that they encountered in classrooms and an interesting set of ideas that is the math of the world, and is curiously different and surprisingly engaging.

To teach math successfully, parents need to face down the voices in their heads that claim, I'm terrible at math, and experiment with materials that reflect the subject's multi-faceted reality.

Maura Muller, from Rock Hill, N.Y., is one parent who's managed to overcome her childhood experiences. She hated math growing up. "I had a terrifying nun who would slap our hands with a wooden stick when we got an answer wrong and tell us how stupid we were."

She didn't want her son to suffer the same math trauma, so tried to make math fun, reading books like Grapes of Math and The Adventures of Penrose, the Mathematical Cat, and later, as her son got older, The Man Who Counted and The Number Devil.

I spent months looking for an actual curriculum that was both engaging and rigorous. By chance I came across an article about JUMP, a program developed by a Canadian nonprofit. JUMP breaks math concepts down into tiny, digestible steps, meaning that kids can master each step individually without getting overwhelmed by larger concepts all at once — its advantage for homeschoolers is that adults who fear their own math abilities can do the same.

Delores Caesar, who began homeschooling her middle-schooler specifically because of concerns that her daughter was "slipping under the radar" by knowing facts but not understanding concepts in her math classes. This mom, from New York's Hudson Valley region, says she likes JUMP for daily lessons, but Math Mammoth and Critical Learning workbooks for an all-around deeper understanding of concepts.

Grahamsville, N.Y.'s Vikki Siciliano, who was good at math as a kid but never enjoyed it, has been homeschooling for 16 years. Siciliano initially tried Saxon math, which her 5th-grade son hated because "it was so repetitive," but found the colorful, in-depth Scott Foresman program worked well for them. Two of her kids eventually became math majors.

For those who like formalized math lessons couched in more narrative form, Life of Fred has become a popular series. Maura Muller, who, with her husband, has been homeschooling their 13-year-old son for the past 5 years, switched to using Life of Fred after trying Singapore Math, which her family found "dry, boring, and repetitive." When her son moved into learning algebra, Muller picked up Math Doesn't Suck, by Danica McKellar, which is geared to teen girls but "makes us both laugh."

Muller also employs the techniques common with both rigorous and unschooling homeschoolers: using math in everyday life for activities like measuring out their garden, planning for Christmas shopping, cooking, and estimating miles per gallon for car trips.

Practical teaching methods like these can go a long way to answering the question, "What am I ever going to use this for?"

Hands-on learning

"What absolutely did not work," says Delores Caesar, echoing many homeschooling parents, "is any online program. My nine-year-old just shut down looking at the screen."

The limitations of online programs such as Khan Academy and IXL speak to the importance of connecting mathematics to the physical world.

Patrick Honner, who teaches math at public high schools in New York City, says that he would focus on exploring math "through things kids enjoy, like games, puzzles, paradoxes, physical situations."

One successful program that reflects this approach is from Miquon Math Lab. Miquon was developed in the 1960s for use with Cuisenaire rods—wooden sticks in different lengths and colors representing the numbers 1–10.

I like using Cuisenaire rods because my son knows his "math rods" are a school-only activity, and we can break up lessons by letting him build with them.

Vikki Siciliano, who also used Miquon for her kids' early years, says she prefers using Duplo Legos with the program "because they're easier to manipulate."

These tools can make a big difference for a child who thinks three-dimensionally, or who needs to grasp lessons physically before transferring the computations to paper. And blocks, tiles and linking cubes continue to benefit math learning well into middle school.

Reaching outside the home

If the thought of teaching your child math still makes you break out in hives, outsourcing is an option.

Vikki Siciliano says that a homeschooling friend of hers loathes math so much she hired outside tutors because she "was scared of pushing her own feelings about it on to her 14-year-old daughter."

And as the homeschooling student gets older, their abilities can outstrip the mathematics lessons based on worksheets, manipulatives, and gas mileage calculations. This is where parents can really use the support of homeschooling groups and the Internet. Particularly in math, many students learn better if they are solving problems and discovering mathematical questions in groups.

There are many blogs and websites run by mathematicians and teachers posing fascinating higher-level questions you won't find in textbooks. Patrick Honner's website regularly features math in art, as well as interesting mathematical questions and discussions.

Did you know there's more than one kind of infinity? Or that The Simpsons is packed with mathematical references because most of the writers were math majors?

Not just for homeschooling families, these resources offer all families the chance to think "out of the old-school box" when it comes to math.

Changing your perspective

"Parents, especially mothers of girls, should never, ever say, 'I was hopeless at math!'" says Jo Boaler. Doing so "is a very damaging message, especially for young girls."

Boaler is sympathetic to parents who hate math, but she notes that many of the puzzles, games, books, and methods that make math learning fun and effective can work for parents, too. In short, you've got a chance to start your own math education over again.

"At the heart of it, math is about the study of structure," says Kate Owens, who teaches undergraduate mathematics classes at the College of Charleston. "Most elementary school math is devoted toward studying the structure of rational numbers. But this is just one of many different structures that mathematicians study."

Whether that structure is used to figure out how many miles you can drive on a tank of gas, decipher mortgage applications, or build a foundation for later work on the Higgs-Boson particle, it is essential that the homeschooling teacher, or any parent who wants to support his or her child's math education, presents it as a subject worthy of enthusiasm.

If you give it a chance, you might find you're not so terrible at math after all. Even if you still can't add.

Freelance writer Antonia Malchik has a BA in mathematics from Macalester College. She can be reached through her website, antoniamalchik.com.

Pages

Tips Study Mathematics Blog

Saturday, 13 December 2014