## Pythagorean Pitfalls: Help for Math Students

As I go on my tutoring rounds, I wind up reteaching and clarifying the same material over and over. Certain topics and concepts are just plain hard for students to wrap their heads around. Many kids in grades 6-10 are currently covering Pythagorean Theorem or other geometry topics, and many are struggling (as usual!) with the word problems. If you are a parent, thinking Yipes ! I don't remember Pythagorean Theorem, the good news is that most students find the actual formula pretty do-able. But, they need help in reading the problem and drawing the diagram. Here's a sample problem from one textbook:

## Ratios Are Hard For Student Brains To Learn

Right now, algebra students are studying unit rates, proportions and dimensional analysis. Geometry students are working on similar figures and triangle proportionality theorems. All of these topics are hard for the same reason: They involve ratios, which may seem easy for adults but are actually deeply challenging for the learning brain to grasp. A ratio is the comparison of two numbers, usually using a fraction bar. If there are two dogs and three cats in a room, I could write that the ratio of dogs to cats is 2/3. Like so many things (reading, driving), ratios become second nature with enough practice, and people lose touch with how difficult they were to learn. And like reading and driving, ratios are hard for the brain because they involve simultaneity of thought. The brain is required to multi-task; it must think about the 2 dogs while at the same time thinking about the 3 cats.

## Exam Tip: Make the Cheat Sheet You Wish You Could Use

Teachers often allow students to bring "cheat sheets" to exams.

A cheat sheet is an index card or single sheet of paper which the student can fill with all the facts and formulas she needs to know but is afraid she doesn't have by heart. (When given only a 3x5 space to fill, many kids can achieve some truly amazing, near-microscopic handwriting).

Even if you can't actually bring a cheat sheet to the exam,...

## Tests Are Valuable Learning Tools

When students get a test back, they typically glance at the grade and then stuff the test in their backpack, never to think about it again (unless, of course, the test has a refrigerator-worthy high score). Meanwhile, teachers invest time and effort making careful corrections and thoughtful comments. This feedback is meant to help kids learn and improve. Reviewing test results with students and helping kids digest the information is an important part of what we tutors do, and parents can do the same.

## Rounding Up Three More Usual Math Suspects

We tutors get an interesting perspective into students' math struggles. We find ourselves reteaching the same concepts over and over, to students from 5th through 12th grade.

The human brain has a hard time grasping and retaining certain kinds of information. Terminology is especially hard, which is why you will notice that my Usual Math Suspects List comprises mostly math words and the procedures these words are meant to trigger.

Parents need to realize...

## Math For Dessert Helps Students Remember

My students are working hard to master all the new concepts they've been learning in math class. It's a lot to absorb! The key to getting all these rules and procedures straight is to keep looping back and practicing the material, over and over.  Here's a GREAT study habit:

## A Surprising Benefit of Test Preparation

To get ready for standardized tests, students have to practice answering many different types of math problems, all mixed together. This can be hard, especially at first.

But it turns out that "interleaving" all sorts of math material produces better retention than practicing only one kind of problem at a time. Making the brain work harder causes it to learn more!

One excellent form of interleaving is to go back every...

## 3 Math Facts All Kids Need to Know (But Many Do Not)

With school back in session, I find myself reteaching and refreshing students on a very familiar (to me, anyway) list of math concepts. By now I think of them as The Usual Suspects. I hope parents will find it reassuring to know that it's not just their kid who can't seem to retain certain math facts. Students from middle school all the way up through 12th grade have trouble making some fundamental math ideas stick. But parents also need to to realize that it's these "little details" which trip kids up in big ways and prevent them from being great math students. Indeed, most calculus students who drop out, do so not because they find the calculus itself hard, but because their math foundations are weak.