Archives for Tutoring


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:
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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.
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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.
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Getting a Handle on Academic Anxiety

Do math tutors ever suffer math anxiety?

Sometimes I feel anxious when I'm going to have to tutor a topic that is hard for me. (Yes, even tutors and teachers find certain topics difficult!)

Here's how I cope:

I begin reviewing well in advance. Cramming makes me even more anxious, so I start reviewing early, when the pressure is off.
I use multiple sources. I like watching the videos on Khan Academy because I can just let them roll while I passively absorb some of the material. And I can watch as many times as I want (I "get" more with every viewing). I also read my textbook. Multiple explanations of the same material helps me understand it better.
I go for understanding, not just rote learning. If I can really wrap my brain around this stuff and "own it," I'm going to feel much more confident than if I just learn to plug numbers into some formulas.
I take breaks. This allows the material I just studied to sink in, and it gives me a chance to settle down and let my anxiety level come back to normal.
I deal with my anxiety. When I feel anxiety rising, I stop studying and take some slow, deep breaths. Or I stretch, or take a walk to the mailbox.
I take care of myself. I drink plenty of water, and I eat healthy foods to fuel my brain. Skipping meals can dull thinking and produce headaches, while sugary foods can cause energy spikes and crashes that make anxiety worse.

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Why Vocabulary and Facts Are So Important

How do you know all the words without looking at the back of the cards? 

A fifth grade student was amazed that I knew every word on the American Heritage Dictionary's Top 100 Words Every Middle Schooler Should Know  list. She only recognized five.

I assured her that soon she would also know these words, because we were about to begin learning them now.The authors explain why knowing these words is so important:
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