Archives for Teaching

General

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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Education

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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General

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.
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Education

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...
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Education

Is Math Acceleration A Good Idea?

Way back when I was in school, Algebra I was considered a ninth grade course, and it was only a handful of "honors" kids who took it as eighth graders.

Since then, there's been a trend towards introducing algebra material to younger and younger students, in the hopes that by getting them primed earlier for algebraic thinking and giving them more years of algebra instruction, more students...
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Education

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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