High School Homework: Are American Teenagers Overworked?

This morning I read an interesting teen-written article about homework:

High School Homework: Are American Teenagers Overworked?

The article is fairly well-written, and at the very least gives some good insight into the mind of a seventh grader.  But the teen also makes some good points.  Among them:

• According to guidelines endorsed by the National Education Association (NEA), a student should be assigned no more than 10 minutes per grade level per night.
• A student who receives excessive homework "will miss out on active playtime, essential for learning social skills, proper brain development, and warding off childhood obesity," according to Harris Cooper, Ph.D., a professor of psychology and neuroscience at Duke University.
• A Duke University review of a number of studies found almost no correlation between homework and long-term achievements in elementary school and only a moderate correlation in middle school. "More is not better," concluded Cooper, who conducted the review.
• In countries like the Czech Republic, Japan, and Denmark, which have higher-scoring students, teachers give little homework. The United States is among the most homework-intensive countries in the world for seventh and eighth grade, so more homework clearly does not mean a higher test score.
• Practicing dozens of homework problems incorrectly only cements the wrong method.
• Teachers who assign less homework will be able to check it thoroughly. In addition, it allows a teacher time to focus on more important things. "I had more time for planning when I wasn't grading thousands of problems a night," says math teacher Joel Wazac at a middle school in Missouri. "And when a student didn't understand something, instead of a parent trying to puzzle it out, I was there to help them." 

However, in response to the author's question, "Is homework really necessary?," the answer is yes.  The following information about homework can be found in Chapter 3 of Robert J. Marzano's "The Art and Science of Teaching:"

• Schooling occupies only about 13 percent of the waking hours of the first 18 years of life, which is less than the amount of time spent watching television.  Thus, homework is valuable because it extends learning opportunities beyond the school day.
• Homework has less effect at the lower grade levels, but homework for young children helps them develop good study habits, fosters positive attitudes toward school, and communicates to students the idea that learning takes work at home as well as school.
• Homework has a positive effect across all grade levels when student achievement is measured by unit tests covering the content actually taught.
• It is not time, per se that has a positive effect on student achievement.  Rather, it is the proportion of homework completed that appears to produce the strongest achievement gains.  By inference, small amounts of well-structured homework may be beneficial.

In summary, students SHOULD be given homework.  However, homework should be limited to 10 minutes per grade level per night, and should be carefully checked over.  Practice may not make perfect, but it does make permanent, and teachers should ensure that students are practicing the correct way.

Prime Numbers

“Prime numbers are what is left when you have taken all the patterns away. I think prime numbers are like life. They are very logical but you could never work out the rules, even if you spent all your time thinking about them.” 

― Mark Haddon, The Curious Incident of the Dog in the Night-time

Math Tip!

A Letter to Students Everywhere

Dear students,

Have you ever heard the expression "first impressions are lasting impressions"?  If not, then allow me to introduce you to the incredibly accurate concept that the first impression you make on a person will remain with him or her, no matter what interactions you have in the future.  For example, if I catch you cheating on the first test you ever take in my presence, I will forever think of you as a cheater.  You may change your ways and become a student of the utmost integrity, and in the back of my mind I'll still forever wonder if you are cheating again.  So, please, think about the person you want to be, and make sure that you act accordingly.  And please, please, please don't cheat.  It won't get you anywhere in life, and it certainly won't get you anywhere in my classroom.

Love,
Miss Math

To err is human.

Two common misunderstandings for some important ideas, and understandings that reflect the overcoming of them (from "Understanding by Design 2nd Edition," page 54-55):

1.  When you multiply two numbers, the answer is bigger.  Multiplication is not repeated addition.  Fractions when multiplied yield a smaller answer, and when divided, a larger answer.  How can that be?  Students often see fractions and decimals as separate number systems; learning to see them as alternative means of representing the "same" qualities is the understanding.

2.  Negative and imaginary numbers are unreal.  Negative and imaginary numbers are no less and no more real than ordinary numbers.  They exist to provide the symmetry and continuity needed for essential arithmetic and algebraic laws.*

* I recently had a discussion with a friend about imaginary numbers, and she expressed her confusion about the purpose of numbers that aren't real.  This is just the tip of the iceberg.  Stay tuned for more info on the importance and purpose of imaginary numbers!

Museum of Mathematics to open in Manhattan next year!

MUSIC NUMBER A museum piece will show the interplay of math and music.

          A recent article in the New York Times, One Math Museum, Many Variables, announced that a new Museum of Mathematics, nicknamed MoMath, will be opening at 11 East 26th Street in Manhattan next year!

SHAPES A Museum of Mathematics exhibit will explain tiling patterns on different shapes.

          According to creator Glen Whitney, the museum’s mission is to shape cultural attitudes and dispel the bad rap that most people give math. “It’s the only field you can go to a cocktail party and talk to people with pride about how lousy you are,” Mr. Whitney said.  Under his vision, MoMath will be one small way to bolster mathematics education in the United States by serving as an intellectual catalyst and teaching resource.

RIDES A traveling exhibit has a tricycle with square wheels.

          “There are all sorts of myths about mathematics out there,” Mr. Whitney says — math is hard, math is boring, math is for boys, math doesn’t matter in real life. “All these are cultural myths that we want to blow apart.” 

A Math Lover's Lament

I was tutoring a student in Algebra at the library the other day (BAD IDEA, just for the record.  If you are going to tutor at a library, make sure you check it out ahead of time so that you know whether or not there are quiet areas in which to work) and there was a woman working with a much younger child at a table nearby.  While my tutee was working quietly on a problem I had given her, I couldn't help but overhear the conversation going on at the next table.  Apparently, the young boy was really enjoying working on math and didn't want to move on to reading.  Now, I completely understand that the tutor had a duty to make sure they accomplished some reading during their time together, but I do NOT agree with the method she used to transition.  She told the young boy, "We have to do some reading now so we don't get a headache from doing all this math."

EXCUSE ME???  What kind of message is that sending to that young and very impressionable boy?  Answer:  Math gives you a headache, math is bad, etc.  Poor math, it's no wonder it gets such a bad rep.  From a very young age, students' minds are filled with false impressions of the subject that I think is so wonderful.  Yes, the tutor needed to transition to reading, but she could have done so in a way that encouraged the child's interest in math.  How about, "I'm so glad that you are enjoying math so much, but reading is fun and important too.  So, why don't we spend some time reading, and then if we have time we can work on some more math at the end?"  Or, "Well, we could spend the rest of our time doing math today as long as we spend our next meeting together reading.  Or we could share our time both days reading and doing math.  What would you like to do?"  Then write a little contract and have the student sign it so that he is held accountable for the choice he has made.  There are so many other options besides, "Math will give you a headache."

Imagine what a difference it would make if everyone, no matter their personal feelings toward math, spoke positively of the subject until students could develop their own opinion about the subject.  Imagine how many more students would end up pursuing careers in science, technology, engineering, and math (STEM).  We need more Americans going into these fields, and first impressions are lasting impressions.  Lets make sure that children's first impressions are positive.