What is the real purpose of homework?

Dictionary.com defines homework as "schoolwork assigned to be done outside the classroom (distinguished from classwork)", but is homework beneficial? Teaching on the college level, I see many benefits to those students who have been required to complete real homework in high school. Here are just a few.

1) Homework can improve student achievement. Studies show that homework improves student achievement in terms of better grades, test results, and the likelihood of attending college.

2) Homework helps to reinforce learning and to develop good study habits and life skills. Homework assists students in developing key skills that they will use throughout their lives, such as accountability, self-sufficiency, discipline, time management, self-direction, critical thinking, and independent problem-solving. Homework assignments given to students actually help students prepare for getting a higher education degree. In fact, the more time a student spends honing his skills, the higher his chances are to enter the University of his dreams or later acquire the work he always wanted to do.

3) Homework can make students more responsible. Knowing that each homework assignment has a specific deadline that cannot be postponed makes students more responsible. It requires grit (perseverance), teaches them time management and causes them to prioritize their time for academic lessons.

As you read this list, I know there are many of you, especially those who have small children or teach younger children, who disagree. I am not here to argue about whether homework is appropriate in the lower grades, but I do want to advocate real homework on the high school level. When I say real homework here is what I mean.

In high school, students might finish their homework in the hall right before class and still earn a good grade; that just isn't possible in college. Homework may be due on a certain day, but it is acceptable if it is turned late. This typically doesn’t float on the college level. In high school, a student gets to the end of a semester and needs a few more points to pull up a grade because of missing or incomplete assignments; so, the student asks the teacher for extra credit work. Extra credit does not exist on the college level! You do the work you are given when you are given it!

I teach college freshmen, many who are woefully unprepared for the academic rigors and demands that are expected. For every one hour students take in college, they should expect two hours of outside work. In other words, if a student is taking 12 hours, they should expect to spend 24 hours on homework (12 x 2).  Of course this formula doesn't always work perfectly, but it is a good starting point. Usually, college freshmen are in disbelief that they are expected to spend so much time on work outside of class. In reality, they should expect to spend as much time on homework in college as they would at a job because college is a full time job!

Help, we're sinking!

When I hand out my syllabus, many of my freshmen are astonished when they discover the amount of homework I expect and require them to do (readings, papers, on-line research, projects, etc.)  AND to compound the problem, many instructors (including me) expect it to be done and handed in on time! Unfortunately, several students have to test the waters to find out that late papers are not accepted.

For those college students who've had little real homework in high school compounded by teachers who have allowed it to be turned in late, those students are aboard a sinking ship that is leaking fast! Sadly, those are the 2-3 students who fail my required class and have to retake it the next semester.

So, as you can see, the decision to agree with or disagree with assignments is really up to the student, but also they need to remember that the learning institution they attend has rules in place regarding assignments. And if homework is assigned, then it will need to be completed and handed in on time, or the impact on the final semester grade will certainly be negative.
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Want a quicker and easier way to grade math homework? Try one of these two math rubrics. I still use them on the college level, and they save me a great deal of time!

Making Perfect Circles by Using Coffee Filters

When I teach angles or the properties of circles, I find that most children have difficulty cutting out a true circle (even with a blackline).  I have resorted to purchasing cheap coffee filters (not the cone shaped ones) and ironing them flat. You can iron several filters at one time, and once they are ironed, they form excellent ready-made circles. Here are some of the ways you can teach angles using these circles.

Writing Formulas on the Coffee Filter Circle

1. Introduce the fact that each and every circle contains 360 degrees.
2. Have the students fold their coffee filter in half. Discuss that this is a straight angle. Ask, “How many degrees does it contain if it is one-half of a circle?” (180 degrees)
3. Have the students fold the coffee filter one more time, into fourths. Talk about this angle being called a right angle and that it contains 90 degrees. Ask, "What fractional part of a circle is this?"
4. Have the students use this fourth of a circle to locate places in the classroom where it will fit (e.g. the corner of their desk, a corner of a book, a corner of the board).
5. Explain that these corners are right angles and without right angles, we would live in a crooked world. Nothing would be straight!
6. With older students, have them write the parts of the circle and the formulas needed for solving problems about circles on the coffee filter circle.

Linking Math and Literature for Older Students

Read Sir Cumference and the First Round Table (A Math Adventure) by Cindy Neuschwander. This is a story about a clever knight of King Arthur’s named Sir Cumference. By using ideas offered by the knight’s wife, Lady Di of Ameter, and his son, Radius, King Arthur finds the perfect shape for his table. Basic geometric vocabulary involving circles (circumference, radius, and diameter) is introduced.

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Want more hands-on ideas for teaching angles? Check out Angles: Hands-On Geometry Activities.

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Celebrate March 14th (Pi Day) Using Crossword Puzzles to Review Math Vocabulary

March 14 is Pi Day because March is the third month, and with 14 as the day, we get the first three digits of pi - 3.14! On Pi Day, nerds, geeks, and mildly interested geometry students alike come together and wear pi-themed clothing, read pi-themed books and watch pi-themed movies, all the while eating pi-themed pie. 

Pi is an irrational number that approximately equals 3.14. It is the number you get if you divide the circumference of any circle by its diameter, and it's the same for all circles, no matter their size. You can estimate pi for yourself by taking some circular things like the tops of jars or round plates and measuring their diameter and their circumference. Then divide the circumference by the diameter, You should get an answer something like 3.14. It should be the same every time (unless you measured wrong).  In other words, π is the number of times a circle’s diameter will fit around its circumference

Actually, 3.14 is only approximately equal to pi. That's because pi is an irrational number. That means that when you write pi as a decimal it goes on forever and ever, never ending. (It is infinite.) Also, no number pattern ever repeats itself.

Usually in math, we write pi with the Greek letter π, which is the letter "p" in Greek. You pronounce it "pie", like the pie you eat for dessert. It is called pi because π is the first letter of the Greek word "perimetros" or perimeter.  What is interesting is that in the Greek alphabet, π (piwas) is the sixteenth letter; likewise, in the English alphabet, the letter "p" is also the sixteenth letter.

But hold your horses!  Whether you like it or not, pi is everywhere. Here are a few more places it has popped up:

1. The main character in the award-winning novel (and 2012 film) Life of Pi nicknames himself after π. 
2. A circular room in the Palais de la Découverte science museum in Paris is called the pi room. The room has 707 digits of pi inscribed on its wall. (The value of pi has now been calculated to more than two trillion digits.)
3. In an episode of Star Trek: The Original Series, Spock commands an evil computer to compute π to the last digit which it cannot do because, as Spock explains, “The value of pi is a transcendental figure without resolution.”
4. Pi is the secret code in Alfred Hitchcock’s Torn Curtain and in The Net starring Sandra Bullock.

Here is more arbitrary information related to pi that I found interesting.

1. If you were to print one billion decimal values of pi in an ordinary font, it would stretch from New York City to Kansas (where I live). 

2. 

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   3.14 backwards looks like PIE. 
3. "I prefer pi" is a palindrome. (It reads the same backwards as forwards)
4. Albert Einstein was born on Pi Day (March 14) in 1879.

All this information about pi and circles can be found in a Pi Day Crossword. It includes two different math crossword puzzles about Pi Day and features 20 words that have to do with pi or circles. One crossword includes a word bank which makes it easier to solve while the more challenging one does not. Even though the same vocabulary is used for each crossword, each grid is laid out differently. Answers keys for both puzzles are included.

By the way, notice my "handle" of Scipi.  The Sci is for science (what my husband teaches) and the pi is for π because I teach math.

Using Math Humor in Geometry

 I 've been using Pinterest (as well as Tailwind) for as long as I can remember, and I love it. Not only do I post many resources and teaching ideas there, but I learn so-o-o much. For example, I learned how to pack one suitcase with enough stuff for a week. (My husband is thrilled with this one.) I also learned that when you fry bacon, to make a small cup out of aluminum foil; pour the bacon grease into it; let the grease harden; then close up the aluminum cup and toss it into the trash. That is one I use all of the time!

On my Pinterest account I have a board entitled Humor - We Need It! I post many math cartoons or humorous sayings there. My favorite subject to teach my college remedial math students is geometry, and I have plenty of corny jokes that I intersperse into my lessons. Here's one.

What did the little acorn say when it grew up? Gee- I'm - A - Tree! (Geometry)

Or about this one?

What did the Pirate say when his parrot flew away? Polly-Gone (Polygon)

Here are some other geometry funnies from Pinterest.

Try placing a riddle or cartoon in the middle of a test.  I often do, and I know exactly where the students are by their laughs.  It helps them to relax and maybe get rid of those mathphobic tendencies.  I hope these math cartoons brought a smile to your face.  Have a great week of teaching!

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You might also like Geometry Parodies, a math handout that includes 20 unusual definitions of geometry terms. Each definition is a play on words or a parody. Twenty-six geometric terms that are possible answers are listed in a word bank, but not all of the words are used in the matching exercise. An answer key is included.