Attributes that Require NO Talent

I am an instructor at a community college. Many of my colleagues have unique  posters hanging outside their doors. I found this one by a co-worker's office who teaches English. I believe it is something we can all use during this difficult time of finding the right job even though you have a college degree. In fact, these might good attributes to add to your resume.

Math Ideas for Parents for Those Long Summer Months

Success in school starts and continues at home, but many parents feel inadequate when it comes to helping their children with math. While parents can usually find time to read a story to their children, thereby instilling a love for books, they are often at a loss as to how to instill a love and appreciation for mathematics. Like reading, mathematics is a subject that is indeed necessary for functioning adequately in society. Here are some tips to help you as you work with your child this summer.

Recognize that you make an important difference in your child's education. Most children develop a sense of numbers way before the "regular" school years. If you have a young child, take advantage of those early years through activities at home that teach and at the same time are enjoyable. You might take your child on a counting walk in your neighborhood to count how many trees, shrubs, plants, houses, birds, dogs, etc. you see. Look for twigs or pine cones or leaves, etc. and have your child count as many as s/he can. Then lay them side by side to compare the length and ask your child, "Which is the longest, which is the shortest? Are there any that are the same length?"

Provide experiences at home that help your child be successful, and seek ways to let children, even very young children, know that they are needed and important. Cooking is a fun way to do this. Help your child follow the directions on a Kool Aid packet or frozen juice can to make refreshments for the family. Help your child cut a fruit or vegetable into halves, fourths, thirds, etc. Let them help prepare a meal while asking, "What do you do first? Second? Third?"  or better yet, allow them to measure the ingredients for a recipe.

Children do not need a lot of motivation when it comes to recognizing and learning the value of coins. You know they are interested when they start bugging you for money.  However, it is not sufficient for children to be able to just recognize coins, they must also know the value of these coins. The best way to accomplish this is to use real money.  You might show your child two or more coins and have him/her tell you the total value of the coins. Or hold up a coin.  After your child identifies it, discuss what the coin would buy at the store. When going to the grocery store, give your child his/her own money to buy something. Have them select an item that costs less than the money you have given them.  You can also do a similar activity by asking them to determine what are the fewest number of coins it would take to pay for the item. Give your child a practical math experience by estimating how long it takes to prepare a meal from start to finish.

Parents' attitudes toward mathematics have an impact on children's attitudes; so, be patient with your child. A wrong answer on a math test or a homework assignment is not a time for scolding.  It tells you to look further, to ask questions, and to find out what the wrong answer is saying about your child's understanding. Ask your child to explain how they solved the problem.  Most importantly, relax! Know that neither you nor the teacher needs to be perfect for your child to learn math. Remember, one bad math assignment/test will not destroy your child's ability to learn math.

But what if you need some assistance?  Luckily, in today's world, we can find mathematical help at the click of a button. Below are some great places to go and find outside help if your child is struggling or if you need more information for yourself.

Study Shack is a great place to find or make flashcards, play hangman, do matching activities or crosswords.  It has activities for grades 1-6 as well as addition, multiplication, algebra and geometry.  Cliff's Notes for Math is site that has notes, examples and quizzes for your older children.  The subject areas include Basic Math through Calculus.  There are many on-line math dictionaries.  My favorite is A Math Dictionary for Kids because it includes animation and interactive activities.  Even You Tube is a great resource for students struggling with a concept and needing an alternative way of seeing it. 

Finally, talk about people who use math in their jobs, including builders, architects, engineers, computer professionals, and scientists. Point out that even if your child does not plan to pursue a career in which s/he will use math, learning it is still important because math teaches you how to solve problems and how to think logically. AND we use math everyday!

$3.25

------------------------------------------------------------------
Here is another resource that may prove useful. It is a ten page, comprehensive, extensive and wide-ranging list of over 200 hyperlinked Educational Website Addresses for ALL subjects.

• Organized by a wide range of subject areas
• Broken down into subcategories (i.e. science, then earth science, ecology, etc.)
• Click on the URL and you are automatically taken to the site.

There's a Vinculum in Math? What Is It?

When writing division problems, we can use three different forms, a fraction, the division symbol (÷) or the division house. Why it has been called the division "house" has always been a mystery to me since most math symbols are named something that sounds important. I tried looking it up on-line, but never found a formal mathematical word. Well the mystery has been partially solved thanks to SamizdatMath on Teachers Pay Teachers who mentioned the word vinculum.

I decided to research "vinculum", and here is what I discovered. It is a Latin word that means to ‘bond’ or ‘tie’, and was first used by Michael Stifel in 1544 in Arithmetica integra. It is the horizontal line used to separate the numerator and denominator in a fraction. We also see it above the digital pattern that repeats in a repeating decimal or in geometry above two letters that represent a line segment.

Originally the line was placed under the items to be grouped. What today might be written 7(3x + 4) the early users of the vinculum would write 3x + 4. Today that line is placed over the items to be grouped. The line of a radical sign or the long division house is also called a vinculum.

The symbol is utilized to separate the dividend from the divisor, and is drawn as a right parenthesis with an attached vinculum (see illustration above) extending to the right. The vinculum shows that the digits of the dividend are to be kept together as they represent one whole number.

But when it is all said and done, the entire division "house" symbol seems to have no established name of its own. How mathematically sad! Consequently, it has simply be termed the "long division symbol," or sometimes the division "bracket" or division "house". So the next time you draw the symbol on the board, impress your students with the math word "vinculum"!

Can you find the vinculums in this cartoon?

--------------------------------------------------------------------------

$3.00

Since many students do not know their multiplication tables, working with fractions can be an impossible task, but the divisibility rules, if learned and understood, can be an excellent math tool. This math resource makes it easier to divide numbers, reduce fractions, and determine factors. It contains four easy to understand divisibility rules and includes the rules for 1, 5, and 10 as well as the digital root rules for 3, 6, and 9. A clarification of what digital root is and how to find it is explained.

It's NOT on the Test?!?

Not on the Test

While watching my granddaughter at her tennis lesson, I was visiting with two teachers.  One was a retired fourth grade teacher and the other currently taught Algebra in middle school.  Both we decrying the fact that each year the students come with knowledge that is more narrow than broad.  They both felt this was because more and more time is now spent on testing or getting ready for testing.  As I stated in a previous posting, The Pros and Cons of Testing, "High stakes tests have become the “Big Brother” of education, always there watching, waiting, and demanding our time. As preparing for tests, taking pre-tests, reliably filling in bubbles, and then taking the actual assessments skulk into our classroom, something else of value is replaced since there are only so many hours in a day.  In my opinion, tests are replacing high quality teaching and much needed programs such as music and art."

A long time ago, a friend sent me a song written by Tom Chapin with John Forster called Not on the Test. I saved it, and I listen to it often, especially when I am having a "down" day.  Tom and John wrote the song to express their disappointment in the lack of arts education in many public schools.  Even though the song refers to No Child Left Behind and Common Core, I think you might get a much needed laugh from the song.  Just click on the link under the picture, and let me know what you think!

Bible Activities to Learn and Review the Romans Road to Salvation

$4.25

Memorizing Scripture is a crucial aspect of the Christian faith, but there is one particular set of verses that holds great value for witnessing. The Romans Road is a powerful tool that leads individuals through the essential steps of salvation, from understanding the need for it to receiving it through Jesus Christ. Its straightforward format makes it especially effective in sharing the message of Christianity with others. 

The Romans Road is a powerful Bible tool that leads individuals through the essential steps of salvation, from understanding the need for it to receiving it through Jesus Christ. It is a collection of seven verses from the ESV Version (Romans 3:10, 3:23, 5:8, 6:23, 10:9-10 and 10:13) that serve as a Bible roadmap to the core principles of the Christian faith. With this Romans Road Bible resource, it’s even easier for you to commit these verses to memory by incorporating interactive activities like utilizing pictures, filling in the blanks, and using a word bank to reinforce your learning. In addition, road signs are incorporated to guide you on your spiritual journey.

Included in this resource is…

1. A Table of Contents
2. The seven verses with subtitles for easy recall (All in ESV Version)
3. How to use the Romans Road resource
4. Five different and engaging activities

• Using Pictures Instead of Words (Romans 3:10, 3:23)
• Missing Words (Romans 3:10,3:23, 5:8)
• Road Signs (Romans 3:10, 3:23, 5:8, 6:23)
• Word Bank Activity (Romans 10:9-10)
• Guiding Arrows – All Verses

Master one verse at a time: Instead of trying to memorize a whole passage at once, focus o perfecting one verse before moving on to the next. This will help you retain the information more effectively.

Review, review, review: Before starting a new verse, take a moment to refresh your memory of the previous one. This will help you make connections between the verses and solidify your understanding.

Utilize subtitles: Subtitles can serve as helpful cues to jog your memory about the verse and its placement within the larger passage. Use them to your advantage during the memorization process.

Are Calculators a Crutch or a Useful Math Tool for Students?

Once upon a time, two mathematicians, Cal Q. Late and Tommy Go Figure, were having a discussion...an argument, really.

"Calculators are terrific math tools," said one of the mathematicians.

"I agree, but they shouldn't be used in the classroom" said the other.

"But?" asked Tommy Go Figure, and this is when the argument started. "That is just crazy!  I agree that having a calculator to use is a convenience, but it does not replace knowing how to do something on your own with your own brain."

"Why should kids have to learn how to do something that they don't have to do, something that a calculator can always be used for?" Cal Q. Late argued.

Tommy retorted,  "Why should kids not have the advantage of knowing how to do math?  To me, a calculator is like having to carry an extra brain around in their pockets.  What if they had to do some figuring and did not have their calculators with them?  Or what if the batteries were dead? (Here's a good reason for solar calculators.) What about that?"

Cal reminded Tommy, "No one is ever in that much of a rush. Doing math computation is rarely an emergency situation. Having to wait to get a new battery would seem to take less time than all the time it would take to learn and practice how to do math. That takes years to do, years that kids could spend doing much more interesting things in math."

"Look," Tommy went on, exasperated, "kids need to depend on themselves to do jobs. Using a calculator is not bad, but it should not be the only way kids can do computation. It just doesn't make sense."

Cal would not budge in the argument. "The calculator is an important math tool. When you do a job, it makes sense to use the best tool there is to to that job. If you have a pencil sharpener, you don't use a knife to sharpen a pencil. If you are in a hurry, you don't walk; you go by car. You don't walk just because it is the way people used to travel long ago."

"Aha!" answered Tommy. "Walking is still useful. Just because we have cars, we don't discourage kids from learning how to walk. That is a ridiculous argument."

This argument went on and one and on...and to this day, it has not been resolved. So kids are still learning how to compute and do math with their brains, while some are also learning how to use calculators.  What about you?  Which mathematician, Cal Q. Late or Tommy Go Figure, do you agree with?

------------------------------------------------------

Of course, this argument was made up, but it is very much like the argument schools and teachers are having about what to do with kids and calculators. What do you think?  Leave your comment for others to read.

Two Mind-Bending May Crossword Puzzles in which all the Answers Start with "May"!

I love the beautiful month of May. Here in Kansas, the blustery, cold winds are gone, as are the rains of early spring. Thankfully, the days are getting longer and the nights shorter. May is known as the month of transition and holidays like Mother's Day, and Memorial Day. It is also recognized as Military Appreciation Month. Some other dates that hold significance are May 1st and May 5th.

May 1st is May Day, and marks the return of spring by the blossoming branches of the forsythia, or lilacs or daffodils popping their heads out of the ground, or the weather turning warmer. May 5th is Cinco de Mayo (The Fifth of May). This day celebrates the victory of the Mexican army over the French army at The Battle of Puebla in 1862. Did you know that no U.S. president has ever died in the month of May? In every other month of the year, at least one U.S. president has died.

Have you heard about these fun dates in May?

• May 1: School Principals’ Day
• May 2: World Tuna Day
• May 8: No Socks Day
• May 14 (second Wednesday in May): Root Canal Appreciation Day
• May 14: Dance Like a Chicken Day
• May 28: Slugs Return from Capistrano Day

As I thought about May, I discovered that numerous words begin with "MAY".  After much research, I compiled a list of 20 different such words to create two May themed crosswords puzzles perfect for students in grades 7-10. One puzzle includes a word bank for easier solving, while the other offers a more challenging experience without it. Although both puzzles use the same vocabulary, they have unique layouts, providing two distinct challenges for your students. And don't worry, I've included answer keys for both puzzles. 

$3.00

Here are some ideas on how you might use these puzzles.

1. Try giving the students the crossword with NO word bank to see how much they know.
2. Use the crossword with the word bank as a review of May and its traditions.
3. Use either crossword to work in pairs to complete the puzzle. Solving a crossword puzzle together is a great way to connect.
4. Copy it and make it available for those students who finish their work early.

Happy Puzzling!

The Golden Ratio - Another Math Pattern in Nature

 As stated in a previous blog post, we come across Fibonacci numbers almost every day in real life. For instance, my husband and I were at the Wonders of Wildlife Aquarium in Springfield, Missouri. (If you haven't been, you should go because it is spectacular.) He was noticing how the herrings were swimming counter clockwise and discussing the Coriolis effect with the guide. When we got to the lower levels, where the sharks were, they were all swimming in a counterclockwise direction as well. I asked my rocket scientist husband why this was and again he said, with a straight face, "The Coriolis Effect."

Inside of a Nautilus Shell

I then spied seashells and started talking about Fibonacci numbers and the Golden Ratio. (I know the visitors around us were wondering just who we were!) On the right, you will see a picture of the inside of a Nautilus Shell taken by me! It clearly shows the Golden Ratio. (The Golden Ratio is a special number equal to about 1.6180339887498948482. The Greek letter Phi is used to refer to this ratio. Like Pi, the digits of the Golden Ratio go on forever without repeating.) Many shells, including snail shells and nautilus shells, are perfect examples of the Golden spiral.

Are you still not sure what I am talking about? Have you ever watched the Disney movie entitled Donald in Mathmagic Land? (It's an old one that

The Golden Ratio

you can find on You Tube.) Well, in the movie they talk about the Golden ratio. This is a proportion that is found in nature and in architecture. The proportion creates beauty. And that proportion is the Fibonacci sequence! If you divide consecutive Fibonacci numbers you will always get the Golden ratio. Try it! Start with the big numbers. If you divide 89 by 55, you get 1.61. If you divide 55 by 34, you get 1.61. If you divide 34 by 21, you get 1.61, and so on. You can look up the Golden Ratio and explore it more. It’s fun!

As I close, think about these two questions and try to answer them.

1. Where is the Golden Ratio found in the human body?
2. Why is the golden rectangle important in architecture and art? 

How Will Your Students Celebrate Earth Day on April 22nd?

Earth Day began in 1970, when Gaylord Nelson, a U.S. Senator from Wisconsin, wanted nation-wide teaching on the environment. He brought the idea to state governors, mayors of big cities, editors of college newspapers, and to Scholastic Magazine, which was circulated in U.S. elementary and secondary schools.

Eventually, the idea of Earth Day spread to many people across the country and is now observed each year on April 22nd. The purpose of the day is to encourage awareness of and appreciation for the earth's environment. It is usually celebrated with outdoor shows, where individuals or groups perform acts of service to the earth. Typical ways of observing Earth Day include planting trees, picking up roadside trash, and conducting various programs for recycling and conservation.

Symbols used by people to describe Earth Day include: an image or drawing of planet earth, a tree, a flower or leaves depicting growth or the recycling symbol. Colors used for Earth Day include natural colors such as green, brown or blue.

The universal recycling symbol as seen above is internationally recognized and used to designate recyclable materials. It is composed of three mutually chasing arrows that form a Mobius strip which, in math, is an unending single-sided looped surface. (And you wondered how I would get math in this article!?!) This symbol is found on products like plastics, paper, metals and other materials that can be recycled. It is also seen, in a variety of styles, on recycling containers, at recycling centers, or anywhere there is an emphasis on the smart use of materials and products.

FREE

Inspired by Earth Day, Trash to Treasure is a FREE resource. In it, you will discover how to take old, discarded materials and make them into new, useful, inexpensive products or tools for your classroom. Because these numerous activities vary in difficulty and complexity, they are appropriate for any PreK-3 classroom, and the visual and/or kinesthetic learners will love them.

To download the free version, just click under the cover page on your left.

You are invited to the Inlinkz link party!

Click here to enter

What Is the Fibonacci Number Sequence and Why Should I Care?

Fibonacci

Even if you were taught about the Fibonacci number sequence in school, you probably don’t remember much about it. As with other higher levels of math, many aren’t sure how Fibonacci could possibly be relevant to their real lives; so, why should they even attempt to remember him or his sequence? In reality, Fibonacci numbers are something you come across practically every day. Even so, let’s go back and start at the beginning.

The Fibonacci number sequence is named after Leonardo of Pisa (1175-1240), who was known as Fibonacci. (I love to say that name because it sounds like I know a foreign language.) In mathematics, Fibonacci numbers are this sequence of numbers:

As you can see, it is a pattern, (all math is based on patterns). Can you figure out the number that follows 89? Okay, let's pretend I waited for at least 60 seconds before giving you the answer….144. By definition, the first two numbers in the Fibonacci sequence are 0 and 1, and each subsequent number is the sum of the previous two. For those who are still having difficulty, it is like this.

The next number is found by adding up the two numbers that precede it.

• The 8 is found by adding the two numbers before it (3 + 5)
• Similarly, 13 is found by adding the two numbers before it (5 + 8),
• And the 21 is (8 + 13), and so on!

It is that simple! For those who just love patterns, here is a longer list:

 

Can you figure out the next few numbers?

The Fibonacci sequence can be written as a "Rule “which is: xn = xn-1 + xn-2 The terms are numbered from 0 forwards as seen in the chart below. xn is the term number n. xn-1 is the previous term (n-1) and xn-2 is the term before that (n-2)

Sometimes scientists and mathematicians enjoy studying patterns and relationships because they are interesting, but frequently it's because they help to solve practical problems. Number patterns are regularly studied in connection to the world we live in so we can better understand it. As mathematical connections are uncovered, math ideas are developed to help us be aware of the relationship between math and the natural world.
As I close, here are two questions to think about:

How might knowing this number pattern be useful?
What kinds of things can the numbers in the Fibonacci sequence represent?

Dominoes - An Inexpensive Manipulative to Use in Math

I am always looking for ordinary items that can be used in the classroom as manipulatives. I'm a firm believer in the Conceptual Development Model which advocates teaching the concrete (using manipulatives) prior to moving to the pictorial before even thinking about the abstract. When I was at the Dollar Tree (a great, inexpensive place to purchase school stuff) I saw sets of dominoes for $1.00 each. Since they were inexpensive and readily available, I decided to create several math activities and games to introduce, reinforce, or reteach math concepts.

The Number 52

Think about it; if you lay a domino horizontally, you have a two digit number. Put two dominoes side-by-side, and a four digit number is created. Now you can work with place value, estimation, or rounding.  How about lining up dominoes in a column, and working on addition (with or without regrouping) or subtraction (with or without renaming)? 

Another perfect domino activity is practicing addition or multiplication facts.  How about adding the two sides of the domino or multiplying the two sides together?

The Fraction 1/4

If a domino is placed vertically, you immediately have a fraction.  Placed one way it is a proper fraction, but rotated around, it is an improper fraction which can then be reduced.  A fraction can also be changed into a division problem, a ratio, a decimal, or a percent.

So think outside that box of dominoes and use them as an inexpensive math manipulative because Dots Lots of Fun!

Check out all my Domino Resources available on Teachers Pay Teachers.

The first two are absolutely FREE!

1. Dots Fun for Everyone - FREE  Three math activities and one game for the intermediate grades.
2. Dots Fun - FREE  Three math activities and one game for the primary grades.
3. Dots Fun   A 24 page resource for grades 1-3 that includes 13 math activities and four games.
4. Dots Fun for Everyone  A 29 page resource that features 15 math activities and three games for grades 3-6.
5. Dots Lots of Fun  Seven math games that use dominoes for grades 2-5.

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.
-----------------------------------------------------------------------------

$1.80

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.

$3.50

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

You are invited to the Inlinkz link party!

Click here to enter

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!

$1.80

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.

In Math, what is the Difference Between Drill and Practice?

When I was a kid, one of the things I dreaded most was going to the dentist. Even though we were poor, my Mom took my brother and me every six months for a check-up.  Unfortunately, we didn’t have fluoridated water or toothpaste that enhanced our breath, made our teeth whiter, or prevented cavities.  I remember sitting in the waiting room hearing the drill buzzing, humming, and droning while the patient whined or moaned.  Needless to say, I did not find it a pleasant experience.

I am troubled that, as math teachers, we have carried over this idea of drill into the classroom. Math has become a “drill and kill” activity instead of a “drill and thrill” endeavor.  Because of timed tests or practicing math the same way over and over, many students whine and moan when it is math time.  So how can we get students to those “necessary” skills without continually resorting to monotonous drill?

First we must understand the difference between drill and practice.  In math drill refers to repetitive, non-problematic exercises which are designed to improve skills (memorizing basic math facts) or procedures the student already has acquired. It provides:

1)   Increased proficiency with one strategy to a predetermined level of mastery. To be important to learners, the skills built through drill must become the building blocks for more meaningful learning. Used in small doses, drill can be effective and valuable.

2)   A focus on a singular procedure executed the same way as opposed to understanding.  (i.e. lots of similar problems on many worksheets)  I have often wondered why some math teachers assign more than 15 homework problems.  For the student who understands the process, they only need 10-15 problems to demonstrate that.  For students who have no idea what they are doing, they get to practice incorrectly more than 15 times!

Unfortunately, drill also provides:

 3)  A false appearance of understanding.  Because a student can add 50 problems in one minute does not mean s/he understands the idea of grouping  sets.

 4)  A rule orientated view of math.  There is only one way to work a problem, and the reason why is not important!  (Just invert and multiply but never ask the reason why.)

5)   A fear, avoidance, and a general dislike of mathematics. A constant use of math drills often leaves students uninterested.

On the other hand, practice is a series of different problem-based tasks or experiences, learned over numerous class periods, each addressing the same basic ideas. (ex. different ways to multiply)  It provides:

1)   Increased opportunity to develop concepts and make connections to other mathematical ideas.  (i.e. A fraction is a decimal is a percent is a ratio.)

2)   A focus on providing and developing alternative strategies.  My philosophy, which hangs in my classroom, is: “It is better to solve one problem five ways than to solve five problems the same way.”  (George Polya)

3)   A variety of ways to review a math concept.  (ex. games, crosswords, puzzles, group work)

4)   A chance for all students to understand math and to ask why. (Why do we invert and multiply when dividing fractions?) 

5)   An opportunity for all students to participate and explain how they arrived at the answer. Some may draw a picture, others may rely on a number line, or a few may use manipulatives. Good practice provides feedback to the students, and explains ways to get the correct answer.

$5.00

Let’s look at it this way. A good baseball coach may have his players swing again and again in the batting cage. This drill will help, but by itself it will not make a strong baseball player whereas practicing hitting a ball with a pitcher requires reacting to the different pitches with thought, flexibility, and skill.

I am of the opinion that drill should not be omitted from the math classroom altogether.  Basic math skills should be automatic because being fluent in the basics makes advanced math easier to grasp.  There is a place for drill; however, its use should be kept to situations where the teacher is certain that is the most appropriate form of instruction.  Even though practice is essential, for math it isn't enough. If understanding doesn't come, practice and drill will only leave a student with disjointed skills. If we want to produce strong mathematicians, we must focus on the BIG conceptual ideas through practice in problem-based lessons. We must present ideas in as many forms as we can so that students will go beyond rote drill to insight.

If you are interested in sharing this with your staff, colleagues or parents, check out the EDITABLE power point entitled: Drill vs. Practice.