The Left Angle Mystery - Does Such an Angle Exist?

Geometry is probably my favorite part of math to teach because it is so visual; plus the subject lends itself to doing many hands-on activities, even with my college students.  When our unit on points, lines and angles is finished, it is time for the unit test.  Almost every year I ask the following question:  What is a left angle?   Much to my chagrin, here are some of the responses I have received over the years NONE of which are true!

1)   A left angle is the opposite of a right angle.

2)  On a clock, 3:00 o'clock is a right angle, but 9:00 o'clock is a left angle.

3)  A left angle is when the base ray is pointing left instead of right.

    4)      A left angle is 1/2 of a straight angle, like when it is cut into two pieces, only it is the part on the left, not the part on the right.

5)      A left angle is 1/4 of a circle, but just certain parts. Here is what I mean.

Now you know why math teachers, at times, want to pull their hair out!  Just to set the record straight, in case any of my students are reading this, there is no such thing as a left angle!  No matter which way the base ray is pointing, any angle that contains 90^○ is called a right angle.

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If you would like some different hands-on ways to teach angles, you might look at the resource entitled, Angles: Hands-on Activities.  This resource explains how to construct different kinds of angles (acute, obtuse, right, straight) using items such as coffee filters, plastic plates, and your fingers. Each item or manipulative is inexpensive, easy to make, and simple for students to use. All of the activities are hands-on and work well for kinesthetic, logical, spatial, and/or visual learners.

                                      

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THE O-H-I-O State and the Math Polygon - Octagon

An octagon is any eight sided polygon.  We often use a stop sign as an example of an octagon in real life.  But in a actuality, a stop sign is a regular octagon meaning that all of the angles are equal in measure (equiangular) and all of the sides have the same length (equilateral).  For an eight sided shape to be classified as an octagon, it needs to have only eight sides.

I got to thinking about this since fall is just around the corner, and our family are BIG Ohio State football fans.  Being raised in Ohio and having relatives who taught at Ohio State have fueled this obsession, but so has doing graduate work there.  If you aren't familiar with the Ohio State Buckeyes, here is your opportunity to learn something new.

On the right you will see one of the many symbols for THE Ohio State University.  The red "O" is geometric because it is an octagon (just count the sides). Even the beginning of the word Ohio is an octagon. (I just adore mathematics in real life!)

The Ohio Stadium, a unique double-deck horseshoe design, is one of the most recognizable landmarks in all of college athletics. It has a seating capacity of 102,780 and is the third largest on-campus facility in the nation. Attending football games in the Ohio Stadium or watching the game on television is a Saturday afternoon ritual for most Ohio State fans.  The stadium is even listed in the National Registry of Historic Places. Anyone (and we have) who has been to a game in the giant horseshoe understands why. There are few experiences more fun or exciting!  In the middle of the football field is the octagonal O as seen in the picture below. (Another example of math in real life!)

Before I continue this posting, I must answer the age old question, "What is a buckeye?"  Since I grew up in Ohio, this question is easy for me to answer, but for everyone else, a buckeye is a nut. (I bet many of you thought it was candy.) Buckeye trees grow in many places in Ohio. The trees drop a "fruit" that comes in a spiked ball with a seam that runs around it. If you crack the seeds open, you can remove the "buckeye." When the nut dries, it is mostly brown in color but it has a light color similar to an over-sized black-eyed pea on one end. This coloration bears a vague resemblance to an eye hence the name, buckeye. 

Then there is Brutus Buckeye, (a student dressed in a costume) the official mascot of THE Ohio State University; so, you might say, since I was born and raised in Ohio, I am a nut!  Brutus (as seen on the left) wears a headpiece resembling a buckeye nut, a block O hat, (another octagon), a scarlet and gray shirt inscribed with the word "Brutus" on the front and the numbers "00" on the back.  Brutus also wears red pants with an Ohio State towel hanging over the front, and high white socks with black shoes. Both male and female students may carry out the duties of Brutus Buckeye as long as they are a committed Ohio State fan.

O-H-I-O

Finally, if you ever are lucky enough to see four people with their hands in the air, forming letters of the alphabet, it is most likely four Ohio state fans spelling out O-H-I-O!  That's how our grandchildren learned how to spell it! (The picture on the right is of our youngest son with his four groomsmen on the day of his wedding.)

And it is so-o-o easy to remember.  Just use this riddle:  What is round on the ends and high in the middle?  You guessed it - OHIO!

Making Parent Teacher Conferences Meaningful

Are You….....

• Tired of always talking about grades at parent/teacher conferences? 

• Tired of feeling like nothing is ever accomplished during the allotted time? 

• Are you having problems with a student, but don’t know how to tell the parents? 

• Do you want to be specific and to-the-point? 

When I taught middle school and/or high school, these were the items that really discouraged me. I knew I had to come up with a better plan if I wanted parent/teacher conferences to be worthwhile and effective for both the student and the parents. I created a a checklist that I could follow, use during conferences, and then give a copy to the parents at the end of the conference.  It contained nine, brief, succinct checklists which were written as a guide so that during conferences I could have specific items to talk about besides grades. I found it easy to complete and straight forward plus it provided me with a simple outline to use as I talked and shared with parents.

Since other teachers were able to use it successfully, I took that checklist and turned it into a resource called Parent/Teacher Conference Checklist, Based on Student Characteristics and Not Grades. Nine different categories are listed for discussion.  They include:

1. Study Skills and Organization 
2. Response to Assignments 
3. In Class Discussion 
4. Class Attitude 
5. Reaction to Setbacks 
6. Accountability 
7. Written Work 
8. Inquiry Skills 
9. Evidence of Intellectual Ability 

To get ready for conferences, all you have to do is place a check mark by each item within the category that applies to the student. Then circle the word that best describes the student in that category such as "always, usually, seldom". (See example above.)

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Finally, make a copy of the checklist so that the parent(s) or the guardian(s) will have something to review with their student when they return home.

Now you are ready for a meaningful and significant conference.

Sock It Away! What To Do With Those Annoying Cell Phones in the Classroom

Most of us can't live without our cell phones.  Unfortunately, neither can our students.  I teach on the college level, and my syllabus states that all cell phones are to be put on "silent", "vibrate", or turned off when class is in session.  Sounds good, doesn't it?  Yet, one of the most common sounds in today's classrooms is the ringing of a cell phone, often accompanied by some ridiculous tune or sound effect that broadcasts to everyone a call is coming in.  It’s like “technological terror" has entered the classroom uninvited.  Inevitably, this happens during an important part of a lesson or discussion, just when a significant point is being made, and suddenly that "teachable moment" is gone forever.

What are teachers to do?  Some instructors stare at the offender while others try to use humor to diffuse the tension. Some collect the phone, returning it to the student later.  A few have gone so far as to ask the student to leave class.

In my opinion the use of cell phones during class time is rude and a serious interruption to the learning environment. What is worse is the use of the cell phone as a cheating device.  The college where I teach has seen students take a picture of the test to send to their friends, use the Internet on the phone to look up answers, or have answers on the phone just-in-case.  At our college, this is cause for immediate expulsion without a second chance.  To avoid this problem, I used to have my students turn their cell phones off and place them in a specific spot in the classroom before the test was passed out.  Unfortunately, the students’ major concern during the test was that someone would walk off with their phone.  Not exactly what I had planned!

It's a CUTE sock and
perfect for a cell phone!

A couple of years ago, a few of us in our department tried something new.  Each of us has purchased those long, brightly colored socks that seem to be the current fashion statement.  (I purchased mine at the Dollar Tree for $1.00 a pair.)  Before the test, each student had to turn off their cell phone, place it in the sock, tie the sock into a knot and place the sock in front of them. This way, the student still had control over their cell phone and could concentrate on doing well on the test, and I did not have to constantly monitor for cheating.

At the end of the semester, we compared notes.  Overall, we found that the students LOVED this idea.  Many said their students were laughing and comparing their stylish sock with their neighbor's.  I was surprised that a few of the students even wanted to take their sock home with the matching one – of course.  So here is a possible side benefit....maybe socking that cell phone away caused my students to TOE the line and study!

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Need more ideas for helping with those annoying classroom irritations? Here is  resource that offers a number of practical and realistic ideas about classroom management and how to eliminate those day-after-day aggravating and annoying student problems that keep resurfacing in your classroom. It is perfect for novice teachers, beginning teachers or for student teachers. It is also a good review for those who have been teaching for a number of years.

A Review for A MUST Read Book: "Setting Limits in the Classroom"

Available on Amazon

Setting Limits in the Classroom by Robert J. MacKenzie
How to Move Beyond the Dance of Discipline in Today's Classrooms

Recommended for: All Staff

The theory of education is something we were all required to study in college. It sounded good in the book; it was great for discussion, and it made us feel smart! But that same theory tended to fall apart when you became the teacher of actual students. In addition to theory, what we really needed were practical suggestions for classroom management, effective ideas for dealing with children, and management methods that were classroom proven. Well, look no further; this is it!

In his introduction, MacKenzie states that, “Teachers can’t teach their academic subjects effectively until they can establish an effective environment for learning. Classroom management is simply too important to be neglected or handled ineffectively.” The book discusses effective classroom structure, your approach to teaching rules, how children learn your rules, and establishing consistent rules. Throughout the book, the author wants you to recognize the discipline you might be using that just doesn’t work. He concludes the book with how to develop a school wide guidance plan.

Setting Limits in the Classroom gives answers to your most testing behaviors that you may experience in the classroom. It is solid advice for fixing the way you interact and deal with students. It is also practical in that it gives various real life scenarios to reenact to practice classroom management and apply in your classroom. It offers firm, down-to-earth, and sensible solutions that effectively cut off students' attempts at negotiating, bargaining, and being belligerent towards the teacher. It offers many options to the unsuccessful extremes of permissiveness and rigid authority and all points in between. MacKenzie outlines no-nonsense methods for setting clear, firm limits supported by words and actions. The book is really a step-by-step manual that shows you how to create structure and methods that work, stop power struggles, motivate students, and even solve homework dilemmas. It is a must read, and I highly recommend it for middle school and high school teachers.

To peak your interest, here are a few quotes I especially liked from the book.

1) Your consequences will have their greatest impact when they are immediate, consistent, logically related, proportional, respectful, and followed by a clean slate.

2) Much of what we consider to be misbehavior in the classroom is actually limit testing or children’s attempts to clarify what we really expect.

3) When our words are consistent with our actions, we don’t need a lot of words or harsh consequences to get our message across.

4) When we ignore misbehavior, we are really saying, “It’s okay to do that. Go ahead. You don’t have to stop.”

This is an ideal book for a whole school study or new teacher development training! In the appendix is a study group guide that lists the objectives for each week as well as study-group discussion questions for each chapter. I have successfully used this book with many student teachers who have in turn used it as a discipline and classroom management guide.

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If you are looking for a set of simple rules, try Six Classroom Rules - That's all You Need available in my Teachers Pay Teachers Store.

Using the Periodic Table to Create Science Bulletin Boards

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As many of you know, my husband teaches middle school science. He has never been one to do bulletin boards, never has been and never will be. My daughter (also a teacher) and I usually construct them for him. For many months now, I have been looking for individual tiles of the periodic table.  I saw a bulletin board on Pinterest (one of my favorite places to gather ideas) that I wanted to recreate for my husband's science lab. I finally turned to Teachers Pay Teachers (where I should have gone in the first place) and asked in the Forum if anyone had such an item. I found that The Triple Point had just what I was looking for. It was a set containing 118 images of Periodic Table tiles, one for each of the 118 elements. Since the resource was only $4.00, I purchased and downloaded it immediately.

After copying the individual tiles onto card stock and laminating them for durability, I laid out the bulletin board (see below). To be honest, my husband did staple everything onto the board as well as arrange the other items. Didn't he do a great job?

In case you can't read the meme in the middle, it says, "That will be $5.00 for the Electrons; the Neutrons are Free of Charge." After all, every classroom needs a little bit of humor!

A Dinner Dilemma - Using Math to Solve How Many Bites a Child Must Eat at Dinner

Using Math to Solve
How Many Bites a
Child Must Eat

Being a grandparent lets you try some new discipline methods that you never thought of as a parent. My grandchildren don't always like what I serve for dinner (Unbelievable, isn't it?); so, many times some food is left on their plates. My children want their children to at least take a bite of everything on their plate which often times feels like a monumental task for our grandchildren. The solution? I have an oversized sponge die on hand for such occasions. The child who doesn't want to eat something rolls the die, and the number that comes up is how many bites they must take before dessert is served. Now, the child must argue with the die and not the parent or me! (It's difficult to argue with an inanimate object.)

Besides taking care of a dinner dilemma, my grandchildren are learning to subitize sets. (Oh, there's the math part of this article!) Since there are no numbers on the die, only dots, the child must count the dots to find out the number. Surprisingly, even the youngest are learning to recognize the dot patterns and can state the number of dots without counting. This indicates they are learning to subitize sets, a necessary prerequisite to memorizing the math facts, especially the multiplication tables. If you aren't sure what subitizing sets means, go back and read my blog posting entitled Can't Memorize Those Dreaded Math Facts. In the meantime, enjoy a new way to enjoy dinner because it is pretty dicey!

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You might like a math game that uses dice. It is called Bug Ya and can be purchased at my TPT store. Three games are included in the four page math resource packet. One is for addition and subtraction; the second is for multiplication, and the third game involves the use of money. The second and third games may involve subtraction with renaming and addition with regrouping based on the numbers that are used. All the games have been developed to extend the recall of facts through playful and intelligent practice. Be sure and download the preview.

Making Falcon Hoods - A Hands-On Activity for the Book, "My Side of the Mountain"

Each year, my husband's science students read My Side of the Mountain. The main character in the book is Sam Gribley, a boy in his early teens. For a year, Sam lives in the woods of the Catskill Mountains. One day Sam spies a peregrine falcon pursuing its prey. Sam determines he wants a falcon as a hunting bird; so, he goes to the nearby town of Delhi to learn about falconry (hunting small game by using a trained bird of prey) by searching books at the local library. For several days, he camps near a cliff hoping to find the location of a peregrine falcon nest. While the mother bird attacks him, Sam steals a female chick from the nest. He names the bird Frightful, and it becomes one of Sam's closest companions. 

If you are acquainted with falconry, you know that peregrine falcons will wear a hood to keep them calm and to make certain they are alert for the falconer. The falcons are also trained to go into hunting mode once the hood is removed. A good falcon hood does not bother the falcon. If it fits well, it does not damage the bird’s feathers or hamper its breathing. Under no circumstances does the hood come in contact with the falcon’s eyes. Out of all the falconer's aids, the hood is the most important piece of equipment. In the book, Sam makes jesses (leg straps), leashes and a hood out of deer skin for Frightful. My husband figured if Sam could construct a falcon hood, then maybe his students could as well.

Using the Internet, (Hood Patterns) my husband found several hood patterns. (Most hoods are custom made by hand and can cost $150 or more!) He purchased faux leather from the fabric store as well as special needles and thread. The students practiced sewing on scraps of the material before cutting out their own patterns and sewing them together. Below is a summary of the process in pictures.

What makes every hood unique is that each falconer decorates the hood in an extraordinary way. They may use elaborate feathers, pieces of colored leather, ornaments, etc. Sometimes, they are even hand painted, dyed or uniquely tooled. Here is what a few of the handmade hoods looked like after the students decorated and embellished them.

Overall, this was a successful book assignment which was not only creative and imaginative, but it gave the artistic students a chance to shine. As a result, you might want to try this project in your classroom as well. So I wish you good luck, good reading and good hood making.

If your class is reading this book, here are three supplementary resources for My Side of the Mountain that you might be interested in.

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Two Word Searches - This resource contains two different word search puzzles about the survival materials used by Sam, the main character in the book, My Side of the Mountain. Both puzzles include
the solutions.

A Crossword Puzzle about Birds - This is a free form crossword puzzle that highlights 16 different birds which appear in the book My Side of the Mountain. The 16 clues are based on the bird’s unique characteristics, color, and song.  A solution key to the puzzle is included.

A Crossword Puzzle about Plants - This is a free form crossword puzzle that highlights 18 different plants which appear in the book My Side of the Mountain. The 18 clues are based on the plant’s distinctive characteristics, color, size and physical appearance.  A solution key to the puzzle is included.

Unlocking Fractions for the Confused and Bewildered - A New Approach to Teaching Fractions

I wish I understood this!

I teach remedial math on the college level, and I find that numerous students are left behind in the mathematical dust if only one strategy is used or introduced when learning fractions. Finding the lowest common denominator, changing denominators, not changing denominators, finding a reciprocal, and reducing to lowest terms are complex issues and often very difficult for many of my students.

I classify my students as mathphobics whose mathematical anxiety is hard to hide. One of my classes entitled, Fractions, Decimals and Percents, is geared for these undergraduates who have never grasped fractions. This article encompasses how I use a different method to teach adding fractions so these students can be successful. Specifically, let's look at adding fractions using the Cross Over Method.

Below is a typical fraction addition problem.  After writing the problem on the board, rewrite it with the common denominator of 6.

Procedure:

1) Ask the students if they see any way to multiply and make a 3 using only the numbers in this problem.

2) Now ask if there is a way to multiply and make 2 using just the numbers in the problem.

3) Finally, ask them to find a way to multiply the numbers in the problem to make 6 the denominator.

4) Instruct the students to cross their arms. This is the cross of cross over and means we do this by cross multiplying in the problem.

5) Multiply the 3 and 1, then write the answer in the numerator.  *Note: Always start with the right denominator or subtraction will not work.

6) Next multiply the 2 and 1 and write the answer in the numerator. Don’t forget to write the + sign. *Note: One line is drawn under both numbers. This is to prevent the students from adding the denominators (a very common mistake).

7) Now have the students uncross their arms and point to the right using their right hand. This is the over part of cross over. It means to multiply the two denominators and write the product as the new denominator.

8) Add the numerators only to find the correct answer.

9) Reduce to lowest terms when necessary.

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It is important that students know the divisibility rules for 2, 3, 5, 6, 9 and 10. In this way, they can readily reduce any problem. In addition, it is extremely important that the students physically do the motions while they learn. This not only targets the kinesthetic learner but also gives the students something physical that makes the process easier to remember. The pictures or illustrations for each technique also benefit the visual/spatial learner. Of course, the auditory student listens and learns as you teach each method. 

I have found these unconventional techniques are very effective for most of my students.  If you find this strategy something you might want to use in your classroom, a resource on how to add, subtract, multiply, and divide fractions is available by clicking the link under the resource cover. A video lesson is included to help you.

Geometry Humor Can Make Mathematicians Smile

I 've been using Pinterest 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 four page 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.

Does A Circle Have Sides?

Believe it or not, this was a question asked by a primary teacher.  I guess I shouldn't be surprised, but in retrospect, I was stunned. Therefore, I decided this topic would make a great blog post.

The answer is not as easy as it may seem. A circle could have one curved side depending on the definition of "side!"  It could have two sides - inside and outside; however this is mathematically irrelevant. Could a circle have infinite sides? Yes, if each side were very tiny. Finally, a circle could have no sides if a side is defined as a straight line. So which definition should a teacher use?

By definition a circle is a perfectly round 2-dimensional shape that has all of its points the same distance from the center. If asked then how many sides does it have, the question itself simply does not apply if "sides" has the same meaning as in a rectangle or square.

I believe the word "side" should be restricted to polygons (two dimensional shapes). A good but straight forward definition of a polygon is a many sided shape.  A side is formed when two lines meet at a polygon vertex. Using this definition then allows us to say:

1) A circle is not a polygon.

2) A circle has no sides.

One way a primary teacher can help students learn some of the correct terminology of a circle is to use concrete ways.  For instance,  the perimeter of a circle is called the circumference.  It is the line that forms the outside edge of a circle or any closed curve. If you have a circle rug in your classroom, ask the students is to come and sit on the circumference of the circle. If you use this often, they will know, but better yet understand circumference.

For older students, you might want to try drawing a circle by putting a pin in a board. Then put a loop of string around the pin, and insert a pencil into the loop. Keeping the string stretched, the students can draw a circle!

And just because I knew you wanted to know, when we divide the circumference by the diameter we get 3.141592654... which is the number π (Pi)!  How cool is that?

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If you are studying circles in your classroom, you might like this resource. It is a set of two circle crossword puzzles that feature 18 terms associated with circles. The words showcased in both puzzles are arc, area, chord, circle, circumference, degrees, diameter, equidistant, perimeter, pi, radii, radius, secant, semicircle, tangent and two. The purpose of these puzzles is to have students practice, review, recognize and use correct geometric vocabulary in a fun, non-threatening way.

Palindromes in Words and Numbers - February 22, 2022 Is a Palindrome!

I was getting ready to pay for my meal at a buffet when I noticed the cashier's name tag.  It read "Anna" to which I replied, "Your name is a palindrome!"  The cashier just stared at me in disbelief.  I explained that a palindrome was letters that read the same backwards as forwards. Because you could read her name forwards and backwards, it qualified as a palindrome. She replied that she remembered a math teacher talking about those because of patterns (I love that math teacher), and she remembered the phrase "race car" was a palindrome.  We then began sharing palindromes that we knew such as radar, level and madam while my family waited impatiently in line. (Sometimes they have little patience with my math conversations.)

The word palindrome is derived from the Greek word palíndromos, which means "running back again". A palindrome can be a word, phrase or sentence which reads the same in both directions such as: "Eva, can I stab bats in a cave?" or "Was it a car or a cat I saw?" or "Rats live on no evil star."

But did you know there are also palindromic numbers?  A palindromic number is a number whose digits are the same if read in both directions (as seen on your left).   Whereas "1234" is not a palindromic number, because backwards it is "4321" which is not the same. (This year, the date 2-22-22 is a palindrome. Do you see why?)

Suppose a person starts with the number one and lists the palindromic numbers in order: 11, 22, 33, 44, 55...etc.  Can you continue the list? 

Did you notice that palindromic numbers are symmetrical?  Look carefully at the 17371 shown above.  It is symmetrical (when a figure can be folded along a line so the two halves match perfectly)on either side of the three whether read left to right or vice versa.

Palindromic numbers are very simple to generate from other numbers with the help of addition.

Try this:

1. Write down any number that has more than one digit. I will use 47.
2. Write down that number in reverse beneath the first number. (See illustration below.)
3. Add the two numbers together. (121)
4. 4. The sum of 121 is undeniably a palindrome.

Try an easy number first, such as 18.  At times you will need to use the first addition answer and repeat the process of reversing and adding. You will almost always get a palindrome answer within six steps.  Try one of these numbers 68 or 79.  Be careful because if you pick a number greater than 89, arriving at the palindromic answer will take more steps, but it will still work.  (See the two examples below.)

But don't try 196!  In fact, avoid it like the plague!   A computer has already gone through several thousand stages, and it still hasn't come up with a palindromic answer!

Example #1:

• Start with 75.
• Reverse 75 which makes 57.
• Add 75 and 57 and you get 132.  The answer 132 is not a palindrome.
• SO reverse 132, and it becomes 231.
• Add 132 and 231, and the answer is 363. 
• Since 363 is a palindrome, we are done!

Example #2:

• Begin with 255.
• Reverse 255 to get 552.
• Add 255 and 552. The answer is 807 which is not a palindrome.
• SO reverse 807 to get 708.
• Add 807 and 708. The answer of 5151 is not a palindrome.
• SO reverse 1515 to get 5151.
• Add 1515 and 5151 which is 6666.
• This is a palindrome; so, we are done!

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Never Too Old to Play a Game - Playing Math Games with older students

I currently teach remedial math students on the college level. These are the students who fail to pass the math placement test to enroll in College Algebra - that dreaded class that everyone must pass to graduate. The math curriculum at our community college starts with Basic Math, moves to Fractions, Decimals and Percents, and then to Basic Algebra Concepts. Most of my students are intelligent and want to learn, but they are deeply afraid of math. I refer to them as mathphobics.

We all have this type of student in our classrooms, whether it is middle school, high school, or college. When working with this type of student, it is important to bear in mind how all students learn. I always refer back to the Conceptual Development Model which states that a student must first learn at the concrete stage (use manipulatives) prior to moving to the pictorial stage, and in advance of the abstract level (the book). This means that lessons must include the use of different manipulatives. I use games a great deal because it is an easy way to introduce and use manipulatives without making the student feel like “a little kid.” I can also control the level of mathematical difficulty by varying the rules; thus, customizing the game to meet the instructional objectives my students are learning. However, as with any classroom activity, teachers should monitor and assess the effectiveness of the games.

When using games, other issues to think about are:

1) Excessive competition. The game is to be enjoyable, not a “fight to the death”.

2) Mastery of the mathematical concepts necessary for successful play. Mastery should be at an above average level unless teacher assistance is readily available when needed. A game should not be played if a concept has just been introduced.

3) Difficulty of the rules. If necessary, the rules should be modified or altered in order that the students will do well.

4) Physical requirements (students with special needs). These should be taken into account so that every player has an opportunity to win.

In addition to strengthening content knowledge, math games encourage students to develop such skills as staying on task, cooperating with others, and organization. Games also allow students to review mathematical concepts without the risk of being called “stupid”. Furthermore, students benefit from observing others solve and explain math problems using different strategies.

Games can also….

1. Pique student interest and participation in math practice and review.
2. Provide immediate feedback for the teacher. (i.e. Who is still having difficulty with a concept? Who needs verbal assurance? Why is a student continually getting the wrong answer?)
3. Encourage and engage even the most reluctant student.
4. Enhance opportunities to respond correctly.
5. Reinforce or support a positive attitude or viewpoint of mathematics.
6. Let students test new problem solving strategies without the fear of failing.
7. Stimulate logical reasoning.
8. Require critical thinking skills.
9. Allow the student to use trial and error strategies.

Mathematical games give the learner numerous opportunities to reinforce current knowledge and to try out strategies or techniques without the worry of getting the “wrong” answer. Games provide students of any age with a non-threatening environment for seeing incorrect solutions, not as mistakes, but as steps towards finding the correct mathematical solution.

$3.25

One math game my students truly enjoy playing is Bug Mania.  It provides motivation for the learner to practice addition, subtraction, and multiplication using positive and negative numbers. The games are simple to individualize since not every pair of students must use the same cubes or have the same objective. Since the goal for each game is determined by the instructor, the time required to play varies. It is always one that my students are anxious to play again and again!