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Using the Periodic Table to Create Bulletin Boards

As many of you know, my husband teachers middle school science.  Together, this is our 86th year of teaching; so, you can tell that we both still love what we do. In fact, we can't imagine doing anything else.

Only $4.00
My husband isn't 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 (png) 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 copy 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 bit of humor!

Be-Leaf Me! Fall is Great! Using Leaves in Science Investigations


When Aunt Sue moved to Florida, she would send home some strange requests.  One year, she wanted us to send her a box of fall leaves.  Since Florida lacks deciduous trees, her students were unaware of the gorgeous colors produced by the trees up north.  The only problem with her request was that the leaves we sent would be dry and crumbling by the time she received them. What to do?

I solved the problem by ironing the leaves between two sheets of wax paper.  It was something I had learned in elementary school many, many years ago (back when the earth was cooling).  My granddaughters still collect leaves so we can do the activity together.  Here is how you do it.
  1. Find different sizes and colors of leaves.
  2. Tear off two sheets of waxed paper - about the same size.
  3. Set the iron on "dry".  No water or steam here!
  4. The heat level of the iron should be medium.
  5. Place leaves on one piece of the waxed paper.
  6. Lay the other piece on top.
  7. Iron away!
Up above, on the right, you will see what ours looked like when we were finished.

Only $5.25
You can also use this activity to identify leaves.  According to my husband who knows trees, leaves and birds from his college studies, we "waxed" a maple leaf, sweet gum leaf, elm leaf, cottonwood leaf (the state tree of Kansas - they are everywhere), and two he doesn't recognize because they are some kind of ornamentals. So my suggestion is to get out there and start gathering leaves because your students, children and grandchildren will love it....be-leaf me!

Do you want your students to have fun with leaves? Check out  a six lesson science performance demonstration for the primary grades which utilizes leaves. This inquiry guides the primary student through the scientific method – 1) exploration time, 2) writing a good investigative question, 3) making a prediction, 4) designing a plan, 5) gathering the data, and 6) writing a conclusion based on the data. A preview of the investigation is available. Just click on the title. After all you might have an unbe-leaf-able time!

Dots Lots of Fun - Using Dominoes 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.

A Go Figure Debut for an Illinoisan who is new!

My latest Go Figure Debut is an elementary teacher from Illinois. Jenny believes in making math fun for all students by building their confidence through math center games and small group lessons because confident students are successful students!

Jenny is in her 9th year of teaching. She currently teaches first and second grade math, science and social studies. What she loves most about teaching is sharing her love of math with her students. She loves seeing their light bulbs go off as well as seeing her students enjoy math more as they become confident in their math abilities. Her classroom is a safe place where students know that it is okay to make mistakes or to not know how to do something, but it is not okay to ever give up. Her students learn math through centers, games and small guided math groups. Learning is a team effort in her classroom, and she enjoys hearing her students help each other.

In addition, Jenny likes playing games with her family. She spends lots of time with her girls, ages three and two, playing Candy Land and Soggy Doggy. She also loves traveling anywhere and everywhere. In June, her girls will be surprised with a trip to Disney, and Jenny cannot wait to see their faces when they meet their favorite princesses in real life.

Jenny currently has 102 products in her store called Foreman Fun. Twelve of the resources are free. Most of her resources are for 1st, 2nd and 4th grade math and are aligned to the CCSS.

Only $5.00
One of her resources is called Dice Math Center Games! ~ NO PREP! ~ Add, Subtract, Place Value, and Time. The games are for Kindergarten, first or second grade, and there is NO CUTTING! Just print, laminate, and play! All you need is dice! The games are perfect for centers on addition, subtraction, place value and telling time. You could also use them for independent work or as a fun assessment! Want to challenge your students? Just give them more than a six sided die!
FREE

Jenny’s free item is a quick, half page, no prep geometry assessments on 2-D and 3-D shapes and fractions. They are ideal for exit slips, as pre/post tests before and after a unit, or to use as evidence in a portfolio for standards based report cards. Each assessment is aligned to one specific common core standard making it easy to assess each individual standard.

I believe students will enjoy Jenny's center activities and games because she takes the time to make them simple for you to use.  Take a few moments to check out her store and use the custom categories on the left of her store's home page to make your search easier.

FOIL - It Doesn't Always Work!

Using FOIL
In more advanced math classes, many instructors happen to hate "FOIL" (including me) because it only provides confusion for the students. Unfortunately, FOIL (an acronym for first, outer, inner and last) tends to be taught as THE way to multiply all polynomials, which is certainly not true. As soon as either one of the polynomials has more than a "first" and "last" term in its parentheses, the students are puzzled as well as off course if they attempt to use FOIL. If students want to use FOIL, they need to be forewarned: You can ONLY use it for the specific case of multiplying two binomials. You can NOT use it at ANY other time!

When multiplying larger polynomials, most students switch
to vertical multiplication, because it is much easier to use, but there is another way. It is called the clam method. (An instructor at the college where I teach says that each set of arcs reminds her of a clam. She’s even named the clam Clarence; so, at our college, this is the Clarence the Clam method.)

Let’s say we have the following problem:

(x + 2) (2x + 3x – 4)

Simply multiply each term in the second parenthesis by the first term in the first parenthesis. Then multiply each term in the second parenthesis by the second term in the first parenthesis.

I have my students draw arcs as they multiply. Notice below that the arcs are drawn so they connect to one another to designate that this is a continuous process. Begin with the first term and times each term in the second parenthesis by that first term until each term has been multiplied.
When they are ready to work with the second term, I have the students use a different color.  This time they multiply each term in the second parenthesis by the second term in the first while drawing an arc below each term just as they did before.  The different colors help to distinguish which terms have been multiplied, and they serve as a check point to make sure no term has been missed in the process.

As they multiply, I have my students write the answers horizontally, lining up the like terms and placing them one under the other as seen below. This makes it so much easier for them to add the like terms:

This "clam" method works every time a student multiplies polynomials, no matter how many terms are involved.

Let me restate what I said at the start of this post: "FOIL" only works for the special case of a two-term polynomial multiplied by another two-term polynomial. It does NOT apply to in ANY other case; therefore, students should not depend on FOIL for general multiplication. In addition, they should never assume it will "work" for every multiplication of polynomials or even for most multiplications. If math students only know FOIL, they have not learned all they need to know, and this will cause them great difficulties and heartaches as they move up in math.

Personally, I have observed too many students who are greatly hindered in mathematics by an over reliance on the FOIL method. Often their instructors have been guilty of never teaching or introducing any other method other than FOIL for multiplying polynomials. Take the time to show your students how to multiply polynomials properly, avoid FOIL, if possible, and consider Clarence the Clam as one of the methods to teach. 


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!
Just $2.00

If you want some additional help with other irritations that might "drive you up the wall", try the resource Seven Greatest Irritations for Teachers with Possible Solutions. You can find it in my store for only $2.00.



Fibonacci Numbers and The Golden Ratio

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 (like my daughter who is sitting here), 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 stated previously, 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, here are four questions to think about:
  1. How might knowing this number pattern be useful? 
  2. What kinds of things can the numbers in the Fibonacci sequence represent?
  3. Where is the Golden Ratio found in the human body?
  4. Why is the golden rectangle important in architecture and art? 

A Go Figure Debut for an Australian Who Is New!

Australia with Queensland Highlighted
Our featured teacher lives “down under” in Queensland, Australia which is situated in the north-east of the country. His Teachers Pay Teachers store is Creating Light Bulbs and that is what he loves most about teaching - that light bulb moment. When you teach a child a new concept or a concept that they are finding difficult, and you see the light bulb turn on when they understand it, this is the reason why he teaches. Mr. Light Bulb has been teaching for five years and describes his classroom as fun, innovative with an emphasis on a growth mindset. 

Mr. Light Bulb enjoys running and is currently training to run a half marathon. At times he dabbles in video games and computer coding. He enjoys cooking, particularly desserts and sweets (YUMMY!) such as sticky date pudding or salted caramel tarts. Also, he is 90% confident that he is addicted to coffee.

The majority of his store is based around mathematical activities including open ended questions, games and drills. He also has a range of STEM and project based learning activities. Currently, Mr. Light Bulb has 49 products in his store; six of them are free.

One of his free resources is entitled Free Fact Families – All Operations and is appropriate for grades 3-5. This sample pack provides the teacher and students with the opportunity to try two high quality products covering all four math operations. The full products includes all of the facts from 1-12, rainbow facts, leveled extension activities and blank sheets to create your own. As one person commented when giving this resource a 4.0 rating, it is also “great for stations and interactive notebooks.”

In addition, Mr. Light Bulb has a $10.00 bundle (you save $5.00 by purchasing the bundle) that is called Open Ended Math Questions – MEGA Bundle – Over 65 Different Questions.  Check out the preview of this resource to view some of the questions contained in this bundle. It combines all of his opened ended math questions products and targets number, fractions and decimals, money, chance, data, probability and word problems. Open ended questions are ones that require more than one word answers. The answers could come in the form of a list, a few sentences or something longer such as a speech, paragraph or essay. They provide an entry point for all students and allow the teacher to quickly gauge the varying levels of knowledge and understanding in the classroom. As one of his buyers expressed, This resource is “outstanding value! My students will love these.”  
$10.00

I am especially partial to this resource because of the importance of asking open ended questions, especially in mathematics. I teach on the college level, and many of my students cannot think beyond a yes/no or a couple of words answer. Open ended questions allow me to analyze a student’s response to a question giving me an opportunity to learn how they think. The students’ responses reveal what they know and how they apply that knowledge. Having this type of resource in the elementary grades would introduce students to this type of questioning early and prepare them better for college.

So head on over to Creating Light Bulbs and take a look at his resources. I am sure you will find many items that you can use in your classroom. And while you are there, take the time to download his free item and leave a rating. He would love to know what you think.

How Many Classroom Rules Does A Teacher Really Need?


Now that most of us are getting geared up for a new school year, it's time to think about what classroom rules need to be established. Maybe the ones you had last year just didn’t work, and you are looking for a change. I could recommend many "Do this or this will happen" or "Please don't do this as it will break my heart" statements, but lists can become very long and mind-numbing. Maybe that is why God only gave Ten Commandments. Fewer rules meant less had to be memorized. So, maybe we need to ask ourselves: “How many classroom rules are really needed?” 

I would suggest making a few general rules that are clear and understandable since being too specific often leads to complicated, wordy rules that might cover every possible situation. Most of the time, I post six simple classroom rules (only two words each) in my room which encompass my main areas of concern. I find them to be more than sufficient to govern general behaviors, and because alliteration is used, the rules are easy for all of my students to remember.

1.  Be Prompt – In other words, be on time to school/class/group.

2.  Be Prepared – Bring the items you need to class or to a group. Study for upcoming tests. Have your homework completed and ready to turn in. 

3.  Be Polite – This rule focuses on how we treat each other. Show respect for your teacher(s) and your fellow students in the classroom, in the school, and on the playground.

4.  Be Persistent - The final rule spotlights the need to stay on task and complete an assignment even though it might be difficult. 

5. Be Productive - Always put forth your best effort! Grades are achieved; not received; so, do your best at all times.

6. Be Positive – Bad days happen! If you are having one of those days, I do understand. Please just inform me before class that you are having a bad day, and I will try to leave you alone during class discussion. This is not to be abused.

I firmly believe that class rules must cover general behaviors, be clear as well as understandable. Being too specific often leads to complicated, wordy rules that might cover every possible situation, but are impossible to remember.  (A good example are the IRS tax rules which I still have difficulty comprehending). 
Only $2.35
Here are a few things to consider when communicating your classroom rules.
  • Establish clear expectations for behavior from day one.
  • Use techniques such as interactive modeling to teach positive behavior.
  • Reinforce positive behavior with supportive teacher language.
  • Quickly stop misbehavior.
  • Restore positive behavior so that children retain their dignity and continue learning.
If you are interested in using these six rules in your classroom, check them out on Teachers Pay Teachers. Each two word rule is written as a one page chart, and are ready to download and laminate to hang in your classroom.


20 Study Tips You Won't Forget! Tips on How to Be Successful in School

Students struggle with many difficulties and setbacks in their lives, and because of all of the competing things vying for their attention, it is hard for them to concentrate on studying. And yet if you are a student, you have to do at least a little bit of studying in order to progress from year to year.

Effective studying may not seem like the most exciting topic for anyone, but think of the big picture. The better a student's study skills are, the better the student will do in school, plus mastering effective study habits will make it easier to learn. Also effective studying can lead to better grades (in high school and college) and doing better on standardized tests.  Because I teach on the college level, I encounter many students who lack effective study skills or even habits, but no matter what study skills a student presently has, I know they can learn new strategies that can assist them in the future. 

For example, better time management and note-taking skills are important for many jobs. Being able to break down tasks into more manageable steps can help a student get things done in less time; thus, having more free time for themselves. Being able to handle test anxiety may help a student deal with other stressful situations such as an interview, a speech or oral exam.

FREE Resource
One of my freshmen classes I teach is called "Conquering College" where we discuss useful strategies for effective studying. For this class, I developed a list of 20 study skills or tips that can help students succeed. Since the key to effective studying is studying smarter, not longer, have your students begin studying smarter with these 20 helpful and effective Study Tips You Won't Forget!  It is a free resource in my store on Teachers Pay Teachers.


Common Classroom Irritations

Have you ever noticed that the same old problems keep resurfacing year after year in your classroom? Isn’t it funny how the little things sometime put us over the edge? I can always deal with that “special” child, but the continuous line at my desk about drives me crazy. Here are two different classroom irritations which I find to be the most annoying plus some possible solutions to think about before school starts.

A. Getting a Drink; Using the Restroom

1)  Set the number of times each student may go per the week.

2)  Have a restroom pass so only one student is out of the classroom at a time.

3)  Count when the children are getting a drink at the drinking fountain such as 1-2-3.  This way everyone is given the same amount to time.
.
4)  Keep a bottle of hand sanitizer by the door so children may use it before lunch to clean their hands. (Unfortunately, not all children wash their hands after using the restroom.)

B. The Pencil Sharpener

1)   Have a box of pre-sharpened pencils that all the children may use.

2)   Make a designated time when students may sharpen pencils. If you have an electric pencil sharpener, unplug it during the off limits time.

3)   Designate an individual to be the “pencil sharpener.” This can be a daily job in your classroom. This person performs the task of sharpening pencils before school, after school, or during any other designated time.

4)   Have two cups of pencils near the pencil sharpener, one for dull pencils and one for sharpened pencils. When a child’s pencil is dull, s/he places it in the dull cup and takes one from the sharp cup.

$2.00
Do you want additional ideas on how to solve common classroom irritations plus more ideas for the ones mentioned above? Check out the complete resource that fully discusses:

           1)  Children Who Are Always at Your Desk
           2)  The Pencil Sharpener
           3)  Getting a Drink; Using the Restroom
           4)  Tattling
           5)  Stress – Especially at Test Time
           6)  Teasing
           7)  Unmotivated Students


Is Extra Credit a Worthwhile Option?

Among teachers, extra credit work has its supporters and its critics, and there are a large number of "undecideds" as well. (Sounds like a political poll!) The range of viewpoints is understandable because the whats, when, whys and hows of extra-credit assignments really matter. Many instructors can't determine whether extra credit is a benefit or a liability, whether it is a point of contention or a headache. In other words, often it is a controversial practice.

When considering extra credit, think about these questions.

1) Does extra credit urge the students to spend less effort on their main assignments?

2) Are extra credit assignments meaningful or mere busy work?

3) Will extra credit encourage student behaviors that will not serve them well in the real world?

4) Should extra credit opportunities be extended to every student or be offered only to certain students on a case-by-case basis?

5) Can extra credit work contribute to grade inflation?

Teaching on the college level, I find that particular instructors never offer extra credit under any circumstances. (That’s me!) Others embrace it as a way to help students learn the course material or improve an unacceptable test score. A small minority, if pushed, will confess they only offer it when students wear them down until they finally give in to it. Most instructors understand that if there are too many opportunities for extra credit, it could possibly outweigh the required course assignments to the point where a student could pass the class without meeting all the standards. (YIKES!!)

I have always been anti-extra credit, the central reason being that it can inflate grades and allow students to receive grades that truly do not reflect their abilities or understanding of a subject. (Remember, I teach math.)  This is the way I view it.
  • Extra credit reinforces students’ beliefs that they don’t need to work hard because whatever they miss or choose not to do, they can make up with extra credit. 
  • Often, students who ask for extra credit tend to be those who aren’t succeeding or those who hope they won’t have to work hard because some easy extra credit opportunities will be available to them. 
  • It is an unintended chance to make up for low scores on earlier exams or missed assignments. (I would NEVER create extra credit assignments at the end of a grading period for students who needed a boost in their grades.) 
  • Time spent on extra credit means less time spent on regular assignments. 
  • Extra credit (especially if it is easy) lowers academic standards for everyone in the class. 
  • It is basically unfair to students who work hard and get it done the first time or turned in when it is due. 
  • Extra credit means more work for me in that it has to be graded! 
So after all of my rambling about extra credit work, my question to you is:

"What are your thoughts (pros and cons) about extra credit?" 
Leave a comment to participate in the discussion.


Drill or Practice? They Are NOT the Same!


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 student 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.

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.
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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 power point entitled: Drill vs. Practice