Is Your Data Analysis Missing Out on the Power of Glyphs?

What is a Glyph?

A glyph is a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and necessitates a legend/key to understand the glyph and require problem solving, communication, and data organization.

Remember coloring pages where you had to color in each of the numbers or letters using a key to color certain areas? Or how about coloring books that were filled with color-by-numbers? These color-by-number pages are a type of glyph. Some other activities we can call glyphs would be the paint-by-number kits, the water paints by color coded paint books, and in some cases, even model cars. Some of the model cars had numbers or letters attached to each piece that had to be glued together. These days, this could be considered a type of glyph.

What is the Purpose of a Glyph?

A glyph is a symbol that conveys information nonverbally. Glyphs may be used in many ways to get to know more about students and are extremely useful for students who do not possess the skill to write long, complex explanations. Reading a glyph and interpreting the information represented is a skill that requires deeper thinking. Students must be able to analyze the information presented in visual form. In other words, a glyph is a way to collect, display and analyze data. They are very appropriate to use in the CCSS data management strand (see standards below) of math. Glyphs are actually a type of graph as well as a getting-to- know-you type of activity.

CCSS.Math.Content.1.MD.C.4  Organize, represent, and interpret data with up to three categories;

ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another. 

CCSS.Math.Content.2.MD.D.10  Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. 

For example, if the number of buttons on a gingerbread man tells how many people are in a family, the student might be asked to “Count how many people are in your family. Draw that many buttons on the gingerbread man." Since each child is different, the glyphs won't all look the same which causes the students to really look at the data contained in them and decide what the glyphs are showing.

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Holiday glyphs can be a fun way to gather information about your students. You can find several in my Teachers Pay Teachers store.  My newest one is for Thanksgiving and involves reading and following directions while at the same time requiring problem solving, communication and data organization. The students color or put different items on a turkey based on information about themselves. Students finish the turkey glyph using the seven categories listed below. 

1) Draw a hat on the turkey (girl or a boy?)
2) Creating a color pattern for pets or no pets.
3) Coloring the wings based on whether or not they wear glasses.
4) Writing a Thanksgiving greeting based on how many live in their house.
5) Do you like reading or watching TV the best?
6) How do they get to school. (ride or walk?)
7) Pumpkins (number of letters in first name)

How to Make Fractions Fun: Identify Equivalents and Reduce to Lowest Terms

Here is a Halloween riddle: Which building does Dracula like to visit in New York City? Give up? It's the Vampire State Building!! (Ha! Ha!) Here is another riddle. What do ghosts eat for breakfast? Scream of Wheat and Ghost Toasties!

Okay, so what do these riddles have to do with teaching math? I have been attempting to come up with ways for my students to recognize fractional parts in lowest terms. As you know from this blog, I have used Pattern Sticks, the Divisibility Rules, and finding Digital Root. These are all strategies my students like and use, but to be a good mathematician requires practice - something most of my students dread doing. I can find many "drill and kill" activities, but they tend to do just that, drill those who don't need it and kill those who already know how to do it. So to drill and "thrill", I created fractional word puzzles for specific times of the year.

The one for October is Halloween Fraction Riddles. It contains ten riddles that the students must discover by correctly identifying fractional parts of words. For instance, my first clue might be:

The first 2/3's of WILLOW. The word WILLOW contains six letters. It takes two letters to make 1/3; therefore, the first 2/3's would be the word WILL. This causes the students to group the letters (in this case 4/6), and then to reduce the fraction to lowest terms. The letters are a visual aid for those students who are still having difficulty, and I observe many actually drawing lines between the letters to create groups of two. 

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Here is one from my Halloween resource.

Which part of a road do Ghosts love to travel the most?

1) The first ¾ of THEY. ____________

2) The first 1/3 of DETOUR, the last ½ of GLAD. __________

3) The last 1/3 of USE, the middle 1/3 of AND, and the 

     first 1/5 of DOUBT.    ____________

At first, I thought my students would breeze through the activities, but to my surprise, they proved to be challenging as well as somewhat tricky - just perfect for a Trick or Treat holiday. Maybe this is an activity you would like to try with your intermediate or middle school students. Just click on this link: Halloween Fraction Riddles.

The Absolute Best Ice Cube Science Investigation

As a budget-conscious educator, you know the value of resourcefulness. That's why I'm excited to share some simple yet effective science investigation activities that use everyday objects like ice cubes. These ideas are perfect for teachers like you who are looking to maximize learning potential without breaking the bank. So, let's get started!

Ice experiments are always fun, easy to set up, and often mess-free! Whether you're trying to beat the heat during summer or embrace the chill of winter, ice experiments are the perfect way to engage students and discover the fundamentals of scientific principles. These activities are a great addition to any STEM curriculum that can do in the classroom or at home. Every ice cube holds surprises waiting to be discovered. Supplementing these activities to your STEM curriculum will not only make learning fun but will also help students understand fundamental concepts in a hands-on way.

Hands-on ice cube units invite kids to:

• Ask questions
• Make predictions
• Test ideas
• Observe changes
• Try again when results surprise them

Hands-on ice cube units guide and direct the student through the six steps of the scientific method:

1. Investigating Properties
2. Interactions
3. Making a plan
4. Determining the Investigative Question
5. Prediction and Data Collection
6. Writing a conclusion based on the data.

Why not join this ice cube exploration and uncover the mysteries of ice with engaging hands-on activities that will fascinate, educate and interest your students? Let's turn ordinary ice cubes into unexpected tools for learning; then watch as your students become the ultimate scientists.

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The science unit consists of a three-page student investigation organizer, a property word list, an optional student checklist, and a four-point grading rubric for the teacher. Materials needed for the whole unit, things to do prior to the investigation, and initial instructions are included. Besides simple and clear step-by-step directions for each of the six lessons, specific supplies needed and visual examples of the charts used in the investigation are shown in detail. Each lesson is 30-45 minutes long and the complete investigation will take 6-8 days to carry out depending on the length of your science class. It is appropriate for grade 3-4.

How to Make Your Parent/Teacher Conferences Productive, Efficient, and Stress-Free

If you are like most teachers, you are preparing for your first round of parent/teacher conferences. Now that I teach on the college level, this is one activity I currently don't have to do, but when I did, I really did enjoy them. Why? Because I was prepared with more than just the student's grades. Here are some of the ways I got ready.

First, in preparing for parent/teacher conferences, what can you do on a daily basis? Is the conference based on simply talking about grades or are there additional items that need discussing? How can an observation be specific without offending the parent or guardian? How is it possible to remember everything?

I kept a clipboard in my classroom on which were taped five 6” x 8” file cards so they overlapped - something like you see in the two pictures above. Each week, I tired to evaluate five students, writing at least two observations for each child on the cards. At the end of the week, the file cards were removed and placed into the children's folders. The next week, four different students were chosen to be evaluated. In this way, I did not feel overwhelmed, and had time to really concentrate on a small group of children. By the end of 4-5 weeks, each child in the class had been observed at least twice. By the end of the year, every child had been observed at least eight different times.

Below are sample observations which might appear on the cards.

Student	Date	Observation	IEP	ESL
Mary Kay	9/20   9/23	Likes to work alone; shy and withdrawn;  wears a great deal of make-up. She has a good self concept and is friendly. Her preferred learning style is visual based on the modality survey.	X
Donald	9/19   9/24	Leader, at times domineering, likes to  play games where money is involved. His preferred learning style is auditory  (from the modality survey). He can be a  “bully,” especially in competitive games. He tends to use aggressive language with  those who are not considered athletic.

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By the time the first parent/teacher conferences rolled around, I had at least two observations for each child. This allowed me to share specific things (besides grades) with the parents/guardians. As the year progressed, more observations were added; so, that a parent/guardian as well as myself could readily see progress in not only grades, but in a student's behavior and social skills. The cards were also an easy reference for filling out the paperwork for a 504 plan or an IEP (Individual Education Plan). As a result of utilizing the cards, I learned pertinent and important facts related to the whole child which in turn created an effective and relevant parent/teacher conference.

To keep the conference on the right track, I also created a checklist to use during parent/teacher conferences.  It features nine characteristics listed in a brief, succinct checklist form. During conferences, this guide allows me to have specific items to talk about besides grades. Some of the characteristics included are study skills and organization, response to assignments, class attitude, inquiry skills, etc. Since other teachers at my school were always asking to use it, I rewrote it and placed it in my TPT store. It is available for only $2.00, and I guarantee it will keep your conferences flowing and your parents focused! When you have time, check it out!

Discover the Secret of Using Leaves in A Science Investigation

October, my favorite month.  October means football (Ohio State, of course), cooler weather, and gorgeous leaves. (It is also the month my husband and I were married.) In October, we see the leaves turning colors, and the deciduous trees shedding their leaves.

The leaves in our neighbor's yard have already begun to fall into ours which aggravates my husband because he is the one who gets to rake them. Maybe focusing on some activities using leaves will divert his attention away from the thought of raking leaves to science investigations.  

Remember ironing leaves between wax paper?  We did that in school when I was a little girl (eons and eons ago).  Here is how to do it.

1. Find different sizes and colors of leaves.
2. Tear off two sheets about the same size of waxed paper.
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!

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 come from some unknown ornamental shrubs.

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Maybe you would like to use leaves as a science investigation in your classroom. I have one in my Teacher Pay Teachers store that is a six lesson science performance demonstration for grades K-2. The inquiry guides the primary student through the scientific method and includes: 

1. Exploration time
2. Writing a good investigative question
3. Making a prediction
4. Designing a plan
5. Gathering the data
6. Writing a conclusion based on the data. 

Be"leaf" me, your students will have fun!

Can Pattern Sticks Revolutionize Your Math Understanding?

Most elementary teachers use a Hundreds Board in their classroom.  It can be used for introducing number patterns, sequencing, place value and more. Students can look for counting-by (multiplication) patterns. Colored disks, pinto beans or just coloring the squares with crayons or colored pencils will work for this. Mark the numbers you land on when you count by two. What pattern do they make? Mark the counting-by-3 pattern, or mark the 7's, etc. You may need to print several charts so your students can color in the patterns and compare them. I usually start with the 2's, 5's and 10's since most children have these memorized.

On the other hand, the Hundreds Board can also be confusing when skip counting because there are so many other numbers listed which easily create a distraction.  I have found that Pattern Sticks work much better because the number pattern the student is skip counting by can be isolated. Pattern Sticks are a visual way of showing students the many patterns that occur on a multiplication table.  Illustrated below is the pattern stick for three. As the student skip counts by three, s/he simply goes from one number to the next (left to right).

Martian Fingers

For fun, I purchase those scary, wearable fingers at Halloween time. (buy them in bulk from The Oriental Trading Company - click under the fingers for the link.) Each of my students wears one for skip counting activities. I call them the Awesome Fingers of Math! For some reason, when wearing the fingers, students tend to actually point and follow along when skip counting.

Most students enjoy skip counting when music is played. I have found several CD's on Amazon that lend themselves nicely to this activity.  I especially like Hap Palmer's Multiplication Mountain.  My grandchildren think his songs are catchy, maybe too catchy as sometimes I can't get the songs out of my mind!

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Think about this.  As teachers, if we would take the time to skip count daily, our students would know more than just the 2's, 5's and 10's.  They would know all of their multiplication facts by the end of third grade. And wouldn't the fourth grade teacher love you?!?

IMPORTANT:  If you like this finger idea, be sure that each student uses the same finger every time to avoid the spreading of germs. Keeping it in a zip lock bag with the child’s name on the bag works best. (Believe it or not, when I taught fourth grade, the students would paint and

decorate the fingernails!)

To help your students learn their multiplication facts, you might like the resource entitled Pattern Sticks. It is a a visual way of showing students the many patterns on a multiplication table. It also teaches how you to use the pattern sticks to recognize equivalent fractions, reduce fractions, and to change improper fractions to mixed numbers.

Learn the Foolproof Method to Stop Your Classroom Calculators from Disappearing

I teach at a community college which I love. I also spend three hours a week in the Math Lab which is a place where our students can come for math tutoring, to study or just to work in a group. It is staffed by math instructors. We try to have the supplies available that our students might need like a stapler, hole punch, white boards, pencils, scrap paper etc. We also have a set of scientific calculators which our students may borrow while in the Math Lab. 

Most of our items tend to remain in the Math Lab. Of course, a few pencils disappear now and then, but generally, most supplies seem to stay put EXCEPT for the calculators. Now I must say, students who take these home do so unintentionally. They just pick it up, slip it in their backpack and head out the door. Fortunately, most students are honest and eventually return the calculators to us. The dilemma is we only have so many calculators; so, we want to make sure that if a student needs one, it is on hand. We needed to find a way to make sure the calculators didn’t walk off.

One of our team members came up with an innovative but simple solution.

She purchased small clip boards and attached the calculator to it by using Gorilla tape. The calculators are still accessible, but much too big or bulky to accidentally stick into a backpack. In addition, since they are on a clip board, they are easy to stand and display in the white board trays. At the end of the day, it is simple to count them to make sure none are missing. This idea has worked so well, that some of our math instructors are now using this method in their classrooms.

So if you teach math, and have a set of classroom calculators, why not give this idea a try?

Using a Back to School Glyph to Gather Student Data with Ease

Sometimes I think teachers believe glyphs are just fun activities, but in reality, glyphs are a non-standard way of graphing a variety of information to tell a story. It is a flexible data representation tool that uses symbols to represent different data. Glyphs are an innovative instrument that shows several pieces of data at once and requires a legend/key to understand the glyph. The creation of glyphs requires problem solving, communication as well as data organization.

Remember Paint by Number where you had to paint in each of the numbers or letters using a key to paint with the right color? How about coloring books that were filled with color-by-number pages? Believe it or not, both of these activities were a type of glyph.

For the fall, I have created a Back to School Glyph. Not only is it a type of graph, but it is also an excellent activity for reading and following directions. Students are to finish the Glyph using the nine categories

listed below.

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1. Draw a road to the school (girl or a boy?)
2. Trees (age?)
3. Flowers (pets or no pets?)
4. How did you get to school today? (transportation)
5. School Yard (what do you like to do best?)
6. The Sky (what grade are you in?)
7. School Flag (prefer outside or inside?)
8. Name (number of letters in first name)
9. School House (prefer books or T.V.?)

Reading the completed glyph and interpreting the information represented is a skill that requires deeper thinking by the student. Students must be able to analyze the information presented in visual form. A glyph such as this one is very appropriate to use in the data management strand of mathematics.  If you are interested, just click under the resource cover page.

Streamline Your Classroom Management with Six Simple Class Rules

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 mean less has 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). 

Here are a few things to consider when communicating your classroom rules.

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• 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 is ready to download and laminate to hang in your classroom.

Who Needs Math Study Skills? Everyone!

This semester, I am teaching a new class called Math Study Skills.  We are finding that many of our students who do not qualify for college algebra in reality do not know how to study math.  When you think about it, math is different than other subjects in that it continues to build.  You might do well on the test over Chapter #1, not so hot on Chapter #2, but for sure, you will not succeed on the test over chapter #3.  I am putting together lots of supplemental materials for the class which I hope to share with you on this blog. 

In our next class I am going to ask the students to determine if the following statements about math are true or false.  See what you think.

1. In math, there is only one way to get the answer.
2. To be good at math, you have to be good at calculating.
3. If you are good at math, you skip steps and do all of the work in your head.
4. Men are much better at math than women.
5. There is a "best" way to complete a math problem.
6. You have to have a mathematical mind to understand math.

Believe it or not, all of these are false statements! I think my students will be surprised as well. But of course the best study skill I can give them is depicted in the cartoon!

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Math Profile Sheet

Are you interested in a Math Profile Sheet that will help you to measure the mathematical success of your students?  Check it out by clicking under the resource cover above.

Daily Classroom Irritations that Drive a Teacher Crazy

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.
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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.

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

Beginning of the School Year Survival Guide for Teachers

The beginning of a new academic year is a chance for teachers to start a successful and enjoyable journey with their students. From arranging the classroom to planning lessons and routines, many small steps can make a big difference. For new teachers, this time can feel both exciting and a little challenging. A well laid out plan helps you stay organized, reduce stress, and focus on building strong relationships and positive learning habits from day one. But where do you start? This Survival Guide shares some practical ideas to help teachers start the year with confidence.

The Survival Guide includes:

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• Beginning of the School Year Checklist for Teachers
• Three Lesson Plan Templates that are EDITABLE.
• Six Classroom Management Rules – That’s All You Need!
• The Seven Greatest Irritations for Teachers with Possible Solutions.

The Beginning of the School Year Checklist is a four page comprehensive checklist that walks you through 88 items which ought to be established before the first day of school; these items are categorized by standard operating procedures (i.e. beginning class, interruptions, etc.) and rules as well as accountability (i.e. technology, academic feedback, etc.). Three check-off columns are provided: “Yes”, “No, but Should Have”, and “Not Required”. As you review your list of rules, procedures, and routines, check the column that pertains to your classroom. The results will determine if you have forgotten anything.

The second resource includes three EDITABLE lesson plan templates; one is a generic; whereas, the other two are specifically designed for mathematics (elementary or secondary) and reading/language arts. Checklists are featured on all three plans. Examples are: Bloom’s Taxonomy, multiple intelligences, lesson types, and cooperative learning structures. Hence there is little writing for you to do. On the mathematics lesson plan, the general math objectives are already in a checklist form. However, on the generic and reading plans, space is provided for you to write in the objectives of what you are teaching.

A classroom list of rules and/or expectations can become lengthy and tedious; the longer the list, the harder it is for students to commit the rules to memory. This resource lists six clear and understandable classroom management rules which are brief (only two words each), specific and uncomplicated. They encompass the main areas of concern and are more than sufficient to govern general behaviors in any classroom. Because alliteration is used, the rules are easy for all students to remember.

The Seven Greatest Irritations is a short, four page resource that offers a number of practical ideas about classroom management and how to eliminate those day-after-day aggravating and annoying 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. The seven problems discussed are:

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

By purchasing this bundle of four items, you save about 20%. Not interested in the bundle? Each item may also be purchased individually by clicking on the title of the resource.

You are invited to the Inlinkz link party!

Click here to enter

How to Study Math and Be Successful

Math is hard work, but you can't let that prevent you from being successful.  Anyone who has succeeded in anything has put in "tons" of hard work.  Think about the Olympians and all the practice that is required to even make a local team.  How about anyone who is good at athletics?  Do football players say, "Learning all of those plays is just too hard.  I think I'll quit!"  I don't think so.  The same holds true for learning a subject, any subject whether you like it or not. Below are eleven things to know and think about before you study math or take that next math class.

1) Remember, an extra step is required to pass math. You must use the information you have learned to correctly solve new math problems.

2) You must be able to do four things....

a)   Understand the material
b)  Process the material
c)  Apply what you have learned to correctly solve a problem
d)  Remember what you have learned and apply to new material

3)     Math has a sequential learning pattern; material learned one day is used the next day and the next, etc.  All of the building blocks must be included to be successful.

4)     Math classes should be taken each semester with no breaks to enhance the probability of remembering previous material.

5)      Math is similar to a foreign language; practice it or you will forget it.

6)     Math is a skill subject.   You have to actively practice the skills involved to master it – like learning to play a musical instrument, a sport, or using auto mechanic skills.

7)     Math is a fast-paced subject.  You must learn a lot of information in each class so you are ready to move on to the next class.

8)      Society doesn’t help students.   It says it is OK to hate math, to not be able to do it. You will often hear from parents, "I was never any good at math either."

9)    A bad attitude shouldn't prevent you from doing well in math if you decide you are going to do well. You may not like history or English either, but you have to take the required classes and do well in them if you plan on passing/graduating.

10)  Math is objective, and you will receive the grade you earn. There is no talking a teacher into a better grade BECAUSE you must know the material before you can move forward, or you will fail.

11) Study to make an A on the first test in any math class. It is probably the easiest test, but it counts the same as all of the others. An A shows you know the basics you need to succeed. An A is a good motivator to do well on future tests. An A on the first test improves your confidence that you can do well.

Recognizing and Describing Patterns in Math

In this post, I will present two patterns for you to look at with the hope that you will try to dissect them and be able to answer a few questions.  Are you ready?  Here is the first one that I call Consecutive Number Series.

What counting pattern do you see in this sequence?  How would you describe the sequence of numbers that are being added?  What pattern do you see in the answers?  Can you figure out the pattern for 8 × 8 and 9 × 9?  Notice this pattern made a triangle.  Do you know what kind it is?

My next pattern I call The Eights, and you will readily see why. It, too, forms a triangle, but a different kind. Do you recognize this triangle as isosceles?  If you take a ruler, you will find that the base is 4" while the sides are both 3".

What do you think will happen if we take this same pattern and add a 0?  Notice that this pattern does not begin with adding an eight.  Can you figure out why?

I use this type of patterns with my remedial math college students because I consider it important to do some problem solving while recognizing and describing patterns.  After all, problem solving is a part of life.  It doesn't occur in a vacuum. Because students must reason about some specific content, I think patterns are a great place to begin.  Problem solving also helps students to make connections to other parts of mathematics and find some relevance to what they are learning.  And did you know, that problem solvers are typically better test takers?  So take these patterns, and create some of your own questions for your students.  Use them in a journal or as a small group activity.  But whatever you do, have fun learning and discovering patterns in math.

Investigating Math Number Patterns

Mathematics is the science of patterns.  In this post, I want to target some mathematical problems in which we investigate developing patterns.

In the first example below, you will notice we begin by multiplying one by one; then 11 by 11, and so forth. Each time we multiply, the number of digits in the multiplier and the multiplicand increases. Do you see the pattern that progresses in the answer (product)? Notice how this multiplication pattern forms a triangle? Can you figure out what kind of triangle this would be if we added a "peak" or a row at the top?

Here is another interesting pattern. In this one, instead of multiplying by 1, then 11, then 111, the answer (product) looks like the multiplier in the pattern above. Do you notice anything else significant?

Yes, we are multiplying by 9 each time. Now look at the number being added, and count the number of ones you see in each answer. Surprised? Isn’t it amazing how math is ordered, methodical and precise? Maybe that is one reason I love to teach it! Encourage your students to look for and make sense of math patterns and structure in order to deepen their mathematical understanding and retain what they learn.

Summer Fun Using Shaving Cream

Again, I am going to deviate from the subject of math and offer a fun summer activity I do with my grandchildren. It involves a can of shaving cream, cleaning rags and lawn furniture that has set out all winter.

Were you aware that there are many unusual ways to use shaving cream besides using it for shaving? Did you know that you could...

1) Clean jewelry with it? Spray it on your jewelry and use a soft “old” toothbrush to get off the grime. Rinse with water.

2) Give chrome faucets a brilliant shine? Apply the shaving cream to a sponge and rub it on the faucet. Then wipe it off with a damp cloth.

3) Easily remove paint from your hands? Rub the shaving cream onto your hands; then rinse it off with soap and water.

4) Remove carpet stains? Blot the soiled area with a damp sponge and then spray on the shaving cream. Wipe clean with a damp sponge and let the area dry. It will also work on various clothes stains.

5) Clean vinyl lawn furniture? Spray the lawn furniture with the shaving cream and wipe the grubby areas with a damp rag. Rinse when finished.

Item #5 is what I do each summer. Our lawn furniture sets out over the winter on our patio and even though it is covered, it is filthy when summer comes. I always go to the store and purchase the cheapest shaving cream I can find. (Here, Barbasol sells for about $.89 a can. Depending on the number of grandchildren coming over, determines how many cans I purchase. This year, it was three.)  No matter their age, this is one activity that they all look forward to because it is messy!

I write the child’s name on their can of shaving cream and then assign them a piece of furniture to clean. When everyone is done scrubbing and wiping, we get out the garden hose to spray off the remaining shaving cream, and frequently we end up spraying each other.

But what happens to the leftover shaving cream? I think the pictures say it all!

A Short Tutorial on What is Growth Mindset and Fixed Mindset

At my community college, I teach a course entitled Conquering College because many of the students entering college are not prepared. They lack study skills as well as the soft skills of being on time, regularly doing homework, turning in assignments - on time, etc. This class is now required for every student who tests into developmental math and/or reading.  It has three purposes:

1. To enable students to learn and use Advancement Via Individual Determination (AVID) strategies necessary for persistence and success at the college level, 
2. To develop a learning plan based upon personal abilities and goals, and 
3. To become more self-reliant in fulfilling academic goals.

During the sixteen weeks, we spend time focusing on the the growth and fixed mindset. If you haven't heard of the fixed mindset and the growth mindset, I'll summarize it this way - it is our attitudes, thoughts and beliefs about something.

Study the two charts below. In which category do you fit? Where would you place many of your students?

Carol Dweck has done a great deal of research on Growth Mindset. There is a ten minute video on You Tube which is well worth watching and sharing with your fellow teachers. It is called How To Help Every Child Fulfill Their Potential. (click on title) If for no other reason, watch it to discover what 15 years of praising children for their intelligence has done to our students. It is definitely eye opening!

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.