A Vote for Vocabulary

Posted by & filed under Math Activities, Math Games, Mathematics.

“Language permits us to see. Without the word, we are all blind.” –Carlos Fuentes


“Language is not merely a means of expression and communication; it is an instrument of experiencing, thinking, and feeling … Our ideas and experiences are not independent of language; they are all integral parts of the same pattern, the warp and woof of the same texture. We do not first have thoughts, ideas, feelings, and then put them into a verbal framework. We think in words, by means of words. Language and experience are inextricably interwoven, and the awareness of one awakens the other. Words and idioms are as indispensible to our thoughts and experiences as are colors and tints to a painting.” —William Chomsky, Hebrew: the Eternal Language (Philadelphia: Jewish Publication Society, 1957), p.3.

Many students are challenged when solving word problems, not by the procedural contained in the problem, but by the WORDS. One of my students once told me that word problems wouldn’t be such a problem if there weren’t so many words in them. I agreed, but there are many words in mathematics. Knowing those words is one of the keys to problem solving.

This blog contains activities and games that can be used in the math block to make vocabulary come alive. These are perfect for Vivid Vocabulary Instruction during the first part of every day of the Tabor Rotation Structure.

Scenario:
You’re pre-assessing a series of mathematical concepts that will be explored during the next unit. Your class has completed many K-W-L charts, so you want to see what they know in a way that would be more fun, so you introduce your class to Boggle.

Boggle:
•    Think of all the words you know about the concept we are about to study.
•    In the time given, list these words and/or terms on a sheet of paper.
•    Partner up with someone.
•    Give yourself one point for every idea they don’t have written.
•    With your partner, select the 3 most important words to remember.
•    Be ready to share, with the whole group, which words you chose and why.

Scenario:
You and your class are about to spend a week studying geometric shapes. You tell them they will be thinking about the concept writing what they think they know in their math notebooks. To help them to connect to prior knowledge and reflect, you use the four corners structure.

4-Corners

  • Move to a corner.
  • Think about the reasons why you chose that corner.
  • Partner up with someone you do not know and share your reasons.
  • Be prepared to share what your partner said.

4-Corner Questions and Choices:
If you had to choose a shape to be for a whole day, which one would it be?
1.     Triangle
2.     Square
3.     Circle
4.    Hexagon

If you were a building, which shape would you be?
1.     Rectangular Prism
2.     Pyramid
3.     Cone
4.    Cube

Which of the following best describes you?
1.     Ray
2.     Angle
3.     Line
4.    Line Segment

Think about everything that occurred in the four corners. Now write in your journal about what we are going to study this week and what you would like to know more about.

Scenario:
You and your class have just completed a week studying fractions. You tell them they will be writing, presenting, and sharing a class book about fractions. The book will be written for students who are anxious about the concept. To help them think and reflect, you use a brainstorming circle.

Brainstorming Circle

  • One person talks at a time.
  • “Piggy-backing” is allowed and encouraged.
  • Only positive responses and facial expressions.
  • Practice fluency= answers must be given in three seconds; no repetition of answers

Scenario:
You and your class have just completed studying a topic. You would like for them to be able to summarize what they have learned. To scaffold support, you use the student, non-threatening structure of team webbing.

Team Webbing

  • Select a marker from the table.
  • Choose a recorder according to the rule.
  • Have the recorder write the subject in the center of the web.
  • “Web” (think about ideas that relate to the topic and connect them to the web) about the topic.
  • Move to a new web and add ideas.
  • Return to your “home” web and find 3 interesting themes.

Scenario: Your class has just completed a week of studying area and perimeter of polygons and circles. You want them to place the vocabulary they have learned into long-term memory, so you use music to help them connect.

Mix and Freeze

  • List, on an index card, at least 5 terms we used this week when studying math.
  • Write, in your own words, what the words mean.
  • List at least 2 examples of the words beside your definition.
  • When the music starts, mix silently.
  • When the music stops, partner up with someone close by and share 2 of the words on your card.
  • Continue with a new partner each time the music stops.
  • Return to your home group.
  • While the music plays, write 10 of the words you remember.
  • Use talking chips and share with your group 3 of the words.

Talking Chips

  • Write your name on a post-it, an index card, or a poker chip.
  • Bring this chip to the discussion circle.
  • When you’d like to share with the group, place your chip in the center of the table.
  • Continue the discussion with only the ones with chips speaking.
  • When all have shared, everyone gets their talking chip back and the process begins again.

Math is full of declarative and procedural knowledge. Using the best strategies you can to help the students make meaning of mathematical vocabulary is invaluable. If a student masters a word and can use it with automaticity, then it’s hers forever. You, as their teacher, have just given them a gift that will live in their minds forever!

“A man has made at least a start on discovering the meaning of human life when he plants shade trees under which he knows full well he will never sit.” -D. Elton Trueblood

Flexible Grouping in Tabor Rotation

Posted by & filed under Differentiated Instruction, Fundamentals of Differentiated Instruction, Mathematics, Response to Intervention, RTI, Tabor Rotation.

“The rung of a ladder was never meant to rest upon, but only to hold a man’s foot long enough to enable him to put the other somewhat higher.” -Thomas Henry Huxley

I’ve been receiving a lot of questions about Tabor Rotation (a highly successful, research-based strategy for rigorously differentiating instruction in mathematics) and how to implement the essential components of T.R. Most of the questions have come from resource teachers and math specialists who are trying to help their schools think about teaching math in a different, more effective way.

The next series of Wednesday Blogs will feature a different essential component of Tabor Rotation. Today is about flexibly grouping students. Why think about the grouping of students, especially if you teach in a school that has high test scores and may be exemplary? What’s wrong with delivering the instruction to the whole group, passing out a worksheet, and circulating to help the students? What’s wrong with the “spray and pray” method?  I’ll let a few other researchers address that.

“Textbooks and worksheets structure 75 to 90% of all learning that goes on in schools. Worksheets are worse. Worksheets have nothing to do with genius. No genius ever attributed his or her success to a worksheet.” -Thomas Armstrong, from Awakening Genius in the Classroom

“The passive child learner, unconnected to other children, not involved in meaningful activities cannot learn as well…to sit still and learn is not the best possible way to learn… teaching math facts in the context of real experiences is succeeding beyond anyone’s expectations.” -David Berliner, ASU, 1990

“When a teacher tries to teach something to the entire class at the same time, chances are, one-third of the kids already know it; one-third will get it; and the remaining third won’t. So two-thirds of the children are wasting their time.” -Lillian Katz

Over the last two decades, I’ve worked with many teachers, grade levels, administrations, and schools to develop a structure to teach the qualitatively challenging and engaging mathematics to all students. Teachers had heard they needed to implement small groups, RtI (Response to Intervention), and differentiated instruction. Educators wanted a way to include as many essential elements of differentiated instruction as possible in an easy-to-implement way. That was the beginning of my mission in life–to help change the way mathematics is taught and learned.

My 4th grade class, in 1992, named their math group rotation time Tabor Rotation. The name Tabor Rotation stuck and so did their success as the highest performing class in the school. When creating the structure, I studied all the successful components I used in my balanced literacy block. One of these was flexible grouping. Since the needs of the learner in literacy didn’t change just because we began our math block, it made sense to flexibly group students in math.

Tabor Rotation requires teachers to flexibly group students in a variety of ways. Each week includes partner work, whole-group instruction, teachable moments with individual students, small group work with students of mixed abilities, and working with small groups of students who are grouped together according to their level of understanding of the concepts that are being explored that week.

Students are grouped heterogeneously for rotation through the four stations on Tuesdays and Wednesdays. This type of grouping promotes the communication between students in the group and between the teacher and the students. If students who are at-promise in general ability in mathematics are sat between a couple of other students who have a little bit greater ability, then the teacher isn’t the only person in the Teacher Time group who can explain or clarify how to process a concept. This varied perspective gives students a chance to learn from each other at the other stations.

Just as important is the homogeneous grouping of students on the continuum of readiness for the concepts that are being explored that week. The students’ placement on the continuum is determined by pre-assessments, curriculum compacting, informal assessments, formative assessments, and clipboard cruising. Readiness grouping takes place on Thursdays and Fridays. After Vivid Vocabulary and the Whole-Group Mini-Lesson, all students are involved in an application of a simple or previously learned concept. As all students are working, the teacher uses the information gathered during the week to pull readiness groups.

ALL students deserve qualitatively challenging, respectful, and meaningful work. ALL students deserve to meet with the teacher in a small-group, readiness-level setting to receive personalized assistance that moves them a little bit further than they were the day before. Varying the grouping of students is a powerful way to make sure this occurs!

“What we call differentiated is not a recipe for teaching. It is not an instructional strategy. It is not what a teacher does when he or she has time. It is a way of thinking about teaching and learning. It is a philosophy.” -Tomlinson

For more about flexible grouping and Tabor Rotation, please read past blogs. If you’re ready to try Tabor Rotation in your classroom, then download the Tabor Rotation Planning Guide and begin your journey in rigorously, systematically, and effectively differentiating instruction in your classroom!

My Favorite Teacher

Posted by & filed under Inspiration.

“The most extraordinary thing about a really good teacher is that he or she transcends accepted educational methods.” -Margaret Mead

“The dream begins, most of the time, with a teacher who believes in you, who tugs and pushes, and leads you onto the next plateau, sometimes poking you with a sharp stick called truth.” -Dan Rather


Who was your favorite teacher? Why?

I sometimes ask this question during the mind warmer phase of workshops. I love hearing the stories teachers tell about their favorite teacher. Mine? Her name was Mrs. Kraul. She was my 6th grade reading/language arts teacher.

Why was she my favorite teacher? It was the way she thought “outside the box” and encouraged all of her students to do the same. Instead of making us do round-robin reading to comprehend text, we wrote and recorded plays, commercials, and T.V. shows that were our interpretations of the stories we were reading. I’m giving my age again, but the only technology she had available was a cassette recorder. We didn’t care! We just like doing something different!

Mrs. Kraul believed that poetry expanded the mind and made you a better person. That meant that every month we studied different types of poetry and then wrote some of our own. Every single one of my poems was posted on a wall for everyone to read. One of my poems was published in Seedlings. I was part of a book publishing party. I read my poem out loud in front of a huge crowd. At the age of 12, I was convinced that I would grow up to be a poet. (I’m still a poet for my family…)

What Mrs. Kraul taught me about grammar in 6th grade helped me make it through college. One day she drew an ant and a hill on the board. She asked us to think about everything that the ant could do to the hill. “Go up the hill, down the hill, around the hill, in the hill.” By the time we finished the list, we knew what a preposition was. Because Mrs. Kraul used physical movements and chants to teach us the parts of speech, I made it through Advanced English Grammar in college.

Mrs. Kraul was one of my strongest inspirations for becoming a teacher. Every year, before my students walked in the room I sat in each of their chairs. I tried to think like Stephen Covey, Jay McTighe, and Grant Wiggins and “begin with the end in mind.” The end I wanted? I wanted my students to think that coming to class was the very best part of their life. I wanted them to pray not to be sick. I wanted them to learn more than they ever thought they could.

And, one day, when my students are asked, “Who was your favorite teacher?” I want them to answer, “Mrs. Tabor.”

I know it’s March and there are only a few more months of school, but it’s never too late to begin with the end in mind. What do you want your students to say when they leave your classroom on the very last day?

“I have come to believe that a great teacher is a great artist, and that there are as few as there are other great artists. Teaching might even be the greatest of the arts since the medium is the human mind and spirit.” -John Steinbeck

A.K.A. Decimals

Posted by & filed under Differentiated Instruction, Inspiration, Math Activities, Math Games, Mathematics, Middle School Math, Tabor Rotation.

“We learn more by looking for the answer to a question and not finding it than we do from learning the answer itself.” -Lloyd Alexander

“I never teach my pupils; I only attempt to provide the conditions in which they can learn.” -Albert Einstein

I was never more aware of how important hands-on instruction is until I taught concepts like decimals. Many students have responded to decimals in ways that surprised me.

A few years ago, I was working with a junior high to help the 7th grade math teachers understand how to better use small groups and differentiated instruction. One class was learning about conversions of fractions, decimals, and percents in problem solving situations. As I circulated amongst the students during independent work time, I stopped at one desk. The student, who had been the most belligerent during the teacher-directed instruction, was struggling with the following problem:

Larry has a closet full of shoes. He has some brown ones and some black ones. If ¾ of Larry’s shoes are brown, what percentage of the shoes is brown?

The student had written at least five different equations out beside the problem, but wasn’t arriving at any of the possible answers. I asked her if she’d ever thought about fractions, decimals, and percents in terms of money. She got a puzzled look on her face and asked me what I meant.

I pulled a quarter out of my pocket and asked her how much the coin was worth. When she responded that it was worth 25¢, then I placed four quarters on the desk and asked her how much those coins were worth. We discussed how four quarters equaled 100¢. I asked her if she saw any relationship between 100 cents and 100 percent. I drew a circle and asked her if her teacher had used a circle to explain percents. The student nodded yes. I then divided the circle into 4 equal parts, and shaded 3 of the parts.

Next, I stacked up three of the quarters beside the circle and asked her what fractional part of the set was represented by the quarters in the stack. She said ž. I pointed to the shaded circle and the stack  and asked her if they looked alike. I asked her how many cents were in the stack. She said 75. I asked her to think if there was any connection between fractions, money, and percents based upon what was on her desk.

Then, I did what is sometimes really challenging for a teacher to do…I waited and gave her time to use deductive reasoning.

After a minute, she laughed and said, “The 3 quarters are ž of a dollar. A dollar is worth 100 cents just like 100 percent. So, if I have 3 quarters I have 75¢ which is the same as 75%. You mean I could have been using money all along to figure out decimals and percents? Isn’t that cheating?”
I explained to her that it wasn’t cheating. It was relating all of it to something she knew about…money! I know this may sound silly, but many times we fail to help students make this type of connection. Pointing out the use of decimals in monetary amounts gets their attention and helps the student make a connection to their world. Some students never realize that decimals, fractions, and percentages are three ways of relating the same value.

The following offer valuable information as you prepare to help students truly understand what a decimal is and how simple conversions can be. Each link provides good questions for use during Tabor Rotation Teacher Time and the Whole-Group Mini-Lesson.

“Another Look at Decimals and Percent,” by Lola May, Teaching PreK-8, April 2000. [http://findarticles.com/p/articles/mi_qa3666/is_200004/ai_n8898042/]
Mrs. Glosser’s Math Goodies, “The Decimal Dance” and “Repeating Decimals and the Monster That Wouldn’t Die.” [http://www.mathgoodies.com/articles/creative_ideas.html]

Of course, coolmath.com has an amazing number of high quality lessons about decimals in their pre-algebra section.

Remember,


“It’s not what is poured into a student that counts, but what is planted.” -Linda Conway

“A mind is a fire to be kindled, not a vessel to be filled.” -Plutarch

If this blog didn’t inspire you to think about doing something meaningful with decimals, then maybe the next quote will provide a little chuckle…

“If a doctor, lawyer, or dentist had 40 people in his office at one time, all of whom had different needs, and some of whom didn’t want to be there and were causing trouble, and the doctor, lawyer, or dentist, without assistance, had to treat them all with professional excellence for nine months, then he might have some conception of the classroom teacher’s job.” -Donald D. Quinn

Have a great weekend, everyone! See you on Monday for more inspiration!

Differentiating Test Preparation

Posted by & filed under Assessment, Differentiated Instruction, Mathematics.

“Stress is when you wake up screaming and you realize you haven’t fallen asleep yet.”     -Anonymous

Welcome to March, April, and the 1st half of May. For most people in the United States, this means the coming of warmer weather and spring. For teachers and schools it is the season of state tests.

For me, a long-time advocate for small groups and differentiated instruction in mathematics, it’s the time of year for questions like, “How do we continue to differentiate instruction while intensely preparing students for state tests? Where do we get the time to engage students when we need them to pass the test?”

I am often surprised by how schools “react” to tests instead of being “proactive.” One school I worked with, who had fully implemented Tabor Rotation for several years and was realizing great results, decided to completely change the instructional program. In the second semester, they began to use only a state test coach book as their instructional material. Every adult in the building was working with a small group of students, reading some information to them, then having the students complete the multiple choice questions. No manipulatives, no tone-setting, no games, no fun, nothing but paper-and-pencil tasks. Every group I observed had most students off task within the first two minutes of instruction. 90% of those students never paid attention again.

After pushing my jaw up off the floor that afternoon, I asked if I could work with two of the groups the next day. I wanted to compare the response of my groups to two other control groups. I created a hands-on, meaningful activity to go with the “coach” lessons. The students in my group were engaged, intrigued, and were on task. They also made a 39% improvement over the control groups. After seeing the results, the administration hired me to write interactive activities to go with the rest of the coach lessons. This made a remarkable difference in the response of the students (and the teachers) and assisted them in making AYP that year.

As an administrator or leadership team, what message do you want to send at this point in the school year? That we should stop good, sound, effective instruction and prepare for the upcoming state tests? Or, we must keep engagement, depth of understanding, and meaningful application at the forefront of instruction. If you’ve been preparing them correctly all year long the upcoming tests aren’t going to be an issue.

Here is a way to differentiate and prepare for tests:

One Hour Math Block for Two-Week Test Preparation:
*Identify tested skills that have not been taught/learned.
*Identify any possible weak concepts.
*Assess the above to determine readiness levels of all students.

Schedule:

  • 10 min    Vocabulary needed for state test—constructivist approach
  • 10 min    Conceptual development through meaningful application,    engagement of student a priority
  • 10 min      Test Preparation—Grade Level Discretion
  • 20 min        Independent and/or Partner Practice
  • Teacher meets with at-promise readiness groups
  • 10 min        Student reflection, skill check for mastery, “grabber”

If you’d like to read more about this topic, John Nortan wrote an intriguing article, “Is Test Prep Educational Malpractice?”
[http://www.edweek.org/tm/articles/2009/04/01/040109tln_norton.h20.html?qs=test+preparation+doesn%27t+engage+students]

NCTM (National Council of Teachers of Mathematics) posted a chat with Cathy Seeley that offers answers to many teacher questions on the topic.
[http://www.nctm.org/about/content.aspx?id=842]

And, if you’d like to put just a few more tools in your test season belt, Nell Duke and Ron Richhart offer some really practical strategies in, “No Pain, High Gain: Standardized Test Preparation.”
[http://www2.scholastic.com/browse/article.jsp?id=4006]

“If you can find a path with no obstacles, it probably doesn’t lead anywhere.”     -Frank A. Clark

Go, “think” about it!

Posted by & filed under Inspiration, Mathematics, Thinking.

“Now, go “think” about it!”


I was in a school a few weeks ago and heard this phrase being repeated by a math teacher after discussing a difficult concept with her students. I woke up the next morning at 5:30am—partly because there was a large truck backing up and beeping loudly—but mostly because that phrase had reminded me of a student I had named Reggie. This blog is about one of the students who inspired me to “think about it.”

It was my first day in an urban school that had great diversity and many challenges. I was the new math resource teacher who ran the math lab for grades K-6. I opened the door for my first class of 5th graders. There, standing right next to his teacher, was the young man who had called me names just a few minutes before when he passed me on his way to homeroom. His teacher led the rest of the class inside, then introduced me to Reggie.

I had heard about Reggie during new teacher training that summer. He had a reputation for making teachers cry. Rumor had it that two teachers quit the profession after having him as a student. And, there he was, one of my first students to teach how to “think critically and creatively about mathematics.”

He looked at me, eye-to-eye since I’m only a little over 5’ tall, and said, “So, you’re the new math teacher.”

I smiled and answered, “So, you’re Reggie. I’ve heard so many incredible things about you and how creatively you think. I have been dying to meet you. Welcome to the class that is going to change your life.”

It took me just one class period to figure out that Reggie was one of those students who doesn’t learn sitting down. I know this may come as a shock to some teachers…

…there are millions of people around the world, who are not sitting silently in a chair with their eyes on the teacher, who are busy LEARNING WHILE MOVING!

I placed Reggie at the back of the room with a desk and chair that were quite sturdy. When he was really paying attention to what was going on in the classroom, he often perched his entire body on the desk and rocked back and forth. It didn’t mean he wasn’t paying attention the movement, for him, actually meant he was paying attention.

I also put two, long, masking tape lines at the very back of the room. Any student who needed to move while they thought or worked could walk the lines. Reggie used these lines on a regular basis. Now that I’d made a physical environment that was best for Reggie, I had to find a way to engage him in a thoughtful environment.

I decided to use a set of books called, 20 Thinking Questions from Creative Publications. The students were grouped in mixed-readiness pairs and were given a bag of 50 centimeter cubes for the first problem solving session. The question was, “If one cube represents one horse and it takes 8 cubes to build a corral to go around it, how many cubes will it take to build a corral for 100 horses?” They had 90 minutes to find a way to solve the problem. No one had enough cubes to build the actual corral.

There were an odd number of students, so Reggie and I were partners. (The class didn’t mind my being part of a pair since I never looked at the answer pages.) Reggie and I started to work. We got stumped several times and decided to walk the masking tape lines to help us think. After a couple of minutes, we sat down and agreed that there must be a pattern to finding the answer. If we could find the pattern, we’d solve the problem.

We created several charts but still couldn’t see a clear pattern. Then, Reggie pointed to the relationship between two of the columns. We worked on the equation for the pattern. Five minutes later, Reggie and I were jumping up and down yelling, “We got the answer! We got the answer!”

I’ll never forget the look on Reggie’s face as he explained to the class how he had found the pattern (he did this while moving back and forth in the front of the room, of course). As he spoke, several of the students were whispering that they couldn’t believe Reggie solved the problem first since he wasn’t one of the “smart” students. Reggie overheard this and just grinned.

As the discussion ended, one of students asked Reggie if he cheated. Instead of being angry, he simply replied, “I didn’t have to, man, all you had to do was think about it!”

When Reggie returned to his seat I asked him how he felt. He looked at me, with tears in his eyes, and said, “It’s weird, Mrs. Tabor, I have this quivering feeling inside me and I think I have tears in my eyes. I don’t know what’s going on.”

“That’s what happens when you accomplish something. That’s what it feels like. Sometimes people tear up because of the emotions that are inside them because they are proud of themselves. This problem today wasn’t for a grade or for a prize. The work you did today was because you wanted to prove you could do it—and you did!”

Those moments, the ones when a student’s “light turns on,” are the priceless moments in teaching. Thanks to all the students with whom I’ve worked, I’m addicted to students’ thinking!

“There is virtually no problem you cannot solve, no goal you cannot achieve, no obstacle you cannot overcome if you know how to apply the creative powers of your mind, like a laser beam, to cut through every difficulty in your life and your work.” -Brian Tracy

Why not try some action research of your own? Give your students a handful of centimeter cubes and have them “think about” how many cubes it will take to build a corral for 100 horses. What happens? Write me and let me know!

I’m off to central Texas for the rest of the week to help schools create Tabor Rotation Lesson Plans for the rest of the year. Check in on Wednesday for more about Differentiated Instruction/Tabor Rotation and Friday for Games!

More Great Games for Tabor Rotation

Posted by & filed under Differentiated Instruction, Math Activities, Math Games, Mathematics, Tabor Rotation.

“There are two ways of being creative. One can sing and dance. Or one can create an environment in which singers and dancers flourish.”     Warren G. Bennis

“I’m always thinking about creating. My future starts when I wake up every morning. Every day I find something creative to do with my life.”     Miles Dewey Davis

The quotes above describe so many teachers I know who are being creative in their approaches to helping students truly understand mathematical concepts. Two of these creative people have graciously allowed me to share their original games with you.

The first two games were created by Kathryn and help students explore number sense in really creative ways.

Flip 3 and Cupcakes

Cupcake Score Cards

One of the best things about these games is that they could be  played at home with materials parents have available. Thanks, Kathryn!

The next game was developed by a 2nd grade teacher.  She volunteered (I think she might have been drafted)  to help her grade-level team by creating a game for fractions. Fraction Fun is engaging, meaningful, and FUN! Thanks, Margaret!

When I was working with Margaret’s team a few weeks ago, I determined to create several games that would help students at the primary level explore fractional parts of a set. If you can find a bag of buttons and some two-colored counters, I think this games will do the trick! (If you don’t have two-colored counters, then spray paint some large beans!)

Color Count

Fractional parts of a set is a new indicator the primary-level mathematics classroom and I found just a few games to explore the concept. I loved the game created by Carol Goodrow called, “Jog, Tempo, Sprint!” [http://www.carolgoodrow.com/games/jogtemposprint.htm]. She took a math concept that is difficult to learn and incorporated it into a physical activity that is sure to get the attention of all of your students.

Sorry this blog was late in coming…my head was about to explode for most of the last 48 hours, but the sinus medicine finally kicked in and, with a box of tissues beside me, my Friday blog is finished.
Thanks, again, to the incredible teachers who were willing to share their work with us this week—YOU MAKE A DIFFERENCE!!!

“The greatest good you can do for another is not just to share your riches but to reveal to him his own.”     Benjamin Disraeli

Strength or Weakness?

Posted by & filed under Inspiration.

I was looking for quotes for my inspiration blogs and found this story. As I struggle with how to best help all the teachers and schools with whom I have worked, this story will always encourage me. I hope it does the same for you.

Sometimes your biggest weakness can become your biggest strength. Take, for example, the story of one 10-year-old boy who decided to study judo despite the fact that he had lost his left arm in a devastating car accident.


The boy began lessons with an old Japanese judo master. The boy was doing well, so he couldn’t understand why, after three months of training the master had taught him only one move.
“Sensei,” the boy finally said, “Shouldn’t I be learning more moves?”


“This is the only move you know, but this is the only move you’ll ever need to know,” the sensei replied.
Not quite understanding, but believing in his teacher, the boy kept training.

Several months later, the sensei took the boy to his first tournament. Surprising himself, the boy easily won his first two matches. The third match proved to be more difficult, but after some time, his opponent became impatient and charged; the boy deftly used his one move to win the match. Still amazed by his success, the boy was now in the finals.

This time, his opponent was bigger, stronger, and more experienced. For a while, the boy appeared to be overmatched. Concerned that the boy might get hurt, the referee called a time-out. He was about to stop the match when the sensei intervened.


“No,” the sensei insisted, “Let him continue.”
Soon after the match resumed, his opponent made a critical mistake: he dropped his guard. Instantly, the boy used his move to pin him. The boy had won the match and the tournament. He was the champion.


On the way home, the boy and sensei reviewed every move in each and every match. Then the boy summoned the courage to ask what was really on his mind.


“Sensei, how did I win the tournament with only one move?”
“You won for two reasons,” the sensei answered. “First, you’ve almost mastered one of the most difficult throws in all of judo. And second, the only known defense for that move is for your opponent to grap your left arm.”


The boy’s biggest weakness had become his biggest strength.

Irregular! Impossible? Important!: Area & Perimeter of Irregular Polygons

Posted by & filed under Differentiated Instruction, Math Activities, Math Games, Mathematics, Tabor Rotation.

“Information’s pretty thin stuff unless mixed with experience.” -Clarence Day, The Crow’s Nest

Last week I received a comment and a request from Anne, an academic coach at an Elementary school in Georgia. I first heard from Anne this August when she visited my website looking for information about differentiating instruction and using small groups in math.  Her school has been using the free resources about Tabor Rotation that I’ve been providing on my website and Blog and they have been implementing Tabor Rotation in their school.

I was intrigued by Anne’s request to post activities and games for exploring and understanding the concepts of area and perimeter of irregular polygons. I knew that many other teachers would also benefit from the information in today’s Games Blog.

First of all, remember to make the connections of any concept to the students’ world. It’s one of the most basic comprehension strategies used in literacy, but is rarely emphasized in mathematics. If the students don’t make a real-world connection to what they are learning and why they should be learning it, then the instruction sounds like the “wha, wha, wha” of Charlie Brown’s parents.

This video, about calculating how much paint is needed to cover a wall that has a window, would be an excellent springboard for small-group discussion. [http://www.teachertube.com/viewVideo.php?video_id=20966]

Integrating the subjects you teach (math & science for instance) would be another opportunity to apply the concepts of area and perimeter in a real-world setting.  One performance task I created years ago asks the “scientists” in the classroom “lab” to work with a team and design the first space station on the moon.

FunBrain.com has an excellent online game for exploring area and perimeter of regular polygons.   The polygon generator shows a rectangle with the dimensions labeled. The student must calculate the area or perimeter of the rectangle.  For each problem the student answers correctly, she will receive a piece of an archeological puzzle.  The game ends when the learner gets all the puzzle pieces.[http://www.funbrain.com/poly/index.html]

There are some comprehensive units, with multiple lessons and resources, on several other websites. The Utah Education Network provides lesson plans for the use of manipulatives to help students create various geometric shapes and measure their area. [http://www.uen.org/Lessonplan/preview.cgi?LPid=21544]

The UEN page includes 14 PDF files, games, background for teachers, instructional procedures, extension, and assessments. Everything would be of value in helping students understand, concretely and representationally, the area of a polygon.  This is good stuff!

NCTM also has a good unit of lessons on the topic of using the area formula for a rectangle to discover the area formulas for triangles, parallelograms, and trapezoids. Several of the lesson focus on helping students consider irregular figures whose areas can be determined by estimation or decomposition.

[http://illuminations.nctm.org/LessonDetail.aspx?ID=U160]

All of these online games would be perfect in the Tabor Rotation Games Station and/or the Technology/Application Station. After a teacher-directed exploration and review in the Whole-Group Mini-Lesson, students would find The Shape Explorer incredibly engaging. The Shape Explorer generates shapes, allows students to respond with area and perimeter, checks the answers, and then generates a new shape.

[http://www.shodor.org/interactivate/activities/ShapeExplorer/]

BUT WAIT… there’s MORE!

Do you want your students to truly understand what you have taught so they can apply it in other situations and not have to re-learn it in future years? Why not try the real-world task below.

PIZZA PRODUCTION

  • Have students research information about factories. This is an interesting social studies topic (especially when the students read about child labor in the early 1900’s).
  • Have students brainstorm ingredients they like on a real pizza and what is needed to make a paper replica of a pizza.
  • Ask each pair of students to create a topping (polygon) or part of the pizza that will be used in the production line process.
  • In order to make their ingredients, the students will have to determine how big one ingredient is (surface area), how many ingredients will go on one pizza (multi-step problem solving), how many pizzas they think the class can make (estimation), and how much paper will be needed to make the total number of ingredients they will supply (surface area).

Post a picture of your class “pizza factory” and the engagement of students in a reason why they need to know the area of irregular polygons! Let me know what happened when you helped your students make a connection to something that seems irregular and impossible, but winds up being pretty important!

I hope that I’ve given you plenty of resources to use in your implementation of Tabor Rotation.  This truly is the easiest way to provide real differentiated instruction to your students and meet the needs of all learners in your classroom.   STAY TUNED!  I have a bunch more good stuff coming!

“In the end we retain from our studies only that which we practically apply.” -Johann Wolfgang Von Goethe

Look at what’s possible with students all the time…

[vimeo]http://vimeo.com/21851805[/vimeo]

Formative Assessment via Clipboard Cruising

Posted by & filed under Differentiated Instruction, Tabor Rotation.

“A good question is never answered. It is not a bolt to be tightened into place but a seed to be planted and to bear more seed toward the hope of greening the landscape of idea.” -John  Ciardi

“The test of a good teacher is not how many questions he can ask his pupils that they will answer readily, but how many questions he inspires them to ask him which he finds it hard to answer.” -Alice Wellington Rollins

When I began thinking about this blog it was going to be a few short paragraphs about a type of formative assessment called “Clipboard Cruising.” My research  led me down some “roads less traveled” and has expanded this topic into the next few Differentiated Instruction/Tabor Rotation Blogs.

Formative, on-going assessment is vital part of any differentiated classroom Clipboard Cruising is a type of formative assessment. It is a term I heard while listening to a conference session on tape (Yes, I’m old enough to have a collection of cassette tapes that I just can’t bring myself to throw away). I am into catchy phrases and this one sounded good when I said it the next week to my students. So, it stuck!

What is Clipboard Cruising?

  • An anecdotal finding of observations for record-keeping purposes. –Gregory
  • One way to observe as you walk around the room.   –McDonald
  • Classroom assessment that mirrors the content in a classroom.     –West Salisbury Elementary
  • Noting a certain behavior or understanding on the clipboard.     –Brunsell
  • A teacher-friendly strategy to monitor [understanding] while building relationships with students.     –Binoniemi

Clipboard Cruising is also an essential component of Tabor Rotation (Simplifying Small-Group Instruction in Mathematics) [For more about Tabor Rotation see the Educational Resources Page of glennatabor.com] because it requires teachers to be constant observers. Clipboard Cruising can be as sophisticated as a planning guide or  a page of stickers that will be placed into a teacher’s notes at the end of the day, or simply a sheet of paper upon which the teacher writes a few things he is observing. It doesn’t really matter the way it looks, as long as it’s being done consistently. Why?

“The goal is to create explorers who have an idea of what they are looking for, who have a methodology with which to search, but who come to the exploration with open minds so that, should they discover America, they will not assume they have landed in India, just because that’s where they intended to go.” -Thomas Cardellichio & Wendy Field, “Seven Strategies that Encourage Neural Branching”

I have used the above quote for the last 12 years in workshops concerned with critical and creative thinking. However, I think it incredibly appropriate for the discussion of continual assessment to inform instruction. Notice how I said to INFORM INSTRUCTION?

Angelo and Cross, in Classroom Assessment Techniques, A Handbook for College Teachers, list two fundamental questions that have to be answered with regard to classroom assessment:

1. How well are students learning? and
2. How effectively are teachers teaching?

They continue, in their book, to explain what an incredible power a teacher has when classroom assessment is used correctly. [http://honolulu.hawaii.edu/intranet/committees/FacDevCom/guidebk/teachtip/assess-1.htm]

“Faculty have an exceptional opportunity to use their classrooms as laboratories for the study of learning and through such study to develop a better understanding of the learning process and the impact of their teaching upon it. It provides faculty with feedback about their effectiveness as teachers, and it gives students a measure of their progress as learners.”

As I bring this blog post to a close, I have to share the quote I use most frequently in response to the question, “How often should I be assessing?”

“The only man I know who behaves sensibly is my tailor; he takes my measurements anew each time he sees me. The rest go on with their old measurements and expect me to fit them.” -George Bernard Shaw

If a tailor finds it important to take new measurements of clients because he wants them to wear clothes that fit well, shouldn’t we, as educators, be taking the measurements of our students every time we see them. After all aren’t our students’ brains more important than clothes?

Are you constantly assessing yourself, your students, your instructional pedagogy? Do you see lower student scores on assessments as failure on their part or a need for change on yours?

Why not take this as an opportunity to assess your strengths and weaknesses  as a teacher then chart out a new course of action for the way you assess and instruct your students?   Try Clipboard Cruising for four weeks and if you don’t think you are better positioned to assess your students skill sets, then just go back to what you were doing before…

I’m looking forward to working with San Antonio ISD the latter part of this month.  They have been piloting Tabor Rotation in first through fifth grades since the beginning of this school year.  The feedback from teachers so far has been great and I’m seeing some teachers really raise the bar for learning and understanding.

Until next time, here’s just a few words of encouragement to my friends and colleagues with whom I’ve had the honor of working:

“Follow your dream…take one step at a time and don’t settle for less, just continue to climb. Follow your dream…if you stumble, don’t stop and lose sight of your goal, press on to the top…For only on top can we see the whole view, can we see what we’ve done and what we can do, can we then have the vision to seek something new…Press on, and follow your dream.”
– Amanda Bradley

“Never, never, never, never give up.”
– Winston Churchill

Never, never, never, never give up.
— Winston Churchill