Grouping Students via a Value Line & Folded Spectrum

Tabor Rotation Training of Trainers' Folded Spectrum

How can a teacher ensure simultaneous interaction in their classroom? How do you easily and quickly group students? How can one assess the depth of their students’ understanding of a concept? One simple, interactive, and non-threatening way to do this is by using a “Value Line” and a “Folded Spectrum.”

Folded Spectrum & Value Line (Presentation Slide)

  • Participants line up, in a value line, according to how comfortable they are with the topic.
  • Participants talk to the people next to them and share why they chose that location.
  • The leader finds the midpoint of the line and “folds” the line by having the back half step forward and walk to the front of the line.
  • Each person practices active listening sharing the “starter” with the partner whom they are facing.

What would this look like in a classroom? Let’s say we’ve been studying the squaring and cubing of numbers for about two weeks. We’ve had activities and games in Tabor Rotation. We’ve played the 24 Game: Algebra/Exponent Edition each day for practice. Now I ask my students to think about how comfortable they feel about exponential notation. Are they closer to the “Hmmm” side of understanding and still need more experiences with the topic or are they on the “Woo Hoo!” side of understanding and could teach another student all about it?

I ask the students to create a Value Line at the front of the classroom or in the hallway. They need to stand shoulder to shoulder. The “Hmmm” side is on the left and the “Woo Hoo!” side is on the right. After they have created the Value Line for Exponents, they count off from the first person to the last. We find the middle person and ask the last half of the line to step out. The middle person goes and stands in front of the very first person and so on. We have now created a Folded Spectrum.

The the first thing students share, with their new partner, are the reasons why they placed themselves in that location on the Value Line. After sharing their reasoning, they discuss the most challenging part of using exponents and the simplest part of using exponents.  After giving the students at least five minutes to share, I give each newly formed pair a real-world problem to solve that uses the concept of exponents.

At the end of the class period, I ask each student to share the most important thing they learned from the activity and from their new partner. The grouping of students in this way has never failed to bring about positive results and an increase in the depth of understanding for the concept being explored–and the responsibility of the learning was placed exactly where it should be–on the shoulders of my students!

“Looking back, you realize that everything would have explained itself if you had only stopped interrupting.”  -Robert Brault

Teachers, Tailors, & Swimming Pools

“The only person who behaves sensibly is my tailor.  He takes my measure every time he sees me.  All the rest go on with their old measurements.”

-George Bernard Shaw

I was reminded of the importance of on-going assessment while watching my children swim at the neighborhood pool. My children have taken lessons and know how to swim, but they were trying to dog paddle to reach the other side of the pool. I know I sometimes make connections from A t0 W to L, but hang with me on this one.

My junior year in college I transferred to a different state university. The dean of the college of education told me I had to take a physical education class. I had been told to agree with whatever he said or it would become worse. So, I decided to take swimming. I thought it would be easy since I’d taken swimming lessons my entire life and was at the junior life-saving level. (I know no one out there has ever taken a college-level course just because it would be easy, right?)

On the first day of class I forgot my goggles. I decided not to open my eyes while the instructor watched us take our “test” lap across the pool. Somehow, since I didn’t open my eyes, I went the wrong way. After a few minutes, I sputtered up. The instructor looked at me and immediately said, “Beginner level. You can go sit next to the shallow pool.” That one lap served as my permanent assessment of swimming abilities. She never asked me what I knew about swimming. She never again gave any of us an assessment of what we had learned to move us to the next level. She took our measure the first day, labeled us, and just kept on teaching.

The beginning level group of swimmers soon realized I knew how to swim, but they didn’t tell anyone else–especially the instructor! (Sound like any classes you’ve taught?) Every class period for weeks, I came to class, got a kick board and practiced floating.  It was a waste of a semester, but it has been the best illustration of the danger of assessing only once. On-going assessment, sometimes known as Clipboard Cruising, is an essential element in every effective classroom. This clip, from the new Tabor Rotation Training Series, gives a good visual for what it looks like in a classroom.


As for my “dog paddling” experts in the pool…I closed my semi-wet summer read of “Friday Night Lights,” went to the edge of the pool, and reminded my children how much faster they move when they use the strokes they know. They both laughed, turned, and kicked water all over me and my book! The Texas sun took care of drying the book…

Engagement Matters!

A friend, knowing how strongly I feel about the power of engaging students in a classroom, sent me a link to a news article. After reading the article, she said it sounded like my kind of classroom. The study, conducted with Canadian college students, compared a lecture format with an interactive format. The interactive format included short, small-group discussions, in class “clicker” quizzes for monitoring of conceptual understanding, demonstrations, and question-answer sessions. The students who weren’t “just sitting and absorbing” information scored twice as high on tests. They were being respectfully, meaningfully, and qualitatively challenged–yes, that is my kind of classroom!

Last week, I presented on Tabor Rotation: The Perfect Framework for Simplifying Small-Group, Differentiated Instruction in Mathematics at the RtI (Response to Intervention) Symposium in Corpus Christi, Texas. I met a large number of secondary educators who were interested in “shaking up” what was going on in their classrooms. I hope that the findings of this article will support them on their journey of doing what is best for all students…

[It’s Not the Teacher, but Method that Matters]


Simultaneous vs. Sequential Interaction

What is the difference between simultaneous and sequential interaction? When I first pose this question to students, I ask them to think about the definition of each word for a couple of minutes. Then I ask them to share with their partner what they thought (Think-Pair-Share). Next, I ask them to share what their partner thought with another set of partners (Think-Pair-Square). After they have shared with the quad, I ask them to return to their table and determine the most important idea shared. The leader of the group shares the most important ideas with the whole group.

After I have recorded the responses of the class, I call on one person to read one of the responses. I call on another person to read the next response. I repeat this process for the remainder of the list. After the students have just sat for about 10 minutes listening to one student at a time, I ask them to talk to their group about the difference between the first part of the activity and the last part. I ask them to tell me which part kept them more engaged and why.

This activity clearly illustrates the difference between simultaneous and sequential interaction and the importance of active and constant involvement of students in the learning process. Simultaneous Interaction is one of the Essential Elements of Tabor Rotation. This clip, from the Tabor Rotation Training DVD, is a clear illustration of the power of all students interacting with each other and the teacher. Watch the clip and try it with your class to see what happens.


A Sneak “Peek” at Small-Group, Differentiated Instruction

How can a teacher become more efficient in the classroom?

How can our schools make the most of

mathematical minutes?

What does RtI (Response to Intervention)

look like in a high school classroom?

What does a week of small-group, differentiated instruction look like?


Elementary & secondary level teachers, administrators, leadership teams, departments, and districts are looking for good examples of small-group, differentiated instruction in mathematics. The Tabor Rotation Framework is a perfect plan for helping every student, at every level, meet and exceed their potential.

The New Tabor Rotation DVD Training Series  “walks you through” the Essential Elements of the Tabor Rotation Framework and a typical week of sophisticated, differentiated mathematics instruction. The Training Series will be offered at elementary and secondary level with Basic, Bonus, Premium, and Elite Packages. There will be something for everyone!

Here’s a sneak peek at what’s coming in May…


Want more information?

Small Groups & Games in High School Math…Really???

“Without initiative, leaders are simply workers in leadership positions.” -Bo Bennet

Why do I need to change the way I teach high school students? What’s the big deal with small groups? What does differentiated instruction have to do with high school math—that stuff is for the little guys!

As secondary teachers and schools begin to set goals for the coming school year and planning this summer, these are some of the questions which can be overheard in the faculty meetings.

I had the honor of sharing the Tabor Rotation Framework with a group of high school students this week. I’ll let some of their math journal responses answer the above questions.

“Today I learned that the brain learns best by concrete information, then pictures, then those worksheets. Doing math this way is helpful because we got to do actual “hands on” experiments, and it just made things make sense. My goal next week is to do even better.” -Sarah

Sarah and team played the game, “Are You FUNCTIONing?” This game included centimeter cubes, coordinate graphs, and value tables—all of which help students understand how to locate points on a coordinate plane using a given domain and range of a set of number. They could also determine whether or not a table of x and y values is a function using the vertical line test. All of this was done in a hands-on way to deepen the understanding, not just memorize the algorithmic procedure

Value Table I for “Are You FUNCTIONing” Value Table II for “Are you FUNCTIONing?” Value Table III for “Are You FUNCTIONing?”

“Today I learned that it is okay to need things put into real life terms using math. This would help other students because it helps relate algebra to real life. [It] gives students the awareness to try…I also learned it’s okay to need to “hold” things to learn.” -Shelby

“This activity helped me see clearly the relationship between the x and y values or the different parts of a function. It’s better than writing out the rules and having the teacher talk at me.” -Mary Grace

Mary Grace, Shelby, and team used large cards to create a graphic organizer in “It Depends, or Does It?” This engaging vocabulary game helps strengthen the student’s memory of independent and dependent variables.

It Depends or Does It, Answer Key, It Depends or Does It? cards set 1, It Depends or Does It? cards set 2, It Depends or Does It?cards set 3

“I learned that putting it into your hands and actually doing it with others will greatly increase the learning level. It really helped me to work with others. I laughed a lot when the pasta broke! I learned that putting things into your hands and actually doing something helps you learn and want to learn more.” -Bradley

Bradley and team were trying to find a linear function which fits a set of real-world data using pasta, pennies, cups, and string. They gathered the information into a table and used the table to create a line. Everyone left the class ready to try it at home.

Spaghetti Strength Directions, Spaghetti Strength: Linear Functions

“I wish all my teachers had taught math this way. Maybe I’ll get lucky and they will!” -Brianna

Why bother with small-group instruction in high school? Try just one of the activities in this blog post and watch what happens in your room. The energy, the enthusiasm, and the engagement should convince you to bother and try another bit of small-group instruction!

Have You Made Your Own AYP?

This weekend we spring forward in time. For some, this weekend is the beginning of spring break. For others, this weekend was the chance to do a little spring cleaning.

Every year this season marks the beginning of state testing. The focus, for so many, becomes how well the students will perform. Will we make our AYP, Annual Yearly Progress? Will we remain a school of excellence? Will we continue to be recognized? How will we move those “bubble” students?

During all of that pressure, educators need to refuel and remain inspired till the end of school. Ask yourself,

Have I reached my own AYP?

Here are a few books I would recommend to help you reach the progress you want to make for yourself. Even if you go get a cup of coffee and read it in a book store, it’s worth the effort!

The Butterfly Effect: How Your Life Matters by Andy Andrews

The back of the book says it all, “Every single thing you do matters. You have been created as one of a kind. You have been created to make a difference. You have within you the power to change the world.” One teacher affecting one student…it matters.

Q B Q: The Question Behind the Question
by John G. Miller

When everyone is looking for “someone or something to blame” in a school, this book would be a guide for how to help people develop personal accountability and to avoid the traps of victim thinking or blame. It’s a quick, easy read which can transform your thinking toward solutions.

How Full is Your Bucket? by Tom Rath and Donald O. Clifton

What would happen if everyone with whom you worked was positive? What if school improvement meetings were all about solutions instead of causes? This book shows how the positive moments in your work and your life can affect your relationships, your productivity, and your health. There’s even a plan at the end to help you implement this way of thinking into your own classroom. (Thanks for my first copy, Dr. Anderson!)

Even if you just spend five minutes a day reading one of these books, it will give you the strength and encouragement to continue to do what is best for you and your students. Why would I bother to compose this blog post during most people’s spring breaks? As Colonel Joshua Chamberlain was quoted in “The Butterfly Effect,”

I was only a stubborn man and that was my greatest advantage in this fight, ‘I had, deep within me the inability to do nothing.’

I hope the same lies deep within you, too…

Pre-Asssessing, Gathering Information, Making Waves!

“Why go into something to test the waters ? Go into it to make waves.”

Pre-Assessment and On-Going Assessment are some of the Essential Elements of the Tabor Rotation Framework. They’re also foundational components in a differentiated classroom. Whether you’re sophisticating your methods for assessing your students or just beginning to use on-going assessments, they’re a great place to begin a journey differentiating instruction in a classroom. Here are some of the questions typically asked about Pre-Assessment and On-Going Assessment (Clipboard Cruising).

Should I used pre-assessments to group my students or should I use Clipboard Cruising to group my students?

Actually, you use both. The pre-assessment, which should typically be given at least 3-4 weeks before concepts are introduced, helps the teacher determine what concepts are weak and which are easily understood. A comprehensive pre-assessment could also be used to determine which activities should be placed in a concretely manipulated station and which ones could be placed in the Games Station for practice.

As the week progresses, the teacher conducts informal assessment via Clipboard Cruising. He is looking for his instructional strategies to be effective with the majority of students. If the strategies haven’t been effective, then the teacher knows which students need something different in the Readiness Groups. If a student shows mastery of the concepts being taught for the week, then they don’t need additional practice. Instead, they need to be qualitatively challenged with something different.

Some teachers may not bother to give pre-assessment because they think most of their students know little about a topic. Here is where teacher attitude, or the Pygmalion Effect, readily shows up in classrooms. What is the Pygmalion Effect? Simply put, people tend to live up to what’s expected of them and they tend to do better when treated as if they are capable of success. When teachers pre-assess they are seeking information, not conviction. Teachers should always be looking up and expecting their students to do well. There should always be that type of attitude. The Pygmalion Effect studies have proven this over and over with students. It’s even been proven with lab rats. []

A really good example of this is what one teacher is able to do with the students who are considered, by others, to be “too challenging.” If she believes in her students, gives them respect, continually challenges them with meaningfully engaging work, and regularly gives them opportunities to prove to themselves they are worthy, then it changes everything!

Should pre-assessments be multiple choice or problem solving?

It is optimal to vary the type of questioning. Some teachers give the multiple choice questions and then have the students develop at least two possible answers. You could use a multiple choice question and have the students select a response but explain why they made that choice.

What is the best way to Clipboard Cruise, especially when I’ve never done it before?

I typically recommend to teachers to begin with a Planning for Readiness Groups sheet. You list the concepts currently being studies. You list pre-assessment results. You might want to begin one week by determining to observe at least one of the other stations when you are in Teacher Time. You might also determine to write something about at least five students a day. Any type of written goal, for Clipboard Cruising, will assist you in making good observations. However, if a student does something out of the blue, write it down so you will remember it!

Could I give the pre-assessment again, after the unit has been taught, to determine whether or not the students mastered the information?

Giving the pre-test again is a good way to determine if the students have made improvement. You could share the pre-test results individually with your students and have them write their improvement goal in their math journals. After they take the ore-test again, or take a summative assessment, then they compare their results. This places the responsibility on the students, too. It also teaches your students to be goal-oriented.

What about unit quizzes?

The quiz or test which will be used to assess the students at the end of the unit MUST be created before the unit is taught. How else can the instruction and activity be directed to “hit the goal?” The teacher needs to begin the unit with complete knowledge of how the students will be assessed. This allows them to instruct appropriately. Instruction should mirror the assessment. The assessment is then given and informs the next set of instruction.

Assessments are best used as information to help us change our instruction to meet the students’ needs. I know that’s not how states are doing it (some districts even hold results over teachers’ heads), but that is what is best. If there is no improvement, then the teacher and the students need to reflect on what needs to be changed the next time. No mistakes–just opportunities to make changes! If the final quiz or test is created ahead of time, then one or more of the Exit Questions should be formulated just like the quiz. The wording shouldn’t be exact, but similar enough that the teacher and students know whether or not they have developed a conceptual understanding.

Should I use state tests to help create my assessments?

Yes! Remember that the state and national standards are driving the curriculum in your room. Any state or district tests, public-release questions, etc. which will reflect the way they will be tested at the end of the year could be incorporated into the assessment in a course so students are preparing for the test all year long.

If you’ve read all of this blog post, then you’re digging a lot deeper into your instructional practices than most teachers ever do. Most of the time, if a teacher or department/school is convinced to conduct any type of pres-assessment, the administration is thrilled. If you’re giving the pre-assessment, or any assessment for that matter, use the results to help guide decisions about instruction! Otherwise, it was a complete waste of everyone’s time.

“Knowledge is power, only when it’s acted upon.” -Anthony Robbins

“The test is to recognize the mistake, admit it and correct it. To have tried to do something and failed is vastly better than to have tried to do nothing and succeeded.” -Dale E. Turner

So Much to Do…So Little

As I took my “To Do” list from today and used it as a reference for tomorrow’s “To Do” list, I wished for more time. I’m starting to make lists of my lists! All of this reminded me of the following illustration. As we explore measurement and time with our math students, have we thought about the following, too?

Imagine there is a bank that credits your account each morning with $86,400. It carries over no balance from day to day. Every evening the bank deletes whatever part of the balance you failed to use during the day. What would you do? Draw out every cent, of course!!!!

Each of us has such a bank. Its name is TIME. Every morning, it credits you with 86,400 seconds. Every night it writes off, as lost, whatever of this you have failed to invest to good purpose.
It carries over no balance. It allows no overdraft. Each day it opens a new account for you. Each night it burns the remains of the day. If you fail to use the day’s deposits, the loss is yours.There is no going back. There is no drawing against the “tomorrow”. You must live in the present on today’s deposits.

Invest it so as to get from it the utmost in health, happiness, and success! The clock is running. Make the most of today.

To realize the value of ONE YEAR, ask a student who failed a grade.

To realize the value of ONE MONTH, ask a mother who gave birth to apremature baby.

To realize the value of ONE WEEK, ask the editor of a weekly newspaper.

To realize the value of ONE HOUR, ask the lovers who are waiting to meet.

To realize the value of ONE MINUTE, ask a person who missed the train.

To realize the value of ONE SECOND, ask a person who just avoided an accident.

To realize the value of ONE MILLISECOND, ask the person who won a silvermedal in the Olympics.

Treasure every moment that you have! And treasure it more because you shared it with someone special, special enough to spend your time.

And remember that time waits for no one. Yesterday is history. Tomorrow is mystery. Today is a gift. That’s why it’s called the present!

A Tasty Serving of Small-Group Instruction

“For some reason, when you become a support to others, you become bigger than you are.” -Susan Jeffers, from “Feel the Fear…and Do It Anyway”

This morning was spent filming parts of the new Tabor Rotation DVD Training Series. My cinematographer, Chris Shepherd [], is amazingly creative and dedicated to making this an incredibly informative AND entertaining film. After spending several hours recording the intros and voice overs for the 14 Essential Elements of the Tabor Rotation Framework and a week’s worth of planning, I needed a break.

I headed over to a local restaurant for chips, salsa, and tortilla soup. Being after the lunch rush, the server spent more time making conversation. I was reviewing notes from the day and he asked me what I was doing. I gave him a brief explanation of my mission to help change the way we teach and learn mathematics in schools. I also told him about the schools who were currently doing their best to improve their strategies for using small-group, differentiated instruction in the classroom. He really enjoyed the analogy of math (a combination of declarative and procedural knowledge) and playing basketball (also a combination of declarative and procedural knowledge). He also agreed that the math teacher’s attitude toward and belief in the students is like a coach’s attitude and belief in her athletes–it’s the difference between mediocrity and greatness!

Five minutes after our conversation he came back with an “aha” look on his face. He said he hadn’t been able to quit thinking about the fact that what I was trying to help teachers do is what was happening to him in the restaurant business. He told me that he began working for one restaurant. The owners were more laid back and were extremely positive with their waitstaff. When training new servers they partnered them with a veteran to help them learn the correct procedures. The manager taught them how to learn the specials of the day, how to explain the menu, and how to give that “something extra” which would make the customer want to come back. He also said he felt appreciated at his first job…like he made a difference in people’s lives.

Because he had been trained so well, three weeks into his new job he was offered a job as a server at another restaurant. The person who offered him the job was a manager of another restaurant. He was eating at the first and was so pleased with the service that he offered the server a job.

Here’s where the server made the small-group instruction connection…his second job is frustrating, unrewarding, and sometimes extremely difficult. He said his training was brief and he didn’t receive the type of individualized instruction he needed. He said he had to learn a full menu with over 300 items and at least 10 specials every day. No one complimented him for his hard work. No one gave him any bit of attention or additional instruction. He said he needed both jobs, but only one inspired him to work harder and learn more.

“It’s like what you’re trying to help schools do. What works in a school would work in a restaurant.”

Now that is a tasty serving of small-group instruction! I’ll be back next week for another!

“When you’re chewing on life’s gristle
Don’t grumble, give a whistle
And this’ll help things turn out for the best…
And…always look on the bright side of life…
Always look on the light side of life.”
– from Monty Python’s “Life of Brian”