More about AHA Moments

An Aha Moment, according to the Merriam-Webster Dictionary, is a moment of sudden realization, inspiration, insight, recognition, or comprehension. But the question is,
Why would this be the content of a keynote speech I presented today at the South Carolina Council of Teachers of Mathematics (SCCTM) Annual State Conference?

brain activity

It’s simple. SCCTM’s Annual Conference is filled with so many incredible sessions that explore a wide variety of topics. The most challenging part of the day is selecting the sessions to attend and knowing there are so many other really good sessions.

However, none of these sessions will bring full results unless the information shared during them impacts the lives of students. I believe this and it’s why I set aside time during every training session to share ways for teachers to cultivate a classroom atmosphere that encourages aha moments.

There are many good sources for learning more about aha moments. To keep this blog post from being way too long, I’ve included some key points and the links to the entire source. All of them are well worth the few minutes it takes to read them. Each of them would also be excellent read alouds for your whole class as you help them fine-tune their recognition and use of aha moments.

Maximizing Aha Moments

Bruce Dorminey’s article for, “Maximizing Those Aha Moments Still Key to Our Future,” describes what insight is and the difference between insight and intuition.

Intuition is use of patterns we’ve already learned while insights are the discovery of new patterns. With an insight you don’t necessarily have a feeling that there’s something there.  It hits you without warning.  It shifts the story that you’re telling yourself, whereas intuition uses the patterns that you already know or have.  An insight suggests new patterns.

“Aha!” moments hit us all.  Although they can range from new ways to tie a shoelace to ideas for the latest smart phone, acting upon such “insights” remains key to our collective future. Read all of Bruce Dorminey’s article.

Barbara Morris, President of LaserImage, shares how to maximize your aha moments in her article, “The Art of Leaning into Your Aha Moment.” Even though she is focusing on aha moments in a corporate setting, the ideas are definitely applicable in an education setting.

A lot of great ideas start as scrawled notes on bar napkins. And a lot of those same great ideas are tossed away and never become what they could. People are scared to take risks, they don’t have enough money to turn their idea into a reality, or they’re too busy to transform themselves from followers into innovators. Just because you face challenges, though, doesn’t mean you can’t turn a big idea into a bigger reality. Read all of Barbara Morris’ article.

The Science of Aha Moments

For those readers who are becoming skeptical at this point, there is scientific proof that aha moments exist. Aha moments can be seen inside the brain. describes a scientific study in which researchers found an increased activity in a small part of the right lobe of the brain when the participants reported creative insight during problem solving. Little activity was detected in this area during non-insight solutions. Web MD’s Scientists Explain the Science of Aha Moments

If you want to read more about scientific evidence for aha moments, the study by Kounios and Beeman is fascinating!

In a series of experiments, Kounios and Beeman found that volunteers who experienced insight experienced a distinctive spark of high gamma activity that would spike one-third of a second before volunteers consciously arrived at an answer. Additionally, the flash of gamma waves stemmed from the brain’s right hemisphere—an area involved in handling associations and assembling parts of a problem.

Gamma activity indicates a constellation of neurons binding together for the first time in the brain to create a new neural network pathway. This is the creation of a new idea. Immediately following that gamma spike, the new idea pops into our consciousness, which we identify as the Aha! Moment. More about Kounios & Beeman’s Aha Moment Experiments

Educators and Aha Moments

As an educator who believes in giving students time for information to absorb, Daniel Goleman’s post, “Maximize Your Aha Moment,” really hit home.

The pre-work for the gamma spike includes defining the problem, immersing yourself in it, and then letting it all go. It’s during the let-go period that the gamma spike is most likely to arise and along with that the “aha” or “light bulb over the head” moment. Read all of Daniel Goleman’s article on maximizing your aha moments.

“Reassessing the Aha Moment” by Janet Rae-Dupree really addresses the role that the classroom teacher plays in the facilitating of aha moments.

…as soon as you dig into what happened five minutes before that magic moment, or a day, or a week, or a month,” he said, “you realize that there is a much more complicated story in the background.” That more complicated story most often begins and ends with a determined, hard-working and open-minded person trying, and failing, to find a solution to a given problem.
It’s not that these magical moments of epiphany don’t happen. In small ways, they happen all the time. But they are not nearly as important as what the innovator did before – or ultimately does after – the magic light bulb goes on. “Reassessing the Aha Moment” by Janet Rae-Dupree

What if a teacher or professor just simply believes in a student and shares his or her enthusiasm with their students? It changed the life of Sharon Matola, known as the “Zoo Lady” to over 12,000 children who visit her and Belize’s only zoo for orphaned animals that she founded in 1983. She doesn’t remember all the details of her inspiration, but she does remember the power of belief in your students,

“My professor told me I was smart. He was the only professor who said that.”

Read Sharon Matola’s story and others who experienced aha moments in education.

The “How to” of Aha Moments

Dr. Marcia Reynolds, in “Creating the Aha Moment,” lists the following Brain Tips for creating aha moments.

Brain Tip 1. Do something else. Give your brain a chance to restructure itself, letting your right hemisphere access your long term memory to bring a new solution into view.

Brain Tip 2. Give it a rest. If you can, take a nap or put the problem away for a day to let your brain sleep on it. While you sleep, the hippo campus goes to work connecting data with knowledge in new ways.

Brain Tip 3. Have fun. While you are eating that ice cream cone or watching a funny movie, your middle brain is unconsciously looking at your problem from different angles.

Brain Tip 4. Work with your coach. An experienced coach is well trained to ask you the question or provide the metaphor that breaks through your frame of thinking. You literally look at the problem from a new angle.

Learn more about how to create aha moments.

Dr. Bruce Johnson describes the failures of schools to cultivate creativity. He discusses the theories of Jeffrey Selingo, editorial director of The Chronicle of Higher Education, who encourages teachers to break the traditional teaching practice of memorization and regurgitation. Instead, students should be completing projects that require creativity and application of the knowledge they’ve gained.

Dr. Johnson also lists some ways to tap into your inner creative self.

1. Know When to Work and When to Stop
When you feel the need for a break that’s an indication you either need an alternate perspective or additional information. And research shows you are likely to get the insight or “aha” moment once you step away from the project or problem.

2. Tap Into Your Imagination
You can synthesize experience; literally create it in your own imagination. The human brain cannot tell the difference between an ‘actual’ experience and an experience imagined vividly and in detail.” Walt Disney said “if you can dream it, you can do it.” That forms the basis for creativity, being able to dream and then put your imagination to work.

3. Develop a Mindset for Creativity
This is probably the one barrier that prevents students from learning to develop their creative capacity, a limiting self-belief. The statement, “I’m not a creative person” can limit your possibilities. You can train yourself to be creative simply by allowing time to use your imagination.

Train yourself to think more creatively.

Final Thoughts on Aha Moments defines aha moments as…a moment of clarity, a defining moment where you gain real wisdom-wisdom you can use to change your life. Whether big or small, funny or sad, they can be surprising and inspiring. Each one is unique, deeply personal, and worth sharing.

Would you like to read more aha moments? has many aha moments from many different perspectives.

You still want more? Public Radio International has aha moments you can listen to or read.

Daniel Goleman found that nurturing the creative insight is vital. When a person offers a novel idea, instead of the next person who speaks shooting it down—which happens all too often in organizational life—the next person who speaks must be an ‘angel’s advocate,” someone who says, ‘that’s a good idea and here’s why.”

I hope this is what occurs in schools when teachers and principals have a novel idea that will help students. I know our world will improve if every teacher provides space for students to have “aha” moments. Along the way, these teachers will have aha moments, too!

Life is not measured by the number of breaths we take, but by the moments that take our breath away. —Maya Angelou

Bonus? Aha Moment Slideshow from Tabor Rotation Institute participants.

Guided Math via the Teacher Time Station

The most popular math station during a week of Tabor Rotation? In every survey, formal or informal, the answer is always Teacher Time. This is the guided math station, of the Tabor Rotation Framework, where teachers plan to teach a small group of  the most difficult concepts for the week. But, what goes into a Teacher Time Station?

Teacher Time Sign

Let’s look at the contents for Teacher Time with students exploring the concept of fractional parts of a set for the first time.



Based upon a pre-assessment given four weeks before the next fraction unit began, the data indicated that none of my students knew how to determine the fractional part of a number. A few students recalled the term reciprocal, what they called “flipping it over” and thought that you had to do something with the numbers to find the fraction.  But no one really understood and could explain fractional parts of a number. This information helped me develop the content for the station activities and student passports to the stations. Passports serve as an individual accountability measure and check for understanding for the stations.


The questions included in the passport are EXIT QUESTIONS and are a bridge from the hands-on activity at the math station to the way the students will be asked the question on the state test at the end of the year. This research also helped guide the type of questioning I use at the Teacher Time Station and the questions included on the formative assessment quiz.

At the bottom of each of the pages of the passport I put the REMEMBER IT! box so that students could note the most important terms or ideas from the stations. remember itKind of like a one or two-word summary. (Thanks for this idea, Natalie Eppert, who began using this with her Algebra II and Geometry students a few years ago.)

Next, I create pair bags with manipulatives. There are enough pair bags in the station bag for each pair of students. Since my students are going to take on the real-world role of clothing designers, they will be using buttons, bling, and tiny shirts. I also give each pair of students a rectangular piece of felt to serve as their work mat. This helps define the “personal space”of each pair of students. All of these items are available from any craft or discount store. I use bandanas for the shirt fabric.



Peace ShirtsThere are several other items that are included in the Teacher Time Station Bag. The Leader Folder is always part of the Station Bag, even when I am the one guiding the instruction at the station. This way the Leader can always help facilitate the activity and the Co-Leader can ask the Exit Questions. [For more about Leader Folders and Station Bags, read the blog posts about these critical components for successful math stations.]

White board

I also include a white board and dry erase marker for every pair of students and one for myself. This way I can move to the abstract algorithmic procedure or steps for determining fractional parts of a number, if and when the students are ready.

My favorite components for the Teacher Time Station for exploration of fractional parts of a number have to be my “bling” apron and my metal Scotch Tape button container. The “bling” apron shows the students that they really could take the knowledge they are gaining at the station and design clothing.Scotch tape

My personal button container is the most powerful tool I use at the Teacher Time Station when teaching this concept, because it helps the students connect to the concept. The Scotch Tape container was given to me by my mother when I began sewing. It was given to her by her mother, so I have buttons that are almost 100 years old and each one has a piece of my history connected to it. Before the lesson begins, I ask each pair of students to pull a button and I tell the story behind the button. The students are so engaged in the lesson at this point, that finding fractional parts of a number never intimidates them. They are already hooked and connected!

But wait…there’s more…

I move these same Teacher Time Station Components to the Technology/Innovation Station the next week. Pairs of students work together to create a script for teaching other students how to find fractional parts of a number using the same manipulatives that they used. After practicing their script, the pair records the lesson using the app, Educreation. Follow this link to watch what one pair of students recorded–it’s really amazing and completes the circle of learning for the students as they use technology to innovate and create!


Why spend the time to gather buttons, pieces of bling, and cut out tiny shirts? The “aha” moments when your students truly understand fractional parts of a number will provide the answer to that question. Besides all that, it’s ENGAGING, MEANINGFUL, and FUN? Isn’t learning supposed to be exactly that?

Does Tabor Rotation work with…?

Does Tabor Rotation work with…

…CCSS-Common Core State Standards?

…TEKS-Texas Essential Knowledge & Skills?

…CCGPS-Common Core Georgia Performance Standards?

…my district’s mandated curriculum?

…the new program my district just adopted?

The list could go on and on, but the answer to every one of the questions above is YES!

Why is the answer yes? It’s simple. Tabor Rotation works with all of the above because it is an instructional framework that effectively differentiates instruction in mathematics. It’s not program–that’s the beauty of it! It’s a plan that gives teachers a way to help every student explore concepts in varied modalities and in varied groupings. The 14 Essential Elements of Tabor Rotation are good teaching practices that provide teachers and schools with a structure for best meeting the needs of every student.

Because Tabor Rotation is a framework for instruction that highlights 14 Essential Elements of effective instruction, it works at any level, with any resources, any curriculum, and any time frame!

girls at station

The Tabor Rotation Framework helps teachers provide their students with many opportunities to explore, experience, practice, apply, and deeply understand math concepts.

Leslie Skinner, a 3rd grade teacher who began implementing Tabor Rotation in her classroom after a Tabor Rotation Institute in January, 2013, explains it well,

“[Tabor Rotation] is not a program, but a framework that helps teachers like me, do what I should already be doing. …All the needs of my students are met with Tabor due to the focus it places on one skill in heterogeneous and homogeneous groupings.  The stations have real-world connections with lots of hands-on manipulatives and games, which helps reinforce the skill for better long-term retention. The students work in mixed ability groups to generate a more student-centered classroom by giving them the opportunity to learn from each other.  The ability groups [Readiness Groups on Days 4 & 5 of the Tabor Rotation Framework] afford the students more specific instruction to help them reach their highest potential.

I strongly believe all my students passed the STAAR [State of Texas Assessment of Academic Readiness] test because of the implementation of Tabor Rotation in my classroom.”

Now for the next big question…

How can I cover all the standards, teach everything I need to teach, and use Tabor Rotation?

According to the most recent research on the skills needed in the 21st century, teachers can’t afford not to! Michael Brick, in his article,  “Three Cheers for School! Building a Better School Day,” for Parade magazine, listed some “inspiring ideas to deepen learning, engage students, close achievement gaps, and better prepare our kids for a 21st-century world.”

Many of these inspiring ideas are easily accomplished if teachers use the Tabor Rotation Framework, because they’re embedded in a week of Tabor Rotation.

  • Emphasize Learning, Not Testing- Our country’s emphasis on test-taking has increased pressure on teachers to “teach to the test” when students need to be able to deal well with confrontation and see two different sides to a problem [Working inTeams and completing activities at Tabor Rotation Stations, Challenges and Problem Solving in Readiness Groups and at the Teacher Time Station].
  • Teach 21st-Century Skills- Students benefit in the real world when they have encountered projects that are like the real world. Long-Term Projects [Projects in the Technology/Innovation Station] teach them to persevere, revise, reflect, and hone their skills.
  • Flip the Class Work- Instead of spending class time listening to the teacher lecture, students should spend class time having the concepts reinforced with interactive labs and discussions. {The entire Tabor Rotation Framework is student-centered and emphasizes students interacting with the concepts to make meaning of them and to apply them in multiple situations.]

The entire article is thought-provoking and well worth your time.

Does Tabor Rotation work?

Do I really have the time to use it?

I’ll let Charles Bucher, a secondary teacher and avid user of Tabor Rotation, answer that,

“With Tabor Rotation, I found a framework through which I was able to teach my district’s required curriculum, yet find new ways to engage and motivate students, and streamline the hurricane of paperwork and accountability required of all teachers.

With Tabor, you focus on what is important: small group and individual time with students to teach, assess, and correct. As a benefit, you get unique ideas and tools for classroom management and organization, with every element carefully tailored to the math classroom, but easily adaptable to any curriculum.

Tabor Rotation has made me the teacher I am today:
A veteran teacher ready to mentor the four new math teachers we will have next fall,
Confidently in control and calm in the classroom,
Prepared to punt in any emergency,
Organized so that data is at my fingertips and informs my teaching strategies for individual students,
Expecting more of myself and the students – we all learn every day.”

boys at station

How do we create the conditions at home, in our schools, and in our communities for students to create, learn, produce, and to innovate?”     -Tony Wagner

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Math Stations: Big Classes Need “Pair” Bags


“Talent wins games, but teamwork and intelligence wins championships.”     -Michael Jordan

That’s why teams working together at math stations are a vital component of the Tabor Rotation Framework. Effectively equipping teams for their work is imperative—especially in a math classroom at a math station!

When teachers begin to sophisticate their use of students working in math stations in a classroom, many questions arise. Here are some recently submitted after conference and institute sessions:

“How do I do this with a class of 30 students? Do I increase the team size?”

“Do you have 4 stations in large groups of students or do you implement mulitiple stations?”

“Will this work with more than 25 students? More than 30? 35?”

I created and began using the Tabor Rotation Framework when the size of my classes was close to 40 students at a time. I tried making more than four stations to accommodate more students, but I found that while I was working harder, the station rotations had to be shorter, and the in-depth understanding of concepts I wanted for my students wasn’t occurring on a regular basis.

So, I decided to make keep 4 teams–whatever the size. For an 8-member team, I divide the team into 4 pairs. The Leader helped facilitate the activity for 3 other people and the Co-Leader facilitated the activity for the remaining 3 students. Some Tabor teachers appoint two Co-Leaders when they have large team sizes.

Let’s look at an example. A class is studying geometry. On Days 2 & 3 of a week using the Tabor Rotation Framework, the Manipulative Station is set up with an activity called, “Angles and Triangles.” This activity helps students use concrete manipulatives to build a foundation for all types of angles and triangles. The activity also serves as a practice or review for students who are already familiar with most angles and triangles.

At the Manipulative Station there is a Station Bag. Inside the Station Bag are 4 Pair Bags and a Leader Folder. (10-member team = 5 Pair Bags, 12-member team = 6 bags, etc.) For more about the contents of the Station Bag and the Leader Folder, please read my last blog post, “Effective Math Stations? Leader Folders!”

multiple sets

A “Pair” Bag for Every Two Students on a Team

For the “Angles and Triangles” Manipulative Station Activity, each Pair Bag contains:

A set of directions


A set of cards to turn over and know what to create with anglegs


A set of anglegs

 bag of manipulatives

A work space mat

work mat

And, an answer key

answer key

“But, does this really work?”


During the piloting phase of the Tabor Rotation Framework, multiple schools and multiple teams of teachers were asked to try 4 stations, 6 stations, and even 8 stations. The number that led to the greatest success every time was 4. The Tabor teachers who tried more than 4 stations found the same things I did. They worked harder with fewer results and less in-depth understanding from their students.

Rotating through 4 Stations, with a Heterogeneously Grouped Team, during Days 2 & 3 of a week using Tabor Rotation was the most effective grouping of students to explore concepts in varied modalities. Your classes and teams can be as large as the original Tabor Rotation ones (8-10 to a team) or as small as two. When teachers use fully-equipped Pair Bags inside fully-equipped Station Bags, everyone can focus on the mastery of math!

Download these two activities for your Manipulative Station and make as many pair bags as you need!

It Figures: Creating Congruent & Similar Figures

Congruent, Similar Spinner

Angles and Triangles Game

Angles and Triangles Cards, 1

Angles and Triangles Cards, 2

If you’re reading this and still asking yourself, “Why bother building math teams and creating math work stations? Maybe a thought from Mary Barnett Gilson will help,

“…there are persons who seem to have overcome obstacles and by character and perseverance to have risen to the top. But we have no record of the numbers of able persons who fall by the wayside, persons who, with enough encouragement and opportunity, might make great contributions.”

Effective Math Stations? Leader Folders!

How do I make math stations more effective?

What’s the most important resource for Leaders and Co-Leaders?

How do I make sure that students aren’t just receiving guided math instruction from me but are also guiding each other and themselves?

station bag

One answer is,

“Make sure you create a Leader Folder for every station and every activity during the Rotation to the 4 Stations [One of the 14 Essential Elements of the Tabor Rotation Framework and a vital component of a week of Tabor Rotation].”

At the end of a math conference session on Tabor Rotation last week, teachers were at the front of the ballroom looking through the sample Tabor Rotation Station Bags. As they busily studied each component of the bags, they commented on how powerful the Leader Folder must be in the success of math stations. And then, the conference center representative began “cleaning up” the station examples so the next person could prepare to present. As the rep grabbed the Leader Folders and materials from them, the teachers all looked to me for help… (at this point, I think the rep should have been afraid, but he just kept pulling all the materials)

That is why I’m blogging today about the Leader Folder and other components of a Tabor Rotation Station Bag. I asked one of the teachers to email me and ask me to write a blog on Leader Folders and she did. (I also agreed to write a blog in order to keep the conference center representative from being attacked by teachers who weren’t through studying the Leader Folders and Station Bags!)

The first item for effective math stations is a container for the station activity. Tabor Teachers have tried baskets, file boxes, crates, and colorful gift bags. The least expensive and easiest to store container for stations are the Hefty Jumbo Ziploc bags available at Target. hefty w frame


Inside the station bag is the Leader Folder.

folder cover

Directions for Everyone

The Leader Folder has complete and thorough directions inside a clear pocket for the Leader and Co-Leader to use. There are also enough copies of the directions for each of the assigned partner pairs to study and use. Here is a sample of directions for a game for Algebra II that helps students understand, in a concrete, hands-on way, how to factor trinomials. Tri” Factor Direction Sheet




The next clear pocket in the Leader Folder contains examples of how to complete the activity. The algorithmic procedure or steps can be shown using colored illustrations or pictures. Poly Pull Examples is an example sheet I created to help students understand how to create a polynomial using algebra tiles. Again, there needs to be enough extra copies in the side pockets of the folder for every pair of students to use.

poly pull example





Workmat for leader folder

Work Mat

Extra copies of work mats can be tucked into the side pockets, too. Double Ten Frame and a Place Value Chart are both examples of work mats.





There are two more items that should always be included in clear pockets inside the Leader Folder for a math work station. The state standard connected to the activity and a question, similar to the one they will be asked on the district or state test, should be included. This question will be asked by the Co-Leader as part of the Exit Questions that bridge the activity to the standard and state test.

On the back of the Leader Folder, most Tabor Teachers glue a copy of the Simple Exit Questions. Exit Questions are one of the 14 Essential Elements of the Tabor Rotation Framework and are asked at the end of every station rotation. You can download and use the standard Simple Exit Questions from the Tabor Rotation Framework to get you started.

exit questions, multi

Exit Questions

Along with the Leader Folder, here are some other items teachers include in a Tabor Rotation Math Station Bag:

  • Felt rectangles or cookie sheets to define a student’s work space and to keep manipulatives from making too much noise or rolling off a desk or table
  • Bags of manipulatives– enough for each pair of students to have a bag and enough manipulatives to complete the activity without frustration
  • Colorful components to grab the students’ attention and engage them in the activity
  • Tiered portions of the activity to ensure that the activity is qualitatively challenging and respectful to all levels of students [Tiered Instruction is one of the 14 Essential Elements of the Tabor Rotation Framework]

Felt to Define a Work Space


Manipulatives in Bags for Pairs of Students

fraction bag

Colorful & Inviting Materials

tiered cards

Tiered Components

“Now that I have the Tabor Rotation Station Bag and the Leader Folder prepared, how do I prepare my students to be Leaders?”

First, keep in mind that the student Leaders and Co-Leaders are not teaching the concept to their team, they are facilitating the activity, keeping their team on task, and being positive models for their team. The guided instruction for the activities at the station is planned for and occurs in the Whole-Group Mini-Lessons of a week of instruction using the Tabor Rotation Framework. [For more in-depth exploration of how to plan for and implement this type of instruction, you may want to attend a Tabor Rotation Institute.]

There are quite a few books on cultivating the leadership capacity in others. For this purpose, one of the books I read aloud to my students is John Miller’s, QBQ: Practicing Personal Accountability at Work and in Life. This book is an easy, interesting read and provides examples of the actions of true leaders. The book also illustrates how everyone can become a responsible, contributing member of any community.

Another book I provide to my students to cultivate their leadership capacity is, Shackleton’s Way, by Margot Morrell, Stephanie Capparell, and Alexandra Shackleton. Ernest Shackleton is known as one of the greatest leaders in history because of his ability to guide others, make decisions, keep the goal, and maintain morale. As so many corporate leaders and theorists have described, Shackleton was a man of great resilience and service.

Fascinated by his story and his dynamic model of leadership, I simply couldn’t put this book down. In fact, during my first reading of the book, I formed an informal book club by sharing portions with students and with participants in all of my trainings. I was making connections and just wanted to share my thoughts about his abilities and how I wanted to put those same traits into my own life.

Below are just a few excerpts about Shackleton.

“Shackleton’s first thought was for the men under him. He didn’t care if he went without a shirt on his back so long as the men he was leading had sufficient clothing.”       –Lionel Greenstreet, ship’s First Officer

“Resiliency involves both the hardihood and courage to take on risks and challenges, and the ability to bounce back from difficulties and disappointments. Shackleton would face hardships that almost defy belief, and it was his iron-clad resilience that allowed he and his men to survive.

The story of the Imperial Trans-Antarctic Expedition is the story of surging optimism met with crushing defeat manifested over and over and over again. That the former never failed Shackleton, and the latter never broke him, is truly what brought his men through to the other side.”     – Brett & Kay McKay, from a Man’s Life [ Read more thoughts from the McKay’s.]

This type of leadership is exactly what I want to see in all of my students, not just in math, but in every aspect of their lives. By implementing Leadership Academy, Rotation to Math Stations, and providing effective tools such as the Leader Folder and Station Bags, I am hoping to help them continue on their journey to become creators, innovators, and productive lifelong mathematicians! By writing this blog, I’m also hoping to help you on…

…your own expedition to more effective math stations!

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Aha Moments and Tabor Rotation

An Aha Moment, according to the Merriam-Webster Dictionary, is a moment of sudden realization, inspiration, insight, recognition, or comprehension.

Aha moments can also be seen inside the brain. describes a scientific study in which researchers found an increased activity in a small part of the right lobe of the brain when the participants reported creative insight during problem solving. Little activity was detected in this area during non-insight solutions.

In a LinkedIn post by Daniel Goleman, “Maximize Your Aha Moment,” he describes the conditions whereby the gamma spike is more likely to occur. The pre-work for the gamma spike includes defining the problem, immersing yourself in it, and then letting it all go. It’s during the let-go period that the gamma spike is most likely to arise and along with that the “aha” or “light bulb over the head” moment. []

Providing the conditions for aha moments is one of the goals of Tabor Rotation Institutes. Participants are immersed into the Framework from the moment they walk in the door and provided with “letting go times” to share throughout the day. One of the most meaningful times is sharing our aha moments as we bring closure to the day.

TR Blog, aha moments, 6.21.13

Here are a few aha moments that were recently shared at the end of a Tabor Rotation Institute:

  • With this framework, I can get everything taught and reach everyone.
  • You need to plan sooner than a week ahead.
  • You don’t have to start with all 5 days [of Tabor Rotation]. You can just work your way through it.
  • If every student has a team role, then everyone is important.
  • Seeing how to use the 6-Week’s, Long-Range Planner showed how all the pieces fit together and everything just flowed!
  • Always hold Leadership Academy—then you’re not the only one in the room who knows what to do!
  • Teach only what is needed to those who need it.
  • The on-level, average student rarely gets the attention they deserve and need!
  • Pull the above-level students as the first Readiness Group so you can challenge them.
  • Innovation…my students must become innovators!
  • If I use different clipboards during Clipboard Cruising, the students will know when I’m a process observer and when I’m going to stop and reteach.
  • Why ½ x ½  = ¼…who knew it would be so easy to understand using pattern blocks???
  • Algebra can be hands-on and makes sense with Algebra Tiles.
  • Learning to fail supports learning from experience.
  • Passports will keep individual accountability in the stations.
  • Team Names and Freeze Words should come from a list of the most important tested vocabulary terms.
  • Teach the most difficult concepts in Teacher Time.
  • Front loading is so much more productive than remediation.
  • Reflecting with my team—they were BRILLIANT!
  • It really is possible to get it all done in a way they understand!

In his article, Daniel Goleman describes “the physical marker we sometimes feel when we have a gamma spike or “aha” moment. It’s associated with pleasure and joy. He goes on to describe the fourth stage of “aha” moments…implementation, where a good idea will either sink or swim. He found that nurturing the creative insight is vital. When a person offers a novel idea, instead of the next person who speaks shooting it down—which happens all too often in organizational life—the next person who speaks must be an ‘angel’s advocate,” someone who says, ‘that’s a good idea and here’s why.” This should be what occurs in schools when teachers and principals have a novel idea that will help students…

I also like the definition (and all of the aha moments people share on her website) of an aha moment from

…a moment of clarity, a defining moment where you gain real wisdom-wisdom you can use to change your life. Whether big or small, funny or sad, they can be surprising and inspiring. Each one is unique, deeply personal, and worth sharing.

Watching “light bulbs” go off in the classroom, encouraging aha moments– that’s one of the reasons why teachers use Tabor Rotation. Not only does it give teachers a plan for meeting the needs of and helping every student reach their potential, but it also provides space for students to create, innovate, and think! Hopefully, along the way, teachers are busy having aha moments, too!

Super Secondary Manipulatives: Anglegs!

When I showed a set of Anglegs to a high school math department and everyone said, “What are those?” I knew I needed to blog about these amazing manipulatives!

anglegs, 2

Anglegs come in six lengths of plastic that easily snap together to explore plane geometry. When you snap two Anglegs, of any length together, you can snap a special 4” protractor to explore angles. When you snap three legs together, you form triangles; 4 legs quadrilaterals, and so on.

These manipulatives are quite powerful even if you simply use them to explore the creation of polygons and angles. The vocabulary of geometry standards is easily understood when accompanied with a manipulative. Students understand the term when they can create it. In fact, middle school students were fascinated by high school geometry concepts that “made sense” when they were right in front of them. Transversals and bisectors become simple with Anglegs.

I created a review an “Angles and Triangles” game for the Games Station of Tabor Rotation. The students not only LOVED the game, but kept laughing as they easily created the angles and triangles named on the cards with their Anglegs. The first pair of students to create what was named on the card then had to explain how they knew it was correct by stating at least two characteristics of the angle or triangle. This was a great bridge to their justifications on course exams.

Now, let’s go a little deeper using Anglegs…

  • Congruent and Similar: Create pairs of triangles that are similar and pairs that are congruent. Prove their classification using the snap-on protractor.
  • Triangular Sum Theory: Build at least 3 different triangles with 3 different combinations of legs and measure each angle. What is the sum every time?
  • Properties of Quadrilaterals: Find the sum of adjacent angles and the sum of opposite angles.

Here’s the Angles and Triangles Game with Angles and Triangles Cards, 1Angles and Triangles Cards, 2 and a set of Geometry Vocabulary Cards [Vocabulary cards, Geometry, p. 1, Vocabulary cards, Geometry, p. 2, Vocabulary cards, Geometry, p. 3, Vocabulary cards, Geometry, p. 4, Vocabulary cards, Geometry, p. 5for End-of-Course Review. Both will work with craft sticks until your Anglegs arrive. You might also want to use the Congruent vs. Similar Spinner and It Figures! Activity for exploring congruency and similarity.

I use a class set of Anglegs and they bring about the same results every single time with so many concepts! They are worth every penny! I also recommend Anglegs Plus for high school Geometry and Algebra II. Both of these manipulatives can be purchased from Amazon or ETA and can be shipped to you in just a couple of days.

My students call Anglegs the “Legos of Math” and can’t wait to explore with them. Watching the “aha” moments and connections my students make was amazing.

And, just in case anyone out there thinks that Anglegs are “silly” and “unnecessary,” I’ll end with this quote from Robert Frost,

“Forgive me my nonsense, as I also forgive the nonsense of those that think they talk sense.”

Increasing Scores via Financial Literacy

How can you increase scores on a state test by teaching financial literacy?


That was one of the questions asked by several teachers who were recently trained in M-Cubed: Meaningful Math Management. This resource is used nationwide to teach accountability and personal financial literacy at the same time. I created M-Cubed a couple of decades ago when trying to give my students a real-world application of math concepts.

After reviewing their pre-assessment on decimals, I knew I needed something that would grab their attention besides decimal rules. I sat in one of the desks in my room and tried to think like my students. When did decimals, computational proficiency, conversions, and percents become important to me? My first idea ended up being the students’ favorite one, too.  It was my first checking account that was my first taste of using mathematical concepts in a real-world setting. Why not create one for them?

Now, back to the increase in scores.

How could using a pretend checking account help students’ scores increase? Here are just a few examples.

1. Students earn salaries for working hard and applying themselves in the classroom. Test Connection: It becomes habitual for students to work hard and apply themselves on everything that is done in the classroom. This includes tests. Plus, every time I gave a quiz or a test during the school year, and they used their repertoire, it earned them extra income. Every student worked hard because it was what you did.

be a better person

“Having a checking account will make us more responsible people.”

2. Students begin to see the connections between what they studied in school and the real world. The more income they want, the more extra work they do, the more money they have to spend in the classroom store. Test Connection: The harder you work on a test, the better your score, the more you know about math, the more you can do with it to earn money in the real world. This is exactly what happens with the class checking accounts.

3. Students have to pay debits for not being prepared for class. Borrowing a pencil during class time costs 3 times as much as buying a pencil when the classroom store is open. And, you have to calculate the difference in cost correctly in order to borrow the pencil. Test: Students start coming to class prepared and begin to train themselves to buy pencils ahead of time,  even if no one from home purchased one. This leads to them being more responsible with supplies, homework, and learning. The test scores go up as the amount in their bank account increases.

Before any student may open an account, the teacher requires them to write why they deserve the first $200 in their account and why having a checking account is a good idea. After reading the first few written by their students, teachers are always convinced it will be worth their efforts. But I’ll let you read for yourself…

fab idea

“…most high school and college students are not saving enough money.”

I’m always surprised by one of the concerns that teachers have about using M-Cubed. They are concerned about the response from teachers who think that extrinsic motivation isn’t a good way to improve a student’s work habits or behavior. These teachers believe that students should do well in school because they have an intrinsic desire to do so.

How do you respond? I always ask this question.

“Do you come to work for free?”

Interestingly enough, the students in these classes were quick to tell me that they knew their teachers were paid to teach them, but they weren’t getting paid extra for creating a meaningful way for their students to learn concepts. They realize that their teacher’s intrinsic desire to do what is best for their students is the driving force for using M-Cubed. M-Cubed provides the extrinsic motivation to get students to “the table of learning.”

However, without intrinsically engaging and qualitatively challenging instruction that leads to competence, relatedness, and autonomy (Deci & Ryan, 1985; Ryan & Deci, 2000; Self-Determination Theory), M-Cubed is worthless. [Read more about the balance of intrinsic and extrinsic motivation.]

Because this management system is the perfect compliment to the Tabor Rotation Framework and is applicable at every age level, it’s available to anyone for free. (There’s even one to use at home and one to use with preschoolers.) A Slideshow Presentation explaining M-Cubed can be downloaded and/or watched from the FREE RESOURCES page.

Here are some of the components you might want to use as you implement this incredible management system with your classes: M-Cubed Checkbook Cover, M-Cubed Earned Income Spreadsheet, M-Cubed Checks, M-Cubed Debit and Credit Examples, and the M-Cubed Check Ledger.

Can learning about financial literacy increase scores? It has in every classroom where it’s been implemented. Why not try it with your students and see what happens!

get us in gear

“Something to get us in gear with learning!”