Math Stations: Big Classes Need “Pair” Bags

team

“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

directions

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

cards

A set of anglegs

 bag of manipulatives

A work space mat

work mat

And, an answer key

answer key

“But, does this really work?”

“YES!!!”

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
pairs

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

 

examples

Examples

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

Examples

 

 

 

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

Felt to Define a Work Space

manipulatives

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. WebMD.com 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. http://men.webmd.com/news/20040413/scientists-explain-aha-moments

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. [http://www.linkedin.com/today/post/article/20130312165729-117825785-maximize-your-aha-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 Oprah.com

…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.  http://www.oprah.com/packages/aha-moments.html

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?

M-cubed_tag

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!”

Hands-On Algebra: A Scavenger Hunt

Scavenger Hunt, small group, comp

An all-male group completely engaged in the task!

How do you engage students? How do you teach them to be innovative and creative? You think outside the box as a teacher. Recently, an Algebra I teacher sent me an email sharing an incredible task she created for her students. I was fascinated by her meaningfully application of the concepts she was teaching and asked her if I could share her task.

Algebra Scavenger Hunt

To make your own scavenger hunt:

  1. Make a map of your school on a coordinate plane.
  2. Hide clues in 8 different locations throughout the school. Each clue will have problems on them.
  3. Give each pair of students a system of equations problem. They will need to solve it, graph the solution on their map, and go to that location to find another problem. That problem will send them somewhere else in the school.
  4. Make play money to use as a “point” system. (For my money, I took one of those school pictures I never know what to do with and placed that on top of the money on the dollar sign. The kids really got a kick out of that!
  5. Give each group 5 dollars before they begin. Allow them to spend a dollar to get a hint from you if they need one. As they continue, they will either earn money (getting a question right) or lose money (making inappropriate choices such as disrupting another class or going somewhere on campus they should not have been.)
Scavenger Hunt, 3, clue

Using what they know for the next clue…and they didn’t pose for this shot!

 

To create a system of equations from an order pair:

  1.  Take the ordered pair you want to use as the solution of system of equations. I chose (12,8)
  2.  Create the first part of both equations. For example, -2x+3y = _______ and 4x -3y = __________.
  3. Then need to plug in the x and y values to get what they equal. So using the same two equations from before I used -2(12)+3(8), -24+24 and got 0, so the first one is -2x+3y=0. Then the second one is 4(12)-3(8), 48-24 and you get 24 so that one is 4x-3y=24.
  4. Now you have a system of linear equations -2x+3y=0 and 4x -3y = 24 and have 7 more to make.

All of my prizes (except for the pencil) were things that I didn’t purchase. The students were very
excited about the grand prize, 100% on the unit quiz. After all, if they could just solve the four system of equation problems then they have already mastered the quiz. As a side note, very few groups asked for a hint and my systems were hard, too!

I’m so proud of my students! They worked very hard and had a good time!

Scavenger Hunt, small group, 2, comp

This group found the next clue. It was on the school’s mascot-the lion!

Don’t you wish you had this teacher when you took Algebra? Don’t you wish your own children had an experience with Algebraic concepts like this? I think Lisa Nielsen [Visit Lisa’s blog for more innovative ideas and thoughts.] had the best quote, from Will Richardson, in one of her posts,

“What I want from my kids’ school is to help me identify what they love, what their strengths are, and then help them create their own paths to mastery of their passions. Stop spending so much time focusing on subjects or courses that ‘they need for college’ but don’t interest them in the least. Help them become learners who will be able to find and make good use of the knowledge that they need when they need it, whether that means finding an answer online or taking a college course to deepen their understanding. And finally, prepare them to create their own credentials that will powerfully display their capabilities, passions and potentials.” [More from Will Richardson]

Download copies of the description of the Scavenger Hunt Store and Directions for the Scavenger Hunt.

Thank you, Kari, for sharing this incredible task!

Side Note: This teacher uses small-group differentiated instruction in her classroom on a regular basis using the Tabor Rotation Framework and engages her students like this on a weekly basis. AMAZING!!!

More Questions, PLEASE!

??????????????

A friend recently shared with me her winter break experience taking her daughter to a hands-on museum. She said they spent six hours at the museum. She really wanted to share the questions her daughter was asking as she was interacting with the hands-on exhibits. She shared all of them with me because she knows how important questioning is in a classroom.

“What would happen if we redid it like this? Can we try and see?”

“Would that airplane go higher if we built it in a rocket shape? What is that shape called?”

“How many pulleys does it take to lift me up? What about you? Daddy’s not here, so how can we figure out how many pulleys to lift him up if we know how many for me?”

“What would make my car go faster? Hmmm…can I try a different way?”

“Look Mommy, the pieces to the road can only be put together in one way. Isn’t that part of a fact family?”

Questions were literally flowing out of every child in the museum. In fact, there is a constant buzz in the museum from the excitement of wanting to learn. They weren’t completing a worksheet or looking at a picture…they were doing something with the knowledge and gaining more knowledge as they proceeded.

This list of questions arrived in my inbox with perfect timing. I was rereading Chapter 5 of Tony Wagner’s book, Creating Innovators:The Making of Young People Who Will Change the World. The chapter is entitled, “Innovating Learning” and I had just finished watching an incredible clip that featured Amanda Alonzo, a highly successful science teacher who emphasizes the importance of discovery and questioning with her students. [Click here for more about this INCREDIBLE book.]

Why write a blog about questions? I’ll let an expert explain…in that same chapter, Tony Wagner states,

“One problem with this traditional approach to learning, however, is that the way in which academic content is taught is often stultifying: It is too often merely a process of transferring information through rote memorization, with few opportunities for students to ask questions or discover things on their own—the essential practices of innovation. As a result, students’ inherit curiosity is often undermined and ‘schooled out’ of them, as Sir Ken Robinson and others have written.” [This TED talk by Sir Ken Robinson explains more and is well worth your time!]

Curiosity is nothing new. Throughout time, so many have attributed their creations, explorations, and inventions to questioning. When asked why he was able to develop so many theories and think the way he did, Albert Einstein repeatedly stated,

“I have no special talents, I am only passionately curious.”

In Simon Sinek’s book, Start with Why, he describes the dichotomy between Samuel Langley and the Wright brothers.  Langley had the funding, the resources, and everyone thought he would be the first to fly—including Langley himself. The Wright brothers had no money, few resources, but they had such a passion to fly that they inspired the enthusiasm and commitment of a dedicated group in their hometown. This group banded together in the basement of a bicycle shop and made their vision real. Did they have questions? Did they expect to fail and fail often? Yes, but they also expected to fly. (Personally, I love the fact that the Wright team always took 5 sets of parts with them to every flying test or trial. I share this with my students to encourage them to try and try and try–and bring extra parts!)

My friend’s last question to me made me think the most,

“After watching all these children all day long, it just makes me ask…why aren’t we teaching this way in schools?”

No time like the present to begin. Here are a few simple ideas to help you begin:

  1. Put up an “I Wonder” chart on the wall of your classroom. Whenever a student simply “wonders” about something, have them write it on a sticky note and put it on the chart. Once a week, select a question from the “I Wonder” chart and develop a plan for finding the answer.
  2. Bring in an old box and label it “The Question Box.” If a student has a sincere question, they drop it in the box. Questions are pulled out at the end of every class period. If no one knows the answer, then everyone goes home to “wonder” about it and share what they discovered with their partner the next day in class.
  3. Use Exit Questions at the end of every activity. Have students think about what they learned and how the information could be used in their world.

 

I’ll let Amanda Alonzo, whose students regularly finish among the 40 finalists in the Intel science competition, finish this post,

“To be a successful science teacher, you have to make it fun, and for kids that means making it theirs—so that they have ownership over what they are learning. It’s what motivates them…The most important thing is allowing students to ask questions and then giving them the space to find the answers.”

Why Learn Conversions???

sale sign

 

“The journey for an education starts with a childhood question.”     – David L. Finn

As I played “Conversion Concentration” with a small group of students at the Games Station, one student asked the inevitable question about conversions,

“Why do we have to learn this stuff?”

These students had been completing a conversion chart every week since the beginning of school, but their teacher knew the value of partnering conversion memorization with meaning, so before the students began creating conversion charts, he had the students use manipulatives at the Manipulatives Station to help them develop a concrete understanding of the relationship between fractions, decimals, and percents.

The week after experiencing conversions concretely at the Manipulatives Station, their teacher began to have them play games that used the visual representation of the fraction, decimal, and percent partners. I just happened to be there on a day when they had moved to the abstract and were playing “Conversion Concentration”  to help them memorize the conversion “facts.”

“Conversion Concentration” asks pairs of students to match the fraction to the equivalent decimal to the equivalent percent. If a pair finds at least one match, then they take those two cards and win a point. If a pair finds the third, then they win 5 points. t

[Play Conversion Concentration with your students. Download Conversion Concentration Directions, Conversions, Sheet One; Conversions, Sheet Two; Conversions, Sheet Three; Conversions, Sheet Four]

Every card that is turned over remains visible for the next pair. This encourages constant review of the cards and comparison of the possible matches between the fractions, decimals, and percents. To add challenge to the game, a timer can be used and each pair has only one minute to find the matches.

The steps this teacher had used, concrete to pictorial to abstract, must have been effective, because these students were faster than I was at matching the three cards and winning the 5 points—something they absolutely loved!

But let’s get back to that question, “Why learn conversions?” Recently, a store provided the perfect example and I shared my story with the students. Two of my children and I were going into a store and were looking through the carts of seasonal items that had been marked down for a quick sale. Several of the carts held big bags of candy and had a 75% off sign on them. This was a bargain, so I got several bags.

At the check-out register, the cashier scanned the first bag of candy. It rang up at $3.24—NOT the sale price at all! I mentioned the 75% off cart and she agreed that it was on sale.

Cashier, “But, I have no idea how much to charge you. If you can tell me the price at 75% off, then I’ll give it to you for that amount.”

I looked around the group of students and asked them if it was worth my mental energy to calculate how much the items really cost at 75% off. Everyone enthusiastically agreed. So, I asked them, being experts in conversions, to share how they would figure out the discounted price of the items—knowing what they did about conversions.

Student 1: “Easy. You just convert the 75% to a fraction. The fraction is ¾. You know that the total number of parts is 4 so you divide $3.24 by four.  That will give you 81¢.”

Student 2: “How did you get 81¢?”

Student 1: “Again, easy! You divide 32 by 4 and get 8. I still have 4 cents left, so I divide that by 4 and get 1. That’s 81¢.”

Student 3: “What’s that called when you do that?”

Student 4: “Front-end estimation. Remember when we learned how to do that a few years ago? What do you know—we’re using that stuff, too!”

This group of enthusiastic and engaged students were amazed at the practical and meaningful use of what they had been learning in math. We talked about discounts and ways to use conversions and mental math in stores every day. They never dreamed that they could actually use conversions except for regurgitating information on a test.

The most genuine statement from a student?

“You saved over $2 a bag for that candy. That’s why we learn conversions—so our moms can buy us more candy!”

“It’s not that I’m so smart, it’s just that I stay with problems longer.”    – Albert Einstein

Thanks to this teacher, these students have learned conversions, a little bit more about personal financial literacy, and, as Albert Einstein stressed…they aren’t just smart, they now have the tools to stay with the problem longer!

Common Core & Personal Financial Literacy

A math teacher at a recent Tabor Rotation training session came up during the break and began sharing her frustration with me,

“I’m just learning the CCSS (Common Core State Standards) that our state recently adopted. Now our district is mandating small group instruction, math workstations, and regular intervention.

The latest? They’ve decided that the math department needs to fix the economy by incorporating personal financial literacy into the curriculum. I may even have to teach financial literacy next year. Of course, they want me to make sure that every student passes the end-of-course exams, too.

I’m sorry my students can’t balance a checkbook, but I only have 60 minutes or less in a class period. How am I supposed to do all of it?”

Over a decade ago, Lewis Mandell, Dean of the UB School of Management, made a similar poignant statement in his Final Word Editorial. The title of his piece sums it up, “Why Johnny Can’t Balance a Checkbook.” Mandell wrote that,

“Millions of American teenagers graduate from high school every year without a basic understanding of how to manage their money. As they venture out from under their parents’ protection for the first time, what awaits these young adults is an increasingly complex society that asks that they make immediate and sometimes irreversible financial decisions- decisions that will likely impact their livelihoods for years to come. Unprepared by teachers or parents to make those decisions, the consequences can be quite severe.”

After sharing some of the content of the articles linked to this blog post, I shared news from other states who are designing and requiring year-long financial literacy courses. Virginia is one of them. Vivian Paige says that a course in economics and financial literacy was a long time in coming and has been greatly needed by students who graduate not even understanding what a mortgage is and how credit cards calculate interest. Her brief article is worth the read.

As the discussion continued, I assured this teacher that Common Core was actually going to be an incredible tool for helping her and her students accomplish the goals set out by their district. I also assured her that putting a structure or framework in her classroom that would assist her students in becoming mathematically proficient would provide for complete exploration and in-depth understanding of the CCSS, a great passing rate on the EOC exams, and address personal financial literacy. In fact, I told her she was in the right session to find some answers. All she had to do was hang in there for the second half to learn how Tabor Rotation, Common Core State Standards, and Meaningful Math Management would fit together beautifully.

As she shared her concern about teaching personal financial literacy with the entire group, many other participants shared the same concerns. Wanting the financial crisis to remain in the past, many states are looking at what they can do to facilitate financial literacy.  The state of Maryland, who was one of the first states to adopt Common Core State Standards in June, 2010, has sought to write their own financial literacy standards since these are not specifically written in Common Core.

“Today’s students need a strong foundation in personal finance to help them budget and manage their money. Many students work during high school; some even have credit cards in their own names. After high school, young people often make uninformed decisions that can negatively impact their credit ratings and their ability to gain security clearance for employment. With the nation currently in the midst of a financial crisis, far too many people are deeply in debt and are faced with the reality of losing their homes and their financial security…the state curriculum lays the foundation for a new generation of competent, confident, and financially literate adults.”

Other teachers were concerned about the fact that Common Core asks teachers and districts to find a balance for mathematical content in the combination of procedures and understanding.  The next statement,

“There aren’t any personal financial literacy standards in Common Core. They want us to find ways to combine math standards with social studies and reading/English language arts standards.”

Yes, I told them, that’s true, but the clustering of the CCSS is an amazing way to make learning meaningful. Even Tony Wagner, author of Creating Innovators: The Making of Young People Who Will Change the World, would probably agree that clustering standards from different disciplines is a way to encourage students to find purpose and passion about what they are learning. This has been of great concern to Georgia as well. The Georgia Performance Standards Mathematics Curriculum, mirrored in the CCSS, is designed to achieve a balance and a connection among the disciplines and emphasizes rigor and relevance.

“The Georgia Performance Standards Mathematics curriculum is designed to achieve a balance among concepts, skills, and problem solving. The curriculum stresses rigorous concept development, presents realistic and relevant tasks, and maintains a strong emphasis on computational and procedural skills. At all grades, the curriculum encourages students to reason mathematically, to evaluate mathematical arguments both formally and informally, to use the language of mathematics to communicate ideas and information precisely, and to make connections among mathematical topics and to other disciplines.”

I shared that the state of Pennsylvania is asking their state department of education to develop cross-curricular materials that would take the Common Core Standards for Math and incorporate the state’s academic standards in arts and humanities with the Common Core Standards for ELA to help develop financial literacy skills.

At this point, the body language in the room indicated they had had enough of the facts and wanted more–a plan that would work. We had explored The Tabor Rotation Framework for several hours, but they wanted to know about the connection or clustering for financial literacy. I shared Meaningful Math Management with them. Meaningful Math Management was an instructional tool I created at the same time as Tabor Rotation. It was developed as an answer to cultivating classroom communities with my students, providing real-world application of math concepts while teaching financial literacy and personal accountability. All of the information is available on the FREE RESOURCES page of my website. There is a slide presentation and all of the materials you need to put this incredible structure into place in your classroom. But, rather than explain it to you myself, I’d like to share a teacher’s experience that she sent to me in a recent email.

“One of the most exciting ideas we gained from the Tabor Rotation workshop in June was the management system.  For years we had complained about our students being irresponsible with their work, supplies, and behavior.  Using manipulatives was such a disaster that we seldom used them, knowing the importance but not willing to deal with the chaos.  Many students didn’t have pencils so time was wasted as they borrowed or teachers furnished them. Neither solution was acceptable and only facilitated dependency. Obviously, you can’t do math without pencils, at least with all the paperwork we did before Tabor Rotation. Every six weeks we agonized over all the students who had missing work, newsletters that weren’t returned signed by parents, behavior problems, lack of supplies, etc.

The change in all these areas has been phenomenal since using the Meaningful Math Management system.  Students are caring for their supplies and responsible for purchasing pencils rather than borrowing, which really means taking.   Just the stress and time involved in this alone has been unbelievable.  It may seem like we’re overstating this, but believe me we are not. As the math inclusion teacher, I volunteered to oversee the store.  Students can buy supplies and snacks from me between classes or before school.  If they go to class without necessary supplies, the teachers sell pencils at double the price.

Using this system is what makes the rotation stations manageable.  The students have their jobs and are rewarded for working together as a group appropriately.  I especially love the emphasis on positive behavior.  It’s a big change in mindset for our grade level from the past system of giving marks for misbehavior.  After a few negative responses, that system becomes ineffective.  As Glenna demonstrates in the workshop, a positive response, such as “every one at that table gets $5 for….” makes an immediate improvement in the entire room’s behavior.  This is exactly what I learned in my classes 38 years ago at TWU.  Unfortunately, it’s much easier for us to respond negatively, but  research has proven that behavior improves more effectively from positive reinforcement than negative.

Learning to write checks, balance check registers, and make spending decisions is providing a lifelong benefit.  If students do need to pay a fine and have no funds, they go to our assistant principal. Rather than receiving a punishment, he discusses the value of money management and doing what is necessary to earn money rather than paying fines.

Because of students managing themselves, using Tabor Rotation has made for much happier students who are enjoying math rather than dreading it.  In the past we have bombarded them with worksheets, which also caused stress from grading and pleading for missing work.  Now, we have fewer worksheets but are using them more effectively with more direct teacher interaction.  I actually heard two students today say, “I love math! Yes, it’s work, but Meaningful Math Management is worth it!”

As Vivian Paige said,

“And we expect everyone to save for their own retirement, use credit wisely and manage their money.  How do we get there from here?”

Simple—create the perfect storm in your classroom.

Common Core State Standards + Tabor Rotation + Meaningful Math Management