Co-Creating Solutions. A CTL-sponsored blog to foster and encourage professional conversation about teaching and learning.

I can still sing the lyrics to a song written to the tune of the Notre Dame Victory March by my third grade teacher, Barbara Goldberg, for a class play entitled “Paul in Foodland,” built around our science curriculum on food and health: “March, march to the salad bowl/Join with the ranks of the salad patrol/Pour on dressing if you choose/You’re on the right side/You can’t lose…” Now, I became a professional singer/actor as a teenager and continue to perform today, so song lyrics tend to implant in my brain–but since third grade was a few decades ago, I’m going to give a lot of credit here to Mrs. Goldberg.

I can also clearly recall a lesson delivered by my ninth grade social studies teacher, Lew Shaten, who began our exploration of world history with an activity he called “Country X.”  We were provided with a list of political, economic and social facts about an unnamed country, and had to guess how it would interact with its world neighbors.  The payoff came when we learned that Country X was actually pre-World War I Germany and compared our adolescent predictions with the facts of history.

I still thank my eleventh grade math teacher, Jim Rubillo, for cheerfully insisting day after day that instead of memorizing pre-calculus formulas, we commit to memory instead the principles that guided the derivation of the formulas.  “If you understand how and why the forumla applies,” he would say, “you’ll always be able to solve the problem.”  Believing that I lacked an intuitive understanding of math, I was thrilled to discover that there were multiple ways of tackling a problem.

And my twelfth grade English teacher, Marie Hildebrand Bintner, continues to watch over the shoulder of this professional writer on a daily basis:  “This is wonderful, Barbara…but is that the best way you can say it?  What do you really mean?  When you’re comparing two ideas, keep the comparison close–hip to haunch!” she would say with a wink and a smile.

What did all of these teachers have in common?  In one way or another, each personally engaged and challenged my classmates and me.  They provided information, but asked us to step up and actively contribute to the discussion.  And they consistently let us know that they had confidence our contributions would be of value.

My children had similar experiences with the best of their teachers when they were engaged, challenged and inspired with self-confidence.  What skills and strategies must a teacher have at his or her disposal to provide such memorable and effective learning experiences?  What are your most memorable classroom experiences as a student or as a teacher?  In future posts, I’d like to tease out the specifics and explore how these translate into meaningful, practical approaches to learning that all educators can use.

What obstacles stand in the way of students being successful? Maybe our students are being trailed by a lifetime of barriers both academic and personal. Perhaps the thought of putting themselves out on a limb is too risky for fear of the limb splintering. Possibly they have spent their time drifting and paddling against the currents to find they are barely surviving.

This video serves as a metaphor for our struggling students as they fight to survive in their habitats.
Like the cub we watch struggle along the mountainous terrains, our students are facing their own obstacles along life’s course. For that reason, like the mother bear, I will be stationed along the path to watch over them as they discover the roar behind their voices. I will be shouting Abe Lincoln’s wise words, “Always bear in mind that your own resolution to succeed is more important than any other.” Consider what you want your students to always bear in mind as they come face to face with their own predators.

Observing the world around you for gaining insight and making analogies; recognizing patterns for extrapolating information and predicting rules; and solving problems by representing what you know in multiple ways: all themes illustrated within recent CTL blogs. As I read through the BLOG entries, I couldn’t help but to be reminded of how those themes are critical skills for thinking mathematically and solving problems. In my work with mathematics teachers, I am constantly in search of materials and experiences that will support them in moving students forward in developing those critical process skills. Recently, I was sent a National Council of Teacher of Mathematics Illuminations (NCTM Illuminations illuminations@nctm.org) link with a unit on Paper Pool that provided opportunities for just that support.

The Paper Pool unit is an investigative, interactive series of mathematics lessons that sequentially engage students in making observations by connecting to the sport of pool. As a way of introduction, there is an interactive applet for exploring patterns when the dimensions of the pool table change and discovering the rule for the number of hits and the pocket in which the ball will land. As students interact with the applet, they gather and organize data and make predictions.

Within the Paper Pool Unit there are five lessons and within each lesson there are necessary materials with ample illustrations of multiple ways by which students can represent what they know through tables, graphs, algebraic equations, words, and modeling with pictures (an addition from an earlier BLOG on multiple representations).

The NCTM model provided is:

The mathematics content developed through the Paper Pool Unit is: ratio, proportion, equivalent fractions, greatest common factor, least common multiple, and similar figures. Additionally, students use the process of mathematical thinking through gathering and organizing data, exploring patterns and formulating rules.

The link for accessing the materials is:

http://illuminations.nctm.org/LessonDetail.aspx?ID=U165

As you and your students begin to interact with these Paper Pool lessons, please post evidence of student mathematical thinking through comments made, student work, pictures of students engaged with the materials, etc.

For me, playing pool will never by the same.

Early in the week I had an interesting conversation about momentum. Not in a physics lab, but in a principal’s office. The very next day, with a group of administrators, university partners, and literacy coaches, the topic emerged again. And now today, guess what subject managed to make its way into my coaching conversation…momentum…What keeps it going? What kills it? How do you restart it? Everybody’s talking about it. And I can’t stop thinking about it.

Around here, the snow days have nearly sucked the life out of the school calendar and the dreary weather has left everyone feeling out of sync. One of my literacy coaches described the feeling like she was waiting in line; lots of stopping and starting but no real rhythm to the movement. It’s an odd dilemma because we all know that if we can just get one wave started, momentum grows quickly and soon enough everyone is back in the swing of things. So, I’ve spent a significant amount of time this week asking folks to consider how they might pull focus back to priority issues and drive new energy into the work at hand. One thing we all agreed on was that when teachers feel affirmed and empowered, they are more easily motivated. So we brainstormed, asked questions, and made plans for spotlighting and celebrating outstanding practice in hopes we could restart the momentum engine. I’ve included here some of our best ideas.

• Allow time for commercial breaks in faculty meeting for teachers to share a successful strategy, sample of student work, testimonial of an academic risk that paid off, or think-aloud of how a successful lesson plan came to be
• Use technology applications like animoto, voicethread, or moviemaker to show off digital images and video of exemplary work
• Invite teachers to take a school walk (tour the halls and peep into classrooms) as if they were new to the building. What does a quick spin through the building reveal about the school’s values or emphasis?
• Shake up the traditional faculty meeting schedule by sending critical whole-school information in an email and allow teachers to meet by departments or grade-level teams to share (and capture in print) what’s working.
• Invite a student to share (in a department, team or faculty meeting) a brief story about an engaging assignment or classroom experience that had a lasting impact
• Identify a core group of teachers to start a wave of sharing by asking them to pass on an invaluable tip, inspirational quote, valued resource, or piece of text in relation to the school’s focus. Recipients, in turn, “pass it on” by sharing something new with someone else.
• Leave a sticky note compliment when you visit a classroom. Find something to celebrate!

When I was thirteen, I got a Dr. Kildare diary complete with a small, gold lock.  As a thirteen year old the dashing portrait of Richard Chamberlain was alluring and provided inspiration for countless swooning entries.   I was a loyal diarist and kept track of events and feelings every day. My diary helped me problem-solve, wax poetically or just jot down what I’d done that day.  As I discovered my love of the visual arts I began to keep sketchbooks and sketch journals. These were places to capture images of things that I found interesting, and perplexing. The sketches represented things I was curious about and images I wanted to study.  My sketchbooks became places to capture my sense of wonder about the natural world as well as what I was imagining.

A couple of months ago, I got a Flip Video camera to use in my work with schools. It has allowed me to create a visual record of conversations between teachers, and among students. I can capture moments in time and interactions between people, allowing me to revisit, mull over and share these conversations with others.  The “teachable moment” has become the “videoable” moment.  The camera has become an indispensable tool that I carry with me all the time.

This little camera has opened up new worlds for me and rekindled my interest in all things visual. The camera has helped me learn how to use my eyes again, to listen closely and wonder about what I’m seeing.

In my last post I shared a snippet of video from a college instructor discussing the successes she was having using literacy strategies in her accounting classroom. The clip above represents something that caught my eye while I was making a phone call. As I began filming, the object came into clearer view and I became more curious about what I was looking at. How did the light hit the glass and create the shadows? How would the shadows change as the light moved? What would happen if I shook the table and the water in the glass moved? How would this change the shadows?   The more I looked, the more questions I had.  The act of recording brought me closer to the object.

I know many teachers are integrating Flip Video cameras into their work.  Students are using  videos to create movies and presentations. Teachers are using the cameras to take snapshots of learning that is happening in classrooms.

How are you using Flip Video cameras in your school and classroom?  What opportunities do students have to use video as a learning tool to explore the world and generate their own questions? Please share your videos and experiences so we can learn from one another.

As much as I dislike sitting down and crafting a completed writing product, I love writing to learn.

Writing to learn adds to my understanding of content.  As a student writing notes was an important part of my ability to do well on tests.  I wanted to be a good student and please my teachers.  My notes may not make sense to anyone else but they continue to be an important part of my understanding.  As I have gotten older my notes have more scribbles, symbols, arrows, bullets and I use a variety of colored pens.  These notes look different but are still very important and when I need to go back and check on something – the color pen I used is usually the first thing that comes to mind.

I was the first science teacher in my area to apply and be accepted into the Writing Project.  Participating in this project was one of the milestones of my teaching career.  The biggest thing it did for me was give me a deeper understanding of the importance of feedback.  Feedback needs substance but it can be brief and to the point.  Number Two was the discovery of Learning Logs and the potential value in the science classroom.

The science notebook wasn’t working for me.  I wanted students to have access to information over a period of time but the notebook seemed to be just a collection of papers not the important personal information I thought students needed.

Stenographers notebooks and composition books were my Learning Logs of choice and I never decided which was the best.  Both have pluses and minuses and I traded back and forth between grading periods and sometimes entire years.  Every grading period we started fresh with a new Learning Log and it was a running record of what we accomplished.  I liked the permanent line down the middle of each page in the steno book because I could have students reflect on one side and then I could respond with my feedback on the other.  I could have students respond to something they were reading by taking notes on one side and asking questions on the other.  This Double Entry journaling worked very well but I didn’t have a name for what we were doing until many years later.

Students completed or placed their sponge activities, admit/exit slips, data collection, hypothesis formulation, conclusion writing, procedure listing, problem solving, note taking, etc in their learning logs on a daily basis.  Pages were never to be torn out and thrown away.  Scientists keep notebooks like this.  They aren’t necessarily neat and beautiful, they are written with different colored pens, important items are taped and pasted where needed, more than one person’s writing is evident, and they become treasures.  Most scientists have a few of these hidden in a safe place.

Learning logs were never graded.  This is where the students practiced and practicing is a must for a scientist.  One of my class mantras any student could repeat was: Once is never enough; two, three or one hundred times would be much better.  This doesn’t mean that I didn’t look at what students were doing or that I didn’t check on something periodically.  Learning logs were used by students’ everyday and I viewed them in some capacity each day.  I responded to questions, I checked answers and wrote additions and corrections with the students and sometimes I went through the classroom placing checkmarks in each notebook in order to record that each student had complete understanding of an assignment.  The constant daily use of the learning logs were my formative assessments.  This is how I kept check on the pulse of the classroom.  Most of the time there was a constant steady beat with the occasional frustrated student or group of students that needed more consistent monitoring.  Occasionally there was a rapid pulse, students would be scribbling furiously when taking notes.  They didn’t want to forget a single thing and they were desperately working to get everything down correctly in their notebook.  These were exciting times, students were engaged in what they were learning and understood the importance of taking notes for future reference.  Students were encouraged to use the information in their logs when we were having group or class discussions.  Students were taught that their responses and understandings were valued but they had to have evidence to back up what they were saying.

If you haven’t tried using a learning log I would suggest you give it a whirl.  I will gladly work with you and answer any questions you might have.

Last week, I attended events in Frankfort Kentucky for Arts Day 2010.  Even though the day turned out to bitterly cold, windy and snow- and ice-packed, a couple hundred of us die-hards showed to support the arts in education and in the daily lives of all Kentuckians. 

I served on a volunteer committee to help plan the day’s events. I put together the following points for a flyer to be distributed at the event and am happy to share in hopes that you will find them helpful in your local context.

The Arts are Good For…

Students

• Arts-rich schools teach to the whole child, taking in mind differences in learning styles and addressing the cognitive, social, and emotional domains of all learners.
• Teaches students that there are multiple correct answers to many problems; asks them to apply creative thinking for possibilities to each challenge.
• Helps students understand themselves as in control of their own learning experiences and outcomes, and able to craft effective solutions as individuals and in groups.
• Builds a healthy self-esteem and provides them with outlets for creative expression though a learning atmosphere that is supportive and responsive
• Helps them come to value their school experience; students actually want to come to school.

 Teachers

• Provides them with valuable “aha” moments. They see their students in a different light, even helping them see exciting new potential in “problem” students based on observed new roles, involvement in learning and doing, and positive interactions with fellow students and teachers.
• Helps them come to know more about their students’ interests and abilities based on what their students know and can do in creating, performing and responding to the arts.
• Provides their students with multiple entry points for learning and helps them address content based on prior knowledge, experience and skills.
• Creates a classroom learning environment that is charged with excitement and energy; challenges their students to learn through creative, real-world applications to problems.
• New understanding and experiences required through the arts helps teachers see themselves as “learners” along with their students, often bringing a fresh approach to their instructional practice.

Schools

• Helps reduce the achievement gap by reaching and teaching students in new ways, especially students from economically disadvantaged circumstances as well as those who find more language-based instruction difficult.
• Helps create a teaching and learning culture that is charged with excitement and supportive and responsive to the learning needs of both teachers and students. 
• Provides a continuous, fresh approach to teaching and learning.  Both faculty and students want to be at school.
• Helps address the unique social, emotional and cognitive learning needs of problem students, who often thrive in supportive settings where they can address challenging content through creative new approaches.  The arts enable these kids to shine.
• Provides multiple avenues for engaging the larger community and parents through activities and events that showcase their children and that are aimed at accomplishing larger community and parent engagement goals of the school.

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References and Resources

I’ve been planning my session for the upcoming Kentucky Gearup Alliance Institute, Use of GeoGebra: free mathematics software to help students understand and apply concepts in geometry, algebra, and calculus.

Geogebra is an incredibly powerful dynamic mathematics software (DMS) designed for teaching and learning mathematics at the secondary and  college levels. It combines mathematics disciplines of Geometry and Algebra, hence the name Geometry Algebra. As I plan my session I keep coming back to the changes that occur in high school mathematics for students. Much of the work they have done to this point is very concrete; real number operations, data analysis, simple geometric relationships, measurement, and proportional thinking. In algebra I there is a major shift to a very abstract approach to algebra instruction, especially in the United States (National Research Committee, 2005). Additionally, the new CCSSO standards that many states are adopting place an increased emphasis on conceptual understanding and development of student ability to work holistically with functions rather than work primarily from a skill based approach.

So why do a session on Geogebra? Why is it different?

Technology has progressed a long way in recent years, and the dynamic nature of tools that are available make them powerful learning tools. Eighteen years ago James Kaput, a leader in the use of technology in the mathematics classroom, “predicted that in regard to continuing growth of electronic technology, “major limitations of computer use in the coming decades are likely to be less a result of technological limitations than a result of limited human imagination and the constraints of old habits and social structures (Priener, 2008).” I think Geogrebra may be the tool that more teachers of mathematics will be able to see as viable in their classroom.

The reason I think Geogebra may be a game changer in creating opportunities for students to interact with content differently and the reason I think it is the exception to Kaput’s prediction is it’s simplicity and flexibility. Yes, I know I’m a technology geek, and I know I’m an evangel of dynamic applets, but Geogebra does what no other tool has been able to do, does it easier, cheaper, and more flexibly. Let my provide you a case in point.

Let me take a few moments to show you a quick sample of what Geogebra can do: In an algebra I course developing understanding of linear functions is a major focus of the course, and creating contextual understanding has been proven to help students creating deeper understanding.

Notice in the example pic that students not only see the graphical representation in connection to the story problem. Students can manipulate the situation by changing car speeds using the sliders on the left, can see the impact of their changes as the cars move and as the time/distance graph changes.

Here is an example of just how easy it is to create objects using Geogebra. If teachers want to have students create objects to explore slope it can be as easy as…

As I put more planning into my presentation, I’m reading “How Students Learn: Mathematics in the Classroom” by the National Research Council, and I keep coming back to making connections between the different representations, having students create objects, manipulate those objects, and observe the characteristics of those objects as being central to the principles that the National Research Council has identified as being crucial to deep student learning and understanding.

Finally, we have a tool that is only limited by our own imaginations, so even if you aren’t very imaginative, let your students be and let their learning soar with the endless possibilities of a tool like Geogebra.

I have always been a writer.  As Communications Specialist here at CTL, I work on public relations and marketing, and on the development and writing of grant proposals, publications and outreach materials.  Before joining CTL, I worked for many years as a freelance writer for a variety of publications, and for producers of educational television programming.  My writing repertoire includes everything from snappy press releases to highly visual video scripts, entertaining (yet informative!) magazine features, and lengthy (let’s hope not ponderous) research reports.  To tweak the famous Latin phrase, I write, therefore I am.  

As a writer, I find it particularly fascinating  to work with professionals who not only communicate with clients in part through writing, but also are charged with helping teachers to use the writing process as part of a comprehensive approach to the teaching of literacy.  As resident wordsmith around the office, I am often asked for feedback on staff writing, and so try to do for my colleagues what they do for educators–coach them through a complex process while respecting and preserving the unique approach and voice each brings to the assignment at hand.  I frequently remind them that a polished piece of writing is like a beautifully executed ballet or feat of athleticism:  It only looks easy, the end product of many attempts and a fair number bruised shins along the way.  But like the dancer or the athlete, a successful writer emerges not only with a finished work that reads well and communicates clearly, but with new clarity of personal thought.  To tweak that Latin phrase again, we think, therefore we write, so that others may think.  Your thoughts?

In working with many schools and districts, I regularly hear much concern, comment and effort from schools that are attempting to meet the requirements of RTI – Response to Intervention. RTI is a simple idea that seems to have become complicated in its implementation.  As with anything that has an external accountability component, it has taken on a life of its own – and unnecessarily so.  

As we look at the critical components of a systematic approach to adolescent literacy, RTI can become clearer, less complex, and less frightening.  Here are the fundamentals of an effective programmatic approach to literacy at middle and high school levels:

• foundational literacy instruction – teaching all students to read, and continuing that instruction throughout their schooling years, gradually shifting from literature to informational text, as complexity of learning needs deepen
• cross-content literacy integration to apply core literacy strategies in service of content learning and continued skills development
• intervention that works at multiple levels; intervening in the classroom for students who have temporary issues with content or process, and intervening outside the classroom for students who have more long-term learning issues.
• solid professional training and coaching for teachers, focused on all three core program elements noted above; and job-embedded in nature
• distributed leadership structures that engage all stakeholders in the dialogue, planning, and implementation of literacy improvement strategies

So, back to RTI:  The first three components of a systemic approach to adolescent literacy fulfill the requirements of RTI . . . on paper.  If all students have access to program content, and that content includes varied chances for support when needed, then the requirements of RTI have been fulfilled.

However, there are multiple questions that remain.  First, are these different components consistent with one another?  Second, do schools have sufficient scaffolding in place for teacher learning and practice, such that they can be assured of program fidelity and quality?  And third, is there a sustainable commitment to the plan and its consequences in a school community?

These questions drive us to look at the last two program components noted above – professional development/coaching, and distributed leadership.  Too many schools are looking for the quick fix, the program-in-a-box that they can put into classrooms to not only fulfill RTI requirements, but to fix all that may be wrong with practice and student performance.  This is impossible.  It takes the effort of the full community to change their instructional habits for good.

A friend of mine once said “change happens in an instant, we just get ready for it and used to it for a very long time.”  It is possible that program implementation alone can create an instant change.  After all, something is now different.  However, to prepare for that change and to sustain that change takes long and well-supported effort to create new habits of mind.  RTI and other external policies can create the playing field for real change, but they can’t make it happen.  That’s up to school communities that are willing to take a problem on for deep and sustained work.