Saturday, August 25, 2012

"Bridging the Gap Between Math and Art" Scientific American

We need to stop boring our students and work to instill a love of learning and an excitement to be in school. I become more and more convinced all the time that this is the foundation of a great learning environment-fostering a place where kids want to be. A place where they really want to come everyday. Is this a bit pie-in-the-sky? Maybe, but I choose to believe that we can make schools places that crackle with excitement instead of snooze in boredom.

I remember taking math in high school; I got good grades, but I was bored stiff! In fact I hated it and learned very little. It's not that I hated the subject; I hated the unimaginative methods used to teach it--ones that were mired in the outdated paradigm that we still throw at our kids today: drill and kill and make no relevant connections to why we were studying this stuff. Why do we do this to our students? Why can't we find the joy in learning? Why can't we put the reasons why we need to learn this stuff out on the table and make it relevant to their lives? And if we can't do that, then why are we teaching it to them? Is it because it's always been taught that way? Maybe the worst reason of all!

Okay, so what sent me off on this rant? A wonderful slide show called "Bridging the Gap Between Math and Art" in Scientific American, a magazine I'm liking more and more all the time (and science was another subject I hated in high school, so I'm feeling another blog post coming on with that one). These artistic renderings of mathematical principles and concepts are astounding and something that I would love to have done in my study of math, and something that I would guess most students would like to do rather than sit at their desks and solve problem after problem.

The caption to the project pictured reads:

"Mitered Fractal Tree I," by Koos Verhoeff and Anton Bakker

(This sculpture was awarded Best of Show at the Bridges conference.) "Mitered Fractal Tree (designed late 1980s, first executed in wood), constructed from a beam with a rectangular cross section in the ratio 1:√2. When this beam is cut at 45 degrees, the result is a square cut face. When this beam is cut twice at 45 degrees, where the cuts are perpendicular, the result is a "roof" consisting of two smaller square panels. On this roof, two smaller copies of the entire tree are grown. No two branches point in the same direction. The result is an awe inspiring organic structure that is both highly structured and chaotic."—Koos Verhoeff  [Less] [Link to this slide]

Koos Verhoeff (design) and Anton Bakker (construction). Copyright Stichting Wiskunst Koos Verhoeff. Used with permission.
All I can say, as I wrap this up, is I wish that someone had given me the opportunity to work on a project like this when I was studying math. But that's in the past, and I like to live in the present moment, so the positive takeaway from this is that we can do this now with the kids who are coming into our classes this September. Let's work on changing the paradigm!

Thursday, August 23, 2012

Thoreau Knew it in the 19th Century!

How much time do our students spend in their seats? A good question to think about as we move back into our classrooms. Another question is how many of them need to "move to think" as Sir Ken Robinson reminds us. Henry David Thoreau knew it back in the 19th Century as he wrote in his journal:

Get Moving!How vain it is to sit down to write when you have not stood up to live! Methinks that the moment my legs begin to move my thoughts begin to flow--as if I had given vent to the stream at the lower end and consequently new fountains flowed into it at the upper. A thousand rills which have their rise in the sources of thought--burst forth and fertilize my brain. . . . Only while we are in action is the circulation perfect. The writing which consists with habitual sitting is mechanical wooden dull to read.

Take stock of your students when you go back to school and see which ones need to move around to get their thoughts to flow. The dividends may be huge.

Thursday, August 16, 2012

"Fear and Anxiety Effectively Shut Down Higher Order Thinking" from MindUP

As educators we are in the communication business--whether it's with students, parents, administrators, colleagues it doesn't matter. In order to communicate well, we need to have the language to help others understand. To that end I'm always on the lookout for cogent, succinct language that will make any point I'm attempting to make accessible to the given audience. Lately I've been on a search for such language to explain how stress, anxiety and fear will shut down learning. Mindfulness Educator Lori Corry gave me an insightful lesson and introduced me to the MindUP curriculum from the Hawn Foundation. Here's the language that I understood and think others may as well.

When we are calm and peaceful the filter [amygdala: an information filter regulated by our emotional state] is wide open and information flows to the prefrontal cortex, where the brain's so-called executive functions take place. On the other hand when we are feeling negative and stressed out, these executive functions, which provide cognitive control, are inhibited. Indeed information stays in the amygdala; it doesn't flow into the prefrontal cortex for executive processing. Instead it's processed right on the spot as fight, flight or freeze. In this way, fear and anxiety effectively shut down higher-order thinking (Scholastic 9).

So there it is: simply put and easily accessible. An important piece in getting ourselves and others to understand the importance of teaching mindfulness in our schools and having the research to back up what we are doing. If we can get policy makers to understand that social and emotional learning is just as important as core subjects, because they open up the learning pathways, then we'll be well on our way to improving learning and the well-being of our students.

The MindUp Curriculum. [brain-focused Strategies for Learning-and Living]. New York, NY: Scholastic, 2011. Print.

8 Ways to Reduce Stress at Work (or at School)

Stressed employees dread coming into the office each day. These workers are often distracted and produce substandard work. Workers can use several strategies to reduce their stress levels and work more effectively. So begins Eric Thompson in his blog post "8 Ways to Reduce Stress at Work" on worthwhile read.

Most of us can probably relate to this regarding work, but with a few minor modifications it would fit in school as well and look something like this:

Stressed students dread coming to school each day. These students are often distracted and produce substandard work. Teachers can use several strategies to help reduce student stress levels and help them learn more effectively.

Brain research is telling us that this is true from a physiological standpoint: students cannot learn when they are stressed out--it's just not possible. So the solution is to take the time to help relieve student stress so they can be ready to learn.

Here are some of the suggestions that Thompson posits with my comments in brackets and underneath:
Take a Walk/Frequent Stretch Sessions
Students learn better on their feet than in their seat, so it's imperative to incorporate movement into the class time.
Invest in a Stress Toy
Some students do well if they have a stress ball at their desks or are allowed to doodle.

Cubicle [Classroom] Decorations
Classroom decorations that speak to the students are important. Try getting away from inspirational posters and other things that mean nothing to students. Instead let them have a say in what goes on the walls and better yet let them make it.

Meditate [Mindfulness]
I'm convinced that mindfulness has a prominent place in our classrooms and should be taught the same as English and Math. It helps to open the students up to learn what they need.

Develop Friendships
Taking the time to foster relationships between peers in your classroom is time well spent and will pay huge dividends as the year progresses.

Use Music to Reduce Stress
Many students have reflected on how much the music I play in class helps them relieve stress and concentrate. Let's face it, most of our students play music while they study anyway, so is quiet the right mode for them to learn in? I frequently allow students to listen to their iPods when it's appropriate-the concentration level goes way up. And with apps like Spotify and Pandora, you can stream the music you want into your classroom and really change the dynamic. 

Tuesday, August 14, 2012

So...What are Executive Functions Anyway?

I see this term start to show up more and more in the educational lexicon, so I thought it might be a good idea to find a working definition and put it out there for the readers.

This is from the Encyclopedia of Mental Disorders:

The term executive function describes a set of cognitive abilities that control and regulate other abilities and behaviors. Executive functions are necessary for goal-directed behavior. They include the ability to initiate and stop actions, to monitor and change behavior as needed, and to plan future behavior when faced with novel tasks and situations. Executive functions allow us to anticipate outcomes and adapt to changing situations. The ability to form concepts and think abstractly are often considered components of executive function.

Stress Relief Can Be the Key to Success in School from Scientific American

It's becoming more clear to me all the time that as educators we need to provide a safe container in order to facilitate learning for the students who are entrusted to us. It's not just a "nice thing to do" for the kids as more and more brain research is telling us that students cannot learn when they are under great stress. The prefrontal cortex which oversees executive functions is compromised when a person is under great stress and when this happens...learning does not. It seems to be just that simple. One solution is to make sure our classrooms are safe and comfortable places for students to inhabit. Reducing stress at our classroom doors is the first step to laying the foundation for learning to take place. Mindfulness training is the next...but more on that in another post.

Scientific American's article "Stress Relief Can Be the Key to Success in School" by Clancy Blair goes on to say, "An even more insidious effect [of stress] is the assault it can launch on a child's brain, impeding the development of critical cognitive skills. A number of researchers, including myself, have discovered that psychological stress affects the thinking skills and brain development of even very young children, likely beginning prenatally. It is no mystery that stress thrives in difficult situations, but research is now showing that a disadvantaged upbringing may set back children in profound, lasting ways. In fact, stress may be one important mechanism through which poverty adversely affects children's ability to perform well in school."

The article, of which only the preview is free, is well worth reading and thinking deeply about as we get ready to move back into our classrooms this fall.

Tuesday, August 7, 2012


As educators we are always searching for new and specific ways to gauge student learning and formative assessments fit that bill.  These strategies from are some of the best I've come across. Check them out. The quote from Easley & Zwoyer is right on in the sense of not making judgments but finding out what students are thinking which is part of the essence of great teaching and powerful learning experiences. It also addresses how we need to get away from being disseminators of information which is something we have been championing here for years.


"If you can both listen to children and accept their answers not as things to just be judged right or wrong but as pieces of information which may reveal what the child is thinking, you will have taken a giant step toward becoming a master teacher, rather than merely a disseminator of information." -Easley & Zwoyer, 1975

Proof Points

Black and William (1998), two leading authorities on the importance of teachers maintaining a practice of on-going formative assessment, defined it as, “all those activities undertaken by teachers, and by the students in assessing themselves, which provide information to be used as feedback to modify the teaching and learning activities in which they are engaged.”
Formative assessment encompasses a variety of strategies to determine student progress toward achieving specified learning goals.  As Menken (2000) pointed out, “for assessments to be effective and useful for educators in instructional practice, they must be deeply entwined with the classroom teaching and learning driven by the standards.”  Timely teacher feedback is an essential ingredient of this process.   The habit of embedding formative assessments at key points during instruction yields information that teachers can use to identify and respond to problem learning areas.
The strategies for investigating student learning identified below provide different types of data from and about students.  Many of these approaches are also suitable to use as homework assignments.  It is appropriate to include the work generated through formative assessments in the comprehensive assessment system used to evaluate student performance.


3-2-1 Reflection
Serves as a post-instructional activity that helps students to focus their ideas and synthesize large amounts of information.
As I See It
Sentence stems that elicit opinions or understandings about key issues associated with a topic.
Prompts students to reflect upon a matter that is “out there,” and which, at first glance, appears to have little or no affect on them.   Binoculars challenges learners to recognize how seemingly unconnected issues may influence them.
Changes In The Wind
Assesses the impact of reading, listening, viewing, etc.
Definitions Are Us
Prompts students to develop their complete understanding of a term by creating their own definition.
Directed Paraphrasing
Builds personal definitions or explanations of concepts presented in class.
Exit Ticket
Prompts students to answer a question targeting the big idea of the lesson.
Examines a piece of text in terms of identifying factual information, eliciting questions, and generating personal reactions.
How Do I Know What I Know?
Uses a tightly focused question set to determine a student’s level of understanding about key ideas or concepts.
Is That a Fact?
Prompts students to examine the difference between a factual statement and an opinion-based statement.
Let’s Compare Notes
Provides the opportunity to build note-taking skills, characterize information, synthesize data, and assess student understanding.
Make It a Priority
Prompts students to generate and rank order alternative strategies to address an issue, solve a problem, or meet a need.
The Microscope
Asks to students reflect upon a specific experience, article, task, etc. and make generalized statements and connections to their personal, social, and academic lives.
The Mirror
Allows students to reflect upon themselves, their experiences, their knowledge, etc.
What’s Still Confusing Me...
Provides students with the opportunity to express to the teacher what they identify as the least understood aspect of the lesson.
One Last Question
Uses a final question to facilitate critical thinking about a specific concept covered in a lesson.
One Sentence Summary
Uses tightly framed answers to a number of questions to summarize the big idea about a topic in a single sentence.
Personal evaluation of a piece of text, object, picture in terms of its positive, negative, and interesting aspects.
Sequencing Events
Employs different visual forms: timeline, flowchart, etc to aide students in ordering things.
Thinking Diagram
Compares and contrasts two objects or events in terms of their key attributes.
Venn Diagram
Compares and contrasts two different objects, ideas, or events.
Wait a Minute
Reveals reactions to course materials, activities, and assignments.


  • Angelo, T. A. & Cross, P. K. (1993).  Classroom Assessment Techniques (2nd ed.). San Francisco: Jossey-Bass.
  • Black, P. and William, D. (1998, March). Assessment and classroom learning. Assessment in Education, pp. 7-74.
  • Boyd, Barry L. (2001). Formative Classroom Assessment: Learner Focused. The Agricultural Education Magazine, 73, 5.
  • De Bono, E. (1999). Six thinking hats. Boston: Little Brown.
  • Hanson, H. F., Strong, R. J., Schwartz, R. W., & Silver, P. B. (1996). Learning styles and strategies. Woodbridge, NJ: Thoughtful Education Press.
  • Hyerle, D. (1996). Visual tools for constructing knowledge. Alexandria, VA: ASCD.
  • Keely, P., Eberle, F. & Farrin, L. (2006). Uncovering student ideas in science. Arlington, VA: NSTA Press
  • ohnson, D. W.; Johnson, R.T.; and Houlbec, E. J. (1993). Circles of learning. London: Routledge Press.
  • Lawler, J. C., Neuber, G. A., and Stover, L.T. (1993). Creating interactive environments in secondary school. Washington:National Education Association.

Monday, August 6, 2012

"Dinosaurs Across America" and Reading with Pictures

Economics is not a subject that I'm remotely interested in and was even less so when I was an eighth grade history student. But why do I remember it so well even to this day? The teacher taught it to us using a comic book. This simply underscores my belief that having fun in class and delivering concepts to students in a way that they enjoy and are interested in makes for some serious learning opportunities. To that end I highly recommend Reading with Pictures (thanks to our reader Mat for bringing it to our attention)-check it out and see if there is something there your students might enjoy learning from.

Remember learning Geography in the old way with lots of those window-shade roll-up maps and memorization? If I could have learned this way I think I would have enjoyed it and it would have stuck with me. Take a look.


Geography, like many subjects, can be boring, fraught with the nasty notion that simply memorizing states and capitals constitutes learning. Phil Yeh, while presenting basic information about each state, also gives the reader a look into other aspects of the state, such as human interaction with the place, as well as history about the music, art, or technology that has shaped each state. There is even a little story to go along with the information to help the reader move along. It is a good thing.
We can forget, sometimes, that nonfiction has a special allure for some children. My wife is one of those who does not enjoy reading fiction. When I got DINOSAURS ACROSS AMERICA in the classroom, she commented that, as a child, this book would have been one of her favorites in the comic category. She was one of those children who enjoyed geography, including the memorization of states and capitals. Children like her need comics like this.
The pages are split in half with two states appearing on each page. The illustrations are colorful and include not only an outline of the state and major cities, but also includes art that is distinctive to the state.

My Rating: All Ages
All Ages Reads: No Rating
Comics in the Classroom: No Rating
DINOSAURS ACROSS AMERICA is the perfect place for children to begin to study geography, which is more than just memorizing the states and their capitals. The study of geography also includes the place, human interaction, movement and regions. Phil Yeh does a good job with presenting aspects of these major geographic themes throughout his book. For instance we learn that W.C. Handy, the father of The Blues, lived in Memphis, Tenn. We also discover that Nebraska was referred to as a desert until humans started irrigating. Students could discover how that irrigation transformed Nebraska into the state it is.
AUTHOR: Phil Yeh
PUBLISHER: Nantier Beall Minoustchine
GENRE: Nonfiction
FORMAT: Hardback
PAGES: 32 pages
COLOR: Full color
ISBN-10: 1-56163-509-X
ISBN-13: 978-1-56163-509-2
Highly Recommended
Students need excellent nonfiction resources when studying all kinds of subjects, and DINOSAURS ACROSS AMERICA meets that need perfectly. Geared for elementary students, it is the go-to book when students begin to look at a place within the United States. It belongs on the classroom and school library shelf.

Five Easy Drama Games for the Early Elementary Classroom from ArtsEdge

So many of the teachers who take our courses are hungry for quick and easy drama games to help engage students, enliven the classroom and help to teach that day's lessons. Here are five from ArtsEdge that are worth trying. Have fun!

Adjective Monster

Learning grammar the traditional way can be a mind-numbing experience to say the least; this lesson called Adjective Monster from the ArtsEdge/Kennedy Center website is anything but! Here's the summary from their site; this one is definitely worth a try.

"This lesson explores the connections between visual art and language arts, and how both are used to creatively tell stories and express emotions. Students will read the book Go Away Big Green Monster by Ed Emberley. They will be introduced to adjectives as descriptive words then create their own monsters using paper sculpture techniques."