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Representing Data

Recently, I read an excerpt of a case study from a fourth grade math classroom.  The researcher, Olivia, was working with the class to figure out a way to represent the number of people in the students’ families.  During this activity, a number of sophisticated questions and concerns arose, demonstrating a high level of cognition on the part of the students.

Among the questions that arose, the children especially grappled with the following:

  • How do we define a question, and why is it necessary to do so?
  • In this particular project, what might be the consequences of allowing everyone count whomever they wanted to?
  • How can we represent the data in a way that can be understood by others?
  • What values needed to be included in our representations?
  • How do we begin to interpret and evaluate this data?
  • What can we tell from the range, measures of typicality, gaps in data, and so forth?
  • How does zero function as a placeholder in numbers vs. representations?
  • How can we convey multiple levels of information in a coherent and concise representation?

The students were able easily use the data collected to answer the question posed.  This was never really questioned.  Rather, the interesting aspect of the investigation came about when the representations opened up the multitude of questions above.  Nothing was necessarily decided during the class time, but the higher-level questions demonstrated that students took the assignment as a jumping off point to grapple with some very advanced questions about data representation.  It demonstrates how authentic activities allow children opportunities for learning that simply cannot exist through rote activities. The ability to let go and give children space to legitimately explore their ideas is not always an easy one, but examples like this demonstrate its effectiveness.

Recently, in my own classroom, we had the students graph their birthdays on a chart.  Some of the ideas above came up for us as well.  For example, the students realized that if they wrote their birthdays on different kinds of paper depending on their sex, we could easily add another level of meaning to our graph.  The fourth-graders in Olivia’s class came to that conclusion as well.   Another thing that came up was the idea of defining our question.  We quickly realized that some of our children do not celebrate their birthday.  Not only that, a few don’t know when their birthday is!  While the question was designed to be one that was meaningful and relevant to all students, we quickly found that our assumption wasn’t necessarily correct.  Thus, we also addressed and tackled with the question, “How do we define a meaningful question and why is it necessary to do so?” much like the students in Olivia’s classroom.

When it came time to evaluate our representation however, our students were struggling.  It seems that they do work to get it done and don’t think much about it after the fact.  We are finding it difficult to get them to really think about their work once the “product” is completed.  For this reason, we never got to some of the other interesting questions shared above.  My hope is that we can begin to do so as the year progresses.

How can teachers facilitate….

QUESTIONING

  • Read a story aloud and give students an index card to jot down questions.  Have students share ideas and compare questions
  • Question Web
  • Color-coded index card

SCHEMA

  • Pick a topic and have students think of three things that come to mind
  • Read Chrysanthemum and talk about Text-Self connections
  • Stress that everyone has their own strengths

MONITORING

  • Have teacher show how she monitors
  • KWL charts
  • Higher-level thinking questions (Ex:  What part of reading are you best at?) to help push kids into metacognition

IMPORTANCE

  • Modeling for the students how to think about the main ideas
  • Graphic organizers
  • Breaking down story writing
  • Class story
  • Class theatre

INFERRING

  • Guided reading
  • Show an image and write about it
  • Read an excerpt and draw a picture of what it means

SENSORY and EMOTIONAL IMAGES

  • Draw a picture and THEN write
  • Read aloud and let students draw what they are hearing as they hear it
  • Emotional and cultural background
  • Cross curricular connections
  • Class skits/plays

SYNTHESIZING (laid out chronologically)

  • Model thinking
  • Discussion
  • Big Ideas (explicit/implicit)
  • Concept Maps
  • Graphic organizer
  • Background knowledge
  • Revisit text/lesson
  • Ordering key points of texts/writing
  • Summary: finished product

Why did I become a teacher?

It may come as a surprise that I did not always want to go into education.  Most teachers (or teaching candidates) that I have met seem to have known since childhood that education was their calling.  I, on the other hand, believed wholeheartedly that teaching was droll, domestic, and suburban.  I was incredibly wrong.

Growing up as the oldest child, I was always fiercely independent.  There was a great exciting world out there, and I was determined to investigate every inch of it.  When my parents dropped me off at kindergarten for the first time, the tears shed were not my own.  I jumped at any chance for adventure, and was reading at a fifth-grade level by the end of first grade.  Books allowed me to experience the world in a way that no six-year old possibly could.  I was the child huddled in a corner, hiding in a closet, or sitting in a tree with one book in her hand and another in her pocket ready-to-go.  Though exciting for me, it did not bode well for my social life, and I had difficulty relating and interacting with my peers.

As I matured into a young adult, a longtime infatuation with ballet turned serious.  I was accepted into numerous summer internships and intensive programs and was dancing year-round at the Pittsburgh Ballet Theatre while still in high school.  My family remained in Michigan, meaning that I was living 350 miles away from my parents at the age of 17.  I loved everything about ballet, but the independence that came with it was a definite draw.  Cities, with their teeming streets and pulsing conflicts, feel like home to me, and ballet companies can only exist in areas like these.  There is something about the intensity and control of ballet that juxtaposes itself just so against a careening torrent of that lifestyle, which strikes a perfect, if tenuous, balance.  As exciting as this environment was for me, it is not well suited to children, who need air and space and trees and summer gardens.  I was convinced that children had no place in my life.

As expected, the inevitable fall from grace left me spectacularly stunned and completely confused as to the direction of my life.  A car accident and subsequent injuries made a career in ballet nearly impossible, and suddenly I was enrolling in college with no idea of what to do there.  I chose the most familiar, comfortable thing I knew, and enrolled in English Language and Literature at the University of Michigan.  Here, I found an entirely new world that excited me in ways that I had never expected.  I found that I loved academia, and routinely signed up for 18 credits a semester, because I couldn’t bear to miss out on any of the offerings.  I studied French and Latin, where I learned more about the evolution and intimate workings of language than I had in any English course.  I added a second major of Classical Archaeology.  I became politically active for the first time in my life, and began volunteering for the Detroit Project, a student organization that devoted themselves to low-income areas of Detroit.  During it all, I taught dance classes at a local studio to help cover my expenses and was surprised to discover that I adored children.  More importantly, they seemed to connect with me as well.

It was at the end of my undergraduate career that a career in education became my top priority.  Working at the Detroit Project had opened my eyes to the injustice of social reproduction and had ignited a passion to implement social change.  I thought about joining the Peace Corps, and through that, discovered Teach for America.  I attended meetings, met with advisors, filled out applications, and drafted essays.  I read books by Freire, Delpit, and Kozol, cementing my belief that working in education put you on the front lines in the battle for social justice.  However, before submitting anything, I ran into a friend of mine from high school who was a member of the Teach for America program.  She was overworked, burned out, and going back to school to be a nurse.  I realized that my best chance at success would be though education itself.  I needed theory, facts, and experience on my side before I would be ready to teach in the way that I wanted.

I applied to Michigan State’s Post-BA program in Elementary Education, and have been working on my degree since.  This is my last semester, and I can honestly and wholeheartedly say that this decision was the best one that I could have possibly made.  I have made some wonderful contacts, liaisons, and friends during my time here, and passionately believe that this is my true calling.  While developing my views on critical pedagogy, I began to investigate the role of technology in education, and honestly found it lacking.  I believe that technology perfectly embraces the goals of critical pedagogy, and that it should be an integral part of any critical curriculum.  I applied to MSU’s Master’s Program in Educational Technology and am two-thirds completed at this point in time.  I will be finished in the summer of 2009.

New Year!

Notice the new blog title?  It’s a brand new school year and I’m now a third-grade teaching intern.  I’ve also changed not only schools, but also districts.  The difference couldn’t be more apparent.  The disparity between schools and districts is shocking.  I don’t want to sound critical of my new district, yet the lack of resources and administrative support are disheartening.  Also, as someone working on a Master’s in educational technology, it’s frustrating to be in a school with no technology focus.  This should be a great opportunity, but also a great challange.
My students this year are some of the most interesting I’ve worked with.  Many students come from situations have left them battle-scarred and distrustful.  In spite of this, the are among the most caring, funny, and resiliant kids I’ve ever met.  If I received no other support this year (which I have plenty), the children themselves would be inspiration enough.  If they can come to school from their environments, I can certainly come from mine.

So in short:

  • Third grade
  • Urban district
  • Low-income school

Here we go!

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