Central Bucks Schools Teaching Authentic Mathematics in the 21st Century


Data Analysis Step One: Description



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Data Analysis Step One: Description

Like the scrap-booker who looked through every picture that was developed to get a sense of what she had before she began her book, action researchers begin data analysis by reading through their entire data set, with no other objective than to get a descriptive sense of what they have collected. They might complete the description step by talking it through with another member of their action research community, they might do this in written form, or they might choose a combined approach and take detailed notes as they talk. The following questions guide this step in the data analysis process:

What did I see as I inquired?

What was happening?

What are my initial insights into the data?

Data Analysis Step Two: Sense-Making

After the scrap-booker looked through each picture initially, her next step was to create and play with different groupings of her photos to find a sensible way to represent them in her book. Similarly, action researchers begin the sense-making step by reading their data and asking questions such as, "What sorts of things are happening in my data?" "What do I notice?" "How might different pieces of my data fit together?" and "What pieces of my data stand out from the rest?" To answer these questions, action researchers may take notes in the margins of their data or may physically cut data apart and place the evidence in discrete piles or categories. Organizing data is one of the most creative parts of the sense-making process.

Sometimes inquirers get stuck at this stage and need some prompts to help begin this sense-making process. Table 1 offers some organizing units that serve as prompts for helping teachers begin analysis (Dana & Yendol-Silva, 2003).

Table 1: Examples of Organizing Units



Examples of Organizing Units




Chronology

Key Events

Various Settings

People

Processes

Behaviors

Issues

Relationships

Groups

Styles

Changes

Meanings

Practices

Strategies

Episodes

Encounters

Roles

Feelings

For example, teachers might look at their data and see if a story emerges that takes a chronological form. Teachers may notice that their data seems to be organizing itself around key events. Or, teachers may see some combination of organizing units that are helpful. This table is by no means exhaustive, and they should let the organizing units emerge from their own data rather than forcing an external set of units.

Based on answers to the questions posed above and a teacher's emerging units of analysis, action researchers identify common themes or patterns. Next, they begin a process of grouping or sorting data by theme or category, a process likened to the woman's initial sorting of her Australia pictures by "stops on the travel itinerary." One way to group data is to use a different color marker for each theme or pattern identified, and highlight all excerpts from the data that fit this theme or pattern. Another way of grouping data might be to physically cut it apart and place the data in different piles. Before scrap-bookers cut apart their photographs, they often make a second set and keep these filed with the negatives, in case they make a mistake or decide to use the same picture in a different way. For this reason, if teachers do decide to cut the data apart, it is suggested that they keep a complete set of data as a back-up.

Just as the scrap-booker found some pictures from her daughter's fourth birthday, as teachers engage in sense-making, they will notice that not all of the data they collected will be highlighted/coded or will fit with their developing patterns or themes. These diverging data excerpts should be acknowledged and explained if possible (i.e., "Those pictures must have been at the start of our first role of film and don't really belong.") Likewise, just as the scrap-booker realized she had no photographs of the Aboriginal Cultural Park and would need to find the brochure to add to her photographs, teacher researchers may find that they need to collect additional data to inform an emerging pattern. Finally, like the scrap-booker who decided to regroup some pictures into new piles called "Family Stays" and "Assorted Candids" as teacher researchers' findings emerge, they may regroup, rename, expand, or condense the original ways they grouped their data.

Data Analysis Step Three: Interpretation

Just as the scrapbook teacher invited her student to create her first page by writing a statement that expressed the meaning of a group of pictures held for her, in step three of the data analysis process for the action researcher, patterns or themes yield statements about what a teacher researcher learned and what the learning means. Action researchers often construct these statements by looking at the patterns that were coded, and then ask and answer questions such as:



What was my initial wondering and how do these patterns inform it?
What is happening in each pattern and across patterns?
How is what is happening connected to . . .

  1. my teaching?

  2. my students?

  3. the subject matter and my curriculum?

  4. my classroom/school context?

The findings from this step can be illustrated by the action researcher in a number of ways including but not limited to: themes, patterns, categories, metaphors, simile, claims/assertions, typologies, and vignettes (Dana & Yendol-Silva, 2003). Table 2 provides a definition of these possible illustrative techniques as well as examples.

Strategies for Illustrating Findings

  1. Themes/Patterns/Categories/Labels/Naming- A composite of traits or features; a topic for discourse or discussion; a specifically defined division; a descriptive term; set apart from others.
    Example: Collaboration, Ownership, Care, Growth

  2. Metaphors- A term that is transferred from the object it ordinarily represents to an object it represents only by implicit comparison or analogy.
    Example: "The Illustrator," "The Translator," "The Reporter," "The Guide," "Casting the Play"

  3. Simile- Two unlike things are compared often in a phrase introduced by "like" or "as."
    Example: "Music as a motivator," "Music as a confidence builder," "Music as a Context for making meaningful connections," "Writing as Conversation"

  4. Claims/Assertions- A statement of fact or assertion of truth.
    Example: Inappropriate expectations discouraged many of the learners in my classroom and hindered my effectiveness as a writing teacher.

  5. Typologies- A systematic classification of types.
    Example: Different uses for puppets- instructional, entertainment, therapeutic

  6. Vignettes- A brief descriptive literary sketch.
    Example: "The Struggle for Power; Who is in Control"
    The children were engaged in conversation at the meetings, jobs were continuing to get done, but there was still a struggle centering around who was in control. With the way the class decided to make a list of jobs, break the jobs up into groups, choose the people they wanted to work with, there were breaks in communication. Conflicts were arising with the groups. Everyone was mostly aiming to get "their own" way.


These strategies help illustrate, organize, and communicate inquiry findings to an audience. Once teacher researchers have outlined their organizing strategy, they will need to identify the data that supports each finding presented in the outline. Excerpts from these data sources will be used as evidence for their claims.

Data Analysis Step Four: Implications

The scrap-booker created one final page of her book entitled, "Home Sweet Home," that shared the overall impressions of the family's Australia excursion. Similarly, when action researchers complete the first three steps of the data analysis process, they ask and answer one last set of implication questions as follows:



  1. What have I learned about myself as a teacher?

  2. What have I learned about my students?

  3. What have I learned about the larger context of schools and schooling?

  4. What are the implications of what I have learned for my teaching?

  5. What changes might I make to my practice?

  6. What new wonderings do I have?

These questions call for teacher researchers to interpret what they have learned, to take action for change based on their study, and to generate new questions. For, unlike the scrap-booker who can marvel at her completed book, the scrapbook for an action researcher is never quite finished, even after intensive analysis. Hubbard & Power (1999) note that "Good research analyses raise more questions than they answer" (p. 117). While teachers may never be able to marvel at a perfected, polished, definitive set of findings based on the data analysis from one particular inquiry, they can marvel at the enormity of what they have learned through engaging in the process, and the power it holds for transforming both their identity as a teacher as well as their teaching practice. Cochran-Smith and Lytle (2001) propose that:

. . . a legitimate and essential purpose of professional development is the development of an inquiry stance on teaching that is critical and transformative, a stance linked not only to high standards for the learning of all students but also to social change and social justice and to the individual and collective growth of teachers (p. 46).

As a result of data analysis, teachers can marvel at the growth and the impact they can have as an individual teacher who has joined a larger community of teacher researchers. Through engagement in action research as a member of this community, they are contributing to the transformation of the teaching profession!

Further information and illustrations of the four step data analysis process for action researchers can be found in The Reflective Educator's Guide to Classroom Research (2003), by Nancy Fichtman Dana and Diane Yendol-Silva.



Article References

Beyer, T. (2007, April). Reading habits of high school seniors. Paper presented at the third annual University of Florida Teaching, Inquiry, and Innovation Showcase, Gainesville, Fl.

Cochran-Smith, M. & Lytle, S. L. (2001). Beyond certainty: Taking an inquiry stance on practice. In Lieberman, A. & Miller, L. (Eds.). Teachers caught in the action: Professional development that matters. New York: Teachers College Press, pp. 45-58.

Dana, N. F. & Silva, D. Y. (2001). Student teachers as researchers: Developing an inquiry stance towards teaching. In J. D. Rainer & E. M. Guyton (Eds.) Research on the Effects of Teacher Education on Teacher Performance, 91-104, Iowa: Kendall/Hunt Publishing Company.

Dana, N.F., & Yendol-Silva, D. (2003). The reflective educator's guide to classroom research: Learning to teach and teaching to learn through practitioner inquiry. Thousand Oaks, California: Corwin Press.

Glaser, B. (1978). Theoretical Sensitivity: Advances in the methodology of grounded theory. Mill Valley, CA: Sociology Press.

Hubbard, R.S., & Power, B.M. (1993). The art of classroom inquiry: A handbook for teacher researchers. Portsmouth, NH: Heinemann.

Hubbard, R.S., & Power, B.M. (1999). Living the questions: A guide for teacher researchers. York, Maine: Stenhouse Publishers.

Schwandt, T. A. (1997). Qualitative Inquiry: A Dictionary of Terms. Thousand Oaks, California: SAGE PUBLICATIONS, Inc.

 

© Copyright 2007 Learning Sciences International.


All Rights Reserved.
Job-embedded Activity: Assessment Data Collection

In this activity you will create a data collection chart similar to the sample provided. You will use the chart to identify and collect the necessary assessment data based on the previously identified action research question.



  1. On the following pages locate and review the "Assessment Data Collection Chart" and template.

  2. Using the template provided, create a similar chart based upon your personal action research inquiry identified in the previous activity. This chart will include the information needed to answer the question, and the data collection strategies that will generate this information.

  3. Based upon your chart, begin collecting your classroom data.

  4. Answer the following questions:

    1. Action research on authentic instruction asks for non-traditional forms of data collection to be represented. Was it difficult to look outside the box and identify non-traditional forms of data?

 

 


    1. Did you ask for assistance from a colleague? If so, please describe how you asked for this assistance.

 

 


    1. Describe your process for selecting non-traditional forms of data for the authentic instruction action research.

 

 


    1. Using multiple sources of data and multiple strategies for collecting data will enhance your inquiry as you gain different perspectives. What forms of non-traditional data did you collect and why did you select them?

 

 


    1. Describe the insight that you gained from gathering non-traditional forms of data. What surprised you or what new ideas were generated?

 

 


    1. What higher order technology-based assessment data could be utilized and considered as non-traditional forms of data? How and where could you incorporate higher order technology into the collection process?

 

 


  1. Summarize your responses in the space provided. Be prepared to add the summary to your Learning Log.

 

 


  1. Enter your summary in your Learning Log by clicking on "Resources" and then "Learning Log." (Label your entry "Assessment Data Collection")

  2. Close the Learning Log window to return to the course.

  3. Return to the course.

Personal Notes for Implementation:
 

 

 



 
Job-embedded Activity: Identify Instructional Needs

The purpose of this exercise is to analyze the data collected in your classroom using the four steps in the Assessment Data Collection Chart. This information will help you identify instructional needs.



  1. Complete the "Assessment Data Collection Chart" as directed in the instructions to work through the data that has been collected.

Assessment Data Collection Chart

The chart is set up with the following specifics:



  • Title of chart is the main inquiry question

  • Left column: What information might help answer the question?

  • Right column: What data collection strategies would generate this information?

Sample: In What Ways Do Socratic Seminars Enhance Student Understandings of (Content) Concepts?

Information that will help me answer my question

Data collection strategies that would generate this information

Knowing how students' conceptual knowledge develops during our unit

Collect students' (content) journals

Knowing what students saying during Socratic Seminar

Audio taping Socratic Seminar

My thinking about what happened during the Socratic Seminar after they occur

Teacher journal

Students opinions about Socratic Seminar

Surveys

Literature on Socratic Seminars and unit concepts

Do a search for other books, articles, or web researches that are connected to Socratic Seminars, unit concepts, and building conceptual knowledge, etc.

 

Learner Template:
Blank Data Collection Chart

The chart is set up with the following specifics:



  • Title of chart is the main inquiry question

  • Left column: What information might help answer the question?

  • Right column: What data collection strategies would generate this information?

Insert Title:




Information that will help me answer my question

Data collection strategies that would generate this information

 

 

 

 

 

 

 

 

 

 

© Copyright 2007 Learning Sciences International.
All Rights Reserved.

  1. Once you have completed the "Assessment Data Collection Chart" answer the following questions:

    1. What was the most challenging aspect of the data analysis process for authentic instruction? How did you overcome the challenges?

 

 


    1. What are some individual student needs based on the data analysis?

 

 


    1. How can higher order technology be utilized more effectively as a result of your findings? (Please refer to the "Range of Instructional Practice" chart and the "Technology: Productivity Use vs. Higher-Level Thinking Use" chart.)

 

 


    1. Is there a correlation between the authentic instruction research findings and the specific characteristics of the 21st Century student? Describe how this will affect your inquiry findings.

 

 


  1. Summarize your responses in the space provided. Be prepared to add the summary to your Learning Log.

 

 


  1. Enter your summary in your Learning Log by clicking on "Resources" and then "Learning Log." (Label your entry "Identify Instructional Needs")

  2. Close the Learning Log window to return to the course.

  3. Return to the course.

Personal Notes for Implementation:
 

 

 



 
Topic 4.1.4: How Do I Plan and Deliver Instruction Based on Individual Student Needs?

Connecting Action Research to Individual Student Needs

Nancy Fichtman Dana


University of Florida

Those outside of the teaching profession sometimes lament that they wished for a "teacher's life." After all, from an outsider's perspective, how difficult could it be to get up in front of a group of kids for 45 minutes and talk about a subject he/she is passionate about? To top that off, teachers end their workday by 3:00 and have the summers off!

Good teachers know that teaching is anything but simple. They have to laugh when they hear their work characterized in such a naive way! To illustrate, let's talk about what it means to be a teacher for a moment. Effective teachers must know their content deeply, know pedagogy, know human development, and know the over one hundred students they interact with each day, including identifying each one of these learners' academic, social, and emotional needs. Teachers must attend to 25 or so of these individuals' needs, all unique and varied, all at the same time during each instructional moment of a class period. Teachers must understand lesson planning, and understand that with every lesson taught, there will be a unique outcome that results from the interaction of the context in which one teaches it, the timing of the teaching, the interaction with the teacher him or herself, and the learners in the room. Teachers must attend to management and transitions of large groups of learners before, during, and after each lesson. Teachers are bombarded with decision making each minute of their day, ranging from deciding the next steps when a planned lesson is not progressing productively to deciding if Johnny, who just asked to use the bathroom for the third time that day, should be given permission to leave the lesson to take care of his personal needs. In addition, teachers must constantly assess their students' learning and progress formally and informally. Teachers make contributions to the management of the school with such duties as collecting field trip money and monitoring bus and lunch times. They must communicate and collaborate with parents and other education professionals such as guidance counselors, the principal, school psychologists, and other teaching colleagues. In their spare time, they serve on committees, attend faculty meetings, and read professional journals and books to keep abreast of the latest developments in their field. They do all of this while simultaneously keeping an eye on high-stakes testing and their students' performance, balancing preparation for test taking, and the teaching of test-taking skills with real teaching and learning of content.

This picture of a teacher's work is by no means complete, yet it is complete enough to illustrate what is meant by the inherently complex nature of teaching. Because teaching is so complex, it begs for a process to help teachers untangle some of the great complexity and gain insights into teaching and learning in a systematic, intentional way. The study of one's own practice is one powerful way to thrive in the complex world in which teachers work.

Elliot (1991) describes teachers' engagement in researching their own practice as a continual set of spirals consisting of reflection and action. Each spiral involves:


  1. Clarifying and diagnosing a practical situation that needs to be improved or a practical problem that needs to be resolved.

  2. Formulating action-strategies to improve the situation or resolve the problem.

  3. Implementing the action strategies and evaluating their effectiveness.

  4. Clarifying the situation resulting in new definitions of problems or of areas for improvement, and so on to the next spiral of reflection and action (p. 163).

The self-study of teacher practice is being actualized in many different ways across the nation including teachers engaging in book study groups, teachers forming professional learning communities using protocols to structure professional conversation, teachers engaging in action research, and teachers engaging in Japanese lesson study (See, for example, Dana & Yendol-Silva, 2003; Wiburg & Brown, 2007; Sammon, 2007). However the self-study of teaching practice is actualized, the ultimate goal is to create an inquiry stance toward teaching.

To achieve this stance, first, teachers acknowledge the inherent complexity of teaching, as illustrated in the opening to this article. Because teaching is so complex, it is natural and normal for teachers to face many problems, issues, tensions, and dilemmas as they practice. Rather than "sweeping the problems under the carpet" and pretending they do not exist, teachers embrace problems by deliberately naming them, making them public, and making a commitment to do something about them.

The first step is to develop a plan to study the problem, issue, tension, or dilemma thoroughly. For example, if teachers wish to gain better insight into teaching high poverty students, they create a plan to meet monthly and read a particular text about children and poverty. They discuss the text in relationship to their own teaching context. Or, if a teacher is concerned about students' abilities to attack word problems in Algebra class, she decides to collect student work over a 6-week time period and chart the growth and development of particular students based on looking at their progress in solving word problems over time.

Once the problem, dilemma, issue, or tension is named and explored, teachers articulate what they learned about practice through the process and develop an action plan for change in their classroom based on what was learned. Finally, teachers share their learning with other colleagues, and the process of inquiry continues.

An inquiry stance actually becomes a professional positioning, owned by the teacher, where questioning one's own practice becomes part of the teacher's work and eventually a part of the teaching culture. By cultivating this inquiry stance toward teaching, teachers play a critical role in enhancing their own professional growth and ultimately, the experience of schooling for children. Thus, an inquiry stance is synonymous with professional growth and provides a non-traditional approach to staff development that can lead to meaningful change (Dana & Yendol-Silva, 2003).

The most important benefactors of taking an inquiry stance towards teaching and actualizing that stance by engaging in action research are the students one teaches. Just as teaching is complex, so is the make-up of each individual student that walks through the classroom door. Each individual student enters with unique life experiences as well as differing social, emotional, and academic needs. Yet, in the ways traditional school structures are set up, individual needs can easily become lost. Through engaging in action research, teachers can generate valuable knowledge about their learners' readiness, interest, learning styles and more! With this knowledge, teachers make adaptations to instruction, increasing the probability that the needs of all learners will be met within one single class period.

For example, through engaging in action research to better understand the reading habits of his high school seniors, Beyer adjusted his summer reading list and built in choice for students to accommodate the vast differences he found in their interests through his research. Through engaging in action research to ascertain better ways to structure chemistry extra help sessions, Steve adjusted his approach to these sessions to accommodate both his general chemistry students who benefited from an enriched repeat version of a lesson on a particular chemistry concept taught during the regular school day, and his honors students who benefited from independently working though more challenging chemistry problems based on the particular concepts to be tested on the upcoming exam. Through engaging in action research to better understand student anxiety associated with the upcoming probability and statistics unit, (Kristin rewrote her lessons that strictly followed the adopted mathematics textbook to introduce the same concepts through studying the upcoming NCAA basketball tournament and the odds of each team reaching the Final Four.

Action research is a wonderful tool teachers can utilize to differentiate instruction, ultimately making schools a better place for all students, regardless of their interests, abilities, background, and learning styles. For, according to Barth (1990), "when teachers observe, examine, question, and reflect on their ideas and develop new practices that lead toward their ideals, students are alive. When teachers stop growing, so do their students (p. 90)." Engaging in action research to reach every individual learner keeps teachers and students alive!




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