Central Bucks Schools Teaching Authentic Mathematics in the 21st Century


Appendix A: Questions for Student Journals



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Appendix A: Questions for Student Journals

  1. Think about how you learn in math class. What is the easiest way for you to learn math—small-group work with your peers? One-on-one explanations with your teacher? Class discussions and explanations by your teacher?

  2. Do you pay attention when we have whole-class discussions?

  3. What helps you or prevents you from paying attention when we review problems as a class?

  4. What changes in the class structure would help you improve in math class?

  5. Compare your class this semester to your class last semester. How are the classes different? Do you find it easier or more difficult to learn this semester? Explain your answer.

  6. With whom should you sit so you can learn most effectively?

Appendix B: Student Interview Questions

  1. In which part of math class do you feel you learn the most, and why? (Class discussion? Group work while teacher circulates? Group presentations? Homework? Tests? Journals?)

  2. About how much time does the teacher spend with you, on average, during every class? Is this enough? How does this compare to your other classes? How does this compare to your previous math classes?

  3. We have X number of students in our class. Would you prefer that size increase, decrease, or stay the same? Explain your answer.

  4. Are you doing better, worse, or the same in math class compared to last semester (and last year)? Can you explain the difference, if there's a difference?

  5. What motivates and/or encourages you to concentrate and think hard during math class?

  6. What helps or prevents you from following class discussions? How could class discussions be restructured to help you get more out of them?

Appendix C: Student Survey

Name (Optional):

CLASS SURVEY QUESTIONS: choose one answer for each question.


  1. The most valuable time during math class is when we:

    1. Review homework problems on the board

    2. Work on our activity guide at our tables while the teacher circulates (moves) from table to table

    3. Work in groups on problems that we then teach to the class as a group

  2. I concentrate most in math class when:

    1. I work independently (by myself)

    2. The teacher explains a problem to the class on the board

    3. I work on a problem with a friend or with my group

    4. The teacher sits next to me and explains a problem

  3. Compared to last semester, my grades in math class are:

    1. Better

    2. Worse

    3. The same

Explain why.

  1. About how much time does the teacher spend with you during math class?

    1. 0-5 minutes

    2. 5-10 minutes

    3. 10-15 minutes

    4. More than 15 minutes

  2. Would you prefer that our math class have:

    1. More students

    2. Fewer students

    3. The same number of students

Explain why.

 

Used with permission of the publisher, Heinemann, a division of Reed Elsevier Inc. Originally appeared as chapter 6 of Taking Action with Teacher Research—Outcomes of Reduced Class Size in High School Math Classrooms, by Natasha Warikoo. ©2003.


Job-embedded Activity: Identifying Instructional Implications

In this activity you will identify the instructional implications from your progress monitoring and post assessment. Just as a scientist works to validate his or her hypothesis, you will identify the implications of your instruction for the purpose of sharing your learning with colleagues in the next step.



  1. Locate the progress monitoring and post assessment data identified in the previous section.

  2. Identify the implications from your instructional adjustments in the "plan and deliver" phase using the following questions:

    1. Was there an increase in student achievement? Discuss the issues and implications.

 

 


    1. Was there a decrease? Discuss the issues and implications.

 

 


    1. What exactly did you learn from the research and what does it mean in terms of your authentic instructional practices? What changes will you make as a result of your findings?

 

 


    1. What would be the most valuable information for your colleagues to know? What would be helpful information to share? What suggestions would you offer colleagues?

 

 


    1. Did you notice any difference with your students when they were actively engaged with higher order technology? (Note: One of the benefits of technology is that generally students are more engaged and motivated when they are allowed to use higher order technology tools.)

 

 


  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 "Identifying Instructional Implications")

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

  3. Return to the course.

Personal Notes for Implementation:
 

 

 



 
Topic 4.1.7: How Can I Collaborate With Peers to Share the Results and What I Learned From my Action Research?

Study Group Protocols for Sharing Action Research

Nancy Fichtman Dana


University of Florida

When action researchers have developed a question, collected data, analyzed data, and written up their work, they near the end of their inquiry journey. Yet, a final, critical step in the process is the sharing of action research with others. To illustrate the importance of sharing their work with others, they should consider the following story about a man and his teen-aged son:



A young man took his thirteen-year old son to the lake. He was looking forward to spending the beautiful spring day making fond memories with his son, who was growing much too quickly for his father's comfort. The weather was perfect — the sun was warm, and the air was fresh with just a little nip of cold remaining from the long winter months. Being it was early spring, they had the entire park to themselves, and not another family was in sight.

The day was going just as he had planned. After the perfect morning canoe trip, they headed to the shore and ate their picnic lunch. After lunch, the man gazed out to the shore, and admired the peaceful, calm lake before him. His thoughts drifted to replaying the wonderful morning he and his son had shared together, and he was feeling quite proud of the all-day excursion he had planned for his son during these delicate teenage years – it couldn't have been going any better. Just then, his thoughts were abruptly interrupted by his child's voice. "Dad, I'm bored."

The man was taken aback – stunned that his son could feel boredom in the face of the beautiful glassy-still lake before them. "How could you be bored, son?" his father queried. "The lake is so beautiful — peaceful and still."

"That's just it, Dad," his son replied. "You might see beauty, but I see stagnation." His son's comment provided a stark reality check for the man – They had sat for too long, and he needed to think quickly to save the perfect day he had planned with his son from spoiling.

"Son," his father said, "I think it's time to put an end to the stagnation. You see all of these rocks along the shore? Have I ever told you I was my town's rock-skipping champion when I was a kid? I can give you a few pointers, and teach you how to skip rocks like nobody's business!"

The teenaged boy looked skeptical, "Aw Dad, I'm too old for that stuff."

"You're never too old to have fun and to learn something new. Now watch me."

The man searched for the perfect rock on the lake shore, and tossed it into the water. It skipped three times before it finally fell to the bottom. Its hops across the water's surface created an interesting pattern of ripples.

While the boy didn't want to admit it, he was impressed. He watched his father throw five more rocks in quick succession — one even skipped four times! He decided since no one was in sight to see him, it would be OK to participate with his father.

They threw for an hour, his father teaching him technique and form to get as many skips as possible out of each rock. As they tossed stone after stone, the clear, stagnant lake became alive with small swells, ridges, and swirls. Some of the ripples even reached the shore of the lake! The man was once again proud of his quick thinking – the stone throwing game had saved the day.

An unshared action research project is like the stones laying on the lake shore that have no chance of impacting the still water unless tossed in by the man and his teen-aged son. An unshared action research project has little chance of changing practice unless that inquiry is tossed into the professional conversation and dialogue that contributes to the knowledge base for teaching. Once tossed in, it disturbs the status quo of educational practices, creating a ripple effect, beginning with the teacher herself, her immediate vicinity (the students and her classroom) and emanating out to a school, a district, a state . . .eventually reaching and contributing to the transformation of the perimeter of all practice — the profession of teaching itself.

Hence, it is critical that action researchers "jump into the lake" and disturb the stagnant waters (Dana & Yendol-Silva, 2003)! For action researchers, the process of preparing findings to share with others helps to clarify action researchers' own thinking about their work. In addition to clarifying their own thinking in the actual sharing of their work, action researchers give other professionals access to their thinking so that they can question, discuss, debate, and relate. This process helps action researchers and their colleagues push and extend their thinking about practice as well.

Clarifying, pushing, and extending thinking are not the only benefits of sharing. Fellow professionals also benefit from the knowledge created through the action research process. For example, veteran teacher researcher, George Dempsie's passion for utilizing puppets as a form of pedagogy with young children led him to study and to publish the results of this practice (Dempsie, 2000; Dempsie, 1997). In his own district, he has inspired puppetry as pedagogy in dozens of teachers, across 11 different elementary buildings. His presentations at conferences and his publications allow his work to spread outside his immediate vicinity (classroom, school, district) as well.

For students, sharing action research with other professionals can change the very ways these students experience schooling. For example, one teacher who completed an action research project focused on an individual second grade child who was having great difficulty fitting into the structure of schooling as it existed socially, but was not receiving any services because she did not qualify in any traditional ways. Her action research illuminated many critical insights into the child that traditional forms of assessment would not have generated. Becoming an advocate for this child, the teacher shared the results of her inquiry with other specialists and the principal. Eventually, a full time paraprofessional was hired to work individually with this child within the regular classroom each school day. In a year's time, the child made great strides in her academic and social development.

These are just two specific examples to illustrate the power, and therefore, necessity of sharing action research. While both of these examples were elementary that same powerful experience is possible for high school levels. Some action research inspires small, local change. Some inspire large, sweeping change. All change, large or small, is significant in that the changes that are occurring are emanating from those best positioned to make a difference in education, and those that for years have been kept from making that difference — teachers themselves!

Kincheloe (1991) writes about the ways teachers have been kept from making that difference using a comparison between teachers and peasants within a Third World culture with hierarchical power structures, scarce resources, and traditional values:

Like their third world counterparts, teachers are preoccupied with daily survival — time for reflection and analysis seems remote and even quite fatuous given the crisis management atmosphere and the immediate attention survival necessitates. In such a climate, those who would suggest that more time and resources be delegated to reflective and growth-inducing pursuits are viewed as impractical visionaries devoid of common sense. Thus, the status quo is perpetuated, the endless cycle of underdevelopment rolls on with its peasant culture of low morale and teachers as 'reactors" to daily emergencies (p. 12).

By getting into the lake and sharing action research, as a teacher, one contributes to breaking the cycle described above and contributes to educational reform:

The plethora of small changes made by critical teacher researchers around the world in individual classrooms may bring about far more authentic educational reform than the grandiose policies formulated in state or national capitals (Kincheloe, 1991, p. 14).

By getting into the lake and sharing the action, a teacher contributes to changing the ways some people outside of teaching view teachers and their practice and tries to change education from the outside – in. In the sharing of action research, one contributes to reforming the profession of teaching . . . from the inside – out!

What are Some Ways for Teachers to Share the Work?

There are many structures in place that offer opportunities for teachers to share action research. If they have written up their work, they have not only clarified their thinking, but they have produced a product that can easily be shared with others in multiple ways. First, they might begin simply by sharing their written work with local colleagues, their principal, or other professionals, asking them for some feedback. This sharing could potentially lead to the formation of a study group to discuss their particular inquiry and related topics. There are a number of text-based protocols developed by the National School Reform Faculty (http://www.harmonyschool.org/nsrf/default.html) that can be adapted to the process of sharing action research within a professional learning community.

Another way to share their written work is to submit it to one of the many journals designed with a teacher researcher audience in mind such as Teacher Research: The Journal of Classroom Inquiry, and Teaching and Learning: The Journal of Naturalistic Inquiry. Finally, they can share their written work on-line by exploring one of the many actions research web sites, listservs, and on-line journals. For example, action research completed by teachers in Florida can be found at http://education.ufl.edu/csi. Other action research websites and journals summarized by Mills (2003) include Educational Action Research at http://www.triangle.co.uk/ear-o.htm, Networks at http://www.oise.utoronto.ca/-ctd/networks/, Action Research International at http://www.scu.edu.au/schools/gcm/ar/ari/arihome.html, Action Research Electronic Reader at http://www2.fhs.usyd.edu.au/arow/o/m01/reader.htm, Participatory Action Research Network (PARnet) at http://www.parnet.org, The Collaborative Action Research Network at www.uea.ac.uk/care/carn, and Centre for Action Research in Professional Practice (CARPP) at www.bath.ac.uk/carpp.

In addition to writing, other mechanisms that give the learning that occurs from action research a form so that it can be shared include the creation of posters, iMovies, and PowerPoint presentations. Many action researchers utilize these mechanisms to share their work orally in informal and more formal ways. Informally, some groups of action researchers organize a gathering outside of the school structure (i.e., an after-school meeting at a coffee shop) to discuss their work. Within the school structure, formal sharing of action research is often accomplished through relegating special portions of faculty meetings to action research or totally reconceptualizing faculty meetings to allow space for the on-going sharing of inquiry (Dana, 1994; 1995). Some districts also devote entire in-service days to teacher inquiry, where colleagues gather and share their work.

Finally, many teacher researchers present their work at conferences. There are numerous national forums that showcase presentations by action researchers. Perhaps the largest and most well known is the American Educational Research Association (AERA). The professionals who engage in action research that are members of this organization assemble together in a Special Interest Group called "Teachers As Researchers."

While becoming a part of a national network such as AERA is a wonderful experience, the reality in almost every school district is that conference travel money for teachers is small or non-existent. Many teachers are limited in support for conference endeavors and must pay out of their own pockets to attend and present. For this reason, the cost of national travel is often prohibitive for many teachers, especially on a yearly basis.

They can still experience the exhilaration that comes from presenting their work formally to an audience by connecting to conferences that occur in their vicinity. Most national organizations such as AERA described above and ASCD (Association for Supervision and Curriculum Development), NCTM (National Council for Teachers of Mathematics), NCSS (National Council for the Social Studies), NSTA (National Science Teachers Association), NCTE (National Council for Teachers of English), and ATE (Association of Teacher Educators) have state affiliates that hold conferences at least once a year. Finally, in addition to the journals dedicated solely to action research described previously, many of these state affiliate organizations also publish journals that offer another outlet for their written work (see, for example, Dana, Gimbert & Silva, 1999).

How action researchers share their work matters much less than the fact that they do share it! Sharing constitutes the final destination in one action research journey. The act of sharing and listening to others share provides a spark to plan and begin the next journey – a new action research project, with new learning and change in store for teachers and their students. Engaging in continual cycles of action research is the ultimate journey all educators embark on. No other author captures the nature of this ultimate journey as eloquently as William Ayers (1989):

Teaching involves a search for meaning in the world. Teaching is a life project, a calling, a vocation that is an organizing center of all other activities. Teaching is past and future as well as present, it is background as well as foreground, it is depth as well as surface. Teaching is pain and humor, joy and anger, dreariness and epiphany. Teaching is world building, it is architecture and design, it is purpose and moral enterprise. Teaching is a way of being in the world that breaks through the boundaries of the traditional job and in the process redefines all life and teaching itself (p. 130).

Through embarking on the action research journey, teachers break boundaries. They redefine life. They redefine teaching itself . . . Bon voyage!

Article References

Ayers, W. (1989). The Good Preschool Teacher: Six Teachers Reflect on Their Lives. New York: Teachers College Press.

Dana, N. F. (1994). Building partnerships to effect educational change: School culture and the finding of teacher voice. In Mary John O'Hair & Sandra J. Odell (Eds.), Partnerships in Education: Teacher Education Yearbook II (pp. 11 – 26). New York: Harcourt Brace College Publishers.

Dana, N.F. (1995). Action research, school change, and the silencing of teacher voice. Action in Teacher Education, 16 (4) 59-70.

Dana, N. F., Gimbert, B., & Silva, D. Y. (1999). Teacher inquiry: Staff development for the 21st century. Pennsylvania Educational Leadership, 18 (2), 6-12.

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.

Dempsie, G. (1997). Using puppets in a primary classroom: A teacher-researcher's findings. Teaching and Learning: The Journal of Natural Inquiry, 11 (3), 5 –13.

Dempsie, G. (2000). Can I love you? A child's adventure with puppets and play. The Journal of the Imagination in Language Learning, 5, 28 – 36.

Kincheloe, J. (1991). Teachers as Researchers: Qualitative Inquiry as a Path to Empowerment. New York: The Falmer Press. 

© Copyright 2007 Learning Sciences International.


All Rights Reserved.
Job-embedded Activity: Sharing with Peers

In this activity you will collaborate with your peers and share with them your action research findings. This can be conducted with a small group of peers who work at your school but are not participating in this course.

For an advanced application, try conducting this activity using online collaboration tools. Consult your technology coordinator for additional help.


  1. Consolidate the information that you gleaned through your authentic instruction focused action research:

    1. What process did you follow?

 

 


    1. What were your key findings?

 

 


    1. What recommendations would you make to your peers to help them enhance their instruction/avoid pitfalls?

 

 


  1. Identify three to six peers who are not taking the course, and the environment where you will meet to share your findings.

    1. Identify the necessary participants.

 

 


    1. Identify and secure the location for you meeting.

 

 


    1. Identify the time for the meeting.

 

 


    1. Produce an informal agenda and communicate the meeting information identified (time, locale, etc.).

 

 


  1. Conduct the meeting and take notes during the meeting in the space provided. Finally, 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 "Sharing with Peers.")

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

  3. Return to the course.

Personal Notes for Implementation:
 

 

 



 



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