Educational Change … Making “It” Happen

Posted on October 29, 2010. Filed under: Math Education Philosophy, Math Education Researcher, Math Teacher Educator | Tags: , , , , , , , , |

October 29, 2010

by Carol V. Livingston, PhD

In ancient Greece, there were severe penalties for introducing non-existent laws during court, as alluded to in Socrates’ trial (Jowett, 1973).  That had to have been an interesting trial … kinda like those patent medicines that claimed to cure all ills but they really don’t.  Today, there are certainly fewer snake oil salesmen than there used to be, however the same cannot be said for the interpretation and implementation of educational research.  Now, notice I did not say educational research.  I said the interpretation and implementation of educational research … there’s a big difference there … like the awkward things internet translators do to foreign languages at times.  If you think about it, that’s how we got into trouble with New Math in the 1960s, Back to Basics in the 1970s, the “New” New Math in the 1980s, and then yet another round of Back to Basics in the 1990s.  Some things are great in theory.  But like putting a bookshelf together without reading the directions (or even understanding them), unexpected things can happen when you have good intentions.

All research does not need to occur by some boring person wearing a white coat while working in a lab.  And research doesn’t have to be interpreted by experts.  If you recall Martin Luther’s 95 Thesis, the first schism with the “one true” Christian church came about because those in charge of the church at the time had set themselves apart from the average practitioner of the faith.  They purt’much told the average Joe, “You, my fine fellow, are totally incapable of reading and interpreting the Bible.”

Likewise, in our schools, the way that educational research is interpreted happens in no standard way, but that may be due to change with current federal mandates concerning research-based and data-driven instruction that is a result of the No Child Left Behind act (NCLB … I used to joke that the letters stood for No Conductor Leading the Band … heheh).  However, the time may soon come when ignorance concerning the body of educational research will no longer offer a reprieve to the classroom practitioner.  A minimum level of research prowess on the part of key educational decision makers, such as classroom teachers, is clearly needed.  Teacher research in the classroom, called “Action Research,” has been proposed as a way for individual educators to analyze, reflect, and construct explanations for the instructional practices they use.

What is Meant by Action Research?

Some researchers credit John Dewey (1859-1952), Kurt Lewin (1890-1947), and Jean Piaget (1896-1980) as founding the approach to learning while doing.  All three were able to provide both qualitative and quantitative results to place their philosophies on a firm scientific foundation on which others could build.  Dewey offered the process of inquiry and reflection, Lewin offered a method, and Piaget offered small doable tasks that a teacher could perform in the classroom.

Throughout his long life and vast amount of writing, Dewey emphasized learning through doing and experiencing.  He explored the role of thinking and reflecting as they shaped a person’s conceptions and generalizations.  Dewey was convinced that thought stemmed from interactions with the environment in much the same way that Charles Darwin believed that organisms evolved as a result of what they are surrounded by.  Dewey did extensive studies on the processes of inquiry and reflection as organisms experience problematic situations, and then go on to propose and implement solutions for that problem.  He considered non-reflective activities to be habits, rather than purposeful choices (Boydston, 1976).  However, he wrote from the perspective of the child learning by doing rather than proposing the teacher use inquiry and reflection as a process to effect change within the classroom.

The concept of action researchers can be traced back to the work of Lewin while at the Research Center for Group Dynamics at Massachusetts Institute of Technology.  Lewin discovered through his field research that learning occurs best when there is a conflict between a person’s immediate concrete experience and their reflective analysis.  His learning cycle consisted of a perpetual passage from formation of abstract concepts and generalizations, to testing the implications of those concepts in new situations, to having the concrete experience, to personal observations and reflections, and then reforming concepts for personal meaning (Kolb, 1976). 

Lewin gained renown for his field theory, whereby human behavior is a function of the person and the environment.  In other words, behavior is related to both one’s personal characteristics and the specific social situation in which one is found.  It was the innovation in methodology introduced and researched by Lewin that led to the formation of the discipline of group dynamics and action research.  Lewin had a conception of what is now known as experiential learning, whereby if a person truly wants to understand something, be the one who tries to change it (Miettinen, 2000).  The idea was that by participating in the change process, a better understanding could be gleaned of various underlying group dynamics, which are difficult to express in explanation, for instance, intuition.  Lewin introduced the notion that groups were hesitant to change beliefs unless those beliefs were tested.  However, at that time, teacher groups were not perceived as being hesitant to change.

Piaget spent years studying his own children and the children of others with one goal in mind: how does knowledge grow?  His answer was that knowledge could be shown to progress constructively from structures that were embedded personally, but it was not necessary for it to be generalized logically to everyone.  Those same structures might be replaced as higher and more powerful thought processes were brought into use.  Piaget was able to show that the thinking of a child during defined developmental levels was very different from the thinking of a mature adult.  He devised a series of small tasks, along with offering explanations of what he perceived to be developmental levels, as a way of inviting educators to actively experience what his research had shown him that children were capable of understanding (Inhelder & Piaget, 1958, & Piaget, 1965).  He very nearly told the world: if you do not believe me, try repeating my outlined tasks and then compare your results with mine (Kamii, 1989 & 2000).  His journal-style of writings would be valuable resources for qualitative and quantitative lived experiences (Van Manen, 1990).

These four steps:  inquiry, reflection, a methodology, and small doable tasks — just the recipe for a teacher as researcher since most traditional educational research is limited in its usefulness for classroom teachers.  As traditional educational research is cost prohibitive and time invasive for a classroom teacher, it is doubtful that many of them feel a part of the current reform movement (National Council of Teachers of Mathematics, 2000), perhaps caught in a riptide would be a more adequate description.  Unfortunately, the findings of university level research often appear to speak in tongues, so it is no wonder that the average, non-specialized classroom teacher avoids approaching the body of research to develop any personally hypothesized conclusions about best practices.  To define what is meant by action research, I defer to the eloquence of Max Van Manen. 

Pedagogical situations are completely unique, and the “research method is only a way of investigating certain kinds of questions” (p. 1, Van Manen, 1990).  The actual questions raised, the method used to divine an answer, and the way the researcher comes to understand them creates a tripodal arrangement that will also be unique.  In other words, what might be concluded by one person, could be the discarded hypothesis of another.  Study within the human dimension is necessarily phenomenological; after all, intervention through a specific action is a repeatable process, but only via replacement of the samples, subjects, or situation.  According to Van Manen, many outstanding scholars were left to learn epistemological methods by process of “osmosis or apprenticeship” (p. 2, Van Manen).  Usually only the most talented researchers succeeded, and the others, who may have gone on to become dedicated scholarly researchers, were left behind.

Rather than merely having a refined technique, and technique being able to be programmed into inanimate objects much more consistently anyway, experiencing the human phenomenon of the curious researcher requires actually being that curious researcher (Van Manen, 1990).  And curiosity is an odd and useful thing. It is not merely a human invention, for other animals also exhibit an engaging curiosity.  What seems to separate Homo sapiens from all others is their ability to use their curiosity, along with the curiosity of others, as a tool for change.  And this is where a connection is made with classroom action research. 

The process of action research allows the teacher to have full control in selecting specific areas of focus.  For instance, suppose a teacher wishes to determine whether certain cooperative group strategies are affecting student outcome.  By way of example, Mills presented a vignette concerning unmotivated students and group work.  The teacher has been informed, through certain official channels, that working in cooperative groups improved study skills.  The lived experience of the teacher was tending to show otherwise, so the teacher collected data through surveys, interviews, and attendance records (Mills, 2000). 

Upon analyzing the data, this teacher determined that the unmotivated students revealed peer pressures within the cooperative group tended to create situations where they fed off one another’s lack of motivation. The teacher made a decision o either discontinue the practice or group students in other ways in the future (Mills, 2000).  In this case, it seems like this may be a case of adolescent herd mentality, which is perhaps more prevalent in the teenage population than adults find acceptable.  However, informal findings of this type confirm Piaget’s theory that children really do think differently than adults (Inhelder & Piaget, 1958, Kamii 1989 & 2000), and it throws a shadow on the generalization that cooperative groups always result in improved student achievement (Linchevski & Kutscher, 1998).  And in the long run, it seems better for the teacher to have had the lived experience necessary to become a better action researcher (Van Manen, 1990).

The Pros and Cons of Action Research

Rather than relying on the generalizations of absentee researchers, many teachers feel a responsibility to act upon their specific school, class, or student.  While traditional research has tended to be difficult to understand quantitative works, action research is qualitative in that it readily describes what happens and attempts to come to terms with the effect that an identified educational intervention is having (Mills, 2000, Sweeney & Tobin, 2000, & Van Manen, 1990).  The use of journal writing is often indicated in lieu of scholarly tomes or burdensome quantitative statistical results.  The idea of strengthening teacher judgment, with a resultant self-directed improvement in educational practice, under girds the philosophy of action research (Ruddock & Hopkins, 1985).  As a lived experience, personally working through the process of action research unravels a lot of undue speculation over suggested interventions, or as in the case of Socrates, divulges non-existent rules for what works best in each unique situation.

Action research is a practical way of conducting inquiries without the stress of becoming burdened with philosophical issues (Mills, 2000).  Its methods, no matter who authors the process, show an amazing consistency of simplicity (Edwards & Hensien, 1999, George, Craven, Williams-Myer, & Bonnick, 2003, Johnson, 1993, Kemmis, 1993, Mills, 2000, & Sweeney & Tobin, 2000); what happens is the researcher asks a question about an intervention, reads what is available on the subject, puts the intervention into practice, and then observes and reflects upon what happens in order to make decisions about future use of the intervention.  It can be as simple as a good teacher informally examining the effects of teaching on learning or it can be a valuable systematic, formal presentation (Mills, 2000).  To be frank, many teacher-authored action research reports have been published.

While most of the literature on action research is positive, there are certainly aspects of the “politics of research” (p. 17, David, 2002) that bear consideration.   One of the pitfalls of educational innovation, such as action research, is a supervisory mandated approach that begins at the top and works its way down to the classroom teacher.  Research has shown that a professional development approach, where teachers are made to perform certain tasks with no clear understanding of their critical advantage or are not offered ongoing support, do not have lasting effects (Knight, 2000, Pehkonen, & Törner, 1999, Sanders, 1999, & Scott, 1994).  On occasion, certain attributes of the intervention are even misapplied (Anderson, Reder & Simon, 2000). Action research should not be looked on as a cure all for a school’s educational woes, and teachers should not be made to feel that they are left to bear the brunt of coercion to find better ways of performing mandated tasks. 

For instance, the very nature of the identification process for learning disabilities now creates an onerous amount of intervention and documentation on the part of the regular classroom teacher, who may know very little about what researchers in the field of special education are doing (Boudah & Weiss, 2003, & Education for all Handicapped Children Act, 1990).  Before a special education teacher can interview a student, regular classroom teachers must provide documentation of the perceived disability and evidence showing a lengthy period of failed interventions.

Action research is meant for those with a healthy curiosity and those who wish to improve their practice, not as a legally culpable diagnostic tool.  The subtle threat of subrogation, should a child be misidentified, is real.  In my opinion, using action research in this way creates a misapplication of the process, considering that in this state only 4.9% of teachers can be expected to have attained the educational level which requires research training (Alabama State Department of Education, 2002).  To continue to encourage promising practices among educators to realize good results requires teacher training and the availability of additional materials such as easily accessible academic research.  Demands, for which there are no guarantees that the methods used are being applied correctly, can only undermine the improvement process.

A Stand For Action Research

In the end, all teachers make decisions daily about whether certain instructional strategies work for them and will be useful in their classrooms (Boudah & Weiss, 2003, Edwards & Hensien, 1999, George, Craven, Williams-Myer, & Bonnick, 2003, Johnson, 1993, & Kemmis, 1993).  Rather than feeling a sense of detachment from the research community, action research allows teachers to feel a sense of commitment to a greater community with whom they share goals (David, 2002).  Once a teacher becomes familiar with the process of action research, it is fairly easy to accommodate it into one’s daily activities (Mills, 2000).  It does not necessarily involve groundbreaking innovations, but it does create a thoughtful practitioner who is flexible and actively involved in educational reform efforts (Sweeney & Tobin, 2000).

The qualitative nature of action research can add to studies of patterns and trends in education (Sweeney & Tobin, 2000).  From a phenomenological viewpoint, action research, with the published field notes produced by it, have the power to intervene in many more individual cases than is possible by laboratory trials alone, even if those notes fail to appear the highest of brow publications.  Educational practices can change if the suggested practice is lived, and if informed, reflective decisions are consistently made (Mills, 2000, & Van Manen, 1990).  Learning by experiment should not occur solely among students.  By modeling the experiential process and its product, teachers can help students to possess the concept that if someone truly wants to understand a thing, try to change it (Miettinen, 2000).  Many advances in mathematics and science came about for the simple reason that someone thought of another way of doing or explaining something.

Teacher researchers who personally explore the relationship between classroom learning, student understanding, and achievement assessments through action research are able to make informed decisions with regard to information that filters down both as university findings that are accompanied by a review of literature and commercial findings which often are not.  Most published scholarly research involves student participation and achievement rather than how effective teachers became the way they are (Gutierrez, 2002).  From Dewey’s philosophy and Lewin’s learning cycle, the conclusion can be made that master teachers must be forming abstract concepts and generalizations, then testing their implications and analyzing the concrete experience with regard to observation, reflection, and intuition (Boydston, 1976 & Kolb, 1976).  And, from the Piagetian school, teachers who have a knack for recognizing when optimal learning moments slip quietly into their classrooms surely must spend a significant amount of time actively observing children.

Education is perhaps the most discussed and criticized system for which people have high expectations.  Given the sheer number of individuals involved, remaining in touch with all of the advances in pedagogical issues is troublesome, since there are often value judgments attached to academic papers.  It can’t simply be an issue of disseminating the information or passing along mandates.  Action research can be useful in recording changes and documenting critically made reflections.  Although it is not a highly sophisticated method, action research is effective in producing immediate feedback.  For some issues regarding time or insight, other resources may need to be employed.  However, the written or spoken word that can be preserved via this phenomenological approach offers possibilities.

In 1827, a little known Scottish botanist was investigating grains of pollen using a microscope.  In order to view the small particles better, he placed them in a drop of distilled water.  To his amazement, they danced randomly around.  At first he thought they might be alive, but further investigations with 100-year-old pollen and other small particles revealed that all particles, if small enough, could be shown to move randomly about in water regardless of how still the water was.  Robert Brown could not come up with a rational reason for why the pollen grains moved as they did and nor could anyone else at the time.  He described the phenomenon in some journals and it became known as Brownian motion.  In 1905, an obscure clerk working in a Swiss patent office at last had the insight to make sense of Brown’s odd observations (Chown, 1968). 

One of the four papers written by Albert Einstein during 1905 contained the explanation that Brown’s humbly recorded observation offered proof for the existence of atoms; Einstein derived a mathematical explanation for the phenomenon.  So you see, recorded observations, whether they have rational conclusions or not, contain the descriptive power of words in a way numbers cannot.  Whereas laws must be justified, observations need only be witnessed.  Action research allows classroom teachers to come to their own conclusions based upon their own observations.

REFERENCES

Alabama State Department of Education. (2002). State board of education school report
card for 2001-2002: Highest college degree held by teachers. Retrieved on March 28, 2003 from http://www.alsde.edu/ReportCards/2002/058/0580005.pdf

Anderson, J. R., Reder, L. M., & Simon, H. A. (2000). Applications and misapplications
of cognitive psychology to mathematics education. Retrieved on January 9, 2003 from http://act-r.psy.cmu.edu/papers/misapplied.html

Boudah, D. J., & Weiss, M. P. (2003). Looking for good ideas: A guide for teachers to
interpret experimental/intervention research reports. Council for Learning Disabilities. Retrieved on July 26, 2003 from http://www.cldinternational.org/c/@JjylKgyEj.GZY/Pages/scienceP4.html

Boydston, J. A. (Ed.). (1976). The influence of Darwin on philosophy: The middle works
of John Dewey. Carbondale: Southern Illinois University Press.

Chown, M. (1968). The magic furnace: The search for the origins of atoms. New York:
Oxford University Press.

David, M. (2002). Problems of participation: The limits of action research. International
Journal of Social Research Methods: Theory and Practice, 5(1), 11-17.

Education for all Handicapped Children Act of 1975, Pub. L. No. 94-142, § 6, xxx Stat.
xxx (1990).

Edwards, T. G., & Hensien, S. M. (1999). Changing instructional practice through action
research. Journal of Mathematics Teacher Education, 2, 187-206).

George, N. A., Craven, M., Williams-Myers, C., & Bonnick, P. (2003). Using action
research to enhance teaching and learning at the University of Technoloty, Jamaica. Assessment & Evaluation in Higher Education, 28(3), 239-250.

Gutierrez, R. (2002). Enabling the practice of mathematics teachers in context: Toward a
new equity research agenda. Mathematical Thinking and Learning, 4(2&3), 145-187.

Inhelder, B., & Piaget, J. (1958). The growth of logical thinking from childhood to
adolescence: An essay on the construction of formal operational structures. USA: Basic Books.

Johnson, B. (1993). Teacher-as-researcher. (ERIC Document Reproduction Service No.
ED355205)

Jowett, B., Tran. (1973). The Republic and other works by Plato. New York: Anchor.

Kamii, C. (1989). Young children continue to reinvent arithmetic. New York: Teachers
College Press.

Kamii, C. (2000). Young children reinvent arithmetic. New York: Teachers College
Press.

Kemmis, S. (1993). Action research and social movement: A challenge for policy
research. Education Policy Analysis Archives, 1(1). Retrieved on July 28, 2003 from http://epaa.asu.edu/epaa/v1n1.html

Knight, J. (2000). Another damn thing we’ve got to do: Teacher perceptions of
professional development.  Paper presented at the annual meeting of the American Educational Research Association, New Orleans, LA. (ERIC Document Reproduction Service No. ED444969)

Kolb, D. (1976) The learning style inventory: Technical manual. Boston: McBer.

Linchevski, L., & Kutscher, B. (1998). Tell me wit who you’re learning, and I’ll tell you
how much you’ve learned: Mixed-ability versus same-ability grouping in mathematics. Journal for Research in Mathematics Education, 29(5), 533-555.

Miettinen, R. (2000). The concept of experiential learning and John Dewey’s theory of
reflective thought and action. International Journal of Lifelong Education, 19(1), 54-72.

Mills, G. E. (2000). Action research: A guide for the teacher researcher. Upper Saddle
River, NJ: Merrill.

National Council of Teachers of Mathematics. (2000). Principles and standards for
school mathematics. Reston, VA: Author.

Pehkonen, E., & Törner, G. (1999). Teachers’ professional development: What are the
key change factors for mathematics teachers? European Journal of Teacher Education 22(2/3), 259-275.

Piaget, J. (1965). The child’s conception of number. New York: Norton.

Ruddock, J., & Hopkins, D. (Eds). (1985). Research as a basis for teaching: Readings
from the work of Lawrence Stenhouse. Portsmouth, VA: Heinmann Educational Books.

Sanders, R. (1999). Exploring obstacles to educational reform: Observations from
Finding a Way. Professional Geographer, 51(4), 578-585.

Scott, F. B. (1994). Integrating curriculum implementation and staff development.
Clearing House, 67(3), 1-6.

Sweeney, A. E., & Tobin, K. (Eds). (2000). Language, discourse, and learning in
science: Improving professional practice through action research. Tallahassee, FL: Southeast Eisenhower Regional Consortium for mathematics and science education.

Van Manen, M. (1990). Researching lived experience: Human science for an action
sensitive pedagogy. New York: State University of New York Press.

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Common Core State Standards for Mathematics

Posted on October 25, 2010. Filed under: What I'm Reading ... | Tags: , , , , , , |

October 25, 2010

If I had a dollar for every time someone has said to me, “I’m not any good at math,” I would be a richmathteacher instead of a goodmathteacher.  Usually, when someone tells me they are not good at math, I smile and say, “That’s because you didn’t have ME for a teacher!” 

When I say stuff like that, I really mean it.  Mathematics is not something you are either good or bad at, like swimming.  I mean, everyone can swim … we’re just not all equal in style or talent.  Mathematics is something you’ve either had a chance to come to understand or not.  And I truly think that for many people, they are never offered that chance.  They get hustled down the hallways and up the grades rather energetically and end up leaving school believing that the essence of mathematics is a bewildering array of algorithms which are not necessary to understand.  Go ahead and titilate them with a nekkid math problem if you must, but don’t you dare cloak the gist of a problem with … gasp … words.

Well, this ole miss has been up and down the street and around the block for quite a while now in the business of being either a math student, a math teacher or a math teacher educator.  When I said in an earlier blog that there seem to be variables in classrooms that are incredibly enduring and that make educational change problematic, I wasn’t just whistling dixie.

With the coming of the Common Core State Standards (CCSS)  Initiative, we’re about to throw ourselves wholeheartedly into a big ol’ can of educational change.  Actually, if you think of math education as being some sort of magic potion, what is being initiated is not so much a change as it is a distillation … the ingredients have been out there all along; we’re trying now to improve the quality of the brew. 

I’ve attended several presentations on the CCSS for Mathematics, since many states including mine have adopted them for use in our K-12 schools.  Much of the conversation so far has been about how do they match up with the curriculum framework we currently have in place.   So far I am intrigued by three things, towit

  1. They managed to get enough consensus to create common state standards at all.  This is not only intriguing, it is purt’near a miracle.
  2. The high school curriculum stands a purt’good chance of being unraveled from its historical alternating layers of Algebra I, Geometry, Algebra II, Trigonometry and reknit into a garment with a more vibrant texture.
  3. Somebody thought enough of the NCTM‘s Process Standards and Goals for Mathematical Proficiency to invite them to the party.

The next few years should be an interesting ride.  The diagram below is from a graphic organizer I made to hand out in my classes.  PS stands for Process Standard.  GMP stands for Goal for Mathematical Proficiency.  Problem Solving is in the middle because, as I always tell my students,  it is the “mother” of all process standards … if you start with problem solving, all the others will naturally arise from it!

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