Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

download Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

of 147

Transcript of Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    1/147

    JenniferMarkidesCraigDwyerMikeCraig

    UniversityofCalgary,FacultyofEducationMathematicsforTeaching2013

    NURTURINGCOLLECTIVEARTISTRY

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    2/147

    The authors like to sincerely thank all of our professors and advisors who have oriented usthrough the courses we have taken during the last two years. This has been an eye-opening and career changing re-conceptualization for the three of us.

    Thank you to to University of Calgary and our advisor Brent Davis for providing the

    conditions for our collective learning to emerge. Thanks to Lissa D'Amour for taking thetime to know each of us as learners and challenging and perplexing us to re-imagineourselves. Thanks to Moshe Renert for deep friendship, inspiration, encouraging words,and giving us occasion to march to our own beat. Thank you to Anne Watson and JohnMason for helping us to remember what it is like to be mathematical learners. Thanks toElizabeth Mowat for continually pushing and challenging our thinking. Thanks to StevenKhan for a keen editing eye and encouragement. Thanks to our cohort classmates, youabove all are the reason we are here doing what we love, and chasing our own questions.We could not ask for a better group. Special thanks to Amy Tetz and Emily Brown forspeedy emails, kind words, and keen editing eyes.

    Craig - To my family, Hiromi and Tabito, for support and giving me time and space to think,write and sleep. You make my world richer and our wanderings together are justbeginning. You inspire me to be the best I can possibly be, and even when I am not, youstill love and supportive me.

    Mike - To my wonderful family for their never ending encouragement, love and support. Tomy better half Travis for standing beside me throughout the writing of this and making sureI always had balance. To my friends Brian, Cheryl and Heidi for being ears and soundingboards. And to Theresa, who first pointed me at the world of complexity. I am trulyfortunate to be part of this collective.

    Jennifer - To Derek, my husband, for the rich and engaging discussions outside of class.You managed to push my thinking while supporting me on our journey through thisprogram together. To our boys, Ashwin and Evren, for forgiving us the class time andbeing good for the babysitters. And to our family and friends who were always willing topitch in on days we presented or had assignments coming due. It took a village.

    ACKNOWLEDGEMENTS

    2

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    3/147

    CHAPTER1An Introduction toNurturing Collective ArtistryMichael Craig, Jennifer Markides, and Craig Dwyer

    At any moment in the classroom, there are a multitude of factors at play in the

    teaching, learning and knowing of mathematics. We, as educators, are charged with the

    responsibility of creating lessons that will set up the best conditions for students learning.

    As Einstein (date unknown) famously said, I never teach my pupils. I only attempt to

    provide the conditions in which they can learn.

    Some lessons in life, like tying ones shoes, can be modeled and practiced until the

    skill is learned. Other concepts are more complicated and even abstract, yet the goal of

    teaching remains the same - to provide experiences that will support the development of

    knowledge. We have an array of sources to draw from when determining how we are

    going to teach: personal experiences, teacher preparatory classes, educational philosophy

    courses, mentors and colleagues to name a few. Often, we have great autonomy in

    deciding how we prepare a lesson and we also possess the authority to change course as

    we see fit. With great power, comes great responsibility - Voltaire (Beuchot, 1940).

    Throughout the course of our careers, it is important that we do not lose sight of the

    earnest pursuits that our jobs entail. We must strive for better practice while accepting that

    3

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    4/147

    this goal is and will always be a moving target. There appears to be no one right way to

    teach mathematics; however we learn from sharing, research, stories, and experiences, in

    the hopes of gaining insight to the possibilities of better teaching practices.

    Through our collective efforts, we are attempting to learn both with and from each

    other. Our experiences and learnings inform our understandings and knowledge of

    teaching. While many paths have led us to this point, we have some common goals and

    shared beliefs about teaching. Our individual convictions have coalesced in the writing of

    Nurturing Collective Artistry. Independently and co-implicitly within the complex

    interconnective web of relationships, each of the words carries with it a host of

    associations and entailments, metaphors, diverse perspectives, and a plentitude of

    possibilities.

    Mapping this in a linear progression of scholarly articles seems problematic.

    Instead, we would like to invoke the image of a network. Each term will be explored by

    three different individuals with different histories and styles. They will be presented

    sequentially. However, this sequential presentation is a function of the human senses.

    What we hope to imagine in this collection of articles is a network of connections. We

    hope to see how three very different people with diverse interests can occasion a network

    of thoughts that illuminate the whole.

    To begin, picture if you will, a network comprised of nodes interconnected in a web

    of associations. For the purposes of this paper, we will focus on five nodes essential to

    our current discussion. We will each represent one of three nodes: nurturing, collective,

    and artistry through a written exploration. We will represent the nodes as they situate in

    the world around us. As conscious beings personifying each node, we connect with and

    affect the world around us. To take ourselves out of this network, we feel, would lead to

    detachment and a lack of authenticity. Also, picture the node at the centre of the research

    questions surrounding Mathematics for Teaching, and another node representing

    4

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    5/147

    Complexity in Education. We are, the three of us, embedded in these research questions,

    and informed by complexity as a framework for education (Davis, 2008).

    It is the interplay and dynamic exchange of these five nodes that has led us to a

    guiding question: If a Profound Understanding of Emergent Mathematics and an open way

    of being are at the root of the mathematics that teachers need to know, then how might

    that knowledge be enacted within a classroom? One answer to this question that we

    propose and explore is the idea ofnurturing collective artistry.

    Each of us intends to explore this answer of sorts by taking on the voice and

    perspective of one of the aspects of the answer. In a recursive manner, we will then

    respond to each paper in the voice of that perspective, exploring each others spaces from

    the perspective of our own. Finally, we will loop back again and reflect on the reflections,

    making further connections in the vast network.

    As a final step, we hope to write, with a collective voice, what our thoughts and

    feelings of the entire process have been. In this way we hope, not to provide a reductive

    or definitive answer to the rich complexity of Mathematics for Teaching but instead to

    further elaborate the field. We hope to open this space and see what emerges, and in

    which directions the field evolves.

    We begin however, by examining the five nodes, their networks of associations and

    the affordances they entail.

    Node one: the evolution of the M4T question

    In continuing to draw on the metaphor of a network of relationships, the node

    which could be said to represent the domain of mathematics-for-teaching could also

    represent an evolving network or system; fractal in nature, self-similar and scale-

    independent. From a historical perspective, it might appear to be a linear progression of

    causality moving from one idea to another, albeit with minor trails and tracks diverging

    from it, ultimately leading to the juncture where we situate ourselves now and yet along5

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    6/147

    that path the domain of mathematics-for-teaching itself has been questioned, re-

    interpreted, and transformed by significant ideas encountered along the way. In this way,

    the evolution of the domain is both linear and emergent.

    Begel, 1979: A Surprising Discovery

    The evolution of the mathematics-for-teaching question began with a landmark

    study by Begel in 1979. Prior to this point it seemed to be taken for granted that it is

    important for a teacher to have a thorough understanding of the subject matter being

    taught (Begel, 1979, p. 28). In this study, which was primarily focused on a the question

    of how to determine teacher effectiveness, Begel concluded that while it "is widely

    believed that the more a teacher knows about his subject matter, the more effective he will

    be as a teacher, [the] empirical literature suggestthat once a teacher reaches a certain

    level of understanding of the subject matter, then further understanding contributes nothing

    to student achievement (p. 51). This would prove to be significant for two reasons.

    The first was that prior to this point, teacher preparation and training was based

    on ensuring that the teacher knew as much as possible about their subject matter. This

    was based on the assumption that all an effective teacher needed to know to teach

    mathematics was more advanced mathematics. The second significant finding was a lack

    of any definitive answer as to what did constitute effective teaching. As a result, Begel

    argued, we are left simply with the conclusion that "the effects of a teachers subject

    matter knowledge and attitudes on student learning seem to be far less powerful that most

    of us had realized (Begel, 1979, p. 54). We are also left with the question: What

    mathematics do teachers need to know to teach mathematics?

    6

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    7/147

    Shulman, 1986: Content, Pedagogical Content, and Curricular Knowledge

    A significant perspective in answering this question would come from Shulman in

    1986. Shulman began to draw a distinction between the mathematical content and

    general pedagogical knowledge required by teachers (Shulman, 1986). He suggested that

    there were three kinds of knowledge required by teachers: Content Knowledge, the

    amount and organization of knowledge per se in the mind of the teacher (p.9);

    Pedagogical Content Knowledge (PCK) which goes beyond knowledge of the subject

    matter per se to the dimension of the subject matter knowledge for teaching (p.9); and

    Curricular Knowledge, a broad category encompassing programs, materials, and the

    relative benefits and disadvantages of the use of any curriculum, techniques or program

    materials based on the given situations (p.10). In the third, Shulman also noted a

    necessity to be aware of both the lateral and vertical aspects of curriculum knowledge;

    understanding the full scope and sequence within a particular discipline and the

    connections between other content knowledge at the same level.

    As a result, Shulman suggested that effective teacher preparation would entail

    propositional knowledge, case knowledge and strategic knowledge (Shulman, 1986). The

    teacher is not only a master of procedure but also of content and rationale, and capable of

    explaining why something is done (p.12). As for the determination of teacher

    effectiveness, this would be provided in the form of assessment by members of the

    profession, not legislators or laypersons (p.12).

    Liping Ma, 1999: Profound Understanding of Fundamental Mathematics

    Shulmans framework would seem to have sufficed as an answer to the question

    for over a decade until Liping Ma, a researcher in China, conducted a study comparing the

    effectiveness of teachers in both the United States and China. According to Ma, the

    teachers from the United States, despite having the pedagogical knowledge suggested by

    7

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    8/147

    Shulman, were less effective than their Chinese counterparts. Additionally, she states that

    a teachers comprehensive knowledge of a topic may contribute to students opportunities

    to learn it, (Ma, 1999, p.52) and that even "their pedagogical knowledge could not make

    up for their ignorance of the concept (p.60). Ma would go on to describe a model for the

    knowledge required by teachers of mathematics as a "deep, vast, and thorough

    understanding" (p.104).

    Coining the term aprofound understanding of fundamental mathematics (PUFM),

    Ma suggested that this could be accomplished through the study of teaching materials,

    learning from colleagues, learning from students, and learning by doing (Ma, 1999). She

    emphasized that this understanding would entail the Connectedness, Multiple

    Perspectives, Basic Ideas, and Longitudinal Coherence of mathematical content (Ma,

    1999), the last being comparable to Shulman's sense of vertical curricular knowledge. For

    Ma, PUFM was "the awareness of the conceptual structure and basic attitudes of

    mathematics inherent in elementary mathematics and the ability to provide a foundation for

    that conceptual structure and instill those basic attitudes in students (p.135). Up to this

    point, the mathematics that teachers needed to know seemed to align closely with the

    discipline of mathematics and mathematicians.

    Ball and Bass, 2003: Unpacking

    In 2003, Ball and Bass introduced a different perspective. They observed the

    compression of knowledge that accompanies increasingly advanced mathematical

    work (Ball & Bass, 2003, p. 3), and postulated that this compression was opposite in

    nature to the work teachers engage in as they deconstruct mathematical understandings

    for the process of teaching.

    Ball and Basss research focused on the work that teachers do and how that work

    demanded mathematical reasoning, insight, understanding and skill (Ball & Bass, 2003,

    8

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    9/147

    p. 5). They suggested that it was not sufficient for teacher to be able to solve

    mathematical problems but in fact required them to inspect alternative methods, examine

    their mathematical structure and principles, and to judge whether or not they can be

    generalized (p. 7). The key feature of their research was the unpacking of mathematical

    knowledge. Teachers work with mathematics as it is being learned, which requires a kind

    of decompression, or unpacking, of ideas (p. 11) and connecting those ideas across

    mathematical domains at a given level, and across time as mathematical ideas develop

    and extend (p. 11).

    Davis and Simmt, 2003: Established and Emergent

    It was at the same time that Davis and Simmt brought a radical new sensibility to

    the mathematics-for-teaching question when they drew explicit attention to a different

    metaphoric model for mathematical knowledge and learning based on complexity science.

    For Davis and Simmt, individual understanding could be seen as enfolded in and

    unfolding from the broader phenomenon of collective dynamics (Davis & Simmt, 2003, p.

    296). The body of knowledge associated with formal or established mathematics became

    inexorably intertwined with the process by which that mathematical understanding became

    established.

    Davis and Simmt saw an interconnectedness between Mathematical Objects and

    Curriculum Structures, both of which they viewed primarily as categories of knowledge

    which were generally seen as established, and Classroom Collectivity and Subjective

    Understanding, which they viewed as categories of knowing and as evolving, changing or

    emergent (Davis & Simmt, 2003). Ultimately, Davis and Simmt suggested that

    mathematical knowing is rooted in our biological structure, framed by bodily experiences,

    elaborated within social interactions, enabled by cultural tools, and part of an ever-

    unfolding conversation of humans and the biosphere (p.315).

    9

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    10/147

    Renert and Davis, 2010: An Integral Reinterpretation

    Later, Renert and Davis would reinterpret the question of mathematics-for-

    teaching through an integral framework, leaving us with an answer that is generous,

    challenging, provocative, and complex.

    [Mathematical knowledge for teaching] is an open way of being

    with mathematics in different educational contexts. What is called

    for is a broad awareness of the dynamic evolutionary tensions that

    are at play during each pedagogical encounter with mathematics.

    MfT at the integral wave must include a willingness to live in

    these tensions dialogically, not privileging either one of their dual

    ends. Living in dynamic evolutionary tensions also requires

    teachers to be open to the many perspectives through which

    pedagogical occasions may be engaged and interpreted. (Renert

    & Davis, 2010, p.22).

    Renert and Davis (2012) also introduce an extension of Mas PUFM, suggesting

    a Profound Understanding of Emergent Mathematics (PUEM) that also accounts for

    enacted realizations and complex processes within mathematical knowledge. They

    discuss a dynamic process of concept study, where groups of diverse teachers unpack

    their previous understanding of mathematical concepts, and re-imagine those conceptions

    in terms of their situated place. Concept study is an attitude towards learning and

    teaching (that) ..... is simultaneously inquiries in how individuals learn mathematics, how

    mathematics is taught, and how disciplinary mathematics arises (Davis, 2008, pg. 90).

    Node two: complexity as a relevant dialogue for mathematics education

    Learning is a hard thing to define. The definition of learning is inextricably linked to

    the definition of knowing. Over the last several thousand years, our conceptions of10

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    11/147

    learning and knowing have evolved in much the same way as our cultural and social

    institutions and human values have. From the learning as out there waiting to be foundof

    the ancient Greeks, to learning as an entity of drawing minds into the tenets of centralized

    authority(i.e. the church), our perception of learning in the 21st century is taking on a

    more ecological, and a more networked understanding. It is easy to understand why these

    values have emerged in a time of great ecological change and the rapid technological

    networking of human intelligence.

    If you were giving a speech to a group of educators, and you started with the line;

    learning is a complex phenomenon you would get almost unanimous nods of approval.

    We may collectively agree with it, but what does it mean? If learning is complex, how do

    we think about it? Admitting that something is complex is only the first step. Now, we

    need a way to study and frame that complexity.

    The emerging field of complexity science, and the researchers that are applying

    Systems Thinking to the field of learning, offer a different way view that question; if

    learning is complex, and complex systems learn, then complex systems are learning

    systems (Davis, 2010).

    Emergence of complexity as a dialogue for education

    Complexity emerged as a coherent theory first out of the biological and ecological

    sciences and according to Davis and Simmt (2003) it is defined more in terms of the

    objects of its study than its modes of investigation (p. 137). It grew to encompass many

    of the social sciences including economics, political science, and psychology and is now

    being seriously considered for it application in the study of learning systems. Indeed,

    complexity now includes any phenomenon that might be described as a living

    system (Davis & Simmt, 2003, p. 138). The key elements to be considered are that the

    system must be adaptive, able to change its own structure and as such is better

    11

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    12/147

    described in terms of Darwinian evolution than Newtonian mechanics (Davis & Simmt,

    2003, p. 138) and emergent, composed of and arises in the co-implicated activities of

    individual agents (Davis & Simmt, 2003, p. 138).

    (Mathematical) Learning as a Complex Adaptive System

    Moving from the idea that complex systems are systems that learn (Davis,

    Sumara & Luce-Kapler, 2008, p. 78), Davis and Simmt co-implicate a nested sensibility

    and suggest that mathematics learning environments are complex systems and could be

    viewed through a complexity lens. This does not however negate previous theories

    associated with constructivism, nor does it deny that there may be a Kantian objectively

    real noumenal realm (Campbell, 2002, p. 428). Rather, these are perspectives on

    something that we cannot truly define or explain due to the complexity associated with

    learning but also hold true in their descriptions of particular phenomenon. Additionally, the

    simultaneity of various learning theories, such as radical and social constructivism, are not

    problematic in a complexity lens as complexity science explicitly rejects any attempt to

    collapse such phenomenon into instances, variations, or elaborations of the same

    thing (Davis & Simmt, 2003, p. 142).

    And finally, complexity does not discount that some learning phenomenon might be

    best described in Newtonian mechanics, and as such, those artifacts of classroom culture

    associated with such a pedagogical view may have a role to play, however it does make

    the distinction that these situations would be ones best described as simple systems,

    determinate and tend[ing] to involve only a few interacting objects or variables (Davis &

    Simmt, 2003, p. 139). These might include routines such as fire drill procedures and

    library book exchange. But in the learning of mathematics, many events and systems

    emerge in the interactions of agents that are themselves dynamic and adaptive (Davis &

    12

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    13/147

    Simmt, 2003, p. 139) and as such this is where a complexity approach may be more

    appropriate.

    Davis and Simmt (2003) go on to identify five common features of complex

    systems. These are internal diversity, which may be described as a systems ability to

    respond to a variety of external and internal circumstances; redundancy, commonalities

    between agents in a system that allows for communication and accommodates for system

    stressors; decentralized control, where decision-making is shared by the system with no

    specific centralized agency; organized randomness, a dynamic balance between system

    diversity and redundancy; and neighbor interactions, the ability of agents in the system to

    come into contact and communicate, exchange with, and affect each other.

    Davis and Simmt (2003) go further to demonstrate that while these features are

    useful in describing the mathematics classroom as a complex learning system, they can

    also be employed in a proscriptive fashion to create complex environments where

    emergent mathematical learning may occur.

    Node three: Jennifer, Nurturing

    In Montessori education, we teach from the big picture and draw on history,

    geography and culture to ground the students learning in real world examples. It is

    important to know what has come before us to give insight as to where we are going next.

    Significantly, we are encouraged to recognize and appreciate the contributions made by

    the generations that came before us, with an emphasis on finding our own way to

    contribute to the betterment of the Earth.

    On my path to becoming a teacher, I had a practicum in a lower elementary

    Montessori classroom, within the public school system in Prince George, British Columbia.

    It was so different from a traditional classroom; it took me quite a while to wrap my head

    around the teachers role. With a lot of support and guidance from my mentor teacher, I

    learned that I could relinquish some of my power (control) as a teacher and share certain13

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    14/147

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    15/147

    In the summer of 2009, my first son was born and I chose to remain away from

    teaching for the 2009-2010 school year. Upon my return in September 2010, I found that

    the climate of our school had changed. There was a new uncertainty about how we

    should be teaching, especially in the area of mathematics. Although the new math

    curriculum had been unfolding before I had gone on leave, I was informed by the

    administration that I had missed out on a lot of change in my year away. This comment

    troubled me deeply: How much could have possibly changed in a year? Was my teaching

    practice that out of date? Was I off base even before my leave?

    I found the 2010-2011 school year to be very tumultuous for me, questioning

    everything about my teaching practice and resenting the doubt that had been cast on the

    things I had held most dear: Montessori lessons and problem solving work. To this point I

    had been proud of my math program. Montessori lessons were personalized and taught to

    individuals or small groups and the problem solving questions provided a framework for

    multiple strategies and peer collaboration. Now all of this was to be thrown out the

    proverbial window.

    Our administrators strongly discouraged teachers doing several common practices

    such as, a) giving lessons on how to use materials in specific ways, even if the Montessori

    material was designed to support concept development in singular areas, b) giving the

    same questions to a large number of the students, even if you deemed them grade-level

    appropriate or useful for review, and c) assigning questions that had definitive answers

    (considered not to be real problems). They were not appropriate, even for practice.

    Teachers were made to feel inadequate, with little support in finding new ways to teach

    math.

    I understand that change can be difficult, but I could not understand why everything

    had to be changed all at once? Why was I so opposed to the change? Was everything I

    had been doing wrong? Should I conform to the change without question? Was it new

    15

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    16/147

    school board policy? Was 2009-2010 a groundbreaking year in mathematics education

    research? Where could I learn more about the research and reasoning that brought about

    the new math?

    I had more questions than answers. My frustration finally gave way to resolve; I

    saw three options: quit and look for a career that pays more, anticipating less or different

    politics and bureaucracy; stay and accept what was being passed down from above, at the

    risk of becoming complacent; or seek out and engage in opportunities to become informed

    about current research and beliefs about mathematics education, arming myself for

    debates about my own beliefs and practices. Inspired by the writings of Ghandi (1913), I

    had to become the change I wished to see in the world.

    Fortunately, the Mathematics-for-Teaching program offered at the University of

    Calgary afforded me this opportunity: to study the philosophies in mathematics education,

    to examine the developments in practice and to collaborate with other like-minded

    individuals passionate about teaching mathematics. Perhaps the latter is the most

    important, orienting me to the potentialities of collective learning engagements.

    As I became acquainted with the history and research in M4T, I was intrigued by the

    growth and change in mindsets surrounding teacher knowledge of mathematics.

    Immersed in my practice, I have sometimes found it difficult to articulate exactly what it

    was that I am doing well and what I need to change. Perhaps because I enjoy math, I

    have had an easy time moving between metaphors and understanding differing

    perspectives. Using Montessori materials to support concept development at multiple

    entry points, I have been able to introduce materials suited to each students readiness

    and context of understanding. This way of teaching has been for me organic in a sense -

    natural; through the study of M4T, I have come to see that this is part of the PCK utilized in

    teaching.

    16

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    17/147

    Recently, Renert and Davis (2010) re-defined the movement of Mathematics for

    Teaching:

    MfT, when understood as an open way of being, asks teachers to always remain

    curious about mathematics and the ways in which it connects to human

    experience. The career of a mathematics teacher offers a path of growth and

    deepening through encounters with new perspectives and the ongoing process of

    harmonizing evolutionary tensions. (p. 23)

    This message resonates with my personal journey and quest for knowledge within

    the framework of MfT.

    A lot of my personal positioning involves folding back from what I know now to what

    brought me to this point. My understanding of the past is inextricably connected with the

    learnings I have experienced in this program. Earnestly, I began my teaching career with

    abounding optimism for the difference I could make in the world through education. The

    push from my administration put my system of understanding of what mathematics

    education should look like into a place of disequilibrium. In order to re-orient myself as a

    teacher, I fell back on my love of learning, re-engaged in the pursuits of knowing and

    renewed my confidence in teaching. Once again, I find myself looking for the joy in each

    situation and celebrating the many successes of the students. I draw on my

    understanding of nurture to inform my practice towards educating the whole child and

    maintain a long term goal of arming them with skills, strategies and self-awareness that

    may help them to be successful in life.

    Node four: Craig, Collective

    Sasano-sensei (teachers in Japan are referred to by their family name and the

    marker sensei, which means teacher) was the grade 3 shunin (team leader) at a very large

    elementary school in Takasaki, about an hour and a half north of Tokyo by train. The

    school itself had about 1500 students from Grade 1 to Grade 6. My role was the Assistant17

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    18/147

    Language Teacher, which is a fancy title for the token english speaker. I worked at six

    different schools and I would spend a week or two at each of them, and then move on.

    Needless to say, it was hard to remember any of my students names.

    During one of my many meetings with the staff at Sano Elementary School,

    Sasano-sensei posed the challenge of making the lessons more interactive and fun. He

    gave me a blank slate to provide the kids with an experience they would not forget. Over

    the next several weeks, we worked closely together planning a real marketplace in the

    schools gymnasium where the kids could use math, English and basic conversational skills

    to complete a shopping list. Sasano-sensei and I bounced ideas back and forth, and we

    became of one mind. We could read each other, and anticipate what the other was

    expecting.

    The experience was an astounding success and opened my eyes to teaching as a

    profession. At the same time, it showed me that teaching could be a profoundly creative

    act. It was also a profession that relied on the interactions between others in the system.

    There was no idea that was not influenced by others.

    I was hooked. I became a teacher.

    As usually happens in Japanese schools, Sasano-sensei moved on to a new post

    (Japanese teachers usually stay at a given school for 3-7 years). I found myself craving

    that creative blank slate where my imagination could run wild. It was also around this time

    that I became interested in ecology, ecological philosophy, and zen buddhism. Reading

    David Suzuki, Rachel Carson, Fritjof Capra, Thich Nhat Hanh, and EF Schumacher, I

    became increasingly curious about the connections that abound in and to the world around

    me.

    I got married. Had a child. Left Japan.

    Deciding to get my Bachelor of Education at the University of Toronto was a big

    change that brought with it a new direction in my life. For the first time I felt as if I was

    18

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    19/147

    doing what I wanted to do it. I was challenged and I was able to make connections to the

    topics I was curious about, to the process of learning. For the first time in my life, I felt that

    I possessed creative characteristics. I felt I had found my element.

    It was at OISE that I was first introduced to complexity science as a lens for viewing

    learning. Although, at the time, I dismissed it as too abstract and disconnected from the

    real world of a classroom. I was barely keeping my head above water with the

    coursework, having an infant, and being back in a country that now seemed so foreign to

    me. In true recursive nature, it would return to me.

    After OISE, I found myself back in Japan, working at a small international school in

    a rural village, teaching the children of physicists at an EU nuclear fusion research site.

    Again, my thoughts came back to Capra and his systems thinking. I began to integrate the

    core principles of ecological thinking into my learning program (crudely and without

    direction I must add). I wanted to set about a paradigm shift in the perceived purpose of

    education. Using the systems thinking guiding principles set forth by the Center for

    Ecoliteracy (an institute founded by Capra) and their core ecological concepts;

    Guiding Principles(shifts in perspective)

    Core Ecological Concepts

    Parts to wholeObjects to relationshipsObjective knowledge to conceptualQuantity to qualityStructure to processContents to pattern

    NetworksNested SystemsCyclesFlowsDevelopmentDynamic Balance

    adapted from Center for Eco-Literacy, 2011

    Using this as my guiding philosophy, I set about to create an experiential, inquiry

    based program that was grounded in a sense of place, both in regards to an internal self,

    and through our local environment. That ended on March 11th 2011, as a 9.0 magnitude

    earthquake struck the East coast of Japan (where I was living) and a chain of events

    started that eventually led to me finding a new school.

    19

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    20/147

    Before the 3.11 earthquake, however, I was also introduced to the work of Kath

    Murdoch, an inquiry learning consultant based out of Australia. She led us through some

    very powerful activities that changed the way I viewed learning and teaching. After her

    workshop, I found myself searching for a M.Ed degree, and serendipitously ended up at

    the University of Calgary, where I was introduced to the work of Brent Davis, and

    Complexity in Education.

    It was at this point that many emergent lines came together. My curiosity about

    ecology and systems thinking, my previous experience and dismissal of complexity, and

    my craving for authentic, creative teaching. I find it intriguing that all these nodes in the

    network of my journey as a learner and a teacher, that I find myself back where I started,

    and researching what got me into teaching in the first place. All those years ago working

    with Sasano-sensei, I was introduced to the notion that teaching and learning can be acts

    of creativity which are accessed through collective interactions. At the time I do not think I

    understood why, but the prospect ofdoing itexcited me. Now, I hope to peel back another

    layer and start to explore the howand why.

    Node five: Mike, Artistry

    I began my teaching practice over eight years ago. Having studied, under Dr.

    David Jardine, a particular pedagogical interpretation of inquiry-based learning, I was

    comfortable with the ideas of unpacking the essential understandings related to big

    concepts or questions and subsequent integration of curriculum into tasks designed to

    explore those understandings. I took on my first position as an elementary generalist,

    teaching grade six at a charter school. As part of that assignment, I was tasked with the

    responsibility of interpreting the mathematics curriculum and planning the mathematical

    tasks, inquiries and assessments for myself and the other three members of my team.

    Given that my academic background to this point focused on drama and English language

    arts, I found myself quickly trying to make sense of both the content and pedagogical20

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    21/147

    knowledge required, using metaphors of mathematics as both a language and an art form

    to support and structure my mathematical activities and sensibilities - metaphors that I

    continue to use this day when working with peers and colleagues.

    A chance conversation with Dr. Sharon Friesen that year, introduced me to a world

    of mathematical disciplines beyond the Euclidian geometry and algebraic numeracy that

    dominated the Alberta curriculum. Working with the Centre for Gifted Education over the

    next four years, I began to explore disciplines such as game theory, cryptography,

    combinatorics, fractal geometry, logic, network theory, chaos theory, and complexity

    mathematics. Each of these I would unpack and explore alongside gifted elementary

    students, further developing my own

    understanding of mathematics.

    At the same time, I was also introduced to

    the work of Dr. Rocky Rohwedder and the six

    core principles of ecoliteracy: networks, nested

    systems, cycles, flows, development and

    dynamic balance (Centre for Ecoliteracy, 2011).

    These principles would eventually form a core

    component in my emerging interests in complexity

    science and later complexity as a metaphor for mathematics education.

    It was during my first year as a grade six teacher however that I began to recognize

    in my students a fear and dislike of mathematics, despite my best efforts to engage them

    in relevant, meaningful, and creative tasks. I wondered if this general dislike towards

    mathematics was due in part to potentially negative experiences early in their academic

    lives. At the end of the year, I made the decision to move to the Calgary Board of

    Education where I could work with students in early elementary, an option not available to

    me in the charter school. For the next three years, I worked with grade one and two

    adapted from Center for Eco-Literacy, 2011

    21

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    22/147

    students, trying to develop not only their mathematical capacity but also the passion for

    and confidence in mathematics that I found lacking in my previous students. Continuing

    my work with inquiry-based practice, I consistently strove to integrate mathematics with

    both science and humanity studies. It was during this time that I was introduced to the

    work of Dr. Brent Davis in complexity theory as it relates to mathematical education. At

    this point, my efforts as a mathematics autodidact redoubled as I began to unpack the

    metaphor of complexity and how it related to my work as an educator.

    Three years later I left my position as a teacher to take on a one-year assignment

    with one of the Calgary Board of Education Alberta Initiative for School Improvement

    teams. In that role I worked with five other educators as part of a mathematics response

    team, going into area schools that were requesting support in mathematical pedagogy and

    practice, particularly in light of a new Alberta curriculum of studies in mathematics. Initially,

    my work with the team required a deep investigation into the scope and sequence of the

    new curriculum in addition to debate and discussion around some of the key

    understandings with which it was associated.

    Being the only member of the team with division one experience, I found myself in

    great demand. I began working with teachers in over 15 schools, collaborating on

    mathematical projects, unpacking curriculum, and developing programs and resources for

    early elementary education. Through this process, I had the opportunity to work with both

    new and master educators, often engaging in informal deconstructions of mathematical

    concepts. In my role I often worked as a conduit between educators in different

    classrooms, and often different schools, sharing pedagogy and practice while allowing

    those to influence the development of my own.

    At the end of that year, I joined the leadership team at an elementary school in

    northeast Calgary whose mission and vision included inquiry-based learning, Reggio

    Emilia principles inspired practice, and arts-centered instruction. Brought on board to

    22

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    23/147

    further develop their mandate around inquiry learning, I was additionally tasked with

    professional development and support with mathematics instruction, often integrating it

    with a fine and performing arts curriculum. This, in addition to the high percentage of

    English Language Learners in the school community, added further levels of complexity to

    mathematics instruction, providing me with many opportunities to deepen my

    understanding of content knowledge in relationship to other disciplines.

    All the while, on a personal level, I had been exploring a parallel journey in

    spirituality, seeking enlightenment and personal fulfillment through a study of various world

    religions. Moving from traditional Christianity to pagan traditions in Shamanism and Wicca

    to the eastern philosophy of Buddhism, I finally discovered Taoism, the principles of which

    no doubt have contributed to my emerging interests in integral theory and complexity, in

    addition to raising questions around the ethnography of mathematics in both western and

    eastern cultures.

    While it appears self-evident now, each of these experiences represent co-operant

    forces in my emerging interests in mathematics for teaching research and my interest in

    the artistryof mathematics, mathematics curriculum, and mathematics teaching. However,

    despite the illusion of a linear progression from that point in the past to where I stand, I

    recognize that it is more of an evolution out of complexity rather than a series of cause and

    effect relationships and it is this meta-awareness of both the linear nature and the

    emergent phenomenon that give rise to my current research interests.

    The Emergences

    It is here that we now find ourselves, in the space of the interplay between these

    five nodes specifically and in the broader domain of mathematics education. It is here that

    we begin to recognize significant emergences in the form of domains for new study.

    23

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    24/147

    Situating ourselves in educational literature while grounded in classroom teaching,

    we recognize the tensions between educational theory and practice. In the Masters of

    Teaching program at the University of Calgary, we have developed and reinterpreted our

    own beliefs about mathematics education by engaging in relevant coursework, thought-

    provoking readings, and rich discussions - all facilitated by professors at the forefront of

    mathematics education research. The M4T question of what mathematics do teachers

    need to know has evolved to what mathematics do teachers already know, how do

    individuals learn mathematics, how is mathematics taught, and how does mathematics

    come to be? (Davis, 2010).

    If we are to investigate the claim by Davis and Renert stated earlier that viewing the

    class as a system that learns requires living in dynamic evolutionary tensions also

    requires teachers to be open to the many perspectives through which pedagogical

    occasions may be engaged and interpreted, (Renert & Davis, 2010, p.22), we find

    ourselves confronted with a newfound awareness and open way of being with

    mathematics, how do teachers begin to challenge the strongholds of traditional teaching

    practices and the footholds of a factory model education system?

    Viewing the classroom as a complex adaptive system, we posit that elements of

    nurturing, collectivity and artistry are at play simultaneously in the spaces of effective

    teaching. Nurture in the mathematics classroom creates a safe space for risk-taking, idea

    sharing, mistake making and flexible learning. Collectivity embraces internal diversity and

    redundancy within the group of learners towards shared mathematical understandings

    greater than the sum of the individual parts: emergence out of multiplicity. Artistry elicits

    both an interpretive approach to mathematics curriculum and pedagogy as well as a

    dynamic and responsive role of educators as necessary agents within the complex system

    of education. In the body of this paper, we will endeavor to embody and re-present each

    of these nodes respectively.

    24

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    25/147

    We will consider the affordances of Nurturing Collective Artistry, looking closely at

    each node and responding to the relationships between the nodes as we have come to

    know them within the robust systems of knowing and learning. All three nodes (and not

    limited to these three nodes), separately and collectively, inform teaching practice in our

    classrooms. We anticipate that through individual node analysis and node connectivity

    study, we might gain emergent insight into the lively interplay that lends to effective

    teaching practices in the mathematics classroom.

    It is our belief that nurturing collective artistry is a potential avenue for further

    exploration in terms of occasioning and engaging with the pedagogy and teachers

    disciplinary knowledge of mathematics and of the mathematics classroom. These varied

    and diverse perspectives may open new possibilities, and afford us to grapple with the

    dynamic tensions that are play when considering the math class as a learning system. We

    are curious in what ways is nurturing collective artistry may occasion us to think of the

    webs of associations and how they are co-implicated in grander systems of mathematics

    as a subject, knowing and learning mathematics, teaching mathematics, and as well as

    even larger systems of language, culture, and human ecology.

    Essentially, we believe that how a teacher engages with students is as important as

    what a teacher teaches, and perhaps nurturing collective artistry shares rhizomatic roots

    with concept study in mathematics education today. To this, we invite further and future

    dialogue.

    25

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    26/147

    CHAPTER2The Need for Nurture withinEducationJennifer Markides

    Looking Ahead and Hurtling Forward: how has our changing world re-emphasized

    the need for nurture in education?

    These days, it would seem as though what students need to knowis changing

    rapidly. The technological advancements of the last 35 years have brought us in-home

    and portable computers, pocket-sized cellular telephones, personal electronic devices,

    global positioning systems, television special effects, the Internet, Google and social

    media. Information is at our fingertips. Students can find answers to many of their queries

    within seconds of wondering or posing a question. They are exposed to more information

    and involved in greater instant communication than ever before. Teachers are finding

    ways to incorporate technology in the classroom, integrating lessons with Smartboards,

    iPads, robotics and much more. With daily blogging, classrooms are participating in social

    media as a means to meet the needs of their parent communities. Whatand how we

    teach may be changing, but the need fornurture in the classroom remains.

    Students familiarity with technology creates a false sense of developmental

    maturity. They are doing these things sooner than their parents generation, but that is

    26

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    27/147

    more a reflection of timing and availability rather than advanced technological literacy for

    their age. Students of nine years old only have nine years of experiences to draw on.

    Their experiences may differ greatly from those of their parents but that does not negate

    their need for guidance and teaching.

    The reality of the world that they are presented with on television, through video

    games and on-line is often distorted. It may not be unrealistic for them to expect to be on

    a reality television show, to become famous and have everything that a celebritys life

    entails. In contrast to the tragic and often rationalized violence associated with wars,

    students now see killing depicted in ways that glorify and dehumanize the act. They may

    begin to believe that violence is commonplace and an acceptable part of everyday life. An

    alarming number of people in Western society are also living in a culture of consumer

    debt, contributing to a must have generation. Media literacy has become a necessary

    focus within education and students reliance/dependence on technology borders between

    entitlement and necessity.

    The work of parents and teachers must now also include teachingchildren and

    students how to use technology responsibly, how to filter and evaluate the information that

    is presented in various media, and how to think independently and self-advocate in a world

    that is ever changing. Savvy advertisers, opportunistic predators, and propaganda-

    pushing extremist groups often target societys most vulnerable and impressionable

    groups, including our youth. Now, we have to explain to our students that posting geo-

    tagged pictures provides people with the exact location and that this can be exceedingly

    dangerous when accompanied with names and other details from their personal lives.

    We cannot protect students from everything, but we can try to make them wiser

    to potential hazards in their world. In particular, schools aim to create cultures of safety.

    Through a nurturing approach, many teachers aspire to provide opportunities for

    communities of learners to think creatively and make conscientious decisions.

    27

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    28/147

    Nurture has been an integral part of education throughout history. It is a biological

    phenomenon shared by many species. As a node in a network of associations, nurture

    has many entailments, connections and implications for education. The definition of

    nurture needs to be explored at the hub of the node, distinguishing it from its close

    association with care. I believe that the varying degrees of nurture teachers exhibit within

    the (mathematics) classroom may offer significant benefits and at times drawbacks too.

    By sharing anecdotal narratives from my own teaching practice and offering insights and

    connections from research literature on similar topics, I hope to open dialogue about the

    complexities ofnurture as it manifests in teaching practice and perhaps informing

    emergent implications for education.

    Beginning at the Node: what does nurture entail?

    Merriam WebstersOnline Dictionary (2013) defines nurture as training, upbringing,

    something that nourishes1 (food), the sum of the environmental factors influencing the

    behavior and traits expressed by an organism, to supply with nourishment, educate, to

    further the development of, foster. Synonyms include: advance, cultivate, encourage,

    forward, further, incubate, nourish, nurse, foster, and promote. The Latin origin brings an

    association with nursing or suckling, to nourish. With these connotations in mind, a

    connection to the feminine is evident.

    Looking at the web of associations, nurture evokes images of maternal instincts and

    relationships. In this way, male teachers may be seen to be taking on feminine roles2 in

    28

    1 Under trusted advisement, I would like to acknowledge that nourishment has a twofold meaning.It can be interpreted as feeding the body and it also suggests feeding ones sense of belonging.The first falls within the Montessori teachings of Needs of Man, while the second is a component ofthe needs of youth described by Brendtro, Brokenleg and Van Bockern (1990). In their book, theydescribe the Circle of Courage as it originates from the Blackfoot peoples spiritual beliefs (oftensymbolized by the medicine wheel).

    2 Further under advisement, I would like to elaborate that by feminine roles I am referring to theassociations of nurture that conjure images or impressions of mother and child (nursing, suckling,and nourishing) - the maternal and, in turn, paternal aspects of nurturing a child while acting in locoparentis.

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    29/147

    the classroom. Teachers, both male and female, live in the tension between nature and

    nurture as first described by Galton (Nature versus Nurture, 2013) - they must consider

    both whatthe students bring with them to the classroom and howthe students experience

    occasions for learning, both deliberate and unplanned.

    The definition and prevalence of nurture does not differ from one setting to another,

    but how it manifests in practice and experience will be unique to each teacher and each

    teaching context. Nurture in various contexts may be expounded by teachers in many

    ways, such as: acknowledging a students efforts towards a goal, asking and genuinely

    caring about the students life outside of school, sharing ones passion for the subject

    matter, holding a student accountable for their actions, or searching purposefully for new

    strategies to support student learning3. If anything, the purposeful nurture that is specific

    to the realm of education is perhaps self-similar to the nurture of parenting. Nurture, as a

    skillset in teaching, may be tacit in the same ways that Shulman (1986) describes

    teachers pedagogical content knowledge: existing and influencing (practice), but

    essentially unexploited.

    Some Connections to the Nurture Node: what are the pre-existing associations?

    As previously mentioned, there has been a longstanding debate as to whether a

    persons abilities are predetermined at birth: nature, or whether they are learned as a

    result of experience and environmental factors: nurture. The false dichotomy setup by the

    nature and nurture debate does not give rise to a distinction between the two (dare I say)

    dominant influences in ones cognitive development. Instead, the interplay between nature

    and nurture affords a necessarily inseparable coexistence of inextricably connected parts.

    Since nature represents biological and innate factors that are out of the teachers control,

    29

    3 This is not an exhaustive list of examples, but perhaps a starting place for thought anddiscussion.

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    30/147

    the teacher should aspire to and maintain a cognizant awareness of each childs nature.

    Purposefully informed by nature, the teachers efforts should then be focused on nurture.

    Canadian, van Manen (1982) purported that reflection on interactions with children

    through a phenomenological approach could inform pedagogical practices more deeply

    than other research approaches, suggesting also that tact and sensitivity be at the

    forefront of consideration. He went on to describe the need for a conscious awareness of

    both what is said and what left unsaid. These beliefs resonate with specific aspects of my

    teaching practice.

    First, I endeavour to reflect on my practice often, trying to take the students

    perspectives. At times, the phenomenological approach allows me to see when an

    instruction may have been confusing or when a conflict resolution strategy may have

    appearedunfair. Second, I always try to explain my reasoning when addressing students

    work habits, social behaviours and other concerns that may cause a student to be

    defensive or unsure about something. I am very conscious of what is saidby not speaking

    up about certain choices the students make, I am asking you to move tables because I

    care that you get your work done; if I didnt care about you being successful, I would just

    ignore the fact that you are visiting and not working. It would be easier and less hassle.

    In this instance, not saying anything would signal to that the student that I am okay with

    their behaviour and lack of work ethic. They would be sadly mistaken. It takes time and

    purposeful effort to be forthcoming about reasons for choices in the day-to-day goings on

    in the classroom, but it is worth it to lessen my image as an authoritarian teacher in the

    students eyes. They often express resolve and sometimes gratitude when an explanation

    has been offered. These are ways I try to demonstrate care and respect for my students.

    Influenced by Kohlbergs justice-based stages of moral development and Gilligans

    feminist perspective ofempathyand compassion, Noddings (1984) put forth her theory of

    the ethics of care. She suggested that there are three requirements for caring. The

    30

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    31/147

    [r]elationship between the carer (one-caring) and the cared for (cared-for) must

    demonstrate[:] (a) engrossment and (b) motivational displacement, causing (c) a response

    from the cared-for (1984, pp. 1112). Thus, the teacher has not caredfor the student,

    unless the student responds in some way to the care. The response may be as audible as

    a verbal acknowledgement, as visible as a smile or nod, or as subtle as a change in

    subconscious awareness or affect. This also speaks to the intentionality of nurture needed

    to elicit the sense or impression of being cared for.

    Aoki (1990) articulated the difference between theplanned curriculum and the lived

    curriculum, suggesting that more attention should be given to the lived experience of the

    classroom. While the teacher may plan a lesson to teach a given concept, students may

    learn or place importance on something completely different from intended purpose of the

    lesson. This gives rise to the importance of a healthy classroom culture. The attitudes,

    predispositions and relationships influence the course of the planned and lived

    curriculums.

    Sidorkin (1999) proposed the benefits ofcarnivalas a type of unique contributory

    experience that would bond a group of people together through shared purpose. He

    reported how greatly invested the participants became in a short time frame and how

    memorable the experience was for those involved. Although Sidorkin describes the

    phenomenon as it occurred with a disenfranchised group of youths, the underlying concept

    may apply in the typical classroom setting. Nurture requires a connection or relationship of

    trust that may be initiated and/or strengthened through an embodiment ofcarnival.

    Further, Davis, Sumara and Luce-Kapler (2008) introduced collectivityas a more

    simultaneous view of interactions within a learning system. They also suggested that the

    internal diversity and redundancy within a collective are the tensions that generate the

    systems vibrant sufficiency. Similar to Sidorkins (1999) carnival, occasioning for

    31

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    32/147

    collectivity may sometimes necessitate a common goal or shared purpose in educational

    pursuits.

    The many connections at this node suggest the importance of nurturing. These

    include collectivity, memorable experiences, perspective taking, acknowledged care, and

    meaningful relationships. Without the nurture node, the associated connections would be

    weakened and less stable.

    Fostering a Community of Risk-takers: A re-view ofwhy nurture is important in the

    classroom?

    It is hard not to be affected by the many significant ways our lives are influenced

    and shaped by our day-to-day experiences. Recently, I took on an unfamiliar teaching

    assignment: grades 4 and 5. Considering that I was in the final year of my masters

    program and a new mother of two, I hesitated to take the position, preferring the safety of

    the quasi-familiar. Fortunately, I was pushed to take a risk, trying something new and

    expanding my experiential knowledge.

    The group of students ranged in age from eight to ten year olds. It surprised me

    to learn that many were struggling with low self-confidence and poor self-image; they were

    also very concerned with how others saw them: their reputations. I was forewarned to

    expect individual behaviour issues and anticipate problematic group dynamics.

    Looking to my Montessori training to inform my practice, I revisited her insights as

    to the developmental stages of the child. Specifically, Maria Montessori (1976/1948)

    describes the second plane of development, experienced by six to twelve year olds, as a

    time of metamorphosis. During this period she noted that the children tend to work and

    socialize in groups. This stage is marked with the childs increased aptitude for tasks

    involving imagination, independent thinking, and moral reasoning. The child may also

    become self-conscious at this stage of development.

    32

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    33/147

    Considering these elements within the context of my classroom, I set out to

    develop positive relationships with and among my students that would reflect their positive

    self worth. Additionally, I aimed to nurture the students strengths and passions while

    creating a climate of safety for everyone, realizing that many factors were outside my

    control (but I at least had to try).

    Beginning with kind, consistent messages and an expectation of mutual respect,

    we embarked on a year of significant growth for individuals and community building

    between all members of the class. It was not all perfect or easy, but the expectation for

    care and respect set a tone for persistence, perseverance and intrinsic motivation.

    Our yearlong inquiry focused on identity. We explored the aspects ofhow we

    shape our identityand how our identity shapes us. The majority of the students

    demonstrated a great aptitude and interest in art. The passion for the arts allowed us to

    consistently revisit the notion of identity, while reflecting on aspects of self: image,

    confidence, and advocacy.

    Nurture was the underpinning of every assignment, conversation and experience

    that we shared in our classroom collective. My goal as a teacher is to develop a

    meaningful relationship with each student such that they know that I am in their

    corner (please pardon the boxing metaphor, colloquial but apt). Just as my grandparents

    have successfully made every child, grandchild and great grandchild feel as though they

    are the favourite (without ever saying it), I have worked to make a unique and significant

    connection to every student.

    Whenever possible, I take time to hear both students sides in an argument. In

    many recent instances, I have suggested, we are all working on stuff. Ive given the

    students concrete examples of what I know they were working on, and then I offer,

    perhaps Fred (pseudonym for a peers name) is working on learning how to be part of the

    game too (or other relevant issue that bothered their classmate). This seemed to help

    33

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    34/147

    bridge the feeling that others are so different than them and that no one else has

    problems or issues to deal with. With this age group, I found these conversations

    particularly helpful towards building empathy and understanding towards each other. If

    nothing else, they had a chance to cool down and cut each other some slack. In a few

    cases, students who started the year at odds learned that they were not so different from

    each other, worked together on a few assignments (by choice) and even became friends

    as the year progressed.

    The relationships they nurtured between one another were equally as important.

    Through small group challenges modeled afterThe Amazing Race, the students worked in

    groups that they normally would not have chosen for themselves. Along with the

    Montessori Great Lessons, experiences such as this evoke the spirit ofcarnival, creating

    shared experiences and vibrant memories that endured throughout the year.

    Through the collective decision making process, students were supported in

    discussing, evaluating, and determining personal choices with respect to the group. They

    expressed appreciation for having a say in shaping their educational experiences.

    Through nurture, collectivity and care, ourlived curriculum was inextricably

    connected to the identities of the individual agents within our class. The community

    thrived, occasioning for growth beyond the scope of any individualized or personalized

    program plan4. The students responded to their experiences of nurture, by nurturing

    others and importantly, themselves.

    34

    4 I really value individualized/personalized program plans (IPP/PPP) for what they represent. Theinformation in the assessment documents that lead to an IPP is invaluable in program planning forsome kids. I once taught a student that was beginning to exhibit behaviour problems as a way todeal with his frustrations in school. He was in grade 4 already and not in the cue for aneducational assessment. Sensing his deep-rooted anxieties, I made a case to my administrator tohave him assessed before the end of the year. Surprisingly and not unexpectedly, the educationalpsychological assessment revealed that the student was cognitively functioning at a very highlevel, though his processing/output was of a level that constituted a learning disability. He left our

    school knowing his strengths and areas of weakness. His mom returned to our school thefollowing year and reported on his progress. He now loved going to school and was able toexpress his needs to his new teachers, requesting alternative forms of presenting and sharing hisknowledge with others.

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    35/147

    Nurture anew: what are the implications for the (mathematics) educators of today?

    With the new mathematics curriculum, it has become very important that the

    students feel comfortable enough with their peers and confident enough with themselves

    to take risks, apply strategies, hypothesize and revise, accordingly. This heuristic,

    problem-based approach to mathematics has pushed many students (and teachers) out of

    their comfort zones. They are being asked to thinkdifferently.

    Azzouni (2006) asserts that within our society, we are quick to see and point out

    errors in our mathematical thinking. This tends toward the masculine mathematics,

    which Bibby (2010) hazards is a mathematics characterized by logic (ism),

    authoritarianism and stoicism. Similarly, de Freitas (2008) recognizes that the feminine

    mathematics may be seen as a threat to the masculine way of knowing math, but argues

    that narratives of the human experience may offer entry points for divergent and possibly

    creative thinking about mathematics. Despite the reputation of math being hard, rigid and

    orderly, math can be seen conversely/adversely as soft, malleable and messy. By

    embracing qualities of the feminine, nurture allows forlearning from ones mistakes,

    cultivating ideas with others, and fostering a sense of peaceful resoluteness in the midst of

    the unknown. Perhaps, teachers might consider nurture as a means to support students in

    becoming more resilient, collaborative and confident mathematicians.

    So Much Change, So Little Progress An appeal to nurture shared goals within the

    educational community

    Maria Montessoris vision for the future from 1948:

    My vision of the future is no longer of people taking exams and proceeding on

    that certification from the secondary school to the university, but of individuals

    passing from one stage of independence to a higher, by means of their own

    35

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    36/147

    activity, through their own effort of will, which constitutes the inner evolution of the

    individual

    (p. 1).

    Nel Noddings plea to the global community in 2005:

    We will not find the solution to problems of violence, alienation, ignorance, and

    unhappiness in increasing our security, imposing more tests, punishing schools

    for their failure to produce 100 percent proficiency, or demanding that teachers be

    knowledgeable in the subjects they teach. Instead, we must allow teachers and

    students to interact as whole persons, and we must develop policies that treat the

    school as a whole community (p. 8).

    Within the unique setting of the classroom, teachers have opportunities to nurture students

    differently and purposefully in relation to others. Parents nurturing often involves putting

    their childs needs first (and rightly so). Teachers consider the needs of the collective

    simultaneously with the needs of the individuals. In our role as educators, we nurture

    children to contribute within a group and to accept the contributions of others; we nurture

    children to be friends, to recognize the attributes of a good friend, to maintain positive

    friendships, and to reciprocate the qualities of healthy friendships. Where else in life can

    this type of learning be so deliberately supported?

    Many teachers, caring teachers, look beyond a students strengths, rather than

    trying to pigeonhole them for a future vocation. These teachers see the whole child,

    acknowledging that the strengths will only take them so far; and that by nurturing all

    aspects of their development, they may help to prepare them to work with and learn from

    others within society. Their goal is to have a positive impact on a students life, such that

    they may go farther than they ever hoped or imagined. Without nurture, what job is left?

    Teachers can be replaced in all other capacities: organizational, managerial,

    informational, evaluatory, and even experiential. It is only the aspect of nurture, deliberate

    36

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    37/147

    and caring, that cannot be mimicked, imitated or re-generated with any genuine

    authenticity. Teachers are not perfect; in some ways, it is our fallibility that the students

    relate to and that allows them to truly connect to us. Ourhuman qualities bring us all

    together and set us all apart. It is our willingness and persistence to nurture, each in our

    own unique ways, that afford us as our greatest opportunities to impact students lives in

    truly meaningful ways.

    37

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    38/147

    RESPONSE

    Nurturing CollectivesCraig Dwyer

    What exactly does it mean to nurture the collective? This was the thought running

    through my mind as I read the previous chapter by Markides. I believe there are no quick

    answers to this questions. It is entangled within many more questions. Teachers, as

    Markides points out, are human beings, and we are fallible. This fallibility allows us to

    connect with each other, and this connection, allows us to thrive, if the soil is fertile and the

    conditions are ripe. it is so much more than just the conditions, and I think the concept of

    Nurture offers a much more human way of looking at learning systems.

    Empowerment

    Students should feel a sense of ownership over not only their learning environment,

    but also the content they learn. By listening to their collective concerns, we can better

    react to their understanding and personalize the learning. That personalization also allows

    for the collective to flourish. As Davis, Sumara, and Luce-Kapler (2008) point out that

    collectivity starts by being as individual as possible. Perhaps, it is then through the

    nurturing of a caring environment, that we arrive at a place where individuals feel free to

    share with the collective. Teachers can nurture an environment of sharing by bringing

    awareness to healthy social dynamics, and explicitly making these dynamics an object of

    38

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    39/147

    study. Perhaps by empowering learners to take control of their learning, we can open

    windows to viewing the classroom as a collective system?

    Peer to Peer Culture

    This collective connection requires an increased emphasis on the concept of work

    in progress (note, I hate the term workas it applies to school, so I will switch to learningas

    a noun). For students to be able to share, they need to be able to trust each other. Here

    the teacher has a powerful role by enabling students to learn together and help each other

    with their learning with one another. While they are sharing, it is important to not only listen

    to the feedback from the collective, but to allow that feedback to change your perception. I

    wonder if by nurturing an environment of sharing, we can occasion a shift from individual

    students learning in isolation, to a collective learning from each other?

    Open Communication

    If our students are communicating with other, and sharing their learning openly

    and honestly, then teachers need to provide an atmosphere with decentralized lines of

    communication. They need access to each other just as much as they need access to the

    teacher. By controlling the communication, teachers can unknowingly create a

    bureaucracy that stifles creativity. The feedback will not be able to change the learners

    perspective if it is not free to move throughout the collective. Maybe nurturing requires a

    close relationship between all individuals in the collective but it also requires knowing

    when to get out of the way?

    Growth Mindset

    Dweck (2006) provides a compelling look at the ways in which our thoughts about

    learning affect the practice of learning itself. She argues that teachers and coaches are in

    a key position to affect these mindsets, and subsequent shifts in mindset. Perhaps then,

    39

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    40/147

    nurturing is about helping kids to see challenges as a part of learning, and helping children

    to be intrigued by mistakes, rather than afraid of them?

    The role of the teacher

    This is by no means an exhaustive list, or an end to my questions. Yet, it forces me

    to reconsider the role of nurture, and love, in my classroom. By nurturing the individuals

    within the collective, we can open new spaces. Markides paper suggests to me that these

    spaces point to the culture of the classroom, and culture is a product of human interplay. It

    emerges from the collective interactions of individuals. Perhaps then, nurturing a

    community is about providing a safe space where a unique culture can emerge?

    40

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    41/147

    RESPONSE

    Art as nourishment:A response to the need fornurture within educationMichael Craig

    Art for me is a form of nourishment - Andy Goldsworthy (Riedelsheimer, 2001).

    In The Need for Nurture within Education, Markides (2013) offers us a way of

    viewing the complex (mathematics) classroom that embraces learning from ones

    mistakes, cultivating ideas with others, and fostering a sense of peaceful resoluteness in

    the midst of the unknown (p. 35.). This is primarily accomplished, as suggested by

    Markides, through a culture of nurture. As I explored this culture from a perspective of

    artistry, the notion of nurture as nourishment (p.28) stood out for its parallel to the arts asnourishment and my own history as a theatre performer. As I explored these parallels

    further, there were particular aspects of nurture that seemed to mirror strongly the role of

    arts, specifically the performing arts, in complex systems based classrooms. These

    aspects included: a) nourishment for the artist, b) nourishment of the performing collective,

    and c) the relationship of artist and audience.

    41

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    42/147

    Nourishing the Artist

    As a actor, theatre always seemed to fill a void for me. I was always seeking ways

    to express myself and often it was through speech or role play. As a child, my games

    focussed on creating roles and characters to play. Not one for sports, I was always

    seeking a way to stand out, to find that thing that made me special. Throughout schooling,

    I struggled with my own identity, never really fitting in until I discovered drama in high

    school. There I found a place to express myself, to explore creativity with characters and

    motivation, and to draw out the gifts that I had within. Ironically, it was through made-up

    characters and roles that I found my own identity and learned to share it with the world.

    Theater both nourished and nurtured my individual development.

    As she explored her own practice, Markides described a yearlong inquiry into

    identity that had student exploring notions of image and confidence with a goal towards

    advocacy. This inquiry was marked by a majority of students demonstrat[ing] a great

    aptitude and interest in art (p. 33). This would seem appropriate in that it drew on the

    aptitude for tasks that involve imagination, a characteristic of the Montessori stage for six

    to twelve year olds (p.32).

    As with my own journey, it would seem that the arts serve as a vehicle for the

    individual student to meet a need for imagination and creativity, nourishing and nurturing

    their aptitudes.

    Nourishing the Collective

    There is a sense of collective when one is part of a theatrical endeavor. As an

    actor, I always found a deep appeal in the near immediate bonding that would occur when

    actors would take up a script and open themselves up to the experience. It was as if the

    individual that was myself was yearning to be part of something bigger. More than just

    making a connection to the other performers, we were, together, creating something bigger

    42

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    43/147

    than ourselves, greater than the sum of our individual performances. As actor or director, I

    could feel this moment where the play ceased to be individuals coming together and took

    on a life of its own. At a deep level I knew that I was part of something that nourished that

    emergence and I was a key part of its nurture and development.

    Markides captures this aspect to the performing arts in Siodrkins (1999) concept of

    carnival, which Markides describes as an unique contributory experience that would bond

    a group of people together through shared purpose (Markides, 2013, p. 31). What would

    seem to be called for in this experience is a strong shared empathy between the

    participants in order to nurture the collective emergence. A byproduct of this nurturing

    empathy is in the network of connections between the participants. In Markides classroom

    experience, she speaks to a profound empathy that enabled greater understanding

    between her students that allowed them to see each other as individuals with different

    needs to be nurtured, by either the teacher or the other students in the classroom.

    Artist and Audience

    Ask any performer and they will tell you that during the moment of performance,

    there is a special bond between the performers and the audience. While the performers

    are delivering joy or laughter or tears or introspection or any number of complex emotional

    reactions to their audience, at the same time performers are feeding off the energy of their

    audience. This is not always a growth experience. There were times on stage where I

    could feel the audience was no longer with us and the performance suffered greatly.

    However in those time when the energy fed the actors, the show would take to new

    heights. And in those times, the audience was treated to a heightened experience of the

    show. It was a reciprocal thing. The show nurtured the needs of the audience and the

    audience nourished the show.

    43

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    44/147

    Markides parallels this experience through her discussion of Noddings (1984)

    ethics of care. The relationship between the carer (one-caring) and the cared for (cared-

    for) must demonstrate[:] (a) engrossment and (b) motivational displacement, causing (c) a

    response from the cared-for (1984, pp. 1112). Markides (2013) would seem therefore to

    be describing nurture as a reciprocal relationship between the teacher and the student by

    suggesting that the teacher has not caredfor the student unless the student responds in

    some way to the care (p. 31). This would in turn suggest that in a nurturing environment,

    much as in the performing arts environment, both the needs of the carer and the cared

    require nourishment.

    Food for Further Thought

    The parallels between Markides experiences in her classroom and my own as

    performer highlight for me the parallels between art and nurture. As with art, nurture

    requires empathy, openness to others, and reciprocity if it is to fully nourish both the carer

    and cared for. And as with art, the benefits of a nurturing environment in the complex

    (mathematics) classroom, are creativity, care, flexibility and solutions to problems of

    violence, alienation, ignorance, and unhappiness (Noddings, 2005, p.8).

    So in the words of the William Shakespeare from Twelfth Night, If music be the

    food of love, play on.

    44

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    45/147

    CHAPTER3wandering throughcollective spacesCraig Dwyer

    Autumn was everywhere you looked in Tokyo. The subways were crowded with

    workers in suit jackets. Gone were the short sleeved shirts and sweaty brows. A pleasant

    smell of kinmokuse flowers hung in the air. Evenings were crisp, but not cold, and the

    cicadas had long since gone silent. Trees were shedding their leaves and the wind would

    pick up the offerings and twist and turn them in the air, leaving not-so neat little piles on the

    side of road. Though Tokyo is a city that never sleeps, there were occasional moments of

    silent clarity, as if the city were trying to rid itself of the noise and motion and just enjoy the

    moon on a cloudless night.

    It was the autumn of 2010, and I found myself sitting in a cleared out music

    classroom at Tokyo International School with about one hundred other teachers. There

    were drum kits stacked in the corner and we were sitting next to a pile of trumpets. I had

    made the 600 km trip south from Aomori, where I lived and worked, to join a workshop with

    an Australian education consultant. The topic was Teaching and Learning Through Inquiry.

    We spent two days engaged in deep questions about the purpose of school, what a

    thinking curriculum should look like, and how to evoke a sense of wonder in our students,not wonder in the sense of amazing, but rather a profound sense of curiosity.

    45

  • 7/28/2019 Nuturing Collective Artistry MEd Capstone, Craig, Markides, Dwyer

    46/147

    We came back from a wonderful lunch on the second day to find a shroud of red

    and white tartan cloth sitting on our table. Our facilitator asked us n