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A Year in the Life: Ambient Math Wins the Race to the Top!

May 10th, 2014 · No Comments · Homeschool Math Curriculum

Day 124

For one year, 365 days, this blog will address the Common Core Standards from the perspective of creating an alternate, ambient learning environment for math.  Ambient is defined as “existing or present on all sides, an all-encompassing atmosphere.”  And ambient music is defined as: “Quiet and relaxing with melodies that repeat many times.  Why ambient?  A math teaching style that’s whole and all encompassing, with themes that repeat many times through the years, is most likely to be effective and successful.

Today’s blog features Part II of Cassie’s guest post.  In light of the current trend toward more technology in the classroom and less direct teaching, less art, less movement, less of all that after all, makes us human, should we not reassess the value of the hand-made, human, teacher to student connection?  Every teacher every one of us has valued in our lives, who in fact helped shape our very lives, had taught us on a human scale, touching the heart of every student in his or her care.  This is doubly true of parents who choose to teach their children at home.  Please read Cassie’s words with all of this in mind.  And remember that knowledge ensues in an environment dedicated to imaginative, creative knowing, where student and teacher alike surrender to the ensuing of knowledge as a worthy goal.

Philosophy of Education – Part II
Cassie Lipowitz
Ph.D. Student, Graduate Theological Union
Lecturer, Religious Studies, Notre Dame de Namur University

Professor Davidson’s story (to read the story, see part I of this blog, posted yesterday) beautifully illustrates a paraphrased saying by educator Rudolph Steiner, that “To teach is to stand in the rain without an umbrella.”[i]In other words, to truly teach, one must become vulnerable, and learn to live in that space of vulnerability.  It is in this space of vulnerability where teacher, students, and subject matter meet.

Parker J. Palmer, an educator and Quaker, insightfully articulates the interplay between these three—teacher, students, and subject—in his book The Courage to Teach: Exploring the Inner Landscape of a Teacher’s Life.  Palmer emphasizes the extent to which a teacher’s “inwardness” or the condition of his or her soul, impacts the classroom.  As a result, he writes, it is vital and imperative that as teachers we must come to intimately know ourselves, in addition to knowing our subject and our students:

Teaching, like any truly human activity, emerges from one’s inwardness, for better or worse.  As I teach, I project the condition of my soul onto my students, my subject, and our way of being together.  The entanglements I experience in the classroom are often no more or less than the convolutions of my inner life.  Viewed from this angle, teaching holds a mirror to the soul.  If I am willing to look in that mirror and not run from what I see, I have a chance to gain self-knowledge—and knowing myself is as crucial to good teaching asknowing my students and my subject.[ii]

As Parker goes on to argue, self-knowledge is perhaps the foundation of this three-part equation

…knowing my students and my subject depends heavily on self-knowledge.  When I do not know myself, I cannot know who my students are.  I will see them through a glass darkly, in the shadows of my unexamined life—and when I cannot see them clearly, I cannot teach them well.  When I do not know myself, I cannot know my subject—not at the deepest levels of embodied, personal meaning.  I will know it only abstractly, from a distance, a congeries of concepts as far removed from the world as I am from personal truth.

The work required to “know thyself” is neither selfish nor narcissistic.  Whatever self-knowledge we attain as teachers will serve our students and our scholarship well.  Good teaching requires self-knowledge: it is a secret hidden in plain sight.[iii]

And yet, in today’s educational milieu, it seems that many teachers have forgotten this vital aspect, or have simply found it too daunting and difficult to integrate such approaches while teaching in a system that stresses “hard results” (student learning outcomes geared more towards the sciences than humanities and liberal studies) and that “teaches to the test.”  Likewise, many students do not seem to possess the tools to make what they learn relevant to their own lives.  As a result, both teaching and learning suffer.  As bell hooks asserts in her book, Teaching to Transgress: Education as the Practice of Freedom, “There is a serious crisis in education.  Students often do not want to learn and teachers do not want to teach.”[iv] Rather than fostering true learning, it seems that far too many classrooms become information storehouses, in which teachers act as information siphons, with students falling into the role of passive learners.  In such an environment, it is far too easy for students to slip through the cracks, or get by without learning much of anything.  And yet, in spite of this crisis, “The classroom remains the most radical space of possibility in the academy.”[v]

As an antidote to the corrupt banking system of education, hooks proposes an “engaged pedagogy.”  Engaged pedagogy emphasizes well-being, which means that “teachers must be actively committed to a process of self-actualization that promotes their own well-being if they are to teach in a manner that empowers students.”[vi]In such a pedagogy, education is envisioned as a libratory practice, in which teachers and students experience freedom through teaching and learning.  hooks argues that

That learning process comes easiest to those of us who teach who also believe that there is an aspect of our vocation that is sacred; who believe that our work is not merely to share information but to share in the intellectual and spiritual growth of our students.  To teach in a manner that respects and cares for the souls of our students is essential if we are to provide the necessary conditions where learning can most deeply and intimately begin.[vii]

Like hooks, I was disillusioned by many of my learning experiences during my first few years in college.  I had expected to find highly intelligent and self-aware individuals—professors who would not only have access to information, but who would also understand how to apply it in the “real world.”  Instead, I found myself continually disappointed by professors, who, though they lectured on fascinating material in the Humanities, and raised interesting questions in Philosophy, seemed for the most part incapable of bringing the subject material to life, and practicing what hooks terms “engaged pedagogy.”  In addition, some of my professors seemed afraid to invite discussion (perhaps they feared the discussion might bring up uncomfortable issues, or provoke heated responses from students).  In fact, I came to recognize a pattern that seemed to perpetuate in several of the classes I attended: whenever the discussion seemed poised to move in an intriguing direction (often prompted by a student’s question) the professor would almost invariably shut it down and move on to the next lecture slide, the next information bit.  Sometimes, another student would immediately raise a similar question, or directly invoke the first students’ question, clearly indicating that this idea had sparked interest.  More often than not, unfortunately, the professor would dismiss the second question as well, citing the need to “stick with the lecture and not fall behind schedule.”

In these moments, I found myself frustrated and sad—disappointed that once again, we had missed out on something that seemed to move beyond information and pre-determined structures—something that would have integrated the students fully into the conversation because it was an issue that truly engaged them, about which they expressed a passionate interest. The sense of frustration and the feeling that “there could be something more” has remained with me through my years in higher education.  As I have transitioned into the role of teacher in the last few years, I have gained a new appreciation for the difficulty of balancing pre-planned lecture material with student-focused interests.  Though I have more sympathy and understanding now for my professors who remained intent to “stay on task” (after all, stepping into the unknown can be frightening, as no one knows for sure where the conversation will lead!) I still maintain that student-directed learning (illustrated by the above story from Professor Davidson) is more effective, in certain ways, than any pre-fabricated lecture I could provide.  This is perhaps because such discussions are “organic”, responding to the requirements and conditions of the moment.

As a humorous illustration of the way in which a lecture may fail to meet the needs to moment, I can relate a summarized version of a story from Book I of Rumi’s Masnavi:  in the story, a deaf man learns from a wise man that his neighbor is sick.  The deaf man, thinking that he will do good by paying a visit to his sick neighbor, but knowing he will not be able to properly hear what the sick man tells him, prepares in his head what he will say and how the sick man will respond.  For example, he assumes that when he asks after the sick neighbor’s health, the man will reply with something along the lines of “I am fine,” and so he plans to respond with an exclamation of “thank God!”  Next he decides he will ask the man what he has had to drink, and he assumes the man will answer with a positive response—such as sherbat or broth.  Based on this, the deaf man thinks, he should respond with the exclamation, “I wish you health!” and then “Which doctor is treating you?”  The deaf man surmises the sick man will answer such-and-such a doctor (presumably of reputable practice) upon which the deaf man plans to assure the sick neighbor of the physician’s deft skill, and that the sick man is now in excellent hands.  Having preplanned this dialogue in his head, he goes to visit his neighbor.  Of course, things do not go according to his plan, for his sick neighbor’s answers do not accord in the slightest with the deaf man’s assumed responses.  When he ask the man how he is, the sick man essentially tells him he is on death’s doorstep, to which the deaf man gives his preplanned response, “Thank God!”  This offends the sick man, and his anger only grows as the dialogue continues: in answer to the question of what he has had to drink, the sick man replies “poison,” and the deaf man says, “May it bring health!”  When questioned about which doctor is treating him, the sick man tells him that Azrael[viii] is treating him.  The deaf man then reassures the sick man that “His foot is blessed”—in other words, he is a reputable physician.  Understandably, the sick man feels angry, betrayed, and hurt, and tells the deaf man to leave him alone.

In applying this story to the learning environment, we can make the following analogies: the deaf man may be seen to represent a teacher who, though well-intentioned, does not have the ability to truly know the needs of his students (“deafness” equals the inability or unwillingness to carefully listen, understand, and respectfully and articulately respond).  Knowing this about himself, the deaf man decides he will preplan not only what hehimself will say, but also the sick man’s responses.  This “preplanning” may represent a prewritten lecture, which the teacher sticks to in spite of whether it promotes true learning or not.  The sick man, in this story, may represent the students, where sickness equates to a certain “lack” of knowledge, while the prospect of health represents learning, or gaining knowledge.  Just as, in the Islamic tradition, it is considered a religious act to visit one’s sick friends and relatives, so too, the vocation of the teacher is, as bell hooks asserts, in some sense itself a sacred vocation and responsibility.  While the deaf man has the best of intentions, he does not have the capacity or desire to truly listen, and thus only angers the sick neighbor.  This anger can be equated to the disillusionment students may feel when they realize the sort of learning that happens in some classrooms is not genuine—or not all it could potentially be.  In my experience, when students sense the instructor is not truly listening to them, they simply shut down, and essentially fall into a mindset of “get the grade and get out.”  It is not fair, of course, to place the burden or blame entirely on the teacher’s shoulders—the problem is systemic and far too complex to fully explore in the present work.  However, I would argue, along with bell hooks, that too often in college classrooms, we see “students…[who] do not want to learn and teachers [who] do not want to teach.”[ix] This frequently translates to teachers who do not truly listen to their students, and students who do not listen to each other and only selectively listen to the teacher for the information that “will be on the test.”

In spite of the above criticisms, this is not to say that lecture and memorization don’t play a role in higher education, for they certainly do.  Rather, as Belenky, Clinchy, Goldberger, and Tarule point out in their feminist pedagogical study, Women’s Ways of Knowing: The Development of Self, Voice, and Mind, “received knowledge”—that is, knowledge or information one acquires through “listening to the voices of others,” and especially those perceived as authorities—is only one of the ways of knowing, and co-exists alongside other kinds of knowledge, such as subjective knowledge, procedural knowledge, and constructed knowledge.[x]Unlike received knowledge, which depends upon external authority only, subjective knowledge arises from within—from the learner’s own experience—as part of what Belenky, et al identify as “intuitive” knowledge.  While both received knowledge and subjective knowledge are dualistic in nature, insofar as they assume there is only one means for arriving at a correct answer to the given issue or problem[xi], procedural and constructed knowledge allow for multiple means of arriving at an answer or solution.  According to the authors, procedural knowledge consists of two subdivisions: separate knowing and connected knowing.  For separate knowers, the primary method of learning consists in critical thinking and testing: “Presented with a proposition, separate knowers immediately look for something wrong—a loophole, a factual error, a logical contradiction, the omission of contrary evidence.”[xii] Connected knowers, on the other hand, seek to understand, and even enter into—as fully as possible—the worldview of others:  “Connected knowers know that they can only approximate other peoples’ experiences and so can gain only limited access to their knowledge.  But insofar as possible, they must act as connected rather than separate selves, seeing the other not in their own terms but in the other’s terms.”[xiii] While separate knowers and connected knowers have different approaches, both “…learn to get out from behind their own eyes and use a different lens, in one case the lens of discipline, in the other the lens of another person.”[xiv] Finally, constructed knowledge integrates, in a sense, all of the other approaches or “voices”—it incorporates “reason, and intuition, and the expertise of others.”[xv] Ideally, a great teacher, acting as a metaphorical “midwife”, will be able to help the student “birth” the constructed knower within him or herself.

Fortunately, I had the honor of attending courses with a few professors who, indeed, had the capacity to act as “midwives” in the sense described above.  Like Norman Davidson, they allowed themselves to be vulnerable enough to let learning evolve in the moment; further, they also intuitively understood how to guide their students (rather than simply feeding them the answers) so that students themselves would “learn how to learn.”  It wasn’t that these teachers were “lazy” in terms of preparation or in structuring their classes—rather, they saw new possibilities for what the classroom could be.  Somehow, almost miraculously (though undoubtedly it required much hard work on both personal and professional levels) these professors found their way into an approach that allowed them to meet the needs of their students in the moment.  In short, they had gained the ability speak about—or even embody—the subject matter in a way that ignited the students’ interest and passion for learning, and thus bring together the three core components of the classroom: teacher, subject, and students. Teachers such as the ones described above are able to create an environment wherein, in the words of professors Susan E. Hill, Linda May Fitzgerald, Joel Haack, and Scharron Clayton, students “…begin to question the structures of social reality and their assumptions about it.  Once this occurs, the professor is no longer seen as the beginning or end of students’ learning, but rather as a catalyst for their continued reflection and questioning of the phenomena around them.”[xvi]

In contemplating my own philosophy of education in the context of the above quote, a particular story comes to mind, which I first heard over 10 years ago in Dr. Amir Sabzevary’s Introduction to Philosophy class at Sierra College.  As I recall, we were discussing Jean Paul Sartre that day, and, in particular, the concept of “bad faith.” To illustrate the ideas we were discussing, Professor Sabzevary told the following story:

There was once a man who had spent his entire life working for a master architect. He toiled for many years and grew skillful in his trade, building many beautiful houses.  However, the houses he built were always for others; never for himself.  Finally, after a lifetime of work, he said to the master architect, “I’m tired; my body and soul are weary. It’s time I retire.” But the master architect said, “just build one more house–just one more, and then I promise I won’t ask you for anything more.” The man reluctantly agreed, but his heart wasn’t in it anymore. And because he was tired, when he went to the lumber store, he selected the cheapest, flimsiest materials; and when he built the house, he did not use as many supports as he should and was generally lax in the construction. Finally, when he finished, he went to the master architect, and, dropping the keys to the house in his boss’ hand, said, “The house is finished. I wish to retire now.” And the master architect smiled and gave the keys back to the man, saying, “The house you have just built is my retirement gift to you.” Only then did it occur to the man how poor was the house’s foundation and construction, and by then it was too late…[xvii]

In this story, the man builds houses his entire life, and, under the guidance of a master architect, even becomes competent at his craft—yet the houses he builds are never “his own.”  In the same way, a student may study for countless years, even acquiring certain skills, but unless he or she learns to integrate the information and make it relevant within the context of his or her own life experience, he or she will eventually burn out, become discouraged, or simply arrive at the conclusion that there is no point to such efforts.  In this case, he or she will be left to live in a flimsy “house”—a house that is strung together solely by means of other people’s ideas, and constructed without any self-insight or self-knowledge.  One point of this story, as I see it, is that we are each responsible for our own education, and that, in the end, the “house” we choose to build is the house we will live in for the remainder of our lives.  If, with a combination of skill, creativity, self-insight, and guidance from a master teacher (who is, him or herself, always also a learner!), we are able to construct a solid, spacious, and aesthetic house, we have accomplished more than most.

[i] Rudolph Steiner, Study of Man: General Education Course (East Sussex: Rudolph Steiner Press, 2004), 24.

[ii] Parker J. Palmer, The Courage to Teach: Exploring the Inner Landscape of a Teacher’s Life (San Francisco: Jossey-Bass, 1998), 2.

[iii] Ibid., 2-3.

[iv] bell hooks, Teaching to Transgress: Education as the Practice of Freedom (New York: Routledge, 1994), 12.

[v] Ibid.

[vi] Ibid., 15.

[vii] Ibid., 13.

[viii] In the Islamic tradition, Azrael is the angel of death who comes to take those who are on the brink of death.

[ix] bell hooks, Teaching to Transgress: Education as the Practice of Freedom (New York: Routledge, 1994), 12.

[x] Mary Field Belenky et al., Women’s Ways of Knowing: The Development of Self, Voice, and Mind (New York: Basic Books, 1986) 35-133.

[xi] According to these authors, “received knowers” assume the correct answer exists outside themselves only, while “subjective knowers” assume that instinctual or intuitive knowledge is more reliable than any external authority, and initially tend to reject “outside” answers, especially when those answers contradict what their own instincts tell them.

[xii] Belenky et al., Women’s Ways of Knowing, 104.

[xiii] Ibid., 113.

[xiv] Ibid., 115.

[xv] Ibid., 133.

[xvi] Susan E. Hill, et al., “Transgressions: Teaching According to ‘bell hooks.’” The Nea Higher Education Journal,

p. 45

[xvii] Amir Sabzevary, lecture, Sierra College, Rocklin, CA, February 2003.

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