The front wall of the Cathedral. (Photo credit: Wikipedia)
It’s the end of the school year, and the first grade capped off our work with another research project, this time on Cathedral Church of St. John the Divine. The Cathedral School began as a choir school for the cathedral, and we remain deeply connected to it. Our premises occupy its close and the school still provides singers for the cathedral’s choir. St. John is an increasingly less hidden New York treasure; it’s the largest gothic cathedral in the world and an integral monument in the history of architecture, immigration and social activism in the city.
Growing throngs of tourists are beginning to appreciate “our” cathedral, but, understandably, kids who go to school in its shadow every day can grow a bit jaded. The cathedral is a much larger institution than our school, both physically and in its historic and social reach. However, our students sometimes seem to think of it as an extension of our school simply because spending time there is embedded in our routine. We venture into the cathedral for everything from our weekly chapel service to math projects. Often, our students don’t quite seem to understand why busloads of foreigners are milling around with cameras.
Hence, the class is collaboratively writing a guidebook for the cathedral, a project that long predates my arrival in first grade. We spent weeks touring the Cathedral, taking scrupulous notes on its history and architecture. For the students, the cathedral served as a treasure trove of hidden symbols and artwork, secret stairways and peculiar stories. Our exploration revealed the depth of mystery housed in this familiar space. The revelation of how little they really knew about the cathedral as well as the realization of how far the cathedral’s significance extends beyond our school was a humbling experience for my students. We began to see them staring ponderously at and asking questions about previously ignored corners of the building, examining its artwork and speculating about its construction.
Yet the project was also a celebration of our privileged relationship with the cathedral. Foregoing their frequent sense of entitlement, my students took the authentic brand of ownership qualified by deep knowledge and genuine appreciation. We’ve impressed upon them that the cathedral “belongs” to everyone, but the fact remains that we possess certain entitlements to the building that others do not. Our study conducted them towards an understanding of the origins and uniqueness of that privilege. Pursuing expert knowledge of the cathedral does a great deal to help my students situate their small community within our city’s history, architecture and religious heritage. Our study allows the cathedral to become an intermediary in my students’ long effort to orient themselves in the world.
Culminating the project with the composition of the guidebook — which the students used to take friends and family on a tour — directed the purpose of our study beyond our classroom. The work felt purposeful for the students. The guidebook was a means of sharing the benefits of our special connection to the cathedral, if only with those close to them. For my students in particular, who are fortunate enough to attend a highly effective independent school in New York City, awareness that privileges should be understood and their benefits shared with others may go a long way.
This project, which took quite a few weeks to complete, was a wonderful way to celebrate our community at the end of the year. As the kids in my class a venture into summer, I expect that they’ll leave firmly grounded in their community and with a strong sense of its place in the physical and cultural landscape of our city.
For much of my academic career, I failed to understand what mathematics is really about. I always approached math as the pursuit of skill and concept mastery (or in my case, competence). Teaching revealed that skills and concepts are, in fact, only means to an end. The real aim of math education isn’t building a mathematical toolbox, but promoting flexible, abstract thinking. The most successful math students aren’t necessarily those who can use the tools teachers provide, but those who can think beyond them. Many students can develop astute problem-solving strategies, but lack the flexibility to apprehend multiple modes of representation or variable lines of reasoning. I’ve often misidentified keen application of taught skills as real understanding, but I’m coming to appreciate who, in my class, are really growing as thinkers.
It was easy to loosely sort my students into four basic categories as mathematicians: those who struggle with basic mathematical tools (counting skills, addition and subtraction facts, number families), those who rely on strong memory to implement and integrate mathematical tools, those who use higher reasoning to develop original problem-solving strategies and those who can truly think flexibly. Students in the last category look at problems from multiple angles and take a truly experimental approach to mathematics. I’d like all of my students to be experimenters, although it seems that even among adults, thinkers like this are rare. What initially surprised me, but now seems obvious, is that the kids who struggle the most in math also have the most experimental outlook.
Early on, I fell prey to the common temptation to treat classifications as hierarchical and fixed. I saw the creative problem-solvers, the abstract thinkers, as simply superior mathematicians to the kids who were still approaching math through concrete and semi-concrete processes. The child who quickly wrote an equation to solve a problem simply looked like a more sophisticated thinker than the one who painstakingly worked through a drawing. I perceived my role as helping students move onward and upward through a progression without considering the unique challenges and opportunities of each mode of thinking.
Of course, as with many ways we classify students, these categories are fluid, and students move between them as the demands of our math curriculum change. As our curriculum has come to place greater emphasis on word problems, it’s become clear that many kids who manipulate numbers with great facility lack the analytic skill to deconstruct a problem. They pick out the salient numbers and identify the operation they need, but may fail to apprehend what their answer means. These are kids who, when asked how many gloves are in the room if five kids have blue gloves and three have red gloves immediately declare eight, without considering the fact that gloves come in pairs. Many students even arrived at an incorrect answer after carefully organizing their work into the tables and tally marks. Students who took a more literal approach - actually drawing each kid and each glove - didn’t overlook this detail. They paid attention to the problem, not just the numbers. These are the children who solve problems by trial and error and who may start out working with little sense of exactly where they’re headed. They’re not sure how to solve the problem, so they just start drawing gloves. Their experiences struggling in math make them amenable to open-ended thinking.
We also just finished a delightful unit on surveys and data analysis in which the students surveyed one another. They had to develop both a method of recording their survey data and of displaying it for others. The catch was that they had to display it in a different way than they recorded it; one sheet would be used to take down survey answers, a different one to present the spread after the survey had been completed. I hoped that the students would come away with the all-important understanding for statisticians that the way data is presented influences how it is interpreted. Many of my most efficient mathematicians simply couldn’t do it. I was surprised to see kids who can develop highly reasoned problem-solving strategies staring in frustration at a display and a recording that looked exactly the same. Many had developed tidy and effective devices for recording their peers’ answers: careful tables, class lists, labels, and check marks. These children could clearly see the procedure for the taking the survey from start to finish, but the comprehensiveness of their vision hindered them. Their recordings lacked errors, so they couldn’t envision a different way of presenting their data. Their process didn’t leave room for experimentation; they got it too right the first time.
Meanwhile, the kids who struggled to develop a clear recording strategy thrived on the opportunity reconstruct their data in a new way. They saw the errors and limitations of the strategies that they had developed and took them as inspiration for alternatives. Hence, kids who had made discombobulated lists or written out cumbersome charts translated their data into clear and original displays. They worked flexibly because they’re used to having to change course. They don’t expect things to work out the first time. In the end, they experiment the most and are most receptive to different perspectives and approaches. Number sense is plenty helpful in life, but this is the real ability that we teach for in math. Math is more about flexibility than efficiency, which early aptitude for numbers can get in the way of. We want kids (and grown-ups) to learn to see problems from different angles. It’s easy to conflate mathematics with computation, but really math teachers are trying to create open-mindedness, not procedural knowledge.
Culture certainly may have impelled the change in my students. Our understanding of “growing up” is deeply entwined with the passage through school. As my students ascend the school hierarchy, they accommodate themselves to changing models of a child their age. The archetypical first grader is intrinsically more sophisticated than a kindergartner and accordingly, they became more sophisticated. The presentation of a new self-concept facilitated change.
Neither culture’s deep impact on development nor the principality of self-concept in a child’s developmental tendencies are radical ideas in the educational community. Lev Vygotsky posited eighty years ago that cognitive development was an inherently socio-cultural phenomenon. He pointed out that culture, not biology, creates most of the tools we use to develop and the impulses that drive development. “Self-concept,” as far as I can tell, entered common educational parlance more recently, but nowadays research abounds on academic self-concept and how schools can influence it. The cultural construction of childhood and education may dictate a developmental course.
However, I’ve come to appreciate the beguiling simplicity of the change in my students. Who deserves credit for their growth? Not me, not school, not biology. “Culture”? That’s a useless answer and a cop out on my part. They do. Each of them has set new expectations for themselves and risen to meet them. School, culture and I only contributed through suggesting standards. Development might be fluid, but children govern themselves autonomously enough to consciously adjust to the structure of school, to reconsider their self-image and to create new ambitions. Despite spending most of my day in the classroom, I run abreast of dividing my critical thought about educational theory (to which I have only moderate exposure) from that about the needs of my students. I hope this is a common pitfall for fledgling teachers. The students’ needs are immediate; theory abstruse and ever changing, both are new and the two demand different sorts of consideration. Yet, ultimately, children’s decisions and goals have the biggest impact on how they grow. Theory, of course, only serves them if it helps us provide guidance in shaping and actuating those decisions.
In the first period of first grade, we set down to work on weekend news, a weekly routine continued from kindergarten. The kids’ handwriting was tidy, their accounts thoughtful. They spelled sight-words correctly and each wrote several sentences. Some of their best writing to date – even from students who struggled with writing last year – completely self-motivated. They intended to realize their standard for a first grader. With a confounding array of theories and concepts to inform my practice, all of which are thrilling at this point in my career, I keep reminding myself what really has the biggest influence on my students’ development: my students.
Many schools arrange curricula and instruction to provide children with resources for their developmental tasks. Teachers strive to operate as guides who help children safely and comfortably grow — and sometimes cope — in their early encounters with the challenges of development. We know that many developmental needs do not permanently abate, but we hope that children leave school able to grapple with them self-sufficiently. This guidance accounts for some correlation between educational practice and a child’s course of development. It doesn’t explain the leap my students made between June and October, which occurred mostly outside of school, but in accordance with the way school is organized. After only a year of formal schooling, my students’ development fell into step with the academic calendar. I see no direct way that either a teacher’s or a curriculum’s shepherding can prompt their simultaneous independent upswings in self-regulation and cognition.
Developmental theory certainly informs the practice of any decent teacher. It influences everything from how we arrange the furniture in our room to how we plan lessons. We need it to anticipate children’s behaviors and needs. Development has a clear influence on teaching, but school’s effect on development is more nebulous. How, exactly, is school as a totality congruent with actual development? Teachers and schools structure the school year and grade levels to lend them a narrative quality; there’s a distinct passage through the year, punctuated by vacations, exams and projects. We have benchmarks for mastery after which students ascend to new challenges. However, the increments by which we arrange the school experience seem to exist more for organizational purposes than developmental ones. They help us assess students — to know what we expect from them and when we expect it (even if the children in our classes are not developing at the same pace). They also help us arrange curricula in cohesive ways that permit some form of culmination and evaluation.
Unlike curricula, development doesn’t culminate and its mutability makes it difficult to evaluate. Piaget did formulate a sequence of cumulative developmental stages, but even he admitted the pliancy of development as a whole. Development is a continuum, but it lacks the inherent linear narrative and touchstones of school. Developmental tasks shift and mutate in a highly plastic process that, depending on your view, can last a lifetime. Needs like navigating social interactions, thinking abstractly, building competence in a skill or knowledge set, understanding individual identity, regulating thoughts and actions and overcoming egocentricity can be equally meaningful at five and 50 years of age. Development is not the process by which we overcome these issues, but by which we come to address them in new ways. I realize that an examination of the correspondences and discords between school and development warrants more than a couple of paragraphs, so rather than getting started on a dissertation, I’ll say this simply: development is fluid and school is pretty rigid.
What happens in the classroom doesn’t account for my students’ growth, so I need to look beyond the classroom for explanations. How might the socio-cultural context — the concept — of school have impacted them?
Most teachers leave off with their students in June and pick up new ones in September, relegating a holistic picture of the transition between grades to glimpses and estimations. For perhaps the only time in my career, I’ve gotten to advance with my students. Our move from kindergarten to first grade has proved a bit peculiar and I’m not sure either my students or I quite knew what to anticipate. Our arrival in kindergarten was, of course, an enormous benchmark; their first year in school, my first year of teaching. Eric Carle considered entering school the greatest trauma of childhood. kindergarten marks the beginning of student-hood and thereby entrance into a way of life that will persist into adulthood. We all arrived, excited, terrified and energized. Moving to first grade isn’t so dramatic. The beginning of the year is, ostensibly, business as usual. Language Arts, Reading and Math all pick up where kindergarten left off and performance expectations are raised a notch from where they were at the end of last year. The routine that we spent the kindergarten year establishing and acclimating to falls neatly into place.
Nonetheless, I’ve been confounded by the sophistication of my students’ work and thinking just in the first five weeks of school. Almost immediately, they were able to perform well beyond expectations that were challenging at the end of kindergarten. In Math, they decipher permutations, add automatically and subtract with confidence. Recently shaky number facts have solidified and are readily recalled. Almost all of my first graders sit down with chapter books and at least make a concerted effort to read them, peering into the pages for over half an hour. In kindergarten, they were hardly ever asked to read without guidance. They write stories several pages in length and edit their work for grammar, spelling and expressive language. The most writing we required for a single piece in kindergarten was five sentences and editing was limited to a basic (literal) checklist. Most astoundingly, they do it all independently. In kindergarten, my students needed a great deal of support and scaffolding to meet our expectations. Now, with little prompting, they refine and develop their thinking and pursue their work with determination. I don’t look over their shoulder or walk them through tasks. Mostly, I just tag along and take some notes.
What happened? Clearly, much of this new performance originates with a leap in self-regulation. My first graders approach their learning strategically and with high motivation. They can evaluate and monitor themselves. Even their social skills have improved. The students who had the most difficulty regulating their emotions and impulses in April are able to focus, participate and resolve conflicts with aplomb. Everyone seems more respectful of and sensitive to one another. Of course, this kind of progress is the developmental task of a six or seven-year-old, but they didn’t demonstrate this level of self-regulation in May.
I’m no expert, but I know enough about child development to understand that the school calendar and the passage through grade levels isn’t organized around developmental stages. All children develop at different paces within a two to three year normal range, a long time for a group six-year-old with birthdays up to eight months apart. It seems unlikely that such a variety of children could have experienced a developmental surge over the same, narrow period of time. Moreover, isn’t development more of a continuum than a series of leaps and bounds? Other teachers tell me this shift is typical of first graders, but why? How did three months off from school and a new class send them rocketing up the developmental spectrum? My students’ precipitous growth prompts me to wonder why development progresses in any particular way at all.
In a 2002 symposium on “Unraveling the ‘Teacher Shortage’ Problem,” the National Commission on Teaching and America’s Future noted that debate over teacher recruitment detracts from the more pressing issue of teacher retention. Ten years later, a strong focus on recruitment persists. Teaching attracts highly-qualified recent graduates. New York City public school teachers start at $45,530, with benefits and three months off, in the worst job market for young graduates since the Depression. Teaching offers respect, authority and purpose to a competitive and socially conscious generation. Unfortunately, half of new teachers quit within five years, a grim number in a profession with a steep learning curve. Associate teacher programs, popular at independent schools, can alleviate attrition and maximize young teachers’ effectiveness.
The NCTAF highlighted low attrition among “beginning teachers who have access to intensive mentoring by expert colleagues” and high student performance in schools with extensive faculty induction programs. Associate teacher programs, essentially apprenticeships, demonstrate why. Associates teach under the direction of a head teacher, in the head’s classroom, often while pursuing or after finishing a Masters degree. Independent schools employ associates as utility teachers and distribute them to where they are most useful. Associates reduce student-teacher ratios and can take responsibility for any aspect of instruction, from a lesson to an entire subject. They typically work with one class or grade-level each year, participating in every aspect of classroom life. Almost all aspire to head teaching positions. Their standing resembles that of an associate lawyer; educated, qualified, less experienced and working in the field with promotion opportunities.
Associate programs create fluidity in faculties without sacrificing consistency. Associates connect different classrooms and grade-levels by working with different head teachers during their tenure. The programs allow new teachers to join faculties without turnover among heads and schools can efficiently fill vacancies from within their own ranks. Most associates become head teachers elsewhere, creating professional networks among schools through teachers who have worked closely together.
If “intensive mentoring by expert colleagues” reduces attrition, then associate programs can address high teacher turnover while quickly improving schools. The NCTAF urged, “we must develop and sustain professionally rewarding career paths for teachers, from induction through accomplished teaching.” Associate programs make teaching a true growth profession in which a classroom with your name on the door becomes an aspiration.
Associate positions are mostly limited to the lower grades of independent and some charter schools. Financial limitations and credential requirements keep them out of public schools, which instead employ aides, assistants and paraprofessionals. Nonetheless, associate programs offer a model of a teaching career path that can improve instruction and help new teachers grow in all schools and grade-levels.
Nicholas Stone is a First Grade Associate Teacher at the Cathedral
School in Manhattan. Now in his second year, Nick spent his inaugural
teaching year as a Kindergarten Associate and a middle school athletics
coach. He studied History ...Read More