A few years after I was in the fourth grade in the late Forties I came across a pamphlet (I think in the Principal’s Office) that laid out the fourth grade curriculum and I found it an accurate description of what had happened in the real classroom. The pamphlet provided a list of the topics that are to be and were in fact covered. That included short and long division and multiplication by two digit numbers. It also included a lot about the history of New York City and New York State. There were the four governors of New Amsterdam and the building and significance of the Erie Canal. There was also the introduction of maps so that students could read the visualizations of the five boroughs of New York City and the expansion West of the American nation. The students learned about Sutter’s Fort and the Pony Express. I was very impressed by the careful consideration of what topics to include and their sequencing. Not to push students too quickly and make sure that there would be just a bit more complexity with each topic in arithmetic and basing history on what was already known so that the stories made sense. Don’t go into maps before you introduce Henrick Hudson and his eventual dire fate in Hudson Bay. I sensed education as carefully crafted.The students could trust their teachers to guide them through the shoals of their ignorance.
The preparation of the curriculum, I realized many years later, was based on two assumptions. The first was that the curriculum was cumulative in that a student had to master the earlier lessons so as to master the later ones. You wouldn;t likely learn long division ( which is when the divisor has at least two digits) if you had not already earned short division (which is when the divisor is a single digit) or that the times when the West was added by the Louisiana Purchase and then the Mexican Cession would not make sense if you did not already see that New York City had expanded from Lower Manhattan to include its five boroughs (Queens just a new place filling up with post-World War II housing developments). The second point, a consequence of the first, was that student attendance was important because you had to catch up if you missed a day of school and had not been there to learn that day’s lessons. I worried I might lose track and get lost in the carefully articulated curriculum. Even reading was graded. There were readers that mixed poetry and stories and nonfiction and that got more difficult as you progressed in the book for the semester, or so I then believed the case to have been. A lot of students, I thought, might never catch up but what in fact happened was that they just learned more slowly, moving along ever more behind than the more able students.
A profound inference or premise could be drawn from the fact that education was structured as a collective exercise whereby students learned more over time, so that at the end of the fourth grade most of the students in a class knew more than they had, when entering that grade. It provided a metaphor for how education happened and so resolved the mystery whereby something unknown was replaced by knowing, some fact and theory with which one was comfortable that had replaced the fogginess of unknowing, long division mastered after just short division had been perplexing, an operation a student could not yet apply. That metaphor was about time: that knowledge too place over time and, moreover, with more time, knowledge could not merely increase but deepeen. That idea that knowledge is graded is different from the idea that some people can learn and some people can’t, that people can either be learners or not, or at least exceptional learners, who are the only ones that count, while others may learn their ABC’s but that is about all. People could master their Euclid by being ex[osed to a book, while others did not, but midshipmen learned calculus by the group instruction of their officers, perhaps because they had been tutored on lower level mathematics before joining the Royal Navy.
There is something to be said for the idea that inclination rather than accumulation results in learning. Spinoza thought that philosophy was just beyond the ken of some people, however much they applied themselves. I was astonished at how much Frank Kermode knew about minor plays when I, an English Major, was able to master or just read the major plays and novels, or the ability of a professor of mine to push through every Victorian novel he could come across because he thought it illuminated the various ploys and devices of the authors of the age, though I was not at all sure that it had deepened his appreciation of Dickens, which was already of a very high luster because of a deep contemplation of the texts.
But inherent in the idea that time mediates for or allows learning leads to a sense of levels of depth rather than just greater accumulation. As time moves on, you move from the usual books to the more esoteric ones and then to the outright strange ones, so that Stephan Greenblat was able to know enough to analyze an emblem for all of its references and so illuminate how the Elizabethan Age worked. Maybe if I worked hard enough I might progress to do that.
The same is true in the fourth grade.I knew that in the multiplication table the next number in the nine’s column was to add ten minus one, but I had no conception of number theory (or still do), but I could still manage to get harder and harder math problems so as to get through my statistics exams. A bit later, maybe in the seventh grade, you might learn that there was the Kansas-Nebraska Act, wherein there was unrest over whether one or both of these territories would become free states and so was one of those events that tumbled down the hill into the Civil War. But it wasn’t until I read McPherson’s “Battle Cry of Freedom” that I gathered his perception that the Kansas Nebraska conflict was pivotal because it was when Northerners and southerners were now willing to kill one another. That struck me as a deep insight, earned from pondering what makes a revolution or just a flame of intuition concocted by a deep thinker. Whatever my models. It seems to me cumulative learning is not just more learning but deeper learning so that when I had my doctoral degree I would presume who a young relative should vote for in a municipal election because I knew political sociology rather than because I had known about politics ever since I could remember.
Curricula have changed. Last I looked, they set goals rather than topics. Reading in the fourth or any other grade means reading more demanding material, more complex grammar, rather than a particular reader or set of books. Arithmetic means having more understanding about numbers rather than learning particular operations. Also, students don’t have to advance at a modal pace because there are so many individual programs on the computer so every child can learn at their own pace even if they have missed a few days, though experience suggests that group learning is more successful than individual or at home learning for reasons that are still a mystery. And abandoning a time oriented and sequenced curriculum is not really necessary. A high school English teacher told to offer his lesson plans for the week said for the slot for each day “Discuss ‘The Magic Mountain’ some more”, and no one could fault his results.
But, in fact, there are curricula in high school. What is offered is organized around textbooks. They provide the logical development of the subject matter rather than how to explain or urge students to learn. It is the body of the subject matter rather than the way to move from easier to harder. The well known Calculus textbook of my time, Thomas’ “Calculus” made sure to include early on the discussion of the Mean Value Theorem even though it was harder to master than differentiation, which followed, and integration, which followed later on. The book unfolded the theoretical basics before going on to applications, just as my college Shakespeare professor began with the poems and then “Comedy of Errors” all the way down to “The Tempest”, the last of the plays, though there was no reason to do it that way,especially since the plays roughly break down from histories to comedies to tragedies to problem plays before reaching that pinacle of “The Tempest”, which remains a mystery.I also liked it when my college physics teacher laid out Newtonian mechanics by adding one variable at a time so as to build from Force=Mass times Acceleration to Work= Force times Displacement. But I was a poet taster, dipping into calculus and physics only to find the water too deep for me.
Colleges also have curricula, also through textbooks. Literature courses have anthologies which shift, from one decade to another, as thinking what are the important writers to experience as deep as well as artful. So twenty years ago, American literature anthologies included Chief Seattle, whose contributions do not seem ageless,even if he did indeed write what was attributed to him. The more important textbooks are in science and social science. We can divide those who are true scientists who lay out their disciplines in logical order, as in physics and mathematics, even though there are topics which are selected as usually associated with the topic, such as number theory, but are nevertheless coherent in building up from basics, and so are like the fourth grade arithmetic curricula, while the social sciences are not cumulative but just a set of topics, where the chapters about religion or the economy are not based on conclusions drawn from the earlier chapters but independent, just on their own not at all he larger institutions relying on the earlier chapter about small groups or the idea of customs, the early chapters just having to be covered because those are topics of historical interest. No Mean Value Theorem or its equivalent in sociology. More the pity unless the textbook writer thinks that Durkheim is the glue that ties everything together and there were for a while textbooks that treated Mertonian functionalism as a through theme for everything sociology offered. So there is something profound about curricula: they claim that what is to be known is really known, a science rather than a set of topics, history real because you can unfold it as it hesitates and then crosses the Alleghenies, the story making sense to a degree that you really can’t dispute it except at the edges, just elaborated so as to fill out its lacunae. I liked the fourth grade curriculum.