Wednesday, November 21, 2018

My dad’s first teaching job was in a one-room schoolhouse on a reservation way out a dirt road in northern California in the early 1930’s. He was responsible for teaching all of the children from first grade through eighth grade in that one room. Besides teaching math, reading, and history at eight different grade levels, he also taught music, sports, and drama-and was the administrator, counselor, secretary, and janitor. Whether the children were advanced for their age or needed remediation, anything they learned was taught by him; he was their special ed teacher, their subject-matter and resource specialist, and their gifted-and-talented mentor. I don’t know how he did it all. By today’s standards, such an assignment would be considered primitive, inefficient, overwhelming, and nearly impossible.

But from a teacher’s point of view, there is something immensely appealing about a one-room schoolhouse: you are in total control of the situation! And the all-encompassing nature of the work gives you a fully informed perspective: you know what the younger pupils are going to study when they get older, and you know what the older students worked on when they were younger. If you don’t feel your sixth-graders are adequately prepared for the rigors of seventh-grade math, you are not at the mercy of another teacher’s presumed incompetence. All you have to do is consult with yourself, and then do something about it to prepare them properly. You have the opportunity to address surmountable difficulties, organize your thoughts and resources, and work until the problems have been resolved to your satisfaction. Then if things don’t turn out the way you want, you have only yourself to blame. And when things do go right, you deserve and get the praise. If there was ever a profession where “the-buck-stops-here,” teaching in a one-room schoolhouse was it.

Things are so different nowadays. Take a typical seventh-grade math class for comparison. In a usual middle school situation, the math teacher is likely to have only three classes to prepare for: sixth-grade math, seventh-grade math, and eighth-grade math. Without all those other subjects to prep, the seventh-grade math teacher can be clearly focused one thing and one thing only: seventh-grade math standards and content. The teacher’s job-it is supposed-is to lead the class through all the chapters in the book, expose all the children to all the concepts and skills, and prepare them to do well on the inevitable standardized test.

If only it were that simple. Unfortunately, not all seventh-grade students are actually ready to learn seventh-grade math. Some of them were taught by another math teacher during the previous year, who didn’t succeed in having them master sixth-grade concepts and skills. Some of the sixth graders were taught by the teacher who also teaches seventh grade, but they were so poorly prepared by the fifth-grade classroom teachers that they didn’t have full access to the sixth-grade curriculum and spent a major part of the sixth-grade year struggling with remedial topics. And some students moved into the school district during their seventh-grade year, coming from other districts where their education was inadequate. And many struggles with English, which is not their native language, so they have trouble understanding directions, doing homework, and taking tests.

So the typical seventh-grade math instructor has to struggle with teaching a mixture of students who are at grade level, above grade level, below grade level, and far below grade level-all in the same classroom. In other words, the math teacher is still working in a one-room schoolhouse! There are, of course, some differences. In my dad’s classroom, there were students of many ages working at a variety of different math levels. In the modern classroom, there are many students of the same age operating at a variety of different math levels. In the historic classroom, the teacher had actually taught all the students year by year at the lower levels of instruction. In the modern class, the seventh-grade teacher knows what the students should have learned previously, but often has little direct experience in exactly how to develop those underlying lower level concepts and skills when the need arises with older pupils.

In the old-time schoolroom, it was not that hard to differentiate challenge levels to accommodate individual levels of readiness. Older students could temporarily join in with younger students to address a lower level math topic that was still challenging. Likewise, younger students could join in with older students to study topics for which they were ready. And even though the students might be working on math above or below the level thought suitable for their age, they could still be held accountable for doing the classwork, the homework, and the tests-and receive credit for doing that work. In the modern math class, students are sometimes offered remedial instruction by the math teacher within the whole-class setting but are not always offered credit for the hard work they must do to catch up. They may be encouraged to seek help, but are not generally required to do so.

In reality, students have very little chance of mastering seventh-grade content if they have not already mastered the prerequisite concepts and skills presented in the previous grades. But in the egalitarian world of American education, students are typically given a choice in an issue that is actually a matter of necessity. Heaven help the teacher if she should have the common sense to vary the demands for different students in the same class, and actually require individual students to master crucial remedial work. “No fair! Why should I have to do what he doesn’t have to do?!” Imagine the outrage of children and parents at such unfair treatment-especially if a majority of the students needing remediation are of the same racial/ethnic background. Addressing the individual needs and learning styles of low-achievers, and optimizing individual opportunity through individual accountability then becomes twisted into perceived racism.

More realistic objections might be, “Why are students asked to learn material for which they have clearly demonstrated a lack of readiness? Isn’t that unfair?” “Why do educators assume that just because all students are roughly the same age in a given math class, that they all have the same background, and are all ready to learn the same concepts and skills at the same time and at the same pace? Isn’t that unfair?” Differentiating the challenge level for different students in the same class is more than a good idea, more than savvy professional practice. It is a necessity. Groups don’t learn math; individuals learn math. Groups do not take a math test; individuals demonstrate their personal level of mastery on a math test. Instruction that only addresses the whole class as a group with a single style of presentation, and ignores different learning styles and individual needs for differentiated challenge levels, is out of touch with reality. And instruction that acknowledges different needs, but does not require remedial work to be mastered nor give credit for its completion, is not realistic.

Experienced seventh-grade math teachers might object, “Addressing individual remedial needs is a good idea, but I don’t have time for it! There are only so many minutes in a math class, and I have to spend that time getting students through the new material. There are a huge number of content standards to be addressed, and if I slow down to accommodate individual needs, there is no way I can get through the whole book in one year’s time. And the pressure to make that happen is significant. If we don’t cover the whole seventh-grade curriculum, the students will not be prepared for the eighth-grade curriculum-and that’s just not right. And the students must be prepared to succeed on the standardized tests. If they don’t do well, there are nasty repercussions for my school and for me. And besides, what right do the low-achievers have to prevent the quicker learners from learning all that they can learn by monopolizing the teacher’s time?”

“I believe that all students are teachable, but you just can’t reach everybody in the time allotted, given their lack of preparedness. I don’t mean to sound hard-hearted, but the best I can do is to help the students who are prepared to succeed to learn the new material and it’s just tough luck for the others. The most efficient use of my time is to concentrate on teaching the seventh-grade curriculum, and not waste time focusing on concepts and skills that the children should have learned before. I’m teaching seventh-grade math, not fourth-, fifth-, and sixth-grade math. Is it not right for me to assume that the students should know something by the time they reach seventh grade? We’re dealing with some very abstract material here. I just can’t dumb it down and still get the job done. If I slow down to ensure that all the students learn the material, we would only get through half the book in a year’s time.”

True, the issue of efficiency is very important. But the teacher is not the only person spending time in the math class. The students are spending time there, too. Is it more efficient for the slower students to spend a whole year “covering” the whole math book while learning virtually nothing, or to spend a whole year learning half of the material in the book really well? Is it efficient to demand that slower students proceed at a pace that they cannot manage and sustain? Is it efficient to demand that the faster students slow down to accommodate their slower peers? Knowing that some people learn better in small groups with a more tactile and deliberate approach, is it efficient to always instruct the class as a whole with abstract lectures? Is it impossible to instruct quicker students quickly in a small group, and then demand that they help each other to proceed at a fast pace? Can the teacher not organize the students to help each other get the job done, while she devotes at least some time helping those that seem least able to help themselves?

The problem with lack of student readiness plagues every grade level, beginning with kindergarten. But the teacher has a curriculum to teach and must move on, whether all the students are ready or not. While agreeing that it is a good idea not to leave any children behind, most teachers consider it impossible to hold themselves responsible for making sure that the job gets done with every child. It was somebody else’s job to properly prepare the students so that they would be ready for the current course of instruction. But that didn’t happen. So what can you do? Move on. It will be somebody else’s job to make sure that your students learn later what they were unable to learn with you now. Unfortunately, as the students move to the next grade level, it is too late to learn what they missed the year before because the teacher is preoccupied with “covering” the next year’s curriculum. The year before, it was too early for students to learn certain concepts and skills because they were not ready; but the year after, it is too late for them to learn it because it should have happened before. One cannot help wondering: when exactly is the right time for this learning to take place, and who is responsible for making it happen?

In a one-room schoolhouse, it is clear that the teacher is the only math teacher for every child in the room. No one else is appointed to get the job done. There is no resource teacher, no separate after-school program, and no intervention specialist to fall back on. And having a child waste a whole year in anguished confusion, with the hope that it will all be rectified during summer school or the following year is seen as an obvious inefficiency. The one-room schoolteacher not only teaches seventh-grade math: she is teaching kids seventh-grade math. That is an important distinction. She is not just teaching the seventh-grade math curriculum; she is teaching it to seventh-grade kids-all of them that are in her charge.

The illusion of teaching in a modern-day classroom is to believe that you are no longer teaching in a one-room schoolhouse and that someone else is responsible for getting the job done with the hard-to-teach; that all students are supposed to come to you equally prepared, and that something is terribly wrong and abnormal if they are not; that your proper mission is to focus exclusively on the state-mandated seventh grade curriculum. Influenced by these misconceptions, it is easy to forget that you are those kids’ only math teacher and that you are teaching kids seventh-grade math-all of them. Guided by the fiction that we are not teaching in a one-room schoolhouse, it is easy to believe that it is always too early or too late to meet individual learning needs with artful flexibility and efficiency. Governed by that illusion, it is easy to assume that it is someone else’s job to get the students ready for what they must learn now.

But it is only an illusion. Teachers in every class are still teaching in a one-room schoolhouse because there are many students operating at a variety of different math levels in the same room and there always will be. For any given class of seventh graders, their math teacher is the only math teacher that they will have for an entire year; everything they learn is the responsibility of that teacher; all the catching up they do will be because of that teacher. Some of the lowest achievers may truly not be ready to learn very much of the current seventh-grade curriculum without major adaptations, but they are ready to learn something in math, and it is no other teacher’s responsibility to make sure that happens. It might be true that those children’s interests might best be served in another setting, but if it is not possible for them to be transferred to other classes, then it’s of little practical value to complain about the situation; their current math teacher is solely responsible for preparing those low-achievers for what they can learn now. If there are gaps that need to be filled in order to make that happen, then that adult is solely responsible for making sure that those gaps are filled.

Strategies for filling concept and skill gaps are topics that are too big to address in this article. Suffice it to say that the teacher may need to acquire a wide variety of teaching techniques that are new to her to effectively fill those gaps. But change is difficult for everyone, including teachers-most of whom have already developed ways of interacting with their classes that they feel comfortable with. As one middle school math teacher put it, “I like what I’m doing; it works for me.” (Unfortunately, it wasn’t working for a lot of his students, but either he didn’t recognize that, or figured that it was just one those things that you can’t do anything about!) Significant change requires new ways of thinking and a prodigious amount of hard work. That change is driven by a change in attitude-the establishment of the conviction that it is the math teacher’s rightful responsibility to teach all of the students in her charge, not just the ones that are the easiest to teach; that “covering the book” is not the only job that is to be done; that instruction must take into account where the students’ minds actually are not where they are supposed to be. Assenting to this perspective frees the teacher’s mind to seek and perfect new instructional techniques and new ways of organizing student efforts, to the end that every student will be enabled to progress from their current state of mathematical understanding and skill towards the mastery of their grade level curriculum. Changing our perspective is the first step towards learning how to achieve what was formerly thought to be impossible.—

Resisting this perspective (either through active opposition or the passive resistance of entrenched habit) tends to prevent teachers from doing what really can be done in a challenging situation. It is true that teaching to a variety of concept and skill levels, rather than focusing exclusively on the grade level curriculum, is grossly inefficient. But inefficient, compared to what? Allowing large groups of children to pass from year to year without making appreciable mathematical progress is a colossal waste of everyone’s time, and the negative impact of their incompetence on their higher-achieving classmates is far from negligible. And the longer it goes on, the worse it gets. That is inefficiency with an exponential growth factor!

It is time for math teachers to mentally get back into teaching in a one-room schoolhouse. If my dad could successfully teach all subjects to eight different grade levels, taking into consideration the huge range of topics to be covered, as well as the vast diversity of learning styles and levels of readiness, then seventh grade math teachers can realistically accept the goal of nurturing the mathematical thinking of every single student in their classes. This applies, of course, to every grade level-including high school, where the ages of students in math classes may actually vary by as much as four years, and where the presumption is very strong that all students in a given class are or should be at the same level of readiness to learn. This assumption needs to be recognized as the fiction that it is so that teachers can get down to the business of teaching kids math.

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