| My dad's first teaching job was in a one-room | | | | seventh grade math, not fourth-, fifth-, and |
| schoolhouse on a reservation way out a dirt road in | | | | sixth-grade math. Is it not right for me to assume |
| northern California in the early 1930's. He was | | | | that the students should know something by the |
| responsible for teaching all of the children from first | | | | time they reach seventh grade? We're dealing with |
| grade through eighth grade in that one room. Besides | | | | some very abstract material here. I just can't dumb it |
| teaching math, reading, and history at eight different | | | | down and still get the job done. If I slow down to |
| grade levels, he also taught music, sports, and | | | | insure that all the students learn the material, we |
| drama-and was the administrator, counselor, | | | | would only get through half the book in a year's |
| secretary, and janitor. Whether the children were | | | | time." |
| advanced for their age or needed remediation, | | | | True, the issue of efficiency is very important. But |
| anything they learned was taught by him; he was | | | | the teacher is not the only person spending time in |
| their special ed teacher, their subject-matter and | | | | the math class. The students are spending time |
| resource specialist, and their gifted-and-talented | | | | there, too. Is it more efficient for the slower |
| mentor. I don't know how he did it all. By today's | | | | students to spend a whole year "covering" the whole |
| standards, such an assignment would be considered | | | | math book while learning virtually nothing, or to spend |
| primitive, inefficient, overwhelming, and nearly | | | | a whole year learning half of the material in the book |
| impossible. | | | | really well? Is it efficient to demand that slower |
| But from a teacher's point of view, there is | | | | students proceed at a pace that they cannot |
| something immensely appealing about a one-room | | | | manage and sustain? Is it efficient to demand that |
| schoolhouse: you are in total control of the situation! | | | | the faster students slow down to accommodate |
| And the all-encompassing nature of the work gives | | | | their slower peers? Knowing that some people learn |
| you a fully informed perspective: you know what the | | | | better in small groups with a more tactile and |
| younger pupils are going to study when they get | | | | deliberate approach, is it efficient to always instruct |
| older, and you know what the older students | | | | the class as a whole with abstract lectures? Is it |
| worked on when they were younger. If you don't | | | | impossible to instruct quicker students quickly in a |
| feel your sixth-graders are adequately prepared for | | | | small group, and then demand that they help each |
| the rigors of seventh-grade math, you are not at the | | | | other to proceed at a fast pace? Can the teacher |
| mercy of another teacher's presumed incompetence. | | | | not organize the students to help each other get the |
| All you have to do is consult with yourself, and then | | | | job done, while she devotes at least some time |
| do something about it to prepare them properly. You | | | | helping those that seem least able to help |
| have the opportunity to address surmountable | | | | themselves? |
| difficulties, organize your thoughts and resources, and | | | | The problem with lack of student readiness plagues |
| work until the problems have been resolved to your | | | | every grade level, beginning with kindergarten. But |
| satisfaction. Then if things don't turn out the way | | | | the teacher has a curriculum to teach and must |
| you want, you have only yourself to blame. And | | | | move on, whether all the students are ready or not. |
| when things do go right, you deserve and get the | | | | While agreeing that it is a good idea not to leave any |
| praise. If there was ever a profession where | | | | children behind, most teachers consider it impossible |
| "the-buck-stops-here," teaching in a one-room | | | | to hold themselves responsible for making sure that |
| schoolhouse was it. | | | | the job gets done with every child. It was somebody |
| Things are so different nowadays. Take a typical | | | | else's job to properly prepare the students so that |
| seventh-grade math class for comparison. In a usual | | | | they would be ready for the current course of |
| middle school situation, the math teacher is likely to | | | | instruction. But that didn't happen. So what can you |
| have only three classes to prepare for: sixth-grade | | | | do? Move on. It will be somebody else's job to make |
| math, seventh-grade math, and eighth-grade math. | | | | sure that your students learn later what they were |
| Without all those other subjects to prep, the | | | | unable to learn with you now. Unfortunately, as the |
| seventh-grade math teacher can be clearly focused | | | | students move to the next grade level, it is too late |
| one thing and one thing only: seventh-grade math | | | | to learn what they missed the year before, because |
| standards and content. The teacher's job-it is | | | | the teacher is preoccupied with "covering" the next |
| supposed-is to lead the class through all the chapters | | | | year's curriculum. The year before, it was too early |
| in the book, expose all the children to all the | | | | for students to learn certain concepts and skills |
| concepts and skills, and prepare them to do well on | | | | because they were not ready; but the year after, it |
| the inevitable standardized test. | | | | is too late for them to learn it because it should have |
| If only it were that simple. Unfortunately, not all | | | | happened before. One cannot help wondering: when |
| seventh grade students are actually ready to learn | | | | exactly is the right time for this learning to take |
| seventh grade math. Some of them were taught by | | | | place, and who is responsible for making it happen? |
| another math teacher during the previous year, who | | | | In a one-room schoolhouse, it is clear that the |
| didn't succeed in having them master sixth grade | | | | teacher is the only math teacher for every child in |
| concepts and skills. Some of the sixth graders were | | | | the room. No one else is appointed to get the job |
| taught by the teacher who also teaches seventh | | | | done. There is no resource teacher, no separate |
| grade, but they were so poorly prepared by the fifth | | | | after-school program, and no intervention specialist to |
| grade classroom teachers that they didn't have full | | | | fall back on. And having a child waste a whole year in |
| access to the sixth grade curriculum, and spent a | | | | anguished confusion, with the hope that it will all be |
| major part of the sixth grade year struggling with | | | | rectified during summer school or the following year |
| remedial topics. And some students moved into the | | | | is seen as an obvious inefficiency. The one-room |
| school district during their seventh grade year, coming | | | | schoolteacher not only teaches seventh grade math: |
| from other districts where their education was | | | | she is teaching kids seventh grade math. That is an |
| inadequate. And many struggle with English, which is | | | | important distinction. She is not just teaching the |
| not their native language, so they have trouble | | | | seventh grade math curriculum; she is teaching it to |
| understanding directions, doing homework, and taking | | | | seventh grade kids-all of them that are in her charge. |
| tests. | | | | The illusion of teaching in a modern-day classroom is |
| So the typical seventh grade math instructor has to | | | | to believe that you are no longer teaching in a |
| struggle with teaching a mixture of students who are | | | | one-room schoolhouse, and that someone else is |
| at grade level, above grade level, below grade level, | | | | responsible for getting the job done with the |
| and far below grade level-all in the same classroom. In | | | | hard-to-teach; that all students are supposed to |
| other words, the math teacher is still working in a | | | | come to you equally prepared, and that something is |
| one-room schoolhouse! There are, of course, some | | | | terribly wrong and abnormal if they are not; that |
| differences. In my dad's classroom, there were | | | | your proper mission is to focus exclusively on the |
| students of many ages working at a variety of | | | | state-mandated seventh grade curriculum. Influenced |
| different math levels. In the modern classroom, there | | | | by these misconceptions, it is easy to forget that |
| are many students of the same age operating at a | | | | you are those kids' only math teacher, and that you |
| variety of different math levels. In the historic | | | | are teaching kids seventh grade math-all of them. |
| classroom, the teacher had actually taught all the | | | | Guided by the fiction that we are not teaching in a |
| students year by year at the lower levels of | | | | one-room schoolhouse, it is easy to believe that it is |
| instruction. In the modern class, the seventh grade | | | | always too early or too late to meet individual |
| teacher knows what the students should have | | | | learning needs with artful flexibility and efficiency. |
| learned previously, but often has little direct | | | | Governed by that illusion, it is easy to assume that it |
| experience in exactly how to develop those | | | | is someone else's job to get the students ready for |
| underlying lower level concepts and skills when the | | | | what they must learn now. |
| need arises with older pupils. | | | | But it is only an illusion. Teachers in every class are |
| In the old-time schoolroom, it was not that hard to | | | | still teaching in a one-room schoolhouse, because |
| differentiate challenge levels to accommodate | | | | there are many students operating at a variety of |
| individual levels of readiness. Older students could | | | | different math levels in the same room-and there |
| temporarily join in with younger students to address | | | | always will be. For any given class of seventh |
| a lower level math topic that was still challenging. | | | | graders, their math teacher is the only math teacher |
| Likewise, younger students could join in with older | | | | that they will have for an entire year; everything |
| students to study topics for which they were ready. | | | | they learn is the responsibility of that teacher; all the |
| And even though the students might be working on | | | | catching up they do will be because of that teacher. |
| math above or below the level thought suitable for | | | | Some of the lowest achievers may truly not be |
| their age, they could still be held accountable for | | | | ready to learn very much of the current seventh |
| doing the classwork, the homework, and the | | | | grade curriculum without major adaptations; but they |
| tests-and receive credit for doing that work. In the | | | | are ready to learn something in math, and it is no |
| modern math class, students are sometimes offered | | | | other teacher's responsibility to make sure that |
| remedial instruction by the math teacher within the | | | | happens. It might be true that those children's |
| whole-class setting, but are not always offered credit | | | | interests might best be served in another setting, but |
| for the hard work they must do to catch up. They | | | | if it is not possible for them to be transferred to |
| may be encouraged to seek help, but are not | | | | other classes, then it's of little practical value to |
| generally required to do so. | | | | complain about the situation; their current math |
| In reality, students have very little chance of | | | | teacher is solely responsible for preparing those |
| mastering seventh grade content if they have not | | | | low-achievers for what they can learn now. If there |
| already mastered the prerequisite concepts and skills | | | | are gaps that need to be filled in order to make that |
| presented in the previous grades. But in the | | | | happen, then that adult is solely responsible for |
| egalitarian world of American education, students are | | | | making sure that those gaps are filled. |
| typically given a choice in an issue that is actually a | | | | Strategies for filling concept and skill gaps are topics |
| matter of necessity. Heaven help the teacher if she | | | | that are too big to address in this article. Suffice it to |
| should have the common sense to vary the demands | | | | say that the teacher may need to acquire a wide |
| for different students in the same class, and actually | | | | variety of teaching techniques that are new to her |
| require individual students to master crucial remedial | | | | to effectively fill those gaps. But change is difficult |
| work. "No fair! Why should I have to do what he | | | | for everyone, including teachers-most of whom have |
| doesn't have to do?!" Imagine the outrage of children | | | | already developed ways of interacting with their |
| and parents at such unfair treatment-especially if a | | | | classes that they feel comfortable with. As one |
| majority of the students needing remediation are of | | | | middle school math teacher put it, "I like what I'm |
| the same racial/ethnic background. Addressing the | | | | doing; it works for me." (Unfortunately, it wasn't |
| individual needs and learning styles of low-achievers, | | | | working for a lot of his students, but either he didn't |
| and optimizing individual opportunity through individual | | | | recognize that, or figured that it was just one one |
| accountability then becomes twisted into perceived | | | | those things that you can't do anything about!) |
| racism. | | | | Significant change requires new ways of thinking and |
| More realistic objections might be, "Why are students | | | | a prodigious amount of hard work. That change is |
| asked to learn material for which they have clearly | | | | driven by a change in attitude-the establishment of |
| demonstrated a lack of readiness? Isn't that unfair?" | | | | the conviction that it is the math teacher's rightful |
| "Why do educators assume that just because all | | | | responsibility to teach all of the students in her |
| students are roughly the same age in a given math | | | | charge, not just the ones that are the easiest to |
| class, that they all have the same background, and | | | | teach; that "covering the book" is not the only job |
| are all ready to learn the same concepts and skills at | | | | that is to be done; that instruction must take into |
| the same time and at the same pace? Isn't that | | | | account where the students' minds actually are-not |
| unfair?" Differentiating the challenge level for different | | | | where they are supposed to be. Assenting to this |
| students in the same class is more than a good idea, | | | | perspective frees the teacher's mind to seek and |
| more than savvy professional practice. It is a | | | | perfect new instructional techniques and new ways |
| necessity. Groups don't learn math; individuals learn | | | | of organizing student efforts, to the end that every |
| math. Groups do not take a math test; individuals | | | | student will be enabled to progress from their current |
| demonstrate their personal level of mastery on a | | | | state of mathematical understanding and skill towards |
| math test. Instruction that only addresses the whole | | | | the mastery of their grade level curriculum. Changing |
| class as a group with a single style of presentation, | | | | our perspective is the first step towards learning |
| and ignores different learning styles and individual | | | | how to achieve what was formerly thought to be |
| needs for differentiated challenge levels, is out of | | | | impossible.--- |
| touch with reality. And instruction that acknowledges | | | | Resisting this perspective (either through active |
| different needs, but does not require remedial work | | | | opposition or the passive resistance of entrenched |
| to be mastered nor give credit for its completion, is | | | | habit) tends to prevent teachers from doing what |
| not realistic. | | | | really can be done in a challenging situation. It is true |
| Experienced seventh grade math teachers might | | | | that teaching to a variety of concept and skill levels, |
| object, "Addressing individual remedial needs is a | | | | rather than focusing exclusively on the grade level |
| good idea, but I don't have time for it! There are | | | | curriculum, is grossly inefficient. But inefficient, |
| only so many minutes in a math class, and I have to | | | | compared to what? Allowing large groups of children |
| spend that time getting students through the new | | | | to pass from year to year without making |
| material. There are a huge number of content | | | | appreciable mathematical progress is a colossal waste |
| standards to be addressed, and if I slow down to | | | | of everyone's time, and the negative impact of their |
| accommodate individual needs, there is no way I can | | | | incompetence on their higher-achieving classmates is |
| get through the whole book in one year's time. And | | | | far from negligible. And the longer it goes on, the |
| the pressure to make that happen is significant. If we | | | | worse it gets. That is inefficiency with an exponential |
| don't cover the whole seventh grade curriculum, the | | | | growth factor! |
| students will not be prepared for the eighth grade | | | | It is time for math teachers to mentally get back |
| curriculum-and that's just not right. And the students | | | | into teaching in a one-room schoolhouse. If my dad |
| must be prepared to succeed on the standardized | | | | could successfully teach all subjects to eight different |
| tests. If they don't do well, there are nasty | | | | grade levels, taking into consideration the huge range |
| repercussions for my school and for me. And besides, | | | | of topics to be covered, as well as the vast diversity |
| what right do the low-achievers have to prevent the | | | | of learning styles and levels of readiness, then |
| quicker learners from learning all that they can learn | | | | seventh grade math teachers can realistically accept |
| by monopolizing the teacher's time?" | | | | the goal of nurturing the mathematical thinking of |
| "I believe that all students are teachable, but you just | | | | every single student in their classes. This applies, of |
| can't reach everybody in the time allotted, given their | | | | course, to every grade level-including high school, |
| lack of preparedness. I don't mean to sound | | | | where the ages of students in math classes may |
| hard-hearted, but the best I can do is to help the | | | | actually vary by as much as four years, and where |
| students who are prepared to succeed to learn the | | | | the presumption is very strong that all students in a |
| new material-and it's just tough luck for the others. | | | | given class are or should be at the same level of |
| The most efficient use of my time is to concentrate | | | | readiness to learn. This assumption needs to be |
| on teaching the seventh grade curriculum, and not | | | | recognized as the fiction that it is, so that teachers |
| waste time focusing on concepts and skills that the | | | | can get down to the business of teaching kids math. |
| children should have learned before. I'm teaching | | | | |