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The Public School Issue is a
Public Health Issue
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/8/13_The_Public_School_Issue_is_aPublic_Health_Issue.html
8ecdbeb687564174a1b46ee9ed1dfef2
Wed, 13 Aug 2008 15:36:56 0400
(Note: This essay is still in draft form. A pdf file containing it is available <a href="http://melconway.com/Urban_Teaching/pdf/Education_and_Public_Health.pdf">here</a>.)<br/><br/>This title can have more than one meaning; the one I intend is the one that isn't obvious. I'll explain. <br/>What follows is an example of what can come out of multidisciplinary inquiry. <br/>Lesson 1. My wife Ruth is a licensed mental health counselor; one of her specialties is working with people who have had trauma (both bigT and littlet) in their lives. This summer she took a oneweek course taught by Bessel van der Kolk, MD, a well recognized trauma investigator and clinician [1]. The subject of the course was observable changes to the brains–and to the behaviors–of trauma victims. I spent the days in the library and was briefed from her notes at the end of each day. <br/>Bottom line. Many victims of psychological trauma have major attention deficits as the result of their traumas. There can be a lot of overlap between the symptoms of ADHD and Post Traumatic Stress Disorder. [2] It is possible to confuse hypervigilance associated with PTSD with “hyperactivity.” If such hypervigilance is not noted a diagnosis of PTSD can fall through the cracks and show up simply as a learning disorder. <br/>Some clinicians use the term of art not present to describe the cognitive state of some trauma victims. Every teaching day of my four years at Chelsea High School I looked into the faces of many people who were not present. <br/>Lesson 2. Several therapists taking the course stayed in the same B&B where we were, and breakfast conversations were lively with shared experiences. One person suggested that I learn about the ACE study, and I spent that day researching it. What an eyeopener that was. “ACE” stands for “adverse childhood experiences.” The initial study examined the emotional histories of over 17,000 adult patients at Kaiser Permanente, and correlated these histories with adult morbidity. To quote from the first page of a 2002 paper [3] I strongly recommend to every reader: <br/>“The ACE Study reveals a powerful relationship between our emotional experiences as children and our physical and mental health as adults, as well as the major causes of adult mortality in the United States. It documents the conversion of traumatic emotional experiences in childhood into organic disease later in life. How does this happen, this reverse alchemy, turning the gold of a newborn infant into the lead of a depressed, diseased adult? The Study makes it clear that time does not heal some of the adverse experiences we found so common in the childhoods of a large population of middleaged, middle class Americans.”<br/>The researchers defined a number from 0 to 8 called the “ACE Score.” This number counts the number of different categories of childhood abuse and household dysfunction (not the number of incidents) reported by the adult patients. To quote from the paper (the numbers and the word change were added for clarity by me): <br/>“The abuse categories were: (1)recurrent physical abuse, (2)recurrent severe emotional abuse, and (3)contact sexual abuse. The five categories of household dysfunction were: growing up in a household (4)where someone was in prison; (5)where the mother was treated violently; (6)with an alcoholic or a drug user; (7)where someone was chronically depressed, mentally ill, or suicidal; and [sic. i.e., or] (8)where at least one biological parent was lost to the patient during childhood–regardless of cause. An individual exposed to none of the categories had an ACE Score of 0; an individual exposed to any four had an ACE Score of 4, etc.” <br/>Then the researchers correlated the ACE score of each patient with the current state of health of the patient. The results are amazing. Here is one (emphasis is the author’s).<br/>“Chronic obstructive pulmonary disease (COPD) also has a strong relationship to the ACE Score, as does the early onset of regular smoking. A person with an ACE Score of 4 is 260% more likely to have COPD than is a person with an ACE Score of 0. This relationship has the same graded, doseresponse effect that is present for all the associations we found. Moreover, all the relationships presented here have a p value of .001 or stronger. <br/><br/><br/>…”<br/>Emotional disorders are also considered:<br/>“When we looked at purely emotional outcomes like selfdefined current depression or selfreported suicide attempts, we find equally powerful effects. For instance, we found that an individual with an ACE Score of 4 or more was 460% more likely to be suffering from depression than an individual with an ACE Score of 0. Should one doubt the reliability of this, we found that there was a 1,220% increase in attempted suicide between these two groups. At higher ACE Scores, the prevalence of attempted suicide increases 3051fold (3,0005,100%)! Our article describing this staggering effect was published in a recent issue of the Journal of the American Medical Association. Overall, using the technique of population attributable risk, we found that between twothirds and 80% of all attempted suicides could be attributed to adverse childhood experiences.<br/><br/><br/><br/>…”<br/>There is no mention of school performance having been measured, but the following sentences appear. <br/>“Occupational health and job performance worsened progressively as the ACE Score increased. Some of these results are yet to be published….” <br/>Bottom line. By now you see where I am going with this. It could well be that already existing data show correlations between school performance and Adverse Childhood Experiences. <br/>If a connection between ACE Score and school performance is known, it must be put into the public conversation about education. If it is not known, there must be research examining this possibility. <br/>My own informal research strongly suggests a correlation between poverty and several of the categories in the ACE Score. [4] <br/>Lesson 3. The author of the paper finds that the results of the study seriously question the investigators’ conceptual frameworks as physicians (the added emphasis is mine): <br/>“Clearly, we have shown that adverse childhood experiences are common, destructive, and have an effect that often lasts for a lifetime. They are the most important determinant of the health and wellbeing of our nation. Unfortunately, these problems are painful to recognize and difficult to deal with. Most physicians would far rather deal with traditional organic disease. Certainly, it is easier to do so, but that approach also leads to troubling treatment failures and the frustration of expensive diagnostic quandaries where everything is ruled out but nothing is ruled in. <br/>Our usual approach to many adult chronic diseases reminds one of the relationship of smoke to fire. For a person unfamiliar with fires, it would initially be tempting to treat the smoke because that is the most visible aspect of the problem. Fortunately, fire departments learned long ago to distinguish cause from effect; else, they would carry fans rather than water hoses to their work. What we have learned in the ACE Study represents the underlying fire in medical practice where we often treat symptoms rather than underlying causes.” <br/>The author is making two points here: <br/> 1. The ubiquity and severity of the consequences of ACE make them a public health issue.<br/> 2. There is cause to question seriously the traditional medical treatment paradigm as applied to many chronic adult diseases. <br/>Bottom line. We as educators have the same problem the doctors do. We have addressed our performance issues in terms of the variables under our control when, in many cases, the causes of what we observe in the classroom lie well outside our control. As the doctors do, we struggle mightily using the methods given to us and we get results, but often they are mysteriously disappointing. How can we expect to “teach” a child who is not present? <br/>* * *<br/>It is not politically correct, and we educators do not have permission, to suggest that school is part of a larger social system and that a solution to our education problems requires consideration of that larger system. Indeed, the territorial ferocity surrounding the public education debate tells me that here is yet another corollary of Conway’s Law: Our solution will be no better than our ability to reorganize ourselves to encounter the system as it truly is. [5]<br/><br/>Endnotes<br/>1. <a href="http://www.traumacenter.org/">http://www.traumacenter.org/</a><br/>2. (Recent reference needed. “Psychological Trauma”, van der Kolk, 1987, Chapter 4 is not current enough.)<br/>3. “The Relationship of Adverse Childhood Experiences to Adult Health: Turning gold into lead,” Vincent J. Felitti (English translation of: Felitti VJ. “Belastungen in der Kindheit und Gesundheit im Erwachsenenalter: die Verwandlung von Gold in Blei.” Z psychsom Med Psychother 2002; 48(4): 359369). The document from which the present excepts were taken was found at <a href="http://www.partnershipforsuccess.org/uploads/200701_GoldintoLeadGermany102cGraphs.pdf">http://www.partnershipforsuccess.org/uploads/200701_GoldintoLeadGermany102cGraphs.pdf</a><br/>4. See <a href="Entries/2006/7/19_Anger.html">http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2006/7/19_Anger.html</a>; <br/>a table of supporting data is at <br/><a href="http://www.melconway.com/Urban_Teaching/pdf/MuniStats.pdf">http://www.melconway.com/Urban_Teaching/pdf/MuniStats.pdf</a> .<br/>5. Conway’s Law is a theorem in Sociology that states a relationship between the communication structure of a design (i.e., problemsolving) organization and the structure of any design (i.e., solution) it is able to produce. See the description in Wikipedia: <a href="http://en.wikipedia.org/wiki/Conway's_Law">http://en.wikipedia.org/wiki/Conway's_Law</a> .<br/><br/>© Copyright 2008 Mel Conway PhD

A Radical Proposal
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/3/10_A_Radical_Proposal.html
583c02f45b304e609961818b6b1261cc
Mon, 10 Mar 2008 12:58:06 0400
(Note: a pdf file containing this essay is available <a href="http://melconway.com/Urban_Teaching/pdf/A_Radical_Proposal.pdf">here</a>.)<br/><br/>My wife Ruth was a creative and highly regarded educator for 25 years before she took on a second career at about the time that I became a publicschool teacher. Our conversations would go round and round. I would say “No child left behind” and she would say “One child at a time.” I would say “Learning standards” and she would say “Meet the child at the place of readiness.” Of course she was right every time. The conversations would stop when I said “How?” In this essay I offer an outline of one answer to “How?”<br/>At the beginning of each year I started each of my three Geometry classes with a room of about 24 young people, many discouraged, many having had their mathematical development stunted before they entered high school, many with English skills that made the rate of acquisition of the required vocabulary a severe challenge in itself. From that starting point we began a wild ride, encountering and having to absorb a new lesson with a new set of concepts every two or three days, for about 150 class periods. By the end of the year a significant fraction of the students had fallen irretrievably behind, with others barely hanging on. Yet, by the time they became seniors, almost all of our students had passed the Massachusetts standard math test, and they graduated with a diploma. <br/>Creating a mathliterate person is like building a brick building: you do it one row at a time. Trying to skip steps is like trying to lay bricks on air. What’s bizarre is that we attempt it all the time and we can even believe that we’re succeeding sometimes. The source of our delusions is production quotas. It’s painful and perhaps unfair to draw this extreme analogy, but processing poorly prepared students through high school mathematics reminds me of the Sovietera factories that met their fiveyear plans by building what they were told to build, even if nobody could use it. <br/>If we’re going to do better we first need to identify the problem. As the person at the point of contact with—and the personal obligation to—the students, my take on the problem is this: I had been presented with a tragic dilemma. I had to fulfill two important yet conflicting mandates. Let us call these two mandates “The Material” and “The People.” The mandate we call The People is our duty as responsible teachercitizens to help prepare all of our students for productive and fulfilling lives. The mandate we call The Material is our legal obligation to deliver a specified body of content within a specified time. <br/>The public school politicallegal environment has declared that The Material is the supreme value (the code word is <a href="http://www.doe.mass.edu/Assess/">accountability</a>). This leads to a delivery strategy I shall call “Material First.” The logic of Material First is that if we can deliver the content successfully then the students will be well on their ways, and we will have therefore also performed The People. <br/>Given the classroom scenario I describe above, it doesn’t seem to work that way, because the assumption within the logic of Material First isn’t true. My efforts to deliver the specified body of content in the specified time routinely generated hundreds of missed opportunities for my students to experience the daytoday successes they needed so badly in order to have a more general success. In fact, neither The Material nor The People was being at all well performed. Yet we were making our numbers, more or less, so the reality was being masked. <br/>Meanwhile, what are the metaeducators doing? When I learn about the research in mathematics education that is going on in colleges of education, I see exciting and interesting work, almost all of it with young children. The education strategy inherent in this research seems to be: if the teacher deeply understands the underlying mathematics and uses that understanding strategically while applying the teaching techniques being developed, he or she should focus on eliciting the daily classroom successes of the students, and the learning will occur. It is a wonderfully optimistic idea, based on repeated observations that, given the right learning environment, children will learn. <br/>My students, however, arrive at my classroom bearing experiential baggage that obviously differs between primary and secondary students. My observations of my students were not consistent with these repeated observations of young children. <br/>As educators we carry an article of faith that, given the right environment, the students I have described above will indeed learn what is put in front of them. Clearly, then, our task is to find the right learning environment for them. The knot we have not figured out how to unravel is how to do this within the Material First mandate. <br/>I shall propose an alternative strategy for delivering our services. To distinguish it from Material First I shall call the alternative strategy Bounded Preparation First. The following table compares these two strategies. <br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/><br/>In order to meet the needs of the students with whom I am familiar, in the course with which I am familiar (high school Geometry taught in grade 10) I foresee dividing the total curriculum time equally between preparation and content delivery. Stated another way, I am suggesting that it might well be necessary to reduce by half the size of the body of content to be delivered. <br/>Immediately two important questions arise.<br/> 1. What makes it possible to believe that the Bounded Preparation First strategy would be any kind of an improvement? <br/> 2. Given a satisfactory answer to the first question, what will be going on in the classroom differently that will make Bounded Preparation First work?<br/>What makes me believe that the Bounded Preparation First strategy will in fact lead to improved student performance is my intimate familiarity with the great inefficiency of the present method. Here is the essence of this proposal: within the suggested limit of a half year, a greater bottomline student performance improvement can be obtained per class hour by addressing this inefficiency than by addressing the content delivery process. <br/>At a gross level, here are the characteristics of this inefficiency that must be addressed by the preparation process. <br/> 1. Virtually all of my students arrive with no understanding of working in teams. They have neither expectations nor skills for working together in order to work more effectively. I have experimented extensively with attempting to create team problemsolving environments in my classes, and I have concluded that what is arguably the most important workplace skill that can be given to high school students, the ability to create and work together in teams, has been almost completely ignored. Yet working in teams is a seriously underexploited technique for success in high school, since the students can often learn better from each other in small groups than they do from the teacher. <br/> 2. Most of my students arrive with no appreciation for the importance to them of using their learning time to the best of their abilities. There are known motivational techniques for dealing with this common sideeffect of adolescence, but it seems not to have occurred to many people that these techniques have a direct application in the mathematics classroom. <br/> 3. Most of my students arrive with varying, often unsatisfactory, skills for attacking and overcoming unfamiliar content that must be learned. For whatever reason, many are not willing and/or prepared to persist in an effort to overcome new material. <br/> 4. Most of my students arrive with varying, often major, gaps in their mathematical preparation, gaps that must be filled for them to be able to absorb the course content. <br/>It is no accident that, of these four issues, only one is related to math preparation; the other three relate to effective socialization and personal discipline. The socialization and discipline deficits of many students make any attempt to deliver difficult new knowledge grossly inefficient. <br/>Much progress is possible toward remediation of these deficits, provided that the teacher and students cooperate in creating an affirmative learning community within the classroom. My experiments in my MCAS classes, where I had control over the balance between communitybuilding and content, have given me confidence that this is possible with almost all students; this is where much of that freedup class time should go. <br/>Having stated all this I am not prepared to assert that any of us know how to create reliably such an affirmative learning community in an environment where resistance is the norm. But I am prepared to assert that this is how we should be using our professional development resources. <br/>* * *<br/>Now I shall present a simple numeric model that supports the assertion that, using the form and scoring method of the MCAS math test, a good knowledge of half of the course content can lead to a score near the bottom of the Proficient range. <br/>In the fall of 2003 I wrote a paper for my students that explained the structure and scoring method of the MCAS test. You can see the paper by clicking <a href="http://melconway.com/teaching/papers/rationale.pdf">here</a>. Following is a brief summary.<br/>Scoring the math MCAS test leads to a “raw score” in the range 0 to 60. The test has three kinds of “items” (questions), in a total of 42 items:<br/> 1. There are 32 multiplechoice items, each with four choices given. Each multiplechoice item receives a score of 1 if it is answered correctly and a score of 0 if it is answered incorrectly or not answered at all. The multiplechoice items contribute 32 of the possible 60 total points of the raw score. <br/> 2. There are 4 shortanswer items, which ask the student to write a short answer in a box on the answer document. Each of these items receives a score of 1 if answered correctly, 0 otherwise. The shortanswer items contribute 4 of the possible 60 total points of the raw score.<br/> 3. There are 6 openresponse items. Each openresponse item has several parts that progressively discuss a single mathematics problem. Each openresponse item can receive a score between 0 and 4, according to welldocumented criteria (unknown to the student) in which the scorers are trained. The openresponse items contribute 24 of the possible 60 total points of the raw score.<br/>During the four years I was teaching the threshold for passing ranged between 19 and the mid20s, depending on the difficulty of the test. Notice that an expected score of 20 can be reached by getting a 2 on each openresponse item (this is within reach with a competent partial answer) and answering all the multiplechoice items randomly. Since every student knows the answer to at least a few multiplechoice items, and some students are able to rule out two choices of a few multiplechoice items they don’t know and then do the equivalent of flipping a coin, the test hasn’t been difficult to pass. This suggests that the bar was actually set pretty low. (I understood before I left that the bar was soon to be raised radically.) <br/>The model I show here quantifies this reasoning. In the model the independent variable is f, the “fraction of knowledge,” expressed as a fraction between 0 and 1 or as a percentage between 0 and 100. Assigning a value to f divides the test into two portions: the portion the student knows and the portion the student doesn’t know. (If f = 0 the whole test is the unknown portion; if f = 50% half the test is known and half is unknown.) In scoring according to this model, the student is assumed to do B work on the known portion and F work on the unknown portion. For multiplechoice items, B work means all the items in the known portion are answered correctly (1 point per item) and F work means that one quarter of the items in the unknown portion are answered correctly (the result of random choice). For shortanswer items, B work means all the items in the known portion are answered correctly (1 point per item) and F work means that all the items in the unknown portion are answered incorrectly. For openresponse items, B work means that all the items in the known portion receive 3 points; F work means that half the items in the unknown portion receive 1 point. <br/>This is a continuous model that leads to fractional scores, but since it is not meant to be rigorously predictive, that should be of no concern. <br/>The following chart shows how the raw score varies as a function of f, the fraction of knowledge. <br/><br/><br/><br/>Since historically a raw score in the mid20s was passing and a raw score in the mid30s was (close to) proficient, this model suggests that a “Needs Improvement” (but, at present, passing) score is achievable with 25% knowledge, and 50% knowledge is near Proficient. This model therefore gives some credence to the assertion that if the students learn well one half of the material on which they will be tested, their work will be considered proficient. I am persuaded that this will be an improvement over current practice for many, perhaps most, students in the math classes I have known. <br/>* * *<br/>One point of creating an affirmative learning community in the classroom is that the students will indeed learn well the assigned half of the total content. An arguably more important benefit is that the students will have learned a life lesson they will carry with them far beyond the mathematics classroom. Bounded Preparation First can turn Material First upsidedown: finding, and using well, the right mix of valuable classtime resources between content delivery and creating an affirmative learning culture in the classroom will put the students first—where they belong—and will assure satisfactory performance of our content delivery mandates. <br/><br/>© Copyright 2008 Mel Conway PhD

A Comprehension Experiment
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/2/27_A_Comprehension_Experiment.html
453679a09e484df8ad61d3202d7944df
Wed, 27 Feb 2008 13:33:42 0500
As I have stated elsewhere in these essays, I have tried to understand why my students’ abilities to learn and retain the material I was teaching were below my expectations. Several times I gave exams in which I attempted to measure explicitly their comprehension of questions and problem statements. I reported on one early experiment in the essay <a href="Entries/2006/7/17_What_Am_I_Supposed_to_Do.html">What Am I Supposed to Do?</a> <br/>I wrote the essay below before I had come up with the thesis of <a href="Entries/2008/1/28_The_Classroom_Language_Hypothesis.html">The Classroom Language Hypothesis</a>, and I present it here as originally written. The analysis I report below was a major input into the formation of the Hypothesis. <br/>In the experiment I report here, I showed students Geometry problems from worksheets that had already been assigned and which we had discussed in class, and I asked questions, not about the Geometry problems but about the problem statements (i.e., the worksheet questions): what are these questions asking you to do? In this way I sought to measure the students’ comprehension of the problem statements. I attempted to design my questions in such a way that a person who read and comprehended English well but had no knowledge of Geometry content could answer the questions correctly by studying the wording of the problems statements.<br/>I built each question to look like an MCAS multiplechoice question, whose style was familiar to the students. At the beginning of the test I told the students in more than one way that the geometry problem statement in each box was from a worksheet they had been assigned, and that they were not to try to solve that problem but to answer the multiplechoice question right below the box. <br/>As an example, between these lines is question 7 of the 10question test. <br/><br/>Multiplechoice question 7 refers to this problem statement:<br/><br/><br/>______7. What can a correct answer to each of questions 11, 12, and 13 contain?<br/><br/>A. A length in inches.<br/>B. Two lengths in inches.<br/>C. The word “yes” or the word “no.”<br/>D. The word “yes” or the word “no,” and a length in inches.<br/><br/>The correct answer is “C.” The percentages the four choices received were as follows:<br/> A. 33%<br/> B. 14%<br/> C. 25% (The correct answer)<br/> D. 27%<br/>(Note that if all the students made their choices randomly, the expected percentages would be 25% for each of the four choices.) Assuming, as I am, that the students were being earnest and not perverse, and believing, as I do, that there is something that needs to be understood behind these results, one is forced to ask: What is operating here?<br/>The Whole Test<br/>You can see the whole 10question test in pdf form by clicking <a href="http://melconway.com/Urban_Teaching/pdf/comp_test.pdf">here</a>. (I encourage my readers to study the test, perhaps give it to a few people, and reply whether you believe it is fair and/or whether you think it is usefully measuring anything interesting.) After handing out the test I asked the students to read the instructions at the top of the first page as I read them aloud, with the emphases shown, and even with some additional interpolated explanations.<br/>On average, 40% of the questions were answered correctly in a population of 51 students. (Given a few reasonable assumptions, a little analysis shows that of this 40% of the questions answered correctly, half were answered correctly by students who understood the question and the other half were lucky guesses.) I wrote a paper describing the results and presented it to the faculty of the math department. The general reactions of the teachers were (1) to see the results documented this way was shocking, but (2) these results were consistent with their (the teachers’) own experiences. You can see my report in pdf form, together with the original test (annotated with the answer statistics) as an appendix, by clicking <a href="http://melconway.com/Urban_Teaching/pdf/comp_report.pdf">here</a>.<br/>Designing an effective assessment instrument is not easy and cannot be done well without extensive experimental evaluation. Therefore my results should not be seen as having precision; nevertheless they raise puzzling questions. The following discussion of what can go wrong in the design of question 7, for example, will throw some light on the context in which I gave the test. <br/>What Can Go Wrong With Question 7?<br/>There are many ways a reader can go astray trying to answer question 7. Several sophisticated, literate adults have gotten it wrong. Here are some issues with question 7 that occur to me.<br/> 1. The language of the worksheet problem statement in the black box is obscure.<br/> 2. The language of the worksheet problem statement is at too high a level for the reader.<br/> 3. The language of my multiplechoice question 7 is obscure.<br/> 4. The language of my question 7 is at too high a level for the reader.<br/> 5. The reader is not trained to distinguish, or is not capable of distinguishing, the separate natures of the Geometry problem in the box and the question about the Geometry problem immediately below the box. (A logician might call these the question and the metaquestion.) Is making this distinction too much to ask of a highschool student?<br/> 6. The reader, not having comprehended the original instructions not to try to solve the geometry problems, finds the whole affair too confusing.<br/>I suspect that each of these issues is present in varying degrees with different students. Here are concrete examples of these issues.<br/>Issue 1. It may not be clear that there are three separate geometry problems in the box, numbered 11, 12, and 13. This information is carried by one word: each. At what point in the student’s development of reading comprehension does an understanding of this usage of “each” occur? <br/>Issue 2. “Determine whether” is definitely a problem, and it appears multiple times in the workbook. I established earlier in the year that almost nobody in my classes knew what it meant. I actually gave a lecture (well before I gave this test) in which I wrote on the board in front of every class and repeated with examples:<br/>“Determine whether” means “answer yes or no.”<br/>Given that fact, I propose a seventh issue, which is general, not specific to this test question: Issue 7. Many of my students do not retain the material that is put before them (and that they are expected to study) to a degree a highschool math teacher can reasonably expect. (I know from multiple experiences that this statement is true. For example, two years in a row I had students asking me the week before the final exam the meaning of the upsidedownT “perpendicular” symbol; it was introduced the first month of the school year and used hundreds of times throughout the year.) <br/>Issues 3 and 4. “What can a correct answer contain?” might be obscure. (If so, the whole test is worth little.) I was hoping, in part, that the four choices I presented to each question would make specific the meaning of this question. Also, in question 7 I attempted to clarify the meaning of “each” by being explicit in my wording of the question. <br/>Issue 5. (If it is not reasonable to ask a metaquestion then I probably can’t use a test like this to try to understand my students’ low comprehension; indeed, is it possible to teach highschool Geometry to someone who does not understand this distinction?)<br/>Issue 6. The fact that some students tried to solve the Geometry problems tells me that this issue is applicable in some cases. Clearly one must take a different approach with these students.<br/>Lessons<br/>Creating problems and test questions that do not unfairly penalize students depending on their language abilities is very hard. I know from my classroom experience that the creators of the textbook system we used did not succeed very well at it. (Added later: I see now that part of our problem is insufficient understanding of the structure of what we call “language abilities;” the problem is much more than inadequate vocabulary.) That lesson then leads to the question of textbook adoption and curriculum planning. I was not involved in the selection of our text, but I strongly suspect that considerations such as I have raised here were not given much weight. Given that a large fraction of our students do not hear much English at home, I have come to believe that these considerations are crucial to the success of our students, yet they play a very small role in our approach to the way we present the material. <br/>Another observation: you will see that the Geometry problem statement in the box on page 1 of the test presents a decoding problem that will challenge many native speakers. When I had discussed the solution to this problem earlier in the year I found it necessary to teach my students how to parse the sentence; this was a skill that was absent in my classes. <br/>A great many of my students could converse in a way that was indistinguishable from their primarily Englishspeaking peers. Yet I learned from extended contact with many of them that their vocabularies were very shallow. The introduction of one important word that is not part of a student’s normal vocabulary can shut down his or her comprehension for a while. We as a faculty have tried to address this problem, but I was not seeing results. I conclude that the traditional literary approaches to increasing comprehension that we have been using have not been sufficiently helpful to students who have to take the kind of course I was teaching.<br/><br/>© Copyright 2008 Mel Conway PhD

Some Resources
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/2/26_Some_Resources.html
771b69504d4b4f5ba098ea45e19aac71
Tue, 26 Feb 2008 15:06:35 0500
This is a point of entry to several papers I wrote in the course of teaching. <br/>Geometry Patterns <br/>Creating this paper was a oneyear project that required another year to refine, and it is still a work in process. I wrote it for two distinct reasons.<br/> 1. Our onesizefitsall Geometry textbook weighed five pounds. This was not so different from the weights of the textbooks for other courses my students were taking. Many of my students were not taking the books home to do homework and were not bringing them to class, or they would simply leave them in the classroom. Although some of my colleagues built courses around the assumption that students would take their books home to do homework and bring them to class each day, only a few of my exceptionally motivated students were doing this. (One enterprising student submitted a formal requestwith an ostensible medical basisfor a second book to keep at home; it was granted.) I felt compelled to create a course around handouts reproduced from the worksheet masters provided with the textbook plus materials I originated. "Geometry Patterns" became my 21page version of "<a href="http://www.cliffsnotes.com/">CliffsNotes</a>"(R) for the course, containing all the principles for which the students were to be held responsible, (For the usual endofyear reasons the chapters on measurement did not make it into the document.) <br/> 2. In mathematics in general, and particularly so in Geometry, solving a problem starts with recognizing a pattern that leads you to a principle you have learned and that you can then apply. There seem to be three distinct patternrecognition skills required for Geometry, and I could not assume that any given student was strong in all three skills: 1)the English description of the principle, 2)a picture illustrating the principle, and 3)an algebraic or other formal expression of the principle. The Pythagorean Theorem offers an example. 1:”The Pythagorean Theorem: The measure of the hypotenuse of a right triangle is equal to the sum of the squares of the measures of the two legs of the triangle.” 2:a picture of a right triangle with the sides labeled, perhaps with the classic three squares one of whose sides coincides with a side of the triangle. 3:“c squared = a squared + b squared.” I felt it would be useful to organize the three patterns for each principle so that the student could use any of the three recognition skills as a point of entry to find a principle. This led to the threecolumn form of the document in which each row describes one principle. <br/>The latest version of the Geometry Patterns document is a 1.6 MByte pdf file. You can obtain it by clicking <a href="http://www.melconway.com/Urban_Teaching/pdf/patterns.pdf">here</a>. <br/>I have licensed this and other documents referenced here under a Creative Commons AttributionShare Alike license. You the reader are therefore invited to copy, distribute, and improve upon them subject to the <a href="http://creativecommons.org/licenses/bysa/3.0/us/">provisions of the license</a>. This is an "open source" license in the sense that I am willing to cooperate with educators intent on improving this work under the license by providing, for example, the original source materials used to create the pdf file. There is no restriction to noncommercial use. My attribution specification: any copy or derivative work must accurately display the document’s copyright notice. <br/>Linear Function Worksheet<br/>Use of this worksheet succeeded in engaging several of my most discouraged students. It teaches that three mathematical forms: linear graph, linear table, and linear equation are just three views of the same underlying object: a linear function. (I have a chimpinthebox lecture explaining what a function is that I have not yet written up.) After a little practice I could give a minimum amount of information in any of the three forms and the students would fill in the whole sheet. There is a natural segue from this activity to understanding how slope and intercept look in all three forms. The pdf file is <a href="http://www.melconway.com/Urban_Teaching/pdf/linear_function.pdf">here</a>. <br/>Units in Measurements<br/>I have felt that there must be a way to convey to my students the ease in calculating with physical units I had developed as an undergraduate Physics student. This ease can be creative; for example, it makes unit conversions and rate problems trivial. Most students acquire this ease by osmosis if they acquire it at all; I was looking for a way to teach it explicitly. I wrote this paper when I realized that a “measurement” is not a number but is something more inclusive than a number, and that the additional thing, the unit word, can be treated exactly like a prime factor of a number. The pdf file is <a href="http://www.melconway.com/Urban_Teaching/pdf/units.pdf">here</a>. <br/><br/>© Copyright 2008 Mel Conway PhD

The Classroom Language Hypothesis
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/1/28_The_Classroom_Language_Hypothesis.html
2fe4a9ffa84945a1b414ead73b9a7b90
Mon, 28 Jan 2008 14:46:56 0500
Chelsea High School has put a lot of resources into reading and comprehension, and teachers have been requested to stress reading and vocabulary in all courses. During the 20062007 school year, my last year at Chelsea High School, my desk was in an open office area where I enjoyed being surrounded by, and learning much from, reading specialists. <br/>Often, my observations about my students were that they might appear to read a problem statement perfectly well but then their behavior suggested that they didn’t understand what they had just read. I decided I needed to understand that better. I designed and gave my students various tests and other measuring instruments to learn what was going on. <br/>Putting it all together, this is what I learned.<br/> 1. My students’ general level of comprehension of Geometry problems and test questions was surprisingly low. <br/> 2. Creating math problems and test questions that do not unfairly penalize students depending on their language abilities is very difficult, and the textbook system from which I was teaching was not good at it. I suspect that issues of language comprehension were not major factors in the selection of these materials, because we are still learning about the extent of these problems. <br/> 3. Possibly related to the above, possibly not, my students’ absorption and retention of Geometry concepts was also surprisingly low. <br/> 4. My attempts to teach specifically to counter the language disadvantages I was seeing in many of my students were not successful. Nor did I see evidence that the emphasis on reading and comprehension being placed by others all over the school was having any effect on my students’ performance in my classes. <br/>At our department meetings the mathematics teachers were aware of, and were attempting to deal with, these issues. Some teachers voiced the view that “math reading” is different from the kind of reading that is being taught in English classes, and they were actually experimenting with this idea in their teaching. In this essay I seek to carry this important idea forward a bit. <br/>***<br/>The following diagram presents a model of what I shall call here the “classroom language hypothesis,” namely that there are three distinct language processing skills that we expect our students to acquire successfully. I call these three language processing skills Literary language processing, Conversational language processing, and Formal language processing. <br/><br/><br/><br/>The lefthand circle encloses the two skills that are taught and used in English classes, and the righthand circle encloses the two skills that are taught and used in Mathematics classes. That is, students in English classes are taught, and are expected to use successfully, Literary and Conversational language processing skills, and students in Mathematics classes are taught, and are expected to use successfully, Formal and Conversational language processing skills. The words inside the circles characterize some of the “products” of using these skills: Poems are manifestations of Literary language processing, ordinary I/You talk is the manifestation of Conversational language processing, and Theorem proofs are manifestations of Formal language processing.<br/>In contrast to the other two languages, formal languages are typically only written, not spoken, although it is usually possible to read out loud an expression in a formal language. A formal language has a finite “alphabet” of basic symbols, and a set of clear “grammar” rules for creating correct expressions from these symbols. Examples are computer programming languages and algebra. <br/>The model above gives me a way to describe what I have observed in the classroom. <br/> • Most of my students, even many who do not hear English at home, are still convincingly fluent, for practical purposes, in Conversational language processing skills. <br/> • Literally all of my students have poor Formal language processing skills. <br/>I think we have been tempted to believe that, because “they are both English,” there is a connection between conversational language processing skill and formal language processing skill. My experience informs me that, even though conversational language skills are often necessary if a student is to describe his or her formal thinking, training in conversational and literary language processing contributes nothing to skill in formal language processing. <br/>Here is my sad conclusion from my most recent four years of teaching highschool mathematics. All my students came to me having had practically no useful training in formal language processing skills. This is something that needs to be taught before high school, and my evidence is that it is not happening. Please believe that I am not singling out Chelsea Public Schools here; although most of my recent experience has been at Chelsea High School, my observations as a citizen tell me that this problem is pandemic. Furthermore, I believe that Chelsea is an exceptional place in that it is working, as hard as it knows how, to do what works best for its children. <br/>I propose the following highpriority research program. Just because our nation’s high schools are clogged with students who were not adequately trained in formal language processing skills, we must not give up on these students. We must find ways to give students these skills even later in their lives than when they should have received them. If we can find out how to do that, we will have discovered a constructive and nonpunitive way, at least in part, to leave no child behind. <br/><br/>© Copyright 2008 Mel Conway PhD

The Ignorance Double Whammy
http://www.melconway.com/Urban_Teaching/Urban_Teaching/Essays_by_Mel_Conway/Entries/2008/1/24_The_Ignorance_Double_Whammy.html
71571408943c4f809aec6d9ab7fb4987
Thu, 24 Jan 2008 11:00:56 0500
I am using “ignorance” here not in any pejorative sense but in the sense of the bumper sticker: <br/>If you think education is expensive try ignorance.<br/>The <a href="http://www.phrases.org.uk/meanings/119750.html">Phrase Finder</a> defines “double whammy” as a double blow or setback. I first saw the term in the <a href="http://www.lilabner.com/">Li’l Abner</a> comic strip. <br/>I followed “Li’l Abner” regularly as a child. The strip was populated by a gaggle of colorful characters from the “uncertain hamlet” of <a href="http://www.lilabner.com/dogpatch.html">Dogpatch USA</a>. Evil Eye Fleegle was a minor figure in Dogpatch, but he had an awesome power: the whammy. The single whammy, unleashed by looking in a particular way with only one of his evil eyes, could, to paraphrase his words, “putrefy citizens to the spot.” According to the official record, a quadruple whammy could “melt a battleship.”<br/>*** <br/>Many of the students about whom I have been writing have double whammies in their futures. Whammy one: because of poor education they will be at the bottom of the economic heap. Whammy two: because of globalization the general living standard of the United States economy will be declining significantly, leaving the least educated even worse off. <br/>Whammy One<br/>As part of my responsibility to inform my students about the world outside Chelsea I put together a presentation I made to both my math and physics students. The <a href="http://melconway.com/Urban_Teaching/pdf/million.pdf">handout</a> contains several charts, obtained largely from Census data, that show a strong direct relationship between education level and expected lifetime earnings. Furthermore, since the mid1980s this income spread as a function of education has been widening. Several charts also suggest that stressproducing factors, such as unemployment and the absence of medical and pension benefits, decrease as education increases. As the bumper sticker says, ignorance is expensive. <br/>Whammy Two<br/>As a regular viewer of <a href="http://www.charlierose.com/search?q=roy+vagelos&searchFilter=roy+vagelos&searchType=guest&searchTopic=1&searchFromMonth=MM&searchFromDay=DD&searchFromYear=YY&searchToMonth=MM&searchToDay=DD&searchToYear=YY">Charlie Rose</a> I learned about a National Academies report commissioned by the President called <a href="http://www.nap.edu/catalog.php?record_id=11463">Rising Above the Gathering Storm</a>. The executive summary has some startling findings on pages 3 and 4, which I summarize here. <br/>No matter how one makes his or her livelihood, one’s economic welfare varies directly with our economy’s general standard of living, which varies directly with the economy’s ability to compete successfully as a trading partner in highvalue goods. <br/>This competitive strength in highvalue trade is directly related to our economy’s technological strength, which is directly related to the amount of science and engineering talent at work in our economy. <br/>The number of science and engineering graduates we are creating (and importing) is decreasing, whereas among our Asian trading partners, this number is increasing strongly. <br/>Furthermore, these technology workers in our Asian trading partners are available at a fraction of the cost of American workers of comparable ability, leading multinational businesses to locate new technology jobs in (and to move existing technology jobs to) the lowcost areas. <br/>The consequences of these facts are partly with us now and are being recognized in our political dialog. I believe that these consequences will be much more with us in the future. The way the impact of these consequences will become fully obvious will be analogous to sitting in a rowboat near the point where a whale breaches the surface of the ocean: one minute the sea is tranquil; then suddenly all hell breaks loose. <br/><a href="http://www.economist.com/">The Economist</a> magazine publishes annually a useful little book called Pocket World in Figures; subscribers often can get it as a freebie. On page 130 of the 2008 edition I learned that the percapita purchasing power (one measure of living standard) of China is onesixth that of the United States. On page 156 I learned that the percapita purchasing power of India is onetwelfth that of the United States. <br/>In another Charlie Rose interview Andy Grove, the former chairman of Intel, noted that economists understand that between tightly coupled highvolume trading partners such as the United States with China and, increasingly, the United States with India, their respective living standards will tend to equalize. That is, our living standards will decrease while the living standards of China and India will increase. This will take time, but the signs are there to see. Some among my readers might already know a manufacturing worker who has lost a job to China or a computer programmer who has lost a job to India and, as a consequence, has had to take a lowerpaying job. Okay, now read this paragraph and the one before it again. <br/>The National Academies report made a series of detailed recommendations, many of which are related to upgrading the science and math parts of our education system. The President addressed this matter in the 2006 StateoftheUnion speech. He proposed training 70,000 high school teachers to lead Advanced Placement courses in math and science, and bringing 30,000 math and science professionals into the schools to teach. With the exception of the usual talk about No Child Left Behind, since that time I have seen no public dialog about the future of public education. <br/>***<br/>I worry about my students’ futures. It appears that the grownups are going to do very little for them. The only hope I see is that the students themselves will catch on to what is ahead and take responsibility for their own futures. There is a lot working against them in this regard, in particular the oftenfutureless stance of their adolescence and their chaotic socioeconomic conditions. This is the tragedy of public education today. <br/><br/>© Copyright 2008 Mel Conway PhD