Define a real valued function on the reals by tex f(x begincases 0, x notin mathbbQ frac1q, x fracpq, gcd(p,q)1, q 0 endcases/tex. Where is this function continuous? The problem appeared in Hyman Basss article in the.
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To summarize, were only in the middle of page 4 of this paper, and weve already learned the following: a) teachers have an effect on both cognitive skills of their students, and non-cognitive skills of their students. The first leads to higher test scores, the second leads to more college going, fewer arrests and better wages. B) In 8th grade, non-cognitive achievement is a better predictor of college going and higher wages, as well as fewer arrests and suspensions, than test scores. C) A teachers effect on these non-cognitive outcomes is as much as 300 greater than can be measured using test scores. But wait, theres more! Okay, im only below the middle of page 4, and already ive read three conclusions that essentially kill off any legitimacy to judging a teachers effectiveness based on test scores, and the good stuff has even gotten started! What Jackson is up to in his paper is something bigger, way bigger: it would be possible to argue at this point that somehow cognitive and non-cognitive skills, while both responsible in some part to positive adult outcomes, are still correlated; that is, if you. This is where jackson goes for the jugular, and, writing as is typical of research papers, he essentially buries the lead. This paper presents the first evidence that teachers have meaningful effects on non cognitive outcomes that are strongly associate with adult outcomes and are not correlated with test scores. (Emphasis mine, italics resume his, by the way.). I have to stop with this blog post here (but I promise to do more deciphering of this paper in the next few days.) my only question at this point would be: why hasnt anybody explained this to Arne duncan, perhaps through the use.
Hes focusing on what non-cognitive effects a teacher can have on a student, which includes things like diminishing their rates of truancy and suspensions, improving their grades (which are different from test scores) and helping increase the likelihood that they will attend college. Which poses the less than obvious question: if teachers have an effect on both cognitive and non-cognitive outcomes, are they correlated or independent? That is, if a teacher is effective in raising test scores, will that lead to beauty less truancy, fewer suspensions, better grades and less grade retention? Even more interesting is the idea that teachers could be more effective on one scale while being low on the other: is it possible for a teacher to be very effective at improving a students non-cognitive functioning while not having an effect on his/her test. By page 4, jacksons paper starts to draw blood: using the results of the nels 1988, jackson concludes that a standard deviation increase in non-cognitive ability in 8th grade is associated with fewer arrests and suspensions, more college-going and better wages than the same standard. Its almost as if Jackson is telling us, hey, 8th grade teachers: want to improve your students future life? Spend less time on test prep and more time helping them show up at school, staying out of trouble and improving their actual grades. This alone would be enough of a takeaway, but this incredibly dense paper continues to hammer away at any thought that test scores are meaningful in any way: in the same paragraph, jackson states that a teachers effect on college-going and wages may. Oh, and just to make things more interesting, it is followed by this statement: As such, more than half of teachers who would improve long run outcomes may not be identified using test scores alone.
His interest is in optimizing measurement systems, not taking positions on either side of the standardized paper testing debate. Although this paper should reek with indignation and anger, it makes its case using almost understated tone and is filled with careful phrasing like more than half of teachers who would improve long run outcomes may not be identified using test scores alone, and one. But lets get to the meat of the matter, because this paper is 42 pages long and incorporates mind-boggling statistical techniques that account for every variable one might want to filter out to answer the question: are test scores enough to judge the effectiveness. Jacksons unequivocal conclusion: no, not even remotely. The first thing Jackson does is review a model that divides the results of education into two dimensions: the cognitive effects, which can be measured by test results, and the non-cognitive effects, which are understood to be socio-behavioral outcomes, which when combined, determine adult outcomes. To paraphrase the old Charlie the tuna commercial, its more than whether we want adults that test good we also want them to be good adults. Clearly, jackson is aiming a little higher than those who would believe that test scores are the end result of good teaching.
For the three in-school waves of data collection (when most were eighth-graders, sophomores, or seniors achievement tests in reading, social studies, mathematics and science were administered in addition to the student questionnaire. To further enrich the data, students teachers, parents, and school administrators were also surveyed. Coursework and grades from students high school and postsecondary transcripts are also available in the restricted use dataset although some composite variables have been made available in the public use file. The survey was followed up in 1990, 1992, 19, which means that it began when students were just about to begin their high school career, and then followed up when they were in 10th and 12th grades, and followed them through post-high school, college and. It is one of the most statistically valid sample sets of educational outcomes available. What should be noted is that Jackson is not an educational researcher, per. Jackson was trained in economics at Harvard and Yale and is an Associate Professor of Human development and Social Policy.
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If youve read the, american Statistical Associations position on the dangers of evaluating teacher performance based on the value-added Model, youre probably wondering how they arrived at this very sobering conclusion. As Albert Einstein was alleged to have stated, not everything that counts is countable, and not everything that is countable counts. In this case, amstat took that advice to heart and so strongly inveighed against vam that they essentially labeled it a form of statistical malpractice. Kirabo jackson, the most understated hero to decimate vam. In this post, Im going to examine one of the studies that no doubt had a profound impact on the members of amstat that led them to this radical (but self-evident) conclusion. In 2012, the researcher.
Kirabo jackson at Northwestern University published a working paper for the national Bureau of Economic Research, a private, nonprofit, nonpartisan research organization dedicated to promoting a greater understanding of how the economy works (Im"ng here from their website.) The paper, entitled. Non-Cognitive ability, test Scores, and teacher quality: evidence from 9th Grade teachers in North Carolina questions the legitimacy of evaluating a teacher based on his/her students test scores. Actually, it is less about questioning and more about decimating and annihilating the practice of vam. I downloaded essay the paper and have been reading it for the past few days. Jackson clearly has done his homework, and this paper is extremely dense in statistical analysis which is rooted in data collected by the national Educational Longitudinal Study 1988, which began with 8th graders who were surveyed on a range of educational issues as described below. Additional topics included self-reports on smoking, alcohol and drug use and extracurricular activities.
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