tag:blogger.com,1999:blog-65700610872767968002015-07-03T12:00:05.756-04:00Out In Left FieldFor left-brainers and kin: thoughts on education, left-brainedness, autism, and right-brain biases. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.comBlogger1545125tag:blogger.com,1999:blog-6570061087276796800.post-33457064552735377672015-07-02T10:00:00.000-04:002015-07-02T10:00:02.024-04:00Math problems of the week: Common Core-inspired 3rd grade test questionFrom the SMARTER Balanced Assessment, <a href="http://www.rcoe.us/educational-services/files/2013/11/asmt-sbac-math-gr3-sample-items.pdf">3rd Grade Mathematics Sample Items</a>:<br /><br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-SuLHeWZ9flI/VVuXKtUry7I/AAAAAAAAC4A/V2uPAFye-Ho/s1600/sb_3_a.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-SuLHeWZ9flI/VVuXKtUry7I/AAAAAAAAC4A/V2uPAFye-Ho/s640/sb_3_a.tiff" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/--kYHIa7mdow/VVuXOAg58KI/AAAAAAAAC4I/nTuInw-ZXXY/s1600/sb_3_2.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="394" src="http://4.bp.blogspot.com/--kYHIa7mdow/VVuXOAg58KI/AAAAAAAAC4I/nTuInw-ZXXY/s640/sb_3_2.tiff" width="640" /></a></div><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-NvFEv2ho_Dg/VVuXRhltqAI/AAAAAAAAC4Q/yt5ONSJwPGU/s1600/sb_3_3.tiff" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="164" src="http://1.bp.blogspot.com/-NvFEv2ho_Dg/VVuXRhltqAI/AAAAAAAAC4Q/yt5ONSJwPGU/s640/sb_3_3.tiff" width="640" /></a></div><br /><b></b><br /><b>Extra Credit</b>: <br /><br />Compare the simple vocabulary and sentence structure of the Sample Top-Score Response with other aspects of its communicative demands, and relate this to the communication skills of 3rd graders.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com1tag:blogger.com,1999:blog-6570061087276796800.post-32774082282592908032015-06-30T10:00:00.000-04:002015-06-30T10:00:05.202-04:00Confusing math with math educationIt strikes me that much of what is wrong with math education results from a confusion of math with math education. Is the goal to teach kids how to do math, or how to be math teachers? <br /><br />Consider two tasks common to today’s math assignments but rare before Reform Math: explaining answers verbally, and explaining what’s wrong with other people’s solutions. Variants include having third graders write letters to second graders about why, say, <a href="http://30thrillingthinkers.blogspot.com/2010/02/letters-about-fractions.html">1/3 is bigger than 1/4</a>, or to Jack “<a href="http://hechingerreport.org/common-core-math-problem-hard-supporters-common-core-respond-problematic-math-quiz-went-viral/">telling him what he did right, and what should do to fix his mistake</a>.” <br /><br />I and others have argued here and <a href="http://www.educationnews.org/k-12-schools/math-problems-knowing-doing-and-explaining-your-answer/">elsewhere</a> that explaining your answers verbally is often a counterproductive waste of time that, in particular, shortchanges second language learners and students with language delays. Similar arguments apply to explaining why someone else’s answers are wrong. But, if you’re in a teacher education program training to be a math or a K6 general education teacher, then suddenly being able to provide these types of verbal explanations is absolutely essential. <br /><br />Ironically, these explanation demands are especially common in elementary school, when students are least able to verbalize things clearly. Perhaps this has to do with the profile of the typical elementary school math teacher, who, in his or her teacher training program, has had to take courses in math education, but not in actual math. To some extent, however, such teachers are simply following the math curriculum that others have written and/or selected for them. So what about those most responsible for creating and selecting math curricula--the <a href="http://www.soe.umich.edu/files/cv_ball.pdf">Deborah Ball</a>s and <a href="http://cemse.uchicago.edu/staff/andy-isaacs/">Andy Isaac</a>s and <a href="https://ed.stanford.edu/faculty/joboaler">Jo Boaler</a>s of the world? Is it possible that most of them get more training in math education than in math? <br /><br />When it comes to educating K12 students, math education should primarily involve math, and not the infinite regress, as it were, that comes from educating students in math education. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-78340397197615056992015-06-28T10:00:00.000-04:002015-06-28T10:00:04.068-04:00Problematizing grit, IIHow hard you work on something isn’t the only effort (or grit)-related variable. Also key—and what Angela Duckworth’s <a href="http://www.sas.upenn.edu/~duckwort/images/12-item%20Grit%20Scale.05312011.pdf">questionnaire</a> doesn’t probe—is how you direct that effort within the project. I realized that recently when, for the first time in over a decade, I decided to learn a new <a href="https://musescore.com/classicman/scores/641766">piano piece</a>. Having allocated myself a mere 15-20 minute window on weekday mornings (a rare stretch of quiet solitude), I was determined to practice as efficiently as possible. <br /><br />And this meant resisting all sorts of temptations that as a student I often succumbed to: the temptation not to bother working out fingerings and using them consistently; the temptation to interrupt my work on the sections I knew the least well, or found the most difficult, for the satisfaction of breezing through easier or more familiar sections; the temptation to play the piece too fast, too soon. It’s not just the distracting temptations outside a project, I realized, but also the distracting temptations within a project, that need resisting. <br /><br />Directing your efforts appropriately involves brains as well as brawn. In learning a piano piece, for example, it helps to realize that muscle memory is essential, and that muscle memory will develop fastest if (1) you use consistent fingering and (2) you play slowly enough to minimize errors.<br /><br />Teachers, too, can be smarter about grit. Neither should they try, vaguely, to "teach" it (e.g., by spending lots of class time on "growth mindsets"); nor should they simply give students tons of work or make them "grapple" indefinitely without guidance. Rather they should give students frequent advice and feedback about performance--and about how best to allocate their efforts. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com1tag:blogger.com,1999:blog-6570061087276796800.post-49522011027322043732015-06-26T10:00:00.000-04:002015-06-26T10:00:05.441-04:00Math problems of the week: Common Core-inspired "algebra" test problemA problem from the "calculator section" of <a href="http://parcc.pearson.com/resources/practice-tests/math/algebra-2/pba/PC194854-001_AlgIIOPTB_PT.pdf">Algebra II Performance Based Assessment Practice Test from PARCC</a> (a consortium of 23 states that are devising Common Core-aligned tests).<br /><br /><br /><a href="http://2.bp.blogspot.com/-EMpVZfVGAMI/VVtpJdjqj_I/AAAAAAAAC3g/fqsiFrpp28Y/s1600/PARCC_trucksA.png" imageanchor="1"><img border="0" height="392" src="http://2.bp.blogspot.com/-EMpVZfVGAMI/VVtpJdjqj_I/AAAAAAAAC3g/fqsiFrpp28Y/s640/PARCC_trucksA.png" width="640" /></a><a href="http://3.bp.blogspot.com/-swZBVnbZtMI/VVtpMRt6mfI/AAAAAAAAC3o/unFjfTKPhAs/s1600/PARCC_trucksB.png" imageanchor="1"><img border="0" height="256" src="http://3.bp.blogspot.com/-swZBVnbZtMI/VVtpMRt6mfI/AAAAAAAAC3o/unFjfTKPhAs/s640/PARCC_trucksB.png" width="640" /></a><a href="http://2.bp.blogspot.com/-yQIgUu7VnBc/VVtpPSaBMsI/AAAAAAAAC3w/mI4RgSntheE/s1600/PARCC_trucksC.png" imageanchor="1"><img border="0" height="236" src="http://2.bp.blogspot.com/-yQIgUu7VnBc/VVtpPSaBMsI/AAAAAAAAC3w/mI4RgSntheE/s640/PARCC_trucksC.png" width="640" /></a> <b></b><br /><b></b><br /><b></b><br /><b>Extra Credit:</b><br /><br />Based on the given information, determine the ratio of algebraic to verbal challenges in this problem. Describe the steps used and explain any assumptions made. Create a model and describe the steps used to create it. Enter your answer, model, explanation, and assumptions in the space provided.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com4tag:blogger.com,1999:blog-6570061087276796800.post-57910429565753981792015-06-24T10:00:00.000-04:002015-06-24T10:00:04.537-04:00Problematizing gritIn her <a href="http://www.ted.com/talks/angela_lee_duckworth_the_key_to_success_grit/transcript?language=en">Ted Talk</a> on “grit,” Angela Duckworth offers the following definition: <br /><blockquote>Grit is passion and perseverance for very long-term goals. Grit is having stamina. Grit is sticking with your future, day in, day out, not just for the week, not just for the month, but for years, and working really hard to make that future a reality. Grit is living life like it's a marathon, not a sprint. </blockquote>All this, Duckworth finds, predicts long term success. So far so good—but (dare I say it?) hardly surprising. <br /><br />What’s a lot less obvious is whether grit can be taught. Of course, this hasn’t stopped the education establishment, ever eager to focus on something other than academic instruction, from jumping to conclusions. Here, on the other hand, is Duckworth: <br /><blockquote>Every day, parents and teachers ask me, "How do I build grit in kids? What do I do to teach kids a solid work ethic? How do I keep them motivated for the long run?" The honest answer is, I don't know. </blockquote>Duckworth says the best idea she’s heard is Carol Dweck’s “growth mindset”: “the belief that the ability to learn is not fixed, that it can change with your effort.” Duckworth cites Dweck’s finding that: <br /><blockquote>when kids read and learn about the brain and how it changes and grows in response to challenge, they're much more likely to persevere when they fail, because they don't believe that failure is a permanent condition. </blockquote>Again, so far so good—but (dare I say it?) hardly surprising. <br /><br />Plus, there’s only so far mere beliefs can get you. Indeed, the <a href="http://www.sas.upenn.edu/~duckwort/images/12-item%20Grit%20Scale.05312011.pdf">questionnaire</a>that Duckworth uses to measure grit (and predict success) addresses how distractible you are, how fickle vs. sustained your interests are, and how hard and how diligently you work on things; not what you think about failure. <br /><br />Given this, perhaps a better way to raise students’ perseverance is to provide extra incentives for hard, concentrated work. Ideally these incentives would be built into the work itself. You make sure that it’s interesting; that students get timely feedback about their progress through it; that completing it results in a satisfying final product, set of revelations, set of new skills, and/or sense of accomplishment. As far as these things go, much school work (whether because it’s busywork, easy work, group work, vaguely defined, and/or lacking in timely feedback) comes up short. <br /><br />But even with some of the best types of assignments, and/or with certain types of students, there may be insufficient incentives for perseverance. In that case, <a href="http://oilf.blogspot.com/2013/12/autism-diaries-value-of-extrinsic.html">as we’ve seen with J</a>, why not resort to extrinsic incentives? For those who fail the marshmallow test, why not incentive them with marshmallows? Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com4tag:blogger.com,1999:blog-6570061087276796800.post-46815320644112713862015-06-22T10:00:00.000-04:002015-06-22T12:07:30.672-04:00All about meteors or all about MEteors?According to Michael Tscholl, a researcher at the University of Wisconsin (as reported in a <a href="http://www.edweek.org/ew/articles/2015/05/06/frontiers-of-digital-learning-probed-by-researchers.html">recent article</a> in Edweek):<br /><blockquote>Most students harbor fundamental misunderstandings about how forces such as gravity and acceleration operate in outer space. That's because their beliefs about physics tend to be based on their experiences in their own bodies.</blockquote>Bodies on earth, Tscholl explains, need energy to keep moving; objects in space don't. <br /><br />How to overcome these fundamental misunderstandings? Guess what Edweek/Tscholl propose? Is it:<br /><br />1. Enhance students understanding of the concepts of friction and inertia. <br /><br />2. Give students "embodied cognition" exercises in which they move their bodies around through earthly friction? <br /><br />Hint: the solution proposed by Edweek/Tscholl is MEteor, <br /><blockquote>a room-size "simulation environment" that calls to mind a space-age version of the popular space-age version of the popular arcade video game Dance Dance Revolution.</blockquote>Still stumped? Here's more: <br /><blockquote>In MEteor, planets and other space objects are projected on the floor and walls. The students must predict the trajectory of an object moving through space by physically moving along the path they think a meteor (projected on the floor) will travel. Laser scanning technology tracks their movements, offering real-time feedback on whether their predictions are correct. Based on that feedback, students adapt their beliefs about scientific principles, then adjust their movements to reflect what they are learning. </blockquote>Final hint: it's probably reasonable to assume that these MEteor-facilitated embodied cognition exercises don't take place in outer space.<br /><br />Another problem reported by Tscholl: "students are scared of symbolic representations." Given this, what do you think his solution is? <br /><br />1. Give students more practice with symbolic representations and their relation to physical phenomena.<br /><br />2. De-emphasize symbolic representations. <br /><br />Stumped? Consider: (a) how facility with symbolic representations, and with manipulating these mathematically, is essential to doing physics, and (b) how little sense there is in anything in this article. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com3tag:blogger.com,1999:blog-6570061087276796800.post-42029850088666790362015-06-20T10:00:00.000-04:002015-06-20T10:00:03.801-04:00You need to do some graphics to make it look like they’re flying, when they’re not really flyingI recently came across this un-facilitated, unedited, in-class assignment that J wrote for his graphic design class. Somehow, with its earnest attempt to cope with whatever the prompt was, and with his years in high school now weeks away from their conclusion, I found it quite endearing. I reproduce it here with permission from the author. <br /><br />Given what I’ve written recently about <a href="http://oilf.blogspot.com/2015/04/the-normal-child-inside-fourth.html">Facilitated Communication</a>, I should note that, in a sense, the author’s in-class communication is facilitated. J’s handwriting being so bad that often even he can’t read it, he regularly uses an AlphaSmart keyboard. But the keyboard remains stationary, sitting on his desk rather than on the palm of someone else’s hand; it offers no text-completion software with pop-up windows of likely next words and grammatical corrections; and no one would even consider hovering over J and supporting his wrist while he types. This is an author who feels strongly about being left alone while the creative juices flow: <br /><blockquote>There are some people who becomes a graphic designer. Like making a fictional movie, you’ll have to do some graphics on some objects. Like when Violet turned into a blueberry, people had to do some graphics since you obviously can’t inflate people into a ball. </blockquote><blockquote>You have to be good at programming. Graphics require some programming. When you make a movie, you’ll want it to look real, and not make it look like it’s edited. Like when we see Violet turning to a blueberry, it looks real, and has not been edited. <br />You have to be good at painting to make some cartoon movies. In cars, Lightning McQueen and other cars look like they’re real, but they were actually painted. You would want to make it look real, and not look like they have been painted. </blockquote><blockquote>You have to have a software to do some graphics. Photoshop is one of the software. It can edit some things out, and put some new things in. Like if you want to change some of the words, you’ll want to remove the words, and put new words in, and you’ll want to make it look like real, and has not been edited. </blockquote><blockquote>So if you want a graphic designer, you need to be prepared. You want to make a movie look real, and not been edited. Like in Harry Potter movie, quidditch is obviously not real. You’ll have to make some graphics to make it look like they’re flying, when they’re not really flying. </blockquote>Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com0tag:blogger.com,1999:blog-6570061087276796800.post-48011046348282237152015-06-18T10:00:00.000-04:002015-06-18T10:00:03.283-04:00Math problems of the week: Common Core inspired 8th grade functions problemsFrom the <a href="http://www.smarterbalanced.org/smarter-balanced-assessments/">Smarter Balanced Assessments</a>, a Common Core-inspired, standardized test consortium now consisting of about 12 states. <br /> <br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-bURTLydoaGo/VVZgwlYv_cI/AAAAAAAAC2s/-6-A8SaThAs/s1600/SB_8.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="466" src="http://2.bp.blogspot.com/-bURTLydoaGo/VVZgwlYv_cI/AAAAAAAAC2s/-6-A8SaThAs/s640/SB_8.png" width="640" /></a></div><br /><strong>The Common Core goal in question?</strong> <br /><br />Grade 8 » Functions » Use functions to model relationships between quantities. » 5 <br /><br />Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally. <br /><br /><br /><strong>Extra Credit: </strong><br /><strong></strong><br />Labels vs. Concepts<br /><br />If you factor out the hurdle of knowing the meanings of the various labels ("linear", "non-linear," "positive slope," "negative slope"), how much mathematical challenge is left, and at approximately what grade level would you put it?Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-9749378485656801062015-06-16T10:00:00.000-04:002015-06-16T10:00:01.114-04:00What we forget about history textbooksIt’s fashionable these days to decry traditional history as all about names and dates and powerful people, and history textbooks as inferior to primary sources. But our collective historical memories are short. <br /><br />People forget that there are textbooks, and then there are textbooks. Some of them are written by committee, are dumbed down for a very general audience, and, written to offend no one, are dull as doorknobs. Others are written in the single voice of a learned historian and raconteur: someone who knows how to make even the driest facts as interesting to you as they are to him or her. <br /><br />People forget that to really appreciate primary sources, you need historical context; that survey courses are the best way to acquire and retain this; and that there are some really good survey-based textbooks out there written by learned historians/raconteurs who know how to make even the driest facts interesting—particularly if you go back in time. <br /><br />Because, finally, people forget—or probably never knew—that there are all sorts of really good history textbooks that were published ages ago, and that aren’t all about names and dates and powerful people. <br /><br />Here’s how one of them opens: <br /><blockquote>Could Louis XIV now see the France he once ruled, how startling the revolution in politics and industry would seem to him! The railroads, the steel steamships, the great towns with well-lighted, smoothly paved, and carefully drained streets; the innumerable newspapers and the beautifully illustrated periodicals, the government schools, the popular elections, and his deserted palaces; the vast factories full of machinery, working with a precision and rapidity far surpassing those of an army of skilled workmen; and most astonishing of all, the mysterious and manifold applications of electricity which he knew only in the form of lightning playing among the storm clouds: all these marvels would combine to convince him that he died on the eve of the greatest revolution in industry, government, and science that the world has ever seen. It is the purpose of this volume, after describing the conditions in Europe before the French Revolution, to show as clearly as possible the changes which have made the world what we find it today. </blockquote><blockquote>If a peasant who had lived on a manor in the time of the Crusades had been permitted to return to earth and travel about Europe at the opening of the eighteenth century, he would have found much to remind him of the conditions under which, seven centuries earlier, he had extracted a scanty living from the soil… </blockquote><blockquote>The houses occupied by the country people differed greatly from Sicily to Pomerania, and from Ireland to Poland, but, in general, they were small, with little light or ventilation, and often they were nothing but wretched hovels with dirt floors and neglected thatch roofs. The pigs and the cows were frequently better housed than the people, with whom they associated upon very familiar terms, since the barn and the house were commonly in the same building… <br />… <br />Even in the towns there was much to remind one of the Middle Ages. The narrow, crooked streets, darkened by the overhanging buildings and scarcely lighted at all by night, the rough cobblestones, the disgusting odors even in the best quarters—all offered a marked contrast to the European cities of today, which have grown tremendously in the last hundred years in size, beauty, and comfort. </blockquote>(From James Harvey Robinson’s <a href="http://www.amazon.com/Outlines-European-history-1863-1936-Robinson/dp/1172433151/ref=sr_1_5?ie=UTF8&qid=1430087551&sr=8-5&keywords=Outlines+of+European+History">Outlines of European History</a>, which my daughter and I started reading a couple of months ago.) Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com4tag:blogger.com,1999:blog-6570061087276796800.post-18718238956736656402015-06-14T10:00:00.000-04:002015-06-14T10:00:02.099-04:00Modern-day Calvinism: predicting predestinationOne longstanding frustration for “autism families” is how much more public money funds research on causes and early signs of autism than interventions and assistance. What’s the point of finding out when your kid is 3 weeks old that he or she is autistic if little is known about what to do next? <br /><br />Something similar might be said of all that K12 assessment. Consider the amount of public money (and public discourse) spent on educational testing--from Common Core tests to <a href="http://www.edweek.org/ew/articles/2015/05/06/frontiers-of-digital-learning-probed-by-researchers.html">assessment technology</a> to the <a href="http://www.nytimes.com/2015/05/12/us/school-districts-embrace-business-model-of-data-collection.html?_r=0">man-hours that teachers spend weekly on assessment forms and “formative assessments</a>.” How does this compare with the amount of money (and discourse) spent on follow-up measures? Education experts praise the new Common Core tests for predicting college and career readiness; they say little to nothing about what specifically to do on behalf of those who, on one or more of the hundreds of standards and sub-standards, don’t fully measure up. What’s the point of making predictions about future success if you have nothing to offer those who need help? <br /><br />In the case of autism research and autism funding, I’ve often suspected that part of what’s going on is the allure of the easy. I’m guessing it’s a lot easier to fish around for genetic and neurological correlates and early infancy symptoms (and to tout early detection as the prerequisite for early intervention) than it is to create and efficacy-test the kinds of early interventions that would truly justify all that’s spent on early detection. <br /><br />Now, as the edworld seems more and more focused on assessing everything from “mathematical thinking” to developmental skills (e.g., organization, attention) to personality traits (sociability, grit, “risk taking”) to readiness for college and careers, with little thought about going beyond measurement to measurement-informed interventions, I have to started to suspect something similar about education. It is, just maybe, a heck of a lot easier to score tests than to teach skills. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com1tag:blogger.com,1999:blog-6570061087276796800.post-19956427566127403752015-06-12T10:00:00.000-04:002015-06-12T10:00:03.001-04:00Math problem of the week: 6th grade Common Core-inspired test questionMore from the Smarter Balanced Consortium and its Common Core-aligned tests: the final items on a <a href="http://www.smarterbalanced.org/smarter-balanced-assessments">6th grade number sense assessment</a>.<br /><br /><strong>Stimulus:</strong> The student is presented with statements about two rational numbers and their position on a number line in relation to each other.<br /><br /><strong>Example Stem:</strong> Select True or False for each statement. <br /><br />The numbers 7 and –12 are both located to the right of 0 on the number line. <br /><br />The number –12 is located to the right of 5 on the number line. <br /><br />The number –12 is located to the left of –8 on the number line. <br /><br /><br /><strong>Extra Credit:</strong><br /><br />Discuss how confusing mathematical conventions with mathematical concepts is similar to <a href="http://oilf.blogspot.com/2015/03/when-it-matters-whether-1-is-prime.html">confusing mathematical labels with mathematical concepts</a>.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com1tag:blogger.com,1999:blog-6570061087276796800.post-56850263074495258782015-06-10T10:00:00.000-04:002015-06-10T10:00:06.226-04:00One thing I don't miss while homeschooling:The mandatory science fair project.<br /><br />But here's a <a href="http://blogs.edweek.org/edweek/curriculum/2015/04/study_to_question_value_of_science_fairs.html">great idea</a> for a project:<br /><blockquote>Is holding a middle school science fair a worthwhile endeavor? A team of science educators and researchers funded by a $2 million National Science Foundation grant is hoping to find out. <br /><br />The group is collecting data on science fairs' cost effectiveness, as well as their impact on learning and on students' interest in science. </blockquote>According to Abigail Jurist Levy, the principal research scientist for the four-year project, "Science Fairs Under the 'Scope," science fairs have "never been really rigorously researched": <br /><blockquote>"As valued as they are by some, and as criticized as they are by others, we really don't know what they offer students in terms of learning experiences and engendering enthusiasm in science."</blockquote><blockquote class="tr_bq">(<a href="http://blogs.edweek.org/edweek/curriculum/2015/04/study_to_question_value_of_science_fairs.html">Education Week</a>)</blockquote>Here's another science project idea, courtesy the <a href="http://www.huffingtonpost.com/susan-messina/that-fake-science-fair-poster-that-went-viral-i-made-it-heres-why_b_5053008.html">Huffington Post</a>:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-HGe79R1PVr0/VVEe38NRIbI/AAAAAAAAC2Q/YSuActTqBDY/s1600/sci_fair.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="240" src="http://2.bp.blogspot.com/-HGe79R1PVr0/VVEe38NRIbI/AAAAAAAAC2Q/YSuActTqBDY/s320/sci_fair.png" width="320" /></a></div><br />From Susan Messina, designer of the above poster: <br /><blockquote>Any elementary school project that requires a lot of parental time, energy, resources, support, cajoling and financial investment is just BAD. Such projects privilege students from higher-income families for all the obvious reasons.</blockquote>They also privileged the extraverted and artistic self-starters over other types of students (among them, some of our future scientists). Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com8tag:blogger.com,1999:blog-6570061087276796800.post-47716533229671069892015-06-08T10:00:00.000-04:002015-06-08T10:36:04.063-04:00Who speaks for children with special needs? <a href="http://oilf.blogspot.com/2013/11/who-speaks-for-autism.html">Who speaks for autism</a>? This was the question I raised a couple of years ago in an earlier post, noting the tensions between what is advocated for by certain high functioning individuals with autism vs. the parents of their lower functioning counterparts. <br /><br />Current events inspire me to ask a much broader question: who speaks for children with special needs? <br /><br />The special needs category, obviously, is several orders of magnitude greater both in terms of numbers, and in terms of diversity, than autism alone is. It includes a large number of individuals who are cognitively neurotypical, but have sensory or motor impairments (e.g., visual impairments or mobility impairments). Even among those with cognitive differences, it includes a large number of very high functioning individuals whose impairments don’t significantly affect, say, their comprehension of written language or of algebraic equations. <br /><br />Despite all this diversity, a large consortium called the Consortium for Citizens with Disabilities, a consortium of approximately 100 organizations ranging from the American Association of People with Disabilities to the World Institute on Disability, has spoken out with a single voice on one particularly controversial issue. That issue has to do with America’s new Common Core-aligned tests. <br /><br />For some time now, I’ve been arguing that the Common Core Standards are <a href="http://www.theatlantic.com/education/archive/2014/02/the-common-core-is-tough-on-kids-with-special-needs/283973/">tough on kids with special needs</a>. The big problem, I argue, is that they impose a one-size-fits-all, calendar-age based sequence on nearly everyone. <br /><br />Currently only the most severely cognitively impaired 1 percent of the student population (about 10 percent of students with disabilities) is exempted from Common Core-aligned testing. But that 1 percent does not come close to including all the children who are reading, writing, or computing well below grade level. <br /><br />Given this, you would think that disability advocates would crying out more exemptions, both from the tests, and from the calendar-aged-based, Common Core-aligned curricula that are proliferating around the country. After all, the more these curricula raise standards for neurotypical students, the more they deprive those with cognitive impairments and learning disabilities of access to appropriate instruction at their Zones of Proximal Development. <br /><br />But nope. As it turns out, the Consortium for Citizens with Disabilities (again, approximately 100 organizations ranging from the American Association of People with Disabilities to the World Institute on Disability) has spoken out with a single voice to <i>denounce</i> a provision that would allow an additional 2 percent of students (or about 20 percent of students with disabilities) to be tested on “modified academic achievement standards” and measured for proficiency on these. <br /><br />This provision, they <a href="http://blogs.edweek.org/edweek/speced/2013/07/advocacy_group_calls_for_end_t.html">argue</a>, is a way to get around teaching students with disabilities on the same academic standards as their typically-developing peers . <br /><br />And, yes, so it will. These anti-exemption advocates are exactly right about that. <br /><br />But, given everything we know about optimized learning environments, not teaching students with disabilities on the same academic standards as their typically-developing peers is a <em>good</em> thing. No matter who you are, starting at just above your current level of mastering results in <i><a href="http://www.nifdi.org/pdfs/StuPro_Align.pdf">faster long term progress</a></i> than starting beyond your current level does. <br /><br />So I ask, who are these anti-exemption advocates who claim to be speaking for all people with disabilities? Who are the real spokespeople here, and what do they have in the way of standing, and/or expertise, and/or experience? Their <a href="http://www.c-c-d.org/">website</a> doesn’t say. <br /><br />So I can only guess. Perhaps these anti-exemption advocates include self-advocates whose only challenges are sensory or motor impairments or other non-intellectual impairments: impairments that can and should be straightforwardly accommodated to provide access to calendar-aged based curricula and testing. Perhaps these anti-exemptions advocates include other self-advocates whose learning disabilities are at the mild end of the spectrum: people with ADHD or dyslexia or high functioning autism who have largely overcome the various impediments to academic success. And perhaps these anti-exemption advocates include hopeful parents and other caregivers that are in some state of denial (a denial perhaps facilitated by “<a href="http://oilf.blogspot.com/2015/04/the-normal-child-inside-fourth.html">facilitated communication</a>”) about the current and future academic readiness of those closest to them. <br /><br />But there’s one thing I’m pretty sure of, and that’s that these anti-exemption advocates don’t include those who actually struggle to teach math, reading, and writing to students with significant learning difficulties--many of whom are extremely frustrated by the requirement that they teach the students calendar-aged-based material instead of material they can actually handle. Nor, or so I’d venture to guess, do they include the students themselves—for example, the language-impaired 11th grader forced to “Analyze how an author’s choices concerning how to structure specific parts of a text (e.g., the choice of where to begin or end a story, the choice to provide a comedic or tragic resolution) contribute to its overall structure and meaning as well as its aesthetic impact” (CCSS literacy goal RL.11-12.5) or the dyscalculic 11th grader forced to “graph polynomial functions, identifying zeros when suitable factorizations are available, and showing end behavior"(CCSS math goal HSF.IF.C.7.C) <br /><br />The special needs of these populations need to be heard by many more people. Wouldn’t it be nice if some of the scores of disability rights organizations would break ranks from the Consortium and help make this happen? Now more than ever, in our Procrustean Age of one of one-size-fits-all Standards and Universal Design for all, where those who don’t span what needs to be spanned are stretched till they snap, the help of those who would be disability advocates is sorely needed. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com1tag:blogger.com,1999:blog-6570061087276796800.post-60293448011374061142015-06-06T10:00:00.000-04:002015-06-06T19:57:17.850-04:00Depression era whole language and project-based learning<blockquote>"Now you tell your father not to teach you any more. It's best to begin reading with a fresh mind. You tell him I'll take over from here and try to undo the damage--"<br /><br />"Ma'am?"<br /><br />"Your father does not know how to teach. You can have a seat now."<br /><br />...<br /><br />"Don't worry, Scout," Jem comforted me. "Our teacher says Miss Caroline's introducing a new way to teaching. She learned about it in college. It'll be in all the grades soon. You don't have to learn much out of books that way--it's like if you wanta learn about cows, you go milk one, see?"<br /><br />"Yeah Jem, but I don't wanta study cows, I--"<br /><br />"Sure you do. You hafta know about cows, they're a big part of life in Macomb County."<br /><br />I contented myself with asking Jem if he'd lost his mind.<br /><br />"I'm just trying to tell you the new new way they're teachin' the first grade, stubborn. It's the Dewey Decimal System."<br /><br />Having never questioned Jem's pronouncements, I saw no reason to begin now. The Dewey Decimal System consisted, in part, of Miss Caroline waving cards at us on which were printed "the," "cat," "rat," "man," and "you." No comment seemed to be expected of us, and the class received these impressionistic revelations in silence. I was bored, so I began a letter fo Dill. Miss Caroline caught me writing and told me to tell my father to stop teaching me. "Besides," she said. "We don't write in first grade, we print. You won't learn to write until you're in third grade."</blockquote><blockquote class="tr_bq">...</blockquote><blockquote class="tr_bq"> The remainders of my schooldays were no more auspicious than the first. Indeed, they were an endless Project that slowly evolved into a Unit, in which miles of construction papers and wax crayon were expended by the State of Alabama in well-meaning but fruitless efforts to teach me Group Dynamics. What Jem called the Dewey Decimal System was schoolwide by the end of my first year, so I had no chance to compare it with other teaching techniques. I could only look around me: Atticus and my uncle, who went to school at home, knew everything--at least, what one didn't know, the other did. Furthermore, I couldn't help noticing that my father had served for years in the state legislature, elected each time without opposition, innocent of the adjustments my teacher thought essential to the development of Good Citizenship... [A]s I inched sluggishly along the treadmill of the Macomb County school system, I could not help receiving the impression that I was being cheated out of something. Out of what I knew not, yet I did not believe that twelve years of unrelieved boredom was exactly what the state had in mind for me.</blockquote><blockquote><br />--Harper Lee (1960).</blockquote>Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-55771062853564418972015-06-04T10:00:00.000-04:002015-06-04T10:00:05.794-04:00Math problems of the week: 6th grade Smarter Balanced "number sense" problems, cont: More from the Smarter Balanced Consortium and its Common Core-aligned tests: the final items on a <a href="http://www.smarterbalanced.org/smarter-balanced-assessments">6th grade number sense assessment</a>.<br /><br /><strong>Stimulus:</strong> The student is presented with a real-world or mathematical context and a graph of ordered pairs. <br /><br /><strong>Example Stem 1:</strong> This grid shows the location of three points. <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-6Pp3vj1T184/VU5-C4TFe4I/AAAAAAAAC1w/bZHKnv-QpAA/s1600/SB_6_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://4.bp.blogspot.com/-6Pp3vj1T184/VU5-C4TFe4I/AAAAAAAAC1w/bZHKnv-QpAA/s320/SB_6_1.png" width="314" /></a></div><br />Enter the distance, in units, between point A and point C. <br /><br /><strong>Rubric</strong>: (1 point) Student enters the correct numeric value for the distance (e.g., 7). Units of measure should be assumed from the stem. <br /><br /><strong>Example Stem 2:</strong> This grid represents the layout of Tom’s neighborhood. Each unit on the grid represents 1 square mile. <br />• Tom’s house is located at (4, 2) <br />• A store is located at (–3, 2) <br />• Tom’s neighbors are located at (4, 4). <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-v8YbFjAUoUM/VU5-LQstWvI/AAAAAAAAC14/lYXo2tFI6GM/s1600/SB_6_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="320" src="http://2.bp.blogspot.com/-v8YbFjAUoUM/VU5-LQstWvI/AAAAAAAAC14/lYXo2tFI6GM/s320/SB_6_2.png" width="316" /></a></div><br />Enter the distance, in miles, from Tom’s house to the store. <br /><br /><strong>Rubric:</strong> (1 point) Student enters the correct numeric value for the distance (e.g., 7). Units of measure should be assumed from the stem. <br /><br /><strong>OILF Extra Credit:</strong><br /><br />1. Follow up to extra credit on last week’s POW: discuss the correlation between conceptual “depth” and mathematical challenge. <br /><br />2. Discuss the lost opportunity in the above problems vis-a-vis a real-world application of the Pythagorean Theorem. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com4tag:blogger.com,1999:blog-6570061087276796800.post-83566019152476369512015-06-02T10:00:00.000-04:002015-06-02T10:00:00.680-04:00It’s not just the Common Core: how vagueness and complexity entrench current practicesOne of the problems with the Common Core Standards is their vagueness. Some people see this as a virtue: the Standards, they reassure us, don’t spell out how or what to teach. Local schools and teachers, they say, still have as much autonomy as ever. The downside is that the CC provides no guidelines on how to attain its goals—the more so because the goals are often vague, not just about how they are to be met, but about what precise skills they involve. <br /><br />Worse, this vagueness can be used by the powers that be to further entrench current practices like Reform Math, which many experts outside the power structures find highly problematic. Because the CC standards are so vague, anyone can argue that their preferred curriculum and pedagogy are supported by them. While theoretically this empowers everyone, in practice it particularly empowers those who already have power and influence over today’s classrooms. <br /><br />But the Common Core isn’t the only vague factor out there that particularly empowers the Powers that Be. There’s also the testing data. Consider the declines in U.S. test scores, or our poor rankings relative to other developed countries. Particularly when this occurs on measures that, like the <a href="http://en.wikipedia.org/wiki/Programme_for_International_Student_Assessment">PISA</a> or <a href="http://www.nytimes.com/2013/10/08/us/us-adults-fare-poorly-in-a-study-of-skills.html?_r=0">this new test</a>, emphasize conceptual understanding, reasoning, and applied problem solving, Reform Math advocates say it’s because we’re not doing enough Reform Math; student-centered discovery-learning advocates say it’s because we’re not doing enough student-centered discovery learning; and technology-in-the-classroom advocates say it’s because we’re not making enough use of classroom technology. So obvious are these solutions that their advocates find no reason to look at what’s happening, or not happening, in the countries that outperform us. <br /><br />It’s the same with the economy—another highly opaque set of factors (opaque, especially, in their complexity). When the economy is perceived to be in bad shape (or, for that matter, in good shape), advocates of current practices say we need more of these practices. The difference, of course, is that advocates of whatever current economic practices are don’t generally have quite the power monopoly enjoyed by those in the educational industrial complex. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com3tag:blogger.com,1999:blog-6570061087276796800.post-30910799703756238852015-05-31T10:00:00.000-04:002015-05-31T10:21:22.071-04:00Boredom and time sinks in child-centered classroomsOne of the most underappreciated of sins is wasting people’s time. Frittering away an hour of someone else’s time, if you think about it, is not that different from shortening that person’s life by one hour. <br /><br />Time wasting is all the more toxic in environments that are difficult to escape, and/or where the opportunity cost (the value of what you could potentially be doing instead) is high. For example, K12 classrooms. Here, the most obvious symptom of time wasting is boredom. <br /><br />Enthusiasts of today’s technology-enhanced, “child-centered,” “real-life relevant” classrooms often describe traditional classrooms as boring. Surely desks in rows, rote drills, and pen, paper, textbooks and chalkboards are inherently duller than manipulatives, interactive screens, multi-media projects, student-led discussions, and students facing one another in desk pods. <br /><br />But some of the core features of today’s classrooms make them more boring than ever. Culprits include having students work in groups rather than independently (a.k.a. cooperative learning), and assigning students of different ability levels to each group (a.k.a. heterogeneous grouping). <br /><br />1. Combining group assignments with heterogeneous grouping ensures that few students are working within their Zones of Proximal Development. This makes the assigned tasks too easy for some students and too difficult for others—disengaging both parties and slowing down everyone’s progress. <br /><br />2. Students are generally less engaging as teachers than teachers themselves are, and student-led, teacher-decentered discussions are often rambling, confusing, and repetitive: slow to move through the material and/or to get to the point. <br /><br />3. Many of today’s solve-in-multiple-ways-and-explain-your-answer math problems and be-colorful-and-creative multi-media projects involve a very high ratio of busy work to actual learning. <br /><br />4. The pod-based seating that facilitates group work means that half the students now have their backs to the front of the classroom. Factor in that today’s teachers spend less time in front and more time moving around, and it’s no longer possible for bored students to shield behind their textbooks and notebooks the more engaging material (the cartoons, the puzzle books, the adult novels) they once snuck in from home. <br /><br />5. Boredom, in turn, is a much-underappreciated source of misbehavior. Aggravating this, student-centered classrooms foster in fewer and fewer students the habit of listening to and learning from their teachers. Students, in short, are harder and harder to teach, and are more and more distracted and distracting (no, you can’t just blame this on extracurricular technology and social media!). <br /><br />For those who nonetheless still do want to learn academics, six plus hours daily in classrooms of restless and distracting classmates is a terrible way to waste a brain. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com9tag:blogger.com,1999:blog-6570061087276796800.post-71581452348757072672015-05-29T10:00:00.000-04:002015-05-29T10:00:03.711-04:00Math problems of the week: 6th grade Smarter Balanced "number sense" problemsIt turns out the Montgomery Public Schools isn’t the only institution going deeper with K12 math. So is the Smarter Balanced Consortium and its Common Core-aligned tests. Here are two sample items from a <a href="http://www.smarterbalanced.org/smarter-balanced-assessments">6th grade number sense assessment</a> (one from the beginning, one from the end):<br /><br /><strong>Stimulus:</strong> The student is presented with a context involving a negative number or zero. <br /><strong>Example Stem:</strong> A Fahrenheit thermometer shows that the temperature is 15 degrees below zero. <br />Enter the integer that represents the temperature in degrees Fahrenheit. <br /><br /><strong>Stimulus:</strong> The student is presented with statements involving absolute value in a real-world context. <br /><strong>Example Stem</strong>: Sea level is defined as being at an elevation of 0 feet. Objects can be above or below sea level. <br />• Submarine J is 35.6 feet below sea level. <br />• Submarine Q is 21.5 feet below sea level. <br />• Submarine Z is 43.8 feet below sea level. <br /><br />Determine whether each statement comparing the submarines is true. <br />Submarine J is deeper than Submarine Q because |–35.6| > |–21.5|. <br />Submarine Q is deeper than Submarine Z because |–21.5| > |–43.8|. <br />Submarine J is deeper than Submarine Z because |–35.6| > |–43.8|. <br /><br /><br /><strong>OILF's Extra Credit:</strong><br /><br />Is it possible that what’s challenging about negative numbers and absolute value aren’t the “deep” concepts that underlie them, but, rather, the more complicated operations on them that emerge in a curriculum less focused on “number sense” and more on (shudder!) mathematical procedures? Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com0tag:blogger.com,1999:blog-6570061087276796800.post-7053665342600194762015-05-27T10:00:00.000-04:002015-05-27T11:46:59.297-04:00How traditional math is more progressive than today's mathIn theory, today’s Constructivist classrooms, inspired as they are by educational progressivism, are supposed to favor child-centered discovery learning. And yet, in many ways, they are less child-centered than ever. <br /><br />We see this, for example, in Reform Math and Common Core-inspired math classes. Here, children are told not just to solve problems, but <i>how</i> to solve them. And they are often required to solve them several times over in multiple ways. Typically, the standard algorithm is only one of several options, and preferred options are things like counting forwards or backwards from “landmark numbers,” “splitting” numbers via “number bonds,” repeatedly adding, repeatedly subtracting, or (if you’re lucky enough to be using Everyday Math) multiplying via “lattices”. Not to mention explaining, verbosely, how you did what you did and why. <br /><br />A more child-centered, discovery-oriented approach to math problems—indeed, a more “authentic” and “organic” approach—would be to let the problems themselves, rather than the verbal directions, suggest one particular type of strategy or another. <br /><br />Consider: <br /><br />999 + 77 vs. 956 + 77 <br /><br />The first of these invites a “landmark” numbers approach: solve it by converting it to a similar problem involving 1000 instead of 999. The second problem is much more rapidly solved using the standard addition algorithm, left to right, with regrouping. <br /><br />1000 – 7 vs. 956 – 77 <br /><br />The first invites a counting back approach (count back 7 from 1000); the second is much more rapidly solved using the standard subtraction algorithm with borrowing. <br /><br />9 × 1004 vs. 9 × 1234 <br /><br />The first invites a “splitting”/distributive approach (split 1004 into 1000 and 4 and multiple each by 9 separately, then add). The second is much more rapidly solved via that standard algorithm for multiplication. <br /><br />8032 ÷ 8 vs. 8032 ÷ 7 <br /><br />The first of these invites a “splitting”/distributive approach (split 8032 into 8000 and 32 and divide each by 8 separately, then add). The first is much more rapidly solved vis that standard algorithm for division. <br /><br />Offering a large number of problems that invite different strategies is the approach taken by so-called tyrannical, teacher and textbook -centered traditional math. Here, it’s much less common for kids to be told how to solve particular problems. Yes, the standard algorithms are “privileged” as the most efficient ways to solve most problems. But students weren’t generally forced to use these—so long as they solved the problems correctly. <br /><br />But the problems themselves were different. There were many more of them than what kids get today; they involved more digits and fewer “friendly” numbers. The result: many more problems for which the most efficient strategies were the standard algorithms. Also, calculators weren’t—so to speak—part of the equation. But speed often was. Timed math tests and timed problem sets were frequent. As I discussed in my <a href="http://oilf.blogspot.com/2015/05/math-problems-of-week-parcc-vs-maryland.html">earlier post</a>:<br /><blockquote>Many people assume that speed tests (especially multiple choice speed tests) measure only rote knowledge. But they’re also a great way to measure conceptual understanding. Performance speed reflects, not just rote recall, but also efficiency, and efficiency, in turn, is a function of reasoning, strategizing, and number sense. </blockquote>In particular, time pressure will inspire you to use the standard algorithms on problems like 956 + 77, and nonstandard shortcuts (landmarks, splitting, etc.) on problems like 999 + 77. <br /><br />This brings up another difference between traditional math and Reform Math. Traditional math doesn’t belabor the shortcuts—or, indeed, even teach them. After all, if you have enough timed tests involving problems like 999 + 77, you will figure it out on your own—in the spirit of true, child-centered discovery. <br /><br />It’s only when you drastically lower the number of problems that you assign, allow calculators, and dispense with speed tests, that you find yourself having to start spoon-feeding students the shortcuts and other ad hoc strategies. (At the expense, of course, of the standard algorithms). Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-3611251159643589562015-05-25T10:00:00.000-04:002015-05-25T10:00:06.028-04:00The Educational Technology Industrial Complex offers yet another reason to make students show their workIt helps sell technology! <br /><br />Specifically, “screen casting technology.” As a <a href="http://www.edweek.org/ew/articles/2015/05/06/frontiers-of-digital-learning-probed-by-researchers.html">recent article</a> in Edweek notes, such technology can get “students to create a multilayered record of their thinking while attempting to solve math problems.” According to one paper presented a few weeks ago at the annual meeting of the American Educational Research Association <br /><blockquote>Such an approach could help teachers “go beyond determining whether students correctly solved the problem, to understand why students solved the problem the way they did.”</blockquote>Here's the screencast example showcased by the article:<br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-mUSzxAcl4OA/VVpTNjQBE5I/AAAAAAAAC3A/PXMXUdgAqlI/s1600/screencasting.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="304" src="http://4.bp.blogspot.com/-mUSzxAcl4OA/VVpTNjQBE5I/AAAAAAAAC3A/PXMXUdgAqlI/s400/screencasting.png" width="400" /></a></div><br /><br />In an ongoing study in which “students generate screen casts of their problem solving processes” and “recorded themselves as they verbally explained their work,” one particularly remarkable result was recorded: <br /><blockquote>One student… incorrectly solved a word problem that required division. By reviewing the screencast of the student’s work in conjunction with her audio-recorded narration, the researchers were able to ascertain that the student had used a sound problem-solving strategy, but made an arithmetic error caused in part by her haste to finish quickly (and thus demonstrate that she was “good at math”). </blockquote>The authors go on to highlight the crucial role played here by the screen casting technology: <br /><blockquote>Without the screencast… “it would have been difficult to pinpoint where exactly the mismatch took place, and it could have been incorrectly concluded that [the student] did not understand the problem from the start.” </blockquote>It really makes you wonder how people functioned back in the dark ages, when all you could do was talk to your students face to face and look directly at the sheets of paper they did their work on. <br /><br />Of course, back in the <em>really</em> dark ages, when students weren’t required to do arithmetic in multiple steps and explain their answers verbally (which, incidentally, allowed them to do at least 10 times as many math problems per problem session as kids do today), <a href="http://oilf.blogspot.com/2015/05/two-approaches-to-math-assessment.html">there must have been no way</a> to tell who didn’t understand the problems and who was simply prone to stupid mistakes. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-71934958113884695512015-05-23T09:44:00.000-04:002015-05-23T09:44:00.107-04:00Right-brained science, again: the myth of the finches<blockquote class="tr_bq">Behold Albert Einstein: not the tidy young patent clerk, working through his most groundbreaking theories, but the scraggly eccentric of his later years. This image speaks volumes about our conception of scientific geniuses. We view those we most admire more as crazy, intuition-driven, mold-breaking, wild-haired artists than as meticulous researchers and rigorous analyzers. We imagine their greatest mathematical and scientific breakthroughs occurring not at desks or in laboratories; instead, we see Archimedes in his bathtub, Newton under and apple tree, and Franklin in a storm with his kite. </blockquote>From an early draft of <a href="http://www.amazon.com/Raising-Left-Brain-Child-Right-Brain-World/dp/1590306503/ref=sr_1_1?ie=UTF8&s=books&qid=1245370742&sr=8-1">Raising a Left Brain Child in a Right Brain World</a>, then called "Out in Left Field in a Right Brain World."<br /><br />I regretted eliminating this section; it didn't fit in with the publisher's reconception of my project as a parent-oriented advice book rather than as a broader cultural critique. But the more I think about it, the more I think that this right-brained conception of science and scientists has contributed to the demise of science education in ways that specifically shortchange left-brained, scientific minds.<br /><br />--The notion that the way you get kids interested in science is to showcase the epiphanies rather than the puzzle solving--downplaying the importance, and the <a href="http://oilf.blogspot.com/2013/07/making-math-fun_20.html">fun</a>, of solving hard puzzles. <br /><br />--The notion that the way to prepare kids for science careers is to promote "creativity" and "out of the box thinking" rather than the analytical and mathematical skills that scientific competence depends on.<br /><br />So it was nice to see physicist Leonard Mlodinow's <a href="http://www.nytimes.com/2015/05/16/opinion/it-is-in-fact-rocket-science.html?_r=0">Op Ed</a> in Sunday's New York Times. As soon as I read the first two paragraphs, I knew just what he was getting at:<br /><blockquote class="tr_bq">The other week I was working in my garage office when my 14-year-old daughter, Olivia, came in to tell me about Charles Darwin. Did I know that he discovered the theory of evolution after studying finches on the Galápagos Islands? I was steeped in what felt like the 37th draft of my new book, which is on the development of scientific ideas, and she was proud to contribute this tidbit of history that she had just learned in class. </blockquote><blockquote class="tr_bq">Sadly, like many stories of scientific discovery, that commonly recounted tale, repeated in her biology textbook, is not true. </blockquote>Noting that "The popular history of science is full of such falsehoods," Mlodinow writes: <br /><blockquote class="tr_bq">The myth of the finches obscures the qualities that were really responsible for Darwin’s success: the grit to formulate his theory and gather evidence for it; the creativity to seek signs of evolution in existing animals, rather than, as others did, in the fossil record; and the open-mindedness to drop his belief in creationism when the evidence against it piled up.<br /><br />The mythical stories we tell about our heroes are always more romantic and often more palatable than the truth. But in science, at least, they are destructive, in that they promote false conceptions of the evolution of scientific thought.<br /><br />Of the tale of Newton and the apple, the historian Richard S. Westfall wrote, “The story vulgarizes universal gravitation by treating it as a bright idea ... A bright idea cannot shape a scientific tradition.” Science is just not that simple and it is not that easy. </blockquote>Perhaps most compelling is Mlodinow's critique of the recent Steven Hawking movie <br /><blockquote class="tr_bq">In the film “The Theory of Everything,” Stephen Hawking is seen staring at glowing embers in a fireplace when he has a vision of black holes emitting heat. In the next scene he is announcing to an astonished audience that, contrary to prior theory, black holes will leak particles, shrink and then explode. But that is not how his discovery happened.<br />In reality, Mr. Hawking had been inspired not by glowing embers, but by the work of two Russian physicists. </blockquote><blockquote class="tr_bq">According to their theory, rotating black holes would give off energy, slowing their rotation until they eventually stopped. To investigate this, Mr. Hawking had to perform difficult mathematical calculations that carefully combined the relevant elements of quantum theory and Einstein’s theory of gravity — two mainstays of physics that, in certain respects, are known to contradict each other. Mr. Hawking’s calculations showed, to his “surprise and annoyance,” that stationary black holes also leak. </blockquote>Not glowing embers; difficult mathematical calculations. <br /><br />Mlodinow notes that "the oversimplification of discovery makes science appear far less rich and complex than it really is." He also touches on broader consequences:<br /><blockquote class="tr_bq">Even if we are not scientists, every day we are challenged to make judgments and decisions about technical matters like vaccinations, financial investments, diet supplements and, of course, global warming. If our discourse on such topics is to be intelligent and productive, we need to dip below the surface and grapple with the complex underlying issues. The myths can seduce one into believing there is an easier path, one that doesn’t require such hard work.</blockquote>To see this in action, one need look no further than the education world--including, of course, the subworld of science education. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com9tag:blogger.com,1999:blog-6570061087276796800.post-6895648247442422022015-05-21T10:00:00.000-04:002015-05-21T10:39:30.265-04:00Math problems of the week: Common Core-inspired "algebra" test problemFrom a <a href="http://parcc.pearson.com/resources/practice-tests/math/algebra-2/pba/PC194854-001_AlgIIOPTB_PT.pdf">Algebra II Performance Based Assessment Practice Test from PARCC</a> (a consortium of 23 states that are devising Common Core-aligned tests). <br /><br /><div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-g4q2BRJDUVM/VVpahBlZexI/AAAAAAAAC3Q/lDrudzVS37A/s1600/PARCC_alg_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="306" src="http://3.bp.blogspot.com/-g4q2BRJDUVM/VVpahBlZexI/AAAAAAAAC3Q/lDrudzVS37A/s640/PARCC_alg_2.png" width="640" /></a></div><br /><strong>Extra Credit:</strong><br /><br />Discuss the relative challenges of the mathematical labels (i.e., for types of methods) vs. the mathematical concepts vs. plain old common sense.Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com0tag:blogger.com,1999:blog-6570061087276796800.post-14082956369718697092015-05-19T10:00:00.000-04:002015-05-19T10:00:00.452-04:00Two approaches to math assessment: quantity vs. "quality" Auntie Ann makes a great point on my <a href="http://oilf.blogspot.com/2015/05/knowing-doing-and-explaining-your-answer.html">last post</a>: <br /><blockquote>Giving many problems and demanding wordy answers on a test are mutually exclusive. In the time it takes to explain in words one problem, a student could demonstrate their proficiency on several problems with different mathematical concepts. Writing wordy explanations is much slower than giving a student a variety of different questions.</blockquote>Assuming that the point of making students explain their answers is to distinguish those who really don't understand the math from those who've simply made stupid mistakes, then there are two possible approaches. <br /><br />1. Assign a smaller number of problems so that students spend time explaining their answers. <br /><br />2. Assign a larger number of problems.<br /><br />Back in the day, we got perhaps ten times as many problems per session as students do today.<br /><br />A student who is prone to stupid mistakes won't get nearly every answer wrong; a student who doesn't understand the math will. The type of answer generated by stupid mistakes often looks different from the type of answer generated by conceptual misunderstandings. Assign enough math problems, and a competent teacher can easily distinguish between the two types of student. Include harder problems that involve more mathematical steps than today's problems do, such that more students will naturally write down their mathematical steps, and it's even easier to distinguish those who understand from those who don't.<br /><br />Doing lots of math problems (and getting timely feedback on them) is probably also a better way for students to overcome conceptual misunderstandings than explaining a much smaller number of problems is.<br /><br />And its a great way for everyone to get better (especially more fluent) at math. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com2tag:blogger.com,1999:blog-6570061087276796800.post-12789246833102023982015-05-17T10:00:00.000-04:002015-05-17T10:00:03.236-04:00Knowing, Doing, and Explaining Your AnswerBarry Garelick and I have a piece up on <a href="http://www.educationnews.org/k-12-schools/math-problems-knowing-doing-and-explaining-your-answer/">Education News</a>.<br /><br />Some excerpts:<br /><blockquote class="tr_bq">At a middle school in California, the state testing in math was underway via the Smarter Balanced Assessment Consortium (SBAC) exam. A girl pointed to the problem on the computer screen and asked “What do I do?” The proctor read the instructions for the problem and told the student: “You need to explain how you got your answer.” </blockquote><blockquote class="tr_bq">The girl threw her arms up in frustration and said “Why can’t I just do the problem, enter the answer and be done with it?”</blockquote><blockquote class="tr_bq">…</blockquote><blockquote class="tr_bq">[For some problems] the amount of work required for explanation turns a straightforward problem into a long managerial task that is concerned more with pedagogy than with content. While drawing diagrams or pictures may help some students learn how to solve problems, for others it is unnecessary and tedious.</blockquote><blockquote class="tr_bq">... </blockquote><blockquote class="tr_bq">Is it really the case that the non-linguistically inclined student who progresses through math with correct but unexplained answers—from multi-digit arithmetic through to multi-variable calculus— doesn’t understand the underlying math? Or that the mathematician with the Asperger’s personality, doing things headily but not orally, is advancing the frontiers of his field in a zombie-like stupor? </blockquote><blockquote class="tr_bq">Or is it possible that the ability to explain one’s answers verbally, while sometimes a sufficient criterion for proving understanding, is not, in fact, a necessary one? </blockquote>Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com7tag:blogger.com,1999:blog-6570061087276796800.post-15030293714640002052015-05-15T10:00:00.000-04:002015-05-15T14:08:09.105-04:00Math problems of the week: Common Core-inspired math vs. Singapore Math<strong>I. The final problem in the Common Core-inspired Engage NY 5th grade <a href="https://www.engageny.org/resource/grade-5-mathematics-module-3">Fractions module</a>:</strong><br /><br />1. Lila collected the honey from 3 of her beehives. From the first hive she collected 2/3 gallon of honey. The last two hives yielded 1/4 gallon each. <br /><br />a. How many gallons of honey did Lila collect in all? Draw a diagram to support your answer. <br /><br />b. After using some of the honey she collected for baking, Lila found that she only had 3/4 gallon of honey left. How much honey did she use for baking? Support your answer using a diagram, numbers, and words. <br /><br />c. With the remaining 3/4 gallon of honey, Lila decided to bake some loaves of bread and several batches of cookies for her school bake sale. The bread needed 1/6 gallon of honey and the cookies needed 1/4 gallon. How much honey was left over? Support your answer using a diagram, numbers, and words. <br /><br />d. Lila decided to make more baked goods for the bake sale. She used 1/8 lb less flour to make bread than to make cookies. She used 1/4 lb more flour to make cookies than to make brownies. If she used 1/2 lb of flour to make the bread, how much flour did she use to make the brownies? Explain your answer using a diagram, numbers, and words. <br /><br /><br /><strong>II. The last two fractions problems in the 5th grade Singapore Math Primary Mathematics 5A Workbook</strong> (in Unit 4, Multiply and Divide Fractions, pp. 98-99): <br /><br />3. After giving 1/3 of his money to his wife and 1/4 of it to his mother, Mr. Li still had $600 left. How much money did he give to his mother? <br /><br />4. Lucy spent 3/5 of her money on a purse. She spent the remainder on 3 T-shirts which cost $4 each. How much did the purse cost? <br /><br /><br /><strong>III. Extra Credit</strong><br /><br />One of the biggest challenges found in Singapore Math problems (and not just in <a href="http://www.nytimes.com/2015/04/15/science/a-math-problem-from-singapore-goes-viral-when-is-cheryls-birthday.html">the one that recently went viral</a>) is in figuring out what the first step is. <br /><br />Compare the obviousness of the first steps in the EngageNY problems to those of the Singapore Math problems above. Katharine Bealshttp://www.blogger.com/profile/02838879769628392605noreply@blogger.com7