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Meghan Cureton

Mathematics must be creative, else it ain't Mathematics - 0 views

  • There are no topics in mathematics; only artificial barriers that we have erected to help organise the curriculum. At school, we study topics in discrete chunks and come to understand them as separate islands of knowledge. Yet the most powerful and interesting mathematics arises when we cut through these barriers.
  • Knowledge has its place; you cannot connect or create what you don’t know. Tokio Myers is a trained pianist; his thousands of hours of deliberate practice are the foundation of his creativity. But he is more than a pianist (he’s a BGT winner!), and that is because he dared to defy the the conventional norms of music. Wiles is similarly the world class mathematician that he is because his field of vision is not restricted to any one topic.
  • If only students were encouraged to transcend their study of individual topics.
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  • The tyranny of school maths lies in the false promise that stuffing oneself with facts and procedures prepares you for creativity. The act of creativity is deferred to an unspecified time — presumably it is for older, more knowledgeable people.
  • Young age is no barrier — my most impressive students are also the shortest; it only takes a well-crafted maths problem to unleash their innate creativity.
  • There are obvious benefits to going deep in a particular area and I always offer a gracious nod to the fluency and fundamentals of mathematics. But mathematics at its most fundamental is an integrated body of ideas, replete in patterns. The patterns and connections are what makes it mathematics. Let that be your next headline.
T.J. Edwards

mathematics is art (all the mathematicians say so) - 0 views

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    via @megcureton
Meghan Cureton

The Case Against Grades (##) - Alfie Kohn - 2 views

  • Collecting information doesn’t require tests, and sharing that information doesn’t require grades.  In fact, students would be a lot better off without either of these relics from a less enlightened age.
  • As I’ve reported elsewhere (Kohn, 1999a, 1999b, 1999c), when students from elementary school to college who are led to focus on grades are compared with those who aren’t, the results support three robust conclusions:
  • Grades tend to diminish students’ interest in whatever they’re learning.
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  • Grades create a preference for the easiest possible task.
  • Grades tend to reduce the quality of students’ thinking. 
  • For example, a grade-oriented environment is associated with increased levels of cheating (Anderman and Murdock, 2007), grades (whether or not accompanied by comments) promote a fear of failure even in high-achieving students (Pulfrey et al., 2011), and the elimination of grades (in favor of a pass/fail system) produces substantial benefits with no apparent disadvantages in medical school (White and Fantone, 2010).
  • Extrinsic motivation, which includes a desire to get better grades, is not only different from, but often undermines, intrinsic motivation, a desire to learn for its own sake (Kohn 1999a). 
  • Achievement:  Two educational psychologists pointed out that “an overemphasis on assessment can actually undermine the pursuit of excellence” (Maehr and Midgley, 1996, p. 7). 
  • There is certainly value in assessing the quality of learning and teaching, but that doesn’t mean it’s always necessary, or even possible, to measure those things — that is, to turn them into numbers.  Indeed, “measurable outcomes may be the least significant results of learning” (McNeil, 1986, p. xviii)
  • It’s not enough to replace letters or numbers with labels (“exceeds expectations,” “meets expectations,” and so on).  If you’re sorting students into four or five piles, you’re still grading them.  Rubrics typically include numbers as well as labels, which is only one of several reasons they merit our skepticism (Wilson, 2006; Kohn, 2006).
  • Portfolios, for example, can be constructive if they replace grades rather than being used to yield them.  They offer a way to thoughtfully gather a variety of meaningful examples of learning for the students to review.  But what’s the point, “if instruction is dominated by worksheets so that every portfolio looks the same”? (Neill et al. 1995, p. 4).
  • Once we’re compelled to focus only on what can be reduced to numbers, such as how many grammatical errors are present in a composition or how many mathematical algorithms have been committed to memory, thinking has been severely compromised.  And that is exactly what happens when we try to fit learning into a four- or five- or (heaven help us) 100-point scale.
  • It’s not enough to disseminate grades more efficiently — for example, by posting them on-line.  There is a growing technology, as the late Gerald Bracey once remarked, “that permits us to do in nanoseconds things that we shouldn’t be doing at all” (quoted in Mathews, 2006).  In fact, posting grades on-line is a significant step backward because it enhances the salience of those grades and therefore their destructive effects on learning.
  • It’s not enough to add narrative reports.  “When comments and grades coexist, the comments are written to justify the grade” (Wilson, 2009, p. 60).  Teachers report that students, for their part, often just turn to the grade and ignore the comment, but “when there’s only a comment, they read it,”
  • It’s not enough to use “standards-based” grading.
  • Sometimes it’s only after grading has ended that we realize just how harmful it’s been.
  • To address one common fear, the graduates of grade-free high schools are indeed accepted by selective private colleges and large public universities — on the basis of narrative reports and detailed descriptions of the curriculum (as well as recommendations, essays, and interviews), which collectively offer a fuller picture of the applicant than does a grade-point average.  Moreover, these schools point out that their students are often more motivated and proficient learners, thus better prepared for college, than their counterparts at traditional schools who have been preoccupied with grades.
  • Even when administrators aren’t ready to abandon traditional report cards, individual teachers can help to rescue learning in their own classrooms with a two-pronged strategy to “neuter grades,” as one teacher described it.  First, they can stop putting letter or number grades on individual assignments and instead offer only qualitative feedback.
  • Second, although teachers may be required to submit a final grade, there’s no requirement for them to decide unilaterally what that grade will be.  Thus, students can be invited to participate in that process either as a negotiation (such that the teacher has the final say) or by simply permitting students to grade themselves.
  • Without grades, “I think my relationships with students are better,” Drier says.  “Their writing improves more quickly and the things they learn stay with them longer.
  • Drier’s final grades are based on students’ written self-assessments, which, in turn, are based on their review of items in their portfolios. 
  • A key element of authentic assessment for these and other teachers is the opportunity for students to help design the assessment and reflect on its purposes — individually and as a class. 
  • Grades don’t prepare children for the “real world” — unless one has in mind a world where interest in learning and quality of thinking are unimportant.  Nor are grades a necessary part of schooling, any more than paddling or taking extended dictation could be described that way.  Still, it takes courage to do right by kids in an era when the quantitative matters more than the qualitative, when meeting (someone else’s) standards counts for more than exploring ideas, and when anything “rigorous” is automatically assumed to be valuable.  We have to be willing to challenge the conventional wisdom, which in this case means asking not how to improve grades but how to jettison them once and for all.
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    HT @tedwards
Meghan Cureton

Grades are for Onions, Beef, and Other Produce; Not Children - 1 views

  • What good is gained in assigning a grade to a child’s work? The concept of 90–100% = A, 80–89% = B etc. is so entirely subjective and fraught with fallacy. Because a child can do every question on your arbitrarily chosen and constructed exam, and do so by anticipating what it is you are looking for with 100% accuracy does not mean they understand or can explain what the mathematics is about.
  • Why should our children be assigned something we also use for factory produced vegetables? Grading is an anachronistic hold-over from the Scientific Management era inserted into schooling during the 19th century.
  • Finnish kids have NO homework, but call me a believer in the idea that the Finns place less importance upon grading their children against each other. Formative assessment replacing heaps of summative assessments.
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  • Finnish national curriculum has been addended to include a multi-disciplinary requirement in each year of schooling. This will require a completely different method of assessment, there is no way to assign a single letter or numeric grade to such a task.
  • Honestly, is ranking an important outcome of education? Do we need to know who was “best” or “worst” at reading the minds of their teachers and regurgitating what those teachers want?
  • My point in this is that we seem to have lost the learning purpose, the goal of growing humans into their best selves is not central to our endeavor.
  • education needs to drop its focus upon grades as being the product of 13 years of a child’s life. Bring to schooling the joy of learning as it will go farther than the negative consequences associated with grades.
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