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In this issue of the Mathematics Undergraduate Newsletter: - Important dates for the remainder of Spring Quarter - Course Highlight: Education 50B and Education 75B - Why do you study Math and what will it do for you? - There is always time for fun! -Important Dates for the Remainder of Spring Quarter Monday May 12 – Undergraduate Withdraw from a Class Ends – Deadline to drop with a W notation ends, except for emergency reasons Monday May 12 – Add by Petition Ends Monday May 26 – HOLIDAY – MEMORIAL DAY! Friday June 6 – Instruction Ends Monday – Thursday, June 9 – 12 Final Examinations Thursday June 12 – Undergraduate Removal of Incomplete – Deadline to file petition ($10) fee and submit class work for an incomplete grade from the preceding quarter. Thursday June 12 – Deadline to complete all requirements for degree and for the Office of the Registrar to receive transcripts from other institutions. - Course Highlight: Education 50B and Education 75B Education 50B. CAL Teach 1: Mathematics (2 credits) Introductory seminar exploring secondary students, teaching, and schools in the context of mathematics instruction. Concurrent participation in a secondary school internship required. Course material supports and enhances students' placement experiences. Prerequisite(s): Acceptance into CAL Teach and concurrent participation in a secondary school internship in a math classroom. Enrollment limited to 25. The Staff Education 75B. CAL Teach 2: Mathematics (2 credits) Examines students, schools, and mathematics instruction with emphasis on developing an instructional project aligned with state-mandated content standards. Course content supports and enhances students' placement experiences. Prerequisite(s): CAL Teach 1 (course 50A, 50B, or 50C), and acceptance into CAL Teach 2 and concurrent participation in a secondary school internship in a mathematics classroom. Enrollment limited to 25. The Staff Some of you may be wondering why we are profiling Education courses when this is a Math newsletter. Of course, there is the obvious connection between Math and Teaching, apparent in their descriptions. Besides this though, did you know, if you complete both these courses, together they waive Math 188, a requirement for Math Education Majors? Not only do they provide you the unique opportunity to step foot into the field of your choice for a few quarters, but both are internships, and as such, they come along with a stipend! Cal Teach is an amazing experience and a group on campus with a lot to offer personally and professionally. For more information, including application instructions and deadlines, please visit http://calteach.ucsc.edu/ Yeah, I’ll admit it, I never liked them much either. If you are like me, and many others, check out this article from the Times, our fears may have merit and are gaining support! New York Times April 25, 2008 “Study Suggests Math Teachers Scrap Balls and Slices” By KENNETH CHANG One train leaves Station A at 6 p.m. traveling at 40 miles per hour toward Station B. A second train leaves Station B at 7 p.m. traveling on parallel tracks at 50 M.P.H. toward Station A. The stations are 400 miles apart. When do the trains pass each other? Entranced, perhaps, by those infamous hypothetical trains, many educators in recent years have incorporated more and more examples from the real world to teach abstract concepts. The idea is that making math more relevant makes it easier to learn. That idea may be wrong, if researchers at Ohio State University are correct. An experiment by the researchers suggests that it might be better to let the apples, oranges and locomotives stay in the real world and, in the classroom, to focus on abstract equations, in this case 40 (t + 1) = 400 - 50t, where t is the travel time in hours of the second train. (The answer is below.) “The motivation behind this research was to examine a very widespread belief about the teaching of mathematics, namely that teaching students multiple concrete examples will benefit learning,” said Jennifer A. Kaminski, a research scientist at the Center for Cognitive Science at Ohio State. “It was really just that, a belief.” Dr. Kaminski and her colleagues Vladimir M. Sloutsky and Andrew F. Heckler did something relatively rare in education research: they performed a randomized, controlled experiment. Their results appear in Friday’s issue of the journal Science. Though the experiment tested college students, the researchers suggested that their findings might also be true for math education in elementary through high school, the subject of decades of debates about the best teaching methods. In the experiment, the college students learned a simple but unfamiliar mathematical system, essentially a set of rules. Some learned the system through purely abstract symbols, and others learned it through concrete examples like combining liquids in measuring cups and tennis balls in a container. Then the students were tested on a different situation — what they were told was a children’s game — that used the same math. “We told students you can use the knowledge you just acquired to figure out these rules of the game,” Dr. Kaminski said. The students who learned the math abstractly did well with figuring out the rules of the game. Those who had learned through examples using measuring cups or tennis balls performed little better than might be expected if they were simply guessing. Students who were presented the abstract symbols after the concrete examples did better than those who learned only through cups or balls, but not as well as those who learned only the abstract symbols. The problem with the real-world examples, Dr. Kaminski said, was that they obscured the underlying math, and students were not able to transfer their knowledge to new problems. “They tend to remember the superficial, the two trains passing in the night,” Dr. Kaminski said. “It’s really a problem of our attention getting pulled to superficial information.” The researchers said they had experimental evidence showing a similar effect with 11-year-old children. The findings run counter to what Dr. Kaminski said was a “pervasive assumption” among math educators that concrete examples help more children better understand math. But if the Ohio State findings also apply to more basic math lessons, then teaching fractions with slices of pizza or statistics by pulling marbles out of a bag might prove counterproductive. “There are reasons to think it could affect everyone, including young learners,” Dr. Kaminski said. Dr. Kaminski said even the effectiveness of using blocks and other “manipulatives,” which have become more pervasive in preschool and kindergarten, remained untested. It has not been shown that lessons in which children learn to count by using blocks translate to a better understanding of numbers than a more abstract approach would have achieved. The Ohio State researchers have begun new experiments with elementary school students. Other mathematicians called the findings interesting but warned against over generalizing. “One size can’t fit all,” said Douglas H. Clements, a professor of learning and instruction at the University of Buffalo. “That’s not denying what these guys have found, whatsoever.” Some children need manipulatives to learn math basics, Dr. Clements said, but only as a starting point. “It’s a fascinating article,” said David Bressoud, a professor of mathematics at Macalester College in St. Paul and president-elect of the Mathematical Association of America. “In some respects, it’s not too surprising.” As for the answer to the math problem at the top of this article, the two trains pass each other at 11 p.m. at the midway point between Stations A and B. Or, using the abstract approach, t = 4. - Why do you study Math and what will it do for you? I know, people ask you these types of questions all the time, right? Maybe, you find there are times you ask them of yourself as well? I know I did! Well, you might find this page useful. Click on the link below to find all sorts of interesting items, such as career information, testimony of mathematicians currently working non-academic positions, and even career planning resources! - There is always time for fun! Isn’t there? Enough about all the boring stuff like dates and careers, etc. It’s time to put your knowledge of mathematics to some productive use – puzzles! Everyone loves them, right? Well, maybe not everyone, but for those of you that do, click on the link below and you can put your skills to the test! They claim no mathematical tools are necessary, but we will see about that! http://www.math.utah.edu/~cherk/puzzles.html Well, the academic year is almost over, you just need to hang in there a little while longer. For those of you who have applied to graduate in spring, you must double check that all of your requirements have been met. Please see http://reg.ucsc.edu/graduation_reqinfo.htm for information about University requirements. For questions in the major, visit http://www.math.ucsc.edu/undergraduate/index.html. Feel free to drop by and see me if there are any issues with your major that still need some extra attention. Have a good rest of the quarter and good luck on those midterms! Andrea Gilovich, Undergraduate Advisor
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