By American Mathematical Society, János Kollár, Robert Lazarsfeld

ISBN-10: 0821808958

ISBN-13: 9780821808955

**Read or Download Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz PDF**

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**Additional resources for Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz**

**Example text**

Has 90-degree angles startat the middleof a side every square every rectangle Figure3. Table 6 presentsmeans and standarddeviations for this item. 001). 001). 01). 01). Means suggest that third-,fourth-,and fifth-gradestudentsimprovedmore in LG classroomsthanin controlclassrooms. These differenceswere less salientfor Grade6 andfor Grade2; the controlgroup made largergains thanthe LG group. For the rectangleconcept, effects tendedto be strongestfor studentsin Grades3-5. , has 90-degree angles; has four right angles).

Interviewer:So, a rectanglehas to have a right angle? Luke: Yeah. Or four 90? angles. Interviewer:How about [indicatesa nonrectangularparallelogram]? Luke: Well, it doesn't have to have a right angle, but the four sides are parallel. ] Interviewer:You seem puzzled. Tell me what you are thinking. 'Causethatlooks like a rectangle,but it doesn't have any 90? angles. ] Luke: I don't thinkthata rectanglehas to have a 90? [angle].... This type of tension between the visual and descriptive/analytic perspectives may indicate the difficulty students have integrating their visually based recognition of figures with their emerging knowledge of the properties of geometric figures.

And you made it as a square. Interviewer:Oh. Okay. But you made it with the rectanglecommand. Robbie: Umm huh. Yes. ] Interestingly, Robbie intuitively uses equal input to the R (Rectangle) command when he wishes to draw a square. But, he is hesitant to call any figure produced by that command a square, as illustrated below. Interviewer:Try to use the rectanglecommand. This isn't a rectangle. Robbie: Interviewer:Whatis it? A square. Robbie: Interviewer:So, what commandswould you use? S and S and then 5.

### Algebraic Geometry Santa Cruz 1995, Part 2: Summer Research Institute on Algebraic Geometry, July 9-29, 1995, University of California, Santa Cruz by American Mathematical Society, János Kollár, Robert Lazarsfeld

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