National Assessment of
Educational Progress (NAEP)
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Information for Parents
There are lots of free learning activities for children in the Kids section of this site. You can also read about the process and rationale for my way of teaching in the Teachers section. Details of my teaching philosophy can be found in the Designers and Researchers sections. Circular Reasoning ParentsI'll use this space to keep a blog on what's going on in our Circular Reasoning class for fourth and fifth graders at Northwestern University. You can also find more information about Circular Reasoning in the Kids section of this site. If you'd like to learn more about courses I teach through Northwestern's Center for Talent Develoment, see Group Programs. January 7, 2006Today we started with a test. I explained to the kids that the test is for my information only. I have very little time with the kids and I need to make sure that I'm not teaching them stuff they've already been shown. The test is not a part of their evaluation for the course and will not become part of their record at CTD or their school. The test wasn't taken by one student who was late and another student who was absent. The test consisted of nine questions taken from the National Assessment of Educational Progress (NAEP). The questions were given nationally to eighth and twelfth graders. Elementary kids who took past versions of this course did not do as well as eighth or twelfth graders on the pretest, but outperformed eighth graders and were on par with twelfth graders in the posttest. You can get more detail on previous work with Circular Reasoning and related activities in Research section of this site. After the test, I showed the kids how to add a fracture to the screen and let them play with the Inspector widgets for a few minutes, and then had one of them come up and demo the Inspector. Next, I asked them to tell me how to draw a sector. One student started us out with "Draw any angle, then draw a curved part from one end to the other. And the straight lines have to be the same length. And it looks like a piece of pizza." I drew a circle with two chords of equal length and asked, "Does this make a sector?" We got to the idea that the straight sides of the sector have to be radii and the arc is the arc of the circle. I went briefly over segment and the other circle parts. Next the kids worked on the first page of Circular Reasoning puzzles. All of the kids worked through the first four puzzle cards. As they were working through the puzzles, we went over adding notes to a page and saving work. As kids finished the puzzles, I showed them how to get onto my web site and play around with stuff in the Kids section. At the end of class, we had a 10 minute discussion to review the puzzles. When going over puzzles 2 and 3, we got into a discussion of pairs of angles whose measures add up to 360. We talked a bit about puzzle #4, but didn't really get into using degree measures to make an exact match. January 14, 2006Today we started with Vocabulary Cards #1 and #2 to review material from last week and share what we learned about arcs, chords, radii, angles, central angles, circle segments and sectors with kids who were out last week. After that, everyone started up Circular Reasoning and began work on Illustration Card #1. Working from the Illustration Card, kids used Circular Reasoning to illustrate the definitions on Vocabulary Card #3. As children finished this activity, they were given the Turns and Sectors packet to work through the Turns and Sectors activities on the LLS web site. When everyone finished work on Illustration Card #1, we took a break. After break, we discussed the definitions and illustrations of congruent angles, parallel lines, bisect, perpendicular, and perpendicular bisector from Vocabulary Card #3 and the illustrations the kids made. Then everyone went to work finishing Illustration Cards #2, #3 and #4. Again, as kids finished, they worked on the Turns and Sectors packet. A few kids finished the cards and the packet with time to spare, so they were given the Angles packet for use with the Angles activities. One of our students discovered that you can make some cool designs with the Fraction Circle in Cirular Reasoning. A number of kids made designs and showed them to the class. Everyone finished Illustration Cards #1 through #4. Anyone who didn't finish the Turns and Sectors packet was given the packet to finish at home. Next week, we'll start off by discussing illustrations for Illustration Cards #2 through #4 and the work children did with Turns and Sectors. If you want to use the LLS web site from home: The activities on the web site require that you use either Netscape 4 or higher or Internet Explorer and install the MicroWorlds Web Player. You'll see links to these browsers and the MicroWorlds Web Player on the Turns and Sectors activity pages. Some kids seem to be picking up speed with respect to others. This is usually the case in the classes I've taught for CTD. Even though all the kids in my class are gifted, they are not all the same age and they haven't all had the same exposure to the topics presented in class. I don't want any of the kids to feel frustrated or bored, so a lot of the work in class is self-paced. One result of this is that different kids will finish a different amount of work in a given session. All children should understand that there's no specific place they need to be at in this course beyond things I specifically require (for example, the Turns and Sectors packet needs to be finished by next Saturday if they haven't already handed it in). For this course, children are evaluated as individuals, not by comparison with other kids in the class. If you have any questions about the Turns and Sectors packet, Circular Reasoning, or general questions about the course, please send me an e-mail at tj@leonelearningsystems.com. January 21, 2006Today we reviewed Illustration Cards 2 through 4 and the Turns and Sectors packet. Next, children did Illustration Cards 5-8 and shared their work. Some of the kids had trouble sharing their files to the right folder. We need to review this next week. In the Illustration Cards used this week, children saw that the radii that divide a circle into four equal pieces are at right angles to each other. They also illustrated acute, right, obtuse, straight and reflex angles, and noted that a circle segment of 180 degrees has the same shape as a circle sector of 180 degrees. We also found that chords get longer on circle segments between 0 and 180 degrees, shorter between 180 and 360 degrees, and are at their longest at 180 degrees, when the chord is a diameter. As kids finished the Illustration Cards they start on the Angles packet. This packet introduced angle measurement using fractions of a circle, a 360 degree protractor, and a 180 degree protractor. It also developed the concept of supplementary angles by showing how to measure supplementary angles with a protractor and how to recognize and calculate supplementary angles given in standard representations. In the packet and related online activities, kids also had the opportunity to learn about complementary angles, angle bisectors, and vertical angles. Howevever, we did not have time to review this packet, so the review will have to be done next week. As happened last week, kids are finishing work at different rates. I decided next week to lay out work on the long table in the middle of the room to make it easier for kids to proceed at their own pace. Some of the kids are also helping other kids with work. In my experience, this is good for the helper because it helps reinforce concepts being learned. It is also good for the child being helped, since the helper is closer to them on the learning curve, which gives them a good perspective from which to make explanations. We had a bit of drama today because another group was somehow given a reservation for our room for 11:00. We ended up staying until 11:30, but I was called out the room a few times to help resolve the issue. Pam Johnson happened to be around toward the end of class. I spoke to her about the problem, and she is taking steps to make sure there won't be any more conflicts for the rest of the session. For next week, those who haven't turned in their Angles packet should have them completed. January 28, 2006We had a small class today. At least two of the kids were taking the EXPLORE test. Kids mostly worked on off-computer stuff, including fraction circles, a special fraction circle protractor, regular protractors, and calculators. Handouts This morning I laid these handouts out on the long table in the middle of the room:
If your child didn't attend class on January 28, I recommend that you not give them the FractionCircles or Fraction Circles and Polygons handouts. I'll bring in the special materials for these exercises again next week (I think these handouts are more fun with the materials). They should be able to do all the other handouts without any special materials. Portfolios Everybody's doing really great work in this class, so I wanted to make sure that they have something to show for it at the end of the session. I made up folders for each child where they can keep a portfolio of their work. At the end of the session, the whole folder will be returned to them. This will also help remind me of everything they've done when I have to write up evaluations. If there's any work that was brought home from class or work done at home from the class web site, kids can bring it in to add to their portfolio. I'm also making available a form for Permission For Web Publication. If kids enter "all Circular Reasoning work" under Project Title, I can post all the work they''re doing with Circular Reasoning software. Fraction Circles, Protractors and Calculators The fraction circles in Circular Reasoning software are partly inspired by Montessori fraction circles, which kids used for the first time today. If you didn't see the fraction circles on the table this morning, you can see pictures of them on the web site for E & D Montessori (I've never ordered anything from these guys, but they have good pictures of materials). One of the ideas we're working on is this: if you take a walk around a closed figure, you end up facing in the same direction as the one you started in. If the figure is a simple closed figure, you've turned exactly 360 degrees. If the figure is regular polygon (assuming a polygon with n corners), you've turned 360 / n degrees at each corner. Some of the groundwork for this idea was laid in the Turns and Sectors packet. The FractionCircles and Fraction Circles and Polygons handouts gave kids the opportunity to work with physical fraction circles and use them to represent external angles. We also started work with similar triangles. Logo A couple of kids started working with MSWLogo today. This is a computer language that was written to be accessible to children, but also provide a great deal of power as a programming language. Logo is a relative of Scheme, which is used in courses for Computer Science majors at Northwestern. I'm currently using Logo in a LearningLinks precalculus course that I'm teachinng for kids in grades 6 through 12. In this course, we'll be using Logo to explore Turtle Geometry, a form of geometry that takes the perspective of an object (a Turtle) moving around in space via local information (e.g., "turn right", "go forward 100 steps") instead of global information such as Cartesian coordinates. This gives kids an alternative representation of geometric objects that can be useful when appropriate connections are made between different represenations. Anybody want to play around with Logo at home? You can find links for downloading Logo and some supporting documents (and a RealPlayer movie) in the section of this site called Introduction to Algebra Logo. Berkeley Logo works on both Windows and Macintosh machines, but I recommend that Windows folks use MSWLogo. February 4 , 2006Today all students were in attendance. Children who weren't in class last week got a chance to work on handouts from previous classes. We discussed ways to name line segments, angles, and arcs. We then used the Parts of a Circle handout as an opportunity to review some of our Vocabulary. Online activities Handouts The following handouts were new this week: Next week, kids will have the opportunity to go over handouts from previous weeks, do activities to further reinforce the concepts we've worked on so far or extend some of the ideas into work with Logo. We will also push ahead with any Circular Reasoning Puzzles or Circular Reasoning Illustrations that kids haven't yet completed. February 11 , 2006We started class with a discussion of answers that kids got to the FractionCircles handout that was first made available on January 28. In this exercise, children are asked to find the number of degrees in fractions of a circle from one third to one tenth. Calculators, standard protractors and a 360-degree protractor were made available. We talked about why students got different answers. Some students who use a protractor simply rounded to the nearest multiple of 5. Students who used calculators showed different levels of precision for the result of 360 divided by 7. I mentioned that the level of accuracy needed for any measurement will vary depending on how that measurement will be used. I'm trying to get the kids to start thinking about when an answer is "close enough" and how to decide if they're getting the precision they need. Children were given the opportunity to review their answers to the Fraction Circles exercise in light of our discussion. We spent a good part of the morning on more Circular Reasoning puzzles. In the afternoon, I introduced Logo to kids who haven't seen it yet. I briefly mentioned the Introduction to Algebra Logo portion of my web site that contains information about downloading, installing and using MSWLogo. February 18 , 2006Handouts
Last week, we talked about levels of accuracy in measuring the degrees in fraction circles, and we saw that it can be more accurate to calculate measurements than it is to measure with an instrument like a protractor. This week, in The Longest Chord, we saw that it is sometimes better to use reasoning than measurement in comparing two lengths. We saw that we can we can think of two radii as a path from the edge of a circle to the center and then to another edge (in The, for example, we have the paths from A to O to C or from A to O to B or from B to O to C). If the two radii have 180 degrees between them, we have a diameter. For any other degree difference, we can find a shorter path by moving in a straight line from one side of the circle to the other, without going through the center. For example, line segment AB is shorter than the path from A to O to B. Since the path from A to O to B is the same length as the path from A to O to C, this means that line segment AB must be shorter than line segment AC as long as B is any point on the circle different from C. This turned out to be a more complicated argument than I thought, but I think some of the kids got it. It seemed like more kids were comfortable with the argument in The Angles in Triangles that external angles of any triangle always adds up to 360 degrees, and this fact implies that all internal angles add up to 180 degrees. The handouts on similar triangles were interesting. With the online activities on my site, kids are really constrained in rotating objects, so the activities with cutouts of triangles gave kids the opportunity to see how problems can arise when different rotations are introduced. For example, in Making Similar Triangles: Part 2, the only way to make a similar triangle with twice the perimiter of the basic triangle is to have three triangles in the same orientation and one triangle rotated 180 degrees from the other three. In Making Similar Triangles: Part 3, angles don't match correctly and corresponding sides aren't aligned or parallel as required if the smaller triangle doesn't have the same orientation as the larger one. As they completed handouts, kids worked with Circular Reasoning or Logo. We discussed all handouts after the break, and kids worked mostly on Logo for the last half hour of class. Everybody got a chance to work on writing procedures. Some children wrote procedures to draw on the screen with the turtle, and some some used procedures to "teach" Logo to "talk". Next week, I'll briefly demonstrate the use of variables in Logo and give a posttest. The last half hour of class will be an open house so children will have the opportunity to show their work to their parents. February 25 , 2006Last day of class! We reviewed vocabulary using the Parts of a Circle handout and a new handout called Lines and Angles. After that, we took the session posttest. Overall, there was a 64% increase in performance on the test. This is great progress considering that these questions range in difficulty from eighth grade level to twelfth grade level. When the posttest was done, I handed out answers so that kids can look at them if they're interested. For the last half hour of class, kids showed their parents what they've been working on all session. Along with a folder with all of theire work, everyone in the class got a certificate of participation. If your child was absent on the last day of class and you didn't already receive a certificate, then your child's certificate is in the mail. Download your Circular Reasoning work For now, Circular Reasoning only runs under windows. Check back in the fall for a mac version and upgrade for the windows version. If you have a windows computer and would like to download the Circular Reasoning work that your child did at school, you can access the files at ftp://ftp.tjleone.com/pub/CircularReasoning/. Under Windows XP, I'm able to access these files by just typing the URL in the Address text box of a regular explorer window. You should also be able to access them using Internet Explorer or your favorite FTP software. If you have any problems, please feel free to send me an e-mail at tj@leonelearningsystems.com. We can also set up a phone conference if necessary. Some time in the coming week, I'll post children's Circular Reasoning work for viewing on the web site. I really enjoyed this class and was happy to hear from the kids that they had fun, too. Except for a workshop at the family conference in June 2006, I won't be teaching at CTD again until at least the fall of 2007 (I'm taking a year off to get a Master's degree in Montessori education). Until then, please feel free to poke around on my web site from time to time and send me feedback on any of the content.
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Leone Learning Systems, Inc. (LLS) is a North Shore company that provides online courses for kids anywhere and local teaching and tutoring services for students in Chicago and the Northern Suburbs of Chicagoland. LLS also provides a free geometry software package for children age 6 and up, and free resources for teachers and parents. This site includes information about classes taught, availability for tutoring, learning activities for kids, lesson plans, and an ongoing software and curriculum research and development effort. |
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