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In ChapterProject I shared the many writing and other type "pencil and paper" activities that our anti-paper/pencil educators are wanting our students to do in Passport to Mathematics, Chapter 1. We saw the students making class collections to go into a classroom museum, organizing those collections, listing/combining those collections into as many different groups as possible, writing about those collections in journals. All of that during Math class time, or Math homework time. And that took us all the way up through Lesson 3 of Chap. 1(1.3)! Now, let us continue through this first chapter to see other activities related to this project. Will they require pencil and paper? How much time away from serious review and practice of math concepts and skill will these activities require? In Lesson 4 (1.4), problem 14, we read:
BUILDING YOUR PROJECT The bar graph shows the number of items (in thousands) in some of the world's largest collections as of 1996. You decide to use the graph in a display in your museum. Write a few sentences to go with the graph that explains what the graph means.(This is referring to a graph depicting various collections.) Having students learn to read graphs is important. But why do they have to 'write' what the graph means? Oh, yes. Yes! I forget! That kind of writing with pencil and paper is wonderful! It's just the use of pencil and paper for drilling facts and practicing algorithms which is 'bad'. In Lesson 5 (1.5), problem 23, we read:
BUILDING YOUR PROJECT Design a poster to advertise your class museum. What size paper will you put it on? How high will the headlines be? Will you include a picture, and if so, how large will it be? What other information will you need to put on the advertisement? Sketch the layout of the ad to use as a model. Then make your poster.
BUILDING YOUR PROJECT To cover the costs of your museum, you charge $.10 admission. a. At the beginning of the first day, you have $1.00 in the cash box so you can make change. At the end of the day, you have $3.30 in the cash box. Use the verbal model below to write an equation that can be used to find how much money you collected that day. Use mental math to solve the equation. Cash at beginning + Money collected = Cash at end of day b. Use the verbal model below to write an equation that can be used to find how many people came to the museum that day. Use mental math to solve the equation. Admission per person x Number of people = Money collected c. Discuss in your group whether you should charge admission to your museum. What did the group decide? Why?Well, GOOD!! Finally, a little math is being used on this Class museum project (in Parts a. and b.) Then you come to Part c. Didn't we know there would be writing? In the sidebar of the T.E. we read referring to this problem 34:
Cooperative Learning Ex. 34 provides an opportunity for students to work in groups to write (bold is mine) and solve equations for real life problems. Note that students' answers to part c will take into account any school regulations about collecting money on school premises.Oh, yes! An opportunity for cooperative learning. We wouldn't want to miss an opportunity for students to learn cooperatively. Is learning cooperatively really better than learning under the direction of a teacher? I'll tell you why this is so BIG in 'new math' circles! It's because they are writing and solving equations for real life problems. It's because they are figuring it out without a teacher's help. If they were practicing how to set up and write equations and were solving equations in my traditional classroom, that time would be considered "wasted" or "boring". Even if I gave them 'real life problems' to use to learn to set up equations, it wouldn't satisfy the constructivist because the students aren't emersed 'deep enough' into the real life problem. I guarantee I can teach them to set up equations and solve those equations in less time than students can figure it out in groups. Even if I give them time to figure out on their own how to set up equations, I will still use less time, less precious, precious time. And they will remember it tomorrow. Did you notice the concern for abiding by the school's regulations about collecting money? The parent and teacher in me wishes they would be as concerned about using the math time for lots of math concepts and practice. In Lesson 7 (1.7), problem 33, we read:
BUILDING YOUR PROJECT You include the puzzle at the right about collections in the puzzles and activities booth of your museum.Oh, so I missed where that booth has been organized and set up.!! But back to the project . . .
Work backwards to find the answer to the puzzle so that you can have it available at the museum. Write a similar puzzle based on your classmates' collections. Exchange puzzles with another member of your class and solve each other's puzzle. Explain to the other members of your group how you created your puzzle.Here is the puzzle problem 33 is referring to:
There are half as many dolls as there are basketball cards. There are 8 more action figures than there are dolls. There are 6 times as man;y postage stamps as action figures, and there are 10 times more postage stamps as there are glass statues. There are 16 glass statues. How many items are in each of the collections?Writing puzzles, exchanging puzzles with classmates, explaining how you created your puzzle. How fun! How creative! How 'into' the museum project! How not to spend enough time on necessary review and practice! And in Lesson 9 (1.9), we read:
BUILDING YOUR PROJECT Make a logic puzzle about the collections in your class's museum.An example of a logic puzzle was given in Lesson 9, problem 13. It had was a table with clues given. Students were to determine which statements were true or false using logic. Let's review the goals and see what students have accomplished, during this math unit: They have collected and organized data, planned exhibit space, devised explanations for the exhibits, considered ways of advertising and earning money, and planned activities to involve visitors. --+++And all of this has been done during math class time. What better uses of Math class time were overlooked or ignored to provide time for this project? These students are being robbed of precious opportunities to review and practice many critically important facts and concepts in the name of "projects" and "cooperative learning" and "real life problems". How many teachers are wise enough to downplay or hopefully ignore completely this "time-waster" and to choose time for needed drill and review of math facts and concepts lost over the summer. -- InterestedTeacher - 18 Jul 2005 KtmGuest (password: guest) when prompted.
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