Create one example of using benchmarks or estimation and fractions (see Example 8-9 on page 186 in the Burris text) that you could use in your classroom. Don’t have your book handy? No problem! Here’s Example 8-9:

Class, we have been studying different countries. Look at the flags that we have hanging at the front of the room. Which flag is the flag of Italy? About how much of the flag of Italy is green? Which flag is Poland’s? How much of the Poland’s flag is red? How about the U.S. flag? About how much of our flag is blue?

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View “Understanding Fractions” and “Just a Fraction” to see how British teachers are using plastic cups to model (addition and subtraction of) the benchmark fractions 1/2 and 1/4 to their students.

Take a minute to view the video reading of 6 Sticks, which I recently recorded.  I have added captions to correspond with many of the pages in the text.  You may need to pause in order to read these. 

Let’s collectively compose 8 Crates, which will follow the same format as 6 Sticks.  

Write one page which would fit into this new book, then compose a short caption which might accompany a teacher’s edition of the story .  (Follow the example of the 6 Sticks captions I wrote.)

• Write an addition story problem that you think would be interesting to elementary school children.
• Create a game or puzzle (or, provide a link to a website with one) that could be used to help students practice their subtraction facts.  Indicate the grade level for your game or puzzle (and how it can be modified for students with special needs).
• Make up a number line activity or game (or, provide a link to a website with one).  Indicate what grade level your activity is appropriate for.
• Write a story problem for either (2 + 3) x 6 = 30     or    2 + (3 x 6) = 20.  Which was easier to write?  Why?

The symbols of mathematics, like the notes of music, are in themselves merely an artificial, intrinsically meaningless script. They will convey life, meaning, richness of thought and beauty only if the ideas and the thinking which the symbols merely record are taught with as little use of symbolism as possible.
—Morris Kline

Put the above quote into your own words. Do you agree or disagree with Kline? Why?

The author of this week’s reading held in high regard the Chinese language for how well it conveys the base 10 numeration system, and also for its simplicity when spoken. While I didn’t take the time to listen to all the numbers, I got the idea after listening to 1-10 and 11-20 of Learn to count to 100 in Chinese (with Flash movies).

Last summer I attended a workshop for teachers who teach future elementary teachers. The workshop leader informed us that his wife, an elementary teacher, teaches her students to say “tenty-one” for eleven, “tenty-two” for twelve, etc. While such practices have not gained widespread popularity in the English-speaking world, they are gaining ground.

After reading this week’s required reading, let’s say you are ready to hop on the “We desperately need to change our language” wagon, will you advocate the use of “tenty-one,” or “onety-one” for eleven? How come?

If you haven’t already done so, please view the “Julia Clips.”

Although she hasn’t even entered kindergarten yet, Julia has learned to efficiently count on her fingers (at times, perhaps, doing so in her head). She also knows how to count on from a number. This skill serves her well throughout the interview process.

How do you think she would tackle the chore of counting piglets? How many levels of the Charlie & Lola germ-counting game do you believe she would successfully complete? (Why?)

How might Julia have answered some of the interview questions more quickly? For which questions would she have been able to do that? Describe (or provide a link to) at least one activity which Julia could participate in (at age 4 years, 9 mos), and which would also introduce skip counting to her. (Hurry! Share your idea/link quickly. No two of you should provide the same link(s)!!!)

I’ll admit it: The only reason I watched this video in the first place was because I enjoy listening to foreign languages, especially ones I don’t speak. While waiting for the video to load, this statement from the video synopsis caught my attention: “The Hungarian approach has informed … English thinking in [teaching primary mathematics], and Hungarian pupils come high in the international rankings.”

A lot of what I saw in the video reminded me of the way I was taught mathematics in elementary school: Our desks were arranged in rows, my teachers always taught in a whole-class setting, and we frequently played “Who’s the fastest?”, drill-type games. A few things, however, seemed much different. For one, I do not think my fourth grade teacher would have been able to mentally generate an alternating sequence of numbers (“this increase[d] by sixteen, and this decrease[d] by nine”) beginning anywhere - certainly not from an odd, three-digit number.

As you discovered from this week’s textbook readings, mathematics instruction in the United States has changed a lot over the last ten-to-fifteen years. Are we headed toward or away from a system like that in Hungary? What are your feelings about this? Furthermore, I find it interesting that policy makers in the U.K. are modeling instructional activities after those found in Hungary. After all, according to this “Highlights from TIMSS” document, by the final year of secondary school, Hungarian students are performing below the international average (p. 7) . (They ranked higher when comparing the achievement of eighth-graders, but not in the top ten (See p. 4).) Interestingly, in one recent study (2003), which tested the “real world” math skills of fifteen-year-olds in forty-one countries, Hungary ranked only slightly higher than the United States.

What do think? How should we react to studies such as the TIMSS, or PISA? What value is there in our comparing ourselves to other countries? Should we model our system of education after that found in the top-performing countries? Why would or wouldn’t this work?