My weekly tutoring gig with "Artemis" is going well. When we started, he didn't know much algebra, didn't really understand distributing. He's learned distributing mostly through experimenting, and has learned an amazing amount of algebra through playing with his TI-84. (I wrote about the first time we played with the calculator here.)

He loves coming in with graphs on his TI and getting me to guess the function. Here's the one he started with last week. (I got it. Can you?) I showed him some similar graphs to see how well he could do. He got them all. (I told his mom I figured we were into what would normally be the third year of algebra, after about two months of untutoring.)

I never have a lesson prepared for him, and we often go into college algebra sorts of topics (it's called math analysis in high school), riffing off those graphs. Some weeks I worry that we won't have a path in to good topics just by our inspirations. But it always seems to work out that we do something solid.

I know all kids wouldn't move this fast, but to me this demonstrates the power of play. That's all we're doing, playing with ideas...

My Other Student

R comes for tutoring about once a month. (I think it's a special treat for him.) He and I have been playing with Kenken and logic puzzles. He decided last week that he wanted to make his own Kenken puzzle. Yeay! That sounded like something Maria Droujkova would have suggested, but that I don't think of so readily myself. So we did it. We started with one box, and figured out what had to be true. Our puzzle isn't standard because we didn't give a total for many of the boxes. If you think about what has to be, you'll figure them out.

Here's the puzzle R and I made...

[I used Excel to make it pretty like this, and used print to save as a pdf. I learned that my blog doesn't want pdf's - it wants jpegs. So I saved the pdf as a jpeg. I don't see a jpeg option in Excel, so that might be the best way to do it...]

Anyone else want to try their hand at making their own kenkens?

## Monday, November 30, 2009

## Sunday, November 29, 2009

### Math Stories

I posted, back in June, about my favorite math books. They're ordered from youngest to oldest readers, and the first one is Quack and Count, by Keith Baker:

I have 7 rubber ducks I borrowed from my son, so we can act out the story with the ducks. And then... Hmm... We have lots of active boys, and maybe a number story like this about cars would appeal to them. Maybe if I wrote it, they could illustrate it. I know they aren't big on extended writing, but maybe they'd get into thinking up other number stories.

Here's my first draft:

Crash and Count!

5 little race cars in a row

Count those race cars as they go

Racing fast and having fun

5 little race cars, 4 plus 1

5 little race cars, 3 plus 2

Looked like a crash, but then some flew!

Now they need to miss the trees

5 little race cars, 2 plus 3

5 little race cars, 1 plus 4

Most of them have crushed their doors

Turn off the engine, climb out fast

5 little race cars stop at last

[Edited to add: I just realized that this story verges on plagiarism. I copied the pattern given by Quack and Count as closely as I could. That seems totally cool for creating math lessons, but maybe not so cool for a story I'm posting online. So consider this a take-off on Baker's work.]

This is a board book, so it's good for the youngest child who will sit and listen to a story. But it stays good because it's so luscious. Great illustrations, fun rhythm and rhyme, cute story, and good mathematics. 7 ducklings are enjoying themselves in every combination. “Slipping, sliding, having fun, 7 ducklings, 6 plus 1.” (And then 5 plus 2, etc.) It would be great to have a book like this for all the number pairs that make 8, and one for 9, etc.I teach the 'big kids' (8 to 14, most 10 and under) at Wildcat, the 'freeschool' my son attends, and another parent teaches the 'little kids' (5 to 7). She has to move from one house to another this week, and I just agreed to sub for her. I have enough trouble getting myself to move down from my college professor level to teach the 'big kids' well. I had a moment's panic when my son said, "Do easy things, Mom." Then I remembered Quack and Count.

I have 7 rubber ducks I borrowed from my son, so we can act out the story with the ducks. And then... Hmm... We have lots of active boys, and maybe a number story like this about cars would appeal to them. Maybe if I wrote it, they could illustrate it. I know they aren't big on extended writing, but maybe they'd get into thinking up other number stories.

Here's my first draft:

Crash and Count!

5 little race cars in a row

Count those race cars as they go

Racing fast and having fun

5 little race cars, 4 plus 1

5 little race cars, 3 plus 2

Looked like a crash, but then some flew!

Now they need to miss the trees

5 little race cars, 2 plus 3

5 little race cars, 1 plus 4

Most of them have crushed their doors

Turn off the engine, climb out fast

5 little race cars stop at last

[Edited to add: I just realized that this story verges on plagiarism. I copied the pattern given by Quack and Count as closely as I could. That seems totally cool for creating math lessons, but maybe not so cool for a story I'm posting online. So consider this a take-off on Baker's work.]

### Number Logic

Jonathan, over at JD2718, has posted a logic puzzle he created, using lies and truths about numbers. I enjoyed it. But then our discussion turned to trying to create them.

I worked for a long time, starting from the answer I wanted and a bunch of things that were true and false about it. I couldn't get it narrowed down enough using just 5 clues. So I tried another number, and another. I think I've finally got a puzzle that works, but it doesn't feel as elegant as Jonathan's. Tell me if you get one possible answer. (But don't post the answer, please.)

And I'd love to know if anyone else has any success making these up.

Who am I?

1b. I do not have any repeating digits.

2a. I'm even.

2b. I have exactly two digits.

3a. I'm prime.

3b. I am one less than a triangular number.

4a. I have just one digit.

4b. I am the product of consecutive primes.

I worked for a long time, starting from the answer I wanted and a bunch of things that were true and false about it. I couldn't get it narrowed down enough using just 5 clues. So I tried another number, and another. I think I've finally got a puzzle that works, but it doesn't feel as elegant as Jonathan's. Tell me if you get one possible answer. (But don't post the answer, please.)

And I'd love to know if anyone else has any success making these up.

Who am I?

*There are four true and four false statements about the secret number. Each pair of statements contains one true and one false statement. Find the trues, find the falses, and find the number.*

1b. I do not have any repeating digits.

2a. I'm even.

2b. I have exactly two digits.

3a. I'm prime.

3b. I am one less than a triangular number.

4a. I have just one digit.

4b. I am the product of consecutive primes.

## Saturday, November 28, 2009

### Richmond Math Salon

Saturday, December 12

2 to 5pm

2 to 5pm

• All ages welcome. (Fun for kids 3 to 90.)

• Explore math in a fun, safe environment, where no one will judge you.

• A family math event: You and your kids can explore math in a way that works for each of you.

This month we’ll be making snowflakes, talking about symmetry, and playing with logic puzzles.

This monthly event is currently held in a small home (in Richmond, CA), so please RSVP if you plan to come. The Richmond Math Salon is hosted by Sue VanHattum, a math professor at Contra Costa College.

Interested? Email me at suevanhattum at hotmail, or call me at 510-236-8044 (before 8pm).

Schedule of salons for 2010: Jan 23, Feb 20, Mar 20, Apr 17, May 15, Jun 12, Sep 18, Oct 16, Nov 13, Dec 11.

## Monday, November 16, 2009

### Why I haven't been posting...

I use an iBook G4 laptop with DSL connection at home. A week and a half ago, I finally said yes to one of those pesky 'please let us update your software' messages I get regularly from Apple. My computer got trashed.

I will probably buy a new computer, but haven't done so yet. I think I'll be buying a desktop (mac, still), and getting my laptop cleaned up, fixed up, etc. Meanwhile I'm limping along, logging in wherever I can get wireless connection, since my ethernet connection doesn't work.

Anyone who wants to discuss this with me is welcome to phone me at my cell phone: 510 367 8 zero eight (one more than four). More gory details below. I've been spending more time reading actual books, hanging out in my yard, and cleaning house since the mini-disaster. It's all good, but I need to get this settled...

Today I'm seeing tons of good math posts, and am wishing I could join in more fully. But there's a 2 hour limit on my connection here, so I'm trying to just catch up on my blog reading. When I do come back, I'll have a few posts I've been working on offline. ;^)

=====

Gory details:

Apple techies graciously spent hours with me, even though I have no tech support contract, after I almost started crying about it being Apple's fault my computer was trashed. They and I agree that software cannot destroy hardware. But they think my hardware is at fault. (My ethernet connection broke back on April 14, and I bought a usb ethernet adapter and got my taxes out on time. So I use a usb port for my ethernet connection. One techie talked about the problem with the ethernet connection 'migrating' to the usb ports. Huh?!) My hard drive is almost full, which may have contributed to the problem. Besides no capacity for etherternet connection, I can't print. Etc

I will probably buy a new computer, but haven't done so yet. I think I'll be buying a desktop (mac, still), and getting my laptop cleaned up, fixed up, etc. Meanwhile I'm limping along, logging in wherever I can get wireless connection, since my ethernet connection doesn't work.

Anyone who wants to discuss this with me is welcome to phone me at my cell phone: 510 367 8 zero eight (one more than four). More gory details below. I've been spending more time reading actual books, hanging out in my yard, and cleaning house since the mini-disaster. It's all good, but I need to get this settled...

Today I'm seeing tons of good math posts, and am wishing I could join in more fully. But there's a 2 hour limit on my connection here, so I'm trying to just catch up on my blog reading. When I do come back, I'll have a few posts I've been working on offline. ;^)

=====

Gory details:

Apple techies graciously spent hours with me, even though I have no tech support contract, after I almost started crying about it being Apple's fault my computer was trashed. They and I agree that software cannot destroy hardware. But they think my hardware is at fault. (My ethernet connection broke back on April 14, and I bought a usb ethernet adapter and got my taxes out on time. So I use a usb port for my ethernet connection. One techie talked about the problem with the ethernet connection 'migrating' to the usb ports. Huh?!) My hard drive is almost full, which may have contributed to the problem. Besides no capacity for etherternet connection, I can't print. Etc

## Sunday, November 1, 2009

### When Too Much Becomes Too Little

Joseph Ganem wrote a great article for the APS (American Physical Society) News, titled "A Math Paradox: The Widening Gap Between High School and College Math". Ganem is a physics prof at Loyola University Maryland, and works with incoming students at orientation. He's also the father of 3 children (aged 14, 17, and 20), and helps with their math homework.

I want to share 3 quotes from his article, and then encourage you to follow the link to read the whole thing.

He satrts here:

After some examples from his kids' homework, he has these questions:

I want to share 3 quotes from his article, and then encourage you to follow the link to read the whole thing.

He satrts here:

We are in the midst of paradox in math education. As more states strive to improve math curricula and raise standardized test scores, more students show up to college unprepared for college-level math.

After some examples from his kids' homework, he has these questions:

So if eighth graders are taught math at the level of a college sophomore why are graduating seniors struggling? How can students who have studied college level math for years need remedial math when they finally arrive at college? From my knowledge of both curricula I see three problems.I'll let him tell you the 3 problems, so I don't steal all his thunder. His conclusion seems just right to me: (President Obama, Secretary of Education Duncan, Are you listening?)

All three of these problems are the result of the adult obsession with testing and the need to show year-to-year improvement in test scores. Age-appropriate development and understanding of mathematical concepts does not advance at a rate fast enough to please test-obsessed lawmakers. But adults using test scores to reward or punish other adults are doing a disservice to the children they claim to be helping.Please read his article in all its glory, over at APS.

It does not matter the exact age that you learned to walk. What matters is that you learned to walk at a developmentally appropriate time. To do my job as a physicist I need to know matrix inversion. It didn’t hurt my career that I learned that technique in college rather than in eighth grade. What mattered was that I understood enough about math when I got to college that I could take calculus. Memorizing a long list of advanced techniques to appease test scorers does not constitute an understanding.

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