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Galileo and Maia on a date at the Unadilla Drive-In movie

It’s a monsoon season here in upstate New York. Today we had one of those storms that used to make bronze-age people believe in things like the apocalypse (or for some Timothy LaHaye readers, still does). But up here in the Catskill Mountains of New York we know better – it’s really Rip van Winkle’s bowling party.

We have two beautiful golden retrievers ,Galileo and Maia. Galileo is almost 110 pounds of majestic muscle and fur. A more noble looking creature you will never find. As he sits here at my feet, constantly on guard against such grave predators as the Tyrannosaurus Rabbit, or of the Groundhoggus Rex, it’s hard to believe that this paragon of heroism crawled onto the couch to lay on me to have me protect him from the thunder. 

He never used to be afraid of thunder. As a ten-pound pup, he’d run around outside in the fiercest of storms. But this year he began showing signs of fear of the thunder-gods. My wife tells me that goldens acquire that trait later in life. 

The first sign was a few months ago, when in the middle of the night he started waking us up during storms with his whining and snuffling at us on the bed. 

Last night, in the middle of the night, he crawled onto my side of the bed to snuggle against me. He doesn’t usually come up on the bed late at night, so I was surprised. I was sleeping and hadn’t heard the storm (my snoring probably drowned it out). 

All of a sudden I feel the side of the bed dip as his weight was distributed on it. Then, with a soulful sigh, he dropped in next to me and put his face right in mine. 

Galileo is an in-your-face kind of dog. He’ll lick you like a puppy. He has no concept of his size. So he licked my face until I pet him, and he wouldn’t let me stop petting him till the storm subsided. 

This afternoon, during another rendition of the storm, he did the same to me on the couch. 

Maia, our “emergency back-up dog” (as Dave Barry would say) hasn’t been bothered at all by thunder, but I think she’s beginning to imitate Galileo. She climbed up on the other side of the couch, boxing me in. I had two hundred pounds of golden retriever sitting on my lap, licking my face. 

Everyone should be so lucky.

P.S. The photo was taken last year at the Unadilla Drive-in, not far from where we live. Yes, there really are still drive-in theaters. And the dogs love it. They play frisbee with us and all the kids at the theater in the field in front of the screen, for about an hour before show-time. 

Last time, we saw the awesome double-feature of Star Trek and Night at the Museum: Battle of the Smithsonian. Eat your heart out.

This is a continuation from the previous posts:

• What if I Fail 9th Grade Math? (Part 1)
• What if I Fail 9th Grade Math? (Part 2)
• What if I Fail 9th Grade Math? (Part 3)
• What if I Fail 9th Grade Math? (Part 4)
• What if I Fail 9th Grade Math? (Part 5)

At the end of the previous post, a reader wrote in:

“i have the same problem. i am in grade 12. i used to grasp those integers, algebra and simple geometric problems with lot of ease and faster than others. then i started falling down not only in grades but also in work ethic. now i got 70 in grade 12 and thats the highest ive gotten in high school, with lowest being 53 in grade 11. I am not able to break the 80 barrier and 70 is a great struggle. I know it isn’t about marks, but in university i need to maintain a nice gpa and need the idiotic marks. I have a stigma “i suck at math” stigma and can never get A, because after i got 60 in grade 9, 10 11 and 12 ive been frustrated and slow to understand concepts. now ppl tell me that my brain is too old to improve. im not a kid, so obv i don’t believe BS like that. But what do I do? Do i Start from grade 9 scratch and work my way up as if I just graduated from grade 8? Or what??”

Professor Homunculus sez:

Tommy,

Well, you’re on the right track. What kind of idiot would tell anyone they’re too old to learn anything? Only someone who’s own brain has prematurely calcified. Modern research has shown that it’s time to get rid of that myth.

I’m going to suggest that there is a possibility (just a possibility, OK, I don’t know your situation well enough to be sure at all) that age is related, but in a totally different way.

(read the rest…)

This is a continuation from the previous posts:

• What if I Fail 9th Grade Math? (Part 1)
• What if I Fail 9th Grade Math? (Part 2)
• What if I Fail 9th Grade Math? (Part 3)
• What if I Fail 9th Grade Math? (Part 4)

A reader (Trevor) wrote in:

i am going to fail math 9 . what ill happen if i fail. i cant go to summer school my family refuses to take me. if anyone knows if i will go to the 10th grade or will be in 9th again please tell me

thank u.

Professor Homunculus sez:

Trevor,

There’s no way for me to tell you what your school will decide. Each school is different. Your family refuses to take you? Man, I feel for you – your school is not supporting you, your family doesn’t sound like it is either – but don’t worry, because the most important part is - that’s you.

You obviously are taking the situation seriously.

Let me tell you a story. (read the rest…)

You may have read other posts about this long division shortcut at Math Mojo. 

Long division shortcut Part 1

Long division shortcut Part 2

The main page to go to to learn the basics of the shortcut is:

Long Division Shortcut at Mathmojo.com

At that page, someone asked:

I have attempted this question using your method: 44872 / 79

 Using your method I get the answer 569, when the answer is 568.

 Please elaborate for me.

When I tried the example myself, I almost got 569 as well, but then I realized what the problem was. I think fellow who wrote, as well as I, fell prey to a very easy trap to fall into, and I’d like to address that now, because I imagine that other Math Mojo readers might benefit from it. 

The best way to illustrate the problem, and the solution, is in a short video. 

Please keep in mind that although I go through the division method in this video, I don’t teach the entire method. The video was made to simply address this one particular trap and how to avoid it. If you want to learn the method, go to:

Long Division Shortcut at Mathmojo.com

(read the rest…)

Ah, math ed. I hate it. Yes, I hate it. It has become a corporate tug-of-war for the hearts and minds of petty pedagogues, and your kids are in the crossfire. 

Should it be Math-U-See? TERC, Singapore, Saxon, or one of the other over-marketed mind-usurpers? 

I like math. I love math. I hate to see it co-opted by these impostors. OK, some are worse than the others. Before you say, “Hey, but Math Mojo is also trying to sell me something…” let me tell you now – you are correct. 

But I’m not trying too hard, and I don’t want you to buy in to my “brand.” There is no “Math Mojo” math. Math Mojo is my own silly wording for the way I like to think about how I deal with math. It has helped me go from someone who was mathophobic to someone who really loves the heart of math and the art of math. I don’t propose that I know anything better than anyone else – I just happen to have some Ideas that seem to prove useful to some people. 

I would NEVER propose that it be used as a “curriculum” for anyone. To me, “curriculum” means, “this is what I think is important for you to know, and you better damned well know it because we will test you on it.” At least that’s what it means in schools. Schools – the same places that define “scholarship” as “money for football players.” I fart in curriculum’s  general  direction.

Something I can tell you is that my judgement should never be considered final for anyone but me (and even I don’t do that), and that no one else’s judgement should be, either.  

But there are degrees. And someone recently wrote me to tell me about some posts he had written which address some of the issues with different curricula currently being hawked to your schools. 

It needs to be stated right now that the posts I am linking to here do not entirely express my opinions. I just feel that they  make a lot of important points. I am offering links to them here simply for your consideration. If you need to debate them, please take them up with the author, not me. 

I will say that I generally don’t find any value in “traditionalist” or “constructivist” arguments. I feel that either extreme is a sham, and the math wars behind them are about as useful as debating how many angels can dance on the head of a pin. I tried to engage in it at one time, but the mind-numbing natterings of the different sides are ….zzzzzzzzz… pardon me, where was I?

The following links actually argue against constructivism, but in a very, ahem, “constructive” way. I don’t find them fodder for the war, just well-reasoned  essays, although they don’t entirely express my views. And that probably speaks for them

My views? Well ….zzzzz.

So hear are some links from Barry Garelick:

http://www.thirdeducationgroup.org/Review/Essays/v5n2.htm

http://ednews.org/articles/one-step-ahead-of-the-train-wreck.html 

Ostensibly, this has nothing to do with math. But it is good Mojo. 

Ayelet Waldman has written a book called “Bad Mother.” 

I read this post on a blog about how to market not-for-profit businesses (something which MathMojo wasn’t designed to be, but has been for much too long a time). The post is about the good-mother/bad-mother false paradigm. 

A lot of MathMojo readers are moms trying to help their children (and/or themselves) learn math. If I can help a mom feel better about herself (or at least have a good laugh) by pointing her to these posts, I’ll have fulfilled my daily quota for good mojo. 

So check out the link above, and then check out the post and the YouTube video at:

http://sandinmyswimsuit.blogspot.com/2009/05/naming-names.html

(The opening scene of the video had me laughing uncontrollably.)

Obviously, I’m not a mom, which goes to prove that you don’t have to be a mom (or a woman) to appreciate those posts. You just have to know, or have known a mom. 

I’m a middle aged guy, and I know I’ll be getting that book for my mom.

It’s been awhile since I’ve posted here, but I’ve been posting like crazy to the http://mathmojo.com/kenken page. I’ve already got 24 videos up about how to do KenKen®, from simple 4×4 KenKen, to sadistic 9×9 KenKen puzzlers without operation signs. 

I’m finding that the feeling I get from KenKen is similar to that “numbers juggling” feeling I get when I do mental calculations, like  large multiplication problems. 

It’s possible that KenKen is about the best mental fitness activity you’ll ever come across. If you homeschool, there’s nothing better you can get your child into. Check out the http://mathmojo.com/kenken  page to find out more.

(this post is a continuation of yesterday’s post - Why do we have to show the work?)

This youtube video is by a woman with Asperger’s Syndrome (a form of autism). Her observations are very insightful. I encourage you to watch it in the entirety, because she covers a lot of interesting points that are not limited to people with Asperger’s syndrome. 

People who do not understand people who are “different” have a hard time reaching them. The loss is on both sides. 

I was pleased to see her analogy about reading different kinds of sentences. It was similar to something I’d been thinking about:

(read the rest…)

“Why do we have to show our work when we do arithmetic?”

I had an interesting phone conversation with a woman this morning. She was a tele-marketer for service I had signed up for to help me with how to make this site better. As she asked me questions about Math Mojo and Magic and Learning, she told me an interesting story about her son’s experience with math.

When her son was about 18 months old, she realized that when she took him to the grocery store, as she read out prices of what she was buying, he could add them up in his head! That is pretty amazing. No one had taught him that. It was an example of a strange, and poorly understood phenomenon that occurs now and then, and produces “savants.”

What made the story even more interesting to me is when she told me what I knew what eventually had to come. She told me that when he got to public school, it  absolutely ruined his math experience by making him “show his work.”

(read the rest…)

Di-llama

Many mathematicians and some math educators are aware that a lot of the stuff that passes for “math” in schools is simply number manipulation, or rote memory of math “facts.” 

If we “teach to the test” or use some state-sponsored curricula, or bureaucratically sanctioned “standards,” we are just providing some hoops for students to jump through, which may or may not have anything to do with actually engaging their minds and leading them to mathematical thought. 

There are great insights to be gleaned from mathematics, which fall by the wayside as we instead try to inculcate the greatest amount of students with “material that must be covered this semester.”

Here’s a little dilemma:

It’s probably true that in most cases students have to be able to proficiently master basic skills. It’s also probably true that the insights should come during that initial learning phase. 

On the other hand, for some of the reasons mentioned above, as well as others, most schools are not set up to handle fostering actual insights. There is no time and there are no resources to try to do that for most of the students. 

So what can we do? 

(read the rest…)