A 4-yr old breathes life into MathNotations!

Ok, so I have neglected MathNotations for over a year and have chosen to express my thoughts in 140 character spurts. I've lost my faithful readership and abandoned the Carnivals.

But the living embodiment of "Kids Say The Darndest Things" will always bring me back. The precious gems uttered by my then 2-yr old grandson still garnered more hits than any Math Ed diatribe or challenge problem, so it's only fitting he would bring me back now that he just turned 4.

Here then are 3 recent anecdotes...

1. He's the only 4-yr old in a summer beginning reading class at our local community college, the other students being 5 and 6. The teacher was reviewing letter recognition and sight words. Each child was asked to come to the board and point to a letter in a word, say, the 'T' in CAT. Things went well until she got to my grandson. "Ok, _____, go to the board and point to the 'B' in BIRD." My grandson, who was sitting with his feet up on the desk, replied with "No thank you. It's the one on the left".

2. My daughter noticed my grandson was spending a lot of time at a party with a certain young lady. On the ride home my daughter teasingly asked my grandson if _______ was his "girlfriend". "No", he emphatically replied, "She's not my girlfriend, she's just a friend!"

3. At the pediodontist the other day, my grandson was doing very well and then the hygienist asked my grandson which of three flavors he would like for his teeth cleaning. My grandson replied, "All three!" She explained they don't do that, he had to pick just one and he came back with, "How many teeth are in my mouth!" She relented and used all 3 flavors. Afterwards she asked which was his favorite and he came back with, "I don't know. They all tasted the same."

Again I suggested to my daughter that she get an unlisted phone number and turn off her cell phone when he starts kindergarten!










"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Update 6-6-11

Now that I am a full-time tweeter, I realize that I've lost most of my followers in the blogophere but I will post every now and then.

1) Twitter enables me to publish my "puzzles" 2-3 times daily. That's probably the best domain for brief math challenges. In the end, it's still all about content. If you're on just to promote yourself, people will see through that quickly, but they will come back if you offer something interesting and substantive.

2) Anyone miss the musings of my now 4-yr old grandson? Well,when he was 3, he was in his preschool class hanging out with his 2 buddies. One started to make loud silly boy noises and the teacher reprimanded him. A moment later my grandson did the same. The teacher approached him and asked why he would do that right after his friend was told to stop. He replied without hesitation, "That wasn't me, it was just an echo of ___." This is why I told my daughter to get an unlisted number immediately!

3) Actually his about-to-be 8-yr old brother is unique in his own right. His interests in and knowledge of science, astronomy in particular, astound me. He is already an expert on galaxies and nebulae. What do you think he wanted for his birthday other than a telescope? An authentic lab coat! Of course, we obliged.

4) It would be remiss of me not to mention my 2 granddaughters. Not only beautiful and very smart, they are filled with love and joy. What a blessing!

5)Looking for some controversy here? Miss my provocative comments about the current state of math education in the US? Sorry, I'm a very boring person. All I want is a blend of procedural mastery (practice!) with conceptual understanding. Although there are numerous ways to help ALL students understand, there are established practices and principles of effective math instruction which cannot be ignored. Using multiple representations, linking to prior learning, motivating with real-world examples and guiding with questions are some of these essential components. These will never go out of style.

6) Although I am a strong proponent of a standardized curriculum, I fully recognize that this leads inexorably to teacher eval based on test scores. This politicizing of education and imposing a strict business model on an essentially human endeavor will have far-reaching negative consequences.





"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Math Teachers Are "UNION" People!

The title is a pun but the need for a "more perfect union" is integral to our Constitution! I don't think our Founding Fathers would support any attempt to dissolve our unions. For this reason I advocate the immediate recall and/or impeachment of all governors and Congresspeople who are attacking the fabric of our nation by a concerted and conspiratorial assault on teacher unions.

Remember, if unions were not effective there would not be such a movement to destroy them. It's all about power and dollars...






"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

List the NINE 2-digit PRIMES which...

Here are the last two math challenges I just tweeted for middle schoolers and beyond. You may want to use this as a fifteen minute activity to improve reading, review basic terms and concepts, develop reasoning and writing in math. There was an error on the 2nd question as it originally appeared on Twitter. I then corrected it.

List the nine 2-digit primes which produce prime numbers when their digits are reversed.




List the SIX 3-digit primes which produce primes when their digits are written in ALL possible orders. 137 fails b/c 371 is not prime.

For both questions students should work in teams of 2-4.

For the first question, students should not be allowed to use a calculator!

For the second one, have them experiment with a calculator for a few minutes. If a student thinks they found one, their teammates must verify it! After 3 minutes ask: "Have you noticed that the numbers you're looking for cannot contain certain digits like 2. What digits and why? Discuss it and one member of the team must record the team's findings and provide a written explanation!

After 3-4 more minutes, have them refer to a table of primes online (or print it and hand out a copy to each team). If they don't find it within the 15 min time limit, have them finish it for extra credit for the next day.

Here is one of the numbers: 113. Good luck!


"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

"You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught." --from South Pacific

Odds and Evens Week of 1-31-11

• Tom Friedman writing in the Opinion Pages of 1-30-11 NYT about Singapore politics, economy and education:

... 

If Singapore has one thing to teach America, it is about taking governing seriously, relentlessly asking: What world are we living in and how do we adapt to thrive. "We're like someone living in a hut without any insulation," explained Tan Kong Yam, an economist. "We feel every change in the wind or the temperature and have to adapt. You Americans are still living in a brick house with central heating and don't have to be so responsive." And we have not been.

Singapore probably has the freest market in the world; it doesn't believe in import tariffs, minimum wages or unemployment insurance. But it believes regulators need to make sure markets work properly - because they can't on their own - and it subsidizes homeownership and education to give everyone a foundation to become self-reliant. Singapore copied the German model that strives to put everyone who graduates from high school on a track for higher education, but only about 40 percent go to universities. Others are tracked to polytechnics or vocational institutes, so the vast majority graduate with the skills to get a job, whether it be as a plumber or a scientist.

...

It is a sophisticated mix of radical free-market and nanny state that requires sophisticated policy makers to implement, which is why politics here is not treated as sports or entertainment. Top bureaucrats and cabinet ministers have their pay linked to top private sector wages, so most make well over $1 million a year, and their bonuses are tied to the country's annual G.D.P. growth rate. It means the government can attract high-quality professionals and corruption is low.

America never would or should copy Singapore's less-than-free politics. But Singapore has something to teach us about "attitude" - about taking governing seriously and thinking strategically. We used to do that and must again because our little brick house with central heating is not going to be resistant to the storms much longer. 

MathNotations' Reaction:

• ..."teach us about 'attitude'..."  I'll second that.  As I have often mentioned regarding Singapore'a attitude toward education:  In Singapore and other rapidly developing nations, education is seen as an investment.  In the USA, it is seen as an expense.  Talk about attitude...

• We can no longer afford to excuse the educational performance of our students in math and science in international comparisons with the hackneyed and questionable argument:

We have to educate all the kids, their population is uniform with little diversity. 

                 

Here's my incredibly simplistic and naive approach to "e-quality" education:

STOP the experimental research! Take each underperforming student and extend the school day using retired or current teachers, pay them and make sure that child does not leave until he/she can do their homework on their own and demonstrate understanding. Supplement and enhance individual instruction with the best learning software out there (*adaptive* software is the most exciting for me). 

Any volunteers? 

• Singapore appears to be attracting the best and brightest into politics - our most recent congressional election attracted some stellar individuals and then some others...

• For me it's all about our nation's values. If we don't deem the education and welfare of our youngest citizens to be our highest priority, then where exactly is our future?

Bravo, Tom, for a compelling piece. Much food for thought...

• Have you been keeping up with the many Twitter Math Problems and Challenges for the past 6 months?  I generally don't post answers so you need to tweet a response, send me a Direct message or retweet it for others to see. Follow me at @dmarain.
  
  
• Remember my tribute problem to Martin Gardner? Jan writes, "Has seriously no-one suggested the 120-25 variant? :)" Ah, simplicity! Or is it Occam's Razor (when you have two competing theories that make exactly the same predictions, the simpler one is the better).
  
  
• I recently asked a version of the following on Twitter:
  
  What special qualities separated your best math teacher from everyone else?
  
  On Twitter, I wanted a response consisting of just ONE quality. Here, I'm looking for the top 3-5. Ok, so I open the floor once again to this oft-repeated query. To focus on math teaching, I would ask you to reference only those unique skills/talents which are inherent to mathematics. I may not get any response to this, but I do believe this list will be of some use for someone.  It would be particularly useful to hear from students and parents as well as from professional educators
  
  
• This little challenge for your Algebra I students is a bit long for Twitter. Let me know the outcome if you use it in class:
  
  Start value = googol (1 followed by 100 zeros)
  Multiply Start value by 5.
  Add 5 to the result.
  Square the result.
  Divide result by 1 more than googol.
  Divide result by 5.
  Divide result by 5 again.
  Subtract googol from result.
  Final result = _______?
  
  This is not meant to be a challenge for your mathletes!

"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

 "You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught." --from South Pacific

Odds and Evens Week of 12-1-10

• Here's my most recent Twitter Problem of the Day:

How many 3-digit positive integers are there in which the absolute value of the difference of their hundreds' and units' digits equals 4?


For students: Reply on Twitter, Facebook or my email (dmarain@gmail.com) by 12-6-10.
For everyone else: Comments are always welcome but please hold off on solutions until 12-6-10. Thanks!

• I've been contacted again by the Education Editor of Parent Paper magazine, a well-known publication here in North Jersey.  I was asked to write a piece on helping parents to help their children with schoolwork, particularly in math. I'm reprinting here in full since it will be most likely edited down to a few sentences. Most of the general suggestions are obvious but sometimes I feel that the obvious needs to be stated. I'm basing this on my experience with 7 children, 4 grandkids and over 30 foster children.

General Suggestions for Parents Helping Children With Assignments

• TV, radio, music, any other distractions turned off when your child comes home after school.
• Establish a consistent location where they will do their homework every day -- dining room table, coffee table -- preferably in the same room as parent until they are older
• Establish a routine where the child takes out the assignment book, folders, etc., before their snack.  If you do it for them, they will come to depend on you for this.  Have them hand you their parent folder with all papers you're supposed to read, sign, etc.
• It's up to you but I would allow the child to have their snack while they start their homework.  Be less concerned about the mess and remember, if they're not allowed to start homework until they 've finished their snack, I guarantee you that snack time will extend for longer and longer periods of time (even if you say the have to finish in 15 minutes!).
• DO NOT OFFER TO HELP THEM WITH THEIR WORK UNLESS THEY ASK!  DO NOT HOVER OVER THEM - JUST BE IN  THE VICINITY!  ONCE YOU'VE MADE THEM DEPENDENT ON YOU, IT'S HARD TO BREAK THE HABIT!
• If they ask for help, ask them to read the directions out loud. If you then ask them what it means or what they are supposed to do, many children will reply something like, "I don't know. I don't get it. I can't do it!"  You know your child best. If you believe they are capable of the assignment, you can help them get started and then say you have to do something, but you'll be around if needed.
• If you cannot make sense of what the assignment is, then ask them to explain it. If they can't, the issue may be they are not yet ready to neatly/clearly copy the assignment form the board. Address this with the teacher the following day.
• Ask the teacher whether they prefer voicemail, email or face-to-face questions after or before school.  Ask them if it's ok if they occasionally email concerns.
• Establish a "social" network of parents in the class - take the initiative!  Set up a class group on Facebook so that parents can help each other with clarifying assignments. Parents can routinely check in.  If electronic networking is not feasible, go back to the tried-and-true getting phone numbers from 2-3 other parents thus making a smaller network.  Trust me, you will need to use this often unless your child is mature, organized and responsible/independent, in which case you will be helping others! 
• Keep repeating to yourself the Golden Rule of Parenting: THE MORE YOU DO FOR YOUR CHILD, THE LESS HE/SHE WILL LEARN TO DO FOR HIM/HERSELF !!

Specific Suggestions for Math

• Most children have more difficulty with the wording of the directions or of the problem than the math itself!  Try to break it down for them.
• Don't be too quick to correct their mistakes. When checking over their work, try "I'm not sure about #5. Would you tell me what you did?" Most of the time they can correct their own errors!
• It is important to become familiar with your child's math program.  You will probably already have heard about it through the grapevine, but you can find out what it is even before school starts by asking the office or leaving a message for the math specialist in the district.  Go to any meeting the school offers to introduce parents to the math program. 
• All new math programs come with extensive parent resource materials. You should receive these regularly but don't hesitate to go online and find them for yourself!  
• Be prepared to ask questions, but don't start tearing the program down b/c you've heard there are problems with it.  The program will not be changed in the current year no matter how parents may feel.  
• Recognize that every math program, whether more traditionally skill-based or reform-oriented (more problem-solving, projects, less drill) has its merits and its weaknesses. Whether you believe there is too much emphasis on basic facts (less likely!), or not enough, you can supplement with the myriad of resources on the web.
• Don't be shy about asking the teacher for guidance with your child or with the math program itself.
• Remember: MATH IS ALL AROUND US ALL THE TIME!  Ask your children lots of questions involving numbers and shapes around them. For example, "I need to cut up this square into two equal parts. I know an easy way (like this) but I think there's more than one way. Can you help me?"OR  "I have a riddle. What movie comes before Toy Story 1000?" OR Place four quarters on the table. "Can you give me a dollar?" Put coins back. "Can you give me a half dollar?" etc... 
• Never assume a concept is too hard for them. If simplified, they can often find a way.    

SOME OF THE BEST MATH RESOURCES ON THE WEB

• Home School Math (http://www.homeschoolmath.net/) - Incredible resource for ANY parent of ANY child!  Free worksheets, math ebooks for elementary grades, extensive link list of games, interactive tutorials & quizzes, curriculum guide, andmath teaching help articles/lessons. The resources emphasize understanding of concepts instead of mechanical memorization of rules.
• Let's Play Math (http://letsplaymath.net/) - Outstanding site by an exceptional educator who knows her stuff and hasd done her homework! Check out her Free (Mostly) Math Resources
• Math.com (http://www.math.com/) - Excellent resource with numerous electronic tools for mastering basics and beyond.  Start with Basic Math and Everyday Math (not the well-known math program) for K-8.
• 10 Best Web Sites to Enrich Your 
  Elementary Math Curriculum
    (http://www.am.dodea.edu/acss/AES/sip/documents/WebSitesforProblemSolving.pdf)
• PurpleMath (http://www.purplemath.com/) - The best resource for algebra! 

• And now for the latest offerings from my 3-year old grandson. The last time I posted his "muffin" comments, I had more views than from any math post in 3 years!
• My daughter has been trying to get him to go to sleep without her staying in the room. She told him that his 3-yr old cousin, with whom he is very close, is getting big now. My daughter commented, "Her mommy reads her a story, gives her a goodnight hug and leaves." My grandson replied, "Do you think I could do that, mommy?" "Of course", my daughter replied, to which my grandson immediately came back with, "Ok, but not tonight!"
• He is all boy, all the time.  Aggressive, loves contact sports and is becoming a rabid NY Giants football fan like his daddy.  He wears his Giants shirt on game day and can throw his little football with velocity.  After seeing him throw the football a couple of times like a pro the other day, she said, "Wow, you threw the football really well, twice." "No, mommy, only once", he replied. "Are you sure? I saw you throw it twice", my daughter asked.  "Yes, mommy, the other time was the highlights!"

"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

Another Cone in a Sphere Problem? - A Guide for the rest of us...

Students who have been out of geometry for a year or so and are preparing for standardized test like Math I Subject Test or SATs/ACTS need occasional review. The following is similar to several other cone problems I've posed before but even our strongest Algebra 2 through Calculus students lose their "edge" when it comes to "solid" geometry questions (yes, believe it or not, my terminal course in high school was called Sold Geometry and we covered topics like spherical trigonometry!).


A right circular cone of height 16 is inscribed in a sphere of diameter 20. What is the diameter of the base of the cone?


Reflections....

1)  Are these kinds of problems somewhat hard merely because students forget? I can think of several more reasons:

• The problem itself is somewhat challenging, however it's far from over their heads!
• The student never experienced a question like this in Geometry; perhaps questions like these were in the B or C or D exercises in the text and were never assigned or only for the "honors" students? Do you recall seeing a problem similar to this in the textbook from which you taught?
• The student did not take a formal course in geometry
• The topic was covered in a cursory manner or perhaps not at all because of time crunch. That's the whole point of a standardized curriculum, isn't it? To know what is needed to be covered and plan accordingly. Of course, I'm  a realist enough to know the myriad of reasons why the best laid plans oft go .........
• Students don't remember how to start because key geometry strategies were not explicitly stated and reiterated ad nauseam. Were your students asked daily to begin by reciting the key strategies such as those for circle and sphere problems? Were they placed on index cards or blocked out in a particular section of their notebook?:
• DRAW THE BEST DIAGRAM YOU CAN (and believe me, I'm no artist!)
• Always locate the CENTER of circles, spheres and label the point
• Label the measurements of all segments (angles) - I know, everyone does that!
• Successful problem-solving in mathematics is based on finding relationships! Were guiding/leading questions asked 
• What do the cone and sphere have in common? 
• TRUE  FALSE  The height of the cone is the same as the diameter of the sphere.  EXPLAIN!
• Was the student exposed to the strategy of comparing the 2-dimensional analogue of the 3-D problem? Would it be a right triangle in a circle? Equilateral triangle inscribed in a circl or???  
• Oh and yes... 
• Draw the radius of the sphere (or circle) so that it is the hypotenuse of some right triangle!

"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860)

You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific

11-22- A Remembrance - Soon It Will Be Half A Century

And the night comes again to the circle studded sky
The stars settle slowly, in lonliness they lie
'Till the universe expodes as a falling star is raised
Planets are paralyzed, mountains are amazed
But they all glow brighter from the briliance of the blaze
With the speed of insanity, then he died.


From Crucifixion, Phil Ochs




"All Truth passes through Three Stages: First, it is Ridiculed... Second, it is Violently Opposed... Third, it is Accepted as being Self-Evident." - Arthur Schopenhauer (1778-1860) You've got to be taught To hate and fear, You've got to be taught From year to year, It's got to be drummed In your dear little ear You've got to be carefully taught. --from South Pacific