MathNotations

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

• 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/WebSitesforProblemSol ving.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!"

Posted by Dave Marain at 9:35 AM 0 comments

Labels: advice for parents, grandson, odds and evens, twitter problem of the day, update

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I decided to post a video solution of the Twitter problem I posted on 8-25-10:

4 red, 2 blue cards; 4 are chosen at random. What is the probability that 2 of the cards will be red?

Because of the 140 character restriction on Twitter, the questions are often highly abbreviated and I actually consider it a "fun" challenge to write the question both concisely and clearly. Of course, as we all know about human interpretation of word problems, "clear" is in the eye of the beholder!

There's no doubt that the question above needs some fleshing out and might appear on the SAT and other standardized tests something like this:

A set of six cards contains four red and two blue cards. If four cards are chosen at random, what is the probability that exactly two of these cards will be red?

I'm sure my astute readers can improve on this wording but we'll leave it at this.

A few questions naturally pop up:

(1) Could this really be an SAT/Standardized Test question? Well, as I state in the video below, a question quite similar to this appeared on the College Board website the other day as the Question of the Day.

(2) For whom is the video intended? Everyone who happens upon it! I certainly wrote it to be helpful to students who will be taking the PSAT/SAT in the near future. Rather than simply presenting a single quick efficient solution, I demo'd 2-3 methods and indicated some important strategies and reviewed key pieces of knowledge to be successful on these harder probability questions. By the way, someone who is comfortable with probability will surely not find this question so formidable, but we're talking here about high school students or even undergraduates who struggle mightily with these.

(3) I'm hoping that the video will also serve as a catalyst for dialog in your math department. From the inception of this blog, I've never even intimated that a suggested way of explaining a concept, skill or a problem solution is in any way prescriptive. I encourage you to continue using whatever instructional methods have worked for you and to share these with our readers! However, for novice teachers or those who wish to see other approaches, I hope it will have some benefit. Of course, the video is not in a classroom. There are no students asking or being asked questions. There are no interruptions and I have a captive audience (except for my dogs who bark incessantly!).

SOME KEY STRATEGIES/TIPS/FACTS FOR PROBABILITY QUESTIONS

(1) It is highly recommended that students begin by listing 2-3 possible outcomes and to include at least one that is NOT one of the desired outcomes! This will help you to decide on a plan: organized list vs more advanced counting/probability methods. Further, you can ask yourself the key question in all counting/probability problems: DOES ORDER COUNT!

(2) Although it appears difficult for most test-takers to be systematic when making a list under test-taking conditions, preparation is critical here. If one practices several of these in the weeks leading up to the test, the chances of success improve dramatically. Did I just suggest preparation and practice could make a difference!

Where do you find these problems? Any SAT/ACT review book or my Twitter Problems of the Day or my upcoming SAT Challenge Quiz book to name a few sources...

(3) The basic definition of probability should always be in the forefront of your mind:

P(an event) = TOTAL NUMBER OF WAYS FOR THAT EVENT TO OCCUR DIVIDED BY TOTAL NUMBER OF OUTCOMES.

As indicated in the video, one can and should think of this ratio as TWO SEPARATE COUNTING PROBLEMS! Do the denominator first, i.e., the TOTAL number of possible outcomes. In the Twitter problem it is 15 if order is disregarded. Whether you arrive at 15 by listing/counting or by combinations methods, the denominator is 15 and is a completely separate question from "How many ways are there to get 2 red and 2 blue cards?"

(4) Finally, there are other methods for solving this probability question using Laws of Probabilities and/or permutation methods. I was going to make a 2nd video but I'm not so sure about that now.

An important point about the video below: I used 4 Blue and 2 Red cards, the opposite of the original Twitter problem but that won't change the final result!




[埋込みオブジェクト:http://www.youtube.com/v/305z8R9d56k?fs=1&hl=en_US]



Look for my other videos on my YouTube channel MathNotationsVids . Look for all of my Twitter SAT Problems on twitter.com/dmarain .

As I develop my Facebook page further, I may start posting these questions there as well as my videos. Facebook allows up to 20 minutes videos, much less restrictive than YouTube's 10 minute limit.

Posted by Dave Marain at 10:49 AM 5 comments

Labels: counting problems, math videos, mathnotationsvids, probability, SAT strategies, SAT-type problems, systematic counting, twitter problem of the day