Notable November

November has been a busy month for the Artist, 13, with both a writing program (National Novel Writing Month Young Writer’s Program) and a math competition.

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She aspires to be a writer someday, and this is her first year participating in NaNoWriMo Young Writers Program.  I hope it will give her some experience and insight into what it’d really be like. We decided that rather than having me interview her, she would write a summary about how it’s going. Then she would be able to write her thoughts in her own words. Here is what she has to say about it so far:

“Hi, it’s the Artist. This year I’ve been participating in NaNoWriMo (National Novel Writing Month). It takes place every November for aspiring writers of all ages, the goal being to reach your Word Count Goal by the end of the month (example: 50,000 words).

Of course, the deeper meaning is to write a novel. I was really pumped to sign up earlier in June. Being a think-ahead kinda girl, I spent the entire summer forming an idea of exactly how I wished my novel to be. Every time a scene would pop into my head, I would mentally apply it to the list of scenes I wanted in my book. I knew every detail about my characters: their personalities, their full name, exactly how they looked, the way they talked. I even went so far as to Google them all to make sure I hadn’t inadvertently named them after some celebrity I’d never heard of.

Then November came, and I went into a trance. Every free second I had would be spent hogging the upstairs computer, typing up a storm. At first it was easy. All I had to do was walk into the scene collection room of my brain and pluck one off the shelf. Then I would type it and edit it and move on. But gradually I ran into some problems.

Problem 1: The voice didn’t sound quite the way I had originally pictured it. But as time went on, I discovered that I was okay with that. My characters were just taking charge of the narration. Plus if I stuck a few instances of grammatical pedantry into my main character’s dialogue, that pretty much took care of the issue for me.

Problem 2: Somehow in all my planning, I had left about 200 pages in the center of the story to be adlibbed. This was a little harder to get around, and it gave me some concern as I was typing the beginning of my novel. Then a miracle occurred. For the first time in my life, I was saved by my bad habit of procrastination. See, being a natural procrastinator, I tend to look at deadlines as distant lands which I have plenty of time to reach. Since I hadn’t paid much attention to my NaNoWriMo deadline, it didn’t stress me out that much. Therefore no panic was in the way of me and any ideas I might have. Sure enough, I began coming up with scene ideas as I needed them for the main portion of my story.

As of today, I have written 31 pages and am 88.09% to my Word Count Goal. In other words, I’m on track to win. NaNoWriMo has been really fun for me, and I am happy I made the decision to sign up way back in June. I would definitely recommend it to anyone who enjoys writing.”

** Update:  She reached her word count goal on Sunday, November 24.  Finally, she’ll be able to rest. I’m thankful she’s finished NaNoWriMo before the Thanksgiving holiday!  **

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The Artist also competed in her first Math competition of the school year this week.  I am again her coach, but my role is minimal.  Now in our second year competing, we more fully understand how things work.  The previous experiences were helpful preparation.  We won’t know her results for a few weeks yet.  I am proud of her no matter what.  All my children inspire me.

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This has been an exciting, yet busy month with plenty of learning experiences.

I recommend these extra-curricular programs to parents whose children may have similar interests; I think the benefits are worth the effort. To learn more, check out: National Novel Writing Month Young Writers Program or the American Mathematics Competitions.

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AoPS Intro to Algebra Review – An Active Approach

For a middle or high school student who is motivated to take a more active role in learning Algebra, check out Art of Problem Solving Introduction to Algebra, 2nd Edition, by Richard Rusczyk.  Intended for students in grades 6-10, I’ve found it to be effective in not only teaching Algebra, but also in developing general problem solving skills.

Appearance

The pages are uncluttered with mainly black and white print and a few boxes highlighted in a peaceful blue – making it easy to follow and not distracting.

Jump Right In

Building concepts in a logical, step-by-step manner, the textbook is thoughtfully written to the student. The method appears to be this: the author carefully introduces new topics and engages the student by posing simple, related example problems, and then gives her a chance to jump in and develop her own solutions before presenting the answer to her.  For example, the chapter on quadratic equations begins by defining quadratic terms and expressions.  Then it leads the student by posing five such questions – gradually increasing in difficulty – related to quadratics.  This starts the student in the process of thinking about how she will answer the questions.  But the solutions are not revealed just yet.  The idea seems to be to motivate the student to reach her own solution before the book explains it to her.  Eventually the solution is explained, but by that time the student will be more aware of it, since she should have at least begun to construct her own.  Contrary to many textbooks I’ve seen, more up front thinking is expected of the student rather than being spoon-fed the material.  This active involvement makes learning math concepts less dull, more enjoyable and easier to remember.

Breaking It Down

Throughout the book there is a parallel with how new material is presented and the fact that complicated problems can often be solved by breaking them into smaller parts or steps.  For a quick example, when imaginary numbers are introducedand defined, the student is asked to evaluate a few simple cases on his own (which he should be able to do by applying the definition).  Next he is asked to solve aquestion that is slightly more difficult, but building off the previous question.  Then another – more difficult, but similar.  Finally, he is to simplify a set of more complicated imaginary number questions.  But if he has been solving the little problems along the way, the difficult questions are more easily diffused because he can break the difficult problem into smaller, simpler parts.  It no longer looks scary or confusing, and he will probably be able to quickly calculate the answer.  As I said above, only after he has had time to develop his own solution are the explanations presented in the text.  This approach makes sense, and is a helpful model for problem solving in general.

Following the above-mentioned example problems, there are Exercises that evaluate the concepts for each section.

At the end of each chapter is a thorough Summary section which highlights definitions, concepts, and/or other important information.  Many of the these sections also contain Problem Solving Strategies, and it is worth your time to read, absorb and apply these.  Next are Review Problems which seem to help measure how well a student understands the chapter.  And finally there is a Challenge Problems section in which will be found the more difficult problems that are likely to really stretch the student’s understanding and help her master the material.

Competitions

Problems previously seen in MathCounts, the American Mathematics Competitions (AMC8, AMC10, and AMC12,) the American Invitational Mathematics Examination (AIME), the USA Mathematical Olympiad (USAMO) and others are included in some of the exercise, review, and challenge problems.  Working these problems not only helps with understanding the idea of the chapter, but also in preparing for future contests.  In our situation, this book greatly contributed to the preparation of my daughter in past competitions.

Additional Helps

AoPS’s website also provides Intro to Algebra Videos which give the student another visual aid if desired.  Though my daughter did not use these, they are there if you would like them – which I appreciate.

There is a Hints section located in the back of the book for selected problems.  Any problem with a hint will note that at the end of the problem.

I strongly recommend the Solutions Manual.  It provides well written explanations with step-by-step solutions.

Caveats

It is important to read the How to Use This Book section at the beginning of the book for clarification.  A student should attempt solving a tough problem several times before looking at any hints in the back of the book.  For example, a student may work on a difficult problem for half of an hour or more, but not solve it.  She may feel frustrated and that she is getting nowhere.  But she is learning where her weaknesses and strengths are.  At some point she may want to look at a hint or review the concept notes of the chapter.

If you find that the lessons are taking too long, another option is to pick and choose challenge problems.

Highly Recommended

Overall, we thought highly of this book because there were challenging problems that made you think. 

The book seems creatively written with the intention of not only teaching Algebra, but also developing robust problem solving skills in its reader.  From the perspective of a teacher and especially if a student uses the materials as intended, I think it accomplishes this goal.

The Making of a Mathlete

I am often on the lookout for ways to broaden the horizons of my children, so this past school year I offered my 7th grade daughter the chance to take part in math contests.  She accepted.  In the fall, she took the American Mathematics Competition 8 (AMC), and this spring she competed in MathCounts.  As a home educating family why and how did we get involved in math competitions, and what was the experience like?

Why sign up? 

The biggest reason I considered this path was that I thought it to be a unique opportunity for her.  She is at ease with math, and I hoped she’d find it interesting.  Also, math competitions give students the chance to develop problem solving skills in a positive environment with others who share similar interests.

How to prepare for the AMC8

The AMC 8 is a 25 question, 40 minute multiple choice exam for middle school students.  Although it was easy to register for this competition,  I did have to locate a proctor.  I was fortunate to find a private school math teacher who gave her the exam.  The AMC 8 website also has additional locations for the AMC 8 at Higher Education Sites.  There is also a similar site for the AMC10/12.  If you want your child to take one of the AMC tests but cannot find a proctor, one of the locators may be worth a try.

To prepare for the AMC 8, she studied past exam problems from the AOPS Wiki.  This worked well for her, but you may also purchase past exams and solutions directly from the AMC website (see the Registration page).

How to prepare for MathCounts

We registered online and submitted a  ‘Homeschool Participation Attestation’ form in early fall.  To be eligible, a student must be in 6th, 7th, or 8th grade.  The process was relatively simple, and we had no problems entering her to compete as an Individual.  Homeschool Teams are also eligible to participate.

Once registered, they mailed us a packet which included the MathCounts School Handbook.  This is one of the several resources my daughter studied (another being Art of Problem Solving textbooks).   The earlier you sign up, the more time you’ll have to prepare.

Since we educate at home, I chose to be her coach.  Parent as coach is something to carefully consider, because it is a time commitment.  We set Fridays as our competition prep day and used Sunday afternoons to go over any problems that needed more discussion.  Another option to consider, depending on the laws in your state, is that you may also be able to find a local public or private school team for your child to join.  There are advantages to each case.

What was the actual contest like?

The contest consisted of a Sprint, Target and Team Round.  These rounds extended to about two hours total including breaks.  The Sprint Round was 40 minutes (30 questions).  The Target Round was about 30 minutes (8 problems in four pairs at 6 minutes per pair) and the Team Round was 20 minutes (with 10 problems solved by a team).  After this mental workout, the students were treated to a pizza lunch while the scores were calculated.  Following lunch, the top scoring 16 students were asked to move to the front to compete in what is known as the Countdown Round.

As the only event open to the public, The Countdown Round was a fast-paced, oral competition in which the students were then called two at a time up to a table in front of the 130+ students, coaches, and spectators.  These two competing students were asked a question on the overhead screen and were given only a short amount of time (about 45 seconds) to answer.  No calculators were allowed.  Once she had figured her answer, she had to respond by first pushing a button and then waiting to be called upon.  The first student who answered three questions correctly remained in the front to continue on to the next round.

It was exciting to watch the Countdown Round.  I’d never witnessed anything like it before.  I was impressed with the bravery the students displayed – competing in front of a large group of onlookers…answering tough questions…under strict time restraints!

The top three Teams, Individuals, and Countdown Round competitors received a trophy.  In addition, students who make it to the national level may even win scholarships.

*Contest Results* 

The preparation paid off.  I’m happy to report that my daughter did win a MathCounts trophy.  It was inspiring to see her be rewarded for her efforts – with several of the students congratulating her.  This encouragement has convinced her to continue, and she will be back to training this summer and fall for the next contests. 

Though it was not an easy thing to prepare for, I’m glad she agreed to take part. The sacrifices were worth it; I think it was a positive experience for her.

If you have a child who enjoys a challenge and would like to be around others interested in Math and Problem Solving, these competitions may be for you.