Jumat, 29 Januari 2010

Multiply and divide decimals by powers of ten (by 10, 100, 1000 etc.)

In this video I show, first of all, the common shortcut: you move the decimal point in the number as many steps as there are zeros in the number 10, 100, 1000 etc. For example:

2.16 × 10,000 = 21,600.0
It is as if the point moved four steps from between 2 and 1 to between zeros.

You can see better examples of this in my lesson Multiply and Divide Decimals by 10, 100, and 100 at HomeschoolMath.net.

Then, I also show where this shortcut originates, using PLACE VALUE charts. In reality, it's not the decimal point moving (it's sort of an illusion), but the digits of the number move within the place value chart (to the opposite direction from the way the decimal point seems to "move"). This explanation can really help students to understand the reason behind the "trick" of moving the decimal point.


Multiply & Divide Decimals by powers of ten

Selasa, 26 Januari 2010

Female teachers pass math anxiety to girls

This is a very interesting piece of research, and I personally believe in this "effect": that a teacher's attitude towards math can easily be passed on to his/her students.

In this case, all the teachers studied were elementary and female. I figure the same could happen with male teachers too, affecting boys, if the teacher feared and/or disliked math. It's just a lot less likely because most elementary teachers are female, and also because math anxiety is more common among females.

Girls may learn math anxiety from female teachers

The article also points to the best solution: the elementary teachers need trained much better in math so they can teach it confidently, including teaching the concepts and the 'why's of math.



Elsewhere:
Girls inheriting math anxiety from female teachers? at Casting Out Nines

Sabtu, 23 Januari 2010

Language Arts resources

You might wonder what is that kind of title all about? Well, while this is definitely a math blog, and I do not claim to be an expert on language arts, I just keep having people ask me about language arts resources, if I have any, or if I can recommend any. So, I want to answer this question here once and for all, and then I can just reference this blogpost whenever someone else asks the same.



I have been doing an "eclectic" mix of various language arts resources with my kids.

1. Learning to read.

Photo courtesy by Yves

I definitely am an advocate of teaching children to read as early as they are able. This is not so much for the purpose of them being able to do school work, but to increase their "horizons" of everything via books. Of course, this age at which a child might learn to read varies. I personally learned to read on my own at age 4. I asked my mom about the different letters and then started reading from a newspaper. But keep in mind, Finnish language is written nearly exactly as it is pronounced, so learning to read Finnish is very easy.

My oldest learned to read at age 2. The second child learned to read at age 3. I didn't force them; I just gently prodded if they'd be ready to learn the letters, and then proceed to reading. With both, I used "Teach Your Child to Read in 100 Easy Lessons" and I liked this book really well. Towards the end, I didn't like how some of the stories turned out, but at that point I was able to start using some really easy books from the library.

Another great resource we used a lot was the website Starfall.com. It is just fantastic for early readers. It has little animated movies for the letters, then little stories and interactive activities and problems, etc. Kids could spend hours on it at a time, if allowed.

I have always encouraged them to read lots of books of all kinds. And now they are both "book worms".


2. Spelling.

I started out by letting my Dear Daughter 1 (the older, or DD1) to just do some copywork from children's books. Then we went on to do the Explode the Code workbooks by a recommendation of a friend. They teach you phonics and spelling, and seemed to work just fine for her.

She's a natural speller and seems to remember words very well. She has not had any big troubles with spelling. I have also done dictation with her a few times here and there (choosing sentences from storybooks), but it has been quite easy for her so I haven't kept up with it continually.

Recently I purchased by DD1's own request a book titled Daily Paragraph Editing for grade 5 and she has thoroughly enjoyed it. It involves finding and correcting spelling and punctuation errors in short stories.

With the younger (DD2), I have used some of the beginning Explode the Code books, but they were going too fast for her. So I changed her into Evan Moor's spelling book for 1st grade. We have both liked that a lot, and I have ordered the 2nd grade one for her as well. She definitely needs much more help to remember how to spell words than her sister.

Recently she has also fallen in love with Spellingcity website. She wants to especially practice various animal words.


3. Vocabulary

Reading lots of books gives children a lot of vocabulary, so that is one means I've relied on (naturally). But besides that, I wanted to try out some vocabulary resources. I have used downloadable versions of 240 Vocabulary Words 4th Grade Kids Need to Know and 240 Vocabulary Words 5th Grade Kids Need to Know from Currclick. Nowadays we are using Wordly Wise books also. Both of these I've found to be quality resources.


4. Grammar

I have mainly used regular, used textbooks that I've picked from The Home School Book Depot. Grammar is, again, something that comes quite easily to my DD1.

I remember playing this silly game to teach her about past, present, and future tense: I would have a drink of water or something in front of me, and I'd say, "FUTURE TENSE: I will drink this water." Then I'd start drinking, and say, "PRESENT TENSE: I'm drinking or I drink now." Once I was finished, I'd say, "PAST TENSE: I drank the water." I remember she had so much fun with that silly thing, and it thorougly taught her the idea of what past, present, and future tenses are all about.

I have also used this cheap workbook: Brighter Child® English and Grammar, Grade 3. It was basic, as expected, but alright.

Some computer games she has played, such as CLUEFINDERS 3RD GRADE ADVENTURES or Smart Steps software have also practiced her grammar concepts and skills.


5. Writing

After learning to write the print letters, I used copywork with my DD1 (from various books). I don't even remember exactly how, but she has not had any problems not wanting to write. In fact, she still enjoys writing little made-up animal stories. The other kind of "story" writing I've used in those early years was to write about what she did yesterday or about some interesting event in her own life (such as a trip somewhere).

I have also always been very happy to see her use writing in her play. She might write a shopping list, or a list of names for her stuffed animals, or a Veterinarian sign for the door, or instructions for a little treasure hunt, etc. etc. Now her little sister is picking up that habit... and I think that's very good. I don't usually correct anything in these writings that are part of the play... because I feel it can encourage them to be confident about their writing skills and see writing as something useful and valuable.

The younger one is following in her sister's footsteps, and has written a collection of short animal stories. She's glued printed pictures of the animals to those pages (the printed pictures definitely inspired her to write them!). The stories are short, but fine for her age, definitely. They are full of spelling errors, of course, and the letters don't always stay on the lines. But I still feel those stories are little treasures - they're like a stepping stone into creative writing.

However, I definitely feel I don't have the capabilities of teaching writing in the manner that real English teachers do, as the grade levels advance. Therefore, I have a plan of getting my children take English courses from an online school (at this moment I'm thinking of Keystone, because they have middle school also). This is still future... and maybe I'll change my mind later on, but at this point it's something I wish to use.

Meanwhile, something else has popped up just recently. In the past, I have made math worksheets for Spidersmart tutoring centers, and they happen to specialize in reading/writing instruction, and they have an online program for that. So... I will be trying their program out for DD1. It involves reading real books, and then answering comprehension & vocabulary questions about the book, and writing some sort of essay or assignment about it. A REAL teacher will check the answers and give feedback! (That's the part I like most, because I feel somewhat inadequate to do that.) The student then has to correct the answers. I'm excited about the program, and I hope this will be beneficial.


So... that's it for now. Quite a mixture of resources, and I'm sure there will be more to add to the list later.

Rabu, 20 Januari 2010

Math Teachers at Play carnival

...is posted at Math hombre. Again lots of interesting things to explore and digest. Go check it out!

Selasa, 12 Januari 2010

Intel Math - a course for K-8 math teachers

I just found out about this and I do find it interesting: Intel is committing a large sum of money to train K-8 teachers to teach math. They're planning to train 100,000 math and science teachers.

Now, this "Intel Math" course is not about computers or technology; it really is about math. According to the flyer,
"Intel Math is an eighty-hour course for K-8 teachers who teach math. The course is co-facilitated by a practicing mathematician and a math educator. The emphasis is on teachers deepening their understanding of math. Intel Math examines the arithmetic, geometric and algebraic aspects of: operations, number theory, place value, rates, rational numbers, linear equations and functions through problem solving."
This course will be available at no cost to school districts. It is part of president Obama's "Educate to Innovate" campaign (see press release). A bit more information is found at www.inspiredbyeducation.com.

That is a step in the right direction. I have always felt that the BEST step to improve the state of math education in schools is to improve the teachers' knowledge of math, and not just to write new curricula or new standards. Those can help too, I'm not saying they won't. But a good teacher can override the influence of a mediocre curriculum - and a teacher that doesn't know math can make a good math curriculum go to waste.

Hat Tip goes to Wild About Math blog.

Minggu, 03 Januari 2010

Choosing a homeschool math curriculum

At this time of year there are traditionally many people who are just starting to homeschool that might be looking for a math program for your homeschool. I'd like to feature the Homeschool Math Curriculum Guide at HomeschoolMath.net to help all of you who are trying to find a math curriculum for homeschooling.

This guide contains:
  1. Articles on curriculum issues; such as "Choosing a homeschool math curriculum";

  2. Lists of cheap or free math curriculum resources;

  3. Lots and lots of reviews of all popular homeschool math curricula that visitors to my site have left over the past six years.
You are also welcome to leave a review of any curricula you have used in the past, and that way help others to decide.

Just head on over to the Homeschool Math Curriculum Guide to find all these resources!

Sabtu, 02 Januari 2010

Multiplying decimals by decimals

To multiply decimals, we are told to multiply as if there were no decimal points, and then make the answer have as many decimal digits as there are decimal digits in the factors.

In the video below, I compare multiplying decimals by decimals to fraction multiplication:


Do you know where this rule or "shortcut" comes from?

It comes from fraction multiplication. For example, 1.1 × 0.005 becomes (11/10) × (5/1000) when it is written with fractions. One decimal digit means the denominator is 10. Three decimals means the denominator is 1,000.

When you multiply the fractions, you get 55/10,000. Ten thousand as a denominator means the corresponding decimal has four decimal digits. So, the answer is 0.0055.

If you are a teacher, you can approach the rule for decimal multiplication by starting out with fractions, and using examples like the one above or the ones in the video to show students where the rule comes from.
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