Homeschool Blog Awards

Check out Belated 2006 Homeschool Blog Awards at a site dedicated to this:

www.homeschoolblogawards.com

Right now is the nomination stage. Voting starts some time in April.

"The HSBAwards Team have made some adjustments to categories, added NEW categories we didn’t have in 2005, are offering some awesome prizes for the winners, and we are settling into our new site to house the fun!"

Do you need drill to learn multiplication facts?

Continuing on the same lines as my previous post, what about multiplication facts and drill?

Well, the principle is similar: show them first the concept and patterns.

Then can come some plain drill.

But, I want to share with you a few more detailed points.

1. The main "patterns" in various multiplication tables of course follow from the concept of multiplication. For example, table of 2 is counting by 2's. You get table of 4 by doubling the answers in table of 2. You get table of 8 by doubling the answers in table of 4.
   
   Table of 10 is counting by 10s. Table of 5 - just take half of what the 10 ×
   
   Here are some resources to give you ideas about these kind of patterns and little "tricks".
   
   * Michele's Math
   * Times Tables' factsheets
   
   


2. We ALSO need them to know the tables "backwards".
   
   Let me explain.
   
   It's not enough to know that 8 × 7 is 56, when someone asks what is 8 × 7. The students ALSO need to know that 56 is 8 × 7, when given just the answer 56.
   
   This is very important. Students need this fairly soon when they start learning division. Later on it will be important when simplifying fractions or factoring.
   



3. Since it's important to know the tables backwards, I do not feel it's enough if the child is able to "figure out" the multiplication problems. I feel they need to memorize them, period, and not just be able to count or use some other method to find the answers.
   
   It's fine initially, and indeed very helpful, if the child figures out 8 × 8 by first going 8 × 2 and doubling that twice.
   
   But this fact also needs memorized so that later on, when she comes to the problem 64 ÷ 8, it won't take her 10 seconds to find the answer.
   
   Now you might ask why is that important? Because of long division, for example. It's going to be a pain to learn long division if you don't know your division facts by heart.
   
   Here's another reason: soon the student is going to have fractions to simplify. If you know your division facts, then simplifying 35/56 will be a breeze, otherwise a pain.
   

See how it all builds on the previous topics? You need to get a good foundation, and multiplication facts "both ways" is part of that foundation.

I have posted online the entire guide to effective oral drilling from one of my books.

The guide explains how the teacher and student can achieve memorizing multiplication tables in this manner where they know the answers and they know which answer goes with which multiplication problem.

Check also a list of online games that practice times tables. These are great after you've done some basic drill and the child needs reinforcement (practice!!!).

How NOT to drill addition facts

Some people think "drill is kill", and many people think it's necessary.

And of those that use it, not everyone knows HOW to actually drill math facts effectively.

You know, this is NOT the most effective way:

Shuffle the flash cards and start asking randomly.

Why? Because you are not utilizing techniques that help our brain remember quicker.

For example, it is easier to remember when the mind can tie the fact into something already known.

This is the idea behind silly rhymes such as "five, six, seven, eight - fifty-six is seven times eight."

Besides those, we want to show our children the PATTERNS in math.

So this is how I start drilling math facts (whether addition or multiplication):

I make a list on paper, IN ORDER. For example, lately we've been doing this with my daughter:

8 + 2
8 + 3
8 + 4
8 + 5
8 + 6
8 + 7
8 + 8
8 + 9

We went through the answers and notice how each one is ONE MORE than the next! That's a pattern!

Then I would point to a fact and say the problem so she'd both see and hear it (using two senses). You can additionally MOVE her finger on the chart with yours - so she's using three senses. This should help the auditory, visual, and kinesthetic learners all.

When I'd point to a fact further down the list, automatically she'd know it's more than a fact that is up on the list. It's a visual pattern.

First, I drilled just a few of them, namely 8 + 3, 8 + 5, and 8 + 8 until she remembered those.

After that, I would go first to 8 + 8 which she knew, and immediately after that to 8 + 9, and she was able to deduce it from knowing 8 + 8.

I would gradually add new facts in a similar manner - using the known facts as "stepping stones" so that the new fact was one more or less than a well-known fact.

And so we go "round and round" on this chart.

NOTICE THIS:
= > The chart creates an organized context for the addition facts.

Obviously, the child is also associating the position of the fact on the chart with the answer, and so after this is well remembered, it will still take another effort to remember the facts when they're in isolated context, such as in a game, or in a math book, or on flash cards.

But at least it is a very good start, I feel!

What are your thoughts?

Developing positive attitude

What are the incentives needed in order to develop a positive attitude in children and other students towards mathematics?

I don't think special incentives is the main factor in developing a positive attitude towards mathematics.

I feel it is sufficient to get a few of the basics right, and then that alone will take care of most of it, and then students will like math just fine.

Disliking math is not something that is inherent in us or in our kids. Little kids don't dislike math or numbers. They're just fine with them! This "I hate math" or "I don't like math" attitude seems to develop during school years.

Now, I also don't think that children are disliking reasoning, because they're happy to do puzzles and play games where you have to think.

And, students' negative attitude towards math also is NOT due to (school) math being difficult. The math we learn in school is not difficult. You don't have to be a math whiz to understand it.

If you can learn to read and to use computer software, surely you can learn basic math. It's not that complex.

So... here are the two main factors that I feel contribute most to what attitude children develop towards math:

1) The teacher's attitude.

If you love math and are enthusiastic about it, it is seen in your teaching, and your attitude will be somewhat contagious.

It's true the other way around as well: if you don't like math, yet you teach it, students will sense your attitude. (I've written about the teacher's attitude in this article.)


2) How the math is being taught.

Children can end up not liking math when it is taught in such a way that they don't understand it. And, when they don't understand math, then they don't like studying it.

When they don't understand it, then they don't like studying more of it.

The teacher obviously can influence A LOT how the math is taught, but curriculum or the book also plays a role.

So, if we as teachers can get these two basic things straightened out, our students should learn to like math... or at least not hate it.

---

See also:
Four habits of highly effective math teaching

Is your math curriculum coherent?

How to motivate and prevent math anxiety

New package products

There's so much going on with my Math Mammoth books that I again have a little "piece of news" along those lines.

I have made two new CD products, besides the one existing:


1) Blue Series package

This package contains all 16 Math Mammoth Blue Series books. It is available as a download and as a CD.

The price for this is $40 (download) and $45 (CD).


2) Golden/Green series package

Golden/Green series package is offered on a CD for $50. Remember that my Green series worksheets collections are totally duplicate content with the Golden ones, but the CD contains both series for convenience's sake. That way you may find quicker the exact worksheets for your needs.


3) ALL INCLUSIVE Math Mammoth CD

This CD contains all of it: the Blue series, the Golden series, and the Green series. Price: $80.

You can order all those above on this page

Los primeros libros Mamut Matemáticas

Finalmente he logrado que los tres primeros libros Mamut Matematicas (traducidos de los de Math Mammoth) están disponibles en el sitio web Mamut Matematicas.

Los libros que están listos son:

1) Valor posicional 1 - se trata de decenas y unidades.

2) Valor posicional 2 - se trata de centenas, decenas, y unidades.

3) Multiplicación 1 - concepto de multiplicar, y práctica de las tablas. Este libro en particular (o su versión inglés) ha recibido algunas reacciones 'muy entusiastas' de los compradores.

Todos los libros son electrónicos, o archivos PDF, lo que permita imprimir sus páginas repetidas veces.

También significa que los precios son bajos (entre $2 y $5) porque yo no tengo el costo de imprimir.

Los libros Mamut Matematicas son para usted, si...

* necesita materiales autodidácticos, los cuales se puede usar sin preparación.
* necesita flexibilidad (imprimir las páginas que necesita, cuándo los necesita, cuántas veces quiere)
*
* Y sobre todo.. usted quiere que su hijo realmente aprenda y entienda los "porque"s de matemáticas - y no solo memorizarla. Algo que explica los conceptos CLARAMENTE.

Estos textos se *encofan* en el entender de los conceptos y principios matemáticos, sin olvidar la repetición necesaria para dominar los procedimientos.

Vease usted mismo... las hojas ejemplares (gratis!) de cada libro le dan un buen vistazo de mis libros.

=> MamutMatematicas.com

Spanish versions of Math Mammoth books - Mamut Matematicas

Finally...! I have three books available on the Spanish website MamutMatematicas.com:

Valor Posicional 1 y 2

Multiplicacion 1

These are the exact translations of my existing books Place Value 1, Place Value 2, and Multiplication 1.

I will make a separate blogpost about them in Spanish as well...

Need multiplication tables practice or games?

Remember, I have created a list of the best online activities, games, tutorials, etc. for this (and other topics as well).

All kids love games, and with multiplication tables, it's one way to give them more practice.

The complete list of online activities is here, but I'll copy and paste a sample to this blogpost:

---

Multiplication grid
Drag the scrambled answer tiles into the right places in the grid as fast as you
can!

Multiplication.com
Strategies, worksheets, games just for times tables.

The Times Tables at Resourceroom.net
Fill in the multiplication chart - partially or the whole thing - or take quizzes, and get graded.

Explore the multiplication table
This applet visualizes multiplication as a rectangle.

Table Mountain
Climb the mountain with 20 questions from a selected table.

Multiplication table Challenge
100 questions, timed.

Multiplication mystery
Drag the answer tiles to right places in the grid as they are
given, and a picture is revealed

Mr. Taylor's Multiplication Facts Drill
Simple practice (click on the right answer) for the easy ones, the hard ones, the monsters, or them all.

Multiplication memory game
Click on corresponding pairs (problem-answer).

---

You will find a few more here, plus some recommended books and software.

News

A few "news" items...

1) I added some images and banners for others to use when linking to Math Mammoth website over here - including images that say "I use Math Mammoth" if you'd like to use such!





2) California Faces Critical Shortage of Math and Science Teachers

3) Kentucky is considering monetary incentives for math and science teachers - as we all know, those qualified to teach math often find better paying jobs elsewhere.

Math and Fun

I strongly believe math can be quite fun in some aspects of it; yet I also believe that not all of it has to be all fun.

It's good for students to learn to work through problems that are just that: work and no fun. That's what real life and real jobs will involve too.

Of course most of us try to get an occupation that we are interested in and can enjoy for the most part, but even then, we probably won't like all parts of our "dream job".

So in math, as in all education, we need to let our students learn to work, struggle, prowl through it.

But we can also let our students have some fun every once in a while. This can make them enjoy math, like math, appreciate it, like learning, and so on. I'm sure it's easy to agree with that.

In lower grades you might have more play than work, and then later on it's more work than play. For example, maybe you're studying coins and their values. Your child can play with real coins, do paper-and-pencil problems, and maybe play an online game about money or coins.

When studying algebra, it is going to be more on the work side, since algebra is similar to learning the "alphabet" and "basic grammar" of a new language. The "fun" topics tend to come after you've learned your basic language and can go off exploring (such as in calculus).

So I feel there is a balance between these two.

---

Along these lines, I've recently turned my attention to a math website Called Googol Learning whose founder Susan Jarema is making math to be googols of fun (googol is the number 10¹⁰⁰, or 1 followed by 100 zeros).

For example, she encourages you to, and gives ideas and resources for starting your own math club! This could be a family math night, or a monthly gathering of a few kids and adults together.

Susan uses a lot of music to make things more fun. She's produced audio CDs that combine math, music, and story telling for better learning.

Susan also gives interactive workshops in schools and homes.

One of these workshops is also now recorded on a CD (Crazy 4 Math), and for another one there is a family and teacher's kit (Discovery Multiplication Math Program).

The site also features a list of virtual field trips about volcanoes, tsunamis, earthquakes, or how many everyday things are made.

And what would be math fun without games? On her site you'll also find a list of best online math games.

Price change ahead...

It just so happens that due to something 'in the works' behind the scenes (to be announced soon!) concerning the Math Mammoth books, I am forced to raise the price on the "blue series" package for 16 ebooks.

I wasn't really planning on it myself, but like I said, it's a situation that cannot be helped, due to something I'm not disclosing as of yet...

This price has always been a tremendous deal. Currently, with the $32, it is a 48% discount as compared to buying the 16 books individually, and $36 on CD.

Now, I will be having the package download for $40, and the CD for $45. This price ($40) is then almost exactly 35% off of the price of buying the ebooks individually.

I have of course been adding a little material to the books even in the last few weeks, and keep doing so, little by little, so its value has increased even in that sense.

The latest calculations are that my 16 books package for $40 delivers you 810 pages of math materials. (That count is NOT including answer keys or copyright pages but just text & problems.)

This price change only applies to the package and CD, and not to any of the individual books. I am not planning to raise the price on those.

So if you are thinking about buying the package for the lower price, please do so before next week.

More info on the BLUE SERIES books

Buy Math Mammoth package deal at Kagi

Some humor

They say laughter is the best medicine - and it has been proven in scientific studies that laughing does help our health. Keeps stress at bay!

So here's a joke for the computer oriented...

and for those frustrated by exams... I especially liked the last picture! You get so deep into your calculations that you feel you get lost or so...

And there's lots more in the internet, some good some bad, some worse etc. Here are two more for you quoted from a certain page (see link at the bottom):

A physicist and a mathematician are sitting in a faculty lounge. Suddenly, the coffee machine catches on fire. The physicist grabs a bucket and leap towards the sink, filled the bucket with water and puts out the fire. Second day, the same two sit in the same lounge. Again, the coffee machine catches on fire. This time, the mathematician stands up, got a bucket, hands the bucket to the physicist, thus reducing the problem to a previously solved one.

An chemist, a physicist, and a mathematician are stranded on an island when a can of food rolls ashore. The chemist and the physicist comes up with many ingenious ways to open the can. Then suddenly the mathematician gets a bright idea: "Assume we have a can opener ..."

Click here to read more of these physicist, mathematician, engineer jokes.