"Understanding the WHY of Algebra" or "Should Elementary Kids Learn Algebra?"

[Rosie]

Since finding Singapore and Miquon math (and reading Liping Ma's book among other things) I've found myself very concerned with whether or not my children have a conceptual understanding of what they're doing in mathematics. I do not want to teach procedure before the foundational understanding is there. We mostly use Base 10 blocks and Cuisenaire rods to demonstrate what we will eventually only be doing on paper with abstract symbols.

 

This has worked out extremely well for us so far. I went through school with mostly a procedural understanding of the algorithms/formulas. I was very good at memorizing so I got good grades but I never really understood what I was actually doing. I didn't have a clear understanding of how place value and the base ten system had anything to do with addition/subtraction/multiplication/division and algebra was just playing around with letters and numbers to me. So now I'm learning along with my girls and seeing the "why" behind it all. I love it and I want them to continue to learn this way and not the way I was taught.

 

With that being said, they are keen to learn a bit of algebra and I know some algebra will be introduced pretty soon in the Primary Challenge Math book which we are doing once per week. My concern is that they will be just memorizing steps (combine like terms, do the same operation to both sides of the equal sign, etc.) without understanding WHY.

 

I don't understand why so how can I teach them what I don't know?

 

I recently went through the Singapore CWP 3 and 4 books to prepare myself for what we're heading toward and I can see how the bar diagrams often give a visual for the algebra that you COULD do if you knew algebra. That was eye opening to me because, as I said, to me algebra was always just a bunch of numbers and letters that you have to move around in certain ways based on certain rules that had nothing to do with anything.

 

Another eye opening moment for me was when I recently watched an AOPS Pre-Algebra video (Square of a Sum) and realized why I was taught the FOIL method for multiplying two binomials. There actually is a reason and it actually has to do with something in real life! Imagine that!

 

I want my girls to always have those moments where they understand what it's really all about...

 

So I guess my two questions are:

 

Would it be a hindrance to them to learn some basic algebra rules right now to satisfy their curiosity?

 

Can someone help me with the WHY of algebra?

[Beth in SW WA]

 

Can someone help me with the WHY of algebra?

 

Hands-On Equations demystifies basic algebra. It shows the 'why' & 'how' in a way that a young student can grasp. HoE has been more helpful to dd8 than cwp bar models -- in terms of prealg exposure.

[regentrude]

My concern is that they will be just memorizing steps (combine like terms, do the same operation to both sides of the equal sign, etc.) without understanding WHY.

 

Would it be a hindrance to them to learn some basic algebra rules right now to satisfy their curiosity?

 

Can someone help me with the WHY of algebra?

 

A few thoughts:

I do not think it can have any ill effect if they learn some basic algebra now.

The bolded above is the ONLY principle of introductory algebra, up linear equations, that needs to be understood: two expressions connected by the equal sign behave like two pans of a balanced scale. Whatever you do to one side, you must to to the other side as well, so the scale remains balanced (and the two expressions on the two sides of the equal sign remain equal.). Why? Because that is the meaning of the equal sign!

That's it. Period. The rest is practicing the application of this simple concept. All problem solving is based on this principle. You do manipulations to both sides of the equation with the goal of isolating your variable. (it gets a bit more complicated with quadratics, but this basic principle is in effect throughout all of algebra.)

 

As to the WHY of algebra, I am not sure I understand your question. Do you mean: why do I need algebra?

You need algebra techniques to solve problems that contain unknown quantities. The equations you have to solve can come from everyday examples (shopping, age, geometry) or from science (physics gives a lot of examples, such as: if I go at speed v for a time t, what distance d do I cover? )

Or do you mean: why do I write the equation to describe a certain problem the way I do? That will be explained and trained in an algebra course; you need some practice to do that.

Using algebra effectively consists of two steps: translating a problem into equations (which is the harder part) and solving the equations (which is where the procedures come in that must be mastered until they become automatic.)

Edited January 1, 2012 by regentrude
"consists" instead of "contains". Typing faster than thinking.

[Rosie]

Hands-On Equations demystifies basic algebra. It shows the 'why' & 'how' in a way that a young student can grasp. HoE has been more helpful to dd8 than cwp bar models -- in terms of prealg exposure.

 

I've seen this mentioned a few times on the boards here. I'll look into it. Thank you!

[Beth in SW WA]

Using algebra effectively contains of two steps: translating a problem into equations (which is the harder part) and solving the equations (which is where the procedures come in that must be mastered until they become automatic.)

 

:iagree: and could not have said it nearly as clearly as Regentrude. Whatever she says is golden. :)

 

HoE Verbal Problems book deals with the translation of problems to equations in a way that youngers can understand. It's at their fingertips. Literally. (Sorry if I sound like a HoE commercial. I believe in it THAT much.) The 200 verbal problems in the kit offer a big headstart to algebraic thinking.

[Rosie]

As to the WHY of algebra, I am not sure I understand your question. Do you mean: why do I need algebra?

You need algebra techniques to solve problems that contain unknown quantities. The equations you have to solve can come from everyday examples (shopping, age, geometry) or from science (physics gives a lot of examples, such as: if I go at speed v for a time t, what distance d do I cover? )

Or do you mean: why do I write the equation to describe a certain problem the way I do? That will be explained and trained in an algebra course; you need some practice to do that.

Using algebra effectively contains of two steps: translating a problem into equations (which is the harder part) and solving the equations (which is where the procedures come in that must be mastered until they become automatic.)

 

Yes, I mean, "Why do I write the equation to describe a certain problem the way I do?" I took Algebra I & II, Geometry, and Trig/Pre-calc and never even thought to ask WHY. How on earth did I get As in those classes without knowing why I was doing what I was doing? Something seems seriously wrong with that.

 

There's a missing piece of the puzzle and I'm not sure what it is. Maybe that's why my question wasn't clear. I don't know what I don't know.

[Rosie]

Using algebra effectively contains of two steps: translating a problem into equations (which is the harder part) and solving the equations (which is where the procedures come in that must be mastered until they become automatic.)

 

 

But when translating a problem into an equation I would just remember rules like "of means multiply" or "d=rt". I was still just applying rules without understanding... I think. Maybe I understand better than I think I do. I just don't know.

 

I'm going to get an AoPS book to work through. Just trying to decide if I should start with the Pre-Algebra or Algebra one....

[regentrude]

Yes, I mean, "Why do I write the equation to describe a certain problem the way I do?"

 

That is actually the hard part! A good algebra program will teach you and your students to translate a word problem into equations.

 

Many students learn only the procedural steps in school (and teachers who do not understand math are a big part of the problem); they are the ones who claim to be "good at math except for word problems". Ahem, they are not good at math, because they are missing the crucial step.

 

If, however, you recognize the importance of this step, you will learn it from a good algebra program! There is no easy recipe answer; you learn to translate a variety of problems into equations by doing it, by seeing it done, by thinking about the problems. It comes with experience. Once you realize that THIS is what you need to be doing, you can figure it out with the help of a good book - even if your school teachers settled for procedure drill without understanding.

[kalanamak]

I like listening to Khan's lectures.I also work problems.

 

My son gets frustrated with learning the why before the algorithm. He wants an answer. Sometimes he gets going down the right path, sometimes not.

Once we learn the algorithm, I slow down on the problems a little, and ask HIM why. It is my contribution to his "discovery" math. :)

We look at a word problem. (We are currently working on the algorithms for word problems, e.g. what equation will give you the answer. Okay, what do you need to do with given info to GET the numbers for the equation that will give you the answer.) These provide the "why" as in "why are we learning this" and the why "why" of "why we do this" is useful: to solve problems, not fill in the blanks in the workbook.

 

If he mutters and plunges and gets the right answer, next I ask him how. This is harder, but I think he remembers how often I've told him he has to be able to explain the easy stuff so that it easy stuff is EASY while he's doing the hard stuff.

 

Since math is a continual "my, my, something more I don't know", every now and then I go through a problem and point out all the things he now knows and uses without thinking to get to his answers. Adding, remember learning adding? Carrying, remember moving our unit cubes to the next column on the place value mat? Etc. It helps us BOTH keep in perspective just how far we have come.

 

I think I'm raving a little. Not sure if this has anything to do with what you are thinking, but obviously it has been pressing on my mind recently. :D

To sum up: I do word problems here and there on scraps of paper to keep my mind fresh and to see the why of things mathematical (both why they work and why we do them.)

[kalanamak]

Yes, I mean, "Why do I write the equation to describe a certain problem the way I do?" I took Algebra I & II, Geometry, and Trig/Pre-calc and never even thought to ask WHY. How on earth did I get As in those classes without knowing why I was doing what I was doing? Something seems seriously wrong with that.

 

I try to rewrite things in as many ways as I can, even the longer and more complex ways. E.g. from this morning's lesson:

 

2/3 of 144= 2/3 x 144= 2/3 x 144/1= 2x144/3x1= 144/3 x2= 288/3= 576/6=200/300x144= 2(144)/3 etc.

 

I try to write these equivalencies in 5 minutes, filling a whole page if I can. While I've not heard this discussed per se, I think of it as mental juggling to develop my PUFM muscles. As I work my way up math, kid in tow, my juggling has gotten more and more complex.

[regentrude]

But when translating a problem into an equation I would just remember rules like "of means multiply" or "d=rt". I was still just applying rules without understanding... I think. Maybe I understand better than I think I do. I just don't know.

 

Let's take the d=rt problem.

You do not need to memorize this! If you understand what the term "speed" means, you KNOW it is a distance divided by the time it takes to travel that distance (70mph means you go 70 miles in one hour). That is all. No need to memorize anything. If a speed = distance/time, then you can use this knowledge to solve for distance or for time or for speed, just depending on the specific problem.

 

For ANY given problem, there is a way to come up with the equation without memorizing anything. And the cool thing is: once you understand something, you will not ever forget it. (That's what I love about physics - I'd go crazy if I had to memorize a bunch of meaningless formulas.)

[ErinE]

I think regentrude has given you great advice. I would also encourage you to keep the age of your children in mind. So long as you continue to do CWP and Primary Challenge math, the rudimentary algebra skills are being developed.

 

One final piece of advice, if you don't already do so, require your children to write out the equation before solving. Liping Ma gave a great lecture about how in China, the written equation is as important as the final answer. If I can find the link, I'll post it it but just as an example:

 

X + Y = 5

 

For a Chinese student, the X+Y is just as important as the five. Ma said there is a particular name for this that doesn't translate into English because equation would be all parts of the math sentence, not just the addends. In my opinion, making sure the child is articulating and writing out all parts of the equation are very important in developing algebra skills.

[Kathleen.]

Another vote for Hands on Equations. We don't have it, but it sounds like what you're looking for. It definitely explains the why.

[garddwr]

There are ways to present algebraic ideas to children in concrete ways that they can understand. A few months back I came up with a fun way to help my kids solve for an unknown, using a basic balance scale. I blogged about it here.

 

I'm intrigued by the Hands on Equations idea, although I wonder how much of it I could replicate on my own without buying their system (I've spent way to much this past year on homeschooling stuff!) I've also seen a Math-U-See demo video where they represent an equation visually--maybe it was a quadratic equation? I don't remember. I think anything you can do to present things in a hands-on or visual way for young children helps with the conceptual development, and better yet if they get a chance to start figuring out the rules on their own.

 

--Sarah

[letsplaymath]

With that being said, they are keen to learn a bit of algebra ... So I guess my two questions are:

 

Would it be a hindrance to them to learn some basic algebra rules right now to satisfy their curiosity?

 

Can someone help me with the WHY of algebra?

 

In my Elementary Problem Solving Series of blog posts, I demonstrate how to use "word algebra" to solve 2nd and 3rd grade word problems, and then how to transition from the words to regular algebra when your student is ready. By starting with simple word problems and working your way up to the hard stuff, you gradually absorb and make sense of the logic of algebra.

 

This may or may not be helpful to you, but it does give you another option to consider. If you're interested, read these posts:

Elementary Problem Solving: The Tools

 

Penguin Math: Elementary Problem Solving 2nd Grade

 

Ben Franklin Math: Elementary Problem Solving 3rd Grade

 

Algebra: A Problem in Translation

[Rosie]

Hands-On Equations demystifies basic algebra. It shows the 'why' & 'how' in a way that a young student can grasp. HoE has been more helpful to dd8 than cwp bar models -- in terms of prealg exposure.

 

Beth, I just watched a few videos about this. I really don't like how they use a star to represent a negative number. I think my kids could handle negatives better than the whole star thing. You haven't found that to be a problem?

[kiana]

I recently went through the Singapore CWP 3 and 4 books to prepare myself for what we're heading toward and I can see how the bar diagrams often give a visual for the algebra that you COULD do if you knew algebra. That was eye opening to me because, as I said, to me algebra was always just a bunch of numbers and letters that you have to move around in certain ways based on certain rules that had nothing to do with anything.

 

Another eye opening moment for me was when I recently watched an AOPS Pre-Algebra video (Square of a Sum) and realized why I was taught the FOIL method for multiplying two binomials. There actually is a reason and it actually has to do with something in real life! Imagine that!

 

 

Regentrude already said almost all of what I was going to say ... but I'm going to comment specifically on the bolded.

 

That's the specific reason that I really, really, strongly dislike the use of the FOIL mnemonic. In the first place, it only applies to multiplying a binomial by a binomial. In the second place, it obfuscates what's going on -- which is really just applying the distributive property more than once. And in the third place, it encourages memorization over understanding.

[Rosie]

Let's take the d=rt problem.

You do not need to memorize this! If you understand what the term "speed" means, you KNOW it is a distance divided by the time it takes to travel that distance (70mph means you go 70 miles in one hour). That is all. No need to memorize anything. If a speed = distance/time, then you can use this knowledge to solve for distance or for time or for speed, just depending on the specific problem.

 

For ANY given problem, there is a way to come up with the equation without memorizing anything. And the cool thing is: once you understand something, you will not ever forget it. (That's what I love about physics - I'd go crazy if I had to memorize a bunch of meaningless formulas.)

 

 

I can see in arithmetic how my girls have been able to take the facts to 10 that they've memorized and used that to do EVERYTHING else in their heads - even multiplying and dividing some larger numbers. I like hearing that that's possible with algebra on up, too. I've been reading articles here and there by actual mathematicians and they seem to convey that idea, too - that you can take a very small body of knowledge and apply it to a wide range of problems without having to memorize hundreds of formulas. That is one of the things that draws me to AOPS and is part of the reason I'd love for my girls to go through at least a few of their books.

 

I always thought I was so good at algebra because I had all the formulas memorized. I've tutored/taught math to so many people! And now I'm realizing that I really never knew what I was actually doing in the first place. But there's no reason I can't learn what I missed in high school level math! I'm doing it with elementary math. I guess I'll just keep going!

[Rosie]

Regentrude already said almost all of what I was going to say ... but I'm going to comment specifically on the bolded.

 

That's the specific reason that I really, really, strongly dislike the use of the FOIL mnemonic. In the first place, it only applies to multiplying a binomial by a binomial. In the second place, it obfuscates what's going on -- which is really just applying the distributive property more than once. And in the third place, it encourages memorization over understanding.

 

Yes, I can see what you mean. And I always thought I was doing people a favor by teaching them that little trick!

 

I'm starting to see that maybe all the things I learned in algebra actually have to do with each other. Am I right? I always saw it as all these separate pieces of information to be memorized that didn't really form any type of cohesive whole, but that's not how it is, is it?

[Rosie]

Liping Ma gave a great lecture about how in China, the written equation is as important as the final answer.

 

 

If you can find the link, I'd love to hear/read it! Thank you!

[Rosie]

There are ways to present algebraic ideas to children in concrete ways that they can understand. A few months back I came up with a fun way to help my kids solve for an unknown, using a basic balance scale. I blogged about it here.

 

I'm intrigued by the Hands on Equations idea, although I wonder how much of it I could replicate on my own without buying their system (I've spent way to much this past year on homeschooling stuff!) I've also seen a Math-U-See demo video where they represent an equation visually--maybe it was a quadratic equation? I don't remember. I think anything you can do to present things in a hands-on or visual way for young children helps with the conceptual development, and better yet if they get a chance to start figuring out the rules on their own.

 

--Sarah

 

I like your idea of using the balance. I was thinking of doing something like that. It does seem like you could easily replicate the HOE stuff, doesn't it? I need to look into it more....

[Rosie]

In my Elementary Problem Solving Series of blog posts, I demonstrate how to use "word algebra" to solve 2nd and 3rd grade word problems, and then how to transition from the words to regular algebra when your student is ready. By starting with simple word problems and working your way up to the hard stuff, you gradually absorb and make sense of the logic of algebra.

 

This may or may not be helpful to you, but it does give you another option to consider. If you're interested, read these posts:

Elementary Problem Solving: The Tools

 

 

Penguin Math: Elementary Problem Solving 2nd Grade

 

 

Ben Franklin Math: Elementary Problem Solving 3rd Grade

 

 

Algebra: A Problem in Translation

 

 

Thank you, Denise. I've gotten some helpful ideas from your blog before! I'll go check these links out!

[Beth in SW WA]

Beth, I just watched a few videos about this. I really don't like how they use a star to represent a negative number. I think my kids could handle negatives better than the whole star thing. You haven't found that to be a problem?

 

Not a problem at all.

 

Students are not taught that star is 'negative' -- rather that star is the opposite of x.

[jenbrdsly]

Not a problem at all.

 

Students are not taught that star is 'negative' -- rather that star is the opposite of x.

 

 

I agree. We have just done the first few star lessons and it hasn't been a problem at all. Here's a HOE blog post. I love it so much I sound like I'm their salesman, but I'm not! :tongue_smilie:

[boscopup]

I agree. We have just done the first few star lessons and it hasn't been a problem at all. Here's a HOE blog post. I love it so much I sound like I'm their salesman, but I'm not! :tongue_smilie:

 

So does it ever get any harder than what's in your blog post? Since they don't actually use two variables (just x and "star"), the samples looked like they'd stay easy the whole time. We did something similar in MM with balances on the page, and she got into solving for 2 variables (shapes in this case) by using two balances. After that one section of MM, it seems like HOE would be too easy.

 

I too dislike the star thing. Why not use -x? :confused: I don't see the need for star. Reminds me of teachers saying you can't subtract a big number from a small number in 2nd grade subtraction with regrouping. Yes, you can, but you would go negative. Why obfuscate something that isn't really as scary as it sounds. We don't need to avoid negative numbers at all costs. :001_smile:

[boscopup]

I had to look up FOIL. I never heard of it. Of course it's been awhile. ;)

 

I was taught FOIL at one point, but I couldn't remember what it stood for and had to look it up also.

 

I hate hate hate math acronyms! I can never remember what they mean. People will use that acronym for order of operations, and it's easier for me to just remember the order itself. And FOIL? Once again, it's easier for me to remember that you need to multiply each piece by the other pieces because of the distributive property. The FOIL term doesn't even make much sense to me. First, Outside, Inside, Last? It's harder for me to figure out what that's talking about than to just remember that when you have polynomials in parenthesis multiplied by each other, you need to multiply each combination between the two. FOIL is going to fail when you have more than 2 items in the parenthesis, so it seems a silly way to teach. :tongue_smilie:

[Dana]

I too dislike the star thing. Why not use -x? :confused: I don't see the need for star. Reminds me of teachers saying you can't subtract a big number from a small number in 2nd grade subtraction with regrouping. Yes, you can, but you would go negative. Why obfuscate something that isn't really as scary as it sounds. We don't need to avoid negative numbers at all costs. :001_smile:

 

Because the negative notation stands for two different things. One is the operation of subtraction and one is the additive inverse.

 

There are times when the mathematical notation that's developed over the years does cause problems with how a student learns. One other example is with function notation. Students get used to parentheses meaning multiplication with arithmetic and then when you find f(3) they try to multiply rather than evaluate.

 

So I can understand using a different symbol to distinguish between an operation and an inverse at an early level.

 

As for FOIL, when I teach it, I refer to it as "the f word in math". HATE, HATE, HATE it. Yes, a good understanding of multiplication of two binomials is essential for factoring, but it's so limiting with multiplication.

[Poke Salad Annie]

A few thoughts:

I do not think it can have any ill effect if they learn some basic algebra now.

The bolded above is the ONLY principle of introductory algebra, up linear equations, that needs to be understood: two expressions connected by the equal sign behave like two pans of a balanced scale. Whatever you do to one side, you must to to the other side as well, so the scale remains balanced (and the two expressions on the two sides of the equal sign remain equal.). Why? Because that is the meaning of the equal sign!

That's it. Period. The rest is practicing the application of this simple concept. All problem solving is based on this principle. You do manipulations to both sides of the equation with the goal of isolating your variable. (it gets a bit more complicated with quadratics, but this basic principle is in effect throughout all of algebra.)

 

 

 

:iagree:

 

This is the one concept I have taught since we started with MEP 1. I drill this in over and over as we work our problems on a dry-erase board. Of course, once they're working things out in their head, they're flying past those steps, but I make sure to demonstrate by writing on our board what we've done. If something gets out-of-whack by a false step in a problem, I make all kinds of silly sounding alarm noises, and stand up to show my arms at my sides tipped over. Makes for a great visual---cheap too! :D

 

If you can get across the concept of maintaining balance to the equation, you've really laid the foundation for anything else that follows along later.

[Beth in SW WA]

So does it ever get any harder than what's in your blog post? Since they don't actually use two variables (just x and "star"), the samples looked like they'd stay easy the whole time. We did something similar in MM with balances on the page, and she got into solving for 2 variables (shapes in this case) by using two balances. After that one section of MM, it seems like HOE would be too easy.

 

I too dislike the star thing. Why not use -x? :confused: I don't see the need for star. Reminds me of teachers saying you can't subtract a big number from a small number in 2nd grade subtraction with regrouping. Yes, you can, but you would go negative. Why obfuscate something that isn't really as scary as it sounds. We don't need to avoid negative numbers at all costs. :001_smile:

 

Have you seen HoE Verbal Problems Book? It includes word problems that students translate to equations using the pawns/cubes. We also write the traditional alg equation as well.

 

Your second paragraph above implies that you don't understand how the program works. It is used successfully in classrooms all over the country with great results. But most importantly -- it is highly effective here.

 

ETA: My dds are 7 & 8. I can't imagine a better way to teach alg at this young age. :)

Edited January 2, 2012 by Beth in SW WA
clarify

[Tress]

All this talk about HOE, makes me :drool:.

 

Does anyone know of a place that sells HOE, other than the publisher or Rainbow? The shipping at the publisher is 43$....and then there are customs taxes....:001_huh:. Rainbow isn't really better.

[kiana]

I'm starting to see that maybe all the things I learned in algebra actually have to do with each other. Am I right? I always saw it as all these separate pieces of information to be memorized that didn't really form any type of cohesive whole, but that's not how it is, is it?

 

Exactly. 100% correct.

 

What you have just said is honestly one of the main points of any of our 'mathematics for liberal arts' classes.

[Kathleen.]

All this talk about HOE, makes me :drool:.

 

Does anyone know of a place that sells HOE, other than the publisher or Rainbow? The shipping at the publisher is 43$....and then there are customs taxes....:001_huh:. Rainbow isn't really better.

 

ARE YOU SERIOUS???? :001_huh:

[Kathleen.]

I just looked....check out amazon.com ($3.99) and eaieducation.com ($7.99) so they say....

 

:)

[Stellalarella]

Is there a link where I could watch the video from AoPS on the Sum of Squares, or is it something I would need to purchase?

[Beth in SW WA]

Is there a link where I could watch the video from AoPS on the Sum of Squares, or is it something I would need to purchase?

AOPS Prealg videos here.

[Kathleen.]

For those that have HOE...

What's in the three manuals shown in the kit? Are they an absolute must? Could you get by without them? Just wondering what's in them?

I want to get this for my 2nd grader maybe at the end of the school year.

[Tress]

I just looked....check out amazon.com ($3.99) and eaieducation.com ($7.99) so they say....

 

:)

 

I wish....

 

The only seller on Amazon that is willing to ship internationally is asking 148$ for the HOE set :glare:. On the eaieducation.com site they don't even mention international shipping, which usually doesn't bode well.

 

I think I need to move to the US :D, I have a mile long wish list of things I want but can't afford the shipping on :tongue_smilie:.

 

But thanks for taking the time to search, Kathleen! Appreciate it.

[Rosie]

Is there a link where I could watch the video from AoPS on the Sum of Squares, or is it something I would need to purchase?

 

 

http://www.artofproblemsolving.com/Videos/external.php?video_id=30

[Stellalarella]

http://www.artofproblemsolving.com/Videos/external.php?video_id=30

 

 

Thanks much!

[Kathleen.]

I wish....

 

The only seller on Amazon that is willing to ship internationally is asking 148$ for the HOE set :glare:. On the eaieducation.com site they don't even mention international shipping, which usually doesn't bode well.

 

I think I need to move to the US :D, I have a mile long wish list of things I want but can't afford the shipping on :tongue_smilie:.

 

But thanks for taking the time to search, Kathleen! Appreciate it.

 

Sorry, I didn't catch your location until now. :o

[garddwr]

All this talk about HOE, makes me :drool:.

 

Does anyone know of a place that sells HOE, other than the publisher or Rainbow? The shipping at the publisher is 43$....and then there are customs taxes....:001_huh:. Rainbow isn't really better.

 

The Hands on Equations company does free webinars about how to use their curriculum. You could attend one or two and probably figure out enough to create a similar system on your own. It wouldn't be exactly the same, but you could probably get a lot of the benefit that way.

 

http://borenson.com/WorkshopsWebinars/PublicWebinars/tabid/913/Default.aspx

 

--Sarah

[jenbrdsly]

Have you seen HoE Verbal Problems Book? It includes word problems that students translate to equations using the pawns/cubes. We also write the traditional alg equation as well.

 

Your second paragraph above implies that you don't understand how the program works. It is used successfully in classrooms all over the country with great results. But most importantly -- it is highly effective here.

 

ETA: My dds are 7 & 8. I can't imagine a better way to teach alg at this young age. :)

 

That's just what I was going to say. The Verbal book is really tough looking. It reminds me of problems they use to give in our high school Academic League. My plan is to get through the first 26 lessons, and then start working through the verbal book with my son over the summer.

In regards to what is in the kit, I purchased the basic kit and the verbal problem book, but did not buy the video. Beth did buy the video, but she is working with two kids at the same time, so that seems rather cost effective. We have been fine without the video, and our total cost was under $80.

P.S. We are on lesson 10, which my DS6 just asked to do before dinner "for fun". :001_huh:

[Tress]

Sorry, I didn't catch your location until now. :o

 

No, my fault entirely. I should have mentioned international shipping, before giving everyone interested in HOE a terrible fright! ;)

 

The Hands on Equations company does free webinars about how to use their curriculum. You could attend one or two and probably figure out enough to create a similar system on your own. It wouldn't be exactly the same, but you could probably get a lot of the benefit that way.

 

http://borenson.com/WorkshopsWebinars/PublicWebinars/tabid/913/Default.aspx

 

Thanks, Sarah. You and Nansk have given me some very good ideas to try to do this myself.

[Kathleen.]

In case you're interested.....

Last night I saw on Homebuyers Co-op "Hands on Equations" listed under the new items for 50% off section. HOE has only the Home Kit for sale ($7.50 off) when you type in the coupon code. It's the $85.00 kit with the DVD and beginning student book.