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Story-based Algebra?


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Hello!

 

I am in the midst of re-vamping our plans.  A bit late in the season, but there it is.

 

My 12yo has been doing Algebra this year, but it's been slow going.  Not because the math or concepts are hard, but because she doesn't care.  She lives and breathes story, and she really wants to know why she should care about math. 

 

I'm thinking about doing Life of Fred with her, because I know it has a story to keep her going, but will it explain why she should care about binomials, etc?  

 

Are there any other programs that I should have on my radar?

 

Thanks!

Anabel

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This came to mind - Interactive Mathematics Program.  I stumbled upon it when I was trying to find a fun and memorable way to teach integers to my kids.  I watched this video and learned about IMP.  It's a four year math program intended for high school.  When I looked it up it's basically putting math in a story format that I find easy enough to use with kids younger than high school.  The background on the math program is that the publishers are trying to teach students in a more concrete way and so it does not follow the traditional math course sequence of Alg.1, Geo, Alg. 2 and Calc.  The books are loaded with ideas and I think there are a lot of fun stories that might appeal to your daughter.

 

Here's an excerpt of the story they are referring to in the video:

 

In a far-off place, there was once a team of amazing chefs who cooked up the most marvelous food ever imagined. They prepared their meals over a huge cauldron, and their work was very delicate and complex. During the cooking process, they frequently had to change the temperature of the cauldron in order to bring out the flavors and cook the food to perfection. They adjusted the temperature of the cooking either by adding special hot cubes or cold cubes to the cauldron or by removing some of the hot or cold cubes that were already in the cauldron. The cold cubes were similar to ice cubes except they didn’t melt, and the hot cubes were similar to charcoal briquettes, except they didn’t lose their heat. If the number of cold cubes in the cauldron was the same as the number of hot cubes, the temperature of the cauldron was 0° on their temperature scale. For each hot cube that was put into the cauldron, the temperature went up one degree; for each hot cube removed, the temperature went down one degree. Similarly, each cold cube put in lowered the temperature one degree and each cold cube removed raised it one degree. The chefs used positive and negative numbers to keep track of the changes they were making to the temperature. For example, suppose 4 hot cubes and 10 cold cubes were dumped into the cauldron. Then the temperature would be lowered by 6° altogether, since 4 of the 10 cold cubes would balance out the 4 hot cubes, leaving 6 cold cubes to lower the temperature 6°. They would write +4 + –10 = –6 to represent these actions and their overall result.

 

And here are links to the books I found on the Internet:

IMP 1 this link is not working for some reason so just type in "interactive mathematics program year 1" and click on the pdf file for the web address "rowlandblogs.org"

IMP 2

IMP 3

I do not have IMP 4

 

Check it out. :)

Edited by Kathleen.
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You might look at Zaccaro's Real World Algebra.  It's a nice story-like introduction.  We also read through Al and Gebra in the Land of Algebra.  (Actually, we did that first.)  Then she might do well with Mathusee Algebra.  He's good at explaining how you would use these concepts in the real world.  In fact, that's how he starts.

 

 

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This came to mind - Interactive Mathematics Program.  I stumbled upon it when I was trying to find a fun and memorable way to teach integers to my kids.  I watched this video and learned about IMP.  It's a four year math program intended for high school.  When I looked it up it's basically putting math in a story format that I find easy enough to use with kids younger than high school.  The background on the math program is that the publishers are trying to teach students in a more concrete way and so it does not follow the traditional math course sequence of Alg.1, Geo, Alg. 2 and Calc.  The books are loaded with ideas and I think there are a lot of fun stories that might appeal to your daughter.

 

Here's an excerpt of the story they are referring to in the video:

 

In a far-off place, there was once a team of amazing chefs who cooked up the most marvelous food ever imagined. They prepared their meals over a huge cauldron, and their work was very delicate and complex. During the cooking process, they frequently had to change the temperature of the cauldron in order to bring out the flavors and cook the food to perfection. They adjusted the temperature of the cooking either by adding special hot cubes or cold cubes to the cauldron or by removing some of the hot or cold cubes that were already in the cauldron. The cold cubes were similar to ice cubes except they didn’t melt, and the hot cubes were similar to charcoal briquettes, except they didn’t lose their heat. If the number of cold cubes in the cauldron was the same as the number of hot cubes, the temperature of the cauldron was 0° on their temperature scale. For each hot cube that was put into the cauldron, the temperature went up one degree; for each hot cube removed, the temperature went down one degree. Similarly, each cold cube put in lowered the temperature one degree and each cold cube removed raised it one degree. The chefs used positive and negative numbers to keep track of the changes they were making to the temperature. For example, suppose 4 hot cubes and 10 cold cubes were dumped into the cauldron. Then the temperature would be lowered by 6° altogether, since 4 of the 10 cold cubes would balance out the 4 hot cubes, leaving 6 cold cubes to lower the temperature 6°. They would write +4 + –10 = –6 to represent these actions and their overall result.

 

And here are links to the books I found on the Internet:

IMP 1 this link is not working for some reason so just type in "interactive mathematics program year 1" and click on the pdf file for the web address "rowlandblogs.org"

IMP 2

IMP 3

I do not have IMP 4

 

Check it out. :)

 

I just browsed through this a bit, and it looks like it would be such a good fit for my dd!

 

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I just browsed through this a bit, and it looks like it would be such a good fit for my dd!

 

 

 

Yes, it looks fabulous!  That organization has a lot of cool stuff; they have a version that uses traditional US course labels but also does the story stuff.  I'm trying to track it all down now.

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I'm kind of against "story-based" math, because analogy only takes you so far in mathematics.  I'd suggest a deep dive into the Khan Academy algebra videos, which are both in-depth and rigorous.

 

I can't speak to LIfe of Fred Algebra, but the LoF calculus was embarrassingly bad.  That made me not trust the series for anything else.

 

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I am not a fan of Life of Fred.  Barron's EZ Algebra has a story.  It's not super compelling and it's a bit contrived.

 

I have never seen any algebra book explain why a student should care about algebra.  If it helps, I don't require my students to care about the math; I just require them to master it.  If they ask why they need to learn it, I say because it is something an educated person must know.

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I'm kind of against "story-based" math, because analogy only takes you so far in mathematics.  I'd suggest a deep dive into the Khan Academy algebra videos, which are both in-depth and rigorous.

 

I can't speak to LIfe of Fred Algebra, but the LoF calculus was embarrassingly bad.  That made me not trust the series for anything else.

 

"Story based" doesn't have to mean light in math terms. I'm not sure why it implies that the math is only told in analogy either. The story part can be characters learning, explaining, and modeling the math in interesting situations. I'm not sure how that's more "analogy" than a teacher just explaining the math. And it can include plenty of problem sets. Beast Academy is "story based" and I think most posters on this board would agree that it's one of the most challenging and rigorous elementary maths out there.

 

That said, I'm not sure if I'm familiar with an excellent story based algebra. I'm not much of a fan of LoF either. But the idea that having a hook somehow undermines the math is something I really disagree with. Suggesting that Khan is somehow better for a child who needs that hook seems to ignore the OP's request. Khan is fine too, of course, but video explanations aren't inherently superior to characters in a story explaining.

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"Story based" doesn't have to mean light in math terms. I'm not sure why it implies that the math is only told in analogy either.

...

Khan is fine too, of course, but video explanations aren't inherently superior to characters in a story explaining.

 

The question for me isn't "written vs. video".  What makes the KA explanations compelling is not that they are videos, but that the content is superior.  Specifically, the Khan Academy materials:

 

(1) Are accurate.  (You'd think this wouldn't be rare, but you'd be wrong.)

(2) Are comprehensive.

(3) Focus relentlessly on working example after example, which is, in the end, the only correct way to learn math.

 

My objection to "story math" is that it's very easy for the story to obscure the underlying principles.   For some types of math, analogies are helpful and enlighten.  For many other types of math, analogies obscure and confuse - you're actually creating an additional cognitive load and implicitly asking the student to remember facts about the story that have nothing to do with the subject.  Later, when reviewing, the student is going to remember the story, instead of the math, because the story is easier to remember, because we are monkeys, and that is how monkeys think.

 

As Plato said, there is no royal road to geometry.   There are a few areas of math where a story can help illustrate principles (specifically, probability and statistics benefit greatly from this because the story elements serve well as labels to keep track of the many easy-to-lose-sight-of values).  But in Trigonometry or Algebra?  Adding narrative elements to that is only going to get in the students' way.

Edited by CaffeineDiary
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The question for me isn't "written vs. video".  What makes the KA explanations compelling is not that they are videos, but that the content is superior.  Specifically, the Khan Academy materials:

 

(1) Are accurate.  (You'd think this wouldn't be rare, but you'd be wrong.)

(2) Are comprehensive.

(3) Focus relentlessly on working example after example, which is, in the end, the only correct way to learn math.

 

My objection to "story math" is that it's very easy for the story to obscure the underlying principles.   For some types of math, analogies are helpful and enlighten.  For many other types of math, analogies obscure and confuse - you're actually creating an additional cognitive load and implicitly asking the student to remember facts about the story that have nothing to do with the subject.  Later, when reviewing, the student is going to remember the story, instead of the math, because the story is easier to remember, because we are monkeys, and that is how monkeys think.

 

As Plato said, there is no royal road to geometry.   There are a few areas of math where a story can help illustrate principles (specifically, probability and statistics benefit greatly from this because the story elements serve well as labels to keep track of the many easy-to-lose-sight-of values).  But in Trigonometry or Algebra?  Adding narrative elements to that is only going to get in the students' way.

 

Adding elements is only going to get in *some* students' way. The presumption that all students learn the same way is really strong in your statements here. What's an extra cognitive load for some kids is what keeps others on track.

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I'm kind of against "story-based" math, because analogy only takes you so far in mathematics.  I'd suggest a deep dive into the Khan Academy algebra videos, which are both in-depth and rigorous.

 

For some reason both of my school-aged kids detest the videos.  Passionately.  Most of the time I end up explaining the math, which is fine, though annoying.  

 

I'm thinking that "story-based" doesn't have to make stories around math problems, but math tells the story of the universe, right?  It's the language of science. 

 

Ok, can't keep typing now... children seem to want attention.  And help.  With math, LOL.

 

Thanks!

Anabel

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It was Euclid who said there's no royal road to geometry. I heart Euclid :)

 

IMP is not actually a story, but rather problem based in a way that really gets you thinking dare I say similar to Aops. I personally don't like Kahn because there's no chance for discovery. Kahn just feeds you the answer.

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Maybe look into compelling biographies of great mathematicians. Adding that human element might help your daughter get the "why study math" in general, even if it isn't specific to algebra. Even a movie like October Sky can show this.

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Well, not sure if it's what you're looking for, but I am planning to use Asimov's "Realm of Algebra" with DD alongside her algebra learning starting this summer.

 

But, she really loves Danica Mckellar's books too.

 

Algebra Survival Guide is conversational.

 

We've used The Journey of Al and Gebra too but even before we started pre-algebra. DD loved it even though it was pretty goofy.

 

I should probably stop here before I admit to how many other algebra books we've found... 

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My Dh has read one of the "Manga Guides to" books. I know they have one for algebra. 

 

http://www.amazon.com/Manga-Guide-Linear-Algebra/dp/1593274130/ref=sr_1_4?ie=UTF8&qid=1461160050&sr=8-4&keywords=manga+guide

 

Linear Algebra is not the algebra most 12yos study, but rather a college course. I haven't seen any Manga guides to regular algebra.

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I keep thinking about this thread and the bizarreness of assuming that story based means learning math by analogy. I can only assume that means learning the way that Waldorf teaches math - instead of focusing on the underlying reasoning behind the math, in a lot of Waldorf math, everything becomes based on the story. So, for example, you make your long division look like a little house and you do it by remembering all the parts of the house. It's wacky, to say the least. I'm not much in favor of it myself. I do think that adds a "cognitive load" while not providing a strong foundation.

 

I won't even go there about Life of Fred, which I find rambling and odd (and the graphic design makes my brain want to break) but which I know works for a lot of kids. No comment on the highest levels, which I haven't even seen. But it seems to me that something like Beast Academy proves that you can have characters tell a story that includes the math while also going in depth with the foundations behind it. I would argue that things like the Danica McKeller books (which aren't stories per se, but which focus on narrative) or even something like Ed Zaccaro's books with his little Einstein clip art conversations (the graphic design often hurts me in those too, in case you wondered) also show that you can have a narrative structure, which is useful for many kids, without it becoming analogy that takes the focus away from the math the way that Waldorf math arguably does.

 

I am in such agreement with the above statement that Khan takes all the discovery out of math, which is robbing a lot of learners of an essential element. My Miquon and Beast Academy loving kid hates Khan as well. He's doing okay with the Arbor School books at the moment. Which is not to say that stories necessarily include that discovery element either. Just, again, lots of different ways to crack this egg.

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Hello!

 

I am in the midst of re-vamping our plans. A bit late in the season, but there it is.

 

My 12yo has been doing Algebra this year, but it's been slow going. Not because the math or concepts are hard, but because she doesn't care. She lives and breathes story, and she really wants to know why she should care about math.

 

I'm thinking about doing Life of Fred with her, because I know it has a story to keep her going, but will it explain why she should care about binomials, etc?

 

Are there any other programs that I should have on my radar?

 

Thanks!

Anabel

I don't know that a story with math will help her know why she should care about it, and I think she needs to care.

 

Do you know why she should care, and have you shared that with her? If so, does she just not accept your reasons?

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I don't know that a story with math will help her know why she should care about it, and I think she needs to care.

 

Do you know why she should care, and have you shared that with her? If so, does she just not accept your reasons?

 

This particular child lives her whole life in story, and it really does help her where it might not usually help others.  For example, I wanted her to get more physical activity, and the only ways I've found to actually motivate her is to give her audiobooks when she is walking, or for her dance teacher to give her extra lessons on storytelling through dance to make regular dance class palatable.  She has taken a lot of French, but without any connecting narrative, she couldn't remember the grammar rules.  This is also a child who has written almost a dozen complete novels, because the stories her mind tells *needed* to be written down.

 

I have done my best to explain why she should care, and she accepts them in a limited way. 

 

Arg.  I have to go again.  I'll see if I can get back to answer the rest later.

 

Thanks!

Anabel

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I always tell any students I've taught or tutored who seem to think math is boring or unnecessary that math is really a key. Being able to do higher math successfully will open many doors, even those you might not think you need to go through. Success in math will help a person learn to think more critically, to be more logical, to do better on those important college entrance exams, etc. Maybe paint a picture for her of the many doors in her future. One by one she'll have many she needs or wants to open, but some of them will only be reached by going through the math door first.

 

How about sharing some stories of people like this woman who didn't think she could do math and found out she could?  http://www.christineerrico.com/mystory/

 

Perhaps she could learn to love math and then write the stories that show kids like her its importance and beauty!

 

 

 

 

 

 

 

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We watched several YouTube videos about the Fibonacci Sequence and the Golden Ratio today as an extension to a math lesson. Something I NEVER learned in school. And I was a decent math student. The Fibonacci sequence applied in nature covers patterns, addition, algebra, numbers squared, angles, ratios, the order of nature, and beyond. We counted spirals on our pineapple, petals on our flowers, and branch patterns on our trees after watching several videos.

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Linear Algebra is not the algebra most 12yos study, but rather a college course. I haven't seen any Manga guides to regular algebra.

 

However, Larry Gonick has a cartoon Algebra one. I haven't seen it irl though. In college I had to read one of his history cartoon books (not as the sole book for the class), and it was okay, might have been funnier if I'd known something about US History before taking the class.

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