Math the Whatchamacallit Way

[Roscoe]

While we're a bit ahead of ourselves, as our dear little Sprout isn't even born yet, my wife and I were discussing math curricula. I talked about Singapore Math as a default based on what I've read (including WTM, obviously), and she discussed what she thought was Montessori approach. It turned out Montessori math is quite different, but she insists she's seen/heard of it somewhere (paraphrased):

"Basically, we start with Euclid's Elements and move forward through time (or back, if need be) from there, with Al-Khwarizmi's algebra and Cardano's probability and later on to more complex stuff like non-Euclidean math and GEB."

So it's like an Elements>historical approach. Have any of you heard of a math curriculum like this?

[Rosie_0801]

None of that is PreK or K maths, so I'm going to move your post to the general ed board. 🙂

[Slache]

Generally, you're going to want to wait and see what kind of kid you have.

You should read things like The Well Trained Mind and For The Children's Sake. Since you have the time you should check out The Well Educated Mind, A Guide to the Classical Education You Never Had. Go to a homeschool bookstore and get your hands on some books.

I have an autistic kid doing Saxon, an autistic kid doing Beast Academy, and a neurotypical kid doing Singapore, but he will not continue with it after kindergarten. 

[goldenecho]

I haven't heard of that, but it sounds interesting.  Is there an actual curriculum that does that, or is this just an approach?  

[HomeAgain]

7 minutes ago, Slache said:

Generally, you're going to want to wait and see what kind of kid you have.

You should read things like The Well Trained Mind and For The Children's Sake. Since you have the time you should check out The Well Educated Mind, A Guide to the Classical Education You Never Had. Go to a homeschool bookstore and get your hands on some books.

I have an autistic kid doing Saxon, an autistic kid doing Beast Academy, and a neurotypical kid doing Singapore, but he will not continue with it after kindergarten. 

This.

I had one kid thrive with Math U See, another with MEP and Gattegno math.

Others I tutor went from Miquon to Math Mammoth and MEP, with a healthy dose of Gattegno/Cuisenaire work as a foundation.

Each of the kids approach math differently and took off when they had the right elements in place to let them find paths that worked for them.

[EKS]

7 minutes ago, Slache said:

Generally, you're going to want to wait and see what kind of kid you have.

Echoing this.  

That and what it's like to actually teach a young child math.  I can't imagine using a historical approach.

Also, why start with Elements?  Wouldn't you want to start with the first known ideas about numbers?  Which, to be clear, were most certainly not the first ideas about numbers.

[Rosie_0801]

This might be fun for you and your missus to look at: http://stern.buffalostate.edu/CSMPProgram/index1.html
It taught my kid more foundational things than arithmetic, which was a very good thing since she has dyscalculia and wouldn't have learned maths at all otherwise.

[daijobu]

I think it sounds amazing to do a math history course with your students.  I had never heard of Cardano, and came across this article.  But I wish I had assembled a math history course as you describe! 

We never did this, just Singapore for elementary followed by AoPS in prealgebra and beyond, and lots of math contests.  My younger dd AIME qualified every year starting in 8th grade.  (My older dd never got her AIME, but did respectably well on math contests.)    

I myself like to look up random things on wikipedia like the origin or the equals sign https://en.wikipedia.org/wiki/Equals_sign  or different methods to round numbers:  https://en.wikipedia.org/wiki/Rounding .  We take so much for granted about math including popular algorithms or notation.  

[smfmommy]

The Living Math web site has a history of math course.

Living Math Lesson Plans — Living Math

There are also gobs of story based math book lists for all levels.

 

[Dmmetler]

There used to be a math professor on Usenet who claimed that this was how kids should learn math and how his kids had and it was great. One of our friends was a PhD math student at his University and said that his classes were the worst to TA because whoever got them had to completely reteach because he managed to completely confuse about 3/4 of his undergrad students. 

[Shoes+Ships+SealingWax]

On 2/2/2022 at 8:10 PM, smfmommy said:

The Living Math web site has a history of math course.

Living Math Lesson Plans — Living Math

There are also gobs of story based math book lists for all levels.

 

We used her Level One Ancients lesson plans & they were great fun! Very engaging. The lesson plans are essentially an idea + a booklist though, so you’ll need to do some legwork (read ahead to gather supplies, hit the library, etc.).

[Clarita]

On 2/2/2022 at 12:58 PM, Roscoe said:

So it's like an Elements>historical approach. Have any of you heard of a math curriculum like this?

Historically speaking it took people a long time to come up with the decimal system ("place value" system). Prior to that they used a "tallying" system of writing numbers (think Roman numerals). The problem lies in that they were already doing things like multiplication and division, so most arithmetic and perhaps other things as well (geometry also) had already been developed. Arithmetic problems and stuff would have been solved procedurally differently using different counting systems. 

I think historically (not a historian here just shooting the breeze) math was developed based on problems that needed to be solved. So, it didn't always develop elegantly from simple to gradually more complex. I definitely think there are moments when the people who came before us went "Whoa this is so much easier than the way we've been doing it!" Let's move to this new method, place value being one of the ones I know about.

[jboo]

This is absolutely not a full curriculum, but I quite liked David Eugene Smith's "Number Stories of Long Ago", and thought it would be a fun adjunct for a kid somewhere in the 4th - 6th grade. Starts with the history of counting, the numeral systems, then different ways of handling basic operations, then fractions. The back section is full of a variety of tricky math puzzles, some of which could stump a much more advanced student.

There's a copy on archive.org, and if you enjoy it, a physical copy is quite cheap on the used market.  https://archive.org/details/numberstoriesofl00smit_0/mode/2up

[Shoes+Ships+SealingWax]

On 2/6/2022 at 8:21 PM, jboo said:

This is absolutely not a full curriculum, but I quite liked David Eugene Smith's "Number Stories of Long Ago", and thought it would be a fun adjunct for a kid somewhere in the 4th - 6th grade. Starts with the history of counting, the numeral systems, then different ways of handling basic operations, then fractions. The back section is full of a variety of tricky math puzzles, some of which could stump a much more advanced student.

There's a copy on archive.org, and if you enjoy it, a physical copy is quite cheap on the used market.  https://archive.org/details/numberstoriesofl00smit_0/mode/2up

These are utilized by the aforementioned Living Math as well. Very cute stories. 🙂