Anonymous wrote:

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

Yeah, "modern" as in post 1990s.

Before that, it was x's and y's.

It is helpful to remember the history of the math wars as told by David Klein:

Within a month of the release of the Education Department's report, more than 200 university mathematicians added their names to an open letter to Secretary Riley calling upon him to withdraw those recommendations.[23] The list of signatories included seven Nobel laureates and winners of the Fields Medal, the highest international award in mathematics, as well as mathematics department chairs of many of the top universities in the US, and a few state and national education leaders. The open letter was published on 18 November 1999 as an ad in the Washington Post, paid for by the Packard Humanities Institute.[24]

and

The roots of progressive education are intertwined with anti-authoritarian ideals from the Romantic Era. In addition, progressive educators, including a former NCTM president, argued that women and members of ethnic minority groups learn mathematics differently from white males.[29] Such views were harmonious with the politically liberal ethnic identity ideologies popular during this period, especially in universities. Taking into account the anti-elitism and social justice arguments surrounding constructivist mathematics programmes, it is then not surprising that multiculturalists and liberals would be attracted to the NCTM vision, even if they did not understand the mathematical issues involved. As those groups constituted parts of the electoral base for Democratic politicians, the latter would be reluctant to challenge the use of constructivist maths in schools.

This article was written 25 years ago (!).

It's funny to look back now and realize that Virginia was once a leader in winning the math wars by rejecting progressive education.

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

Yeah, "modern" as in post 1990s.

Before that, it was x's and y's.

It is helpful to remember the history of the math wars as told by David Klein:

Within a month of the release of the Education Department's report, more than 200 university mathematicians added their names to an open letter to Secretary Riley calling upon him to withdraw those recommendations.[23] The list of signatories included seven Nobel laureates and winners of the Fields Medal, the highest international award in mathematics, as well as mathematics department chairs of many of the top universities in the US, and a few state and national education leaders. The open letter was published on 18 November 1999 as an ad in the Washington Post, paid for by the Packard Humanities Institute.[24]

and

The roots of progressive education are intertwined with anti-authoritarian ideals from the Romantic Era. In addition, progressive educators, including a former NCTM president, argued that women and members of ethnic minority groups learn mathematics differently from white males.[29] Such views were harmonious with the politically liberal ethnic identity ideologies popular during this period, especially in universities. Taking into account the anti-elitism and social justice arguments surrounding constructivist mathematics programmes, it is then not surprising that multiculturalists and liberals would be attracted to the NCTM vision, even if they did not understand the mathematical issues involved. As those groups constituted parts of the electoral base for Democratic politicians, the latter would be reluctant to challenge the use of constructivist maths in schools.

This article was written 25 years ago (!).

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

+1, this is introduced before math splits into tracks.

Anonymous wrote:I'm talking about solving for X and Y, 3X and that kind of thing, not the quadratic formula and lines/slopes. When do the advanced tracked kids learn this, what grade? RSM says 1st or 2nd grade at the latest, AoPS says ??, our public school says middle school.

My mom recently sent me copies of my 1st grade math notebook. 1970's. Eastern bloc country.

Guess what: equations in x and y right there. Even inequalities. Sure, only small coefficients, but introduced before fractions. Not to gifted kids. To every 6 year old.

I'm sure US textbooks of the time had that, too.

But that was before the Math wars...

There’s a book by Bob Moses called Radical Equations which is a lot about his work on making algebra education a civil rights goal but also has a lot of great stuff on algebraic thinking in early grades.

I have two kids that started AP calculus in 9th. They were learning algebra from an algebra textbook around 3rd-4th grade informally.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

can you explain with a couple of examples? my math is not the greatest.

1 + __ = 6

4 x __ = 60

The addition and subtraction example would exist in first grade, multiplication would be closer to third or fourth grade

Common Core has an algebraic thinking objective in Kindergarten.

The word in itself doesn't mean a thing!

You can do really easy, early-elementary math and call it "algebraic thinking". Doesn't change the fact that it's basic.

Since every school system will have a different definition of when they introduce algebra, I suggest you don't hang your hat on that, and just make sure your child masters essential logic and critical reasoning skills. I recommend Beast Academy (AoPS) for this.

- parent of kids in college and high school.

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

Yes, this is how Math In Focus (Singapore) does it. And they solve it using pictures.

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

can you explain with a couple of examples? my math is not the greatest.

1 + __ = 6

4 x __ = 60

That doesn't really include work with variables though. It took my son a surprising amount of time (and reps) to understand what X meant, while he completely understood that blank meant to do 6-1 or 60/4.

Anonymous wrote:

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

can you explain with a couple of examples? my math is not the greatest.

1 + __ = 6

4 x __ = 60

Anonymous wrote:Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

can you explain with a couple of examples? my math is not the greatest.

Pretty much all modern math curricula introduce algebra concepts in early elementary, but using blanks or pictures instead of letter variables.

I'm talking about solving for X and Y, 3X and that kind of thing, not the quadratic formula and lines/slopes. When do the advanced tracked kids learn this, what grade? RSM says 1st or 2nd grade at the latest, AoPS says ??, our public school says middle school.