When do the top track math kids begin to learn algebraic concepts and thinking? What grade

[Anonymous]

Anonymous wrote:

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...

Wait, what? What are the math wars?

[Anonymous]

Anonymous wrote:

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.

This isn't something that can be *taught*, though. This is a personal brain-development milestone.

[Anonymous]

Preschool

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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...

Wait, what? What are the math wars?

This is what happens when we let "education" experts not listen to mathematicians on how to teach math.

A Brief History of American K-12 Mathematics Education in the 20th Century
"The immediate cause of the math wars of the 90s was the introduction and widespread distribution of new math textbooks with radically diminished content, and a dearth of basic skills"

The National Council of Teachers of Mathematics released An Agenda for Action in 1980. The report called for new directions in mathematics education which would later be codified in 1989 in the form of national standards. An Agenda for Action recommended that problem solving be the focus of school mathematics in the 1980s, along with new ways of teaching. The report asserted that "Requiring complete mastery of skills before allowing participation in challenging problem solving is counterproductive, " and "Difficulty with paper-and-pencil computation should not interfere with the learning of problem-solving strategies." Technology would make problem solving available to students without basic skills. According to the report, "All students should have access to calculators and increasingly to computers throughout their school mathematics program." This included calculators "for use in elementary and secondary school classrooms." The report also warned, "It is dangerous to assume that skills from one era will suffice for another," and called for "decreased emphasis on such activities as...performing paper and pencil calculations with numbers of more than two digits." This would be possible because "The use of calculators has radically reduced the demand for some paper-and-pencil techniques." The report also recommended that "Team efforts in problem solving should be common place in elementary school classrooms," and encouraged "the use of manipulatives, where suited, to illustrate or develop a concept or skill."

Also

In an earlier era:
The effects of the Open Education Movement were particularly devastating to children with limited resources, due to their lack of access to supplemental education from the home, or tutoring in basic skills outside of school. Lisa Delpit, an African American educator who taught in an inner city school in Philadelphia in the early 1970s wrote about the negative effects of this type of education on African American children. Relating a conversation with another African American teacher, she explained, "White kids learn how to write a decent sentence. Even if they don't teach them in school, their parents make sure they get what they need. But what about our kids? They don't get it at home..."

Every educational policy that makes learning "easier" for kids disproportionately affects poor people to their detriment. Rich people either have generational wealth/nepotism where they don't need to learn anything or can supplement any learning by paying for tutors. It's what happened during Covid when they kept schools shut for no scientific reason.

[Anonymous]

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.

We had a math meeting yesterday and students in Algebra 2 and Geometry are struggling with these.

Thank you open enrollment, pushing ahead too fast, unlimited retakes, no deadlines, Desmos, and teachers not being backed and not being allowed to have students repeat courses if they don’t master content.

So I don’t know when they learn these concepts.

[Anonymous]

Anonymous wrote:Preschool

What, exactly, is he he harm in introducing these concepts too early? People learn from repeated exposure. It’s just like a language. If you’re around it a lot then eventually you get it. Kids’ heads aren’t going to explode if you teach them things too early. Even if they don’t completely get it you are laying the foundation for deeper understanding later on.

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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...

Wait, what? What are the math wars?

This is what happens when we let "education" experts not listen to mathematicians on how to teach math.

A Brief History of American K-12 Mathematics Education in the 20th Century
"The immediate cause of the math wars of the 90s was the introduction and widespread distribution of new math textbooks with radically diminished content, and a dearth of basic skills"

The National Council of Teachers of Mathematics released An Agenda for Action in 1980. The report called for new directions in mathematics education which would later be codified in 1989 in the form of national standards. An Agenda for Action recommended that problem solving be the focus of school mathematics in the 1980s, along with new ways of teaching. The report asserted that "Requiring complete mastery of skills before allowing participation in challenging problem solving is counterproductive, " and "Difficulty with paper-and-pencil computation should not interfere with the learning of problem-solving strategies." Technology would make problem solving available to students without basic skills. According to the report, "All students should have access to calculators and increasingly to computers throughout their school mathematics program." This included calculators "for use in elementary and secondary school classrooms." The report also warned, "It is dangerous to assume that skills from one era will suffice for another," and called for "decreased emphasis on such activities as...performing paper and pencil calculations with numbers of more than two digits." This would be possible because "The use of calculators has radically reduced the demand for some paper-and-pencil techniques." The report also recommended that "Team efforts in problem solving should be common place in elementary school classrooms," and encouraged "the use of manipulatives, where suited, to illustrate or develop a concept or skill."

Also

In an earlier era:
The effects of the Open Education Movement were particularly devastating to children with limited resources, due to their lack of access to supplemental education from the home, or tutoring in basic skills outside of school. Lisa Delpit, an African American educator who taught in an inner city school in Philadelphia in the early 1970s wrote about the negative effects of this type of education on African American children. Relating a conversation with another African American teacher, she explained, "White kids learn how to write a decent sentence. Even if they don't teach them in school, their parents make sure they get what they need. But what about our kids? They don't get it at home..."

Every educational policy that makes learning "easier" for kids disproportionately affects poor people to their detriment. Rich people either have generational wealth/nepotism where they don't need to learn anything or can supplement any learning by paying for tutors. It's what happened during Covid when they kept schools shut for no scientific reason.

When our kid was in 2nd grade, the teacher insisted he had to solve addition and subtraction problems by counting up or down, either by using a number line or his fingers. Because he was used to dealing with his allowance, playing number games, and so on, he could quickly compute and write the answer, but that was not allowed. And sometimes he would lose count and miscount. I don't think we are doing enough to just do regular math facts and drills with kids. They absolutely need to practice practice practice addition, subtraction, and in later grades multiplication and division. Maybe I don't understand New Math, but I don't understand the need to count on fingers over just being able to solve the problem quickly and accurately.

[Anonymous]

FCPS curriculum is supposed to introduce algebra and geometry in ES in every grade. I am not sure I know what that looks like, we did not see much math work coming home from school.

We started DS in math enrichment during COVID. He has been with RSM since 4th grade and is now in their national math competition program. He dropped the grade level class in 6th grade because it was too slow and RSM would not move him into the Algebra class for some reason.

[Anonymous]

6th grade

[Anonymous]

Anonymous wrote:

Anonymous wrote:

Anonymous wrote:

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...

Wait, what? What are the math wars?

This is what happens when we let "education" experts not listen to mathematicians on how to teach math.

A Brief History of American K-12 Mathematics Education in the 20th Century

Thanks for posting, that looks great! Have not seen "The reorganization of mathematics in secondary education" referenced before. David Eugene Smith had a great book on mathematical history for kids, "Number Stories of Long Ago", so that he was involved in the report is very promising. https://archive.org/details/bwb_O7-BKS-321/page/2/mode/2up

[Anonymous]

4th grade

[Anonymous]

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.

You can definitely learn that around K-1st if taught well, which is of course extremely rare these days.

https://youtu.be/j9SjFsimywA?t=210

https://www.youtube.com/watch?v=j9SjFsimywA&t=396s - here's two examples with students taught by Dr. Engelmann

https://untitledhomeschoolproject.blogspot.com/2021/07/zig-and-therese-engelmann-on-algebra.html

[Anonymous]

Anonymous wrote:

Anonymous wrote:

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.

This isn't something that can be *taught*, though. This is a personal brain-development milestone.

Nope, you're wrong. If we as a society only taught bike riding to 8th graders, that wouldn't make being able to ride a bike a developmental milestone that can only be met by 8th graders. You would think being able to stand is an incredibly hard skill to teach early, and yet: https://www.youtube.com/watch?v=Dkl_MC1h2_w
https://www.youtube.com/watch?v=BR5ZA5mxBFk

[Anonymous]

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

Did they have prealgebra mastered before starting?

[Anonymous]

Anonymous wrote:

Anonymous wrote:Preschool

What, exactly, is he he harm in introducing these concepts too early? People learn from repeated exposure. It’s just like a language. If you’re around it a lot then eventually you get it. Kids’ heads aren’t going to explode if you teach them things too early. Even if they don’t completely get it you are laying the foundation for deeper understanding later on.

The harm is that you start to realize just how painfully slow the procrustean school system is an might begin to consider alternatives, like homeschooling.