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Comment by csa | Hacker News Reader

> Not a huge leap from there to the concept of equations, inverse operations, and solving for unknowns.

Unfortunately, for a child it typically is a huge leap.

There are certain abstractions that young children simply cannot do. The ability to do certain abstractions is distributed along a bell curve (edit: of age), and maybe your child is on the very far left of that curve, but most kids won’t be able to handle the abstractions you speak of until at least a little later.

To be fair, that “later” is definitely not 8th or 9th grade (much earlier), but it’s also not immediately after learning basic arithmetic.

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The only thing distributed along the bell curve is adults who are willing to help the kids. Yes for some kids it will come pretty easy, even at very young ages, but even very young children can learn these concepts if you would just spend some time teaching it to them.

When you have a system set up to force one adult to teach 30+ children you will never be able to spend the time required to ensure everyone gets the concept, but that neglect comes at the cost of compressing the learning in later years which still only benefits those who have high aptitude. Which is exactly why they are pushing it back further, not because it will help kids learn more, but because more children will have the ability to learn it without much interaction from an instructor.

Incredibly uncommon for 30 kids a class in elementary school. Also many students can barely handle arithmetic without massive handholding. Algebra in elementary school is out of the question

You are correct that 30 is on the high side, but I have seen classrooms in Philadelphia with 30 students to a single teacher ( 3rd grade, during the 2005 school year so it may have changed since then). However even at lower ratio's the point remains, you need to hand hold the kids, and we don't give our teachers the time or flexibility to do that.

> but even very young children can learn these concepts if you would just spend some time teaching it to them.

Many decades of cognitive science disagree with you.

See Piaget for one of the earlier researchers on this topic. Even though his original ideas have been refuted or refined, the basic premises of his ideas are still prominent among the large group of modern researchers that some people dub neo-Piagetians.

Many decades of the lived experiences of children in other countries disagrees with that research. Children in eastern European countries learn advanced concepts from as early as second grade. In asian countries they are introducing Algebra in 6th grade or earlier. This is the problem California finds its self in. They have wonderful "research" showing that kids pick up the concepts better if you wait till they are older, but they ignore the lived reality of the rest of the world, that with the correct teaching you could actually have them doing this work at a much younger age.

Even here in America, tutoring schools such as Russian Math or Kumon are successfully teaching advanced topics to children at much younger ages than the public schools. I know the temptation is to just say its its high aptitude kids that are being sent to these after school programs, but it's not. It is just rich kids whose parents want to give their children a leg up. Almost all children could learn the topics, but we won't put in the effort

> Many decades of the lived experiences of children in other countries disagrees with that research.

Based on your reply, I’m fairly certain that you are not familiar with the research and your not familiar with what is actually happening in Eastern Europe, Kumon, etc. in relation to that research. As a professional in this area of research, I feel fairly qualified to say that I am.

I am happy to agree to disagree about what the problem is here, but I strongly encourage you to look deeper into what is actually happening in the research and the learning environments you are praising/promoting before you propagate a loose collection of anecdotes as data that points to a clear solution.

I am glad that we can disagree, and I hope you would spend some time considering that while the research has progressed we have experienced a rapid decline in the subjective and objective quality of education.

Just because I completely reject the ideas you may be involved with researching doesn't mean I am ignorant of them, I just haven't been convinced that they are based in reality.

> we have experienced a rapid decline in the subjective and objective quality of education.

Interestingly, on this we agree. That’s why throwing more bodies at the problem (your initial suggestion) is not a solution that I think would work. When a typical educator is asked why a certain teaching or learning method works, their answers tend to be both incorrect/incomplete and remarkably shallow (e.g., it worked for them when they were in school).

The research available points at multiple tried and true ways of learning, but getting these ways of learning implemented in households and in the public school system in the US is a Sisyphean task.

Why would we "see" Piaget if his work, as you correctly note, his theories have been refuted? Educationalists, who have never personally and successfully taught anythingmarried simply wrong theories of learning, are a good 50% of the problem.

You left out the “refined” part of my comment.

Most of the broader ideas that he espoused and is famous for were refined in a way that made them accurately generalizable. Typical research timeline where an idea is introduced and is refined over time.

Some of the specific ideas he stated (and typically backed with data) was not generalizable to broader populations and was therefore refuted as an absolute. The data and conclusions were not necessarily wrong for the sample of the population studied, but they were not found to be as broadly true as initially believed.

This additional research led to the refinement of his theories, to great effect, imho.

Counting and arithmetic are themselves abstractions. The concrete reality is "this is a raspberry. this is another raspberry" etc, and that's about where my kid was at 2 (his loveys are named "Owl" and "Another owl"). Then we learn that there can be 5 raspberries just like there might be 5 ducks or 5 bricks, and that taking away 1 raspberry is like taking away 1 duck or 1 brick.

I could believe that the ability to abstract develops at different times in different kids. But I'd caution about taking Western research and generalizing it across all cultures, or generally assuming that kids are less adaptable than they are. There are existence proofs for kids learning algebra at much younger ages than most American schools do (3rd and 4th graders do in eastern Europe, as do Americans who participate in RSM).

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