In my last post, I talked about different beliefs held by math teachers and others regarding when the standard algorithm for multi-digit addition and subtraction should be taught. Some believe that it should be taught only after students have had experience and practice with alternative place-value strategies. The reason is that such strategies provide the conceptual understanding that underpins the standard algorithm, which it is further believed eclipses these concepts. Others believe that it should be taught first, concurrent with the concepts that inform the procedure.

I find it worth asking people who don’t want kids learning some aspects mathematics if they have the same view of music.

In the case where a child has private violin lessons for several years they will be far ahead of any in school music program.

There is a risk they will find the in school program a bit tedious. But in general people don’t think this is a reason to avoid music lessons. I think because everyone values the development of musical ability more than that risk.

With mathematics I suspect enough grade school teachers found math unexciting and don’t value it so make the decision the other way. They will avoid having a bored student even if that means the student misses out on making progress.

They don’t come out and say this and have other justifications. Hence asking them why it is different from music can draw out what is going on.

Any argument that parents will do it wrong can be answered with a pointer to a strong resource such as jumpmath or beast academy.

I think one of the points here is that tutoring, whether in math or music, makes a big difference. This is an argument for smaller class sizes and more staff or volunteers on hand to provide one-on-one instruction.

I’m a native speaker of English. I read Left to Right.

In maths, when multiplying or adding, students are suddenly asked to read Right to Left …as if a speaker of Arabic (where or numbers come from).

This is confusing. We can modify the algorithm to add Left to Right, then sort out ‘carry’ at the end. I find it fun to use alternative algorithms on the whiteboard, showing students different ways to ‘play the music’.

That's fine, but it's good to have them master the standard algorithm first, and after they are comfortable with that, show alternative methods as you suggest. Too many times, math textbooks/curricula show many alternative methods, while delaying the standard algorithm. Also, students catch on to the right to left method of adding/subtracting numbers.

I find it worth asking people who don’t want kids learning some aspects mathematics if they have the same view of music.

In the case where a child has private violin lessons for several years they will be far ahead of any in school music program.

There is a risk they will find the in school program a bit tedious. But in general people don’t think this is a reason to avoid music lessons. I think because everyone values the development of musical ability more than that risk.

With mathematics I suspect enough grade school teachers found math unexciting and don’t value it so make the decision the other way. They will avoid having a bored student even if that means the student misses out on making progress.

They don’t come out and say this and have other justifications. Hence asking them why it is different from music can draw out what is going on.

Any argument that parents will do it wrong can be answered with a pointer to a strong resource such as jumpmath or beast academy.

I think one of the points here is that tutoring, whether in math or music, makes a big difference. This is an argument for smaller class sizes and more staff or volunteers on hand to provide one-on-one instruction.

Another angle on this. Is it a fair assumption that almost all mathematicians was developed by people taught through traditional approaches?

If not almost all then huge parts of it.

How many authors of mathematicians papers prior to 1965 would have had a non-traditional math grade school experience?

The point being that this seems like evidence that a traditional approach clearly doesn’t inhibit creativity in mathematics.

I’m a native speaker of English. I read Left to Right.

In maths, when multiplying or adding, students are suddenly asked to read Right to Left …as if a speaker of Arabic (where or numbers come from).

This is confusing. We can modify the algorithm to add Left to Right, then sort out ‘carry’ at the end. I find it fun to use alternative algorithms on the whiteboard, showing students different ways to ‘play the music’.

That's fine, but it's good to have them master the standard algorithm first, and after they are comfortable with that, show alternative methods as you suggest. Too many times, math textbooks/curricula show many alternative methods, while delaying the standard algorithm. Also, students catch on to the right to left method of adding/subtracting numbers.