Could be. Bill told me a great way to make coffee once upon a time. I am willing to concede on almost all terms in order to show my gratefulness.

I should have read further. Yes, yes, we do agree.

The problem with these discussion is people seem to talk past one another. Like many disagreements, part of the problem involves "defining ones terms. Or rather, not defining ones terms.

The big culprit here is the word *formal* with a supporting role for the word *delay*.

As I suggested earlier, I think many people use *formal* as a synonym for advancing developmentally inappropriate means to force learning on young children who simply are not ready for the means employed. At the extreme this would include using math fact flashcards with infants, or chaining young kid's to desks and giving them hours upon hours of seat-work with drill sheets.

But that sets up a straw-man, as I don't think any sane person believes that is a good idea.

Some use *formal* to mean using anything published as a curriculum, without (from my POV) recognizing that there are published programs designed precisely to help parents teach young children in developmentally positive ways using means that capitalize on play, problem solving, activity based learning, developing understanding using concrete means, learning though real world experiences, and the like.

There are (to my mind) *formal* math resources (under this use of the term) that are very well suited to learning/teaching math with young children, and there are published programs that are not well suited for this aim.

To me, *formal* means "intentional, regular, deliberate, and methodical."

There are all sort of ways to build mathematical understanding in ways that are intentional, regular, deliberate, and methodical" that have nothing to do with seat-work. I can't say how much value we got out of shopping in the produce aisles combined ith deliberate and intentional questions. If these real life activities are "methodical" are they formal or not formal?

If children play with C Rods and base-10 "flats" I'd this formal or not formal?

If children engage in creative activities of the sort outlined in the MEP Lesson Plans is it formal or informal?

If they work on problems that build on ideas they have learned in concrete ways that involve paper is this formal or not formal?

Personally I think it is a mistake to conflate *formal* with "developmentally inappropriate." I think there are many ways to creatively engage with young children with the intention of fostering learning into the play. This does not negate the idea that children left to their own devices (as they should be at times) will find their own ways to learn through play. But these things should be complementary and not antagonistic activities.

I made up all sort of games and activities to bridge the understanding of my young child from the concrete towards the more abstract, and freely borrowed, modified, or used directly ideas from many published sources. This is what I would call "creative engagement."

There is no doubt in my mind that a child who grows up in a home where there is "creative engagement" happening on a regular basis will develop cognitive skills (and actually develop a physically more densly wired brain) than a child who grows up in an unstimulating environment. "Math-play" is surely not the only way to stimulate a young brain, but why exclude it?

And why exclude the interesting and helpful resources that help parents create a rich learning environment for young children? And why not give children opportunities to test their knowledge in ways that might involve paper? There are many fun leaning problems that come in published form that do not destroy children's childhoods.

We really do not need to choose between two bad options. One being forcing developmentally inappropriate work on kids who are not ready for it, and the other of letting them rot. There is a rich alternative of creative engagement, and that is the best path.

Bill