I thought I had found them all, but NO.

Subtraction. Read this

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Kindergarten

Operations and Algebraic Thinking

• Understand addition as putting together and adding to, and understand subtraction as **taking apart** and taking from.

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What has subtraction got to do with taking apart ???

(The examples are all of the form 9 = 3 + 6 and so on).

Also there is **NO mention at all** of subtraction as a way of finding the **difference** between two numbers, or of finding the **larger** of two numbers (anywhere).

While I am in critical mode I offer two more, less awful, horrors from Grade 1:

“To **add 2 + 6 + 4**,…” and “For example, **subtract 10 – 8″.**

The poor symbols are clearly in great pain at this point. Just read aloud exactly what is written…..

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Filed under algebra, arithmetic, language in math, operations, teaching

Tagged as CCSS, common core, comparison, difference, garbage, larger, smaller, subtraction

I think it may be a new method of teaching. My son’s been learning number bonds since nursery, so in theory, subtraction should be easy for him now (in year one), as all he has to do is ‘take apart’ the number bonds he already knows.

Thanks for your comment. I see that.

Starting with 4+5=9 it can be seen as 9=4+5. This certainly shows that if you subtract the 5 from the 9 then you get 4, as you have subtracted (taken away) the 5 from both sides,but I am not at all happy with the way it is expressed, “Understand subtraction as taking apart”.

Reading these equations does not appear to get any emphasis, in the CCSSM or in the teaching.

9=4+5 can be read as

a) If I have 9 things, then that is the same as having 4 things AND 5 things

b) If I subtract (take away) 5 from 9 I have 4 left

c) 9 is 5 more than 4

and possibly as well, the difference between 5 and 9 is 4.

One of the problems throughout school math is due to the unwillingness to see equations as code for sentences and not just “why equals emx plus c”

I agree with you. These new methods they introduce to simplify things for the children, aren’t really that simple after all. I just hope it doesn’t limit their understanding in the long run.

Another problem is that many students aren’t at the developmental stage where they can see a number as its parts adn the whole thing at the same time; they really do perceive subtraction as “taking away.” Early math ed that depends on that development lets a few kiddos grasp it and run … and is why lots of kiddos learn early that they must not be very good at math … even if it weren’t true.

(See Dorothea Steinke’s _Rhythm and Number Sense_ and a few other sources)

I wonder how repeated subtraction is taught these days. As a youngster I remember being quite baffled to learn that e.g. 9 – 5 – 4 has two answers.

According to the new USA Common Core maths programme multiplication is not considered as repeated addition and division is not treated as repeated subtraction. I hadn’t realised this, and I am stunned !!!!!

Regarding 9 – 5 – 4 I think your math teacher was trying to make a point, that as it stands, without a rule or an explanation of its meaning it is quite possible to think that treating the 5 – 4 part as a subtraction and doing it first will get you a different answer to the approved one! They are attempting to circumvent this danger by going on and on about commutative and associative laws, but with no hint that these do not apply with negatives without some rethinking of meaning.

I am going to do a brutal post on this serious omission soon.

I see you are Carnot Cycle – I am waiting for the next post.

My friend was talking about this specific aspect of Common Core the other day. I’m showing this to her when she gets home. The whole thing makes me want to pull my hair out. Professors in college praised this like it was the spoken word of the Lord.

Your reports about math education are really distrubing (though entertaining)! It seems that teachers should turn formulas and logical relations into some cute narrative?

After I had read your posts about multiplication and areas I tried to recapture how I learned all this. In elementary school we were given a set of cubic blocks (a bit like lego perhaps, cubes with holes or pins on each face), from which you could build areas and cubes, and add, and subtract…e.g.like in those animations you showed, about the distributive law… and thus discover playfully how all basic arithmetic works. No need to turn this into more ‘poetic’ language!