Washington Post series on homeschooling

[Coconut Flan]

I remember this one.  ::smh::

Even the 9 year old granddaughter knows the proper order of operations.

[Ozlsn]

My response to these problems is always that I need more brackets! 

[anjulibai]

Order of operations is not Common Core. Yikes. 

[Hane]

My sister, a math/science teacher of 35+ years (and a state math/science teacher of the year) who wrote curriculum for many of them, is always exasperated when people attribute certain teaching techniques to “Common Core,” when they aren’t. She will happily educate anyone on what Common Core actually is.

[Bassett Lady]

On 1/16/2024 at 1:36 PM, Marmion said:

To my surprise , she informed me that in A.C.E. they just work from left to right , unless it's set off by brackets or parentheses

A.C.E. is substandard in so many respects, but it does teach proper order of operations. 
 

I have tested several students who used an A.C.E. curriculum, exclusively, and they had a firm grasp of order of operations. 
 

In my experience, A.C.E.  students have weaknesses with writing formal proofs. 

[Expectopatronus]

I liked the video explanation of how both answers are valid. I would say 1 because of how I  was taught. I actually saw a four method of solving the problem as he was talking 

6/2 (1+2) could also be solved as 2X1 +2x2 = 2+4

6/6 =1 or (3) X 2 =6 6/6= 1

Truthfully, this is why I hate multiple choice for calculation questions. Showing one’s work can show how two answers could be correct. 

[Ali]

53 minutes ago, Expectopatronus said:

I liked the video explanation of how both answers are valid. I would say 1 because of how I  was taught. I actually saw a four method of solving the problem as he was talking 

6/2 (1+2) could also be solved as 2X1 +2x2 = 2+4

6/6 =1 or (3) X 2 =6 6/6= 1

Truthfully, this is why I hate multiple choice for calculation questions. Showing one’s work can show how two answers could be correct. 

Not if order of operations are followed. If order of operations are followed there is only ONE answer. 

Parentheses first. (1 + 2) = 3

Then multiplication and division from left to right in the order it appears.

3 x 3 = 9

Anyone who says any other answer is correct is not following order of operations. 

Signed someone with a bachelor's degree in mathematics who teaches secondary math.

Edited to add if 2(1 + 2 ) is all in the denominator then 1 is correct.

Edited January 22 by Ali

[Expectopatronus]

@Ali I think part of the problem is how it was written. I assumed that 2(1+2) was the denominator. 

[Ozlsn]

3 hours ago, Expectopatronus said:

@Ali I think part of the problem is how it was written. I assumed that 2(1+2) was the denominator. 

This is why I need more brackets!! Or a longer line. Or better spacing!

Edited January 22 by Ozlsn

[Ali]

16 hours ago, Expectopatronus said:

@Ali I think part of the problem is how it was written. I assumed that 2(1+2) was the denominator. 

I agree with @Ozlsnabout the brackets/parentheses. People type things in on the calculator all the time that is not want they want the calculator do. Garbage in, garbage out. If 2(1 + 2) is in the denominator, then it should be 6/(2(1+2)). Scientific and graphing calculators will follow order of operations. It is up to humans to add parentheses as needed.

 

 

Edited January 22 by Ali

[Maggie Mae]

On 1/21/2024 at 11:46 AM, anjulibai said:

Order of operations is not Common Core. Yikes. 

It drives me crazy how stupid people are around the phrase "common core." It's Common Core State Standards Initiative. And it refers to a set of standards for math and English, basic standards that public schools are supposed to meet or exceed.  It's been around since 2010, some states never signed on, some repealed it. And it's just a document that says that students are supposed to do these thing during this year.  

The grouping techniques for arithmetic is not common core.  Its also not rocket science like facebook people make it out to be. 

[JDuggs]

As a former middle school math teacher, the pull is strong for me to solve the 2(1 + 2) part first before dividing because I see imaginary brackets around it when a number is right in front of the parenthesis. If it was written 2 x (1 + 3), then it’s much more obvious that the division comes first.

I would also like to add that this is a type of question that I’ve never seen in a math book, on an assessment provided by a curriculum or on a standardized test like the MAP tests. If someone could direct me to a legitimate source that addresses this exact topic as taught to students, I’d love to see it.

[Coconut Flan]

I would offer you the grandkid's math book if it could be presented here.  There is an entire chapter on order of operations.  It's also in pre-algebra as it's a basic before learning to solve equations with variables. 

[JDuggs]

56 minutes ago, Coconut Flan said:

I would offer you the grandkid's math book if it could be presented here.  There is an entire chapter on order of operations.  It's also in pre-algebra as it's a basic before learning to solve equations with variables. 

I mean the exact situation of where multiplying next to parentheses comes in the order of operations.

[Coconut Flan]

Yes, I've seen it.  It's very common in pre-algebra.  

[Maggie Mae]

You just do what's in the parenthesis and then multiply, right? So 3(4+5) would be 3 x 9 = 27. Or is there another way to do that that I am missing? If it's 3(4+5)^2, it would be 3*81=243, not  27^2=729. 

I kind of miss higher math, it was so fun once I got away from the nuns and the screaming about how we can't rely on calculators for basic arithmetic and how am I so stupid for being bad at route memorization.

[JDuggs]

2 hours ago, Maggie Mae said:

You just do what's in the parenthesis and then multiply, right? So 3(4+5) would be 3 x 9 = 27. Or is there another way to do that that I am missing? If it's 3(4+5)^2, it would be 3*81=243, not  27^2=729. 

I kind of miss higher math, it was so fun once I got away from the nuns and the screaming about how we can't rely on calculators for basic arithmetic and how am I so stupid for being bad at route memorization.

If you look at the problem on the YouTube video, the whole problem is 6/2(1+2) and the controversy is whether to divide 6 by 2 first or multiply the 2 times 3 first. I found something from UC Berkeley that calls these types of problems ambiguous and they need brackets to show the actual intention of the problem. That’s why you don’t see problems like these in textbooks unless someone can please prove me wrong.

Spoiler

 

[Ali]

14 hours ago, JDuggs said:

If you look at the problem on the YouTube video, the whole problem is 6/2(1+2) and the controversy is whether to divide 6 by 2 first or multiply the 2 times 3 first. I found something from UC Berkeley that calls these types of problems ambiguous and they need brackets to show the actual intention of the problem. That’s why you don’t see problems like these in textbooks unless someone can please prove me wrong.

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If they are not included, then middle school math teachers are failing their students. My high schoolers fail to type things into the calculator all the time correctly. It is because they did not properly learn order of operations in middle school and do not know how to tell their calculator how to calculate the problem properly.

The problem is not ambiguous. Order of operations should be always followed without questioning what the person meant. 

If 2(1+2) is in the denominator, then there should be parentheses around it. No parentheses, then assume it is not in the denominator. Math is very straightforward.

 

Edited January 23 by Ali

[Hane]

My sister the middle school science teacher, used to be her district’s math specialist, and will SCHOOL you on the whole order of operations thing!

[KSmom]

I’m a retired math tutor and there were two things that made me crazy, usually when talking with the parent not the students. 1) order of operations and 2) -1^2 is different than (-1)^2. I always felt like telling the parent that if they knew better than me what are you paying me for?

[JDuggs]

This is why I wasn’t an English teacher because I’m not getting my point across at all. Order of operations is definitely taught and assessed, but this particular problem has the slightly different issue with the multiplication of a number by the expression in the parentheses. I absolutely understand the concept of order of operations and how to teach it, but until someone shows me a problem like this from a textbook, I’m sticking to the understanding  that this type of problem is not being taught or assessed due to its ambiguity.

 

 

[bea]

I leave for a few weeks, and I come back and you people are talking about math.  l

Nothing new on WaPo or NYT about homeschooling, but as I said: if you want to read any articles on those sites, I get a fair number of gift articles a month.  I also subscribe to the NYT Cooking section.

[Marmion]

I see that , as is common with this issue , people will argue it to death .  At the risk of getting a dead parrot ,  I just wanted to make two points .  1.  College students and professors don't  tend to entirely agree with middle and high school Math instructors , as to the order of operations . 2. The various calculators do not always agree with each other as to how to solve such equations.  @JDuggs is not wrong about the implicit ambiguity that can exist , in calculating such equations , given the way in which they are presented.  Below are a couple YouTube videos , from an Australian Math professor , explaining what I am getting at .  

Spoiler

 

 

Spoiler

 

 

[JDuggs]

 

@Marmion Thank you so much for sharing those videos. I didn’t have the language of the term multiplication by juxtaposition to explain what I meant. The other issue that other people have addressed is the use of the “/“ for division rather than the obelus sign (which I can’t figure out how to get on my keyboard, under spoiler) which isn’t used past elementary school math. The “/“ implies that everything above it is in the numerator and everything below it is in the denominator where the obelus doesn’t have that same implication which confuses the problem.

Spoiler

 

[bea]

Article on moms who are essentially selling their tween and teen girl’s pictures on social media, largely to men who are “interested” in young girls.