# Just wow...public school math

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I'm tutoring a 6th grade girl who is struggling with reading. It's been a couple of weeks, and yes, she is definitely struggling.

On Mondays, she stays for dinner because my family all goes to her house for Bible study. So, I go ahead and make sure her homework is done and correct.

She had math today. She's learning how to multiply fractions, improper fractions, and mixed fractions. This is how she was taught to do it.

Problem: 1 2/3 x 2 1/4

Answer: 1 2/3 = 5/3 x 2 1/4 = 9/4 = 45/12 = 3 9/12 = 3/4 = 3 3/4

Got it? Makes sense, right? Easy? Won't get confused or forget to pick up things that you didn't write in the last step? Yikes!

Oh, and they use Connected Math 2. According to this review, which fits what I saw in the book, the students are never given the algorithms. They are to do a few sample problems and then write their own algorithms that they deduce from the sample problems.

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That's pretty much how I learnt to do it. Although I'd set it out on separate lines to make it clearer:

1 2/3 x 2 1/4

=5/3 x 9/4

=45/12

=15/4

=3 3/4

How else can you do it? (Not trying to be rude - I genuinely want to know because that's how I would have taught it and my son will be doing this soon.)

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Yeah. That's how I learned.

What am I missing? Fill me in quickly before my kids get there!

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Yeah, the writing out of it had me :001_huh: for a second.

But when I was in middle school, we did it the same as hotdrink says. :)

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I'm tutoring a 6th grade girl who is struggling with reading. It's been a couple of weeks, and yes, she is definitely struggling.

On Mondays, she stays for dinner because my family all goes to her house for Bible study. So, I go ahead and make sure her homework is done and correct.

She had math today. She's learning how to multiply fractions, improper fractions, and mixed fractions. This is how she was taught to do it.

Problem: 1 2/3 x 2 1/4

Answer: 1 2/3 = 5/3 x 2 1/4 = 9/4 = 45/12 = 3 9/12 = 3/4 = 3 3/4

Got it? Makes sense, right? Easy? Won't get confused or forget to pick up things that you didn't write in the last step? Yikes!

Oh, and they use Connected Math 2. According to this review, which fits what I saw in the book, the students are never given the algorithms. They are to do a few sample problems and then write their own algorithms that they deduce from the sample problems.

Well, if that's exactly how she wrote it, the first red flag I see is that she doesn't understand that = means "is the same as" and that everything on both sides of an "equals sign" needs to be ... well, equal. She's going to have a hard time doing ANY math if that concept isn't solid. It took me forever to even begin to figure out what she was trying to "say."

As for thaat curriculum's approach to teaching math ...:huh: That just about sums up my thoughts on the matter.

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Answer: 1 2/3 = 5/3 x 2 1/4 = 9/4 = 45/12 = 3 9/12 = 3/4 = 3 3/4

Does the book really write it that way with equal signs all across? Yikes!

When I taught college algebra (years and years ago), I used to think that if I could just get my students to use the equals sign properly, at least half their problems would go away.

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Only thing I would've done differently is simplify before multiplying the improper fractions, turning 5/3 into 5, and 9/4 into 3/4. THEN multiply.

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Well, this is how we would do it.

1 2/3 X 2 1/4 = 5/3 X 9/4

Cancel out the 3 and the 9, ( 3 into 3 - once/ 3 into 9 - three times) which becomes:

5/1 X 3/4 = 15/4

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Well, if that's exactly how she wrote it, the first red flag I see is that she doesn't understand that = means "is the same as" and that everything on both sides of an "equals sign" needs to be ... well, equal. She's going to have a hard time doing ANY math if that concept isn't solid. It took me forever to even begin to figure out what she was trying to "say."

As for thaat curriculum's approach to teaching math ...:huh: That just about sums up my thoughts on the matter.

That's basically what I was seeing. She's showing her conversions in the middle of the equation, which makes it really hard to keep everything straight. It's all written out in a straight line exactly as I wrote it...not set off to the side or written smaller or anything to set it apart and make it readable. After she writes the conversions, she then has to remember that she is multiplying the second and the fourth factors she has listed while ignoring the first and third factors. When she converts the answer to a mixed number, she drops the whole number for a step before picking it back up in the final answer. In one problem, she circled just the simplified fraction as her answer and forgot to go back two steps to pick up the whole number again.

When the second factor in a problem was a mixed number, her first step was to reverse the order the factors were written. This is really going to mess her up when she gets to order of operations.

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Well, if that's exactly how she wrote it, the first red flag I see is that she doesn't understand that = means "is the same as" and that everything on both sides of an "equals sign" needs to be ... well, equal. She's going to have a hard time doing ANY math if that concept isn't solid. It took me forever to even begin to figure out what she was trying to "say."
Exactly this.
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Does the book really write it that way with equal signs all across? Yikes!

There is nothing in the book to tell you how to do it. This is how she had it written on her paper and how she said her teacher showed them. The book actually doesn't teach you how to do anything. You use what you know to figure out the problems and then you come up with your own algorithms for that type of problem.

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There is nothing in the book to tell you how to do it. This is how she had it written on her paper and how she said her teacher showed them. The book actually doesn't teach you how to do anything. You use what you know to figure out the problems and then you come up with your own algorithms for that type of problem.

Oh, dear... :001_unsure:

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a number of years ago my friend's dh had a "chat" with their dd's math teacher. "oh, we don't worry if they get it right, we want to see how they do the problem". his reply "I'm an engineer, if the math is wrong, the plane will crash." (or the mars probe will crash and cost US taxpayers millions of dollars and years of work.)

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There is nothing in the book to tell you how to do it. This is how she had it written on her paper and how she said her teacher showed them. The book actually doesn't teach you how to do anything. You use what you know to figure out the problems and then you come up with your own algorithms for that type of problem.

:001_huh: I can't believe a teacher would demonstrate like that? Seriously set up for failure later on. PS math made me absolutely crazy when my DS went to school.

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a number of years ago my friend's dh had a "chat" with their dd's math teacher. "oh, we don't worry if they get it right, we want to see how they do the problem". his reply "I'm an engineer, if the math is wrong, the plane will crash." (or the mars probe will crash and cost US taxpayers millions of dollars and years of work.)

My thought, exactly. Math is not open to interpretation. It's math. The symbols have assigned meanings. You don't just randomly plop in = where it looks nice.

It's that kind of lunacy that made me drop Miquon in the first year. "it doesn't matter what answer they get, they should just be creative in measuring the line." Not! :glare:

My head may be spinning around now.

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I'm tutoring a 6th grade girl who is struggling with reading. It's been a couple of weeks, and yes, she is definitely struggling.

On Mondays, she stays for dinner because my family all goes to her house for Bible study. So, I go ahead and make sure her homework is done and correct.

She had math today. She's learning how to multiply fractions, improper fractions, and mixed fractions. This is how she was taught to do it.

Problem: 1 2/3 x 2 1/4

Answer: 1 2/3 = 5/3 x 2 1/4 = 9/4 = 45/12 = 3 9/12 = 3/4 = 3 3/4

Got it? Makes sense, right? Easy? Won't get confused or forget to pick up things that you didn't write in the last step? Yikes!

Oh, and they use Connected Math 2. According to this review, which fits what I saw in the book, the students are never given the algorithms. They are to do a few sample problems and then write their own algorithms that they deduce from the sample problems.

I wouldn't automatically assume that her method is "what they're teaching in schools.". If she's struggling enough to need a tutor, it's VERY likely that she got some steps/details confused. Also, 6th grade girls very often don't care to admit fallibility.

I'd just show her a more organized way to write it and hope she can consistently keep it straight.

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Does the book really write it that way with equal signs all across? Yikes!

When I taught college algebra (years and years ago), I used to think that if I could just get my students to use the equals sign properly, at least half their problems would go away.

:iagree:

One of the worst habits that I see a lot in my college students - it is so widespread that there must be plenty of teachers out there who do not understand that this makes the statement WRONG.

To the people who claim they learned it "this way":

1 2/3 is not equal to 5/3 x 2 1/4 is not equal to 9/4.

I would sit her down and explain the meaning of the equal sign and teach her how to write equations correctly. Only ONE equal sign, then a new equation underneath with the equal signs aligned.

Especially for a struggling student this will be absolutely necessary.

This kind of stuff would have me show up at school and have a talk with the teacher.

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I wouldn't automatically assume that her method is "what they're teaching in schools.". If she's struggling enough to need a tutor, it's VERY likely that she got some steps/details confused. Also, 6th grade girls very often don't care to admit fallibility.

I'd just show her a more organized way to write it and hope she can consistently keep it straight.

:iagree:

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There is nothing in the book to tell you how to do it. This is how she had it written on her paper and how she said her teacher showed them. The book actually doesn't teach you how to do anything. You use what you know to figure out the problems and then you come up with your own algorithms for that type of problem.

Yikes :001_huh:.

My thought, exactly. Math is not open to interpretation. It's math. The symbols have assigned meanings. You don't just randomly plop in = where it looks nice.

It's that kind of lunacy that made me drop Miquon in the first year. "it doesn't matter what answer they get, they should just be creative in measuring the line." Not! :glare:

My head may be spinning around now.

Seriously?! I'm sooo loosey-goosey with much of our learning, but that is something I pound in our kids' heads: "It's MATH. You don't get to be creative here." Since math is not my forte, my son is notorious for proving me wrong ;).

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It's that kind of lunacy that made me drop Miquon in the first year. "it doesn't matter what answer they get, they should just be creative in measuring the line." Not! :glare:

This is a slander of Miquon, as it teaches no such thing. Simply not true in the slightest degree.

Bill

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This is a slander of Miquon, as it teaches no such thing. Simply not true in the slightest degree.

Bill

I'm pretty sure I know the reason I dumped it, and that was it.

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LOL ds13's private school in 6-7th grade used Connections Math. It is a good program for kids who learn by the mastery approach and if they have a great teacher. It is not a great program but fits the learning approach at her old school.

The school is a multiple intelligence school that teaches to each learning style. The teacher would teach the lesson with specifically with verbal, visual, spacial, ect components. Each lesson was thoroughly taught and most work was done in class so they had help with questions.

DD13 did great with the understanding part, but struggled with maintaining her learning. They only had a few problems a day for school work and she needs repetition and a spiral approach to retain her math skills. Her understanding of concepts was strong, but what she was lacking was mastery and speed of basic skills. Skills like multiplication that she had mastered in 4th grade, were crumbling due to lack of use. They were encouraged to use calculators and that made it even worse.

The other problem, was that there is no 'text book' to refer back to and no examples to help if she got lost in the problem at home. There were times that I could not help her, nor could her brother....who is a paid math tutor! The questions are so specific to the program, if you don't have the teachers book to know where the problem is heading, you don't know what to do.

About mid way through her second year there, I talked to the head of school about my disappointment with the Connections program. He agreed and bought her Teaching Textbooks to use instead at home (based on dd's previous success with it). She still listened to the lectures in her class, but did TT on the side. We hand picked the TT lessons to reinforce specific skills. The teacher was amazed that without doing any of the classroom homework, she could still take the test with the class and get an A or B on it. The program under the hands of a good teacher, does teach concepts!

When she switched schools for 8th grade, she tested firmly into Algebra 1. TT reinforced the basic skills, gave her enough problems to build her skills back up and gave her confidence back. The two together were good for her. In 7th grade I we used TT Pre-Algebra to go back and teach her skills like long division, multiplication with decimals, fractions etc. Thing that she could do easily in 4-5th grade (the last years we homeschooled) were gone due to lack of use.

On the other hand, you can give her a real life math problem with multiple facets and she can come up with an algorithm to solve it! I do attribute her ease of solving complex problems with Connections.

I would NEVER use Connections math on purpose, but it isn't the worst I have seen. There are other programs that are not so one sided.

Edited by Tap, tap, tap
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I'm pretty sure I know the reason I dumped it, and that was it.

I'm quite familiar with Miquon and it does an ouststanding job the teaching math accurately and at a deep level of understanding. You are misrepresenting a very fine math program.

Bill

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Yikes :001_huh:.

Seriously?! I'm sooo loosey-goosey with much of our learning, but that is something I pound in our kids' heads: "It's MATH. You don't get to be creative here." Since math is not my forte, my son is notorious for proving me wrong ;).

I live with a mathematician who would consider those fighting words. Apparently, there is a great deal of room for creativity once you get past the tedium that is arithmetic. Of course, his field of math doesn't even use numbers (so he says) so I'm not sure I'd trust him entirely. :D

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It's that kind of lunacy that made me drop Miquon in the first year. "it doesn't matter what answer they get, they should just be creative in measuring the line." Not! :glare:

:confused: What? There is nothing like that in Miquon.

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Connected Math is one of the reasons that my children didn't and won't attend the public middle schools here.

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It's that kind of lunacy that made me drop Miquon in the first year. "it doesn't matter what answer they get, they should just be creative in measuring the line." Not! :glare:

I think this is the exercise where they measure with different rods. You get different answers if you measure with 1 rods vs. 3 rods vs. 8 rods. The idea is that different units of measure give different answers. It's also aimed at developing number sense. Dd and I loved Miquon and finished all the books. Although there are a few hard to understand exercises, the vast majority of it was excellent. It's not for everybody, but don't discount it lightly.

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That's pretty much how I learnt to do it. Although I'd set it out on separate lines to make it clearer:

1 2/3 x 2 1/4

=5/3 x 9/4

=45/12

=15/4

=3 3/4

How else can you do it? (Not trying to be rude - I genuinely want to know because that's how I would have taught it and my son will be doing this soon.)

:iagree:

I am not sure how else the problem would be solved.

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Ahhhh, she actually wrote it all out like that! I see now.

This is my big concern with the Common Core. Schools are dropping their math programs left and right and just "teaching the standards." Well, that doesn't fly for teachers who went to school for elementary and took ONE math methods class!!! They have no clue where the kids are going or where they are coming from, math wise. It's absolutely absurd to expect them to create a way to teach x, y, and z. There are schools doing the same thing with language arts, as well.

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Yes, the biggest issue is the improper use of equals.

We spend a lot of time at university trying to BREAK people of this habit. A common thing I see in algebra classes is 'x - 2 = 0 = x = 2'. This is a particular problem when you are working with multiple equations using transitivity, and the whole point is that a = b = c means that a = c.

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I live with a mathematician who would consider those fighting words. Apparently, there is a great deal of room for creativity once you get past the tedium that is arithmetic. Of course, his field of math doesn't even use numbers (so he says) so I'm not sure I'd trust him entirely. :D

That's why I said my son is notorious for proving me wrong ;). He's actually quite creative at the arithmetic part, too. He's been coming up with alternative methods, to the right answer, since he was a wee thing.

Math. It's just not my thing.

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Why horizontal? I would just teach the student to write it out the proper way, with the next version of the equation underneath instead. Ds9 has his fair share of fine motor issues and hates to write stuff out, but he has adjusted surprisingly well to this (especially when I write out the initial problem from the book). (Maybe it works so well for him because he is a VSL? Or maybe just because he is a good math student?). I always say I don't care how much paper it takes.

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I had this entire argument with my DD in PS teacher yesterday...I told them I am not teaching my kid the way the book is. Im having tons of problems with the way the 4th grade math book makes you go back and break down simple multiplication to some crazy steps...They pretty much told me anything I dont want to teach just circle and send it back in and they will work on it in school so she doesnt have to learn at home.

**They are testing on middle steps in the school system here instead of the final answer...so the question may state...

1. what is one possible step in solving this equation. So the student will need to know... 45/12 where my child would cross reduce and skip that step...and write 15/4 So....the answer would be 45/12 not the final answer. That could be one reason they are stressing that full multiplication across without reducing first. Takes so long.

This is just one reason they may be writing it like that in the book...I could be wrong in this situation...All those = signs are confusing.

Edited by mchel210
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<shrug> as a parent of child who tried to get away with that, I'd say the problem is the fine motor skills and finger strength. Simply put, they are shortcutting to get the answer so they can stop writing so much. My math teacher back in the Jurassic had a really simple solution...the introduction of the term and notation for 'therefore'. => drawn connected, forming an arrow, or the three dots formed into a triangle which I can't reproduce right here. Many students can manage that.

x-2=0=>x=2.

The other solution is to use unlined paper and a 4 color pen, and not be parsimonious.

The problem is that shortcutting with the = leads to writing things that are actively incorrect, and not distinguishing between them in writing frequently leads to confusion between the two. So although I understand people who have writing issues, I think it's important to teach other ways to shortcut (like the ones you've outlined).

I don't like using the implication arrow for this, so I prefer to see the next step written simply as -> (hey! it's one fewer stroke!), but that is a perfectly legitimate way of shortcutting.

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When I taught college algebra (years and years ago), I used to think that if I could just get my students to use the equals sign properly, at least half their problems would go away.

I had the same experience. I graded college algebra papers and got them to break the habit, and it certainly did dramatically improve things.

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I think this is the exercise where they measure with different rods. You get different answers if you measure with 1 rods vs. 3 rods vs. 8 rods. The idea is that different units of measure give different answers. It's also aimed at developing number sense. Dd and I loved Miquon and finished all the books. Although there are a few hard to understand exercises, the vast majority of it was excellent. It's not for everybody, but don't discount it lightly.

It might also be the preliminary exercises in the measurement thread in the Annotations, which suggest having kids create their own measuring units ("The desk is three pencils long" or "The room is 15 math books wide" or the like). The reasoning is to familiarize the students with the idea of measurement and the idea of using different measurements before using the rods and then a ruler.

See, this is the problem for me in being so dismissive toward constructivist teaching in math. There's a purpose to it and a reasoning as an initial activity. The problem comes when math classes, texts or teachers don't then explicitly make sure students have also learned the basic traditional algorithms. I feel similarly about being so dismissive of grading students by the steps they take. It seems perfectly reasonable that when you first begin to learn that your method be judged and examined. That's not a problem. The problem is when, down the road, when the process should be learned, that the school is still doing that when at some point you have to drop it and just show that you can get the answer.

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See, this is the problem for me in being so dismissive toward constructivist teaching in math. There's a purpose to it and a reasoning as an initial activity. The problem comes when math classes, texts or teachers don't then explicitly make sure students have also learned the basic traditional algorithms. I feel similarly about being so dismissive of grading students by the steps they take. It seems perfectly reasonable that when you first begin to learn that your method be judged and examined. That's not a problem. The problem is when, down the road, when the process should be learned, that the school is still doing that when at some point you have to drop it and just show that you can get the answer.

:iagree: with both points.

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I think this is the exercise where they measure with different rods. You get different answers if you measure with 1 rods vs. 3 rods vs. 8 rods. The idea is that different units of measure give different answers. It's also aimed at developing number sense.n

:iagree: I like what I have seen of Miquon a lot. Number sense is really crucial and missing from many programs. The issue with the basics-only type of books is that people get the impression that math is arithmetic only and don't learn any decent fluency in math, just in rote facts. Thus they dismiss math and science types as uncreative and boring. Lame.

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I'm pretty sure I know the reason I dumped it, and that was it.

FTR - It was through Miquon that my dc (two of them now) have essentially taught themselves why and how the traditional algorithms work. Honestly, they do need more work beyond Miquon Lab Sheets to become fast and fluent (to my high expectations;)), but for knowing how and understanding why Miquon is top-notch....and speed and fluency will never happen without the knowing/understanding.

I understand that Miquon is not for everyone, but it certainly does NOT teach "fuzzy math." It teaches real math through the discovery approach. The end goal is not the discovery part, IOW, but the math. In fact, from the start, everything must be proven true. Line up those rods and prove that 5+3=8, kwim. The rods go by the wayside as the child grows, but they still have the habit of lining up what they know against an unknown. The end goal is finding that unknown...the discovery process actually cultivates the drive to know for themselves and NOT take my word for it that it will always work to invert and multiply.

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:iagree:

One of the worst habits that I see a lot in my college students - it is so widespread that there must be plenty of teachers out there who do not understand that this makes the statement WRONG.

To the people who claim they learned it "this way":

1 2/3 is not equal to 5/3 x 2 1/4 is not equal to 9/4.

I would sit her down and explain the meaning of the equal sign and teach her how to write equations correctly. Only ONE equal sign, then a new equation underneath with the equal signs aligned.

Especially for a struggling student this will be absolutely necessary.

This kind of stuff would have me show up at school and have a talk with the teacher.

Yes, there are absolutely teachers who teach like this because they don't know any better. They use an equal sign to indicate the next step, without any indication that it actually means something. It's a great example of what can happen when you don't know the subject beyond the level you are teaching.

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Exactly. The *steps* aren't necessary wrong, and the method is the same as I'd use, but the one long line of equal signs shows a lack of understanding. Here's how I was taught to do the same problem, from the beginning, to make sure the steps were understood:

1 2/3 * 2 1/4

5/3 * 9/4

45/12 = 15/4 = 3 3/4

Same general method... but no confusion, and appropriate use of equal signs. It sounds like this poor girl just isn't getting the teaching that she needs, and for many kids it ends up sinking them.

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