Writing a paragraph to show how to solve a math problem???? Opinions?

[In The Great White North]

 

"If I have five blocks and take away three blocks I will still have two blocks leftover, so I know it five is bigger." 

"5-3=2 which is more than zero, so 5 is larger than 3"

"5=3+2, so 5 is bigger because I have been adding to 3 to make 5"

or a picture. 

 

Great examples of explaining it in words but not really paragraphs.

 

 

 

 Again: the teacher should model what kind of answers he is expecting 

 

This is the detail I expect to be missing.

[Penny_P]

My son started bringing these sheets home last year as a gear up for CC starting this year.  Now my dd is bringing them home.  I LOATHE them.  He is dyslexic- the writing portion was far more difficult for him than figuring out the problems.  And for me, too.  I just don't think that way.

[Arcadia]

For example

 

Page 26 (29 of 48) of 3rd grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_3_math_released_questions.pdf

 

Page 3 (37 of 43) of 4th grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_4_math_released_questions.pdf

 

Page 39 (42 of 60) of 8th grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_8_math_released_questions.pdf

 

Main link here for NY scoring sample  for 3rd-8th grade http://www.engageny.org/resource/new-york-state-common-core-sample-questions

[Tammi K]

I have to ask - what would you write to explain why one number is greater than another? With 5 and 3, for example, I would have to draw a set of 5 circles and a set of 3 circles, and then cross off the 3 in each set leaving the 2 extra showing -

 

Given the discussion about the importance of being ABLE TO construct a written explanation, I decided to see what math boy, a writing hater, really could do. So, I asked him a series of questions including this one above. He looked at me seriously and said, "The first thing I would want to know is, "How smart is the person who is asking?" Because if it's someone who knows math I would just say because when you count 5 comes after three. Or I could say that if you subtract 3 from 5 you are left with a positive number but if you subtract 5 from 3 the answer is negative. But, if it were a two year old, I guess I would need to show them 5 coins and take away three and show them there are still some left."

 

We talked about several other kinds of problems as well and he could verbalize the answers.

 

So, I think I've decided that dear boy CAN explain how to do a math problem, but I still believe that getting him to take the time to actually WRITE an explanation that verbalizes his thought process is going to be a challenge because his math skills far outweigh his written communication skills. And I still think it stinks that a subject he is exceptionally good at is penalized by being a poor writer.

[In The Great White North]

 

 

There is no penalty if the problem is neurological.  Many boys think faster than they can write.  Accomodations are given to those who attend public school and have this issue.

 

Nope.  Accommodations are only given if the child meets the local criteria.  Around here, that means the child must be two standard deviations below average.  A child who is at the 95th percentile in math and the 55th percentile in English would not get accommodations, but would most definitely have his math abilities inhibited by his writing abilities by this policy.

[Kalmia]

Given the discussion about the importance of being ABLE TO construct a written explanation, I decided to see what math boy, a writing hater, really could do. So, I asked him a series of questions including this one above. He looked at me seriously and said, "The first thing I would want to know is, "How smart is the person who is asking?" Because if it's someone who knows math I would just say because when you count 5 comes after three. Or I could say that if you subtract 3 from 5 you are left with a positive number but if you subtract 5 from 3 the answer is negative. But, if it were a two year old, I guess I would need to show them 5 coins and take away three and show them there are still some left."

 

We talked about several other kinds of problems as well and he could verbalize the answers.

 

So, I think I've decided that dear boy CAN explain how to do a math problem, but I still believe that getting him to take the time to actually WRITE an explanation that verbalizes his thought process is going to be a challenge because his math skills far outweigh his written communication skills. And I still think it stinks that a subject he is exceptionally good at is penalized by being a poor writer.

 

I think people are not as much objecting to cultivating the ability of students to explain their answers, but the necessity in a classroom environment of those answers being written and the subsequent penalizing of math-adept kids who may not have the writing fluency of other children. Parents of dysgraphic and writing phobic kids just hope some sort of accommodations are made to allow them to reveal their mastery of the subject (such as verbally explaining their answers). Just think of this equivalent scenario, say students in English class were asked to provide formal (symbolic) logic proofs of their arguments at the end of every persuasive essay, some very gifted writers then would end not end up with the high scores they'd otherwise deserve. I am sure their parents would also express concern that they were being unfairly penalized in their area of expertise by being asked to include analysis from another discipline with which they were less facile. 

 

So yes, it is important to understand and explain the why behind the calculations in math, but parents are aware of the inflexibility of the assessment methods in schools (perhaps only written explanations will be accepted) and are understandably nervous that their child's grade will in no way reflect their understanding of mathematics. Plus, often children (often boys) are late to catch up in writing fluency, but by the time their writing resolves itself, they will have already been tracked to a lower level math program because of their writing skills!

[FloridaLisa]

If a student is actually really good at math and pursues a STEM field he/she will need to communicate what he/she is doing at higher levels. 

 

Yes, but the difference is higher levels.  Stats show that boys' language/writing processing does catch up to girls, but there is a significant difference at primary and even middle school levels.  

 

Good grief.  The kids are not writing page long essays for every math problem.  A paragraph? My guess is that for these problems, 2 or 3 sentences will suffice for their paragrph. I don't understand the uproar. If an elementary student can not put a few words down on paper, then there are bigger fish to fry. For those who have documented learning disabilities, since this is ps, they will probably be exempted. I see the opponents to this as contributing to the dumbing down of education.

 

Bolded the part to which I want to respond.  I agree, Dot.  But I don't think this is an issue of kids that can't write.  The issue I'm raising is that writing is now introduced into yet another area that has traditionally not required it.  And that will, across the board, favor girls and hurt boys.  Interestingly, I actually have some fairly talented male writers in my family, so I'm not sure it would even affect all my boys. ;o)  But I've done enough reading to suspect that this additional writing requirement will hit the boys harder in a school setting.

 

Lisa

[Melissa in Australia]

Good grief.  The kids are not writing page long essays for every math problem.  A paragraph? My guess is that for these problems, 2 or 3 sentences will suffice for their paragrph. I don't understand the uproar. If an elementary student can not put a few words down on paper, then there are bigger fish to fry. For those who have documented learning disabilities, since this is ps, they will probably be exempted. I see the opponents to this as contributing to the dumbing down of education.

:lol:

 

 

 

 I so wish my kids could write a paragraph in primary school. I am so glad for you that you don't have to deal with the realities of Dyslexia and the incredible frustration it brings by being hampered with having to write.

And you know what . My oldest son WHO COULDN"T WRITE a few sentences in primary school and who couldn't write a paragraph until 15 and who did his first essay at 17 is at this moment in university studying Aerospace Engineering. 'cause you know what, He is great at math.

[bolt.]

I think it is important for students to be able to write/verbalize how math works. It is a skill that should be cultivated. I think it is false to divide up 'disciplines' so strictly that merely being able to calculate accurately is enough to be called 'good at math' and therefore deserving of high grades. Math is more than accurate calculation. It involves language, and a student who can't do it is not 'good at math' -- s/he is simply 'good at some aspects of math' and has room to improve on the side of grasping the conceptual level well enough to be able to express it in language. It's not a skill that's very hard to teach, if it is being taught. (Nothing should be tested if it isn't taught.) Any significant gap between 'expressing in language' and 'writing well' might come into play, but that too is an important skill that is relevant in all areas of schooling... except maybe phys.ed. (That's why there is a whole area of curriculum dedicated to it -- because it it both foundational and useful. We don't teach writing for its own sake alone.)

 

I think the word 'paragraph' is being used here loosely to mean '2 to 6 sentences worth of explanation' (or just 'more than one sentence'). I don't think it's the idea of "a thesis and supporting sentences" as noted above.

[FloridaLisa]

I am curious how many currently have their child/ren write out explanations in any form? At what age did you start this? Was this curriculum driven or something that you added to the mix? And what curricula currently include this? 

 

(And ftr, I have no horse in the CC race at this point.  I have, as Dot says (but a different context) much bigger fish to fry right now! ;o)  

 

Lisa

[dirty ethel rackham]

It is extremely useful. Putting math into words clarifies the process and helps detect when a student simply memorized a procedure without understanding.

I ask my children to narrate their solutions to me and to talk me through, especially when they got stuck.

Of course this is not feasible for a classroom teacher, so asking for a written explanation is the next best thing.

Naturally, the response should not be judged about beautiful writing or good language use, i.e. as an "English" assignment" ; it should be about logic of the argument and conceptual understanding, however poorly written.

 

Yes. in the perfect world, this would be the case.  Unfortunately, in the real world where the majority of elementary teachers have only rudimentary math skills and can barely understand the commutative property of addition and multiplication, I could totally see the teacher rewarding what is important to her - those language arts skills.  There are lots of special certificates in language arts, but I rarely see anything extra for teaching mathematics at the elementary level. 

 

I think it's a great skill to have - being able to explain the why behind something as well as the how. However, from the curriculum samples that I've seen and from my conversations with teachers who are actively involved in aligning their school curriculum with the common core, it seems that they are asking these types of questions (at least some of them) at developmentally inappropriate ages. 

 

Of course, this is JMHO and YMMV. 

 

I completely agree.  Having read the CC language arts standards for K and 1st, I think they developmentally inappropriate.  It does not take into account the normal range of development in children that age.  While there are many kids who would be able to meet them, there are many smart kids who are not there yet developmentally.  This doesn't mean they have a learning disability, but they simply have not reached that maturity yet. 

My first reaction: will this adversely affect boys? Will is affect their math grades more than girls'? My hunch (and years of reading about learning/classroom differences between boys and girls) is that across the board, these types of assignments would be tolerated better and performed better by girls.  And while it should be graded on content, there are teachers that grade everything based on neatness/handwriting.  Ask my neighbor who (though super pro-ps) pulled her son after he continued to receive F's for perfect spelling tests that weren't neat. 

 

Lisa

Exactly!  My very smart boys would not have been able to compose a sentence (written) until late 2nd grade.  They may have been able to tell you orally, but the writing was slow to develop. I had a local teacher tell me that my oldest (a National Merit Scholar getting nearly straight A's in college) would not have qualified for the higher groups because he wasn't writing sentences at 6.  He was quite asynchronous as far as development is concerned ... taught himself to read, was talented in math and science, was able to hold intelligent conversations with docents.  He just took longer to write. 

 

Because doing it would require the math teachers to have thorough conceptual understanding themselves. A teacher who has memorized procedures, can teach only algorithms, but does not truly understand (and hence also can not explain) why, for example, division by a fraction is multiplication with the inverse, will be incapable of evaluating students' explanations. Teaching math by discussing math requires subject expertise and not just a solution manual. Sadly, that is asking too much of many math teachers.

:iagree: In my experience with the elementary education programs in our state, this is not valued.  These teachers can spout educationalese mumbo-jumbo, but do not have any understanding beyond the algorithms they memorized. 

 

:iagree:

 

I think it can also lead to kids hating math class, even if they are good at it and would normally enjoy it. Understanding the concepts is important, but having to write paragraphs about them seems like overkill to me. I always liked math, but if I'd had to write little essays about it when I was a kid, it would have sucked the fun right out of it for me -- and I was a child who also enjoyed writing, so I can only imagine how a writing-averse kid would feel about it.

:iagree:

 

Obviously it's a great skill to develop.  "Proficiency" in this skill should not be expected overnight.  With many elementary teachers being more language-oriented than math-oriented, I might be concerned about the expectations or even that they're looking for the wrong things.

 

My big issue is the implementation - how often this would be required, how much actual teaching will be done on how to do this - giving them the language, etc., and really helping them connect their logic to words.  Mainly, I worry that kids who are very strong in math but weaker in language (not an uncommon combination at all!) will be prevented from moving forward appropriately in math based on their written explanations.  If this skill is not taught and developed, the results could be disastrous for such kids, taking their favorite subject, the only thing they do well, and making their success depend on their weakest skills.

 

For example, suppose my 2e-ish ds10 were in a traditional school.  Very good at math, relatively reluctant with the handwriting - his writing and handwriting are at grade level now but he does have significant processing speed issues (note, NOT quite enough for an IEP at this point and even getting a 504 plan would be questionable - he needs fresh private testing as the PS testing was insufficient). Not only would he be stuck at grade level in math (rather than in AoPS Intro to Alg as he is) but explaining what, to him, seem extraordinarily simple concepts might be torturous and make him want to avoid math.  At home (we afterschool his math entirely), I have him explain his reasoning orally (often due to the paucity of written math, LOL) and his reasoning is sound.  His language skills are slowly improving with age.  His teacher (who he has been with for years, long story) sometimes has him explain things to the other kids in his class and she totally gets him.

 

In general, I think it's a great idea to practice this.  I just worry that the devil is in the details.  It must be implemented very carefully so that they're really developing mathematical reasoning skills and actually connecting the math side to the language side rather than purely dealing with language skills.

 

Eta, pre-CCS, this isn't going to come up much in PS until the student hits geometry.  I wonder what the CCS for geometry look like - my impression is that public schools have been moving away from proofs a bit.  Will the CCS move back toward more proofs?  I'm all in favor of that.

:iagree:

 

That would depend on the grade and level, should be practiced beforehand, and the teacher should give clear expectations.

If I were teaching 1st grade, I would expect an answer along the lines of:

"If I have five blocks and take away three blocks I will still have two blocks leftover, so I know it five is bigger." 

"5-3=2 which is more than zero, so 5 is larger than 3"

"5=3+2, so 5 is bigger because I have been adding to 3 to make 5"

or a picture. Again: the teacher should model what kind of answers he is expecting and should state clearly whether drawings, charts, equations or only words may be used.

 

Also, the question should of course be age appropriate! The above question would be appropriate for K and 1st grade and ridiculous for 6th grade. OTOH, the question whether -5 is greater or smaller than -3 would be an appropriate question for a 6th grader.

 

You see, I would not expect most 1st graders to write that as a sentence.  Verbally explain it? Yes.  Write it?  no..  No doubt that some could, though.

There is no penalty if the problem is neurological.  Many boys think faster than they can write.  Accomodations are given to those who attend public school and have this issue.

 

In a perfect world, yes, that would be the case.  But, only if it is recognized.  It can take up to 3rd or 4th grade for some neurological problems to get noticed.  My SPD and ADP kid would not have gotten appropriate accommodations at our local school, for sure. But, even so, many normal,  neuro-typical kids can be asynchronous in development, capable of mathematical reasoning years beyond their written verbal skills.  Do we hold them back in an area of true talent and wait for the other areas to catch up, if they ever do? 

I think people are not as much objecting to cultivating the ability of students to explain their answers, but the necessity in a classroom environment of those answers being written and the subsequent penalizing of math-adept kids who may not have the writing fluency of other children. Parents of dysgraphic and writing phobic kids just hope some sort of accommodations are made to allow them to reveal their mastery of the subject (such as verbally explaining their answers). Just think of this equivalent scenario, say students in English class were asked to provide formal (symbolic) logic proofs of their arguments at the end of every persuasive essay, some very gifted writers then would end not end up with the high scores they'd otherwise deserve. I am sure their parents would also express concern that they were being unfairly penalized in their area of expertise by being asked to include analysis from another discipline with which they were less facile. 

 

So yes, it is important to understand and explain the why behind the calculations in math, but parents are aware of the inflexibility of the assessment methods in schools (perhaps only written explanations will be accepted) and are understandably nervous that their child's grade will in no way reflect their understanding of mathematics. Plus, often children (often boys) are late to catch up in writing fluency, but by the time their writing resolves itself, they will have already been tracked to a lower level math program because of their writing skills!

:iagree: :iagree: :iagree: And for many of these kids, they would have given up on school altogether, thinking they were dumb (or that school was dumb.)

[regentrude]

I am curious how many currently have their child/ren write out explanations in any form? At what age did you start this? Was this curriculum driven or something that you added to the mix? And what curricula currently include this?

I have my children write out fully worked mathematical solutions of their problems beginning with pre-algebra, i.e. when I started homeschooling.

They have to document every step, and sometimes use a few words, or symbols, between equations.

I do not make them write paragraphs because we talk about math - feasible with two, not feasible with 30 students.

We use AoPS which many people consider "wordy" - this is, in fact excellent "talking" about math by the author to the student, replacing a classroom teacher. Everything a teacher would explain is written out in actual language, with clean terminology and logic. It provides a great model for the students to talk about math themselves.

[Arcadia]

I am curious how many currently have their child/ren write out explanations in any form? At what age did you start this? Was this curriculum driven or something that you added to the mix? And what curricula currently include this?

 

Public school curriculum driven.

K to 1st - enVision Math by Pearson in B&M school

2nd to PreAlgebra - K12 math through virtual academy

 

So basically my older started doing that in B&M school since he was in Kindergarten.

[happi duck]

The teacher is really key in whether or not this is a useful approach or a waste of time.

 

When dd was in ps 2nd grade her school required this.  I have no problem with a student being required to explain how they arrived at an answer.  However, dd's teacher did not accept what seemed like reasonable explanations and could not articulate what she expected.  She would not accept a drawing or any of the type of answers like given upthread.

 

I spoke at length with her because math was causing dd such distress.  The teacher could never give me a clear example of what she wanted.  Another strange thing was that the packets of worksheets that constituted math class never left the classroom...not as homework and not when completed.

 

It was all very weird.

[NilaGroveSchool]

You are never going to improve students Math scores by wasting students Math time on writing sentences about their Math problems. It is a faulty idea to begin with.  Math, and Computers for that matter, are learned by performing them, not simply memorizing and regurgitating big words to make it "sound" like you know what you are doing.  Math is the one area where the correct answer is crucial, and in the adult world when math is used, valuable human lives are depending and that extremely correct answer. 

 

When Math and Computer learning goes on, it is not simply repeating the exact same operation over and over again, it is repeating and possibly changing it for another similar but different event that may come along, so that you can safely get a plane up in the air; or after a 60 MPH car crash, the backseat passengers leave the scene unscathed,  where in another time they would have been completely crushed... 

 

 

[bolt.]

I think writing sentences vastly improves math understanding, which translates directly into better skills -- as well as the sentences serving to explain to a teacher why a student who is struggling is 'thinking wrongly' and the particular thoughts that need to be replaced with accurate ones.

[regentrude]

You are never going to improve students Math scores by wasting students Math time on writing sentences about their Math problems. It is a faulty idea to begin with.  Math, and Computers for that matter, are learned by performing them, not simply memorizing and regurgitating big words to make it "sound" like you know what you are doing.  Math is the one area where the correct answer is crucial, and in the adult world when math is used, valuable human lives are depending and that extremely correct answer.

 

Just curious: are you using higher math in your daily life?

 

What do you mean by "performing math"? Math is more than just computations. Math is analyzing patterns, seeing relationships between numbers, functions, geometrical objects, putting those relationships into a statement, and proving them. Math is about the process.

Yes, the answer is important, but the process that leads to the answer is much more important than a final number.

 

Explaining a mathematical relationship has absolutely nothing to do with memorizing "big words". You don't need big words. You need a clean terminology with clear definitions so you can agree what you are taking about, and plain English. And if problems are structured in a way that requires thinking, there is nothing memorizable about the explanation.

 

Btw, any computer programmer must document his code as well, to make it usable and modifiable by others.

[boscopup]

For example

 

Page 26 (29 of 48) of 3rd grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_3_math_released_questions.pdf

 

Page 3 (37 of 43) of 4th grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_4_math_released_questions.pdf

 

Page 39 (42 of 60) of 8th grade sample

http://www.engageny.org/sites/default/files/resource/attachments/grade_8_math_released_questions.pdf

 

Main link here for NY scoring sample for 3rd-8th grade http://www.engageny.org/resource/new-york-state-common-core-sample-questions

 

As a mother of a math adept writing phobic child, I don't have a problem with the responses required in the grade 3 and 4 tests linked here (I didn't look at the rest yet). They don't have to write complete sentences. They just have to explain OR show their work. In the grade 3 example of finding which rectangles had the same area, they accepted just labeling the grid as an explanation. Basically, they're looking for the child to show that they understand the math. Fine by me.

 

We use AoPS now, and my son has to explain why very often. If my son works out a problem, he has to explain each step. We often do that part orally, but eventually I will expect him to write it. For example, if he uses the distributive property, writing, "dist. prop." out to the side would be sufficient. I don't think he needs to write, "I solved this equation by using the distributive property."

 

I guess it's the programmer in me. When writing code, it needs to be very well documented, but the comments don't have to be compete sentences. They'd often be short comments out to the side of the line of code. It needs to be clear to another programmer what you're doing.

 

I don't see much point in asking for explanations of why 5>3, maybe because that's just obvious? I think the explanations are more useful when solving word problems and especially upper level math (Prealgebra on up). If the first grade question was, "Jim has 5 balls and Sally has 3 balls. Who has more balls?" A good explanation, imo, would be, "Jim, because 5>3." I think requiring subtracting and all that is a bit convoluted and unnecessary.

[SMRB]

Quite a leap?  Give me a break. People are acting like these kids are having to write an essay (making math class=literature class!) on why 5 is greater than 4. Whether you "like" the CC or not, asking students to use words to describe mathematical concepts is not unheard of. And no, I have my suspicions that not all of us care deeply about education.

 

Also--shouldn't a fourth or fifth grader be past the process of simple addition? 5 is greater than 4?? This is K or first grade stuff, correct? No one is asking a first grader to write a multi-sentence paragraph for CC, I'd bet money on that.

 

From my son's 1st grade CC math worktext (GoMath!):

 

First it shows 4+2=7. Then it says "Sam showed how he added 4+2. Tell how Sam could find the correct sum." They are given 3 triple-ruled lines to answer.

 

Another one: It shows a picture of 4 red cherries and 5 yellow cherries. The yellow cherries are crossed out. "Explain how the picture shows subtraction." More triple-ruled lines to answer.

 

One more: "Terry added 3 and 7. He got a sum of 9. His answer is NOT correct. Describe how Terry can find the correct sum." Two triple-ruled lines to answer this time.

 

These are all in the first few chapters of the 1st grade book, so work that will be done by Christmas. I believe they are in fact asking a first grader to write a multi-sentence paragraph answer for these, assuming that the teacher actually implements it that way vs. having conversations with each child. My first grader can already absolutely explain these answers one-on-one, but he cannot right now take those thoughts, structure them in sentences, and write them in the worktext. He certainly can't spell many of the words that he would use in his explanation, so he would be more focused on encoding the words than on synthesizing the math. And he is ahead of his peers.

 

Now let me say that I am not against the common core standards for math. They challenge kids in ways that have been sorely lacking in this country for a long time now. As written by the publishers, however, many of the "CC-aligned" programs all totally depend on having appropriate teacher-child ratios in the classroom, which unfortunately is the exception and not the rule. I suspect that, in those rooms, these questions will just be skipped in the book. A real shame, because the conversation is extremely valuable.

 

Conceptually, the questions are developmentally appropriate, as is expecting a child to understand at that level and be able to explain. The task of formulating the answer and translating it onto paper absolutely is not developmentally appropriate for a first grader. We are blessed to be in a smaller classroom, so it likely won't be a problem for us, but in our local public school where there are over 30 first graders in a room with no teacher aide, the paragraph writing is a crazy expectation. My personal opinion, take it or leave it, is that we need to find a more developmentally appropriate way to implement the "explanation challenge."

[Dmmetler]

In many ways, DD being delayed on writing compared to her math scores kind of helped prep her for this, because from the start, I'd write only what she explained to me. So she HAD to put her reasons into words because I'd write exactly what she explained, right or wrong-because I didn't want to do the work for her.

 

Now that she's using AOPS pre-algebra, I can see the benefit of that, because the "explain WHY" questions really do make sense to her-she's been explaining "why" to me since she was telling me how to do number bonds in SM 1a. What we are doing is moving, gradually, to the more formal proof vs just explaining in words, and AOPS is wonderful at modeling that format.

 

I can definitely see the benefit-and definitely see why it would be really hard to implement with a classroom of 6 yr olds with typical 6 yr old writing skills. If my DD struggled even to write 14+6=20 at age 5-6, I can't imagine how she could have managed to write "14 is the same as 10+4, and 4+6=10, therefore 10+10 is the same as 14+6, and 10+10 is 20, so 14+6=20".

 

 

 

 

[J-rap]

This is a little different, but in Videotext Algebra, they would turn major Algebraic formulas into words/sentences. I don't mean literal written-out words of the actual symbols, but different words entirely. They encouraged students to think of the formulas in that way when first learning/understanding them, and it was extremely helpful for both my kids and myself. They weren't forced to write them down; it was really just a different way of understanding the concept.

[Mergath]

You are never going to improve students Math scores by wasting students Math time on writing sentences about their Math problems. It is a faulty idea to begin with.  Math, and Computers for that matter, are learned by performing them, not simply memorizing and regurgitating big words to make it "sound" like you know what you are doing.  Math is the one area where the correct answer is crucial, and in the adult world when math is used, valuable human lives are depending and that extremely correct answer. 

 

When Math and Computer learning goes on, it is not simply repeating the exact same operation over and over again, it is repeating and possibly changing it for another similar but different event that may come along, so that you can safely get a plane up in the air; or after a 60 MPH car crash, the backseat passengers leave the scene unscathed,  where in another time they would have been completely crushed... 

 

:huh:   Have you ever used a computer?  Or done any kind of computer programming?  It's not enough to memorize the code.  You have to understand why you're typing what you're typing, or you're going to crash and burn when it comes time to do any kind of unique work.  And in math, understanding the process and the reasons for doing things is just as important as getting to the right answer in the end.  To "repeat and possibly change" the operation, you have to understand how it works in the first place.

[LeslieAnneLevine]

Quite a leap?  Give me a break. People are acting like these kids are having to write an essay (making math class=literature class!) on why 5 is greater than 4. Whether you "like" the CC or not, asking students to use words to describe mathematical concepts is not unheard of. And no, I have my suspicions that not all of us care deeply about education.

 

Also--shouldn't a fourth or fifth grader be past the process of simple addition? 5 is greater than 4?? This is K or first grade stuff, correct? No one is asking a first grader to write a multi-sentence paragraph for CC, I'd bet money on that.

 

I don't know about other states, but NY test results are online for the CC, and it looks like a third failed miserably.

Yes, it's quite a leap to assume those who don't agree with you that this is a fantastic idea for every student are contributing to the dumbing-down of education. The posts I've read on this thread are by people who seem to care a whole lot about their child(ren)'s education. 

 

My son's 6th grade math workbook, which conforms to State and Common Core State Standards, sometimes asks for written explanations. At least one of the questions does indeed address number size. He was asked to give the smallest 3-digit number that could be made with 3, 4, 7, and 9 (after answering how many 3-digit numbers could be made in total) and explain how he knew it was the smallest number.  

 

There is no reason to slow down a math-loving kid to make him or her write a paragraph or even a full sentence about something obvious (or perhaps not, if we're getting philosophical about it), or something that can be answered in a few words. It's not about dumbing it down; it's about not making them hate math. Why didn't it instead ask him to explain how he concluded that 24 different 3-digit numbers could be made? That would at least make more sense.

 

I would argue that having to write how they know 347 is "smaller" than 793 is dumbing things down. Why not ask how they know that their pants go on their legs? My son has little patience for those kinds of questions, but since he is homeschooled he doesn't have to answer all of them, and for others he can write just a few words. I imagine there are kids like him in school who are regularly frustrated by this.

[LeslieAnneLevine]

I would argue that this is a core basic question for grade 6, not an intermediate or advanced, and that the test is checking for understanding of place value. Students in sixth nonsped should be able to explain. The problem of course, is that it is also a 2nd grade advanced question.  Instead of claiming 'dumbing down' we should be thinking 'including all nonsped learners'..even the nclb "1" s.

You took that sentence out of context--I was not claiming dumbing down, but responding to Dot's assertion that people who oppose asking for paragraphs to show how math problems were solved are in favor of dumbing down education.

 

I am sure it is a core basic question for 6th grade; that's why it's in the book that conforms to Common Core standards. I also understand that the question is checking for understanding of place value. My problem with it is that there are children for whom this is going to make math miserable. There are plenty of other questions (such as which number is in the ___s place? or what place value does the "3" have in 124.03?) that check for understanding without being obnoxious about it.

[LeslieAnneLevine]

 Reality check==not all kids are great at math. Why should my son write essays in college, since he wrote hundreds of them in high school. Will writing one more make him hate writing? Should he whine to the prof? Why should he take an exam in the first 3 chapters of calculus, since he knows it all? It's making a mountain out of a mole hill.  It seems like the first results of the CC exams are showing that way too many are extremely deficient. Really, is this test so much harder than last year's state tests? If one third of the 3rd and 4th graders failed miserably, then they apparently can't do simple math, let alone explain it in a few words. Look at the language arts results--they stink, too.

  I'm done here. People whining and bitching about forcing a student to explain their work makes me ill. A classical homeschooling board. This is going to make great dinner conversation tonight.

 

You purposely misunderstand what people are saying here, but at least it will make good dinner conversation. Should be a hoot.

[Catwoman]

You purposely misunderstand what people are saying here, but at least it will make good dinner conversation. Should be a hoot.

I didn't think we were whining and b*tching, did you? :confused:

 

Maybe she wasn't talking about us.

 

I don't think anyone has suggested that kids shouldn't be able to explain their work, but maybe I missed something.

[LeslieAnneLevine]

I didn't think we were whining and b*tching, did you? :confused:

 

Maybe she wasn't talking about us.

 

I don't think anyone has suggested that kids shouldn't be able to explain their work, but maybe I missed something.

No I didn't think we were and I certainly wasn't trying to make anyone feel ill!

 

I am dealing with this during my son's math lessons. I have seen how those types of questions frustrate him and I am glad we can approach this issue with some flexibility. It's not a matter of "he shouldn't have to do anything he doesn't want to or already knows how to do"; it's about keeping him moving forward in math rather than ruining it for him with what he considers to be inane questions and too much writing. This would have especially been a problem in younger grades when he really struggled with writing. 

[dirty ethel rackham]

Here is an analogy to explain why many of us are concerned about making a child write a paragraph, especially for those who have kids who excel in math (not just memorizing algorithms, but really get it intuitively.) 

 

My son taught himself to read.  No, he didn't teach himself phonics - he had rudimentary phonics as in what each letter sounds like.  He just figured it out.  He could not explain how he knew that the sign in the grocery store said "Bulk Foods" but he just knew that is what it said (and he didn't know what it meant because he had never heard the term before and this is how I knew he was reading.)  By the end of first grade, he was reading at a 4th grade level, with excellent comprehension skills.  But, he couldn't spell.  He didn't learn phonics rules.  Should I have stopped him from reading until he learned phonics well enough to spell?  Heck, no!  We worked on phonics concurrently with continuing to read with gusto.  The same thing with math.  Should I have stopped him from moving on in math because he could not put his thoughts into a sentence?  No.  Math was joy and passion for learning.  Writing?  Not so much.  So, we continued to work on writing, but not use that as a reason to hold him back in math.  He could verbally explain how he knew the answer and he could show his work, but writing it in paragraph form would have brought tears and gnashing of teeth.  He was close to grade level (at least according to older standards, not the newer, developmentally inappropriate standards), but way ahead in math and reading.  The parts of the brain that are used for mathematical reasoning are not the same as the language arts parts of the brain.  The skills needed for reading are not the same skills needed for writing.   If I was going to abandon joy and passion for learning and force him to only learn on a synchronous level, then why homeschool him?  I could have put him in school for that.  Does that mean I don't value writing?  Not at all.  But I take a much longer view of things.  My goal is not to meet this year's standard (or fad for that matter,) but look where they need to be in the future.  Will my elementary-aged child be ready for high-school level work when the time comes?  Will my high schooler be a good candidate for college when we are done?  Overall, will my child be a productive member of society?

 

 

[Spy Car]

Here is an analogy to explain why many of us are concerned about making a child write a paragraph, especially for those who have kids who excel in math (not just memorizing algorithms, but really get it intuitively.) 

 

My son taught himself to read.  No, he didn't teach himself phonics - he had rudimentary phonics as in what each letter sounds like.  He just figured it out.  He could not explain how he knew that the sign in the grocery store said "Bulk Foods" but he just knew that is what it said (and he didn't know what it meant because he had never heard the term before and this is how I knew he was reading.)  By the end of first grade, he was reading at a 4th grade level, with excellent comprehension skills.  But, he couldn't spell.  He didn't learn phonics rules.  Should I have stopped him from reading until he learned phonics well enough to spell?  Heck, no!  We worked on phonics concurrently with continuing to read with gusto.  The same thing with math.  Should I have stopped him from moving on in math because he could not put his thoughts into a sentence?  No.  Math was joy and passion for learning.  Writing?  Not so much.  So, we continued to work on writing, but not use that as a reason to hold him back in math.  He could verbally explain how he knew the answer and he could show his work, but writing it in paragraph form would have brought tears and gnashing of teeth.  He was close to grade level (at least according to older standards, not the newer, developmentally inappropriate standards), but way ahead in math and reading.  The parts of the brain that are used for mathematical reasoning are not the same as the language arts parts of the brain.  The skills needed for reading are not the same skills needed for writing.   If I was going to abandon joy and passion for learning and force him to only learn on a synchronous level, then why homeschool him?  I could have put him in school for that.  Does that mean I don't value writing?  Not at all.  But I take a much longer view of things.  My goal is not to meet this year's standard (or fad for that matter,) but look where they need to be in the future.  Will my elementary-aged child be ready for high-school level work when the time comes?  Will my high schooler be a good candidate for college when we are done?  Overall, will my child be a productive member of society?

 

For just the reasons you outline (simplified: because it is hard for him) I would argue that it is doubly-important to work on this skill. It can (and probably should) be done orally (and the Socratic Method can be your friend).

 

It is important to be able to articulate ones reasoning, and to cultivate that part of the mind, this does not mean one has to "stop" progress, not a bit. But better IMO to incrementally cultivate the skills earlier than hope they magically appear out of nowhere.

 

People don't always like to do what isn't easy for them, but avoiding what's hard isn't always the best course.

 

My 2 cents.

 

Bill

[dirty ethel rackham]

For just the reasons you outline (simplified: because it is hard for him) I would argue that it is doubly-important to work on this skill. It can (and probably should) be done orally (and the Socratic Method can be your friend).

 

It is important to be able to articulate ones reasoning, and to cultivate that part of the mind, this does not mean one has to "stop" progress, not a bit. But better IMO to incrementally cultivate the skills earlier than hope they magically appear out of nowhere.

 

People don't always like to do what isn't easy for them, but avoiding what's hard isn't always the best course.

 

My 2 cents.

 

Bill

 

Oh, I did it orally.  We frequently had conversations about his math work.  I just didn't require it in writing. He had to show his work but he didn't have to write a paragraph.  In third grade, it would have taken 1/2 hour to get him to write one sentence.  He could do a whole page of Singapore problems and explain to me each problem in the time it would have taken to cajole, encourage, order, wipe tears, coach, encourage him to write that sentence.  I saved the tears and gnashing of teeth for teaching writing instead of ruining math.  My oldest is now in his 2nd year of college on a 2/3 tuition National Merit Scholarship at a liberal arts college (where he is required to write.).  While writing isn't his strongest point, he is doing well.  Next month, he will present his summer research at a campus-wide symposium.  I guess not requiring him to write a paragraph about math didn't ruin him.    My second son (a high school senior) is following closely in his footsteps.  He will likely major in Physics or Math.  He is a weaker writer (not for lack of effort but due to some residual processing issues.)  But I don't think that should slow him down.  The world needs big thinkers.  They don't all have to be the most eloquent people on the planet.  That's what politics is for (just kidding.) 

[Spy Car]

Oh, I did it orally.  We frequently had conversations about his math work.  I just didn't require it in writing. He had to show his work but he didn't have to write a paragraph.  In third grade, it would have taken 1/2 hour to get him to write one sentence.  He could do a whole page of Singapore problems and explain to me each problem in the time it would have taken to cajole, encourage, order, wipe tears, coach, encourage him to write that sentence.  I saved the tears and gnashing of teeth for teaching writing instead of ruining math.  My oldest is now in his 2nd year of college on a 2/3 tuition National Merit Scholarship at a liberal arts college (where he is required to write.).  While writing isn't his strongest point, he is doing well.  Next month, he will present his summer research at a campus-wide symposium.  I guess not requiring him to write a paragraph about math didn't ruin him.    My second son (a high school senior) is following closely in his footsteps.  He will likely major in Physics or Math.  He is a weaker writer (not for lack of effort but due to some residual processing issues.)  But I don't think that should slow him down.  The world needs big thinkers.  They don't all have to be the most eloquent people on the planet.  That's what politics is for (just kidding.) 

 

LOL :D

 

If they can explain the reasoning orally it shows they know it. I think doing it orally is a more appropriate method (especially with younger kids) anyway, it's just school-teachers don't often get the time to discuss such things with individual students, so "writing" is often the fall-back. This is an advantage of home education.

 

Bill

[Dina in Oklahoma]

Thank you for reminding me about this strategy. I ran across this resource a few years ago, but put it aside for a "program" that was a waste of money. I really think this may be just what DD needs this year. . .

 

http://www.amazon.com/Writing-Math-Class-Resource-Grades/dp/0941355136/ref=wl_it_dp_o_pC_S_nC?ie=UTF8&colid=I5GY8BYY9GT5&coliid=I15CBXWRVH7EVJ

 

Perhaps others may find it useful.

[Arcadia]

Thank you for reminding me about this strategy. I ran across this resource a few years ago, but put it aside for a "program" that was a waste of money. I really think this may be just what DD needs this year. . .

http://www.amazon.com/Writing-Math-Class-Resource-Grades/dp/0941355136/ref=wl_it_dp_o_pC_S_nC?ie=UTF8&colid=I5GY8BYY9GT5&coliid=I15CBXWRVH7EVJ

 

Perhaps others may find it useful.

Reserved from the library since I am curious. My boys enjoyed her "I Hate Math" and "Math for Smarty Pants".

[Jamee]

A little late to the conversation here.  My mom is a retired math teacher, and she was having her high schoolers write explanations to their math answers over 20 years ago.  But, rather than having to do a page of problems, over and over, they'd have to do 5-10 with explanations.  My husband is a middle school math teacher, and he too requires written explanations and will be doing so even more now. Once again, this is something that has been done long before Common Core was implemented.  

[Chelli]

The math program we use, Math in Focus, actually has math journaling exercises in almost every chapter. I love them. They are the perfect way to assess if my dd TRULY understands what she's learned in the chapter. To me, it's kind of like narration math-style. If she can't explain it to me, then she truly doesn't understand it. The old adage you can't teach what you don't know. When we started doing this in first grade she definitely had trouble putting to words what she was doing with the numbers, but I walked her through it and we worked on it just like when you start teaching your children to narrate in language arts. Now finishing up her 3rd grade book, she does really, really well with the math journaling activities.

 

However, in a class room situation these activities usually are done written instead of orally which is not good for those with delayed writing skills or writing phobia. In a perfect world, the teacher could go around and ask each student to tell them the process. That's probably not going to happen either due to time constraints.

I like the idea that a pp mentioned of having the entire class work together to narrate the math process for first and second grades. Starting in 3rd grade, I think it would be reasonable for children to be able to write a couple of sentences in a math journal.

 

I never had to math journal in school, but I have seen the benefits in my dd of having to really think about and explain how she got the answer. IMO, it makes children who are naturally good at math really have to stop and think about what they are doing. For children who struggle with math it would help them understand the process thus leading to better math knowledge overall.

[lynn]

This has been a thread of which I learned a lot from.  Thank you for sharing and helping me better understand this process.   I just so happened asked my ds a couple of math questions the other day when were going over his Saxon Algebra 1 then had him explain to me again when he had to go back and correct his work.  I was a little nervous I must admit but so happy when he was able to verbalize the steps he took to get the answer and in the process  added  exactly he did wrong with ones he had to correct.  

 

[NilaGroveSchool]

Regentrude asked NilaGroveSchool: Just curious: are you using higher math in your daily life?

 

Mergath asked NilaGroveSchool: :huh: Have you ever used a computer? Or done any kind of computer programming?

 

Answers: I am a mechanical engineer and have written computer programs (both neat and organized). My husband is an electrical engineer, who completely agrees with me on this topic, has also written many computer programs (he is legendary for his neatness and organization skills). I have a 24 yr old public schooled son who has taken many upper level math courses and computer programing courses. My 8 year old daughter is a programmer on Scratch.

 

Neatness and Organization should always be required/demanded in Math and is something I could fully support. But, this paragraph business....

 

One of our college professors visits us regularly (about once a year). He was formerly the Head of the Electrical Engineering Dept. He said for about the last 25 years the Engineering College's curriculum has had to be continuously "dumbed down" so that they can retain and graduate students.

 

I continuously read that highly technical companies are having to go outside of this country to find qualified candidates for their jobs...

 

Writing a 5 sentence paragraph explaining why one number is larger than another is going to STEAL time away from these students that is needed to learn actual MATH!

[Leav97]

...

 

Writing a 5 sentence paragraph explaining why one number is larger than another is going to STEAL time away from these students that is needed to learn actual MATH!

 

If the student can't take 8 words and explain 5>3, they haven't learned the current level of MATH.  Pushing them forward if they haven't learned the current level of MATH would be foolish.

 

When did MATH become all uppercase?

[SMRB]

Out of curiosity, I asked DS6 (1st grade) how he knows that 6 is more than 3. His answer: "because I count 3, 4, 5, 6." Gee - makes perfect sense, short and sweet, and correct. Much simpler than what I was thinking. And he could have written that out. Maybe we're just thinking too hard about things that really are simple and obvious to a child who really gets it. I will be keeping an eye on the answers he gives for similar questions in his book to see if he can do it as well at school.

[SMRB]

From my son's 1st grade CC math worktext (GoMath!):

 

First it shows 4+2=7. Then it says "Sam showed how he added 4+2. Tell how Sam could find the correct sum." They are given 3 triple-ruled lines to answer.

 

DS did this page in school this week. I chuckled when he brought it home, because the answer he wrote was, "He could draw." They apparently talked about it as a class and the teacher liked that strategy, so she wrote the sentence on the board and they all copied it in their workbook.  Maybe asking them to explain really is a molehill, even for a first grader.