Math as an essay-writing subject

by Honolulu Mother

Explaining Your Math: Unnecessary at Best, Encumbering at Worst

This article looks like catnip for Totebaggers. Let’s all complain about how math has been turned into an essay-writing subject! Thank goodness, mine are past the worst of it by now.

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132 thoughts on “Math as an essay-writing subject

  1. I can only thank the heavens that I did not have to go through this nonsense myself or with my children. It makes me so angry I could scream. I am hoping that someone has had a positive experience with this so at least I can understand why and how it helped their child.

    Showing my work neatly (and step by step if necessary) should indicate that I understand how to solve the problem. No written explanation will do any good, at least the way my mind works. Sometimes I do addition or subtraction in my head in weird ways – I would never want to have to write down what I am thinking.

  2. I unsurprisingly agree with most everything here. However, I think most people who find math easy, would. I am curious how we help those who struggle. When I was in high school tutored a young single mother who was trying to get her ba and teach elementary school. All that she needed was an algebra class, that she had already failed once. (She was my mom’s work study, and at $5 hour I was much cheaper than school approved tutors at $10/hr). She could not do story problems to save her life. (Like: Maggie is five years older than Sarah. Sarah is 6 years younger than Karl. Karl is 30. Write an equation to solve. ). She could factor equations, etc. but couldn’t get through the story problems. I doubt I was much help, but I think writing some number sentences when she was 7 might have worked.

  3. And yet, Attwood added, many children on the autism spectrum, even those who are mathematically gifted, struggle when asked to explain their answers.

    With an autism spectrum diagnosis, would one be able to get an IEP that just had you give the correct answer?

  4. Rhett, it is very difficult to get an IEP implemented and followed.

    My youngest is in the throes of this type of math. He is very talented mathematically, and very challenged in language arts. This approach takes away his ability to be good at something.

    My theory on the common core approach is that it is written by people who believe math is confusing, and so math instruction should be frustrating and confusing. I have a Ph.D. In a math related field and I don’t believe I could get a high score on the third grade math question in the article. I literally had no idea what sort of answer they were looking for.

  5. “information and procedures that have been become automatic frees up working memory. With working memory less burdened, the student can focus on solving the problem at hand.”

    This is what makes sense to me. I understand the need to teach kids different ways to attack a problem, because not all kids think alike. I understand the desire to make sure kids aren’t just blindly repeating Computation A without understand when to use that or why. But math has its own language. If you can write out the steps of the equation and follow it through to the end, you *are* explaining your answer.

    These kinds of problems drove DS nuts last year. He could write out all of the math, but his explanations were always of the “because it is” variety (with the implicit “, you idiot,” in the middle).

    Just this week I saw an “explain your answer” that made sense: he was doing his homework online, and there was a word problem about interpreting a bar graph (“there are 50 towns in county X, and the population is evenly distributed. Jim estimates that each town has approximately 400 people. Is his estimate right?” And the bar graph showed about 20,000 people in county X). The official “answer” was a yes/no. But the “explain how you know” section was the mathematical equation, and they needed to fill in the numbers — so the options were “yes, because 20,000 divided by ___ = ___,” or no because the same equation does not equal ___.

    To me, that’s the point of “explain your answer”: you know the yes/no isn’t just a lucky guess, and you can tell from the equation that the kid has translated the word problem into the right mathematical equation. Anything beyond that is just English majors teaching math.

  6. “She could not do story problems to save her life. (Like: Maggie is five years older than Sarah. Sarah is 6 years younger than Karl. Karl is 30. Write an equation to solve. ). She could factor equations, etc. but couldn’t get through the story problems. I doubt I was much help, but I think writing some number sentences when she was 7 might have worked.”

    @Ada — I think it’s the other way around. We need to think of English and Math as two equivalent languages. People don’t need more practice translating Math into English — which is what these “explain you answer” assignments do. They need more practice translating English into Math — i.e., what the heck is this stupid story asking me to do?

    The problem is real, but the solution is bass-ackwards.

  7. I was great in math as a kid, but I was frustrated by math when DD got thrown into the CC in third grade.

    I’m a fan now, BUT it is really hard for a child that struggles with reading and writing because you really have to have these skills too.

    I’ve re learned the math using the new methods. It can be painful( and sometimes stupid), but I know she understands it. I think this is important for a generation that could just scream simple math into their phones and get an answer right away. We want them to be able to do the complex problems that they will encounter at work etc.

    In my experience, if kids stick with the CC math for years, you can see the payoff in the older grades.

  8. In the real world of work, no one sets up the math problem for you. They give you an assignment, they don’t usually directly tell you there is math involved, then you have to figure out what, if any, math applies to get the information you need to complete the assignment. I think this understanding when to apply what is the goal of the common core.

    As a child we did a lot of math where the problem was set up for you, and not a lot of theory behind what you were doing or how you go about setting up the problem. Word problems were then a huge obstacle, but were never a big enough part of a test that missing them all would cause you to fail. We rarely ever when over how to move from a word problem to the equation.

    My kids had a similar experience in the school, but we did Singapore Math on the side, which does give you more of the theory of what you are doing. Then it gives you word problems to see if you can apply what you learned. It required you to think through the process in the early grades….is this word problem addition or subtraction? How do I know that from reading it? Now that I decided that, how to I write the equation? Then, can I actually add or subtract those numbers.

    My HS DD has assignments called “problem sets” that can draw from any level of math learned up to where they are – so Algebra 2 can draw from Algebra 2, Geometry, Algebra 1…1st Grade math. They are all word problems that are applications of math. Like “Ginny wants to recarpet her living room, the room is a 5 sided shape that looks like: (they would be provided a diagram with the dimensions). Ginny chose a patterened carpet and was told she needs to purchase enough carpet to cover the floor, plus 10% to allow for matching. The carpet comes in rolls that are 15 feet wide by 200 feet long. How many linear feet from the roll does Ginny need?”

    This is a multi-step problem that would be hard to have “rote” memory to figure out. Her school gives 3-5 of this caliber of problem every 1.5 weeks. My child balks, but I see her improving on identifying what math is needed for the assigment. She could always solve it once an equation was set up.

  9. I’m going to disagree a little with ssk and agree with Ada. I think that most of us naturally grasped the understanding part easily, so to ask us to explain it–especially to explain it in some overly contrived four-box diagram with Why, Do, See, Whatever–is unnecessary and tedious.

    But I think a lot of average, mortal kids had been trained, consciously or otherwise, to just work the problem by memorizing the process. That works for only so long. Ada’s friend can remember FOIL for factoring but somewhere along the way never picked up enough of the Why aspects to formulate Sarah = Karl + 6 and Karl = 30. I probably hit this same wall; it just happened to be a little bit further down the track in the middle of Differential Equations. (Fortunately, undergraduate engineering, contrary to popular perception, rarely applies math much past Algebra II.)

    So I think adding the Why was a step in the right direction, but it seems like there are a lot of examples where it’s been taken a little too far. The homework my oldest has been doing, compared to what I remember at the same age, is a lot lighter on the repetition and heavier on hitting them with carefully confusing word problems. “Jack, Jill, and Joe have 1000 jelly beans total. Jack has 247, Jill has 179. How many does Joe have?” This is a pre-Algebra problem hiding in 3rd Grade arithmetic. With no further guidance, they have to set up 247 + 179, solve that, then write 1,000 – 426 and solve. I think something like that is the right balance. (Incidentally, I had to run a Google search a couple weeks ago because I was uncomfortable with the mechanics of subtraction borrowing when you have multiple zeroes in the next-highest place. That was a little bit embarrassing.)

  10. @Milo, I agree completely with your example. My pissyness comes from last year’s 3rd grade math, which would have presented the same problem, followed by an “explain how you know” kicker. AFAIAC, being able to write out what you write out IS the explanation.

  11. I was a math minor in college but mostly a plug and chugger with the formulas. I am generally in favor of things that prompt a deeper understanding of things. I understand results will be hit or miss. Our district uses Everyday Math, common core friendly version. Every time the district’s achievement metrics are discussed, Math leads the way and has for 8 years. I will support the program based on these results.

  12. “AFAIAC, being able to write out what you write out IS the explanation.”

    EXACTLY. What they really want to check is for understanding and the metric is demonstrated by the conversion from English to Math. That should be the whole point of word problems. If the student can translate jelly beans into a math problem, then there is absolutely no reason to convert that back to English.

    And Austin’s carpeting example should be the standard for high school.

  13. I remember mention of a kid who answered “how do you know?” with “MATH.” Was that on here?

  14. LfB and Milo – recently (2nd grade) we had a similar problem and my minimalist wrote down the equation under “explain how you know” and I had to go through with her and say they want you to round up 98 to 100 and then round down 62 to 60 and then add the tens place and then add the ones place. So much more work when she had already done the equation correctly!

    Milo, we are no longer supposed to borrow. But the alternative method is insufficiently explained to me, so I taught her how to borrow anyway. ;)

  15. I think I will be in the minority today, but I’m a big fan of having kids learn early on to explain their answers. In the real world, you have to be able to explain how you take a bunch of ambiguous information and turn it into whatever your final product is. Sometimes you even have to explain how you got that information to start with. In engineering school, we were taught to start with the Givens, identify what we need to Find, and write out the Solution. The more steps the professor could decipher, the more credit you would get for a wrong answer. And if you gave a right answer without showing any work, that wasn’t good enough. However, that didn’t go far enough – recent grad engineers I worked with in practice could not explain in writing what they were doing and why it was right. Technical writing comes naturally to some (like me), but others need more instruction. I believe there is much more emphasis on writing in engineering courses now and that is a good thing. Even better if they start young to prepare for STEM education. In engineering practice, we often had to provide a written report to explain the assumptions and input that went into a computer program because the hundreds of pages of computer printouts are indecipherable to anyone who doesn’t look at them every day. The same is true of financial reports, market studies, cost estimates, patent applications, academic papers, etc., etc.

  16. “Milo, we are no longer supposed to borrow”

    Really? Mine are obviously still being taught to borrow. I realized they knew it better than I did.

    I’m surprised they would change it, because the curriculum in the early grades is so obsessed with drilling home the ones place and the tens place and the hundreds place, e.g., to represent 47 you must draw four sticks of 10 little cubes fused together next to seven independent cubes.

  17. But I think a lot of average, mortal kids had been trained, consciously or otherwise, to just work the problem by memorizing the process. That works for only so long

    What difference does it make? It’s not like average mortal kids are going to get jobs that require a lot of high level math.

  18. “Even better if they start young to prepare for STEM education.”

    ITA. Along those lines, one thing that’s really frustrating me with the habits the school is encouraging is the way they give out these “problem sets” like I described on a single Xeroxed worksheet with about eight problems on each side. Each problem gets a tiny little box for the solution. So DD is doing that 1,000 – whatever problem, and the borrowing is going up right into the printed question. That causes an error, because nobody can read even their own writing when it’s superimposed into other words like that. And when I say that there’s an error, of course she just wants to erase, which looks even worse. I have to dictate “cross that whole thing out. Next to it, write ‘see attached.’ Get a blank sheet of paper from the office. You’re going to staple that to your homework. Do your problem there.” Then she set the problem up wrong, subtracting from 1,000 not the combined number of jelly beans between the two, but just from one of the kids. So I said “just throw that piece of paper away and get a new one” and she looked at me as if I had said to cut off her own finger. In the absence of other guidance, they actually take to heart the school’s Earth Day bullsh1t. I love the Earth, too, but saving a few sheets of paper is not worth getting homework problems wrong. So I explained, again, that a typical exam problem in a college engineering course might require about eight sheets of paper, and you need to take up plenty of space setting up givens and variables, etc.

    I am willing to bet that elementary schools would see a significant increase in math test scores if they printed every problem/question on its own sheet of paper simply because it would encourage the kids to spread out their work. What an easy fix that they’re not doing.

  19. “In fact, for years students were told not to explain their answers, but to show their work, and if presented in a clear and organized manner, the math contained in this work was considered to be its own explanation. ”

    Thank God my kids’ MS/HS still takes this approach.

    When my youngest was in 6th grade there was a little bit of the “essay” approach. Not much, but some. I talked to the teacher (a person with a masters in education who freely admitted math was not her strong suit) and said that as long as he has all the steps in a solution, like in the discount price example, he should get full credit. And for things that are given, like generally acknowledged math facts (5×3=15), just using those should be enough. She wasn’t prepared to battle me on this, so I won. The essay approach was dropped for that year.

    AFAIK, the ‘essay’ approach is not used in college math, so I do not see its benefit.

  20. My DD has to explain her answer in a short sentence. It is words but can also be a visual/diagram. The “words”at this level are not an essay or painful but it does make the kid think about the math process. I think this is a good thing. I grew up with traditional Math and I think that was good but lacked the why which was important later in life and on the job. I like the two prong approach of knowing your Math facts but also how you are using them to solve problems.

  21. This was a huge annoyance when my son was in 5th grade. The school had diagnosed him with dysgraphia but he got no accommodations (because he was “bright” so didn’t need them) and did not inform the teachers. So literally every day, he failed to write sufficient narrative to explain the “how”, and had to stay in at recess to do it over. So he never got to play with friends, and the subject he was strong in became something else to hate about school. That was the beginning of the bad frustration and friends issues years, and I think a lot of it had to do with not ever getting to go to recess and play with friends. So yeah, not a fan.

  22. the early grades is so obsessed with drilling home the ones place and the tens place and the hundreds place, e.g., to represent 47 you must draw four sticks of 10 little cubes fused together next to seven independent cubes.

    I see that as well. 3 x 5 = 15 draw out three groups of five. Mastering that concept should take an hour, maybe and afternoon at the very most. I can’t wrap my mind around the idea that teaching that concept to mastery should take more than a few hours.

  23. SWVA’s answer is also sort of what I told my kid. In the work world, you have to figure out a solution. Even many solutions that don’t require math require you to explain the logic and/or steps you went through to get a sign off. Your boss wants to know that you took all the relevant information into account and sometimes how you took it into account. Learning to lay that out concisely (YMMV based on the assignment and profession) and clearly often makes you more valuable.

  24. I just saw Milo’s comment on the attached sheets for Math. My kids HATE to do their homework on another sheet if there is no space. I battled DS constantly on this. He was getting things wrong because he was squeezing the numbers and couldn’t see his own steps. Also on test papers I don’t think there is enough space to solve problems. Growing up we had a test booklet and a separate answer book and could attach as many extra sheets as required.

  25. I am laughing at this discussion. Every night, for the last however many years since DS2 started school, I have listened to the battle – my husband yelling at the kid “EXPLAIN YOUR ANSWER!”. Kid yells back “No, the teacher doesn’ t make me!”. And my husband “But I am MAKING YOU!”.
    My husband is the PhD uber-quant, who, who was recruited by some top secret branch of the NSA to work on cryptography algorithms based on his thesis (no, he did not take them up on it), who had NSF grants for mathematical research when he was in academia, and who now makes his career interfacing between the financial quants and the software geeks because he can speak both languages as well as speak English to the upper management. He believes utterly that if you can’t explain math, you don’t understand it. He also often jokes that he spends much of his workday explaining really difficult mathematical algorithms to extremely smart people.

    Interestingly, he never had battles with my oldest, who is also very mathematically talented – explaining was easy for my oldest. Sometimes, getting him to SHUT UP with his explanation was the harder part, as he would get more and more excited about all the connections he was seeing.

  26. My kids are little and can use writing practice. What they are “learning” in math, though, are concepts that they (and most of their class) understood long ago, so the early grade level math of Common Core doesn’t match where they are developmentally. I would be fine with having to explain your answer if you were asked to explain answers that let you actually learn math, not write/draw pictures about simple addition from kindergarten through second grade.

    If my kids were missing recess over this, I would definitely be pursuing the IEP route. When my kids get to the point where school is academic rather than social, we may consider homeschooling for math once the kids are old enough to be home alone if they want.

  27. Milo, I completely relate to your “attached” story. This is me with all of our kids at some point. Loud and clear, they all got it…DO NOT LET YOUR WORK BE CONSTRAINED BY THE FORM.

    If a teacher ever pushed back / downgraded because they used additional sheets, or wrote on the back or whatever, I engaged. My approach was always “choose what you want: a kid’s full answer, or one that fits in the (too often insufficient) space provided.” Some times, a (boy) kid just can’t write small enough clearly enough to fit an answer in the box. Sometimes their long-winded answer takes more space than a concise answer. But, bottom line, don’t you want to see the work the kid is actually doing?

    To this day, I remain undefeated.

  28. I also remember my physicist father always making me show every step of my math homework, in insane detail, and then explain it to him. I think it was because I was very sloppy and he saw it as a way to prevent careless mistakes.

  29. Rhett, the concept of place value is really integral in CS, and sadly, I often see undergrads who clearly did not learn it to mastery – in fact, they don’t get it at all.

  30. He believes utterly that if you can’t explain math, you don’t understand it

    That the answers are always correct is immaterial?

  31. I often see undergrads who clearly did not learn it to mastery – in fact, they don’t get it at all.

    Were they ever going to get it?

  32. One more thought on this – I don’t think kids should be writing essays about their math problems. Essay form is not a good writing form for explaining math. The explanations should be short and concise – a mix of short sentences, math expressions, and maybe some visuals. When you look at a math book, that is the kind of writing you see. The only time my kids have ever encountered an essay in math was back when our district still did the infamous math feelings journal in middle school. Only my oldest had to do it – the assignment thankfully disappeared once the district adopted Common Core. I haven’t seen any outrageous math writing assignments since.

  33. Rhett, I firmly believe that anyone of even just basic intelligence can master place value if given some time. That is one of the big differences between the Asian approach and ours – Asian countries believe that all kids can master math, at least up to the algebra point. And in fact they do a lot better.

  34. And in fact they do a lot better.

    To what end? It’s not like someone who struggled mightily to master place value is ever going to be successful in a CS job.

  35. makes his career interfacing between the financial quants and the software geeks because he can speak both languages as well as speak English to the upper management.

    That seems to indicate that most financial quants and software geeks can’t speak each others language or speak English to upper management. Yet they are all gainfully employed. What I think your explain everything plan will do is push a lot of gifted but shy, awkward, non-verbal people out of STEM as they will think they are bad at math.

  36. Rhett – You seem to be arguing that if they’re not going to be engineers or mathematicians, then why bother at all. I don’t agree, because I think there’s a lot of room for improvement, even for the sales douche types, when it comes to better understanding everyday things like percentage increases, growth rates, compound interest, polling results, and so forth.

  37. @Milo – the sales douches I knew always had fuzzy Math in their estimates. They wanted a certain result and used tricky Math that no one else could decipher to get there. However, they were sharp enough to know when their commission was off by even a dollar.

  38. Rhett – One point I harp on with my kids is learn things to your ability and don’t blow things off just because now you think you don’t need to know something. The work world changes quickly and the mix of tools you need in your toolbox to be successful changes too.

    In MM’s DH’s world they either aren’t able to get people with the full package of skills they desire so they also employ the “translator” or they are trading off other benefits derrived from more focused groups.

  39. When I took AP calculus exam, there were essay type questions at the end.

    Also @WCE – I totally agree. The basic addition common core is draining all enthusiasm for math.

  40. aren’t able to get people with the full package of skills they desire so they also employ the “translator”

    Exactly. The theory seems to be it would be better to take 8 year old Dave the future gifted developer and make him do endless hours of mindless busywork in order to get him better at explaining stuff so hedge funds don’t need translators anymore. Is that the idea? Because if it is, I don’t think it’s going to work.

  41. Where DH works, the top management all have very excellent math skills, but do not necessarily have the level of specialization needed to understand the quant algorithms, or the math behind program trading. I think there are very few non-mathy types in that sort of hedge fund

  42. My sense is that in the future, the truly good jobs are all going to require something special – either quantitative skills, or salesman abilities or being a really good communicator, or being the person who can translate between all those people.

  43. On one hand, the new Common Core approach does have the kids doing what most mathematically-gifted people I know do naturally – estimate the answer using the nearest ten and then back out the correct answer.

    On the other hand, I think that using this before doing the rote learning has been really confusing for a lot of kids who aren’t mathematically-gifted.

    Add in the requirement to write out the explanation for your answer at an age where many boys aren’t writers, and there are a lot of early elementary kids who are struggling in a subject they are fundamentally capable of understanding.

    DD’s teacher requires a certain number of minutes per day of “math practice,” but does not provide the material – you have to pick your own app, print out your own worksheet, etc. I have been using this to have DD do Khan Academy so she does not die of boredom, because her class is still doing double digit addition and subtraction without regrouping in second grade.

    Until a few days ago, I thought that was kind of ridiculous, but since they no longer level the math classes I can’t go in and complain.

    Then one of my friends proudly posted her son’s second grade Everyday Math test on FB, which had problems on it like 7+___=9. No double digits were involved.

    I was horrified, because a bright 8 year old boy is capable of far more math, and yet his mother is very excited that he can do what used to be a mid-first grade problem. Worse still, several more of my friends posted that their kids in second grade had just taken the same test. So I’m glad we’re not using that program, because DD would have begun spitting on the worksheets by now. And I would have given up and either petitioned for her to be moved to third grade for math, social life be damned, or homeschooled her.

  44. The crazy problems that I’m seeing in sixth grade are real life problems.

    For example, they’re in the decimals and percent unit now. You have to build a dinner with $20. They tell you how many people, how much they eat etc. you have to be able to do the math to buy the right amount of ingredients with the money you have in your pocket.

    Same for planning a school trip and how many buses do we need for each grade etc. I hope the Director of Trsnspirtatuon knows math to achieve the most efficient bus routes within the allotted school budget.

    So many jobs require higher level analysis and there might not always be a software program or app to solve even life’s daily problems.

    I think it’s great that they’re trying to teach kids how to think and analyze stuff.

    As for borrowing, they learn the concept but they aren’t allowed to use the word borrow in our school. They want them to learn that you’re subtracting from the hundreds column vs just saying borrow.

    I can see at the end of the day that they’re still learning arithmetic but they’re actually learning much more for the kids that get it. The problem is that there really are so many kids that struggle with the ELA side. If you’re in cotaught math in grades 5 to 8 in my district, it means that you learn the same material on the same day as the regular math classes. There are two teachers in the room in co taught. One teacher is special Ed certified. The kids might learn one way to solve a problem instead of 2 or 3 methods.

  45. “My sense is that in the future, the truly good jobs are all going to require something special – either quantitative skills, or salesman abilities or being a really good communicator, or being the person who can translate between all those people.”

    I think it’s natural for you to think this, given what you and your DH do. Where I sit, I disagree strongly. I walk around and see hordes and hordes of people who are gainfully–and lucratively–employed at what I call “churn.” It’s government, private sector, bureaucracy, and a steady, exponential increase in things like regulations and compliance and program implementation. It’s specialized and esoteric, but it doesn’t require any particular genius.

  46. “What I think your explain everything plan will do is push a lot of gifted but shy, awkward, non-verbal people out of STEM as they will think they are bad at math.”

    One of the authors of this article has written quite a bit about this, on her blog, in articles, and in her book Raising a Left-Brain Child in a Right-Brain World: Strategies for Helping Bright, Quirky, Socially Awkward Children to Thrive at Home and at School.

    Are Grading Trends Hurting Socially Awkward Kids?  —  Emphasis on group projects, sharing of feelings, and explaining rather than right answers hurt certain types of kids.

    “He believes utterly that if you can’t explain math, you don’t understand it.”

    I disagree.  Of course, being unable to explain can sometimes present limitations for an individual, but that doesn’t mean they don’t understand the concept.  The authors’ explanation makes sense to me.

    The idea that students who do not demonstrate their strategies in words and pictures or by multiple methods don’t understand the underlying concepts is particularly problematic for certain vulnerable types of students. Consider students whose verbal skills lag far behind their mathematical skills—non-native English speakers or students with specific language delays or language disorders, for example. These groups include children who can easily do math in their heads and solve complex problems, but often will be unable to explain—whether orally or in written words—how they arrived at their answers.

    Is it really the case that the non-linguistically inclined student who progresses through math with correct but unexplained answers—from multi-digit arithmetic through to multi-variable calculus—doesn’t understand the underlying math?…

    Or is it possible that the ability to explain one’s answers verbally, while sometimes a sufficient criterion for proving understanding, is not, in fact, a necessary one? And, to the extent that it isn’t a necessary criterion, should verbal explanation be the way to gauge comprehension?

    Of course, especially problematic is the way these CC standards have been implemented by teachers with little understanding of math themselves.

  47. Another aspect of the math word problems is that they require careful reading and understanding of what’s being asked. So “a week” could be 7 days but depending on how the problem is worded it could be 5 working days. I wonder how many kids pick up on things like this and I’d be curious to see the results.

  48. “Consider students whose verbal skills lag far behind their mathematical skills—non-native English speakers ”
    I will bet you that those non native English speakers can explain their work in their own language!

    The Eastern European countries used to be very good at teaching kids very advanced math. Hungary was especially good at it. I worked with a bunch of Polish math and CS grad students one summer years ago, and found that they loved to explain, in their crazy fractured English. I got the impression that they had always been taught to discuss math

  49. MM,

    What about the kids whose verbal skills lag far behind their math skills? Should their teachers just keep failing them in math because while their answers are correct the written explanation is poor?

  50. BTW, MA dropped the CC test in favor of reverting mostly back to its own. Basically, it found that CC standards were lower than those of MA (*shocking*) and therefore were not good for the state’s students.

  51. “Of course, especially problematic is the way these CC standards have been implemented by teachers with little understanding of math themselves.”

    I think this is the fundamental problem right there. An English major hears “explain your answer” and concludes that you need to re-explain your entire equation in English. What that should mean in math-speak is to write out the various steps of the equation so the teacher can see that you know how and when to apply the different concepts.

    I don’t mind the tests and homework assignments when they ask the kid which mathematical principle they need to apply to solve a particular problem, or define what X is, or whatever. I think learning math requires a parallel process of learning the rote processes (e.g., times tables) and learning the larger principles (e.g., commutative property), and eventually they all come together into something like understanding. It’s like writing: you need to know both what words mean and how to put them together into a sentence; you need to know how to structure an essay, but you also need to know the subject matter so you have something to say. I was even relatively patient with the several years of drawing the dots and listing four ways to write a number, etc. — even though my kid didn’t need that, I know that kids learn different ways, and you never know when something is going to click for someone else. But the example in that article of the process flow explanation that the kids have to write out for every problem? Just shoot me now.

    Although I guess that does go a long way to explaining why ES homework now takes an hour or more a night.

  52. I agree with Milo, for certain definitions of the words, “truly good.” I think electrician, air traffic controller (on my mind, as I recently met someone who trains people to do this) and nurse are all good jobs. I don’t believe you need some super special skills to excel at any of these. If we mean “quant at hedge fund” to be “truly good” -well, there aren’t many of those jobs to go around and there never have been. I think the paths to become an radiology technician, school teacher, or hr professional are all pretty accessible, and none of these jobs are likely to be outsourced.

  53. Non native English speakers and math- in the home country, DH had quite a few teachers who had such heavy accents that none of the students understood what was being said. Now, both teacher and students would have bristled at being called “non native English speakers”. The only saving grace was that the students could look at the board in Math class and see how the problem was being solved.

  54. “What about the kids whose verbal skills lag far behind their math skills? Should their teachers just keep failing them in math because while their answers are correct the written explanation is poor?”

    Already mentioned is that one gender lags the behind other in verbal skills. Some have suggested that this is one reason boys are falling behind in school.

  55. I don’t believe you need some super special skills to excel at any of these.

    I believe air traffic controller is one of the most, if not thee most, stressful jobs in the world. I think the ability to tolerate (or maybe even thrive on) extremely high levels of stress would be a very special skill that one would need to excel at that job.

  56. laura said “What that should mean in math-speak is to write out the various steps of the equation so the teacher can see that you know how and when to apply the different concepts.”
    Yes, exactly, with sometimes a bit of verbal glue, or a diagram. They should not be writing essays. But they shouldn’t just be writing down an answer either. I don’t think it takes awesome verbal skills to do this.

  57. We have an electrician relative. He is one of those angry white guys who likes Trump. He has been struggling for years and really can’t get ahead. He isn’t poor, he isn’t doing badly, but he isn’t getting ahead either. I think that is a fundamental problem right now that is feeding the popularity of Trump – these jobs that used to be good jobs are no longer a ticket to the middle class. The people with exceptional skills are the ones who are winning, not the electricians.

  58. I don’t think it takes awesome verbal skills to do this.

    You have to think about who is doing the grading.

  59. What that should mean in math-speak is to write out the various steps of the equation so the teacher can see that you know how and when to apply the different concepts.

    I have zero confidence that your average ES teacher will be able to do this in terms of grading the math English to an entirely different standard than the English English.

  60. “He isn’t poor, he isn’t doing badly, but he isn’t getting ahead either.”

    How do you define getting ahead? Whom should he be getting ahead of?

    I think this might come back to unrealistic expectations.

  61. Mooshi – I had this same thought when I was driving down 81 a few weeks ago and passed an older couple in a brand-new Cadillac with Trump stickers. I’m thinking that they’re probably retired and able to travel safely and comfortably in a new, $50k car. When they say “We’re not winning any more,” I can only wonder what they expected. It looks to me like they already won.

  62. My DD does a great job with her math homework, but then she gets low scores on the tests (70-85% on the tests I’ve seen). They are taking tests on the computer in preparation for SOL testing this spring. (SOL = Standards of Learning in my state. Yep.) I assumed they got some scratch paper, but now I’m wondering if I should talk with the teacher to make sure. DD always seems to know the answer and thinks that is what she selected, but if she makes a careless mistake she can’t go back and check. The teacher gives the option to redo the missed problems and earn half of the points back, but it seems to me that maybe she should check their work to make sure it’s not an issue of translation from paper to selecting A, B, C, or D on the computer.

  63. “They should not be writing essays. But they shouldn’t just be writing down an answer either. I don’t think it takes awesome verbal skills to do this.”

    But Mooshi, that’s not what we’re talking about here. We are talking about telling the kids to write out the equations, show their work, show the various steps, THEN wrap it all up with “explain your answer.” So using Milo’s word problem (1000 jellybeans, Jack 247, Jill 179, how many left?), here is how it would have gone in my kids’ ES:

    First, you solve the problem. So my kid writes 247 + 179 = 426. Then he writes 1000 – 426 = 574. All fine — the kids shouldn’t just be writing down 574.

    But then he has to “explain his answer” (me: you just did). So then he ends up rewriting the problem — Jack had 427 jelly beans, Jill had 179, so I added them together to get 426 and then subtracted that from the total to get 574 left.

    This is what drives me batshit — you have a problem written in English that he properly translated into Math, and now to finish the problem he has to re-translate everything back into English. It’s like your Spanish teacher telling you to write your report in Spanish and then translate it back into English — math is math, the logic speaks for itself as long as the equations are written out properly. It doesn’t need to be translated into another language to make sense or be “explained” or confirm that the kid understands the principles.

  64. Milo – Last night I was behind an Escalade Platinum with Trump and Friends of Coal bumper stickers. First of all, I can’t imagine putting stickers on my $90K vehicle. The combination struck me as weird and I tried to take a picture but couldn’t get my phone out before the light changed.

  65. Explain your answer in the lower grades (k -6ish) is one generally one sentence. I don’t think this is pushing the envelope – especially after 2nd grade. It just means if you get a fraction for how many buses you need for a trip, you have the ability write why you need to round up to the next whole number since a bus has to be a whole number.

  66. I have seen what LfB describes — where they show their work in math terms for a word problem and also have to write out a verbal description of what they did — combined with the crowded worksheets with an overly-small box for each problem that Milo mentioned. It’s a recipe for illegibility.

  67. I can’t speak to MMs Angry White Trump Supporting Electrician Relative, but my AWTSERs do just fine. They are as employed as they want to be. The field is expected to grow faster than most others, 20% over the next 10 years. It is not a bad path for someone who doesn’t want to attend school after high school. The lack of MMs AWSTER’s success could be refusal to relocate, poor work ethic, or a million other things. It doesn’t damn the field.

    In a marginality related note (apropos the use of “damn” above), we were trying to explain the word “naive” to a non native English speaker the other day. During the conversation, someone said the word “stupid” and we were promptly informed that “stupid” is a curse word by our local 7 year old. It provided the perfect explanation sentence: “It is naive to believe that banning certain words will cause small children to act with respect towards one another.”

  68. LfB – I was thinking you were going to say it would be like this:

    To find out of the number of jelly beans are left, I have to subtract the amount taken by Jack (247) and the amount taken by Jill (179) from the original amount (1000). I did that by first adding Jack’s and Jill’s (247+179) to get 426 to get the total that have been taken. Then I subtract the amount taken from the original amount (1000-426) to get the amount remaining (574).

    To me that is an explanation in English of the process I followed.

    One teacher made my kids do it this way:

    Number Left = Original Amount – Those Taken
    Number Left = 1000 – Those Taken

    Those Taken = 247 +179
    Those Taken = 426

    Number Left = 1000 – 426
    Number Left = 574

    She felt it showed that they understood what the equation should be even if they plugged in the wrong numbers and/or made calcuation errors. She said it was easier to figure out what part the kid didn’t get – setting up the equation or performing the calculation.

  69. “It’s not like average mortal kids are going to get jobs that require a lot of high level math.”

    Contrary to popular belief, engineers are not, in general, immortal or superhuman.

  70. @Austin — well, you wrote out the “A” answer. I wrote out what my kid would have written. :-)

  71. I’ve written here before about my experience as a calculus tutor in college, and how that greatly increased my understanding of the subject matter. Having to explain something, IMO, requires a deeper level of understanding than just applying it.

    I’ve passed this to my kids, and DS especially has taken it to heart. In MS, I’d often look over his shoulder late at night and see multiple chat sessions in which he was helping classmates with homework.

    I’m guessing that a program that does something like have 3rd or 4th graders be math buddies to 1st graders would help the 3rd and 4th graders.

  72. “As for borrowing, they learn the concept but they aren’t allowed to use the word borrow in our school.”

    I’ve never liked the use of the word, “borrow,” in that context. You’re not borrowing because you don’t return. You are taking, or transferring, not borrowing.

  73. “It’s a recipe for illegibility.”

    Or very tiny writing, easily readable by young eyes, but very difficult to read for a 50+ teacher who needs reading glasses.

  74. This answer,
    247 + 179 = 426.
    1000 – 426 = 574.
    shows the steps OK, but never would have passed muster in my college chem class where the professor was all about showing our work. He would have preferred something like this

    To compute leftover jellybeans
    247 (Jack’s jellybeans) + 179 (Jiill’s jellybeans) = 426 total jellybeans for jack and Jill
    1000 (total jellybeans) – 426 (Jack and Jill’s jellybeans) = 574 leftover jellybeans

    I realize that there are teachers out there that would want something weirder. but this is what I think explaining a problem like that should be. It isn’t enough to just write down numbers, if it is a word problem. You need to specify the meanings of the numbers. Not only does it communicate your thoughts better, it helps lots of kids not make mistakes.

  75. I see my kids writing about 1-3 simple addition problems, where in the past, kids would have completed a worksheet with 30-50 simple addition problems. I think some kids are being hurt by the absence of repetitive practice. My kids never have any significant quantity of simple arithmetic problems.

  76. Quick hijack. I am hosting a few girlfriends for a wine night tomorrow. We go through a lot of wine and I need to purchase 4-5 bottles. Recs for good but cheap red and white wines I can stock up on?

  77. “He isn’t poor, he isn’t doing badly, but he isn’t getting ahead either.”

    How do you define getting ahead? Whom should he be getting ahead of?

    I think what MM may mean is that his relative status has fallen. In 1980, to use a general example, the starting salaries of engineers at GM and GM factory workers were about the same at an inflation adjusted 50k. Today, factory starting wages have fallen to $24k while the engineering salaries now start in the mid 60s.

    Similarly, MM’s relative c. 1980 might have earned about as much as someone with MM’s husband’s skill set as there was relatively more demand for trade type labor and comparatively less demand for his skill set. However, do to economic and technological changes MM’s husbands wages and relative status are far higher while her relatives status has fallen and his wages are either stagnant or falling.

  78. MM, how about just starting with:

    Leftover jellybeans = total jellybeans – (jack’s + jill’s jellybeans)

    Then just plugging in the numbers and showing the work. It shows that you understand the concept without excessive BS.

  79. @Mooshi — I would be fine if they wanted your approach. No: I would be thrilled. I think that is the best way to teach kids to translate between word problems and math — you sort of talk out the words of the problem and them put them into equation form, and it emphasizes that you’re talking about real things. Heck, I still do this myself when I need to reason my way through something, being so many years out of school (and I can’t tell you the number of times in school I caught my own mistakes just by writing out the units in all my equations).

    But that’s not what they want. They want the math equation (no units or English words), and then they want a separate written description of how the kid got there, in complete sentences, with no mathematical symbols. AustinMom’s example of what she thought I was going to say is exactly what they want to see.

    For the kids who already get it, it’s a waste of time; for the kids that don’t get it, there’s nothing that is going to help them make the connection between the word problem and the mathematical equation.

  80. Quick Hijack – bought an instapot. Didn’t someone say there was a good cookbook to get you going on all its features?

  81. It shows that you understand the concept without excessive BS.

    But many teachers love excessive BS.

    Imagine the following written in scrawling barely ledigble script – 247 (Jacks jelydeans) + 179 (Jils jelybeans) = 426 total jelydeans for jack and Jill ( barely legible script)

    7/10 for the misspelling, poor handwriting and the d b confusion I assume?

  82. SWVA – I read your Escalade story, then I got on the highway and saw another shiny Escalade with a sticker that read “Keep Calm and Carry”.

    I know you want to finish with “On,” but that’s where it ended. There was a silouhuette of a handgun. It made me lol not because I love guns (I don’t) but I’m so tired of all the damn (“damned,” Ada?) Keep Calm and Carry On/Drink Wine/Beat Army/Play Lacrosse/etc. variants.

  83. @Dell — Montepulciano d’Abruzzo — very easy-drinking red that goes for $15-20/bottle, if that’s cheap enough, and goes with anything or nothing. There’s a Zaccarini (?? comes with a stupid twig on the bottle) that is my go-to generic drinking red. Malbecs also tend to be fairly easy to drink and cheap.

    Caveat that I like mid-range wines, not big/Parker-approved things, so if your friends like a big zin, ignore me.

  84. ” the starting salaries of engineers at GM and GM factory workers were about the same at an inflation adjusted 50k”

    How much sense did that make?

  85. No wonder homework requires so much time! My son was constantly getting dinged for not showing his work. He would do as much as he could in his head and only write the bare minimum. The aversion to writing was strong enough that he would take getting scolded and lower grades all day long before he would write more than he deemed necessary. The nice teachers made deals with him along the lines of show your work on the first one of a type so I can see you know what you’re doing, then I’ll let you by as long as you get most correct. I agree that you should be able to explain how you did something, but writing it out for every single problem is ridiculous to me. The writing required at my kid’s elementary was much longer than Lauren’s example, so it is probably very teacher-specific.

  86. How much sense did that make?

    The factory work was boring, physically demanding, monotonous and with little chance of advancement. The engineers had much more opportunity for advancement, the work was more varied and interesting and the work was performed in a more pleasant less physically demanding environment.

  87. ” They want the math equation (no units or English words)”

    No units? So I guess that means no unit analysis? Unit analysis is, IMO, extremely helpful, particularly in converting word problems to equations.

  88. HM, I can get one or two at that cost, but others have to be sub -$10. Thanks!
    like I said, we polish off a few and will have beer too.

  89. @Finn — ITA. I think the way you help kids really get math and word problems is to integrate the two and help kids understand that the equation symbols are really just shorthand for regular words that they already know. Heck, I wouldn’t even mind it if the teacher started out making them write out the problem in words, and only move to the equation and symbols when they had the concepts down (this is what we naturally do when we are figuring out what the problem means anyway).

    But this “do the math, then explain your answer” treats them as two completely divorced things — numbers and symbols here, full paragraphs with complete sentences there — which seems to go in exactly the wrong direction.

  90. Sorry that was meant for both LfB and HM. Thanks again for the recs. Keep me coming.

    P.s. I am cheap when it comes to spending money on alcohol

  91. Dell, in that case, I suggest getting a box each of Big House White and Big House Red. Broke Ass White and Broke Ass Red would be good choices as well.

  92. Naked Grape’s Pinot Noir isn’t bad. You can get it for $9-10 at Target.

    La Crema Chardonnay is a good white for about $12-15. I’ve served this at many parties and it’s gotten good reviews.

  93. WCE, I agree. Yes, you need to understand the concepts, but when you get into algebra and higher, you need to be able to do simple computations quickly. You need to know 8×7=56 without having to compute it. You need to do 18+38 = 56 with going through 18=20-2 and 38=40-2 so 20+40-2-2 = 56.

  94. Dell, please correct me if I’m mistaken, but it sure sounds like a get drunk together night. When I was in college, we got box wines for that.

    Does Trader Joe’s still have 2 buck chuck? If so, that might also be appropriate.

  95. “Yes, you need to understand the concepts, but when you get into algebra and higher, you need to be able to do simple computations quickly.”

    Yeah, if you don’t know the multiplication tables will, you’ll have a hard time when you get to factoring polynomials, not to mention calculus. Even if you understand the concepts, many of the problems will take a lot longer if you don’t instantly recognize numbers form the multiplication tables.

  96. Dell, Trader Joe’s has plenty of decent wines for under $10–that’s where I would head. Personally, I don’t love the Two Buck Chuck wines, but there are lots of other options.

    Black Box Sauvignon Blanc or Merlot are also decent if you’re okay with boxed wine.

  97. My absolute favorite wine is Dark Horse Chardonnay, which I get at Kroger for $6.99, I think. Plus 10% off if you buy at least 6 bottles.

  98. Oh Finn, don’t get me started on units. I still have conversion factors seared into my brain after years of working with water calculations in cubic feet, acre-feet, gallons, cubic feet per second, gallons per minute, acre-feet per hour, etc. And then there was that period of time when the state DOT required everything to be designed in metric units but all of the calculation software was in English units.

  99. Ditto Trader Joes for cheap but tasty wine. I think two buck chuck tastes like cooking wine, but there’s lots of good stuff in the $5-$9 range.

  100. A close family member used to have a big “The 99%” magnet on his Suburu next to other Totebag Liberal cause stickers/magnets. I found this hilarious as this particular family member was probably in “The 2%” but still “felt” Middle Class. Totebag- award worthy.

  101. “The factory work was boring, physically demanding, monotonous and with little chance of advancement.”

    Lots of people had and have jobs like that and earn the minimum wage. The factory workers belonged to a powerful union.

  102. The factory workers belonged to a powerful union.

    Exactly, with the decline of unions, the status of the marginal white industrial middle/working class has declined.

  103. There’s a Kirkland Cote De Rhone that’s not bad for $8 but it’s hard to find. I like the Josh Cab and that is generally around $15. The Cherry Tart around $18 is not bad either.

    Roses (no idea how to do the accent) are generally cheap and as is the La Marca Prosecco.

  104. “The factory workers belonged to a powerful union.”

    One that drove their employers to bankruptcy, or near bankruptcy.

    My grandfather-in-law was an electrician trained by the Navy in WWII. He was not making the equivalent of $50k in the early years, that’s why he had to work a second job at night.

  105. My kids get the math repetition practice by playing the online math games to which the school subscribes. Most of the time, they enjoy it; sometimes we have to push them, especially if they’ve gotten frustrated at a particular level. It monitors individual progress and bombards them with the questions they answer incorrectly or in insufficient time. Teachers log in and monitor progress.

    WCE, I can give you recs if you want. My brother, a bigger Totebagger than me in some ways, paid for their own subscription to a different program.

  106. One that drove their employers to bankruptcy, or near bankruptcy.

    Certainly true. But, I assume you agree, the rise in right wing populism as embodied by Trump is in part driven by the declining wages and status of the white working and lower middle classes.

  107. Thanks everyone! I knew I asked the right group. :)

    Finn, this is more of “get a break from our brats” kind of evening.

  108. I’m not sure I agree. I really don’t know what to make of it, or even if it’s anything new. There have always been populists who perceived disaffection, it’s just that they used to be Democrats. But the folksy aw shucks of Bill Clinton has been wholly replaced by the condescending and patronizing Barack Obama. So now we’ve got them.

  109. I’m not sure I agree. I really don’t know what to make of it, or even if it’s anything new.

    You agree on the change in relative status of certain demographic groups, I assume?

  110. The kids are still required to learn the multiplication tables, and memorize the answers. They just do it after they learn how to multiply. Same with “borrowing”, long division, fractions etc. I noticed that they eventually memorize it the way that we learned it many years ago because they do need the speed.

    I wish NY had different laws about wine because we can’t buy wine in supermarkets so some of these will never be available in NY. My Costco has a store next to it where I can buy wine, but it is separate from Costco and they don’t carry the same quality that I’ve seen in Costco when Ive traveled to other states. I’m just thankful that we can finally buy alcohol on Sundays.

  111. “You agree on the change in relative status of certain demographic groups, I assume?”

    I agree that black Americans have rightfully gained or earned a status closer to socioeconomic parity. But I don’t think that is the source of resentment many Democrats assume it is. I think that when there is resentment, it’s based on a belief, rightfully or not, that they had to work hard to achieve what they have–health insurance, home equity, job skills–and there are other groups, often younger, who expect it to be handed to them, whether that’s in the form of Obamacare or mortgage bailouts (real or urban legend). It’s not racial; it’s more likely my tree guy vs. his lazy 20-something son. Not my tree guy vs. his black coworker–he totally respects and admires him.

    The mistake that I think progressives make is that, from their affluent bubbles, they see my tree guy and figure that he’s so far below them, he’s basically destitute anyway, so why on Earth is he against handouts? What’s the matter with Kansas, after all. Tree Guy doesn’t see it that way at all; he doesn’t see himself as poor but hardworking middle class, and it’s the forced handouts that threaten what position he has worked all these years to achieve.

  112. I’m bummed that I was in meetings all day and missed this discussion. My 1st grader is doing Everyday Math. So far I don’t have any complaints. Her neuropysch testing showed us that math would give her trouble. I’ve very early into the program, but I think she might be the type of child that this method was meant for. She is very verbal and loves reading and writing. So learning math in a way that encompasses her strong points is to her benefit (disclaimer: she also receives extra math help). That being said, i reserve the right to complain about Everyday Math in the future. :)

    No matter what method the school uses there will always be kids that struggle with it. The ideal situation would be for the teachers to evaluate what method is best for each individual student and teach to the child’s strength. But that is just not going to happen. You may recall that I once posted that my DD’s teacher provides extra math worksheets. These worksheets have more traditional math problems (and more challenging) than the Everyday Math 4-6 problems on line hops. My guess is that the kids naturally strong in math are doing those extra problems.

    To Mooshi’s comment on 2:29. Her method of explaining the math is something I do on an almost daily basis to my clients. I’m amazed at how many do not understand how much money they owe, unless I spell it out for them.

  113. I agree that black Americans have rightfully gained or earned a status closer to socioeconomic parity.

    What about factory workers vs. engineers or electricians vs. math PhD hedge fund techies? Are their relative status fixed for all time or have they changed significantly over the past 30 years?

  114. I was thinking about Sky’s DD and what is cool. I was at the middle school band concert yesterday and to me all the middle schoolers as a group honestly look awkward. There is none of the cuteness of elementary kids and not enough put togetherness of an adult. From what I gather, at my kids schools, it doesn’t seem out of place to be in things that in the past were considered geeky. For this, I think we have the nerdy grown up like Bill Gates, Steve Jobs and other tech icons to thank. There is awareness at least in middle school that you don’t want to bully someone who could grow up to be a Sheryl Sandberg or a Marissa Meyer.

  115. “Factory workers” is too generic. I don’t think anyone says “I’m a factory worker” (unless they’re a lyricist for Alabama). However, I’ve interacted with many semi-skilled production tradespeople such as electricians, welders, machinists, crane operators, and I’d say they’re doing OK. They’re living the comfortable lives that Rudy’s father laid out for him as the sensible alternative to college, and that Ada is talking about with electricians.

  116. They’re living the comfortable lives

    At the same relative status as 30 years ago? Or has their relative status changed?

  117. “What about factory workers vs. engineers or electricians vs. math PhD hedge fund techies? Are their relative status fixed for all time or have they changed significantly over the past 30 years?”

    I think these are two different groups — relatively unskilled workers in manufacturing versus skilled tradespeople like plumbers, electricians, and HVAC technicians. There is no question that the blue-collar assembly line workers have lost out in the knowledge economy. That’s not because the power of unions has declined, but because technology and globalization have eliminated many of the jobs that a high school graduate with a strong back could fill. When I was growing up in the Rust Belt during the 1960 and 1970s, those guys could live a comfortable middle class life (as then defined) with a SAHM wife and 3 or 4 kids. Our community was full of them, and my dad was an outlier because he had a college degree. Only half of my high school graduating class of 800 went on to college. Now, in that same community, with a graduating class of only 400 but relative demographics unchanged (no new upscale housing or gentrified areas), most kids are headed to college. I agree with Milo that the guys running the family plumbing business are doing OK. Even better than OK, because they are seeing more of their kids able to attend college. The guys who would have been working in a factory but instead are working at Home Depot, not so much.

    In our current small city midwest home, I see plenty of guys without college degrees working in small manufacturing who are able to buy a decent home for $100,000 or less and support a family. If there is a substantial population of resentful working class white guys, I haven’t encountered it. I rarely overhear anyone discussing politics of any kind at restaurants or grocery stores.

  118. “The guys who would have been working in a factory but instead are working at Home Depot, not so much. ”

    Would they really have been working steadily in a factory, or would they have been more of the “drifters” of the old days, picking up a little bit of work here and there?

  119. Would they really have been working steadily in a factory

    The employment data indicates that many of them would have been working in factories.

  120. This song just came up, and the lyrics seemed apt. For LfB:

    Got myself a factory job
    Where I ran an old machine,
    Bought a little cottage
    In a neighborhood serene

    When I came home every night
    With every muscle sore
    Then she dragged me through the streets of Baltimore

  121. Obviously the employment picture in eastern MA is different from areas with greater unemployment, but my Home Depot is mostly staffed by over 50s – some a second eve/weekend job, some involuntary unemployed piecing together what they can, some retired who want to bring in extra cash. The only younger folks, possibly regular full time employees, are in management or in the service areas that involve special orders or arranging installation. There is absolutely no one who would have been a drifter in earlier times, although not every employee is qualified to give give diy advice. If I need a lot of help with a project, I go to the local hardware or paint store.

  122. The first home DW and I bought together was very near a Home Depot, and I spent a fair amount of time there. A lot of their employees had worked in the trades and thus were quite knowledgeable, e.g., plumbers working in the plumbing dept. Many still worked in their trades, but were attracted to the steady work that HD offered.

    I don’t see as much of that at the HD near my current home. I see some of the above-50 that Mémé mentioned, apparently mostly retirees from other jobs, but my impression is that most of the workers are below 50.

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