You’re An Idiot, Dept.

 

Another article mischaracterizing the way math has been taught, as well as how it should be taught, as well as misrepresenting what Common Core requires. For starters:

“Subjects that are vibrant in the minds of experts become lifeless by the time they’re handed down to students. It’s not uncommon to hear kids in Algebra 2 ask, “When are we ever going to use this?” and for the teacher to reply, “Math teaches you how to think,” which is true — if only it were taught that way.”

I realize that my experience doesn’t count as “evidence” but when I give my algebra students the math word problems held in disdain by people like the author of this article, they are actively trying to solve them. Those that aren’t doing so need additional instruction/guidance which I provide. Students generally ask “When are we going to use this?” when they’re frustrated and don’t know how to do something, and/or because it is played up so much on TV shows and other media. Perhaps we do a disservice by saying that “you will use this later in life” because that is not necessarily true.

The author goes on:

“To say that this is now changing is to invite an eye roll. For a number of entrenched reasons, from the way teachers are trained to the difficulty of agreeing on what counts in each discipline, instruction in science and math is remarkably resistant to change.”

Interesting that he thinks math is being taught in the same old ways. Where has this author been the last 25 years with many parents complaining about the “new” ways of teaching basic arithmetic in the lower grades? It’s true that middle school and high school math have not changed too very much, except for the fact that algebra has been almost totally expunged of any kind of word problem of value, and the requirement to do proofs in geometry has been relegated to the garbage heap of bad educational ideas. But generally, high school still offers a more traditional means of delivering instruction rather than the various pedagogical gimmicks that pass as effective practices.

Also, in articles of this type, there is no attention paid to how students who go on to STEM majors learn their math.  Many students receive help from home, from tutors, or from learning centers–something that didn’t occur that much in the days when “traditional math failed thousands of students” as the reformers like to say. It was possible for many students to make it all the way through calculus without aid of tutors or help at home–something that even today’s brightest kids are finding hard to do. Many need help in the lower grades when foundational math skills are necessary to move on.

The author goes into some history, particularly of the 60’s new math and says “Later manifestations of the impulse away from rote instruction include curricular standards created by the National Council of Teachers of Mathematics in the 1980s and the enthusiasm for “inquiry-based” science in the 1990s.”

Let me skip my usual tirade against the use of “rote instruction” as the main method by which traditionally taught math in the past is portrayed. Instead, I find it interesting that he leaves out the fact that NCTM distanced themselves from the 60’s new math when it fell out of favor, but when they came up with their infamous standards in 1989, they kept the inquiry-based practices that were being tried out in the 60’s new math. So they didn’t hate it all that much, it seems.

The article delves into how well CC approaches the concept of proportionality, and how it connects ratio to rate to proportion and ultimately slope.

“What they’re learning is: The way you find the fourth number is by setting up this gadget called a proportion,” Daro said. “That’s not really learning anything about proportionality, that’s learning how to get answers to problems in this chapter.

I’ve worked with middle school students using texts that emphasize this connection. The connection may be obvious to the teachers who have had the benefit of working with these concepts for many decades, and obvious to the authors who put together the text books. But most students want to know how to do the problems. As far as “cross multiplying”, I and others I know do teach how to calculate “the fourth number”, but in the end, the kids end up with cross multiplying because it is the way they know how to do it–and ironically, when students are coached for Math Counts competitions and standardized tests, there are short-cuts galore that they are taught.

Phil Daro, for those who don’t know the name, was the force behind the shoddy pre-1995 California standards that were responsible for atrocities like MathLand being introduced in schools, and resulting in parent outcries in areas like Palo Alto. He’s back and was one of the driving forces behind the CC math standards.

While the CC standards can be interpreted in ways that are sensible and useful, (see for example this article) one has to work to do so. One also has to ignore all the textbooks that ascribe to the reform-minded interpretations to which these standards have leant themselves.

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12 thoughts on “You’re An Idiot, Dept.

  1. Many students receive help from home, from tutors, or from learning centers–something that didn’t occur that much in the days when “traditional math failed thousands of students” as the reformers like to say.

    In basically every post, you write that Kumon use has risen in the CCSS era. How sturdy is your empirical evidence for that claim?

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  2. Barry, you are exactly correct!! I see many students at Community College who lack the basics for Algebra. I know that this is because that they were not trained rigorously. I will further state that there is known increase in my town for tutors in math in middle school due to the curriculum which is not a traditional curriculum. We keep wanting to reinvent on how to teach math and science. As long as we keep reinventing, the kids will not have the basics to do higher order math or science classes.

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  3. I don’t limit it to the CCSS era, in my other articles; I say over the past 25 years, and the number of establishments over that time period according to US Census data has more than tripled.

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      • Thanks for the link, Barry. Can you help me out here? All I’m seeing is “Educational Services” as a category. I can’t figure out how to open up “Exam prep and tutoring establishments.”

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      • Yeah Barry. Where’s your proof? Everything is just fine right now. Those Kumon centers must be losing money and we parents have never received notes telling us to practice “math facts” at home. All we need is some more Dan Meyer in-class engagement and motivation that wastes time and caters to the vanity of the teacher. That will fix everything. We all know that Dan has proof that his techniques produce more STEM-prepared students than the traditional AP calculus math track in high school.

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  4. Dan,

    You’re right; what a mess. That’s the problem with the US Census website; they change it regularly whether it needs it or not, so what you thought you found a few months ago (which allowed me to open 611691, which is exam prep and tutoring) is put in a new spot. They’re so good at doing this, that even the NSA has given up trying to crack the code. But I persisted, and here is what I think will work.

    You’ll have to wade through the PDF tabulations of data for the year 2000:: http://www2.census.gov/programs-surveys/cbp/tables/2000/cbp00-1.pdf

    On page 124 there’s a listing of establishments under NAICS 611691 which is Exam Prep and Tutoring. I included all establishments. For the year 2000, the total is 3,426. If you limit it to establishments with 10-19 employees, the total is 581.

    For 2014, there is an online tabulation for 611691, at https://factfinder.census.gov/faces/tableservices/jsf/pages/productview.xhtml?src=bkmk . For 2014, for total establishments there were 9,007. If you limit it to establishments with 10-19 employees, the total is 1700.

    Thanks for bringing this to my attention. Now if I can find where US Census hid the data for 1990, I’ll be doing fine.

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  5. Dan, my kids are Kumon success stories and I know of many others who have had no choice but to resort to Kumon for teaching basic arithmetic. My kids went from failing maths to above average in primary and now my eldest, in yr 7 in Australia, is an A grade maths student. She wouldn’t be if it weren’t for Kumon.

    Her teachers told me that she would never succeed at maths but that’s ok ’cause everyone has strengths and weaknesses and she could take basic maths at high school. My children are not mentally deficit and are perfectly capable kids. I blame their “failure’ on the way maths is taught today and the lack of teaching of the basics. Many (approx. 1/2 of my daughters yr 5 class can’t add, subtract, multiply or divide. If the parents don’t intervene these kids will never be any good at maths.

    I know of a single mum who works part time who is sending her 10 yur old to Kumon (somehow she is finding that money) so that she is taught the standard algorithms. Her daughter can’t add or subtract let alone do anything else. The loss of self-confidence is devastating. Have you read what these ideas have done to maths standards in NZ and Canada? There seems to be a correlation between a decline and the introduction of newer ideas that stress understanding and different ways of doing problems. In NZ about 1/2 (it may have been more) could not add 2 three digit numbers together!

    I think it’s really fairly well known that tutoring centres and private tutors are doing a roaring trade. If there weren’t a market for their services they wouldn’t exist. They never existed in Aust. – to my knowledge- during my schooling in the 1980’s. It would be wonderful if someone did a study into the rise of tutoring and determine why so many parents are engaging tutors. One of the reasons is probably because some parents what to give their kids a leg up (nothing wrong with that) but another (I suspect) is because far to many kids are not understanding the way maths is taught today. It’s difficult to determine because some parents feel some shame in admitting that their very intelligent, capable kids are failing so they are not open about it. I would hazard a guess that if you could get parents to open up about it there would be many, far to many.

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  6. For the record the Australian national curriculum does not mandate for the standard, traditional algorithms at all but requests that teachers teach the students multiple strategies. methods.

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  7. I’ve been telling schools to just ask the parents of their best students what they do at home. It’s really simple and cheap. We didn’t just model a love of learning and turn off the TV. We didn’t just take our kids to science museums. We used worksheets and flash cards. My son loved worksheets, but when I naively told his first grade teacher that bit of information, I thought she was going to call the police. Then again, years later, we parents received notes telling us to work on “math facts” at home. Then the school had a parent/teacher meeting because a number of bright fifth grade Everyday Math students still didn’t know the times table. They couldn’t even do EM’s beloved lattice method. So much for trusting the spiral. It’s not a problem of learning the traditional algorithms, it’s a failure to enforce mastery of just about anything. Kids love being able to do math and doing comes from practice and enforcing mastery, not time wasting in-class group projects in the hope that the spiraling and engagement will create mastery. No. it just forces the skill and mastery help and tracking into the home. Just ask us parents. It’s not difficult.

    Look at music education. School bands and orchestras would be nothing without all of their students who get private lessons that focus on basic skills and musicality. Everyone in music knows that. Private lessons teachers might give in and allow students to practice Fur Elise and Fantasie Impromptu well before they are ready, but that’s not because they think it will motivate better skills. It just creates bad practice, which is worse than no practice. Worse yet in K-12 education is that parents have few chances to select a new school or teacher. I found out that even if we paid big bucks for a private school, they STILL used Everyday Math. It’s a fundamental systemic problem.

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  8. Agree Steve that the lack of repetition and practice (ie what the haters would call drill) is of fundamental importance so that they achieve mastery. Spiraling around and dipping in and out on a daily or weekly basis does little towards committing maths concepts to memory. Hence one of the reasons Kumon is so successful, it goes over and over the same thing until it is done well.

    Contrary to what many schools/teachers would have us believe my kids love drilling as well. They enjoy feeling they’ve achieved something. When my youngest memorised her times tables she was brimming with pride. It was beautiful to see and was a turning point for her in terms of ability and confidence.

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