Should students all take the same math class?

WEDNESDAY, MAY 5, 2021

Let's take a look at the experts: Should students all take the same math class? 

Putting it a different way, should every sixth grader be taught the exact same "sixth grade math," and so on, up through the grades?

That strikes us as a crazy idea, but it seems to be catching on with the experts found in Our Town. Yesterday, Kevin Drum reported on a drift of this general type in California's public schools:

DRUM (5/4/21): [California's latest draft framework for K-12 math] takes on the issue of tracking, which has been the source of math pedagogy wars since before I was born. The new framework comes down firmly on the anti-tracking side up through middle school, based on the idea that recent neurological research shows that (a) anyone can learn math up to high levels,¹ and (b) advanced kids who take the standard Common Core classes do better than those who are tracked into honors classes...

In the footnote to that passage, Drum expresses his doubts about the (vague) claim "that anyone can learn math up to high levels," based on recent research. 

Drum found California's public school establishment drifting toward "one size fits all." On Monday, in the Washington Post, long-time  education writer Jay Mathews described the same tendency in the state of Virginia's establishment. Here's how his essay began:

MATHEWS (5/3/21): Pamela Fox is a mother of four and former lawyer who cares about the schools in Fairfax County, Va. She was appalled by the website of the Virginia Mathematics Pathways Initiative (VMPI), described by the Virginia Department of Education as its partner “to consider how to modernize and update math instruction” in the state.

Under the VMPI plan, Fox said, “every student would be required to take the same math class through 10th grade of high school. There would be no classes for struggling students needing remedial help or for advanced students seeking accelerated math.”

We share the old school system tie with Mathews. We went to rival high schools at the same time back in the wonder years. 

His temperament is different from ours. That's one of the reasons why we admire his work. 

When Mathews tried to follow up by speaking with the appropriate officials, it sounds like he may have encountered a bit of doublespeak, with some okey-doke thrown in. That isn't entirely unusual when dealing with public school officials.

Should everyone take the same math class? We were struck by this observation, based on Mathews' voluminous experience:

MATHEWS: [I]t is difficult to find untracked math programs that work well—except at some charter schools in low-income neighborhoods that accelerate all math students. The Virginia plan does not appear to endorse that approach. Similar anti-tracking policies for math have produced an uproar in San Francisco Peninsula public school districts.

(Full disclosure: we attended those rival high schools right there on that very peninsula!)

For our money, the oddness in that passage is this—the charter schools to which Mathews refers decided to "accelerate all math students." Even there, school officials decided that everyone should take the same math class. They just thought that one math class should be harder!

Should everyone take the same math class? The idea strikes us as strange. 

In part, we base that on personal experience. In part, we base it on our acquaintance with basic data.

Are some kids "better at math" than others? We'll guess that the answer is yes!  We'll even guess that some kids are a whole lot better. 

At any rate, here are some Grade 4 scores from the last administration of "America's report card," the National Assessment of Educational Progress (Naep):

Grade 4 math, 2019 Naep, public schools nationwide
90th percentile: 279.46
10th percentile: 198.19

Translation: 

On the 2019 Naep, ten percent of the nation's fourth-graders scored 279 or above. Also, ten percent of the nation's fourth-graders scored 198 or below. 

That's twenty percent of the nation's fourth graders. Moving forward, should they all be taking the same math class? Consider a rough rule of thumb:

As part of a very rough rule of thumb, a ten-point gap on the Naep scale is often said to represent roughly one academic year. 

Such rules of thumb tend to start breaking down when applied to such matters as these. But do we really think that all those kids should be taking the same math class? Beyond that, does common sense really suggest any such thing?

The nation's experts seem to be drifting toward "one size fits all" in the question of public school math. This strikes us as a strange idea, but then, let's consider those experts:

We began writing about cheating on standardized tests back in the 1970s (in the Baltimore Sun). For the record, we weren't talking about "teaching to the test." We were talking about flat-out cheating, of the most ridiculous kind.

We had stumbled upon such behavior by pure happenstance. Still, if you simply examined certain test data, it was sometimes blatantly obvious that some data made zero sense.

(For various reasons, the Naep is not susceptible to outright cheating. Or to specific "test prep!")

Decades went by, and our public school experts remained blissfully unaware of this problem. For a  few years along the way, we worked with Dr. John Cannell as he tried to call attention to this problem through his "Lake Wobegon" reports. ("Where the children are all above average.")

Finally, a few newspapers blew the whistle on major cheating scandals in such large school systems as those in Atlanta and D.C.

Sadly, no! It wasn't the New York Times or the Washington Post which finally called attention to this ridiculous ongoing problem. It was such papers as the Atlanta Constitution and USA Today—with Mathews' wife, Linda Mathews, in charge of the project at the latter, widely-mocked newspaper.

In our experience, Our Town's top experts quite frequently aren't. We've never been able to stress that unfortunate fact quite enough. 

We're inclined to be suspicious of the wisdom of experts. For better or worse,  such attitudes are almost  wholly unknown in the well-ordered streets of Our Town.

On the brighter side: You'll never have to hear about public school kids, or the schools they attend, if you watch "cable news."

You'll hear about Matt Gaetz, and Rudy. To the very end of your days, you'll hear about Trump and Barr.


35 comments:

  1. I'm a math nerd. Math was relatively easy for me. As a result I developed lazy work habits.

    ReplyDelete
    Replies
    1. So - having all students take the same math hurts students at various levels and in various ways.

      Delete
    2. OK, you have an opinion. What facts back up this opinion of yours?

      Delete
    3. Yes, no doubt it hurts the pride of white students when they find out that black students are doing better than they are in math. Can't have that happening!

      Delete
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      Delete
  2. Somerby misunderstands the discussion by Drum, which concerns the top students typically tracked into a gifted or advanced class, not the struggling students. Drum says that the decision to eliminate such tracking arises because studies show no advantage to those special classes for top students. Their performance is no different than those who remained in non-tracked classes. This is therefore an evidence-based decision, not one based on theory.

    Later, Drum dismisses the mindset theory for failure to replicate, then draws an unjustified overly broad conclusion:

    "Frankly, all the social justice stuff bothers me less than the framework's unquestioning reliance on a theory that hasn't panned out in the decade since it was introduced. If this is typical of their approach, there's little chance that the new framework will be successful."

    Failure to replicate can mean that mindset theory is bunk, but it can also mean that the researchers failed to recreate the same experimental conditions and methodology used in the original studies. Because of the ambiguity of a null finding (failure to replicate), one cannot conclude that mindset theory is wrong and therefore that the new math framework won't work, especially in light of the studies supporting non-tracking in specific cases (e.g., with gifted students).

    Drum is good at creating graphs but less good at interpreting data. Meanwhile, Somerby again piggy-backs on Drum's efforts in order to beat his own drum, as if anything Drum discussed has anything to do with those students who are having difficulty and struggling with math. Somerby has long argued that the existence of standards is bad for those children who do not meet them, but if a child has malnutrition and fails to thrive physically, do you blame the ruler because that child is short?

    Meanwhile, Drum blames the framework for using education jargon. I find this criticism odd because no one blames medicine for using medical terms, or engineering for using technical terms, so why cannot a document aimed at trained professional educators use the vocabulary of their own field? The document is not aimed at laymen but at professionals who will be using it. It is only the tendency to treat teachers as if they were not professionals, as if their field had no specific content, that makes men like Drum think they should be able to access it without any training (much as Somerby did when he became a teacher without any preparation for the job). This is what lack of respect for teaching looks like.

    ReplyDelete
    Replies
    1. Drum actually wrote "Using an ungodly mix of pedagogy jargon and social justice buzzwords".

      So his intent appears to be to criticize the mix. You sliced out the second half and hence the context when you sought to criticize his criticism.

      Delete
    2. Here he singles out the pedagogy jargon:

      "I will say up front that the framework is practically bursting with edu-jargon and references to allegedly scholarly papers. "

      The word "allegedly" to refer to scholarly papers is gratuitously offensive.

      Then he spends a paragraph discussing the social justice examples used in word problems, which he doesn't find particularly problematic. He doesn't anywhere say that he objects to a mix of jargon and social justice, he just puts the two into the same bullet point at the end.

      He seems to me to be complaining because education lingo is less transparent, more opaque than he would prefer. It never occurs to him that he may not understand everything he reads, but that is his particular brand of arrogance.

      Delete
    3. I think your criticism is mostly warranted but you should include the full context.

      "I will say up front that the framework is practically bursting with edu-jargon and references to allegedly scholarly papers. This is not my cup of tea, but I won't hold it against anyone. So what does the framework say?"

      His use of "allegedly" is not "gratuitously offensive" because he is clearly describing the references that way because it is not his "cup of tea", implying that he didn't have the drive to follow up and determine if they were indeed scholarly papers.

      You also wrote "He doesn't anywhere say that he objects to a mix of jargon and social justice".

      I would have to disagree here. "Ungodly mix" is not a way to describe a mix to which one has no objection.

      Delete
    4. Yes, these are flippant criticisms without any real effort to flesh them out or think about the issues. Capped off by a sweeping generalization about the failure of the framework. Somerby grabs Drum's sloppy work because it fits his own agenda. Education deserves better from both Drum and Somerby.

      Drum doesn't understand any of the jargon he criticizes but he blames the jargon, not his own lack of familiarity with what the words convey. The mix isn't ungodly at all. It is just more than Drum can understand without more effort.

      How ridiculous would it sound if I were to say of chemistry, that the mix of chemical symbols and terms are "not my cup of tea" but I won't hold it against the chemists? My point remains that Drum shows no respect for education or social justice concerns, and that is his fault, not the develops of this framework. It may have flaws, but Drum doesn't appear capable of analyzing them.

      Delete
    5. "It may have flaws, but Drum doesn't appear capable of analyzing them."

      I like that, and it reminds me of how Somerby writes.

      Delete
    6. Here is a flaw that Drum might have pointed out, but didn't. The advanced students who did less well in special classes than those in untracked classes could have done less well because they spent their time on topics not assessed in whatever test was used to determine performance, whereas the untracked students most likely followed the curriculum more closely. Would that suggest that untracked classes teach more math or better math? Not if the advanced students were learning enriched material or topics not on the exam. Further, one advantage of tracking is that students develop greater self-confidence in math and thus set higher aspirational goals for themselves. That isn't measured by tests either but is important to whether they go on to more advanced elective math later on, or become math majors in college (or major in a subject requiring advanced math).

      Neither Somerby nor Drum chose to engage with the subject of tracking and math. They both use the framework to address their pet peeves.

      While on the subject of jargon, Drum could have noted the way that conservatives address social justice language instead of the ideas behind it. Just as the term "woke" has become a right-wing culture-war shibboleth, the term social justice seems to evoke a knee-jerk negative response and Drum makes no effort to analyze why social justice concepts are bad when schools are supposed to be socializing children in positive virtues such as generosity, sharing, kindness, cooperation and group effort, teamwork, adherence to rules and loyalty to friends and family, etc. School is about acquiring social understanding, not just math facts, so why shouldn't social justice be incorporated into word problems?

      Delete
    7. That's the risk of using and abusing these phrases and terms. When someone says "socialism" are they referring to workers owning the means of production or government welfare programs?

      When someone says "social justice" what sub-set of social concerns are they actually referring to? Most likely race or sexual identity.

      So we're often left fumbling around in the darkness, with bumper sticker phrases bouncing around and varying levels of understanding resulting from the mess.

      Once a topic is politicized, the phrases and terms that describe that topic become footballs in play. They will no longer mean what they had meant.

      This degradation of language can be perhaps mainly attributed to the lazy corporate media and their drive to provide profitable, easily digestible chunks of news that feed each of their respective tribes by reinforcing what they already believe.

      Where is the national discourse? In the gutter.

      Delete
  3. Somerby seems to answer the question “Should everyone take the same math class?” with “Are some kids "better at math" than others? We'll guess that the answer is yes!”

    But that isn’t really an answer.

    And this seems like an oversimplification: “They just thought that one math class should be harder!”

    I’m not at all sure that that is what either California or Virginia are proposing.

    It’s noteworthy that the Post writer Mathews doesn’t link to the actual VMPI website, but he does quote a staunch opponent of the proposal to obtain a description of it.

    Somerby does no real investigation into any of this. He just engages in his knee-jerk “it’s got to be bad if liberals are proposing it.”

    Drum is at least open-minded, if skeptical.

    If Somerby were interested at all in this topic, he could start with this from Drum’s column:
    “The overall achievement of the students after the de-tracking significantly increased. The cohort of students who were in eighth-grade mathematics in 2015 were 15 months ahead of the previous cohort of students who were mainly in advanced classes (MAC & CAASPP 2015).”

    If that is true, and it is consistent, then that should cause Somerby to question his usual assumptions.

    ReplyDelete
  4. It is interesting that Somerby complains about cheating by school districts without ever discussing the structure of financial rewards and punishments that encourages such cheating.

    ReplyDelete
  5. Has Somerby ever written about the conservative attempts to undermine the public schools? They have been anti-public school for years now.

    Their support for vouchers is another marker along that road. I happen to think that conservative support of charter schools also stems from their hatred of public schools.

    The whole “critical race theory” war is just another attempt by conservatives to prove that the public schools engage in “liberal indoctrination.” It’s of a piece with their opposition to the teaching of critical thinking, or facts, because conservatives view those things as threats.

    There is plenty to critique about liberal “school reform”, but a person who truly cared about public schools would not fail to discuss the conservative platform as well, nor would he write “here’s what my gut tells me science and research be damned” type posts.

    ReplyDelete
    Replies
    1. Liberals are pro-public schools
      Conservatives are pro-children

      Delete
    2. Yes, that sounds like a fine bumper sticker, but is it true? What is the evidence that conservatives are pro-children when they refuse to fund measures to help children, especially those in poverty or with special needs?

      Delete
    3. The evidence is that Republicans support giving kids alternatives to the failing inner city schools. Having alternatives is good for the children, even though it takes $ away from the public schools.

      Democrats generally oppose adding more school alternatives.

      Delete
    4. Unlike Republicans, I want to defend this country.
      That's why I support Defense Vouchers.
      Give everyone a voucher and let them choose how to spend it to defend themselves.

      Delete
    5. Northrup Grumman's technology isn't for everyone.
      Giving the citizens alternative uses of our $715 Billion defense budget is freedom.

      Vouchers for Defense!

      Delete
    6. David,
      These are the same people who think the Pentagon knows more about defending children from foreign powers than their parents do.

      Delete
  6. This comment has been removed by the author.

    ReplyDelete
  7. oh the banality of math reform!

    ReplyDelete
  8. This is why kids need a dose of social justice along with their math lessons:

    "A lot of white people are racist. Some white people are so racist that they look for any excuse to show their bigotry off. Last week, an elderly KK-Karen showed her hateful ass at a Burger King in Florida when she reportedly threw a Whopper in an employee’s face and allegedly called the worker a Black bitch as well as the n-word.

    So, what set the woman off? Was she upset because she put her Klan robe in the wash with her colored clothes, confirming her belief that the coloreds ruin everything? Did she leave her favorite noose in the back of the bus after the uppity negroes refused to give up their seats in the front? Was she salty because she’s too old to be a Fox News host but too young to have ever owned a slave? Honestly, it could be all of the above, but all we know is that she was upset because the tomato on her burger was too thick, according to a police report."

    From The Root.

    ReplyDelete
  9. "Should students all take the same math class?"

    Somerby asks this question, but isn't it racist to give some students less math just because they are black, NAEP scores or not?

    ReplyDelete
    Replies
    1. Those NAEP scores that Somerby keeps talking about do not measure individual children's progress but measure the school's performance. Without individually identifiable scores, how would kids be put into special low-functioning math classes? On the basis of their racial group's NAEP score? Hell, why not just put all the black kids in the lowest reading and math groups, away from the deserving beautiful white kids, so the white kids don't have to be bothered by them, and be done with it? Somerby obviously didn't like teaching those black kids, or he wouldn't have spent the last few decades complaining about them and their ratty NAEP scores.

      Every parent of a black child has had the experience of being told that their child is low functioning, while test scores and grades contradict that assessment. My grandson's teacher told my daughter that my grandson couldn't read. She took him to a psychologist for a private assessment and found out that he is gifted and reads at least two grades above his age level. That teacher was a stone cold bigot and she insisted that the school switch him to a different class, which they did. Black kids get labeled by race all the time and race isn't a test score, except that white teachers treat it like one, as does Somerby today.

      Delete
  10. Here's another reason why white kids should be taught social justice along with their math lessons (from Daily Kos):

    "When a white Californian couple decided to follow a Black delivery driver on the suspicion he was speeding, they probably didn’t think it would end in criminal charges for the white people. But sure enough, Julie Walrand, 35, was arrested on April 18, the same day as the incident, on hate crime, battery, and false imprisonment charges, police said in a news release last Tuesday. Witness video captures the moments after Walrand allegedly followed Kendall McIntosh and screamed racial slurs at him. “During that altercation, the driver used force to prevent the package delivery person from leaving and used hateful language disparaging of people of color,” police said in the release. “Based on the above information, officers arrested the driver on suspicion of PC 236—False imprisonment, PC 242—Battery, PC 415(3)—Using offensive words and PC 422.6(a)—willfully threatening a person based on their perceived characteristics.”

    Even though Walrand called 911, McIntosh told KRON4, she started "harassing him" after she and her boyfriend followed him to Delaware Street and McGee Avenue in North Berkeley. “Instantly just started cursing me out like, first sentence I’m getting cursed at,” McIntosh said. “Very derogatory language, you know I was getting constant F bombs thrown at me. I was getting just racially profiled from the jump.” He told the news station that he feared for his safety and that during the encounter Walrand got into his van and tried to take hold of the steering wheel for several minutes."

    ReplyDelete
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