Biting the Hand that Fed You, Dept.

Keith Devlin, outspoken spokesperson (known as “the math guy” on NPR) on mathematics and who apparently has never backed down from a stated position, has this to say in a column written originally in 2011 and revised in 2014:

“As a nation, we should stop the current suicidal cry to turn back the clock to a form of math teaching that did no one any good and which those of us who became professional mathematicians first had to unlearn, and focus on making good, practical, sensible use of centuries old teaching tools (such as word problems) to produce a generation well equipped for life in the Twenty-First Century.”

He is not the only one to make such statement. What is more alarming than the statement itself is how often such statement is taken as truth and rarely if ever challenged.  The older forms of math teaching did no one any good? Really? Including him? Oh, he’s got that covered.  People like him (a professional mathematician) had to unlearn what he learned in his classes.  The word problems that he learned from did him no good whatsoever and he had to unlearn the problem solving techniques?

I get tired of the canard that “it never did anyone any good” particularly as uttered by those who, despite earnest claims with no evidence to support them, benefited from what they feel harmed many.  The ongoing mischaracterization of traditional math as “mindless computing” needs to be challenged.  Take a look at the students who go on into STEM majors and careers and the many problems they solved at home. Yes, they took on challenging problems, but also the very problems he says do not promote thinking and are mechanical and non-thinking in nature.  The “worked example” effect has its merits despite the claims of professional mathematicians who climbed the ladder and then kicked it down after they reached their levels of success, claiming that the ladder never did anyone any good.

5 thoughts on “Biting the Hand that Fed You, Dept.

  1. Devlin’s remarks are yet more evidence that too many educators are shockingly ignorant of the massive amount of unconscious work done during learning. It’s why some criticize memorization, why so many promote critical thinking skills over acquisition of knowledge first, and why almost everyone thinks teaching creativity is entirely distinct from teaching facts and procedures.

    Instead, people like Devlin focus on that tiny portion of cognition they’re conscious of, and think that’s what real learning and thinking is.It’s a form of modern superstition. Something pops into conscious view, and they seem to think the god of magical thinking placed it there for only them to discover and then share with the world, when the reality is the real cause just took place out of sight. Yeah, this gets me pretty worked up.

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  2. Agreed. Devlin appears to swim in the Educational aquarium more than the mathematical ocean, and sees through a different lens than most mathematicians on such matters. His tendency to articulate in terms of straw men about Gradgrindian methods of yore only shows how steeped he is in that literature. As you show in your series on teaching common core with classical methods there is nothing stultifying or unimaginative about conventional instruction, and students more frequently find it a more effective approach to the subject

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  3. Did Devlin define and calibrate the problem? What is (ARE) the problems? When he raises the silly no-one-right-answer key arrangement problem, is that supposed to be emblematic of THE problem in math? What’s 6*7? What’s 2.5 divided by 3/4? Can students do those? Are those just simple, no understanding skills that flow automatically top-down from the (group) solution of a bunch of disjointed “real world” key arrangement problems? What is his proposed curriculum? How does he deal with full inclusion and acceleration versus enrichment? Why does CCSS define a NO-STEM zone in K-12 where their best goal is a 75% chance of passing a college algebra course – no remediation. Why do we parents get notes telling us to practice “math facts” at home? Why could I get to calculus in high school in the 60s with absolutely no help from my parents, but that was not possible with my math brain son who is now a math major with p-sets that are all proofs? Why are all good high school math tracks traditional, but K-6 math fuzzy, low expectation, and NO-STEM? Where are the kids who make that amazing STEM transition naturally?

    People like Devlin are reduced to talking in generalities to vainly claim some sort of higher “understanding” or “thinking” ground in terms of engagement or special word problems. However, they NEVER deal with the real world problems of what actually gets the job done. They don’t define the various types and levels of educational issues. Who can claim or show that engagement and non-traditional word problems do NOT work? But are they the fundamental top-down curriculum driving force? Does Devlin know that his views provide cover for a LOT of silliness and low expectations? Does he care?

    Why do we have a 19th century model of an educational monopoly where students and parents cannot choose based on their own learning style, like traditional bottom-up, skill mastery driven – the one that is now done at home and with tutors and that creates their best students – the one used in high schools to create the best college STEM students? Where are their examples of these other students? I would be their biggest supporter! They don’t exist. It’s all about vanity and their turf. It’s a classic hypothesis and analysis mistake – it’s all about me. The analysis justifies the hypothesis. I was surprised that Feynman felt he had to give his Cargo Cult Science lecture at Caltech, but too many (apparently) smart people can’t separate out vanity, turf, and products that sell. Where are their critical thinking skills and humility?

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  4. Devlin’s recent “research” is published in a paper called:

    “Using video games to combine learning and assessment in mathematics education”
    by Kiili, Devlin (etal)

    From the conclusion, they state:

    “This study showed that well designed digital games can be used for learning and assessment purposes. Considerable mathematical and pedagogical thought went into the design of Semideus and Wuzzit Trouble.”

    [“Can be.” I’ve played Wuzzit and that is a small fraction of a curriculum, neither necessary or sufficient.]

    “Moreover, we want to emphasize that we believe that mathematics games can be more effective if a teacher or an instructor is involved in the game based learning process (assuming that an appropriate pedagogical approach is used).”

    [“Believe” and “can be” with “an appropriate pedagogical approach?” This is a research conclusion?]

    “In fact, our long-term goal is to produce interactive learning experiences and learning analytics tools for teachers based on in-game measures that can predict development of students’ domain specific knowledge and reveal students’ misconceptions and weaknesses as well as their strengths. Such information will be very useful for teachers in individualizing teaching.”

    [“Goal.” Full speed ahead to act on their hypothesis even though they claim the following “limitations.”]

    “Our study has some limitations that call for more reseacrh on the topic. First, the sample size was small, reducing the power of the study.”

    “Second, at the beginning of the study, the rational number knowledge level of the treatment group was much lower than the control group, which may have increased the effect size of the intervention.”

    “Third, due to scheduling restrictions at the participating schools, we could include only one level that was intended to teach the use of the Semideus game to participants.”

    “Fourth, some of the players faced technical problems with the Semideus game because their iPads had the wrong iOS version. ”

    “Finally, the study was spread to period of two months and thus there is a risk that the game playing is not the only factor that has affected the results.”

    [“Not the only factor!?!”]

    “Because of these limitations, more research with bigger sample sizes on the topic is needed.”

    [But let’s not stop their “long-term goal.” Research to justify what they “believe.”]

    Also in conclusion:

    “Furthermore, one of the more interesting possibilities that games provide relies on assessing children’s conceptual development and mathematical thinking in larger contexts. The big data sets that can be collected with games make it possible to uncover dependencies and patterns behind conceptual change, and compare the performance with other groups, including between countries.”

    […even though the games are out of any sort of curriculum context and help at home and with tutors is unknown. Yes, let’s collect lots of big data because lots of data implies validity and no missing key variables.]

    “These comparisons could provide totally new insights for curriculum development and assessment. When we can provide valid analysis about learning processes, conceptual changes, and learning assessment, we can provide something new and complementary to current assessment methods such as PISA, TIMSS and PIRLS.”

    [“Could.” So much for timely individual assessment, feedback, correction, and high expections for students and parents on a weekly unit basis. Does it work based on the needs of STEM and having any chance of getting to algebra in 8th grade? Yearly “assessment” is more than a year late and many tutoring dollars short.]

    I think that computer games could be valuable, but what we need are NOT programs like Wuzzit.

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