Hot off the presses: my critique of FC on Index on Censorship

A PRACTITIONER SITS WITH a child at a table in the corner of a room. She prompts him continually. The child tries to escape but he’s totally boxed in - by the practitioner, the table and the two walls. When he stands up, he’s pulled back down. When he wails and pounds, he’s prompted to get back on task. When he protests (“All done!”) his words are ignored. The session is not done until the practitioner decides it’s done. If you’re tuned into the world of neurodiversity, you might think you know exactly what this is.

You can read the rest of it here. 

Does a subgroup of minimally-speaking autistic individuals have close-to-normal comprehension skills?

Cross-posted at FacilitatedCommunication.org.

One of the pro-FC individuals platformed at last January’s NIH-sponsored webinar on Minimally Verbal/Non-Speaking Individuals With Autism was Matthew Belmonte, a visiting researcher at the Com DEALL Trust, Bangalore and the brother of someone who, Belmonte claims, communicates valid messages through the Rapid Prompting Method. During his turn in a session entitled “a panel of stakeholder perspectives”, starting at around 17:00, Belmonte notes that, while facilitated communication (FC), Rapid Prompting Method (RPM), and “similar methods” do, as he puts it, “admit influence,” many people are investing time in them. The important questions regarding any one of these methods, he concludes, are “Could it work?”, “If it works, how might it work?”, and “If it works for whom might it work?”. He continues:

…we have found in our own work that about a third of minimally verbal, uh, minimally speaking people with autism in our clinical sample have a severe oral motor impairment and receptive language much, much greater than expressive language. We believe that it is this subsample that might be the candidates for something like this.

Matthew Belmont and others at the NIH-sponsored webinar: Minimally Verbal/Non-Speaking Individuals with Autism: Research Directions for Interventions to Promote Language and Communication (Day 1) (NIH, 2023)

The work he references is Belmonte et al. (2013), a paper entitled “Oral motor deficits in speech-impaired children with autism.” This paper is among just a few “participant-suggested” readings listed on the webinar website—along with Jaswal et al.’s infamous eye-tracking study (critiqued here), which purports to find evidence for a variant of RPM known as S2C, and two works attributed to Grant Blasko, a non-speaking individual who has been subjected to both FC and RPM.

So let’s take a closer look at Belmonte et al. (2013), an article we have not yet critiqued on this website. Belmonte et al. report one main finding: namely, that about a third of the autistic children in their early intervention clinic (out of a total of 31) had oral motor difficulties that were associated with expressive language problems (i.e., problems with speaking) that were worse than average compared to receptive language problems (i.e., problems with comprehension).

This finding, in part, is totally unsurprising. Oral motor problems affect your ability to speak but not your ability to comprehend. More notable is that a third of the autistic children in the clinic had oral motor difficulties—a frequency much higher than is generally reported (see Kim, 2014). But perhaps the most surprising claim appears at the end of the article’s abstract, where Belmonte et al. propose that the motor difficulties in autism extend beyond problems with oral-motor control to include “more basic skills such as pointing.”

It is these last two claims that potentially lend support to FC—in particular, to the FC-friendly notion that autism is primarily a motor disorder; that minimal speech in autism results primarily from oral-motor problems (often called “apraxia of speech”); and that autistic individuals also have difficulty making pointing gestures, such that, when pointing to letters on keyboards, they need the kind of assistance (physical support; prompting) provided by FC, RPM, and S2C facilitators.

So to what degree do these claims hold up?

As far as pointing goes, besides saying that pointing is one of the skills taught at their clinic, Belmonte et al. provide no evidence that any of their clients actually struggle to point. One of the measurement tools used in their study, the Com DEALL Developmental Checklist (CDDC), does include assessments of fine motor skills, but neither Belmonte et al. nor the one reference they cite on this tool, Karanth et al. (2010), tell us which fine motor skills are measured or whether they include pointing. The only other mention of pointing occurs at the end of the paper:

There remains of course the potential that fine motor impairments could impede use of alternative and augmentative communication devices, because open-loop motor control which is unintegrated with sensory feedback (Haswell et al., 2009) leads to errors in pointing with a finger or hand to select amongst multiple response options.

The paper Belmonte et al. cite here, Haswell et al., (2009), makes no mention of pointing. Haswell et al.’s experiment had children hold a robotic arm in one of their hands and reach with it to capture toy animals. The researchers examined how well the children controlled the robot when it “perturbed the children's arm movements by producing a force field.” Comparing the performance of their autistic and non-autistic subjects, Haswell et al. found that there were differences in performance, but also that “in the baseline period in which no perturbations were present, both ASD and typically developing groups produced straight reaching movements.” Since pointing typically involves straight reaching, and typically occurs without perturbations from force fields, Haswell’s results suggest that, consistent with our other posts on this subject, pointing difficulties are not a common characteristic of autism spectrum disorders.

What about significant oral-motor problems or apraxia of speech? There is some support for oral-motor difficulties affecting expressive language in minimally speaking individuals with autism. Chenausky et al. (2019), for example, report symptoms of “likely” apraxia of speech in about a quarter of 54 minimal speakers whose videos they analyzed. But oral-motor problems are not generally reported as the main obstacle to communication in autism (see Kim et al., 2014).

Furthermore, though you wouldn’t know it from the NIDCD webpage, several more solid papers (larger sample sizes; measurement tools more clearly described) have been published since Belmonte et al. (2013) that reach rather different conclusions. One is Yoder et al. (2015). Examining a sample of 87 autistic preschoolers, all of whom were initially nonverbal, Yoder et al. find that motor skills, including oral-motor skills, were not significant predictors of expressive language. Rather:

responding to joint attention, intentional communication, and parent linguistic responses were value-added predictors of both expressive and receptive spoken language growth

In other words, language skills—both receptive and expressive—correlate not with motor skills, but with what most people consider to be core autism symptomology.

Another example is Mody et al. (2017). Examining 1781 participants ranging from 2 to 17 years of age, Mody et al. find “significant positive associations” between fine motor skills and both expressive and receptive language skills. In other words, poor motor skills are associated not just with speech problems, but also with comprehension problems. Indeed, Mody et al. found that the motor difficulties that were correlated with comprehension included not just fine motor skills, but also gross motor. In addition, they find an association between both gross and fine motor skills and social interactions, speculating “that the demands of an impaired gross motor system may leave the child on the autism spectrum with fewer resources for developing joint attention abilities.” Their research thus suggests that motor skills, in their contribution to communication problems, cannot be disentangled from the core social symptoms of autism, which in turn impede both speech and comprehension.

Another article, McDaniel et al. (2018) focuses in particular on receptive vs. expressive vocabulary (word comprehension vs. word use). Among its findings are three that are both at odds with Belmonte’s implications and problematic for FC:

1. Compared to typical children, the 65 autistic participants exhibited smaller receptive–expressive vocabulary size discrepancies. That is, “The children with ASD tended to exhibit comprehension of fewer words than expected relative to the number of words they said.”

2. Participants’ oral-motor skills were not significant predictors of the co-occurrence of spoken vocabulary deficits with relatively large receptive vocabularies.

3. What leads to a receptive vocabulary that is, as is the case with typical children, large relative to expressive vocabulary is a factor that taps into the core social deficits of autism: what McDaniel et al. call “attention toward a speaker.”

Indeed, based on these findings, McDaniel et al. suggest that speech in autism is impaired not because of oral-motor difficulties or apraxia of speech (contrary to Chenausky et al.’s impressions from the videos they rated) but, rather, from a failure to tune in and tune up to speech (see also Shriberg, 2011)—a possibility we discussed in an earlier post.

Finally, Chen et al. (2023), summarized in this video from the recent INSAR conference (and also discussed in this recent blog post of ours), reported one more finding that is problematic both for FC and for Belmonte. While there exists a subset of minimal speakers (about 25%) in which receptive skills are relatively high relative to expressive skills, the receptive skills even of this unusual subgroup:

• are still lower than those of non-autistic individuals

• are positively associated with motor skills.

Screenshot from Chen’s INSAR video

That is, as Chen puts it in her video:

[I]n this subgroup, motor skills emerge as the only significant factor predicting the discrepancies between receptive and expressive language above and beyond all other factors. And those with better motor skills are more likely to have much better receptive language than expressive language.

Oddly, some of these later findings are consistent with two findings that Belmonte et al. report in their otherwise much-outdated paper:  namely, that receptive language correlated with gross and fine motor skills, and that both receptive and expressive language correlated with fine and oral motor skills.

So while Belmonte might still think, 10 years on, that his 2013 findings support the notion that there’s a group “that might be the candidates for” FC, RPM, and/or S2C, his own empirical findings appear to be less biased than the conclusions he draws from them.

REFERENCES

Belmonte, M. K., Saxena-Chandhok, T., Cherian, R., Muneer, R., George, L., & Karanth, P. (2013). Oral motor deficits in speech-impaired children with autism. Frontiers in integrative neuroscience, 7, 47. https://doi.org/10.3389/fnint.2013.00047

Chen, Y., Siles, B., Liberti, G., Tager-Flusberg, H. (2023). Discrepancies in Receptive and Expressive Language Profiles in Minimally Verbal Autistic Children. INSAR, 2023.

Chenausky, K., Brignell, A., Morgan, A., & Tager-Flusberg, H. (2019). Motor speech impairment predicts expressive language in minimally verbal, but not low verbal, individuals with autism spectrum disorder. Autism & developmental language impairments, 4, 10.1177/2396941519856333. https://doi.org/10.1177/2396941519856333

Haswell, C. C., Izawa, J., Dowell, L. R., Mostofsky, S. H., & Shadmehr, R. (2009). Representation of internal models of action in the autistic brain. Nature neuroscience, 12(8), 970–972. https://doi.org/10.1038/nn.2356

Karanth, P., Shaista, S., & Srikanth, N. (2010). Efficacy of communication DEALL--an indigenous early intervention program for children with autism spectrum disorders. Indian journal of pediatrics, 77(9), 957–962. https://doi.org/10.1007/s12098-010-0144-8

Kim, S. H., Paul, R., Tager-Flusberg, H., & Lord, C. (2014). Language and communication in autism. In F. Volkmar, R. Paul, S. J. Rogers, & K. A. Pelphrey (Eds.), Handbook of autism and pervasive developmental disorders (4th ed., Vol. 1, pp. 232–363). Wiley.

https://doi.org/10.1002/9781118911389.hautc10McDaniel, J., Yoder, P., Woynaroski, T., & Watson, L. R. (2018). Predicting Receptive-Expressive Vocabulary Discrepancies in Preschool Children With Autism Spectrum Disorder. Journal of speech, language, and hearing research : JSLHR, 61(6), 1426–1439. https://doi.org/10.1044/2018_JSLHR-L-17-0101

Mody, M., Shui, A. M., Nowinski, L. A., Golas, S. B., Ferrone, C., O'Rourke, J. A., & McDougle, C. J. (2017). Communication Deficits and the Motor System: Exploring Patterns of Associations in Autism Spectrum Disorder (ASD). Journal of autism and developmental disorders, 47(1), 155–162. https://doi.org/10.1007/s10803-016-2934-y

Shriberg, L. D., Paul, R., Black, L. M., & van Santen, J. P. (2011). The hypothesis of apraxia of speech in children with autism spectrum disorder. Journal of Autism and Developmental Disorders, 41(4), 405–426. https://doi.org/10.1007/s10803-010-1117-5 [4] Aside from words that label pictures, most written words cannot be learned in

Yoder, P., Watson, L. R., & Lambert, W. (2015). Value-added predictors of expressive and receptive language growth in initially nonverbal preschoolers with autism spectrum disorders. Journal of autism and developmental disorders, 45(5), 1254–1270. https://doi.org/10.1007/s10803-014-2286-4

Going on automatic: should technology supplant penmanship, composition, and translation?

And should ChatGPT supplant (parts of) the writing process? 

And should Google translate supplant foreign language instruction? 

To what extent do we lose out on important cognitive processes by outsourcing these tasks to machines? 

As we ponder these questions, here's an old OILF post about penmanship.

In an article in last weekend’s Times, Anne Trubek, author of The History and Uncertain Future of Handwriting, argues that cursive is no longer pedagogically useful:

People talk about the decline of handwriting as if it’s proof of the decline of civilization. But if the goal of public education is to prepare students to become successful, employable adults, typing is inarguably more useful than handwriting.

Trubek concedes that "a 2012 study of 15 children found that forming letters by hand may facilitate learning to read.” But, she notes, "there seems to be no difference in benefits between printing and cursive." Her conclusion:

If printing letters remains a useful if rarely used skill, cursive has been superannuated. Its pragmatic purpose is simple expediency — without having to lift pen from paper, writers can make more words per minute.

And the expediency argument no longer holds water: now, with computers, typing is faster.

One of the most compelling cases for cursive over typing transcends expediency, and Trubek acknowledges it:

A 2014 study found that college students who took handwritten notes in lectures remembered the information better than those who typed notes.

But Trubek dismisses that study, saying that it

may indicate only that the slower speed of handwriting causes students to be more selective about what they write down.

And it’s here that Trubek’s case falls apart. For the idea that the slower speed of handwriting causes students to be more selective is hypothesized as the very essence of its advantage over typing in note-taking. As an earlier Times article on the 2014 study reports:

Pam A. Mueller of Princeton and Daniel M. Oppenheimer of the University of California, Los Angeles, have reported that in both laboratory settings and real-world classrooms, students learn better when they take notes by hand than when they type on a keyboard. Contrary to earlier studies attributing the difference to the distracting effects of computers, the new research suggests that writing by hand allows the student to process a lecture’s contents and reframe it — a process of reflection and manipulation that can lead to better understanding and memory encoding.

And as I noted in an earlier blog post:

For experienced keyboardists, typing is generally much faster than writing. Handwritten notes, then, require more triaging of content, and, therefore, more active attention to what's most important.

Trubek’s alternative?

Perhaps, instead of proving that handwriting is superior to typing, it proves we need better note-taking pedagogy.

Since it’s been at least half a century since we’ve had any note-taking pedagogy, one has to wonder whether Trubek has spent much time in any actual classrooms, or among any actual education policy makers.

One wonders this anew when she imagines how much better student’s writing skills must be today:

Many students now achieve typing automaticity — the ability to type without looking at the keys — at younger and younger ages, often by the fourth grade. This allows them to focus on higher-order concerns, such as rhetorical structure and word choice.

In fact, the changes imposed by the digital age may be good for writers and writing. Because they achieve automaticity quicker on the keyboard, today’s third graders may well become better writers as handwriting takes up less of their education.

Has Trubek looked at a student paper recently? Handwriting has been “taking up” much less education for a while now, and what I’m seeing doesn’t support her optimism. Nor are students typing any faster than their parents: the ease of correction has allowed many of them to develop sloppy, inefficient keyboarding habits.

That aside, I see downsides to keyboarded compositions that are similar to the downsides to keyboarded note-taking. Just as the speed and automaticity in typing allow you to record the teacher’s words without having to reflect on what’s key, they also allow you to write down your thoughts as fast as they come—with little reason to formulate them first. Yes, there are still those who care enough about their writing to edit it before turning it in—and for these people, word processors are a wondrous boon. But the finished look of auto-corrected, auto-processed prose can make anything look “done,” and many students readily turn in what is often an unedited brain dump (sometimes warped by autocorrection howlers)—prose that is far worse, I’m guessing, than what they would have turned in had they had to write it out first in long hand.

Trubek rightly points out that:

Keyboards are a boon to students with fine motor learning disabilities, as well as students with poor handwriting, who are graded lower than those who write neatly, regardless of the content of their expressions. This is known as the “handwriting effect,” proved by Steve Graham at Arizona State, who found that “when teachers are asked to rate multiple versions of the same paper differing only in legibility, neatly written versions of the paper are assigned higher marks for overall quality of writing than are versions with poorer penmanship.” Typing levels the playing field.

But, apparently unaware that penmanship hasn’t been taught in a generation, she overlooks the possibility that much of today’s poor handwriting is as readily remediable as it is rampant.

Trusdek begins her book with a history of handwriting—which supposedly buttresses her claim that handwriting is history. As Jessica Kerwin Jenkins writes in this weekend's NY Times book review,

Perfecting penmanship became a Christian ideal in 19th-century ­America, one occasionally credited with disciplining the mind, initiating an era of ­pseudo-psychological graphology that lingers today. Handwriting’s sketchy scientific past makes good reading, but Trubek errs in underplaying the contemporary research that shows handwriting’s role in cognitive development. Studies show that a child drawing a letter freehand activates the neurological centers that reading and writing do in adults, while using a keyboard ­produces little effect. Children composing text by hand generate more words more quickly, and also express more ideas. Students who take class notes by hand better retain that information, and, fascinatingly, not only does the brain process capital letters and lowercase letters differently, but block printing, cursive and typing each elicit distinctive neurological patterns. It all seems more tantalizing and tangible than the “advantages ­unimaginable” Trubek believes the future holds. She calls the science behind the new studies “fuzzy” and judges their findings unconvincing. But while American public education has abandoned cursive, France surveyed the evidence and ­began teaching connected script even earlier, at age 6.

…

Though one technology often supplants another, that doesn’t necessitate concession. Considering its rich significance, instead of hustling handwriting off to the graveyard, perhaps what’s called for is resurrection.

Drexel talk on autism basics

 Now on Drexel's YouTube channel:

https://www.youtube.com/watch?v=cSgJOo7r0gc

What is "independent typing"?

A commenter on the FacilitationCommunication.org blog just asked us to address the question of individuals who start out with some form of facilitated communication but then "graduate" to "independent typing."

This is a common question, so I think my answer is worth repeating here:

The issue boils down to what "independence" means. Many people assume that typing on a stationary surface must be independent typing. However, if independence means free from facilitator influence, that is not enough. The facilitator must not be sitting or standing near the person within auditory or visual cueing range. The facilitated person must not be typing out a message that he may have rehearsed ahead of time with a facilitator. 

In the carefully edited videos we see in the movie Spellers of what indeed looks like "independent" typing, we can't be sure whether these conditions hold. These scenes do not guarantee that the person can type spontaneous responses to novel questions when their facilitator is out of the room. In fact, the only way to be sure that facilitation isn't controlled by the facilitator is to blind the facilitator as part of what's called a "message-passing" test. But that is something that proponents of RPM and S2C have uniformly refused to do, even when the stakes are extremely high (abuse allegations; multi-million dollar lawsuits against school districts). 

There have, however, been a few facilitator-blinded tests that have arisen in naturalistic settings, and, as we discuss in this post, the results indicate that even Tito, one of the most seemingly independent typers (see him here), is producing messages that are controlled by his facilitator.

How “non-speaking” and those who call themselves “non-speakers” muddy the waters in facilitated communication

A number of people in the autism-FC universe describe themselves, at least to some extent, as non-speaking. This may sound totally unsurprising: after all, most of those subjected to FC are mostly non-speaking. But the non-speakers I have in mind here are not themselves facilitated.

On one hand, this means that the testimonials attributed to these people about being non-speaking are their own authentic words—as opposed to words that are authored by facilitators. On the other hand, there’s a complication: most of these self-identified non-speakers also identify as autistic. As a result, they seemingly contradict the general findings that minimal speaking in autism means minimally verbal in general: minimally able, that is, to communicate in any linguistic medium, including in written language and sign language.

The existence of such people, therefore, lends legitimacy to the notion that FC potentially unlocks hidden linguistic skills in other autistic non-speakers.

So let’s take a closer look at who some of these people are. They include:

• A prominent autism advocate, consistently characterized as a non-speaker, including in a recent interview by People Magazine and in a recent webinar hosted by the National Institutes of Deafness and Communication Disorders, who communicates at all her public events exclusively by typing on an iPad. This person serves on the board of the pro-FC organization CommunicationFirst.

• Another prominent autism advocate, a former member of the Autism Self-Advocacy Network (ASAN) who has been characterized as “non-speaking.” This person has appeared as a guest contributor on the pro-FC website CommunicationFirst.

• The owner of an autism-themed Instagram account with 38 thousand followers, who is described in this 2022 collection of mother’s day messages from autistic individuals as a “41 year old non-speaking AAC user” and heard in this interview communicating through a speech-generating AAC device. This person is also a practitioner and promoter of a form of FC known as Rapid Prompting Method.

Unlike autistic non-speakers who are subjected to FC, none of these people, however autistic they may be, is a “non-speaker” as most people understand the term: i.e., someone who never speaks and/or is unable to speak. That is, each of them has the ability to converse through speech and/or to speak fluently:

• The iPad user tells us here, through a recorded message on her device, “I can talk. I can even have a conversation with you.” But she says that she finds speaking “very difficult when I am upset or overstimulated.”

• The former ASAN board member turns out to have been a non-speaker only during a 17-year-long stretch of his adult life: specifically from 2001 to 2018, at the conclusion of which he is said to have regained most of his speech and to rely only partially on AAC. Numerous recent videos, for example this one, show him speaking spontaneous, fluent English.

• The autism Instagrammer is heard speaking fluent, spontaneous English during this debate in defense of the Rapid Prompting Method.

With this expanded definition of “non-speaker”—one that includes people who mostly can speak but, for whatever reason, sometimes are unable to or sometimes prefer not to—we can add two more FC-promoting individuals to our list:

• The owner of a YouTube channel about autism with 68.7 thousand followers who identifies as autistic and speaks fluent English. On this episode (starting at around 4:00) she speaks in defense of FC-use and the Rapid Prompting Method and on this episode (at around 6:30) about how she sometimes “go[es] non-verbal” in more spontaneous social situations.

• The Executive Director and Legal Director of the pro-FC website CommunicationFirst, who we can hear here speaking fluent English, whose CommunicationFirst bio says she is “neurodivergent and multiply disabled, and expresses herself most effectively by typing, though is usually able to communicate using speech.”

Is it a coincidence that all these self-proclaimed non-speakers support FC? I think not.

First, as noted above, the existence of autistic/neurodivergent non-speakers who are linguistically conversational and literate opens up the possibility that FCed non-speakers likewise have the capacity for conversational, literate language. Precisely this possibility, indeed, was repeatedly asserted by two of the autism experts at the National Institutes of Deafness and Communication Disorders webinar, where the speech-capable iPad user was (literally) juxtaposed with a non-speaking FC user.

A screenshot from the NIDCD Webinar, with the IPad typer and the FC user juxtaposed.

Second, some of their testimonials make some FC-friendly claims about written language. One is that written language can, by itself, be a route to spoken language and to language comprehension, as we hear in this interview of the autism Instagrammer (on a podcast that has also featured FC-user Ido Kedar). She recounts how it was through the channel of written language that she moved beyond what she characterizes as speech that was 100% echolalic (i.e., meaningless echoes of other people’s speech) into meaningful, communicative language. This lends support to the claim made by many FC proponents that FCed individuals are able to acquire language exclusively through print. (A recent post of ours explains why this isn’t actually possible).

Another FC-friendly claim about writing comes from the iPad user: namely, that typing can be less linguistically demanding than speech. In one of her talks, she includes among reasons why speech is difficult for her that “first I have to think of the word and figure out if I even know what that word means” and “lastly, I’ve got to talk and make sentences.” But the challenges of finding words and making sentences apply equally to typing. She also suggests that the whole process, including figuring out how to pronounce words and how to modulate her voice while pronouncing them takes too long because “my brain moves much faster than my mouth”. But typing is generally a much slower process than speech, even in the case of people who have difficulty pronouncing words, and even if the case of non FCed individuals who type with more than just a single index finger.

But perhaps the two things associated with these non-facilitated “non speakers” that most conflate their authentic communications with FC, and thereby most legitimize FC, are these:

• When the iPad user suggests (at around 3:15 in this video) that people may be skeptical about whether she actually wrote her speeches.  

• When the iPad user is described here as someone who “types to communicate.”

As far as skepticism about authorship goes, the reasons for skepticism about the authorship of FCed messages are far more numerous than the reasons for skepticism about who wrote the speeches of someone who “can have a conversation with you” and can clearly type independently.

And as far as “type to communicate” goes, it, like “non-speaking,” is ambiguous in ways that are convenient for FC. A quick Google search will reveal that “typing to communicate” is now used as one of the standard FC euphemisms. Here is a quote from the FC center at Syracuse University (which, in a second FC euphemism, is now called the Center on Disability and Inclusion):

Typing to communicate (Also known as Facilitated Communication or Supported Typing) is a form of alternative and augmentative communication in which people with disabilities and communication impairments express themselves by pointing (e.g. at pictures, letters, or objects) and, more commonly, by typing.

Sounds so innocuous and unconcerning—right up there with being a non-speaker by preference, as opposed to being a non-speaker because of the actual barriers to language acquisition that characterize much of the autism spectrum.

Does progressive education have to mean watered down math?

One of the most common criticisms of "progressive math", aka "reform math", is that the math itself is highly watered down--a natural consequence of the inefficiencies of child-centered discovery learning.

But every once in a while, I'm reminded that there are other incarnations of "progressive education" in which the math is anything but watered down.

My mother, for example, attended a self-proclaimed progressive private school in the 1950s where she got a very solid education in math (not to mention English, French, and history). In fact, a number of the algebra problems I've excerpted in my math comparison problems (comparing traditional U.S. math with Reform Math) came from her algebra book.

Now we have a very interesting article from this week's New Yorker about 3rd grade math at a progressive school in Chengdu, modeled after John Dewey. Here is one of the third grade math problems the author's twin took home with them:

While multiplying one two-digit number by another two-digit number, Little Sloppy misreads 22 as 25, and as a result his answer is higher than the correct answer by 69. What is the correct answer.

How many American 3rd graders can do this problem--no matter how "progressive" (or not) their math classes are?

Two years later, when the family returns to the U.S. but the twins continue to learn Chinese math through a remote tutor, they're doing problems like:

A certain number, when divided by 3, leaves a remainder of 2; when divided by 4, leaves a remainder of 3; when divided by 5, leaves a remainder of 4. What is the smallest that this number could be?

“Math is virtue"; “Math is a way to cultivate yourself," the author quotes the third grade math teacher as saying. 

America's "progressive math" proponents seem to see things differently.