Why grammar matters for autism, part I

I intend this as Part I of a three part series, collectively addressing the question of why grammar is something that no comprehensive autism therapy should overlook.

Today:  Why grammar isn't trivial.

Later:  Why many autistic children need explicit instruction in grammar; What works and how most therapies fall short

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Why grammar isn't trivial:

Consider how we form questions in English:

1. The person I am thinking of is swimming --> Is the person I am thinking of swimming?

2. The person I am thinking of swims. --> Does the person I am thinking of swim?

3. The people I am thinking of swim. --> Do the people I am thinking of swim?

4. The person I am thinking of swam --> Did the person I am thinking of swim?

5. The person thinking of will swim --> Will the person I am thinking of swim?

6. The person I am thinking of might have been swimming --> Might the person I am thinking of have been swimming?

The Question Rule:  

Move the first auxiliary verb after the subject (here: the person I am thinking of), assuming there is an auxiliary verb (sentences 1, 5, 6), to the front of the sentence. If there is no auxiliary verb (sentences 2-4), take the verb do, change it to the same tense and number as the main verb (does, do, or did), and put it at the beginning of the sentence, while changing the main verb to its bare infinitive form (swims/swam --> swim).  

Key grammatical concepts: 

--inversion:  moving a verb to the front of a sentence 

--auxiliary verb: (including will, may, might, and various forms of the verb to be).

--do-support: (inserting do when there's no auxiliary verb).

--tense marking: (when to keep the tense on the main verb vs. move it to the verb do)

--subject: (can include a relative clause modifier, as in the people I am thinking of)

--main verb: (the verb that agrees with the subject)

Native English speakers who don't have language deficits acquire these concepts implicitly--as well as the complex Question Rule in which they figure.

If we didn't, we might make make the following errors:

1. He is swimming? (failure to use inversion)

2. Swimming he is?  (not grasping non-auxiliary vs auxiliary verbs)

3. Swam he? (failure to use do-support)

4. Did he swam?/Do he swam?  (failure to mark tense on only the auxiliary verb)

5. Is the person I thinking of is swimming?  (failure to parse out and skip over the subject to the main verb)

The complexity of English question formation is just one example of how grammar--even that which most of us apply subconsciously--is anything but trivial.

Parents and math homework

An MSNBC article about a recent study showing that 50% of U.S. parents rate their schools poorly asks why parents are saying that schools should spend more time teaching math. The answer they propose:  parents don't want to teach math at home.

In a subsection headed with this very (bold-faced) subtitle, the author quotes a certain education professor as saying that:

Parents may want more math in school because they feel unprepared to help at home.

and that:

"Math is the subject that parents are often intimidated by. We've allowed a lot of kids to just say, 'I'm not good at math,' .... and those kids become parents."

Said professor, one of whose interests is homework "as a boundary object that links home and school practices," overlooks the following:

1. Raising a generation of kids who think they're good at math but are actually poorly prepared is far worse for future generations than raising a generation of kids who esteem themselves more critically but are better prepared.

2. Reform Math programs prepare kids much more poorly than traditional math programs do, as I've argued here, here, and here.

3. Parents at Reform Math schools, including the "model school" my kids attend whose curriculum said professor has hand-picked, are assuming more, not less, responsibility for teaching their kids at home--precisely because they're so dismayed by the math curriculum.

4. In fact, it was only a few days ago that yet another parent asked me how to get her hands on Singapore Math.

5. The only complaints I've heard from parents about doing math at home concerns the Reform Math homework (the so-called "liaison object"), which is often so poorly explained and so apparently unrelated to actual math that many parents have no idea what they and their kids are supposed to be doing.

6. My parents never had trouble understanding my math homework, nor were they were expected to be anywhere near as involved in helping their kids as I am (all those math games, "applied math" arts and crafts activities, and "math projects.").

No, today's parents aren't shying away from teaching their kids at home; in fact, we are doing more of it--perhaps more than any previous generation. At least those of us who have the time, resources, and education to do so (there are some disturbing class issues here).

Furthermore, much of what we do is above and beyond what schools are asking us to do. Indeed, many of us view what we do as unsanctioned, on the sly, possibly subversive. "I taught my daughter how to borrow and carry last night; I hope that was OK," the parent of a mathematically under-challenged 7-year-old recently confessed to me.

My concern is about the next generation of parents, too many of them Reform Math graduates, not all of them enriched by their parents, who won't be able to do for their kids what these intrepid parents are doing.

And about the widening class rifts that all this so-called "progressive education" is causing.

Minimizing grammar in autism therapy: in whose best interests?

My collaborator just reported to me her experience at this year's IDC (Interaction and Design) Conference at Northwestern University.  It seems our paper was controversial. Apparently there were a number of staunch ABA supporters in the audience. And our paper apparently offended them by making favorable mention of Noam Chomsky and his critique of behaviorist approaches to language.

Chomsky's work has highlighted the complexities of grammar and argued that this complexity cannot be acquired through external stimulus alone.  So compelling have Chomsky's arguments against Skinner and his behaviorist approach been that, for decades now, no serious linguist takes Skinner seriously.

Chomsky is bad news for the two most popular therapies that purport to teach language to autistic children:  Floor Time (DIR) and ABA (Lovaas/Discrete Trials).  Neither approach acknowledges the complexities of grammar, and most practitioners lack the linguistics training necessary to appreciate it.

Instead of taking Chomsky seriously, devotees of both approaches, traditionally rivals, have made him their common enemy.  

Greenspan has co-authored a book, The First Idea, in which he tries to argue that Chomsky is wrong about innate grammar acquisition modules, and that language is acquired entirely through nurturing and socio-emotional reasoning. 

And ABA supporters, at conferences like IDC, dismiss papers that:

1. take seriously people like Chomsky who criticize behaviorism;

2. suggest that there's such a thing as complex grammar; and 

3. propose that that there are, just possibly, more principled ways of teaching grammar to children with autism than through discrete trials of stimulus-response.

As with too many education experts, so too with too many autism therapists:  in whose best interests are they acting?

Math problems of the week: Grade 4 Trailblazers vs. Singapore Math

1. From the beginning of the Trailblazers Grade 4 Student Guide (p. 63):

Homework

Dear Family Member: 

Your child is learning the multiplication facts for 5s and 10s. He or she might find skip counting (5, 10, 15, 2, etc.) helpful in solving the problems below. Remind your child to bring home the flash cards for the 5s and 10s. Help him or her study these handy facts. Thanks for your cooperation.

1. How much is 5 dimes?

2. How much is 8 nickels?

3. How much is 4 dimes and 4 nickels?

5. Jerome placed 5 plates on the table for dinner. Each plate received 4 pieces of silverware (fork, spoon, and knife). How many pieces of silverware were placed on the table.

6. Write a story to show 5 + 9. Draw a picture to do with your story. Write a number sentence on your picture. 

7. Skip count from 0 to 100 by 5s.  Write down the numbers as you count.

8. Skip count from 0 to 20 by 10s.  Write down the numbers as you count.

2. From the beginning of the Singapore Math Grade 4 workbook (Primary Mathematics 4a) (p. 24):

Write the missing factors.  Use only prime numbers.

(a) 64 = 2 X 8 X ____ X ____

(b) 84 = 6 X ____ X ____

(c) 45 = ____ X ____ X 5

(d) 72 = ____ X 4 X  ____ X ____

Write the missing factors represented by n.

(a) 24 + 3 X 2 X n

(b) 18 = 3 X n X 2

(c) 25 X 4 = 5 X n X 4

(d) 21 X 20 = 21 X  2 X n

(e) 3 X 32 = 6 X n

(f) 16 X 2 = n X 4

Any summer projects to share?

Has your school assigned your child an excessively complex, open-ended, off-topic, and/or demanding of time and/or "creativity"? If so, please share it here as a comment. Having excerpted my own children's summer project assignments here and here, I'm hoping to post an anthology of additional summer project assignments in a later entry.

Summer math projects: grade 6

Then there's the 6th grade summer math project that my autistic son will have to do.

I initially misread this as "6th Grade Summer Project." 

Nope:  it's "6th Grade Summer Math Project"

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A Festive Meal

For this project, you will help to plan and prepare a festive meal with family and friends.  It can be for a special occasion, like a holiday barbecue or a birthday party, or just a nice dinner at home.  You must:

-Assemble your project as a booklet or on a poster.

-Write a brief introduction that describes the event--What was the occasion? When did it take place? Where was it held? Make a list of everyone who came to the meal.

-Show the menu for the meal.

-Make an itemized list of everything you bought for the meal showing how much each item cost and find the total, or you can include the receipts from stores.

-Write down a recipe for a main dish, dessert or salad that was served at the meal.

-Save the label from a purchased item and copy everything included in the "Nutrition Facts."

-Describe something from the meal that involves numbers.  Be creative. For example, how many candles were on the cake? How many miles did your cousin from out-of-sate have to drive? How many coals were in the grill? How many cookies did you eat? How many trash bags did you need when you cleaned up? Etc.

-Include photos if you have them or draw an illustration.

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Of special interest:

1. The exhortation, ubiquitous with this sort of open-ended project, to "be creative."

2. The ratio of effort to learning.  Particularly if we factor in the efforts of parents and factor out that which has nothing to do with math.

Summer math projects: grade 2

Accompanying my daughter's report card yesterday was the following assignment for a "summer math project":

*Select a community worker/helper. Write 3-5 sentences about he or she uses math at work. Provide an illustration or model. Make it colorful and be creative. :-)

*Design a phone directory. Include the fire department, police department, hospital, library, school, ____, ____, (The blank lines represent two additional choices that the student should provide for the directory [e.g., church, neighborhood store, community center]).

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My daughter is rather shy, and I'm having trouble thinking of an appropriate "community worker/helper" for her to interview.

Then it hits me: her grandfather!  A retired--but active--math professor, he might have some interesting things to say about how he uses math at work.

...As well as whether "math projects" such as this one make students better mathematicians.