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With so many expressions of LDs, it is not surprising that educators sometimes disagree about their nature and about the kind of help students need as a consequence. Such controversy may be inevitable because LDs by definition are learning problems with no obvious origin. There is good news, however, from this state of affairs, in that it opens the way to try a variety of solutions for helping students with learning disabilities.

Assisting students with learning disabilities

There are various ways to assist students with learning disabilities, depending not only on the nature of the disability, of course, but also on the concepts or theory of learning guiding you. Take Irma, the girl mentioned above who adds two-digit numbers as if they were one digit numbers. Stated more formally, Irma adds two-digit numbers without carrying digits forward from the ones column to the tens column, or from the tens to the hundreds column. Exhibit 2 shows the effect that her strategy has on one of her homework papers. What is going on here and how could a teacher help Irma?

Directions: Add the following numbers.

Three out of the six problems are done correctly, even though Irma seems to use an incorrect strategy systematically on all six problems.
Irma’s math homework about two-digit addition
42 + 59 ̲ 911 23 + 54 ̲ 77 11 + 48 ̲ 59 47 + 23 ̲ 610 97 + 64 ̲ 1511 41 + 27 ̲ 68

Behaviorism: reinforcement for wrong strategies

One possible approach comes from the behaviorist theory discussed in [link] . Irma may persist with the single-digit strategy because it has been reinforced a lot in the past. Maybe she was rewarded so much for adding single-digit numbers ( 3+5, 7+8 etc.) correctly that she generalized this skill to two-digit problems—in fact over generalized it. This explanation is plausible because she would still get many two-digit problems right, as you can confirm by looking at it. In behaviorist terms, her incorrect strategy would still be reinforced, but now only on a “partial schedule of reinforcement”. As I pointed out in [link] , partial schedules are especially slow to extinguish, so Irma persists seemingly indefinitely with treating two-digit problems as if they were single-digit problems.

From the point of view of behaviorism, changing Irma’s behavior is tricky since the desired behavior (borrowing correctly) rarely happens and therefore cannot be reinforced very often. It might therefore help for the teacher to reward behaviors that compete directly with Irma’s inappropriate strategy. The teacher might reduce credit for simply finding the correct answer, for example, and increase credit for a student showing her work—including the work of carrying digits forward correctly. Or the teacher might make a point of discussing Irma’s math work with Irma frequently, so as to create more occasions when she can praise Irma for working problems correctly.

Metacognition and responding reflectively

Part of Irma’s problem may be that she is thoughtless about doing her math: the minute she sees numbers on a worksheet, she stuffs them into the first arithmetic procedure that comes to mind. Her learning style, that is, seems too impulsive and not reflective enough, as discussed in [link] . Her style also suggests a failure of metacognition (remember that idea from [link] ?), which is her self-monitoring of her own thinking and its effectiveness. As a solution, the teacher could encourage Irma to think out loud when she completes two-digit problems—literally get her to “talk her way through” each problem. If participating in these conversations was sometimes impractical, the teacher might also arrange for a skilled classmate to take her place some of the time. Cooperation between Irma and the classmate might help the classmate as well, or even improve overall social relationships in the classroom.

Constructivism, mentoring, and the zone of proximal development

Perhaps Irma has in fact learned how to carry digits forward, but not learned the procedure well enough to use it reliably on her own; so she constantly falls back on the earlier, better-learned strategy of single-digit addition. In that case her problem can be seen in the constructivist terms, like those that I discussed in [link] . In essence, Irma has lacked appropriate mentoring from someone more expert than herself, someone who can create a “zone of proximal development” in which she can display and consolidate her skills more successfully. She still needs mentoring or “assisted coaching” more than independent practice. The teacher can arrange some of this in much the way she encourages to be more reflective, either by working with Irma herself or by arranging for a classmate or even a parent volunteer to do so. In this case, however, whoever serves as mentor should not only listen, but also actively offer Irma help. The help has to be just enough to insure that Irma completes two-digit problems correctly—neither more nor less. Too much help may prevent Irma from taking responsibility for learning the new strategy, but too little may cause her to take the responsibility prematurely.

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
China
Cied
types of nano material
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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many many of nanotubes
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what is the function of carbon nanotubes?
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Source:  OpenStax, Educational psychology. OpenStax CNX. May 11, 2011 Download for free at http://cnx.org/content/col11302/1.2
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