There appears to be a rigidity of thought regarding sticking with "differentiated instruction" without any mention of what might happen if the difference in skills within a classroom turns out to be too great. I am speaking here for mathematics instruction, knowing that instruction in other disciplines may be capable of bridging a greater disparity, but we must acknowledge that there can be a breaking point where all the "professional development" in the world cannot yield appropriate instruction for all students.

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Here's an example:

Let's say 24 faculty from my school enroll in a computer technology course, perhaps "How to Use a SmartBoard." Roughly half of the teachers are new to tech, and half are used to various technologies and use them frequently.

The high-use teachers have installed and learned to use software, are proficient with Office suite tools and are comfortable with running a piece of software and diving into it to learn how to use it. The low-use teachers are still working with Word without 95% of its features and have a very low comfort-level with being pitched into a new software without explicit instruction.

We all take the same course, in the same room, with one teacher. The topic of the course is a software package that behaves remarkably like PowerPoint.

I'm comfortable with PPT so I need someone to say "It's like PPT in the following ways, now let's do something you don't know, something for which SMB is different from PPT." If the teacher attempts to do that, half of the class is still trying to get the software working and they have no idea about much of what I'm asking and get understandably snippy when I try to get clarification on some point that I'm curious about.

I don't need to sit and listen to someone explain how you can use the right-click "copy" or you can use ctrl-c, or if you're using a Mac it's option-c and that key over down there is the option key ... no, you have to hold it down while you press the c key, or you can highlight, drag and drop text into it, but the software will put a link to an image instead if you try. Here, let me help you ... oh, that's not the software we're learning, that's your browser and you can't do that to the browser, but you can from the browser, ... let me help you get the software running. Wait, it's not installed on this computer ...." and we've been here for thirty minutes. (True story)

My half of the group doesn't need to have her tell us about "Adding a picture to the page", "Saving a file", "Layering objects", "Grouping objects", or any of the other things that I already know how to do. I need to have the differences and new things demonstrated. The others half gets nothing while I'm interacting with the teacher and my half gets nothing when they are interacting with the teacher.

What's wrong? Take what are widely accepted principles of educating students

- working from the simple to the complex,
- working from the known to the unknown,
- and starting each lesson near each student's current level of achievement.

The idea of individual "readiness" makes for a good summary of these principles, an appropriate "chunk".

- If one-half of the room is "ready" for what you want to do and the other half is not, no amount of differentiation will cover that gap.
- If the "simple" start for one group is too complex for the other, no amount of differentiation will cover that gap.
- If "what is known" is too different, differentiation is futile. Those who start out ahead are held back and those who start behind are constantly trying to keep up, repeatedly reminded that "Masahiro and his friends" are the smart ones and that there is no point to trying to learn; one can only cling by the fingertips and hope for partial credit.

What results is two classes, held separately but simultaneously, both called "algebra", and neither one doing as much as it should or pushing students as far as they can and should go. That's why math courses should be split into groups whenever numbers and the ability of the scheduler allow.

The weaker math students need and deserve

- more teaching of background knowledge
- more practice with each concept to develop to automaticity
- more time to develop their understanding,
- more time to consider things without interruption,
- simpler examples that have an easier entry point
- and RealWorld applications ... their RealWorld

The stronger math students need and deserve

- less teaching of background knowledge because they are already at automaticity
- all of the same concepts but fewer practice to reach understanding
- teaching of extension topics, the understanding of which is so important in later courses that weaker students will never reach in high school or may never reach at all
- new ideas and challenges, and complex tasks that lead into STEM careers.

A weak student surrounded by kids who all seem to pick things up quickly soon realizes that he is ALWAYS the slowest kid in class. Every single day, every single question, someone else has the answer first and more clearly ... our kid focuses on THAT fact instead of the question.

He always has that bad feeling, as expressed to me by a student just after an honors assembly in which a large part of the school stood up for something ... "Here are all the smart kids in school ... and none of them are you."

A weak student surrounded by other similarly weak students soon realizes that he can learn things, can be successful, and can feel good about himself ... because he isn't constantly being reminded of how stupid he is. Everyone around him has a problem with this new idea. Everyone in the room has trouble with fractions, or scientific notation, or reading the text book, or, or, or.

Curriculum should be adjusted to the ability levels of the students. Classes should be comprised of students with similar ability and who are similarly "ready". |

If you have a small school with one section of 25 algebra 1 students, you're out of luck. Your options are constrained by the reality of your school. If, on the other hand, you have 5 sections of algebra 1 and two teachers who teach it, why not group them by ability? The assumption behind ability grouping is that the curriculum should be adjusted to the ability levels of the students - why not adjust it for the whole classroom at a time?

Schools that propose an "Embedded Honors Credit" are taking the lazy way out. Offering "Honors" to a kid who does one extra project or who builds a model of the LHC is not offering that kid any extra learning, just requiring more work.That kid still has to sit through class and plow through something "extra" ... and will probably be done with that, too, before the other kids in the room are finished with theirs.

Offering "Honors" to a kid who completes a section of Khan Academy is likewise offering little new.

Additionally, consider that students who pass Geometry are considering vastly different options for furthering their math education:

- tech center: mechanic, forestry, videography, or hospitality services
- algebra 2, but that's it ... wants to major something without much math
- pre-calculus, then to a non-math oriented STEM
- or calculus, and then to a math-oriented STEM.

Those are different kids, with different needs. Even though they're all in Geometry, they're not in the same course.