Michigan Student Success Summit

The Michigan Center for Student Success hosted a summit this week, and I gave a short presentation on the New Life model.

Here is the link to that presentation (PDF): http://jackrotman.devmathrevival.net/Prominent%20efforts%20to%20redesign%20developmental%20mathematics%20Stu%20Success%20Summit%20Sept2011%20JackRotman.pdf

 
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Excuse Aunt Sally … part II

Sometimes, an experience in class illustrates a concern.

In today’s beginning algebra class, we were doing order of operations with signed numbers … the first problem for students to do had a quotient and then a product.  MANY students in class were convinced that they needed to multiply first; their rationale was “PEMDAS” — where multiply clearly comes before divide. The problem looked like -16 ÷ (-4) ·2; not very complex … and more than half the class insisted on multiplying -4 and 2 before dividing.

Now, it is true that the type of problem involved is not that important; it’s not needed to model any situation, does not find any reasonable answer, and does not support future learning (outside of order of operations).  The correct answer for this particular problem is not very valuable.

However, our students should be developing a coherent system of knowledge.  In an earlier post, I suggested that “Dear Aunt Sally be Excused” from all math classes; my rationale was that PEMDAS directly causes confusion in algebraic reasoning.  This post is further suggesting that PEMDAS is not very functional even within the original domain of use (order of operations, no variables).

I am becoming more convinced that “PEMDAS” should be avoided in all mathematics classes … whether it is school mathematics or college mathematics.  PEMDAS is short-sighted and misleading; PEMDAS does not support an organized system of understanding.  PEMDAS harms students in the long term, and somewhat in the short-term.

 
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A Worthy Calling

Some years ago, my department was dealing with competing requests to add off-campus sections of our developmental courses.  One of these requests was coming from a local hospital, where the staff was very interested in enhancing their education and professional development.  We decided to invest some of our resources to provide our classes at their hospital because this seemed like a worthy calling.

I suggest that all of us who work in developmental mathematics are living such a ‘worthy calling’.  We provide support and professional instruction to students, some of whom have few other options; we help students find their own ladder to a better life.  In many cases, our passion for helping our students is what makes the difference between a student reaching their dreams … or failing again.

We definitely need to re-create what we do in developmental mathematics; far too many students do not make it through our programs, and we effectively serve as a filter in spite of our collective desire to enable our students to succeed.  I hope you will consider the New Life model and ideas.

However, hold your head up!  The calling is worthy, the purpose is noble, and our students need us.  As we start a new academic year, I hope you begin with a sense of purpose combined with a committment to improve what we do on behalf of all of our students.

Together, we can create a new developmental mathematics and look to a brighter future!

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Dear Aunt Sally … Please be Excused (from math)

In developmental mathematics classes, as in school mathematics, Aunt Sally seems to be everybody’s friend.  As in “Please Excuse My Dear Aunt Sally” as a memory aid for order of operations (aka “PEMDAS”).  I would, indeed, like to excuse Aunt Sally from ever being in my math class. 

In another post, I talked about the “Sum of all Shortcuts”; in this post, the issue is mnemonic aids.  You can improve your students’ “learning” if you minimize the use of these ‘easy to remember’ tricks. 

This may sound counter-intuitive … isn’t it a good thing if students can remember something?  Well, it CAN be a good thing; the issue is what exactly do they remember?  In the case of PEMDAS, they remember ‘do inside parentheses first’ or ‘do parentheses first’.  Fine, to a point — students can evaluate  “8 + 10 ÷ 2” and “(8 + 10) ÷ 2”.

The student then sees these ideas, which do not follow PEMDAS:

• 8x + 2x   (can add before multiply)
• 8x + 2y    (can not add)
• 8(x + 2y)   (can multiply ‘first’)
• (2x²y)³     (can ‘power’ first)
• f(x)=8x + 2    (what does that x mean?)
• f(-3) for that function    (what do we do with the -3 on the left side)

The “P” in PEMDAS is especially worrisome.  Parentheses have multiple purposes in mathematics, and only some of them relate to the order of operations.  We also use other symbols of grouping, some of which are another operation (radicals, fractions, absolute value, etc).

Now, we actually make students do too much with expressions of extra complexity just to see if they can follow the order of operations.  We create our own need for an easy-to-remember tool (PEMDAS) which then results in students having to unlearn later when we do other work in ‘simplifying’.  This is a bit like designing a tool to require disposable parts, in order to keep a business active; I would suggest that our artificial level of difficulty with numeric expressions serves no purpose, not even our own.

It’s important, however, for our students to be literate and comfortable with the basic meanings of expressions and forms.  As I talk with my students, I am impressed by how many of them remember ‘PEMDAS’ years later and by continuing difficulty in doing work that does not involve applying ‘PEMDAS’.  We are not doing our students any favor by giving them an easy thing to remember which does not transfer to future work.

Some readers are likely upset by my suggestion; yes, I know PEMDAS has helped millions of students in their math classes; yes, I am aware of research showing mnemonics help learning disabled students in particular.  However, the benefits for most students do not seem that great to me; the long-term result may be more negative than positive.  [Many of my most struggling students have learning problems, and survived by using tools like PEMDAS; they have difficulty in the situations listed above that do not follow the PEMDAS priorities.]

We know that PEMDAS does not cover most expressions involving variables.  I am suggesting that PEMDAS directly interferes with the algebraic literacy of our students; quite a few students suffer needless discouragement when their algebraic difficulties increase as they painfully discover the real limits of PEMDAS.

Let’s send Dear Aunt Sally on a much needed vacation; she has been used for many years, and perhaps is ready to retire.  Instead, let us focus on basic literacy dealing with reasonable objects of valuable mathematics.

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