Hey, they did NOT ban Developmental Education! And a call to arms …

Florida.

In case you have not heard about this, Florida (meaning the legislature) passed a law which requires colleges to cease requiring courses prior to college level for many (perhaps most) students.  A summary of the bill (which has other interesting components) is at http://www.flsenate.gov/Committees/BillSummaries/2013/html/501

One way this has been reported is that ‘Florida has banned developmental courses’.  In basic ways, this seems to be the intent and the effect.  As is typical for many states in this era, the process involves an outcome designed with little professional input with a process based on no patience (or perhaps based on the attention span of the legislators).

Relative to other states, and our profession, here is the risk I see: The law changes the basic definition of ‘developmental education’.  We can have developmental education without having any courses (or credits).

Historically, ‘developmental education’ has two related meanings:

1. Remedial courses (perhaps done with more student support)
2. Student development as learners (secondary goal of student success in general)

The new definition in Florida is that “developmental education is the extra service provided to enable all students to begin in college level courses” (my paraphrasing).  Most of us would call this ‘just in time remediation’.

If you read the Florida law, and the reports of it, you will see the word ‘flexibility’ repeatedly.  I am sure that this was actually a goal in the process.  However, the new ‘developmental education’ is a risk to our students.  Flexible enrollment does not mean reasonable opportunity; access for all does not mean equality.

We could agree, I hope, that a significant portion of students referred to remediation (old developmental) do not need it — either they have no meaningful gap to fill, or the gap is small enough that they would do fine with a little bit of help (new developmental).  This is a valid criticism.

We could also agree, I hope, that we have been too quick to have more developmental courses (old developmental).  It is not reasonable that a student who passed Algebra II or AP Statistics would need 2 or 3 courses before college math.  Inefficiency was a fatal flaw in the automotive industry, and it is a fatal flaw in developmental education.

Florida has declared, in effect, that the old developmental education is bankrupt and going out of business.  No bailouts.  No loans.  No recovery.  Just gone.

That is the risk raised for all of our students.  Other states have similar pressures and political forces, and read the same reports that were read in Florida.  “We don’t need to waste all that money, and we can solve this problem at the same time.”

We need to rise up.

We need to be clear that we know of problems in our work, and that we are willing to make basic changes; further, we need to show evidence of better ideas so the ‘bankrupt and out of business’ model is not so easily taken.  Yes, we even need to become involved in the political process.

Do YOU know where your state legislator is?

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Inside New Life

The May 2013 issue of the MathAMATCY Educator (AMATYC’s journal) has an article with the background on our New Life project.  This article was done after a request from the editorial staff, and provides a synopsis of the work from 2009 to early 2013.

You can see that article here: Inside New Life 2013MayMAE  (this is a PDF format file)

 
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Contextualized: Does Everything Need an Application?

In some corners, ‘algebra’ is getting a bad reputation.  Algebra weeds students out of programs, prevents completion, and is not identified as needed for most jobs.   Some of us have responded by taking a very  contextualized approach to algebra, so students can see how useful it is.

This is the first week of our summer classes, so I have been working with my introductory algebra class on basic concepts.  We actually do very little with operations on signed numbers (traditionally the start of an algebra course); instead, we spend 3 class days mostly working on the language of algebra.

My interest is in having each student understand the objects we are using.  When we see ‘3x’, I want them to have multiple and correct ways of expression this verbally.  When we see ‘the square of a number’, I want them to have at least one correct symbolic expression they can write.  I deliberately do all of this work without any context for each problem; in other words, the problems are not framed in terms of a situation with physical objects or meaning.

In our Math Lit course, we also do some of this same work.  The difference there is that we introduce algebraic reasoning by talking about some contexts where algebra might be helpful, and then deal with understanding the objects when there is no context.  Does it help to have the context first?  Not really.  It’s fun to have a context, and it motivates some students (though not most).

What seems to happen with context is that ‘understanding the context’ takes quite a bit of energy; I think the brain tends to then organize related information as being connected to that context.  Making the ‘math visible and general’ is not easy, when students begin in a context.  In some ways, beginning in a context comes across as just being a more complicated puzzle word problem (“two trains left at the same time …”).  Students seem to feel like the context was just there to give them another word problem.

One of the myths seems to be that “we need to make it relevant”.  In some cases, we have gone so extreme that we refuse to cover a topic if we can not show students a context that they can see the math within.  I think we have confused math education with something else — having a context for everything is a basic property of occupational training.  Unless we are teaching an occupational math class, context is a tool to use when it helps; context should not be a cage that prevents good mathematics from being learned.

Whatever we might call a course (introductory algebra, mathematical literacy, whatever), a core understanding of basic ideas is critical.  Think about this problem:

2x+4x=??

Without further learning, something like 30% of students will give either 6x² or 8x² as an answer.  [Even among those who generally give the correct answer, their confidence may not withstand a little questioning about ‘why’.]  I’m not talking here about understanding operations on rational expressions, or factoring trinomials with a leading coefficient greater than 1, nor about simplifying radicals with an index of 3 and a radicand containing constants and variables.  The issues here deal with the initial constructs of an algebraic language system.

A related issue is ‘transfer of learning’ — context generally creates barriers to transfer.  Context is a concrete approach, and serves an instructional purpose when used appropriately.  However, an initial learning (in context or not) does not enable transfer to situations where the knowledge is needed.

In reforming the math curriculum, we need to keep aspects of the prior design that have benefits for students.  Think about (1) Transfer of learning and (2) Student confidence.  Known factors support transfer of learning — ease of recall, connections, and flexibility.  Student confidence seems to be impacted by feedback and repetition.  The presence of repetition can support both transfer and confidence — it’s not the presence of any repetition; rather, it’s purposeful repetition (including the use of mixed repetition) that provides the benefits.

When people say that algebra is not needed in occupations, this is often based on people in those occupations looking at a list of typical topics in an algebra course.  I think different results would be obtained if we asked about a different list — variables, algebraic reasoning, functions and models, graphical interpretation, etc.

I’d encourage us, as we re-build our curriculum, to incorporate more context — but not be limited by context.  I’d encourage us to help students learn deeply by providing sufficient repetition (with mixed practice especially).

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Mathematical Literacy and Equity

I just finished watching a talk given by my friend Uri Treisman at the NCTM conference, in which Uri presents some great sets of data and a wise viewpoint on the theme of equity.  Seemingly unrelated, I am often asked “what is so different about that Math Lit course?”

Most of the data I have seen suggests that the traditional developmental math curriculum tends to reinforce existing achievement gaps.  Students who had done well overall, but not in math, pass our courses.  Students who have struggled pass at a much lower rate.  Access is not the same as equity.  In particular, minority students tend to have much lower pass rates than majority Caucasian students.

In Uri’s talk, he tells the story of how Boeing became successful at building airplanes … by designing ‘fault-proof’ planes, where one failure would not cause a catastrophic event.  Uri calls us to design fault-proof educational systems to avoid catastrophic events for our students.

A Math Lit class is one attempt at a fault-proof course.   In the traditional curriculum, there is a tendency for students to be defeated by mathematical ideas that they did not understand.  The Math Lit approach for this problem is to avoid catastrophic failure; within each class, we identify students who did not understand enough to succeed and provide an opportunity to learn.  We focus on the more important mathematics and cover a few less topics; however, the course provides more hope that all students can succeed regardless of their prior mathematics.

A central part of this fault-proof system is the instructor ‘assessing’ every student’s understanding in every class.  Work shown and dialogue reveal a much richer map of knowledge than can ever be achieved by technology such as homework systems.  Online platforms such as My Lab, Connect Math, and Web Assign play a role for students; however, they are not fault-proof — I believe that they tend to be even more ‘reinforcing existing achievement gaps’ than the basic traditional curriculum.

In general, the New Life model looks at the problem of equity by designing a curriculum that provides powerful opportunities to learn.  Our goal is to create a system where hard work will result in progress for every student.  Because equity is so important, we in the New Life project base our work on the value of instructors working with students on important mathematics in prolonged and intense ways.  No student should be blocked from success by the accidents of their prior learning experiences; no student should be blocked from considering STEM fields by faults in their mathematical knowledge.

If you’d like to see the talk by Uri Treisman, it is available on the Dana Center web site at http://www.utdanacenter.org/its-50-of-the-best-minutes-you-can-spend-to-get-a-detailed-examination-of-educational-inequality-in-america-uri-treismans-equity-address-at-the-nctm-annual-conference/

I hope that you will work with us to build a mathematics curriculum that avoids catastrophic failure, where every student can succeed in learning important mathematics.

 http://www.utdanacenter.org/its-50-of-the-best-minutes-you-can-spend-to-get-a-detailed-examination-of-educational-inequality-in-america-uri-treismans-equity-address-at-the-nctm-annual-conference/