Monday, October 28, 2013

Going to AMATYC?

I'm leaving soon for AMATYC where I'll present at the Developmental Math Summit on Wednesday of this week.  This is a 2-day event with speakers from major organizations like Carnegie, NADE, and the Dana Center as well as many faculty who have been leaders in developmental math reform.

On Friday, Heather and I will present a new session we have created that deals with solving authentic problems in a developmental math classroom, specifically the type that appear in pathways classes like MLCS, Quantway, and Statway.  It's a very active session with participants working in groups and then reporting out.  We will discuss findings from groups and then talk about best practices and tips for teaching with this kind of problem solving.  Join us at 2 pm this Friday in Platinum 4 to learn more about it.

Thursday, October 17, 2013

TEDx Cambridge: Inverting the Curriculum

Here is a great talk about the philosophy behind new courses like MLCS.  In 9 minutes, Ariel Diaz succinctly articulates one of the current problems in education and what we can do to make strides in fixing it.

Wednesday, October 16, 2013

Math Lit FAQ: Why are topics in the book ordered in that fashion?

The topic ordering of Math Lit, and all pathways materials for that matter, is decidedly nontraditional.  The traditional ordering of topics such as rational expressions in chapter 7 and writing expressions in chapter 2 is not the only correct ordering.  It's just a conventional one.  It's the one someone chose years ago in a textbook and others adopted.  The traditional order is linear, for the most part.  But there are some topics like proportions, variation, statistics, and geometry that seem to move around from textbook to textbook, always feeling not quite in line with the rest of the chapter.

The problem is that math is not completely linear.  Sure, there are topics which follow from each other in a particular order.  For those topics, we address them in a linear fashion in the book.  But many topics have great flexibility in where they can be explored.  And often, they make more sense when they are not in the traditional order.

So, back to the original question:  why are the topics in the book ordered in that fashion?

Answer:  Because it works.

To me, mathematics education isn't about "covering" topics.  It's about creating capable problem solvers.  To do that, we have to connect lots of areas of math.  Real problems are messy and not tightly defined as only an equations problem or only a geometry problem.  Real problems transcend multiple strands of math at once, requiring the student to integrate and apply.  So we develop the content in an integrated way, constantly applying what is developed.  The result may seem unusual at first, but only because we are so conditioned to a particular topic order.  That order isn't right or wrong; it's just familiar.

Consider this example:  In traditional beginning algebra texts, combining like terms is usually in chapter 1 or 2, in preparation for solving equations.  Later, in chapter 5, the exponents rules will be developed in preparation for multiplying and dividing polynomials.  These ideas are developed weeks apart and as separate ideas, but they need to addressed together to make sense of them.  So we develop like terms right around the time we're working on exponent rules to see if students really get when the rules apply and when they don't.  It leads to a much greater understanding of both topics.  And then we use both ideas in applied problems so that further connections are made.

We know these developmental students have not been successful in traditional algebra.  Doing the same content exactly as it was done the first time is not necessarily going to lead to different results.  Shaking things up and approaching content with problem solving in mind engages these students more and helps them make progress with their understanding.  It is exciting to move from a "check off this skill" culture to one where students are constantly making progress and capable of solving more involved problems.

It's also a lot more enjoyable to ebb and flow between topics, coming back to them regularly in a deeper way, after the mind has had time to work on other things.  This is quite different than taking a topic and going through every perspective of it all at once.  Students can get lost in the trees and forget there is a forest.

Does content being enjoyable matter?  Sure it does.  I don't believe my job is to entertain; it's to educate.  But students have to engage to learn.  And motivating them can lead to engagement.

At first, it may seem like a topic hasn't been "finished" because every facet has not explored before leaving it.  Give it a little time and it will come up again.  Students will be able to do more with it each time and increased understanding follows.  But it takes time and patience to see that.  Looking at three sections of any integrated text won't give the full picture of what it can help accomplish.

I think Einstein said it best:

"We can't solve problems by using the same kind of thinking we used when we created them."

Tuesday, October 15, 2013

Policy article on pathways and MLCS

This week, a new policy article releases on reforms in developmental math, including pathways like Math Literacy for College Students.  Rock Valley College's Math Literacy course using the text Math Lit is one of several reforms highlighted in the piece.  A full copy of the article is linked below.

From the Learning Works website:

"Experiments to reverse low community college completion rates by redesigning the remedial math most students must take are yielding promising results, defying assumptions about the kind of math students really need.  Changing Equations highlights a new movement in a growing number of the nation’s community colleges to prioritize statistics and quantitative reasoning, a major departure from the traditional one-size-fits-all remedial math sequence that emphasizes intermediate algebra.

Early results – including a dramatic jump from 6 to 51 percent in the proportion of students completing college-level math in their first year of college — are lending credence to the theory that the alternative pathways are better tailored to academic majors that don’t require intermediate algebra. About a quarter of California’s 112 community colleges, as well as numerous colleges in at least a dozen other states, have begun to develop these alternatives for non-STEM (science, technology, engineer, and math) students.

The alternative math pathways supplement other remedial math reforms that colleges and college systems have been pursuing for several years – including changes to instructional practices as well as placement policies.

This brief was written for LearningWorks by Pamela Burdman, a nationally recognized education policy analyst, philanthropy professional, and journalist."

Wednesday, October 9, 2013

Math Lit FAQ: Does Math Lit include factoring?

Answer:  Yes and no.

We include some factoring in Math Lit but the treatment is not the usual treatment given in algebra texts.  The reasons for that are logistical and philosophical.  First, there's only so much time.  In 4 months (1 semester), we are working to take a developmental student to college level.  There is a lot to be done and learned in that time.  So there isn't time to do all the traditional topics we once did and all the rich problem solving along with new topics.  We had to make decisions on what was most important.

Second, the decision to give factoring an abbreviated treatment was a philosophical one.  Heather and I decided early on that we would not cover topics in the book just for historical purposes.  Just because something has always been taught does not mean it is still relevant.  At one point in history, students had to know Latin to graduate from college.  But times change and so do requirements.  Factoring is rarely used in realistic settings.  Factoring the GCF is useful for rewriting formulas, so we cover that.  We also talk about factored form and its advantages.  The traditional treatment of factoring implies factoring will occur often so every technique is necessary.  But factored form really isn't talked about in any meaningful way.  Students don't see why factoring might be valuable and why it might not work (outside of simple prime polynomials).

The traditional reasoning for inclusion of factoring is that it develops critical thinking skills and prepares students for the algebra to come.  We already have critical thinking in spades in Math Lit.  Inclusion of factoring as a mental exercise is not a sufficient reason.  Also, it is not necessary for success in the non-STEM classes MLCS feeds into.

Until our STEM curriculum is updated, STEM-bound students need to factor.  So we cover it heavily in our intermediate algebra class, a course students can take after MLCS if they want to bridge to the STEM track.

Still, some schools want to factor in MLCS.  And that's certainly their prerogative.  MLCS does not have one set of objectives; it is meant to flex to the local and state needs of a college.  So some colleges add some additional sections on factoring.  Others make sure factoring is covered in detail in the first STEM course students may take after MLCS, something that benefits all students, not just ones coming from MLCS.

Tuesday, October 8, 2013

Math Lit FAQ: Can I teach MLCS as a 4-credit course using Math Lit?

Answer:  Yes

Actually, most schools that use Math Lit use it for a 4-credit hour course.  Illinois has certain requirements that raise the credit hours needed from 4 to 6.  But a 6-credit version of MLCS is not common outside of Illinois.

There is a lot of content in Math Lit to allow schools to choose the topics they want for their 4 credits.  We did some research to find out what topics schools want in their 4-credit versions.  The results showed a large amount of variation in the topics covered.  Some schools want geometry, others want more algebra topics.  Some want more statistics while others want a course that has a lower prerequisite.  So we couldn't remove topics to make the book 4 credits without removing options for schools and states.  We did not want to dictate what this course looks like.  It looks like whatever a schools wants it to.

We built the book with the idea that schools would be picking and choosing topics to meet their local and state requirements.  To allow for that, we marked several sections in the table of contents that could be omitted without a negative impact later in the course.  We have schools using various sections throughout the book while others basically use the first half or the last half.  The most common approach is to use all of Cycle 1 to set the foundation for the course and any necessary sections from the remaining cycles to address the topics of the school's choice.

Additionally, Heather and I work with schools to help them choose which sections to cover.  If you are planning a pilot or have adopted the book and want some ideas for choosing sections, please email us.  We will go through your goals in terms of topics and what courses you want MLCS to feed into to determine what can be deleted or reduced in terms of coverage to meet your goals.  There are a multitude of ways to mold the book to meet your needs.

New FAQ series starting on the blog

I'm starting a new series of posts, each one addressing a question I receive often.  Many are related to our book, Math Lit.  Others are about the MLCS course.  Questions include:

  • Can I teach the MLCS class as a 4 credit class using Math Lit?
  • Does Math Lit include factoring?
  • Why are the topics in the book ordered in that fashion?
  • Do I have flexibility using Math Lit?
  • Is there enough algebra in Math Lit for students to be successful in intermediate algebra?
  • We have an emporium model at our college.  Is there a way I can use Math Lit?
  • How is MLCS different than Quantway, Statway, and the New Mathways Project?
  • What is the Math Lit approach to statistics preparation?
  • What is the prerequisite for MLCS or Math Lit?
  • How does MLCS relate to the Common Core?
  • Does MLCS dumb down developmental math standards?
  • Do you provide training?
  • Will you offer the MOOC again?

Please check back often.  I'll be posting responses to all of these very soon.

If you have a question you want answered that isn't listed above, please post it in the comments.