Overcoming Obstacles: Making an MLCS Pilot Happen

In a perfect world, we as faculty could create and modify courses as needed to support student learning and success.  But we don't live in that world.  Instead, we are challenged to find solutions for students and then challenged again when we try to implement those solutions.

Here are some common obstacles that come up when trying to pilot a Math Literacy course and some ideas for overcoming them.  All of the ideas shared are above board and do not ignore the rules in place.  I'm a big believer in following the rules and learning ways to work within them.  Some schools are saying they are teaching intermediate algebra but really are piloting MLCS instead.  I don't advise doing that.  It could backfire in a big way in terms of your state regulations and articulation.

1.  Intermediate algebra

Many states, including mine, have a requirement of intermediate algebra before college level courses.  Some states are beginning to allow alternative courses in an attempt to see if they can be successful.  If you are not lucky enough to be in one of those states, here are some things you can try:

a.  Create a large enough course in terms of credit hours and content, making sure all the big ideas from intermediate algebra are addressed.  This means including factoring, quadratics, exponentials, rational functions, and radical functions.  That's not to say that you need to teach all those topics the way we do in intermediate algebra.  Otherwise, what's the point of the course?  But you can show students the typical intermediate algebra topics in a different light, one that focuses on modeling and concepts and applications.

b.  If that's still not enough to get approval for a pilot, go around that intermediate algebra requirement with placement.  Placement is something that nearly every school is in control of.  Use that to your advantage.  We started our pilot with making every student in the course take the placement test at the beginning of the course and at the end.  The data was quite interesting.  Many students placed into college algebra and those who didn't were close.  Our school is contemplating a different placement cutoff for liberal arts math and statistics anyway since being at the college algebra level on the placement test is not necessary for success in those two courses.  It's only necessary for college algebra and precalculus.  That new cutoff would be just slightly less than the college algebra cutoff, similar to how we use ACT scores.  If you have a specific placement cutoff for stats and liberal arts math, you can verify that students passing the course meet that placement number using the exit placement test.  And even if you don't have a special cutoff score, you can still use the placement test at the end.

This approach allows students to use the Math Literacy course as basically a bridge to non-STEM college level math.  They take the course and then retake the placement test.  If your state won't allow the course as entry to statistics or liberal arts math, the placement test result can.  This approach allows you to pilot but still follow state rules.

2.  Faculty opposition

Sometimes faculty in your department will be skeptical that standards will be reduced or students will not be prepared for the outcome courses.  But the reality is they don't know that for a fact.  The data will bear out the truth.  In this situation, ask for a pilot with the stipulation of gathering data and re-evaluating the course after 2 years.  It takes that long to teach the course and track the students after it.  Some faculty, especially ones in math, need hard data to convince them.  Still, some folks just don't like something different than algebra, even if students perform well in the next course.  That kind of emotional reaction is very hard to address because it's not based on facts or logic.

Another suggestion is to make the course an option and not a requirement in your department.  That allows students and faculty who believe in the course to be a part of it and those that don't, aren't.

3.  Factoring

Of all the traditional topics, this one creates the most conversation and conflict.  Fundamentally, many instructors believe students should learn to factor.  Here are the most common cases and what can be done:

a.  Faculty are concerned that students won't be ready for a traditional intermediate algebra class after MLCS if they don't learn all the factoring techniques.  The reality is that students who pass beginning algebra aren't even ready for using factoring in intermediate algebra.  We as educators like to think if we've taught a topic, that it equates to students learning the topic.  But that's just not the case all the time.  Many beginning algebra students still need massive amounts of review of factoring when they go into intermediate algebra, even if it's just a few weeks later.  We saw this firsthand in our redesign.  We tried to address factoring "just-in-time" in intermediate algebra and it never worked.  We saw our intermediate algebra pass rates soar once we added in intermediate algebra as a unit and just taught it directly.  All the students benefited.

So my suggestion in this case is to add factoring to your intermediate algebra class if it's not.  And if it is, it will be enough to help an MLCS student succeed.  Most students moving from MLCS to a STEM path are stronger academically.  That lurking variable matters and benefits the issue greatly.  And nearly all of these students have seen factoring before intermediate algebra.  Remember, because we teach algebra so early in U.S., most students have seen 3-5 years of algebra prior to starting developmental math.

b.  The other concern faculty have is the idea of removing an old standby.  Even if factoring is not useful, many instructors believe we should teach it for historical reasons and for critical thinking.  First, students are not getting the brain exercise we like to think with factoring.  The are ways to make students work hard and think critically AND learn content that will help them in the next course.  We don't have to do topics just for the sake of mental exercise.  We also don't have the luxury of time to do that anyway in MLCS.

But doing something just because we always have doesn't make sense.  My father is a retired math professor.  He knows how to calculate square roots by hand and use a slide rule, but I don't.  I learned trig with trig tables and stats with stats tables, but my students know neither.  Times change and so does content.  100 years ago, a college student had to know Latin to graduate.  We laugh at that now, but at one time it was considered essential to being college educated.  Again, times change, and mathematics education has to evolve with those changes.  We have precious little time with students and need to prepare them for their next course and college in general.  If a topic is not going to serve those goals, it needs to re-evaluated for inclusion in a course.


These are some of the big obstacles and some ideas.  Hopefully they will help some.  If you've tried something that worked and helped you gain a pilot, please share in the comments or send me an email.

MLCS: Where's the math?

MLCS is a very different course, whether you're looking at the materials, the content development, the class structure, or the homework.  Every aspect of the course is different than the traditional algebra courses that are common in all developmental math programs.  Those differences are exciting and lead to great gains in understanding and mathematical maturity for students.  I'm so impressed with what students can do when we get to this point in the semester.  But change is hard.  

Einstein said, "We can't solve problems by using the same kind of thinking we used when we created them."  To get to the point we want students to be at the end of the math literacy course, which is college readiness, we use very different approaches.  And they do work, but they do not look like what instructors expect, especially in terms of the printed page.  For example, I taught a lesson today that started with reviewing linearity and building a model, then moved into solving literal equations, and concluded with factoring the GCF.  All of this worked together in the context of building a model and then working with the most useful and simple form of it.  Everything had a purpose, but nothing was easy.  Beyond that, those topics never appear together in an algebra book.  But they need to if we want students to see connections.  And while that mix of topics may be strange to us as instructors, it can make sense when solving a bigger problem.

College readiness is more than a skill set, but possessing the ability to use that skill set.  To get students there, we use open-ended problems each unit.  This unit, we're having students work on problems framed around the question, "how big is big?"  We want students to grasp the largeness or smallness of numbers in a variety of settings.  We ask students questions like, "could you carpet the U.S. with its own debt if it was in $1 bills?"  $16 trillion is a large number but how large is it really?  Putting it in perspective helps to make sense of it.  That idea is pervasive in real life.  I just used an example:  $16 trillion instead of $16,000,000,000,000.  Writing "trillion" allows me to work with a number that's more manageable:  16.

We ask students to take the U.S. debt and find its weight in quarters, its height if it was stacked in $1 bills, its area, etc.  But the numbers are enormous, so we ask students to make a comparison that's useful and helpful.  To make this idea and goal concrete, we use the example of blue whales, the largest mammal.  But how big are they?  We could find their length or weight but those are just large numbers.  So put them in perspective.  This interactive app provides a great demonstration.  For me, seeing that a blue whale is the length of a basketball court is really illuminating.

This unit project has an amazing amount of math in it to be solved.  Students have to work with scientific notation, dimensional analysis, concepts from geometry as well as do research on quantities and find objects of comparable size to make comparisons against.  If you want a fun challenge, find the weight of the U.S. debt in quarters and then something on the earth to make sense of that number.  It's not a trivial exercise.

Like the quarter problem, the entire open-ended problem description is brief and there are no mathematical symbols in it.  But to complete the project takes pages of calculations and research.  That isn't how we typically provide "word problems" to students because it's really hard for students to complete.  We don't provide short statements and tell the students to figure it out.  As educators, we want to make math accessible so we try to find ways through problems, be it decoding word problems or finding key words or recognizing problem 'types.'  That approach is full of good intentions but the outcome is a student who can't really solve problems.  Students can often mimic their way through, but true understanding is not often gained.  It's like we've left the training wheels on the bike and then expect students to ride without them.  If they never have to ride on their own, we shouldn't be surprised when they can't.

As with the project description, there are lessons throughout the book we've written that are devoid of symbols, at first glance.  Take a look at this page from the manuscript:














It begs the questions, "where's the math?"  Take a look after students complete the lesson:

Like the national debt problem, students start with few words and a problem to solve.  But getting there requires a serious amount of work.  The mathematics is evident and abundant but it was not given to students but instead created by students.
The level of expectation is higher and so is the difficulty level.  But the understanding is deeper.  Students move past skills alone and work to use those skills without constant prompting on when or how.  Not easy, but the payoff is greater.

A colleague of mine said years ago when we began redesigning our developmental math program, "what we're doing is good, but I wish we could do more mathematics with students."  I just looked at him puzzled because what else are we doing with them in an algebra class if not mathematics?  But I understand his point now.  Doing mathematics is rich and complicated and messy and often, circuitous.  Algebra is neat and linear and simplified to a set of procedures.  Do we need those procedures?  Absolutely.  But focusing on them alone is akin to learning all the scales in music.  If we never move past the scales and into the songs, how can we say we've made music?

AMATYC presentation documents

Here is the presentation and handouts from the talk Heather and I did today.

MLCS talks at AMATYC and more!

Heather and I will be at the AMATYC conference in Jacksonville, Florida talking about our course on Thursday, November 8, at 1:40 pm.  The presentation we'll give will be slightly different than the one I've been giving lately, so consider attending if you'd like more information and/or want to hear more about the classroom experience.  Several samples of activities will be shown.

Thursday 1:40 - 2:30      
MLCS: Redesigning a New Pathway for Non-STEM Majors 
Kathleen Almy, Heather Foes

On Friday, November 9, I'm part of the Developmental Math Committee's (DMC) themed session on redesigns.  In 10 minutes, I will very briefly overview our version of MLCS including challenges, progress made, and plans going forward.  If you or a colleague want a quick snapshot of this redesign and others, consider this themed session.

Friday 9:00 am - 10:55 am
Evidence-based Developmental Math Redesigns  (DMC Themed Session)

Embedding Student Success Strategies into Math
Courses Amy Getz

MLCS: One Year Later
Kathleen Almy

A First Look at Developmental Math Students After Course Redesign
James Wolfle

Developmental Math I and II Redesign at Valencia College
Julie Phelps

A Developmental Math Boot Camp
Bill Coe

Washington State’s Developmental Math
Michael Nevins, Carren Walker

On Friday afternoon, I'll assist with Jack Rotman's workshop on the two New Life courses, MLCS and Transitions.

Friday 1:45 pm - 3:45 pm 
New Life Courses: Mathematical Literacy and Transitions
Jack Rotman

Additionally, there are more talks on MLCS, Dana Center's New Mathways Project, Carnegie's Quantway initiative, and other schools trying pathways of their own design.  Definitely the concept of pathways through developmental math beyond beginning and intermediate algebra is taking hold.  The DMC will have a committee meeting on Friday afternoon that anyone can attend.  At it, we'll be voting on an intermediate algebra position statement.  The statement addresses the concept of allowing for innovation and moving away from a universal college-level math prerequisite, intermediate algebra, for all.  Instead, the statement promotes appropriate preparation for all students based on the courses they will be taking.

Lastly, we'll be at the Pearson booth if you have questions.  Also at the booth will be copies of the sampler of our book, Math Lit, in both student and instructor versions.  If you want to talk more, please stop by.  Or, if you'd like to set up a time to meet, please email me.

See you in Jacksonville!

Recording of Math Lit Presentation Now Available

Last month, I gave a talk for Pearson about the MLCS course.  Below is the youtube recording of that talk. 

Flyer for Math Lit book

Looking for more information about the book, Math Lit?  Look no further!

Almy Foes flyer from kathleenalmy

Two MLCS events coming up soon

I'll be in Michigan for a Pearson event and MichMATYC, October 5 and 6.  At the Pearson event, I'll have a small group session with faculty after my MLCS talk.  At the small group session, we'll have copies of the sampler to look at, discuss, and answer questions.

The following week, I'll be at Oakton Community College in the Chicago suburbs doing two MLCS sessions.  The first is a general talk overviewing the course.  The second is an interactive session designed to help schools plan their pilots.  The Pearson site has the session descriptions.