A Flowchart using MLCS

To help understand how MLCS can be incorporated into a developmental math program, I've included a picture of our flowchart below.  We are using the course to provide an accelerated way to statistics or liberal arts math for non-STEM majors.  Because of the requirements of Illinois, ours is a 6 credit course.  Many states are doing a 4 credit version because they may different requirements.  One of the many perks of this course is its flexibility.  Heather and I worked to create materials that would support a variety of implementations of this course.

If a student takes MLCS at our school and decides to head the STEM route or finds out his/her program requires something like college algebra, we have them take intermediate algebra next.  That is our current bridge to STEM.  In our version of MLCS, we have quite a few intermediate algebra topics but the development is conceptual, numeric, graphic, and applied.  The focus is not on procedures.  A traditional intermediate algebra class will give the student the procedural base they need to be successful in a college algebra or precalculus course.

Ultimately, I would like to have a bridge course that picks up where MLCS leaves off and continues the work using this integrated, interactive approach while developing the needed procedural fluency to be successful in STEM courses.  Likewise, I would like a replacement for prealgebra that develops strong number sense and computational fluency.

The benefit to the approach we've taken with our redesign is that it gives everyone options, both faculty and students.  We all learn differently and our goals are not the same.  Providing options respects the differences we have and allows students to be more successful faster since their needs are being met.

For more information on our redesign and the module courses listed in the flowchart, click here for a packet.  Our geometry course is not included in the flowchart below since that requirement is specific to Illinois.  It is mentioned and explained in the packet.

Clicking on the flowchart opens it in a window with a larger version of the graphic for easier reading.

MLCS: Addressing the Common Core

This week ended the third unit of the MLCS course for this semester, concluding with a test and reflection on the open-ended problem for the unit.  Heather and I both noticed growth in the classes.  Our students are working, they are learning, they are progressing.  Connections are being made.  And that's very satisfying because our goals are two-fold:  prepare them for the next math class they will take and prepare them for college level work.  We call that mathematical maturity. 

The place where this growth was most evident this week was their open-ended projects.  Grading them was a very positive experience.  They made connections between algebra, graphs, and numbers while solving a non-routine problem.  We don't hold their hands on these problems.  We let them be problems, not exercises.  Raise the bar but provide the preparation necessary to clear it.  Heather remarked happily when we compared the project solutions, "This is what developmental students can do." 

New courses like MLCS, Statpath, Statway, and the like aren't about lowering standards.  They raise them.  It's an unspoken truth that many developmental students pass developmental algebra without ever doing much thinking.  They learn to decode, memorize, and mimic their way through skill lists and tests.  The idea that algebra is a treadmill for the brain is pervasive but not necessarily a reality.  Certainly algebra can be that, but many students find a way around thinking if given the chance.

In these new courses like MLCS, they don't get the chance.  Students have to read and reason through new problems constantly.  Application, connection, and retention are required to move forward. 

And those goals are the same as the Common Core. 

Nationally, mathematics educators are coming to the same conclusions.  We need to update our curriculum both in terms of objectives but also expectations.  Jobs that require mindless repetitive skill are being eliminated constantly.  Today's employers expect and require much more from their employees.  They expect new hires to learn a new set of skills, integrate them with the knowledge already gained, and apply all of that to new problems.  It's not, "here's a problem I need you to solve.  Here's how you do it and 10 to practice.  Now go."  It's, "here's a problem.  Go."  We do students no favors by shielding them from what's coming down the road.  Life isn't simple.  It doesn't come in bullet points or with View an Example. 

This isn't to say that online homework systems are bad.  They aren't.  Actually, they're a key cog in the machinery of this new course.  I need time to problem solve with my students, not do 10 iterations of a skill.  But the skills have to be learned.  Online systems like MyMathLab make that possible. 

My concern is the overdependence on online systems and the conclusion drawn by many that they are the way out of developmental math.  There is no shortcut to learning.  A student can relearn a skill they didn't get in high school, but that does not equate to understanding, retention, connection, or application.  It means they can now do that skill, whereas they couldn't, period.  And I disagree with the notion that the human element equals lectures and is therefore bad.  My presence in the classroom does not mean I'm a lecturer.  I'm a teacher.  I create lessons, tasks, and problems for my students to solve and facilitate that in many ways.  Sometimes that's direct instruction.  Sometimes it's circling the room to give feedback and keep students progressing.  It's varied and complex and not duplicated by a computer. 

A friend of mine recently pointed out that advocates of computer-based lab models decry lecture only to put students in front of computers to watch lectures.  Yes, students can repeat and rewind the lecture as much as they want.  But there's even less engagement in terms of mathematics because the student can't converse with the instructor.  I believe engagement is more than two students talking in a math class or lab.  It's what they're talking about and what the goals are that matter.  In MLCS, I've seen students really debate and discuss mathematics.  My eyes have been opened to what this student is capable of.  And it's a quite a terrific sight to see.  I'd always believed they were capable of more than skill manipulation but I hadn't honestly seen it to know it could happen.  But it can.

The Common Core seeks to do the same as we in higher education want to do:  raise the bar but make it appropriate as well.  However, training, materials, and support are not yet where they need to be for true change to occur.  Placing a new cover on a textbook and saying it addresses the Common Core doesn't make it so.  To accomplish the new goals of change and growth, we have to throw out some of the structures and mindsets of old and start fresh.  It's hard for everyone at first.  But the outcomes are worth it.  Now my students don't want a different kind of math class whereas when we began in January, they couldn't imagine how this class would work.  They've been pushed and they've risen to those challenges. 

It certainly makes me want to explore what more can be done with the instructional and materials design we've developed in terms of other courses.  I've told my colleagues that MLCS has ruined me on traditional courses.  I've seen more so now I want more in all my classes. 

I guess it's a good thing to have goals.  Keeps one on her toes.

The Ostrich Syndrome: An End to Developmental Education

Connecticut is proposing legislation to end remediation education as it currently is: a separate entity.  Instead, the idea is to place developmental students into college level classes and provide support there.

I refer to approaches like this as the ostrich syndrome.  Basically, ignore it and it will go away.  My hypothesis is that this approach will not be successful and could actually create new issues that are more serious than the current ones.  Having taught developmental and college level math for years, my concerns come from both sides of the fence.

First, this idea is against all the research done in the past 30 years on mandatory testing and placement.  Years ago, most colleges allowed to students to take whatever courses they liked, regardless of a placement test score.  And the outcome?  Students failed.  Research and practice has shown consistently students will not be successful in courses above their placement.

This is not to say the placement measurements are perfect.  They're not by a long shot.  Could some students who place into intermediate algebra try a liberal arts math class and be successful? Absolutely.  And that's why so many of us are working are new pathways to college level courses.  We want to shorten the path but we want to do so appropriately.

There are many remediation programs that can help students brush up and improve placement, potentially out of developmental math.  And data shows those students who place up can often pass those classes.  But this isn't all of the students we teach in developmental math.

The issue are those huge numbers of students who place into beginning algebra and below, and those numbers are significant.  Those students lack so much more than a few algebra skills.  They often have cognitive issues, learning disabilities, and socioeconomic issues.  They are not ready for math specifically and college in general.  So the legislature suggests placing them up but just providing additional support there.

Can that work for some?  Yes, but it's that same body of students I wrote about earlier who could probably brush up and place up.  They aren't that far from college level and the leaps to be made are fewer.  That's why some initiatives include embedding students into college level and giving them help.  I won't be surprised that those ideas can work for some.  But for the majority who place low?  I'm not so optimistic.

The premise behind the proposal of embedding all remedial level students in college level courses is that anyone can learn anything given enough time and support.  Those who teach math and science know that is almost always not true.  I know that I could spend the next 5 years working on astrophysics and it's not necessarily going to make sense for me.  And one semester with intense help in addition to all my other obligations?  Even less likely to happen.  And for some students who are at the level of "what is 3 times 3?", the idea of college statistics or college algebra is like astrophysics to them.  It's intangible.  Pretending they really are college level and just need "some help" is unrealistic and I think, detrimental to this student.  They will feel more frustrated and lose more faith in their future in college. 

Yes, we absolutely need to get developmental education in better shape.  Less money, less time, and better outcomes are the goals.  There are many schools like mine that are getting their developmental programs into tremendous shape.  The pass rates are strong and the outcomes in college level course work is too.  Plus, we now have new accelerated options, like MLCS, that update the curriculum and tailor it to the non-STEM bound population that is not served by the traditional curriculum.

The problems with the current developmental math curriculum is that is fast-paced, tedious, skill-based, a repeat of high school, not engaging to most students, and outdated.  Plus, the student is not getting the "college knowledge" skills they also need to be successful.  Learning how to add rational expressions does not give students what they need in statistics or general education math.  And it takes a really long time to learn how to add rational expressions well.  Is that worth it?

This is what I believe we need to make developmental math work:

1.  Provide course options for all levels and goals (fast, slow, self-paced, online, face-to-face, hybrid, STEM-bound, non-STEM bound). 

This is a huge population of students who don't all learn the same way or at the same speed.  They have differing goals.  Give them options that make sense for their needs.  Then they will learn and pass, therefore, getting out of the program faster while getting the skills and knowledge they need.  We have seen this work in practice at my college.  It's also a trend taking hold at other colleges throughout the country.  In essence, one size does not fit all.  Let's stop pretending it does.

2.  Provide alternatives around traditional placement.

There are some students who just need a brush-up and who will place up and out of developmental math.  Institute sound policies with flexibility.  Data supports that students can place out of developmental math and be successful. 

3.  Improve the courses we offer.

Content needs to be relevant, engaging, and yet still challenging.  It's hard enough to be in a class for which you're not getting college credit.  If it also seems to have no bearing on your life or major, your motivation to learn can drop quickly. 

Instruction needs balance between active parts and direct instruction.  This student is not the same student from 1970.  Our world has changed and students expect more activity.  Their lives revolve around electronic screens with constant activity.  Give them active learning opportunities and they will learn.

The development of content needs to move away from linear approaches that often leave students with a list of skills instead of mathematical understanding.  We need to spiral and connect topics, and bring in new ones that we don't currently cover.  Bring in statistics, talk about data, expose students to modeling.  Connect all of those topics to algebra, geometry, and numbers. 

Keep expectations high.  Put students into courses with college level expectations with some material they haven't seen before so that students are pushed and prepared.  Developmental math is more than plugging holes of missed knowledge.  It's about building a strong base from which to build upon in college level course work.  That base not need be high school all over again.  We need to move away from mimicking and repetition since jobs that require those skills are being eliminated by the day.  Instead, create courses that force students to think and work in new ways (projects, open-ended problems, modeling).  Flexibility, adaptability, agility, and critical thinking are skills that will serve them well in all their college courses, not just math. 

Support these courses by providing strong support structures.  Integrate student success in new ways and talk about traits needed to attain mathematical success.  Give the teacher time to remediate as needed individually during class.  Incorporate online systems for skill development and mastery beyond the time that is provided in class.  Give the student the help they need, but in a course designed to push them up to college level.

4.  Train faculty to work with the developmental student.

Provide workshops, mentoring, ongoing support and collaboration for the faculty teaching this population.  The student has unique needs, necessitating faculty prepared to deal with them.  They are not college level students yet.  We can get them there but it takes knowledge of their challenges to get there.

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I believe MLCS is a good first step in the direction of making significant change to developmental math in ways that embody the four points made above.  It's not the magic bullet, but a sign of progress and change.  We need more innovative options and practices, more pilots, more testing, and continual refinement.  I know from practice that this approach can get a program to a successful level and keep it there.

But throwing the baby out with the bath water doesn't solve the problem.  It simply creates new ones elsewhere.  Those who teach college level courses will be overwhelmed with students who are simply not ready to sit in those courses.  Those students tend to stop attending or make their frustrations loudly known during class, negatively affecting other students.  I've taught classes where the placement was wrong.  As a teacher, one of your options is to forge ahead and leave many behind.  Frustration, irritation, and complaints ensue from students who are not prepared.  The other option is to work with the student at their current level.  Before long, the teacher is not teaching the content of the course, but the course below it:  developmental math.  The complaints will also occur with this approach, but in this case from the student who signed up a college level course and is not getting one.  Ultimately, this approach can water down our college level courses so that they mean little.  They become the developmental courses students were getting before.

I wish developmental education was not necessary, but the fact remains that it is.  Ignoring it is like noticing giant cracks and crumbing rock in your house foundation and choosing to just build a bigger house on top of it so the cracks aren't seen.  Eventually, the cracks make themselves known, but the problem is even greater than originally.  That's not an outcome I want to see.

Upcoming MLCS Webinar

I'm giving a webinar for AMATYC on April 24 at 2 pm CST.  Here is the description and registration information.

Title: New Pathways for Developmental Math: A Look into Mathematical Literacy for College Students

Presenter: Kathleen Almy, Rock Valley College

Description: Mathematical Literacy for College Students (MLCS) is a new course that is part of an AMATYC initiative called New Life for Developmental Math as well as the Carnegie Quantway project. It is an innovative way to redesign the developmental curriculum, providing pathways for the non-STEM student. The course uses integrated, contextual lessons to develop conceptual understanding and technology to improve mastery of skills. In one semester, a student placing into beginning algebra will gain the mathematical maturity to be successful in statistics, liberal arts math, or intermediate algebra. Reading, writing, critical thinking, and problem solving are key components to reaching that goal. Webinar participants will learn much more about the course as well as receive ideas for course development including a sample course outline and a sample lesson.

Date: April 24, 2012

Time: 3pm EDT / 2pm CDT / 1pm MDT / 12pm PDT

Committee: Developmental Math Committee

Click here to register.

MLCS Presentation

Below is a recent presentation on MLCS given at ICTCM and IMACC.  It is related to but different from the workshops I've been giving since November. 

Are you interested in developing MLCS at your school?  If you have questions or would like to see a sample of a unit or would like a training workshop, please contact me. 

View more PowerPoint from kathleenalmy

MLCS Video Excerpt: Shortest Distance

This past week we taught a lesson that begins with a hands-on component.  The video excerpt will show some of the whole class parts of the lesson.  Here is a run-down of the lesson:

Lesson:  Shortest Distance
Objective:  Develop and apply the distance formula

This lesson appears late in unit two.  This unit focuses on understanding numbers and operations.  To that end, we work with many situations that allow us to explore how numbers behave and introduce algebraic ideas at the same time.  By the time we see this lesson, students have learned signed numbers and their operations, number properties, order of operations, exponent rules, Pythagorean Theorem, and slope. 

To begin the lesson, we measure the classroom and make a scale drawing of it using a scale of 1 unit on a grid = 1 foot in the room.  We then decide to place objects from the classroom on the drawing by establishing an origin and axis system based on that origin.  This process of setting an origin and determining locations based on it emulates a simplistic version of what surveyors do.

This leads to a good discussion on where in the room the origin should be and what would make it easiest to work with.  Eventually students settle on the back left corner of the classroom (from their perspective) since that makes the classroom the 1st quadrant.  This choice creates all positive ordered pairs.

Since the measuring tapes are only 25 feet, measuring becomes an interesting challenge.  Discussion quickly ensues on logistics and the role of accuracy.  We try to measure with the tape on the floor, but are careful to keep the tape taut if measuring off the ground.  Students then find ordered pairs for objects in the room they choose.  We pick up the lesson at this point being taught by Heather Foes:



NOTE:  This is not a professional quality video. 

The lesson continues, moving between whole group discussion and small groups with students practicing tasks and digging deeper into the ideas of the lesson.  I've described below what occurred but was not shown on the video.

After finding a few specific distances, we generalize the process using Pythagorean Theorem with generic ordered pairs.  Students need to really understand the order of operations to use the formula accurately.

Students practice using the formula.  As a class, we discuss how a graph can be used to avoid using the distance formula but there are limitations to that method as well.  Lastly, we connect this idea to slope.  Both slope and Pythagorean Theorem can be used on or off a grid.  We want students to see how the formulas look with a grid and without as well as the pros and cons of each method.  The goal is not just apply the distance formula to two random points.  Instead, the goal is to see how the formula can come about and why it is necessary.

A discussion always arises about what can be measured and what cannot.  We also discuss the pros and cons of physical measurement vs. math on paper.  Students usually surprise us by liking the idea of working on paper.  Measuring doesn't require much math, but it is challenging to do it accurately.  Also, it requires them to move and they don't always enjoy that element.

This lesson illustrates the depth of the lessons in the MLCS course.  The algebra or an algorithm are not the only goals of the lesson.  It's the process and discussion of getting there that elicits the most learning and improvement of students' conceptual understanding.  Students quickly see that real life problems are almost always much more complicated than traditional textbook problems.  But those same real life problems are also very rich and interesting.  They are worth the effort necessary to solve them.

MLCS Course Development and Training

Non-STEM courses like Quantway, Statway/Statpath, and MLCS are taking flight across the country and with that comes a lot of questions.  Because we've been working on a course and implementation for over a year, we've learned some things to help make it work.  Here are some tips for course development:

1.  Identify your goal.

We wanted appropriate preparation for the student heading to liberal arts math or statistics.  Sometimes the goal is acceleration.  While that wasn't our first goal per se, we are certainly happy for that to be a by-product of the course. 

Knowing your goals defines your next step.

2.  Determine the course content.

Look forward to where students will go and see what they need when they get there.  For us, that was statistics, liberal arts math, or intermediate algebra.  While we have many intermediate algebra topics in our course, they are covered in a conceptual, applied way that uses modeling.  So yes, we look at rational functions but no, we don't add rational expressions.  If a student will eventually take college algebra or precalculus, they'll need those algebraic manipulation skills.  We wanted them to be able to go into an intermediate algebra (IA) course without issue.  Our IA course has factoring in it, as most do.  So we were comfortable with exposing students to the concept of factoring in the MLCS course and doing one very useful type:  GCF.  Again, they can get the rest of the factoring techniques in an IA course.

Using IA as our bridge forced us to add in a few more objectives on polynomials.  It was funny; at first we didn't like that because it felt contrived.  It seemed like we were only adding them for a next course that many wouldn't take and therefore felt disconnected from the content.  But as we taught the course in the fall, there were times where polynomials came up and I needed to be able to say "degree" or "binomial" and students know what I mean.  They were necessary topics to our end goal.  That was great!  So we embedded them in the second unit of our course to ensure students have that basis for later material.  It also further prepares them for the bridge course.  In so doing, we solved two problems.

How much content you have affects the next step.

3.  Determine the number of credit hours.

It was very important to us that this course not be like all the other developmental math courses we teach:  rushed.  This learner needs time to discuss and think and learn.  We need that time too and we wanted it in the classroom with them.  Plus, our state has a lot of requirements to make this course something that can be articulated.  Add that up and we have 6 credit hours.  It's unlikely that schools outside of Illinois will need anywhere near that many.  The mode for this course as it's being developed around the country is 4 credits. 

Also consider if you want a lab hour embedded within the credit hours or in addition to them.  We use MyMathLab and have considered having an hour with students in a lab while they're working on skills.  We haven't needed to go to that yet but it's something to think about.  Doing this is kind of a hybrid of a self-paced emporium model and a pathways model.

4.  Write a course outline.

Now comes the fun part:  goals and objectives.  State succinctly but clearly the course description, goals, objectives, and content.  Here is our course outline that went to the college curriculum committee if you'd like to see an example.  You can download it as a Word document so that it's editable. 

5.  Choose materials.

In our course outline, you'll read that we have a MLCS course packet and MyMathLab.  The course packet is the book that we're writing for this course that isn't yet in print.  If you're interested in seeing a unit, please email me.  I can request a copy be sent to you from the publisher, Pearson.  It is available for testing this fall if you want to pilot MLCS and will be officially in print in summer 2013.

We started writing because we wanted materials to match the content and goals of this course.  Because this course is new, they did not exist.  You can piecemeal books together but it will be awkward for the teacher and student.  You can also write lessons, but that is a time-consuming undertaking.  Open source materials will be available eventually but that content doesn't cover all the objectives in our course or state.  Plus, we wanted MML.  It was an important requirement with any materials we used.  Lastly, we wanted materials that addressed every possible need for any instructor.  So we have written and designed many tools for instructors in the book.

6.  Plan the execution of the course.

This is the step where you think about how many sections you will offer, when they'll be offered, who will teach them, and how they'll be taught.  If possible, plan schedules so that teachers can get to each other's classes and observe occasionally.  Heather and I did this throughout the fall semester and it was invaluable.  It has improved the materials greatly and educated us on ways to make the class experience even better.  You see things in the back of the room that aren't obvious from the front.  So consider this step.

If this step isn't possible (or even if it is), plan how the instructors teaching the course can converse after lessons to debrief and improve them.  We meet after our classes and talk.  If you can't do that, set up a discussion board.  But this step is so important that it shouldn't be skipped over.  This is not an algebra course.  It's new for everyone.  Having the security of people to talk to helps everyone entering into the course for the first time.  And it helps the course get better and better over time.  This technique is like a Japanese lesson study.  Not identical, but it emulates their philosophy of teaching a lesson and refining it with other instructors over time. 

7.  Training

You may want training before you begin your pilot to understand better what a class feels like, how to make groups function well, what kinds of pitfalls there are to be aware of, etc.  I've been helping schools who are developing the course and will continue to do so.  Experiencing a lesson is so important so that you can see what the classroom will feel like and what you need to prepare for.  I can say without question that teaching in this way has made it very hard to go back to my 100% lecture, traditional courses.  Students are engaged and discussions are rich.  I truly enjoy what we do in the classroom in a way I never have.  And I've always loved teaching so that's saying something.  Yes, it's an adjustment but one that's made quickly for everyone. 

I'm also thinking about creating a training workshop that would allow several schools to come to one location so that I can work with them.  If this is of interest to you, please email me.  If there is sufficient interest, I can try to work out the logistics of making it happen.

My main goal with this post is to let you know you're not alone.  I've been working with schools on various redesign initiatives for years.  I will continue to do that with this course as well.  Having someone to ask questions of and bounce ideas with really helps everyone involved have more confidence in the process.