Tuesday, August 14, 2012

The Emporium Model: Not a Magic Bullet for Developmental Math

I've written and spoken about the emporium model many times.  It's not that I'm against the idea of using computers to offer self-paced instruction.  That model can be excellent for students who are just shy of placing into college level, have few skill gaps, and are motivated.  What I don't support is the across-the-board use of it to replace developmental math programs, from arithmetic through intermediate algebra.

My concerns are many when it comes to this use of the model.  For one, I do not believe learning is mimicking what is seen on a computer screen. It's a far more complicated process that involves humans because the brain is complex. And learning math is not just moving letters and numbers on a page or screen; it is also complex.  Two students figuring out an exercise or an instructor talking a student through steps is not the human interaction I'm speaking of.  Of course, those types are necessary.  But beyond that, there are deeper aspects that only a qualified instructor can offer, insights needed to truly build understanding in a greater way. 

I have a colleague who will joke that no doctor would ever say, "I don't need to understand how to do the liver surgery.  Just point me in the right direction and I'll cut."  That's absurd.  But the type of "learning" we offer through emporium models, particularly in developmental math, is little more than procedures and "how's" with very little "why" along the way.  We break math down into tiny bits so that students can learn them, but we never connect the dots and put the puzzle back together so that students can see the bigger picture.  They get a set of disconnected skills that have no meaning between them, something that is necessary to use the skills in later courses.

It begs the question:  what is our goal here?  As a country we are in a huge rush to get students through developmental math, even to the detriment of the student. We want great statistics, not great learning.  As an educator, good pass rates are important to me because they are a measure of our programs.  But I'm more interested that my students learned something, that they were pushed and came out on the other side better for the experience.  That they did more than endure a series of tests and checked off a set of skills they can do.  Math is a amazing subject, but you have to step back away from the trees to see that beautiful forest.  And it takes a well-versed guide to make sense of what you're seeing.

I'm not saying technology shouldn't be used or that lecture is the number one way to offer instruction. Quite the opposite actually. I believe we need balance and emporium models are too extreme, offering an unbalanced method of math education.  Like the Khan academy, I think they have a place and offer something additional to developmental math programs for particular populations of students.  But as a replacement across the board for all sections and students?  I don't think that respects the great variety of needs or learning styles for students nor the variety of teaching styles and strengths of instructors.  For a redesign to work, respect must be present or faculty will resist.  Or they will succumb temporarily only to reject the model when administration changes.

What got me thinking about this topic was an opinion piece in the Chronicle, Don't Confuse Technology with College Teaching.  One part in particular caught my eye:

A set of podcasts is the 21st-century equivalent of a textbook, not the 21st-century equivalent of a teacher. Every age has its autodidacts, gifted people able to teach themselves with only their books. Woe unto us if we require all citizens to manifest that ability.

Most people find math intimidating.  And most returning adult students find technology intimidating.  So a course on a subject that they struggle with that is solely using technology for instruction and help is a person answering their questions only, is not usually a welcoming prospect.  Students want and deserve more.

Students usually do not move faster through the content either, a often used selling feature of the emporium model.  More often than not, they will move slower.  So policies and deadlines become very important.  The most success our emporium ever had years ago was when it is was so rigid that self-paced could not even be used in the description.  And "success" was a pass rate on paper.  Ask the students and they disliked the model for two reasons:  the experience in the course was not what they wanted and they feared that hadn't really learned anything, causing them to be at a disadvantage in the next course.  After years of trying to make this model work, we dropped it, taking the elements we liked from it and working them into a new, hybrid model of instruction.  That model is just an option in our program, not an approach that every student experiences unless they want to.

My other big concern are the unspoken reasons for choosing the model.  Administrators are often picking this model and imposing it for the sole reason of cutting costs. While a successful developmental math program can save the college costs down the road, that is not usually where the cost-savings come from. Administrators quickly do the math and realize that when the computer is offering the instruction and grading the assignments, there's really no need to cap class sizes at 24 or 30. Some colleges assign several hundred students to an instructor for a section and use tutors or teaching assistants to staff them. The need for qualified, full-time instructors drops quickly. This is the unsaid way of saving money.

From the Chronicle article:

Can technology make education less expensive? College is expensive, but colleges do things other than educate. Many courses simply convey information and provide technical vocational skills. These could be automated, presumably at savings. The price tag includes the campus experience—an education of a different sort—with all its lovely, cherished amenities.

But the core task of training minds is labor-intensive; it requires the time and effort of smart, highly trained individuals. We will not make it significantly less time-consuming without sacrificing quality. And so, I am afraid, we will not make that core task significantly less expensive without cheapening it.

Food for thought.

Implementing MLCS: MyMathLab

MyMathLab is a wonderful online homework tool that provides an excellent way to practice skills to the point of mastery.  It also allows students to see extra examples and work problems multiple times.  But with all technology, it isn't perfect.  Not every problem in math should be algorithmically regenerated.  Problems should remain problems:  difficult and thought provoking.  To me, MyMathLab excels at exercises.

To that end, we use MyMathLab when it is superior and we use paper when it is more appropriate.  Here are some ideas for use of MyMathLab:

1.  Practice skills in MyMathLab.

As part of the book I am writing with Heather, we will have a MyMathLab course with assignments for all skills addressed.  We have a working MML course that can be used when class testing.  But the final course will have many more problems and bells and whistles.

2.  Build self-checks for students.

One of the downsides to MML is the ease of misusing the help aids.  Students like to mimic View an Example, which is not learning.  This course is about understanding, not mimicking.  To help students better assess where they are learning and where they have deficits, we have quizzes regularly on skills without help aids.  These quizzes are done in MML.

Additionally, we have a few questions on every homework assignment in the book with a MML assignment.  These questions are on paper, mirror the MML problems, and do not have help aids.  So students get a feel of what it would be like to be tested on skill problems without using a computer.

3.  Use paper when it is more appropriate.

To push students to connect ideas and apply concepts, we have paper homework with problems.  There are fewer problems and students are expected to do all of them.  Again, they are not exercises.  The odd numbered problems aren't like the even numbered problems with numbers changed.  Each problem is unique and requires students to push past skill-based understanding.  They don't have the typical "word problem" feel because they are like problems students have already been working with in the lesson, and they are realistic.  That doesn't make them easy, but it does remove the "story problem" feel, which causes instant anxiety in many students.  My students find the paper homework is harder, but necessary.  And thus, it's not their favorite.  They prefer MML problems because they are rote and prescriptive.  But since the goal of the course is to think and solve problems, we push students past the skill problems alone.  And unlike traditional algebra classes where skill problems encompass 80-95% of the course, skill problems only take up 50% of the course.

This approach marries technology and traditional methods for doing homework in a math class; it's a happy medium between paper only and MML only.  Similarly, we assess in a similar pattern:  skill quizzes are done in MML and conceptual/applied problem quizzes are done on paper in class.  Because we do not have the facilities for testing online, our exams are done on paper and have both skill and applied problems.

Next up:  Training

Tuesday, August 7, 2012

Implementing MLCS: Student Success

The goal of MLCS is to get a student college ready in one semester for a few non-STEM college level math courses.  To that end, students need much more than the generic student success activities that many courses offer.  MLCS is built with this in mind, that the audience is an adult learner who is not quite ready for college level work.  Components such as readings, writing, long term projects, applications, and more prepare a student for the type of work they will see in a college level class.  College level classes, even ones that are skill based, have high expectations and usually a high rate of speed for covering material. 

Here are some ways the course is structured to address student success (from a previous blog post):

The approach of the course begins with real, relevant content and covers topics differently than they are in a traditional text. That automatically increases motivation, an important component of student success. Students have commented repeatedly that the course is interesting; they like what is taught as well as how it is taught. For example, direct instruction and group work are balanced with each lesson beginning and ending with group work. This improves attention, understanding, and engagement. Students are shown respect for their prior knowledge by allowing them to tackle real mathematical problems instead of working from a premise that all the content is new. Many of the specific skills of the course are not new to these students because in reality, most of them have had several years of algebra prior to the course. What they lack is understanding, retention, and application. To improve that, considerable time is spent on solving thought-provoking problems and seeing traditional topics from a unique perspective. All problems are taught through a context and do not start with abstract ideas. Instead, the development moves from concrete to abstract, which builds student confidence and understanding. Further, students are treated like adults, most of whom work and have many varied experiences. They learn how math is used in the workplace and see those ideas in practice in class. For example, they learn how Excel is used. They also learn how the concepts taught can be used to solve problems they will likely face in and out of college.

Next, specific student success activities are included in every unit. Each student success lesson is different but all have mathematical ideas in them. So beyond the traditional ideas of time management and test anxiety, issues that these students will face are covered. For example, students learn how college math is different than high school math. This is done in the context of determining what components are necessary to be successful in a college math class. To visualize the various components, students hone their skills with graphs and percentages. They study job statistics to compare STEM and non-STEM fields in terms of their earning potential and unemployment rates. This approach brings in some statistics concepts. The topic of grades is addressed often and deeply. Components include how grades can be figured (points vs. weights), how GPA is figured and how it can be increased, and why it is difficult to pick up points at the end of the semester as opposed to the beginning of the semester. Students learn about means, weighted means, what can and cannot be averaged, and how algebra can help solve problems that arise in this context. Additionally, the first week has many activities to help students begin the semester on the right foot in terms of prerequisite skills, working in groups, and understanding course expectations.

Another component of the course is helping students learn how to study. Students think they should just “study more” but do not understand what that means in practice. To remedy this problem, students are given very specific and explicit strategies that they can act upon. Students receive a detailed list with actions they can do before class, during class, between classes, before tests, during tests and after tests. Also, students tend to really like online homework but they can get dependent on help aids and sometimes can’t write out their work. So every online assignment has an accompanying brief paper set of problems similar to the online ones, but they must write them out and have no online help aids. With skill homework, they have conceptual homework on paper that is about quality over quantity. That is, they have fewer problems that take more time so as to work deeply with the concepts at hand. The test review has a detailed plan to teach students how to study for math tests, beyond just working problems. Additionally, students are held accountable for all the work assigned so that they learn good study habits and personal responsibility.

Lastly, metacognition is emphasized regularly. The developmental student often doesn’t fully understand how they think or learn. Most problems are taught using 3-4 approaches to work at verbal, conceptual, graphical, and algebraic understanding. For example, when students solve equations, they do so first with tables, then with algebra, and last with graphs. Once they have learned all those techniques, they are asked to think about which makes most sense for them and keep that in mind going forward. This approach of solving problems in multiple ways is used often in the course to broaden their mathematical skills, but also give them a deeper understanding of the topics. This method has an additional benefit for students on test day. They have several tools in their tool belt to use if one technique is not making sense or their anxiety is affecting their memory.

Together, these techniques support the developmental student in being successful in this course and future math courses.

Next up:  MyMathLab

Monday, August 6, 2012

Implementing MLCS: Grading

The issue of grading in MLCS is in some ways the same as every class and yet also very different.  Like any other class, we need to assess learning and hold students accountable for the work of the course.  But the work is not like an algebra class, due to its diverse nature.  It's not a linear, skill-based course; it spirals and deepens over time.  So assessing it poses challenges.  Here are some ideas we've found to be successful in this course:

1.  Attendance is everything.

MLCS hinges on students interacting while working on rich problems and having lively discussions.  That cannot be replicated by watching a video or getting a friend's notes.  Those measures can help on rare occasions but they are not sufficient on a regular basis.  We have seen attendance and work ethic as two of the strongest indicators of success in the course.  Students have to be in class and do the work there as well as go home and do more work there.

To ensure good attendance, we have an incredibly strict attendance policy:  after the 3rd absence (for a course meeting 3x a week), the student receives an F.  There are no exceptions for pregnancies, military service, or long term illness.  That sounds very cruel.  In the past, we did make some exceptions and those students did not pass because they were not in class.  So the student who has to leave for military service for an extended period of time, while possibly very conscientious and dedicated, cannot overcome the structure of the course and be successful.  So we eliminate the possibly of a student thinking they'll be the exception and have a strict policy.  The reality is that students who miss 4, 5, 6 or more times don't pass.  Might as well have a policy that addresses that upfront.

This is the same approach many lab-based science classes like chemistry and biology take.  Labs cannot be made up; you are present or you get a zero.  Some things cannot be replicated at a student's convenience.

We've debated about having points for attendance, but instead opted for the real world approach that employers take.  There is no reward in real-life for showing up; it's an expected part of the job.  But there are absolutely consequences for failing to show up.

What does it mean to attend?  Students must be present from the beginning to the end of the period, awake, and participating.  Texting, coming in late or leaving early, or just generally doing nothing does not count as present.  Students do not like this but again, it's really no different than what an employer expects.

2.  Points for tests are a substantial part of the grade.

It is very important to us that we have some very typical components to the course so that students can transition into a more traditional course without issue.  One of those components is a test each unit.  The tests count for 60-70% of the course grade.  We also give a comprehensive final exam that counts twice as much as a unit test.

Our tests mirror the emphasis of the course:  skills and applications are in equal proportion.  Skill questions (worth 50% of the test grade) give students a way to show their skill knowledge in a theoretical format.  Applications questions (worth 50% of the test grade) show if students can apply those skills in context.  All test questions have a similar feel as homework and quiz problems but are not necessarily identical.  The course isn't about memorizing a "type" of problem and mimicking a solution.  It's intended to grow students into problem solvers who are prepared for college level expectations.  Thus, we do not give practice tests that look like the real test with numbers changed.  Instead, we lay out a 5-step process for studying in the book so that students really understand what it means to "study" math.  In that 5-step plan are many helpful problems that look like test questions, giving students a good preparation without reducing standards.

3.  Hold students accountable with homework and quizzes.

Students need to practice regularly so we use MyMathLab for homework and quizzes for skills in the course.  Students have MML assignments often, with several due dates each week.  All assignments earn points.

The other type of homework in the course is paper, conceptual homework.  These problems (not exercises) are more involved and require connecting skills and concepts.  They are challenging and because of that, there are not 50 of them in a lesson.  There are fewer and students are expected to do them all.

The problem with paper homework is holding students accountable.  I'm not willing to collect homework and grade it.  If we create worksheets with a sampling of homework problems, students just copy from one another.  We tried that approach of collecting worksheets regularly, hoping students would appreciate the time out of class to work on problems.  They just cheated.  We also tried short quizzes to start each class over one problem from paper homework.  These quizzes took too much time and didn't encourage students to work enough. 

So this fall we will have regular quizzes, around once per week, on paper based on paper homework.  They will be announced ahead of time so that students can make sure all paper homework is done and understood.  Students can't use their notes.  If they've really done the paperwork and worked with problems until they understand them, the quiz will be easy.  If they are only doing MML work, the quiz will be very hard.  But students need that wake up call when the consequences (in terms of points) are lower so that the same mistake is not made on the test.  That would be a much more costly error.

We will budget enough time to allow for the quizzes in class.  We've used this approach in other classes with success.  Some students will still not do the paper homework, but this measure is as good as any as encouraging that type of work while keeping the instructor's workload manageable and maintaining integrity in the grades.

4.  Encourage accountability on projects.

We use a unit project that is done in groups each unit.  Students get a group grade, meaning there is one grade and all students in the group earn the same number of points.  There is one exception:  if a student has not pulled his or her weight, we reserve the right to reduce the points they would receive or to give them 0 points.

The problem is that there will always be students who allow others to do the work and benefit from it.  To combat this, we have a substantial number of points on each test with a problem related to the project.  It becomes very clear who did the work. 


We want students to work very hard and to reward the growth they make.  So in the spring we tried a very non-traditional grading scheme that was built on a gaming/mastery approach.  In some ways it succeeded, but students felt confused about their grades and we were not able to use MML to list their grades the way we wanted.  The negatives seemed to outweigh the positives.  Since the course is so non-traditional, we've learned that there must be some typical elements for students to not feel anxious.  One of those elements includes a grading scheme that is like their other classes.  All of the grading components listed above are worth a certain number of points; we've also used a weights structure, but students struggle with understanding their grade in that format too.

These ideas are not the only way to grade in the course; they're just approaches we've seen have a reasonable level of success.  If you pilot the course and find something that works well for you and/or your students, please share with us.

Next up: Student Success