New Developmental Math Courses

A group of us within AMATYC have been working on new developmental math courses for the past 3 years — the New Life subcommittee of the Developmental Mathematics Committee.  Part of our efforts are meant to help more people understand a different view of what developmental mathematics can be … a model that frees us from the limitations of the old system, and provides better mathematics for our students.

You can find descriptive material about the courses over at the New Life wiki (dm-live.wikispaces.com) ; specifically, information on MLCS (Mathematical Literacy for College Students) at http://dm-live.wikispaces.com/Mathematical+Literacy+for+College+Students, and information on Transitions (the second course) at http://dm-live.wikispaces.com/TransitionsCourse.  We also have presentations on this blog site about the courses (see https://www.devmathrevival.net/?page_id=116).

Currently, we are busy getting ready for a workshop about these courses to be held at this year’s AMATYC Conference in Jacksonville, Florida.  The workshop will share more detailed information about the learning outcomes in MLCS and Transitions.  During this 2-hour session, we will look at the content so that faculty can become more comfortable with these new courses.

The AMATYC workshop is scheduled for Friday (November 9) from 1:45 to 3:45 pm in the Grand 3 ballroom.

A separate session on the New Life model in general will be held on Thursday (November 8) from 9:00 to 9:50am in the River Terrace 1 room.  If you would like to really get to know the model from New Life you might consider attending both sessions.

For information on the conference, see http://www.amatyc.org/Events/conferences/2012Jacksonville/index.html.  Registration has not begun yet … that will start within a few weeks.

 Join Dev Math Revival on Facebook:

Mastery Learning in Developmental Mathematics

I have never met somebody who used Mastery Learning in their classroom, nor have I heard of anybody using this method.  Like all absolute statements, this statement has a ‘if … then’ clause within it.  More properly stated, I would say that “Nobody understands what mastery learning is”.

Mastery Learning is not about a minimum performance level on one assignment; that is unrelated to the theory and conception.  Mastery learning is about the entire learning environment, and is based on two goals and a belief.  The goals are to create a learning environment with flexible and adaptive learning resources so that essentially all students (>95%) are able to learn at a high level (‘masters’), and to reduce the learning variation observed among groups of students.    The belief is that almost all (>95%) of students are capable of learning at the master level if provided the appropriate learning resources and instruction.  For some information on Mastery Learning, see http://www.nathanstrenge.com/page5/files/formative-classroom-assessment-0026-bloom.pdf — it is a good summary.  In the original model, ‘enrichment’ was part of the design for students who achieved the master level quickly — they would have time to explore and investigate, create and design.
Mastery Learning is hard work for the faculty and administration involved.  No excuses … if a student does not understand, you find another way to learn and reinforce.  Mastery Learning is likely to be ‘more expensive’ than other models for that reason.  Of course, ‘more expensive’ depends on your point of view — are we talking about the cost per enrolled student, or are we talking about the cost per passing student?

People often confuse Competency Standards with Mastery Learning.  With online homework systems, people set ‘mastery’ levels — but this has nothing to do with Mastery Learning.  If the instructional system is limited to software and tutoring, this can not be Mastery Learning.  Mastery Learning involves the entire learning process, not just ‘homework’.

What would a course look like in a Mastery Learning model?  Here is a brief sketch, based on a program at my College (long since evolved and eventually closed).

• Students begin with a standard assignment
• Students take an assessment (skills, applications, concepts — including novel situations)
• Those who perform at a master level proceed to the next unit (we were not able to design ‘enrichment’ in to the course).
• Students who performed below master level had a diagnostic interview with an instructor.  Options included:
  1. Media (video and/or audio) help
  2. Tutoring
  3. Computer tools (either custom written programs, or packaged, or both)
  4. Hands-on activities
  5. Small groups
• Students initially below master level then took the assessment again.  If not at master level, prior step repeated (with longer diagnostic interview)
• All units completed at master level
• Cumulative final exam, also done in the same master manner.

People using the ‘mastery’ label are generally only referring to the first step (assignments); however, this is not even an assessment — and Mastery Learning is all about assessments (formative and summative).  In Mastery Learning, we aim for the goal of 95% of the students achieving a master level on the assessments; how students do on the original assignments is not usually considered.

The other comment to make about Mastery Learning is that the model is not just about skills and procedures, even though most uses of ‘mastery’ refer to only that.  Mastery Learning is an approach for any content.  The financial resources make both Mastery Learning and ‘more than skills’ a challenge — they both cost more.  Does your college have the commitment to the goals of Mastery Learning?

In my view, the main disadvantage of Mastery Learning is that it tends to deal mostly with individual situations, not social; group learning processes tend to be very difficult.  I like to create a sense of community in my classes, and that would be very difficult in a Mastery Learning model.  Of course, that is also true of the ‘lesser cousins’ that we see much of today — online homework, modules, emporium, etc; these are all ‘lesser cousins’ of Mastery Learning, as they share disadvantages without any of the benefits.

The best thing about Mastery Learning is the demand it places on us — we seek to have 95% of all students become masters; ethnicity would not be a correlation with success, nor would economic status.  In Mastery Learning, all predictors of success are eliminated because all students (at least 95%) succeed at the master level.  As you know from your test analysis work, the highest discrimination is possible when the difficulty is 40% to 60% — which is exactly where our courses are today.  If we could do Mastery Learning in developmental mathematics, that outcome would be worth the disadvantages and costs.  We tend to reinforce inequities, not overcome them … Mastery Learning can be a part of a solution.

Most of us will not have the institutional commitment to make Mastery Learning work for the 95% of our students.  Look at the emerging models for developmental mathematics (New Life, Pathways, Mathways) for other ways to get our course difficulty out of the high discrimination zone (pass rates).  In those models, pass rates in the 70% to 80% range are possible … and that would be a big step to eliminate the high discrimination we currently see.

Whatever your model, never take the Mastery Learning label lightly.  It’s way more than a setting on a homework system.

 Join Dev Math Revival on Facebook:

What is Our Plan?

In the classic problem solving methodology, the intense effort is placed in two early stages — understand the problem, and make a plan.  In the case of mathematics (especially developmental mathematics), we have seen much hand-wringing and gnashing of teeth, often accompanied by saber-rattling, about ‘the problem’.  However, a problem can only be defined by comparing the current condition to the desired condition.  Looking at data is a first step, but can often lead to short-sighted efforts that do not solve any significant parts of the problem.

Here is one overview of a plan for mathematics in community colleges (focusing on developmental mathematics, though not restricted to that):

• All math courses must provide good mathematics (appropriate and powerful concepts to deal with quantitative situations).
• All math courses must prepare students for mathematical needs that they will encounter in college.
• Community college mathematics is not a repeat of school mathematics.
• Community college mathematics is compatible with, and supportive of, university mathematics.
• Reasoning and problem solving are central goals of mathematics as part of a general education.
• Remediation is needed for some students, ideally limited to one course or a fast-track experience for most of those students.
• Any student might be inspired to higher goals, and many are capable of additional mathematics in a reasonable amount of time.

If a “solution”, whether modules or online homework or emporium model, only deals with the patterns of the data, then the solution will not solve anything important.  In some cases, the ‘pass rates’ might rise temporarily or even long-term; however, there is still likely to exist a substantial gap between a larger plan for mathematics and what is actually delivered to students.  If the traditional mathematics does not contribute to a larger plan (which is my view), then a solution plan involves much more than the delivery system and much more than course organization.

In the case of developmental mathematics, we have a historical artifact which is based on a premise that we need to provide the same mathematics that students should have learned in high school.  Such an approach is arbitrary, unrelated to mathematical needs, and dooms our courses … and dooms our students … at the system level.  Having a sequence of 4 courses in developmental mathematics guarantees that less than 20% of the students will reach college work, based on an unreasonably high 80% pass rate and 80% retention rate.  The response, based on ‘the data’, is to get students to their exit point in this ‘school mathematics’ as quickly as possible (modules); is our plan for mathematics that students should be shoved off the train as soon as possible … or do we want to have an opportunity to inspire students?

The emerging models — AMATYC New Life, Carnegie Pathways, and Dana Center Mathways — are based on a larger plan.  However, many of us are looking at them as responses to ‘the data’.  For these models to work well, the faculty and colleges involved need to have a deeper understanding of a plan for mathematics.   Hopefully, you will see much in the plan outlined above that you can agree with.  One of our basic problems is that policy makers do not have this larger plan for mathematics in mind; they, naturally, focus on the data.  We, and our professional organizations, need to articulate a larger plan so that we can better serve our students.

One of my colleagues said, back in 2008, that pass rates are the least of our problems in mathematics.  I agree.  We need to have a plan for mathematics, and build new curricula to support that plan.

 Join Dev Math Revival on Facebook:

MLCS, Quantway – History and Comparison

In this post, I would like to clarify how Quantway™ and MLCS (Mathematical Literacy for College Students) compare.  Part of this will involve a brief history of these courses; the rest will be a focus on the practical differences — keeping in mind the considerable overlap that exists.

The starting point for this work was fall of 2006, when AMATYC released the standards “Beyond Crossroads” (http://beyondcrossroads.amatyc.org/).  At the heart of the discussions on appropriate content, the standards emphasized quantitative literacy in all math courses.  The release of the standards occurred during the AMATYC conference that year; at that conference, members of the Developmental Mathematics Committee had a brief discussion about models for developmental mathematics … essentially saying that it would be nice to have an actual model to guide our work, instead of a curriculum constrained by history.  Over the following two years, conversations took place about the problems in developmental mathematics and creating a plan.

By 2008, these conversations within AMATYC led to the start of the New Life Project by the Developmental Mathematics Committee (DMC); we formed some work teams which developed a collection of learning outcomes that followed from professional work outside of AMATYC (Numeracy Network, MAA, etc) as well as within AMATYC (Beyond Crossroads).    To help our work, we created an online community in early 2009 — the wiki at http://dm-live.wikispaces.com, and invited professionals to join the community. 

During this same period, foundations were becoming more interested in the needs within developmental mathematics.  The resulting opportunity for collaboration (especially with the Gates Foundation) led to a Seattle meeting in July of 2009; these people (sometimes called the Seattle 15) created the first draft of a curricular model — the first model created for developmental mathematics, designed for broad implementation.  This model identified two courses; the first course was originally called ‘the blue box’ (because that was the marker color used that day), and the second course was called ‘transitions’ (because we thought ‘the green box’ might not work too well).  As the model was developed, it became clear that we needed to deal with other factors — especially professional development.

This timeframe coincided with the Carnegie Foundation for the Advancement of Teaching starting their pathways work.  Members of the New Life Project were included in all of the original planning for the pathways work, and the initial learning outcomes were those of the ‘blue box’ course.    As Carnegie worked with their curriculum partner (Dana Center, University of Texas – Austin), these learning outcomes were vetted by professional organizations  and kept synchronized with the New Life work.   (Most of these same learning outcomes exist in the Statway courses.)  The Pathways work included a deliberate system for professional development, called the Networked Improvement Community (NIC).  Although the NIC was developed without direct input from New Life members, the design of the NIC dealt with the same professional issues that New Life identified.

Originally, the Pathways course was called “Mathway” and the New Life course with the same content was called “Foundations of Mathematical Literacy”.  Each of these names had problems.  By the end of 2010, the current names were identified — Quantway and Mathematical Literacy for College Students (MLCS).    That year (2010) was the first year that faculty at particular colleges became interested in beginning the process to implement the new course; most of the early interest was in MLCS, because the online community could communicate at that time … the Carnegie work with colleges came a little later.  Several colleges that were among the first to be interested in MLCS decided to become part of the Quantway network.

When Quantway colleges developed their courses, they sometimes named their course “MLCS” — the content of Quantway and the New Life MLCS are essentially the same.  Indeed, there are high levels of agreement between Quantway and MLCS in content and professional areas.  Some colleges outside of the Quantway NIC say that they are implementing Quantway — this is not true; implementing Quantway means that your college has been accepted formally into the NIC.  Outside of “the NIC”, colleges are implementing the New Life MLCS.

That is the major difference between MLCS and Quantway: Quantway involves a formal network (NIC), with commonality of implementation; MLCS (New Life) involves a local implementation of a model course adapted to local needs, with an informal network.  The New Life project operates as a subcommittee of the DMC, and we continue to develop resources to support faculty.

A related difference lies in the materials.  Quantway colleges all use the same materials (currently Quantway version 2.0), which includes an online system and common assessment items.  MLCS (New Life) faculty use either commercial texts or locally written materials; in some cases, the locally written materials will be developed by publishers into commercial texts.  The Quantway materials are currently about a year ahead of MLCS materials — MLCS materials are at the pilot or class test phase (1.0) while Quantway is at version 2.0. 

The second major difference lies in the curricular purpose for the course.  Quantway is intended to be the prerequisite to a quantitative reasoning course (aka quantitative literacy); this is how the name was chosen — and Quantway 2 (the second course) is currently being developed by Carnegie.  The New Life MLCS course can also be used for this purpose; however, the MLCS course is seen as playing a larger curricular role — MLCS can be the prerequisite to an introductory statistics course, other quantitative reasoning courses, and the Transitions course.  If colleges implement both MLCS and Transitions, they can completely replace their developmental algebra courses.  In other words, Quantway is designed to serve very specific groups of students; New Life MLCS is designed to be the basis for fundamental change.

The other difference lies in the practical issues of implementation — Quantway colleges must use the implementation process of the NIC, while MLCS faculty can do their own or use the resources of the New Life project.  The New Life project focuses on helping faculty and departments meet local needs with flexibility; the Quantway process emphasizes the NIC with limited options for local adaptations.  Again, both models incorporate needs outside of the content; professional development is critical in both.

All other differences are matters of aesthetics and minor details.  If you remember that Quantway and MLCS share a common source, and that the differences lie in networks and implementation, you will have a fairly accurate view.  The two labels are not equivalent, because the Quantway label includes the NIC and commonality of implementation; New Life MLCS includes the long-term reform of the curriculum (combined with Transitions).

I invite you into this process of bringing new life to the developmental mathematics programs that serve the needs of our students.  We can escape the ‘black box’ of history, and enjoy a ‘blue box’ and a ‘green box’ — MLCS and Transitions.  Your department can begin this work.  Your college might choose to apply to become part of Quantway.  Take that first step on the road to better mathematics for your students.

 Join Dev Math Revival on Facebook: