Doomed to repeat history?

Those who do not remember the past are condemned to repeat it.

George Santayana

I have received questions about Quantway/Statway and the new MLCS course.  Some want to know, "how is this different than the integrated high school curricula of the 90s?"

Good question.

In the late 80s and early 90s, NCTM released a new set of standards encouraging a different way of teaching and learning mathematics K-12.  Following those standards were years of grant projects, pilots, materials, and eventually textbooks with a new approach:  an integrated approach.  The idea was not to do algebra 1, then geometry, then algebra 2 but instead combine content and integrate it.  A worthy concept but definitely not how we typically teach mathematics.  It has strong supporters and opponents, with good cause.  Because while a curriculum like this can work, it takes a tremendous amount to do so.  It requires good materials, a change in mindset, time to learn how teach in a new way, and abundant professional development.  For more on this subject, please read this article from NCTM's website.

Because these necessary elements do not always occur, integrated models are not always successful.  For a different take on this subject, please read this article about Georgia schools and their experiences with integrated courses.  It is very forthright in both the pros and cons of the approach including why they are dropping this instructional approach.

So what can we learn from this?

Integrated courses have a lot to offer students but execution is key.  This is a new approach to teaching and vastly different from the stack of skills approach most instructors are used to.  It forces us as teachers to integrate our teaching and move between multiple contexts and concepts in one lesson.  Truthfully, not all teachers are comfortable with that nor want to teach that way.  And in my opinion, that's ok. 

Just as students learn differently, instructors teach differently.  It is very difficult to find an approach that suits everyone.  So part of the issue with integrated curricula at high schools was that everyone had to do them.  And they're just not right for everyone.  One person's brain may move in several directions at once, circling constantly to connect ideas.  Another's brain work may work very linearly and sequentially, moving steadily from one idea to the next.  Since we think differently about things, it stands to reason that we should have the opportunity to teach and learn to our strengths. 

Adding to this issue is the concern of what people are using to teach from and how they are teaching it.  Good materials are a must.  But teachers have to know how to use them.  Training and support are just as important.

Integrating these issues (pun intended), here are some reasons courses like Quantway's MLCS can work:

1.  MLCS is one course and does not have to replace the traditional beginning or combined algebra courses.  It augments a program and offers an option for the non-STEM student or the school who wants to offer beginning algebra differently.  But beginning algebra can still live and exist for faculty and students who want it.  It's an option, not a mandate.  Thus, it's more likely to be taught by teachers who like an integrated approach and taken by students who want something different than a traditional algebra course.

2.  The initial scale is small.  Meaning, we're just developing the one course, MLCS, right now.  If it's successful and there is demand, I hope to work on its precursor, a course about numeracy using an integrated approach.  Also, New Life has sketched out a Transitions course to follow MLCS for the student bridging back to college algebra.  There has also been talk of a college level version of MLCS that would be different than the general education math courses that are surveys of areas of math.  Ultimately, all these courses would be options, not replacements, to courses that exist.  And they would be built using a model that would be proven to work.  This "start small and build" approach was not always used by high schools.  Many scrapped their traditional algebra 1-geometry-algebra 2 sequence and instituted Math 1-Math 2- Math 3 sequences.  That can work but if it doesn't, it's hard to change horses midstream.

3.  Materials and a training program are being developed with the goal of addressing issues that will always exist.  I'm a big believer in the idea that "how" is more imporant than "what."  We have components and whole courses in my department's developmental sequence that work extremely well but were flops at other schools.  Why?  Because the execution was different and we tried to learn from mistakes of others.  And I know others have used our mistakes and done better on something than we did.  We're all a part of a large assessment chain.  So, one flaw of the implementation of integrated high school curricula was professional development.  Knowing that, we're designing a training program that will support the materials and course development.  But beyond that, we're developing the materials with the known issues in mind.  One of those issues is that a wide range of instructors will likely teach the course, some who are not familiar with a new type of pedagogy. 

For example, notes to the intructor on teaching the ideas are interspersed throughout the lesson plan and materials.  Instructions on pacing, assessment, grouping, rubrics, and examples of each will be provided.  Additionally, the layout of a lesson attempts to address a common concern:  what's the point of this lesson?  Students will often like integrated lessons but get caught in the detail of the context and miss the forest for the trees.  So we close every lesson by asking students to step back and determine what was learned (mathematical and otherwise) and how it can be used again.  To wrap a unit, we are building specific active tasks that students will do to assess where they're at with all the skills, concepts, and techniques of the unit.  Again, we want students to see the bigger picture and connect what they have learned to date so that they don't get lost in the content.


This is all well and good but ultimately we need to know if it will work.  The Pollyanna in me says yes because I've been through the nonstop assessment process of redesign.  Redesign is not about saying, "we're doing X, now we're done."  It's about implementing something, scrapping what doesn't work, and working until a solution is found.  The pilots this fall around the country will tell us a lot.  Having piloted numerous new projects, I know how exciting and educational the pilot process can be. 

When we redesigned our traditional developmental curriculum, we did so on a large scale right out of the gate.  Meaning, all the pre, beginning, and intermediate algebra classes used the new modular approach with MyMathLab, standard policies and new pacing.  That approach was fine because the changes were largely administrative and structural; teachers could still teach how they liked.  When we redesigned our geometry course, it was just me and two sections of students.  That smaller approach to piloting helped when the content and pedagogy were so vastly different.  Each day, I made modifications and by the end of the semester, we had materials and a method that worked.  And it's continued to work for many more instructors and students.  Partly because of lessons learned during the pilot but also because of the training and instructor resources that were developed after the pilot.  That smaller system approach to piloting will be used as we implement the MLCS course as well.  I'm writing materials and instructor notes now that will be revised as they're piloted, but I'm also keeping notes and doing research for the training program to follow.  One can't work without the other.

So yes, we're in wait and see mode.  But I have a strong suspicion we will see something we like.

The Developmental Math Blogosphere

Jack Rotman was AMATYC's Developemental Math Committee chair prior to becoming a liaison to the Carnegie Pathways project.  He has a blog called Developmental Math Revival.  Check it out and you can see a guest blog article I wrote, Redesign:  Not an Either/Or Situation.

Read, write, learn (Part 2)

Continuing with the second part of this two part blog, my goal is answer this question:  How does MLCS embody the characteristics of a quality higher education set forth by Academically Adrift?

1.  We’re asking them to read and write often.

Being able to process information that comes in print form is a valuable skill.  Throughout the course, we are using articles from the news to motivate content and illustrate concepts.  One comment we have received numerous times when faculty see our choice of articles is “what if they can’t read them?”  Keep in mind we’re not choosing scholarly journal articles but instead articles that have the reading level of a mainstream blog or newspaper.  In other words, something entirely expected for an adult.  Yes, there will be students who struggle.  But instead of removing the demands and rigor that reading brings, we’ve chosen to address that concern and teach reading strategies.  Through research and talking with reading instructors, we’re gathering a set of techniques that we’ll embed into the course.  Students will have to try each technique once and then determine which works best for them.  Once they do, they’ll be asked to use it from that point forward. The key point is that students learn how to read better by reading.  Our goal is to help them do that in an approachable way.

Writing comes in the form of brief explanations on written assessments, forming more detailed explanations on open ended assessments, and journals.  Beyond the expected "show your work” instruction that is seen often on math tests, we want them to explain their reasoning and thought process.  It’s not about mimicking our method but instead defending and supporting whatever approach they use.

For both reading and writing, we’re developing ways to keep students accountable.  In other words, they have to read something or write something and then do a follow-up quiz or assignment to prove understanding.  Students don’t do optional so we’re forcing accountability.  They’ll thank us someday.

2.       MLCS is a rigorous course.

Rightfully, many faculty are skeptical of the MLCS course at the concept stage.  I’ve been asked directly, “aren’t you just dumbing down content and rushing them through developmental math?”  Unequivocally, no.  The goal of the course is to differentiate content based on student goals and needs.  The reality is that if you’re going to get an Associate of Arts, which requires statistics or general education math, you don’t need to be able to add rational expressions.  We can debate the merits of topics and never agree.  But we currently spend millions of dollars working to get students through courses that do little to grow their critical thinking skills or have any discernable payoff.  If they’re headed toward STEM paths, yes, the traditional content makes more sense.  But right now, it’s way too much of symbolic manipulation for the sake of it for many students.  Those same students need better reasoning skills that directly apply to mathematics and they’re not getting them.  So the main argument for the course is not to scrap algebra.  But instead teach algebra that makes sense and add some other topics that would benefit students as well.

When you bring in other topics like geometry, statistics, open-ended problems, and analysis of structures in addition to many traditional algebra topics, you get a very rigorous course.  Content can be very challenging and demanding independent of the level of algebra.  Look at statistics if you want a mathematical example.  We fully expect that students who love traditional algebra will balk at the course approach because it asks new things of them, something we often see with traditionally strong students in statistics classes.  Being good at symbolic manipulation does not imply strength with reasoning and problem solving.  Our goal is to have students who can exemplify both.  Again, this is not the Math Wars.  Skills matter but conceptual and applied reasoning do too.

3        The instructional design makes the student a participant, not a spectator.

The authors in Academically Adrift say that faculty need to be approachable to students and connect with them beyond the classroom.  They should also connect with students in other ways than lecture in the classroom.  One of the main premises of MLCS is to not just change what we teach but how we teach it.  Using context, theoretical examples, news articles, cartoons, and case studies, we’re going to teach students to work together and solve problems.  Not everything is truly “real world” but that’s ok. Some things are just food for thought but done differently than we usually do.  For example, instead of saying, “for all real numbers a and b, the commutative property of multiplication says that ab = ba,” we’ll ask “when does order matter and when doesn’t it?”  The commutative property will be defined and explained but so will a lot of other interesting ideas related to operational order. 

There will be direct instruction when we get to points in which the students need and want an explanation so they can move forward.  But we’re not starting with the theory.  We’re doing it when we need it, when it’s cumbersome to not have a method that’s more efficient or a word for what we’re doing.  Give students an interesting problem first and guide them productively through it, still allowing for that uneasiness that comes with confusion and learning, and let them ask what they want to know.  They’ll get to the points we want and at that point, teaching the theory makes sense.

The methods of effective collaborative work are ones that are endorsed by the National Science Foundation and employers everywhere.  If our students are not already employed, they likely will be at some point.  And in that job, they’re going to need to work with another person or persons effectively.

Teaching this way takes skill and is new to many, even seasoned, effective instructors.  It’s different to step aside and let students take the reins for a little while.  Mind you, we’re not saying let them teach the course or never have the instructor in the front of the room.  We’re saying hand over some time to productive problem solving during class that you’re not directly leading all the time.  How much time depends on the teacher and class. 

Because this is a new approach, we’re planning the pilot very intentionally and creating means to make changes and note what’s working or not.  I’ll be attending Heather’s class and she’ll be attending mine.  We’ll be videoing the class as well.  And throughout, we’re
keeping a master binder of the content with notes of how students responded, what needs changing, and what needs more of whatever (time, explanation, etc.).  Following the pilot will be the process of building detailed instructor resources.  Not just answers to problems and sample tests but samples of student work, videos of classes, rubrics for grading, and approaches to sequencing and teaching the content.  Some teachers need all of these, some need none, others are in the middle.  Whatever the needs, we want to satisfy them. Because ultimately, we want this course to have the potential to be taught by any faculty member, experienced or novice, adjunct or full time.

The hope is that we connect with students in and out of the classroom and that they connect with us and their peers.  The great opportunity of this course is that many students taking it will be at the very beginning of their college careers.  They’re not just unprepared for math; they’re unprepared for college.  We can take that opportunity to build skills related to math and college (called college knowledge) as well as support structures that will help them be successful in future classes.  In essence, if they can learn that their instructor and peers are part of the learning equation, they’re more likely to go to those resources when they start to struggle instead of flailing or leaving when the going gets tough.  In the book, the authors claim that students who experience a greater level of learning are more likely to persist when things are difficult.

We hope that these measures along with lessons learned from redesigning the traditional developmental math courses will combine to make a successful new experience for all of us.  And if not, like Edison, then we’ll have at least found at least one method that does not work.  And also like Edison, we’ll keep working until it does.

Read, write, learn (Part 1)

I’ve recently finished reading by Academically Adrift: Limited Learning on College Campuses by Richard Arum and Josipa Roksa. When it came out, it was controversial
because in essence the authors claim that American students are not learning all that much in college. Certainly there are cases where students are learning a great deal but they posit that many students are never really challenged and attain baccalaureate degrees regardless. Employers often echo those concerns as many new graduates lack critical thinking and communication skills. Beyond a specific skill set that accompanies any degree, students should learn how to think critically, read well, and write clearly.

So what are their recommendations?

1.  Ask students to read and write more.

2. Set and maintain high expectations.

3. Connect with students in and out of the classroom.

In essence, if we ask them to do more, they will spend more time reading, writing, and thinking and therefore, learn more. And when we’re with them, we need to do more than just talk. We need to listen and work with students. It's simple and makes sense but of course, simple does not mean easy.

Reading the book made me pause about my own classes. I’m under the same time pressures that all faculty live under which often force me to lecture to “cover” the material. But when I do, I wonder what they’re learning. Whenever we have time to dig into a topic and do an interesting activity or solve an interesting problem, the atmosphere is always different and better. They talk with each other and me.  They talk about math. In other words, they learn. Or at least, it appears that way. If nothing else, it's good for my self esteem.

This phenomenon is one of many reasons the new MLCS course is exciting to me.  It was planned with the idea, “how would we build a course in terms of content and pedagogy if we could?” It isn’t a redesign of a previous course but a new thing in and of itself. And because of that, it has all those things many faculty want or students need: time for collaborative work, reading assignments, writing assignments, and time for lecture. I don’t want to give up lecture nor do most faculty and for that matter, students. But we don’t need it all the time and students don’t either.

Part 2 of this blog will detail how MLCS is being built to invite learning.  And coincidentally, the approach addresses the recommendations given by the authors of Academically Adrift.

From the ground up

I recently read an article about an independent evaluation of Achieving the Dream five years after its inception.  Despite all the efforts made by ATD, some things are virtually unchanged.  The premise of the problem is that ATD is a top down approach.  The evaluation encourages the integration of faculty to lead and create change in community colleges.

This article is particularly interesting to me because it supports a belief I've had for a while.  That is, real change that works and sticks usually starts with the stakeholders.  In this case, that's faculty.  I work with colleges on a regular basis who are in the process of redesigning their developmental math curricula.  Some just want to do it, like our department did, because they see problems and they want solutions.  We knew there were problems for years and definitely our administration noticed.  But redesign started when we said we had had enough. 

However, some departments are being mandated from administration to make change and increase pass rates and retention.  Often the faculty are skeptical and suspicious of such efforts.  They feel put upon and left out of the decision making.  My goal is often to help them make the redesign work on their terms, to show them how it can be successful but in ways that they support.  Redesign means so many things and is not one size fits all.  And thankfully, it can be incredibly successful but have many looks to it.  But until faculty "buy in", change doesn't really occur.  Or it might temporarily, but it may not last.

The way I look at making change in education differs from conventional wisdom.  We did our redesign without a grant and without any large agency funding or guiding us.  That's certainly a hard row to hoe.  Money helps, obviously, and benefitting from someone's experience can save time.  But we didn't need much money, research and reports from other schools were abundantly available, and we could see interest and momentum building.  Grant applications and processes were going to slow that excitement and curtail our control.  As any faculty member knows, we like to do things on our terms.  So we forged ahead using what we had on our timeframe and unlikely as it was, it worked.  We saw huge gains in pass rates and have had a very successful redesign that we're using lessons from to help other schools on their terms.  It's not perfect, as is the reason for developing the new course, but we have solved some problems that existed a mere 3 years ago in our school.

One key to that success was the initiative started with faculty AND stayed with them.  We weren't pulled off the project once things got moving.  We led the task force, made the changes, and worked with various areas on campus to make our vision a reality.  It definitely took a village but the leadership were the people in the classroom who were going to be implementing the project.  Our administration was supportive, so we were very fortunate.  As long as we continued to show commitment, they did as well.

Part of making that change is working where change really happens:  in the classroom.  Professional development, mentoring, and training are large components of our program.  Yes, we use MyMathLab and we have a math lab facility.  All great things that support our goals.  But our redesign is founded on the premise that the vast majority of the classes are being taught with direct instruction.  We don't use the self paced, computer based instruction model.  It works for some, but it didn't for us.  Nearly 10 years of trying that model showed us that.  So if your biggest change is going to be in how the course is taught, working with the teachers has to be a big focus.

We're continuing to use this "from the ground up" model as we work on the new MLCS course.  The work started with faculty and is moving up through the chain of command.  I'm now working with state leaders to hopefully eventually have this course in our state articulation guide.  The state didn't come to us and say, "fix the problem and here is the solution."  We said, "we know there's a problem and here's one way we want to fix it.  Will you work with us?"

One of my main reasons for believing in this model of change is that faculty know their classrooms better than anyone.  Research and money are great and they can help.  But if all it took were research studies and funding, the problem would have been solved 20 or more years ago.  Problems get solved when the people affected by them come together, work on them and keep working on them.  Commitment matters, in other words.  And great things can happen with that approach.  Because teaching is an art as well as a science.  Let the artists hone their craft.

New manual

I've posted our updated Rock Valley College Developmental Math Manual (2011) at the left under Documents.  It includes information and the flowchart that incorporates the new course, MLCS. 

The realities of bringing New Life to life

We're knee deep in implementation mode of the new Mathematical Literacy for College Students (MLCS) course at my school.  And it's a lot of work to say the least.  This course is sort of a square peg in a round hole so there are challenges.  Still, we keep forging ahead because the rewards are already becoming apparent.  Students are finding out about the course and I'm hearing their excitement.  I've had students say, "I've always wanted to understand math.  I just don't get it the way it's usually taught."  The abstraction matters but our traditional approach has too much abstraction and too little concrete for some developmental learners.  And the little we have that's contextual is pretty contrived and "textbook."  The traditional approach can work, but for some, it's not enough.

So I'm buoyed by their reaction.  That's what is keeping me going as writing continues as well as fielding all the questions from other areas on campus and other implementation issues.

Initially, I had planned to spend this semester working with other disciplines to find out who can accept this as a prerequisite "or equivalent."  That's a bigger task than originally anticipated so I'm putting it on hold until this fall when there is more time.  Right now, we're focusing on advertising, good advising, and changing the programming requirements in the system to allow students to register for the course.

My hope is that once we and others have started to create this new path at our schools, we'll be able to help others make their process easier.  And from what I've seen during the redesign process we experienced and now working with others on their redesigns, I believe that to be a realistic goal. 

So we keep on keeping on.