Would You Make This Trade?

Our department is beginning conversations about a new algebra course, with the immediate goal of making it easier to offer a ‘combo’ class for both beginning and intermediate algebra.  We might settle for that outcome, with a savings in credits for many students (from 8 credits down to 6 or 4).  However, the possibilities are not very limited … one advantage of developmental mathematics being on the hot-seat is that those in the approval process are more open to new ideas.

So, here is a possible trade.  We send two courses away (beginning algebra and intermediate algebra) and replace it with one course, for the same number of credits as one of those courses.  We can dream big like this by being willing to consider radical reformulations of developmental mathematics, going in to territory not yet explored by pathways or mathways.

Trade away:  Beginning Algebra and Intermediate Algebra (8 credits)

Receive: One developmental algebra course (4 credits?)

This might one way to get there … start with a set of outcomes from Algebraic Literacy, including the STEM-boosting outcomes, and incorporate a little just-in-time remediation work on basic algebra along with some increase in instructional time each week.  The new course could omit quite a bit of the procedural work that is not that important, and focus instead on goals that are more accessible to a broader section of our population: reasoning and applying.  These ‘higher level’ learning outcomes are more important for further mathematics as well as science.  We might be able to put 30% more students in to this new course than we can with the existing intermediate algebra class.

This type of new course offers great promise for our students; of course, there are challenges for us.  A core challenge: are we willing to give up existing content in this trade?  We get so accustomed to teaching certain skills, these procedures, and those types of puzzle problems; hidden (usually) within this are some good mathematics and valuable learning outcomes.  Getting a world-class course involves being willing to trade in old courses, being willing to let go, being willing to subtract content in a class.

In our situation, we want to expand our mathematical literacy course; this course would be appropriate for most of the students who did not place into the new algebra class, both in terms of prerequisites needed prior to the class as well as preparation for further mathematics.  The Math Lit class gets students ready for a college statistics class and a college quantitative reasoning class.

I do not know how far we will take our current opportunity.  I do know that my vision for a better mathematics program in college starts with Algebraic Literacy.  Whether we make a big change, or smaller, we will be taking another step on this journey.

Have you started the journey away from the old algebra courses?

Note: For those going to the AMATYC conference in Nashville, I am doing a session specifically on Algebraic Literacy; this is session S064 (Friday — November 14, 8am).

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Obi Wan and Mathematics Education

I’ve been thinking about my perceptions this semester.  You see, for the first time in about 4 years, I am not teaching a ‘reasoning’ course — neither our Quantitative Reasoning course (Math119) nor our Math Lit course (Math105).  Of course, I miss those classes.  However, I am actually not aware of missing them on a daily basis.  In fact, I am quite comfortable.

Which led me to the memory of a certain movie moment.  Jedi-to-be Luke is angry with the Jedi master Obi Wan, after learning that Obi Wan did not tell him the truth.

Luke, you’re going to find that many of the truths we cling to depend greatly on our own point of view.

Our point of view is primarily determined by our environment and attitude.  My environment is more traditional this semester; symbolic manipulation and correct answers are high on the list of outcomes.  Like most of us, my attitude when in this environment is impacted by the ‘comfort’ and ‘familiar’ feelings.  I know this … I have competence … this is good.

As a profession, most of us have not yet had the opportunity to take a different point of view about mathematics education.  The majority of math classes are traditional at this time; over the next 5 years, that will change.  So … what comes first: a point of view that supports a reform curriculum, OR experience teaching a reform curriculum?

Like most philosophical questions, there is not a good answer for this question.  However, I will suggest that some of us will need to support a reform curriculum before we have a point of view that is consistent with it.  Understanding comes from experience, and understanding something as complex as the mathematics curriculum in college is a long process.  Early in our New Life Project, some colleagues were suggesting that the best thing to do was to teach a lesson for instructors in the way a reform class would teach it; this would have been a waste of effort: those who do not yet understand why a class would be taught that way … would not understand what they are seeing.

Change just happens.  Progress occurs when some of us are willing to walk a path we do not yet understand.  In some ways, there is nothing more rewarding than beginning a journey without understanding and then finding both understanding and things of beauty along the way.

However you look at issues in developmental mathematics and college mathematics in general, do not let other people put you in a box that says ‘inferior’ or ‘will not change’.  I have faith in each of us, that we are able to become more than we have been.  Our environment determines much about our point of view, and it’s hard to move out of that causality loop.  It takes courage; it takes some inspiration.  I have been impressed by math faculty who have grown in this way.

Especially if you think that the traditional curriculum has much to offer, I hope you will join me on this journey to a better place … a place where we do more for our students, where students are enabled to reach their goals, a place where good mathematics shines in our classrooms.  You are needed; we can not reach our goal without you.

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The Forum on Community College Mathematics (CBMS; Oct 6-7, 2014)

The Conference Board of Mathematical Sciences (CBMS) is a collaborative effort of about a dozen professional organizations in mathematics (including AMATYC and MAA, as well as AMS).  Based on the CBMS view of current events, the group sponsors a Forum on issues related to those events; for example, Forum 4 was related to the Common Core.

This October, the CBMS is offering Forum 5 on “The First Two Years of College Math: Building Student Success”, to be held in Reston (Virginia) on October 6 and 7.  You can see the program at http://cbmsweb.org/Forum5/ .  A unique feature of the Forum is that the breakout sessions are scheduled based on the wishes of those registering; during the registration process, you can select from the 18 offered sessions.  These are in addition to the plenary sessions.

Of course, I have a personal interest in this Forum … I will be doing one of the breakout sessions along with our friends Uri Treisman (Dana Center) and Bernadine Fong (Carnegie Foundation for the Advancement of Teaching).  Our session is #5, with a title “Increasing Student Success: New Math Pathways To and Through Gateway Mathematics Course“.  We are doing this session together because the work the 3 of us lead has had a long history of collaboration and mutual support; our projects are consistent with each other … more importantly, essential aspects of our goals are the same.

As is normal, travel funds are always a challenge.  In the case of the Forums, the CBMS has some funds to support those who wish to attend the forum.  During the registration process, you indicate your interest in these funds.  Priority is given to small teams (’2 or 3 participants’) from the same institution.

I am really looking forward to “Forum 5″ on the first two years of college mathematics.  Perhaps you can consider attending as well!

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Teacher as Confusion Manager — The Key for Student Learning

Early in my career, I focused on being clear — as close to perfectly clear as I could manage.  Class time was easy for students to follow.  Eventually, I realized that my students were not learning very much and decided that I was part of the problem.

Since then, I have seen my role as “confusion manager”.  In planning for what to do in class, I would look for a sequence of activities or problems that were likely to lead to some confusion.  In a basic way, confusion is the brain’s assessment that there is a gap between existing knowledge and needed knowledge.  Without confusion, learning new material is limited for most people.

There is a recent article in The Chronicle  called “Confuse Students to Help Them Learn” by Steve Kolowich  (http://chronicle.com/article/Confuse-Students-to-Help-Them/148385/?cid=cc&utm_source=cc&utm_medium=en)    The initial part of the article covers the experience of another teacher noticing this ‘confusion to help’ property.  Later, the article brings in some experts in psychology.  Certainly, the points in this article are consistent with what I know as a teacher and as a reader of cognitive psychology.

So … here is what I think is so important about the concept of “confusion to help learning”:  There is a great pressure to utilize digital resources, such as short videos.  These videos are almost always created with an emphasis on BEING CLEAR and avoiding confusion.  To check this out, just do a search for videos on your favorite math topics and watch.

Of course, it is possible to create short videos made with productive confusion in mind.  The article listed above suggests that it is not possible; however, I believe that I could create a video that would confuse my students just enough to be helpful.  The problem is that it is much easier to avoid confusion entirely OR to create a lot of confusion.  Productive confusion videos would take the type of planing that goes in to commercial production or movies.  Who has the resources to invest 20 hours in order to create a 5 minute video?

I think students who watch clear videos (or clear lectures) see the experience as validating their existing knowledge — even when their knowledge conflicts with what they just experienced.  A little additional information might survive through short-term memorization, or limited amounts of disconnected long-term information.  If all we are after is recall of facts or replication of simple procedures, clear videos might be sufficient.

As mathematicians, however, we are more interested in goals of reasoning … of application … and connecting knowledge.  This type of learning needs deliberate effort by students, and that means that we need to create and manage confusion.  Confusion, like anxiety, is a natural state for humans; too little of either leads to less learning just as too much of either impedes learning.  Our professional judgment and connection to every student is needed to provide productive confusion.

Have you confused any students yet today?  I hope so!

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