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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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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Colorado Gets it Right with New Life

The New Life Project seeks to make basic improvements in math courses for college students — to provide them with modern courses, focusing on sound mathematical content, designed to serve the real needs of college students.  Although the New Life courses (Mathematical Literacy, Algebraic Literacy) can exist side-by-side with the traditional courses, my hope is that the new courses will replace the old courses.

Colorado has done that.  Effective this fall, the community colleges of Colorado are replacing their old developmental courses with a combination of Mathematical Literacy (Mat050) and Algebraic Literacy (Mat055).  The course titles vary from community college to community college, and colleges offer a co-requisite course for Algebraic Literacy (Mat025) which enables more students to begin with the second course.

For examples of the Colorado design, take a look at:

Pike’s Peak Community College http://www.ppcc.edu/app/catalog/current/mat-055-algebraic-literacy.htm

Community College of Denver http://www.ccd.edu/ccd.nsf/html/WEBB87UAA8-CEA+New+Math+Classes

Arapahoe Community College  http://www.arapahoe.edu/departments-and-programs/a-z-programs/mathematics/syllabi-mathematics-department

Colorado got it right.  Congratulations to them.  Their plan can be an inspiration to the rest of us.

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Quality Instruction and Class Design

Last year, my college created a new structure for departments and programs.  Instead of a chairperson for each department within the 3 academic divisions, we got associate deans and ‘faculty program chairs’.  The associate deans are the administrative players ‘in charge’ of two or three of our old departments.  In my case, math and science share an associate dean.  We have 7 faculty program chairs for the two departments; I am in the role of faculty program chair for developmental mathematics.  [Not much time provided in the workload, but the work is rewarding.]

Currently, I am focusing on one key idea for our program:

How do we create quality experiences for our students?

We want higher pass rates and completion (of course).  However, our students need classes that serve a real purpose.  Designing a course so that grades and scores are consistently higher than a student’s learning does not help students.  Some people talk about this under the umbrella of ‘grade inflation’, though our interest is in the striving for quality in instruction and class design.

So, here are some issues I have been thinking about:

• Should any ‘points’ be awarded for completing homework?
• Should points be awarded based on the level of performance during homework?
• Does “dropping a low test” support or hinder a high quality class?
• If a student does not come close to passing the final exam, should they get a passing grade if their other work creates a high enough ‘average’?
• Is it okay if students with a 2.0 or 2.5 grade are not ready for the next math course?
• Do high grades (3.5 and 4.0) uniformly mean that the student is ready for the next math course?

When courses are sequential, the preparation for the next math course is a critical purpose of a math class.  Assigning a passing grade, therefore, is a definite message to the student that they are ready to take the next class.  In practice, we know that this progression is seldom perfect — we usually provide some review in the next class, even though students ‘should’ know that material.  At this point, our efforts are dealing with the existing course outcomes, which tend to be more procedural than we would like; eventually, we will raise the reasoning expectations in our courses (with a corresponding reduction in procedural content).

Of special  interest to me are the issues related to homework.  Some faculty assign up to 25% of the course grade based on homework.  Like many places, we are heavy users of online homework systems (My Labs Plus as well as Connect Math).  When those systems work well for students, they support the learning process; most students are able to achieve a high ‘score’ on a homework assignment.  Should this level of achievement balance out a lower level on a test and/or final exam?  Take the scenario like this:

Derick completes all homework with a friend; with a lot of effort, his homework is consistently 90% and above.  All of Derick’s tests are between 61% and 68%, and he gets a 66% on the final exam.  The high homework average raises his course grade to 71%, and he receives a 2.0 (C) grade in the algebra class.

This scenario is a little extreme (it’s only possible with a high weight on homework … >15%).  What is fairly common is a situation where homework is 10% of the course grade and the student passes 2 of the 5 tests; one of of the 3 not-passed tests is ‘dropped’, and the student easily qualifies for a 2.0 (C) grade.  One of the cases I saw this past semester involved this type of student achieving a 52% on the final exam.

In our case,we already have a common department final exam for the primary courses (pre-algebra up to pre-calculus).  In the case of developmental courses, we have a policy that requires 25% of the course grade to be based on that final exam.  This design for the final exam is a good step towards the quality we are striving for.  We are realizing that we can not stop there.

Like most community colleges, our courses are taught by both full-time and adjunct faculty; the last figures I saw showed about 40% by full-time and 60% by adjunct.  Because adjuncts are not consistently engaged with our conversations, adjuncts tend to have more variations than full-time faculty.  We will be looking for ways to help our large group of adjuncts become better integrated within the program, even in the face of definite budgetary constraints.  Fortunately, many of my full-time colleagues are committed to helping these efforts to improve the quality of our program.

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