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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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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Curriculum and Instructional Improvement

We are doing some things at my College that might be of interest to others — not the type of thing we do a presentation on, though the information might be helpful.

Like many community colleges, our developmental mathematics courses have some of the highest enrollments on campus.  Therefore, these courses have large number of sections and are taught by a wide variety of faculty — full time/part time, new / experienced, rigid / flexible, etc.  Like many colleges, we follow student progression in the courses as closely as we can.  In the traditional courses (pre algebra, beginning algebra, intermediate algebra) the primary goal of each course has been to prepare students for the next course.  This progression data is not as good as we would like; nothing new there!

So, here is one thing we are doing about the problem.  We wrote a survey to be taken by instructors in a subsequent course.  In this survey, we listed the course outcomes for the prior course.  The survey asked the instructor to rank how important that outcome is, in preparing students for success in the subsequent course.  [The survey itself is being delivered through “Lime Survey”, a nice platform for surveys.]

The first survey asked intermediate algebra instructors about what students needed from beginning algebra.  We are currently working on the results (we had 16 surveys returned, from a pool of 33).    We are looking at the survey results as part of a process involving much discussion, rather than saying “this topic has got to be deleted because nobody needed it …”.  Our content in these courses is a little unusual in that few topics are covered in both courses — systems of equations is only in beginning algebra here, for example, as is most graphing concepts like slope.  Factoring polynomials is one of the few overlapping topics, which is likely why those outcomes were highly rated by instructors for intermediate algebra.

Another area we are looking at is instructional quality.  We have had a common departmental final exam for these courses for many years; we all use the same exams, and grade them with a common rubric.  However, much remains for each instructor to determine — points for attendance?  points for homework?  drop one low test?  making up tests?  We are working on providing instructors with feedback about how their choices impact the student’s probability of success in the next course.  One tool we are starting to use is an easy data-reporting tool that each instructor completes for each course:

The goal here is not to identify individual student issues; we are looking for patterns.  Does a given instructor have a large difference between the pre-final average and the final exam score?  Does an instructor have a large number of students who fail the final exam but pass the course?  [The final exam is required, but passing it is not required.]

We’ve also begun doing a “lesson study” method.  In our modified process, a group of instructors decides on a small topic to focus on, such as integer exponents.  The group talks about the topic — which is usually part of one class day: what makes this difficult?  what do students miss?  what shows understanding in students?  The group then creates a plan for the lesson, and some faculty use this in class while other faculty observe; this happens in 2 to 4 classes.  After these observations, the group meets to debrief … it’s about the lesson, not about students or instructors directly: what went well?  did students understand?  do some parts of the lesson need improvement?  Ideally, the class lessons are video taped for use in this debriefing, though we have not done that yet.  The debriefing itself is very educational, and we would like to record this so other instructors can experience the conversation.  The lesson study process is methodical and focused on the long term, one piece at a time; after a year, we have finished one lesson.

We are finding that a search for curricular and instructional quality is a long road; no maps are available so we are not sure that any particular action will lead to good results.  We do know that the process will lead to improvements if the conversation is centered in the hands of faculty.  None of this work is for administrative purposes.  Our goal is to help every instructor become better over time, and we see the administrative actions as issues of last resort.  We share ownership of the courses we teach, so this is not an issue of “I have the answers … not pay ATTENTION!”; it is more of an issue of professionalism for all instructors.

Hopefully, you found something of interest!

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Math Lit, and Pathways for Faculty

On my bookshelf, I have copies of two of the best math books available today:  Math Lit (Almy & Foes) and Math Literacy (Sobecki & Mercer).  Here are cover images:

Three years ago, this course was not offered anywhere.  As of this month, we have over 40 colleges offering the class with over 160 sections; Mathematical Literacy is an alternative to a beginning algebra course.  With the hard work of faculty, support from their colleges, and wisdom of publishing companies, the New Life Project continues to make a difference in our profession.

The work continues; the next course to be developed is Algebraic Literacy.  This alternative to an intermediate algebra course offers similar advantages; take a look at the “Missing Link” presentation (https://www.devmathrevival.net/?page_id=1807) from last fall’s National Summit on Developmental Mathematics.

I am seeing this progress as part of the pathway for us — a pathway for mathematics faculty.  We are moving from an accidental collection of relatively isolated topics with little benefit to students … to a deliberate design of courses containing mathematics to be proud of, with content designed to help all of our students.

In the process of moving from the old to the new, we are on a pathway ourselves.  We can become inspired by the design, gain skills in teaching mathematics, and experience a course that connects meaningfully to students.  Instead of being seen as “the last course to take, the one that stands in the way of graduating”, we can provide courses that show benefits to students earlier in their program.  Many students will find our new courses enjoyable; they will leave with a more positive view of what mathematics is.

We are on the path that leads to a mirror, a mirror which says “We do important work, and students benefit; be proud!”  I hope to see many of you on this trail.

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