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:

Student Pre-final average Final exam percent Final course average
Abbott
Costello
Brooks
Cabrera

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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Typing Versus Learning

We are all trying to help students learn so that they can succeed; we invest great amounts of time in designing classroom work and other components, and many of us are willing to spend ‘free time’ helping individual students.  Our work will be improved if it is informed by research and theory on learning in general, and learning mathematics in particular.

I ran into an item that referenced a research study conducted on using a laptop to take notes compared to hand-written notes in class.  The reviewed article has not been published yet  but you can read a summary at  https://www.psychologicalscience.org/index.php/news/were-only-human/ink-on-paper-some-notes-on-note-taking.html 

The key findings:

Taking notes on a laptop tended to be verbatim and less useful than hand-written notes.

Students who took notes on a computer memorized the same amount of information as those using hand-written notes.

Students who took notes on a computer performed more poorly on test items dealing with the ideas involved in their notes.

There also appears to be a pattern of verbatim notes (little processing) even if students are directed to not take verbatim notes; the device seems to encourage this type of behavior.

I do not see many students using a computer to take notes in my math classes (though it does happen).  What we all see more often is the use of another machine — calculators in particular, possible internet with a browser.  Would these activities also tend to be at the ‘verbatim’ level of processing?

To a large extent, I think the answer is yes — typing on a calculator tends to be done as a keyboarding activity with little processing of ideas.  I am not about ready to give up the learning advantages of using a calculator, nor am I going to pretend that those internet resources do not exist.  However, I need to be aware of the potential impact on the quality of learning when students do a lot of keyboarding of any kind.

Like many others, I tend to use a graphing calculator as a tool to explore properties and relationships.  This usually involves entering an expression or function, and then looking at some type of results.  Although I believe this is a “good thing”, the results of my efforts have consistently been disappointing — students seldom get the idea in a way that sticks with them.  It’s not like there is no gain; it’s more a sense that the calculator process is creating some type of opposing force that makes the learning more difficult.

We, as a group, may tend to equate “getting something, making it visible” with “learning the ideas”. When we use calculators or other keyboarding technology, the research cited above suggests that students may be processing the activity primarily as one of the keyboarding itself — like transcribing a conversation.  Processing of ideas, and looking for connections, might be more difficult when using calculators or computers — not impossible, just a challenge.  We need to provide a structure will pulls student attention away from the required keyboarding to the level where they think about ideas and connections.

I think our results will improve if we keep these factors in mind as we design instruction and experiences for our students.

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STEM Prep … Make That Path Straight!

We’ve been dealing with two basic issues in our work:  First, helping students succeed in mathematics as a service (general education especially).  Second, helping students realize dreams of being in a STEM program.

Since the current reform efforts started in 2009, most of the focus has been on the first problem (geared toward general education math courses); this is the problem that Statway™ and Quantway™ provide a solution for, and this is also the connection between the New Life course “Mathematical Literacy” and general education (like the Michigan Transfer Agreement).

However, the professionals involved with the New Life project have … from the start … kept the second issue in mind.  We saw a need to provide better mathematics for those in STEM fields, as well as a new model that enabled more students to reach their goals.  This is why we designed the second New Life course “Algebraic Literacy” the way we did; the content is based on professional standards, with special focus on STEM boosting learning outcomes.  I often refer to this Algebraic Literacy course as the “Missing Link” because it seeks to connect more students to the STEM programs with better employment and quality of life.

This week, the Dana Center (University of Texas – Austin) announced that they have launched their “STEM Prep Path”.  You can see some details at http://us2.campaign-archive1.com/?u=f75754127932b3bd8ffbea25c&id=3f956c1b40&e=23e0b88a42#STEMPREPTeams

Throughout our efforts, the Dana Center work on New Mathways has been consistent with our New Life work; in fact, the Dana Center has involved AMATYC members of New Life in all stages of their work.  In the case of STEM Prep Path, they will design a course serving the same purpose as Algebraic Literacy; I’m sure that they will differ in some basic ways, but am also sure that the content will be similar in basic ways.  One thing that is different — the STEM Prep Path for the Dana Center includes work in the domain of College Algebra & Precalculus.  This is very exciting work, and offers the promise of cleaning up the swamp our students face in those courses.

The STEM Prep Path is an effort to make the path straight — in other words, design the curriculum to serve the purpose and combine this with instructional methods and support that allow all students a high probability of success.  Currently, our path to STEM is not good for equity; developmental math classes can be high minority classes (that’s not necessarily a problem) while STEM math classes are very low minority (and that is definitely a problem).  The New Life work in Algebraic Literacy is part of this same effort to support a broader spectrum of students a path to STEM fields.  For information on the Algebraic Literacy course, see the presentation on the “Missing Link” at http://www.devmathrevival.net/?page_id=1807  .

I hope that you will take a look at STEM Prep Path, and a look at the Algebraic Literacy course, so that we make a straight path for our students with a goal of a STEM program.

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Language as an Impediment to Improving Mathematics Education

A recent article in the Chronicle of Higher Education was:

Remedial Educators Contest Reformers’ ‘Rhetoric of Failure’ ( http://chronicle.com/article/Remedial-Educators-Contest/145351/)

This is a good article, worth the time to read and think about.  I was drawn to the phrase “Rhetoric of Failure”, a phrase that Uri Treisman used in a presentation at the NADE conference.  However, I’ve been bothered by another aspect.

Think about the word ‘reformers’ in the title … the word is being used to describe the groups (mostly external) who are trying to impose a different design for getting students in to credit-bearing courses (Florida, Connecticut, etc) with the most common strategy being the avoidance of developmental education.

One can not reform a system by avoiding it.

Reformers are those who seek significant changes in an existing system.  I am a reformer; perhaps you are.  We seem to have little power to resist the revolutionaries who want to avoid the system.  Part of this lack of power is likely due to the fact that few people outside of our profession know of the reform work we’ve been doing.  Sure, many have heard of the Carnegie projects (Statway™ and Quantway™); as a high-profile endeavor, that work has been widely publicized outside of mathematics education.  However, few (very few) outside of our profession have heard of our effective work at truly reforming developmental mathematics — the New Life project.

Do the destroyers know that we have a better model that will accelerate students to credit-bearing courses based on a professional re-design of the curriculum combined with a modernization of teaching?  How many people know that there are far more New Life implementations than any grant funded work, past or present?

Calling a group ‘reformers’ is assigning them an intent to improve a system; when revolutionaries make drastic changes, a better word would be ‘destroyers’.  Now, sometimes we need revolutions … sometimes we need destruction.  As I understand the views in the social sciences about change, revolutions and destruction are usually ineffective at producing long-term change.  I know of no reason why mathematics education would be any different.

As long as the ‘reform’ word is used for revolutionary changes, improving mathematics education will be very limited; we are, in fact, likely to regress (which is the most common result of a revolution).  We need to articulate our visions for reform with clear statements of our rationale; we need to challenge statements that attribute ‘reform’ to a revolutionary process.  We need to be comfortable telling external groups that imposing change (a bullying behavior) is not going to fix a problem; revolutions seldom work.

Calling something a ‘reform’ does not make it a good thing.

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