Cost effective adult education: might it influence secondary education?

An article in The Washington Monthly titled “The College For-profits Should Fear” describes the founding and growth of Western Governors University. It uses an on-line model with some twists:

  • Course credits based on assessments completed. If you pass the final assessment, you get credit for the course… even if you just took the initial course assessment a few days earlier.
  • Tuition is charged per semester, not per course enrollment. This encourages students to complete as many courses per semester as they can, as it can save them money.

From what the article describes , this model seems most successful with older students – people who know what they seek, and don’t wish to waste time getting there. The WGU model is interesting for several reasons:

  • It has tuition levels that are around 40% or less that of other on-line programs, about $6,000 per year.
  • It employs full-time Mentors, who serve as a combination of guidance counselor, tutor, cheer-leader, and ombudsman for students. While they seem to provide a regular point of contact between students and the degree program, the article does not specify how many hours per week of such contact a typical student receives.
  • It uses industry-based standard assessments whenever possible as culminating assessments. The goals of the programs are therefore hopefully better aligned with the professional goals of the industries it is preparing students to enter.

The low tuition means that this model Continue reading Cost effective adult education: might it influence secondary education?

“Teacher” is an inaccurate title

People, both as children and adults, are constantly learning new things. The more actively engaged in the learning process they are, the more likely they are to learn something well and retain that knowledge. So what exactly is the person “teaching” a course doing? Their title implies that they are somehow loading knowledge into student brains. While that may fit the assumptions behind the “lecture model” of instruction, that is not the way learning works.

So what title is appropriate for people who:
– Decide on, or create a sequence of topics and tasks that engage, but do not overwhelm
– Set the stage, pique student interest, then Continue reading “Teacher” is an inaccurate title

Scheduling for Curricular Depth and Challenge

What was “the best” course you ever took? Probably one for which you had to work quite hard, one that you perceived as challenging from the outset, one for which you rose to the challenge. The course probably had a reputation as a tough course, so you probably added it to your schedule with care and made sure you did not take another really challenging course at the same time.

Major time commitments are regularly called for in schools: for musical or dramatic performances, athletic seasons, and some classes too. Could we improve the way such opportunities are scheduled so that  students can experience as many as possible each year without creating a killer workload for themselves at critical times during the year?


What if schools offered “challenges” that lasted for either half or a full semester? Each student could be required to be enrolled in two challenges at all times. A research project, art or engineering project, dramatic or musical performance could each count as a challenge, as could a varsity sport, as could any number of academic and extra-curricular offerings. To qualify as a “challenge”, an offering would have to:

  1. Culminate in a public performance, presentation, or display of student work.
  2. Involve extensive Continue reading Scheduling for Curricular Depth and Challenge

Lecturing: There Are Better Ways ToTeach

Many widely used math textbooks seem written for a traditional “lecture-style” teacher. They can be challenging to teach from if you are trying to reduce time spent “talking at” the class.

Some of the NSF-funded mathematics texts published over the past decade make it much easier for a teacher to avoid lecture mode, but:

– from a parent’s perspective, some texts don’t seem to have much of a role for the teacher, so how can/should a teacher add obvious value (in student and parent eyes) to what is in the text?

– the lack of prominently highlighted boxes around all information needed for the test is a source of student gripes. Students need to re-learn “how to learn” when a text or teacher takes a different approach, so time and effort needs to be devoted to this at the start of the year.

– the format of each unit can begin to Continue reading Lecturing: There Are Better Ways ToTeach

Integrating Mathematics With Other Subjects

What if most activities in school asked students to “reach and defend a conclusion”?

  •  in Math, about quantitative or geometric relationships, about measurements of worldly phenomena, etc.
  • in Music, about the effect of a melody line, about a particular mix of instruments, etc.
  • in English, about effective use of language or metaphor, about storytelling techniques, etc.
  • in Visual Arts, about the effective use of color or negative space, about how a work can be interpreted, etc.
  • in History, about a set of events, about relationships between societies, etc.
  • in Physical Education, about the effects of various activities on the human body, about the effectiveness of various strategies in a sport, etc.
  • in Science about whether two measurements are related in some way, why they might be related, the consistency with which they seem related, about cause and effect, etc.

What might our schools look like under such an approach?

The Purpose of High School Mathematics

The 2011 Anja S. Greer Conference on Secondary School Mathematics at Phillips Exeter Academy provided many opportunities to hears others’ ideas about the purpose of our High School Mathematics Curriculum.  Some of the statements I noted were (with apologies that none are exact quotes, and my lack of attribution on some):

In life, not to mention just about any academic subject, students should question information they come across, then work to support or refute it using numbers as needed.

Quantitative situations can be found in poems, literature, environmental claims, social justice issues, and social service needs.  We teach mathematics so that students can decide for themselves whether the quantities involved make sense or not.  Ray Williams (St. Mark’s School, Perth, AU) presentation.

Let the students ask Continue reading The Purpose of High School Mathematics