A Lesson About Math

An inspection of what goes on in a typical secondary school math class reveals that it is not the fine-tuned, efficient sharing of knowledge people think it to be. It is actually an incredible waste of time that cultivates daydreaming and poor attitudes about learning and work. The typical class goes something like this.

It begins with a hubbub of students arriving from different places, greeting each other and chatting. This continues until the teacher settles them down. Attendance is checked. Homework is checked. Examples from homework are reviewed, and then the teacher gives the lesson.

An attentive student may only need a few minutes to grasp the new material, others may have already known it, but for the students who don’t pay attention, or who are lost at sea, the teacher repeats the lesson using different examples, and repeats it again, and maybe again, targeting questions to command the attention of the disengaged. When the lesson is finished, the teacher minimizes the chance of disruption in the class by assigning enough “homework” to keep the best students busy until the end of class. The other students are expected to finish the work at home, but often they just hurriedly copy other students work when they get to school the next day. When the math class is analyzed we see that very little new learning occurs.

An hour of math for a student in an OPERI type program is quite different. The emphasis on life-long learning skills translates into students developing the capacity to make good use of their time, to learn how to focus, to work smart, in short, to produce an hour of quality learning. They do not need to spend time on things they already know. They do not need to spend time on exercises they do not need to do. They can combine sections where concepts have been broken into pieces, and learn the whole instead of the parts, which can produce a better understanding of concepts. They can choose the time of day that is best for them to work on math. They can choose whom to learn from if they need help – it is said that the best teachers are often the people who have recently learned something because they best remember where difficulties arise. If they get on a roll, they don’t have to stop at the end of the hour. They can keep on working for as long as they want. In short, the possibility of a self-directed learner being able to complete math course requirements in a fraction of the time required of regular students is very real.

The differences in how self-directed learners and students in tradition programs spend their time gives dimension to an idea Tapscott and Caston attribute to Joe Arbuckle, a Toronto-based consultant and author, in their book Paradign Shift.

If you want to control, you design organizations for accountability.
If you want to accomplish, you design for commitment.

Traditional schools are heavy on accountability. The pilot program proposed by OPERI fosters commitment. The former tend to have students putting in time; the latter is more about getting the most out of your time. Taking this thought a step further, it is said that time is money, and that time is all we really have. It follows that public education needs to be conducted in ways that do not waste students’ time.

Lack of ability is often not the cause of secondary students under performing in math. The lock-step approach to learning it, where advancing is governed by a timeline rather than by mastery is a big culprit. It can produce a confusing hodge-podge of misconceptions and missing pieces. Not only do the victims suffer from not having the necessary grounding, their thinking can be constrained by the anxiety created by knowing their future will be determined by what they do not know. We’ve all heard of math anxiety, and we can all imagine the feelings of a student skating on thin ice, of trying to survive on a weak foundation.

The time savings and focus on mastery made possible by self-directed learning programs create the opportunity for students to catch up in math. Mastery of current material requires that essential prerequisite concepts be mastered. Teachers acting as facilitators can help struggling students to identify where their prerequisite knowledge is weak or missing, and help them develop the resourcefulness needed to get back on firm ground. Ultimately, the learning is about more than math. It is about confidence building and developing the skills to deal successfully with life’s challenges.

This small comparison between traditional school programs and self-directed learning programs strongly suggests that collectively we need to be thinking much harder about what traditional schools are doing to students, and the alternatives we have available.

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