The Center for Public School Renewal

NOTE: Published in slightly different form by the NCSM Newsletter, Spring, 1994.

An Image For Change In Mathematics Education
by Barry McGhan

Recently, I assumed district-wide responsibilities for mathematics education in my school system. As a result, my conversations with people often center on the curricular and instructional changes called for by the NCTM Standards. Concern over mathematics achievement has increased in my district because of a new state-mandated test which is more in tune with the Standards. Virtually all the state's districts have had trouble producing respectable results on the new test.

The low test scores are the result of the very short time period that schools were given to prepare for the transformation from a traditional curriculum to one closer to that envisioned in the Standards. As is becoming increasingly apparent, professional development is the means by which the transformation can be brought about, and that will take considerable time to occur. In order to communicate the major elements of the change that the Standards represent, and the difficulties that lie ahead, I created a metaphor which I hope other supervisors may find useful.

The Metaphor

  • Mathematics instruction is a journey that students undertake. The traditional curriculum and the NCTM Standards (representing different mathematical competencies) are distinct destinations that students can reach. The vessel for this journey is a massive ocean liner which can't quickly change course from the traditional destination to a new one. The students are passengers, the teachers are crew members, and the new state test is the radar equipment which measures the degree to which curriculum and instruction have swung around toward the new destination. The reason for the low test scores is that we hadn't made the turn yet.

  • A key change expressed in the Standards is that a wider spectrum of students should be served by the mathematics curriculum. So, changing course also includes the presumption that more passengers will be making the entire trip. During the journey to the old destination we have seen too many students going over the side before the ship made port. Furthermore, the typical "man overboard" was to a disproportionate extent, either a minority student, or female.

The result of these interpretations was the development of the figure below, which I started to use in my conversations with principals and teachers.

Math Curriculum Reform

Oldport is the embodiment of the following activities: paper and pencil calculations emphasizing whole numbers, fractions, decimals, and percents; drill and practice with many similar and routine problems; students working individually; students learning rules handed out by the teacher, etc. In contrast, Newport symbolizes teaching general problem-solving techniques; a much earlier introduction to algebra, geometry, probability and statistics; use of manipulatives, calculators and computers; working in groups to solve multidimensional problems; students constructing their own rules for solving problems.

The dots on the left side of the Oldport-bound ship are passengers who have gone overboard. Some just become lost in the wake of the ship. Others strike out on their own toward some spot where they can dry off and get on with their lives. Some passengers are thrown overboard by the crew, others fall over the side because of rough seas [circumstances outside of school such as poverty, substance abuse, etc.]. Some may even elect to jump overboard because the crew insists that the passengers spend most of their waking hours doing calisthenics [drill and practice].

Most members of the crew still seem to be trying to make landfall at Oldport. They are, after all, the survivors or near-survivors of earlier trips to Oldport, and they understand that journey best. A few of the crew have heard faint radio signals coming from the direction of Newport, and have jumped ship and are swimming in that direction. They are represented by the dots on the right side of the ship. It isn't clear whether these brave souls can reach Newport or not, and I hope we can send the ship's launch [support for being different] out to help them get safely to their destination. Once they've made the journey they may be able to come back aboard and lead the rest of the crew to Newport.

The crew members who see no need to change course don't seem to realize that Oldport is fast becoming a ghost town. So, even if the crew could keep more passengers on board, no one would have anything worthwhile to do once they got there [developments in computing technology and changes in the nature of work itself are the driving forces for this change].

Ultimately, we must not only change our course, but we have to retrofit the ship and retrain the crew. The retrofit is needed because passengers who disembark in Newport need to know how to do much more than calisthenics in order to get along there.

What we need to do is turn the liner into a sailing vessel. The crew needs to be brought up from the boiler room and in from supervising calisthenics and taught how to trim the sails, handle the rigging, read the wind and current, tack and jibe, and so on [how to apply constructivist approaches to learning]. Sailing requires a set of multi-faceted skills, and successful navigation is very dependent on knowledge of changing weather conditions, currents, and underwater hazards. The crew can't just turn on the engine and cruise into port. They will need to help the passengers--who are now on an adventure cruise--learn the elements of sailing, instead of just doing calisthenics. Because the new vessel is under sail and the passengers are learning "the ropes" the journey should be more interesting, although not without hazards.

The crew also needs to develop new safety procedures to reduce the number who go overboard, and new rescue strategies so that anyone who goes overboard can be fished out of the water. Finally, we have to "man" the lookout so that we can see that Newport is a real destination--a city of hope and vision--rather than a mirage shimmering in the distance.


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