Organizing for Instruction in Mathematics

Journal of Instructional Psychology, June, 1999 by Marlow Ediger

A good mathematics instructor is a proficient organizer of pupils for instruction in mathematics (Ediger, 1997, pp 18-38). Here, the teacher has numerous incidental ways for pupils to learn mathematics. Bulletin board displays which illustrate selected facts, concepts, and generalizations in mathematics can assist pupils to obtain needed background information on their very own. The bulletin board display may also be used in direct teaching of pupils as they relate to an ongoing lesson or unit of study. One of the best stimulating bulletin board displays I observed when supervising student teachers and cooperating teachers in the public schools emphasized a history of measurement. Many pupils were fascinated with the display by noticing how the centimeter, meter, and kilometer had their beginning or origin. I think the bulletin board display here helped pupils to learn more about measurement. Many pupils spent much time viewing and discussing the bulletin board display. The mathematics teacher needs to take down a display when it has served its purpose and prepare a new one which encourages pupil learning.

Using Learning Stations

The mathematics teacher may organize pupils for instruction by developing a set of learning stations. Each station needs to be labeled so that pupils know what to expect at the center. I suggest that each learning station have concrete (objects, items, and realia) for pupils to learn from. These concrete materials stimulate and motivate pupil learning. Semiconcrete materials (illustrations, slides, videotapes, filmstrips, CDs, computer software and personal computers, as well as films should also be located at each station, along with abstract learning materials such as textbook and workbook materials, photocopied problems, reading activities, writing experiences, listening/participating through discussions and cassette recordings, among other tasks. The concrete, semiconcrete, and abstract materials may become a part of the tasks on task cards. One task card per center should be in evidence. A fine set of tasks one cooperating teacher wrote was the following as an example:

A Geometry Center (Grade Three)

1. take four geometrical figures from this station and find the perimeter of each.

2. select two geometrical figures and find the area of each.

3. make your own geometrical figures and develop an art project which shows a new scene.

4. view the filmstrip entitled Geometrical Figures and answer the related questions located next to the projector.

5. view and discuss with five other pupils content in the videotape entitled Geometry is fun. Write five main ideas gathered from your discussion.

The mathematics teacher should have an adequate number of tasks at the different stations so that a pupil may omit what does not possess perceived purpose and yet there are ample activities for time on task for each learner. The mathematics teacher assists and guides pupils to achieve and learn at the diverse stations. He/she does not lecture to pupils. Each pupil should be actively engaged in learning. Peer assistance and help should be welcomed as needed. Learners may choose individual as well as collaborative tasks to pursue (see Reys, Suydam, and Lindquist, 1995).

The philosophy in back of learning station use is that pupils will achieve more if they may choose what to pursue and what to omit. A teacher may arrange stations so that pupils may experience the basics as well as activity centered approaches. Much is written about stressing a hands on approach in guiding pupil learning in mathematics. With ample concrete and semiconcrete experiences available in terms of materials and listed tasks at each station, pupils may certainly experience a hands on approach in learning. At the same time, there are ample opportunities for pupil learning that provide for individual differences and learning styles (Ediger, 1995, 13-15). If too many pupils wish to work at a station, the teacher may assign pupils to the different centers so that a reasonable number may work together. Before pupils start working at a station, the teacher should introduce each station to pupils. The introduction should also encourage and motivate pupils to learn. Individual needs are met of pupils through choice of sequential activities as well as by choosing individual versus collaborative endeavors. With an adequate number of tasks available, pupils may omit what does not meet personal needs and learning styles. The teacher evaluates each pupil within the framework of continuous

achievement at the diverse stations. Organization of pupils for learning is an important task of the mathematics teacher.

The teacher needs to communicate clearly to pupils proper rules for learning and enforce these regulations. He/she needs to observe learner behavior and attempt to prevent disruptions form occurring. Many school districts and schools have policies on school discipline that must be enforced. An orderly environment helps pupils to achieve more optimally. The teacher needs to evaluate the learning environment continuously and work in the direction of making changes to continually motivate pupil learning. Materials of instruction should be readily available to pupils. They need to be current and attractive to encourage learning. A safe classroom environment guides pupils to learn. Ridiculing, belittling, and sarcasm are not models for good behavior. There needs to be respect for pupils as well as for the mathematics teacher. All involved in a class need to experience a wholesome environment for teaching and learning (Ediger, 1996, pp 172-192).