Use Math to Solve Problems - Reflections on How Adults Use This EFF Skill

"An outstanding feature of the current mathematics education scene is the rejection of the traditional curriculum and the methods of assessment associated with it. In the traditional view, the curriculum was fragmented into subject areas, such as geometry, arithmetic, algebra, and these subjects further fragmented into topics like notation, numeration, statistics, and so on. Assessment in this curriculum was concerned with the correctness of answers and procedures... Wherever we look in western education systems, this rejection of the traditional paradigm has taken place. There has been a change in emphasis in the curriculum from product to process, from fragmentation and procedural knowledge to integration and problem solving. The basic aim is well formulated in the NCTM Standards (1989) by its concept of 'mathematical power'; the notion of empowering the students to be able to apply their mathematical knowledge, concepts, and abilities in problem solving,communication, and reasoning. In all cases, it has been realized that sustaining this new set of aims requires the use of new assessment techniques geared to the change in direction." 6
-Kevin Collis and Thomas A. Romberg

Insights From Field Research:
Using the Standard to Guide Teaching and Learning

J. Renee Thompson
Knox County Adult Literacy Program, Knoxville, TN
 GED Level 2; Series of lessons on perimeter and area. The context was cleaning, painting, and furnishing new classrooms after a fire.
Teacher data from the second round of field review, conducted 1998-1999.
(Adapted from Equipped for the Future Content Standards, p. 34.)

Describe what you know about the level of performance of your students.

  • Selects appropriate mathematical concepts and techniques and accurately applies them to the purpose and the problem: ME has never decorated, painted or cleaned a living or working place on her own. She knew the formulas for area and perimeter, but only in a math class context. AH told me while painting her mother's house she went and got paint about ten times in one day. She was very interested in finding a way to determine the amount of paint needed before starting. AM has decorated and painted her home many times. She judges how much paint she needs for a room by sight. She did not know the formulas for area and perimeter. She did not know that you can figure the amount of paint needed for a room mathematically. SJ has never planned out painting a room or using mathematical concepts to aid her in determining how much she would need to paint a room.
  • Organizes and communicates data in format appropriate to purpose and audience: ME has never made a scale model of anything. She had never used a tape measure or measured a room. AH knew nothing about scale models and drawings or how to go about designing them or for what purpose you would use them. She was very skeptical about being able to do a scale drawing. AM has not measured a room or used those measurements to make a scale drawing. SJ did not know what a scale drawing was or if she had ever seen one. She has never used a tape measure or measured anything larger than with a ruler. SJ was not sure if she could do this task.

What will you look for in order to know if your students are making progress toward meeting the Standard?

  • Selects appropriate mathematical concepts and techniques and accurately applies them to the purpose and problem: ALL students will be able to determine whether they need to use the formulas for perimeter or area for the results they need to decorate a room. ALL students will be able to accurately measure a room for perimeter and/or area.
  • Organizes and communicates data in format appropriate to purpose and audience: ALL students will be able to use the mathematical formulas for area and perimeter to draw a scale model of a room on graph paper. ALL students will be able to clearly and accurately explain how they used these math formulas to create the graphic description. ALL students will be able to use these mathematical concepts to give them results that will aid them in decorating or redecorating a room.