EIGHTH GRADE OPEN-ENDED MATHEMATICS PROBLEMS TO ENHANCE THE
TEACHING OF PROBLEM-SOLVING AND WRITING IN MATHEMATICS
By Ronna Ewing Eaton
Fall 1995
Students are being challenged to become mathematically powerful. In order to
become powerful students need to gain the ability to do purposeful and worthwhile
mathematics as it relates to usefulness in life. Research shows that problem-solving
increases this type of mathematical competency, and increasing the number of
experiences in solving divergent problems will improve students’ problem-solving
abilities. The interest a student has in the problem assigned has a direct and positive
correlation as to whether the student will successfully solve the problem. The
relationships between problems, problem-solving behavior, classroom environment, and
students affect the outcome for successful problem-solving.
The purpose of this project was to create a series of eighth grade open-ended
mathematics problems. Twelve problems were designed to help eighth grade students
improve their problem-solving skills. The problems address all eight strands of the
Mathematics Framework for California Public Schools, (California State Department of
Education, 1992). The problems were developed to provide students with writing as a
tool and technique in mathematical problem-solving and to provide teachers experience
with holistic scoring (rubrics).
Scoring rubrics were discussed with the students and they were taught how to
score problems to help improve with own abilities to respond to problem-solving in
developing written communication in mathematics. Revision was encouraged to improve
understanding and the overall product.
The results of the field testing revealed that students profited from their
experiences in writing in mathematics using constructed response answers to open-ended
problem-solving experiences.