Interactive Mathematics Program (IMP)
Encyclopedia
The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools, designed to meet the needs of both college-bound and non-college-bound students. It was one of several curricula funded by the National Science Foundation
and designed around the 1989 National Council of Teachers of Mathematics (NCTM)
standards
. The curriculum replaces the traditional Algebra
I-Geometry
-Algebra II/Trigonometry
-Precalculus
sequence. The IMP books were authored by Dan Fendel and Diane Resek, professors of mathematics at San Francisco State University
, and by Lynne Alper and Sherry Fraser.
Designed in response to national reports pointing to the need for a major overhaul in mathematics education, the IMP curriculum is markedly different in structure, content, and pedagogy
from courses more typically found in the high school sequence.
,” the conflict between those that favor more traditional curricula in mathematics education and the supporters of the reform curricula that were largely an outgrowth of the 1989 NCTM standards
.
IMP is among the reform curricula that have been heavily criticized by organizations such as Mathematically Correct
. That organization’s Internet site begins with a statement that “advocates of the new, fuzzy math” (focus) “on things like calculator
s, blocks, guesswork, and group activities and they shun things like algorithm
s and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.” Former NCTM president Frank Allen states, “Trying to organize school mathematics around problem solving instead of using its own internal structure for that purpose … (is destroying) essential connections….”
Criticism often includes anecdotal evidence including stories of school districts that have decided to discontinue or supplement use of the IMP curriculum and of students who did not feel they had been prepared adequately for college. "Regular math is much better, it makes much more sense," says Aimee Lynn Stearns, a student at Taos High School in Taos, New Mexico.
On the other hand, some IMP students describe the program in positive terms. "It's fun, but it makes you really think," according to Ziouck Gonzalez, a student at Wells High School in Chicago, Illinois. Looking beyond student response, IMP was one of five mathematics education programs designated "exemplary" by the US Education Department in 1999, for "outstanding quality and demonstrated effectiveness." Key Curriculum Press, the publisher of IMP, points out “the IMP first edition was published after more than 10 years of research, pilot testing, evaluating, field testing, revising, and detailed reviewing.”
Supporters point to statistical studies that compare the performance of students enrolled in IMP courses with their peers enrolled in traditional high school mathematics courses. Merlino and Wolff, two such researchers, report that in their several studies IMP students consistently outperformed traditionally taught students on both the math and verbal sections of the PSAT
, as well as on the SAT-9. Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, and Webb and Dowling reported IMP students performed significantly better on statistics questions from the Second International Mathematics Study, on mathematical reasoning and problem solving tasks designed by the State of Wisconsin, and on a quantitative reasoning test developed by a university to administer to entering students.
National Science Foundation
The National Science Foundation is a United States government agency that supports fundamental research and education in all the non-medical fields of science and engineering. Its medical counterpart is the National Institutes of Health...
and designed around the 1989 National Council of Teachers of Mathematics (NCTM)
National Council of Teachers of Mathematics
The National Council of Teachers of Mathematics was founded in 1920. It has grown to be the world's largest organization concerned with mathematics education, having close to 100,000 members across the USA and Canada, and internationally....
standards
Principles and Standards for School Mathematics
Principles and Standards for School Mathematics are guidelines produced by the National Council of Teachers of Mathematics in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada...
. The curriculum replaces the traditional Algebra
Algebra
Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from them, including terms, polynomials, equations and algebraic structures...
I-Geometry
Geometry
Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
-Algebra II/Trigonometry
Trigonometry
Trigonometry is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves...
-Precalculus
Precalculus
In American mathematics education, precalculus , an advanced form of secondary school algebra, is a foundational mathematical discipline. It is also called Introduction to Analysis. In many schools, precalculus is actually two separate courses: Algebra and Trigonometry...
sequence. The IMP books were authored by Dan Fendel and Diane Resek, professors of mathematics at San Francisco State University
San Francisco State University
San Francisco State University is a public university located in San Francisco, California. As part of the 23-campus California State University system, the university offers over 100 areas of study from nine academic colleges...
, and by Lynne Alper and Sherry Fraser.
Designed in response to national reports pointing to the need for a major overhaul in mathematics education, the IMP curriculum is markedly different in structure, content, and pedagogy
Pedagogy
Pedagogy is the study of being a teacher or the process of teaching. The term generally refers to strategies of instruction, or a style of instruction....
from courses more typically found in the high school sequence.
- Each book of the curriculum is divided into five- to eight-week units, each having a central problem or theme. This larger problem serves as motivation for students to develop the underlying skills and concepts needed to solve it, through solving a variety of smaller related problems.
- Each year of the IMP curriculum integrates the algebraic, geometric, and trigonometric topics traditionally taught in separate courses, as well as topics from statisticsStatisticsStatistics is the study of the collection, organization, analysis, and interpretation of data. It deals with all aspects of this, including the planning of data collection in terms of the design of surveys and experiments....
and probabilityProbabilityProbability is ordinarily used to describe an attitude of mind towards some proposition of whose truth we arenot certain. The proposition of interest is usually of the form "Will a specific event occur?" The attitude of mind is of the form "How certain are we that the event will occur?" The...
that are not included in many traditional programs. - There is an emphasis on students working together in collaborative groupsCollaborative learningCollaborative learning is a situation in which two or more people learn or attempt to learn something together. Unlike individual learning, people engaged in collaborative learning capitalize on one another’s resources and skills...
. Together, they tackle problems that are usually too complex to be solved by any one individual. - The development of communication skills is embedded throughout the curriculum, through the use of group and whole class discussions, the use of writing to present and clarify mathematical solutions, and formal oral presentations.
- The IMP curriculum expects students to make nearly daily use of a scientific graphing calculatorGraphing calculatorA graphing calculator typically refers to a class of handheld calculators that are capable of plotting graphs, solving simultaneous equations, and performing numerous other tasks with variables...
. Students become comfortable with the calculator to such an extent that a Year 4 project tasks students with using their knowledge of trigonometry, matrix algebra, geometric projectionsGraphical projectionGraphical projection is a protocol by which an image of a three-dimensional object is projected onto a planar surface without the aid of mathematical calculation, used in technical drawing.- Overview :...
and transformations, and computer programming to design and present an animated cartoon on the screen of the graphing calculator.
Debate
Nearly every one of these distinctive characteristics has generated controversy and placed the IMP curriculum right in the middle of the “math warsMath wars
Math wars is the debate over modern mathematics education, textbooks and curricula in the United States that was triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics and subsequent development and...
,” the conflict between those that favor more traditional curricula in mathematics education and the supporters of the reform curricula that were largely an outgrowth of the 1989 NCTM standards
Principles and Standards for School Mathematics
Principles and Standards for School Mathematics are guidelines produced by the National Council of Teachers of Mathematics in 2000, setting forth recommendations for mathematics educators. They form a national vision for preschool through twelfth grade mathematics education in the US and Canada...
.
IMP is among the reform curricula that have been heavily criticized by organizations such as Mathematically Correct
Mathematically Correct
Mathematically Correct is a website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards...
. That organization’s Internet site begins with a statement that “advocates of the new, fuzzy math” (focus) “on things like calculator
Calculator
An electronic calculator is a small, portable, usually inexpensive electronic device used to perform the basic operations of arithmetic. Modern calculators are more portable than most computers, though most PDAs are comparable in size to handheld calculators.The first solid-state electronic...
s, blocks, guesswork, and group activities and they shun things like algorithm
Algorithm
In mathematics and computer science, an algorithm is an effective method expressed as a finite list of well-defined instructions for calculating a function. Algorithms are used for calculation, data processing, and automated reasoning...
s and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.” Former NCTM president Frank Allen states, “Trying to organize school mathematics around problem solving instead of using its own internal structure for that purpose … (is destroying) essential connections….”
Criticism often includes anecdotal evidence including stories of school districts that have decided to discontinue or supplement use of the IMP curriculum and of students who did not feel they had been prepared adequately for college. "Regular math is much better, it makes much more sense," says Aimee Lynn Stearns, a student at Taos High School in Taos, New Mexico.
On the other hand, some IMP students describe the program in positive terms. "It's fun, but it makes you really think," according to Ziouck Gonzalez, a student at Wells High School in Chicago, Illinois. Looking beyond student response, IMP was one of five mathematics education programs designated "exemplary" by the US Education Department in 1999, for "outstanding quality and demonstrated effectiveness." Key Curriculum Press, the publisher of IMP, points out “the IMP first edition was published after more than 10 years of research, pilot testing, evaluating, field testing, revising, and detailed reviewing.”
Supporters point to statistical studies that compare the performance of students enrolled in IMP courses with their peers enrolled in traditional high school mathematics courses. Merlino and Wolff, two such researchers, report that in their several studies IMP students consistently outperformed traditionally taught students on both the math and verbal sections of the PSAT
PSAT/NMSQT
The Preliminary SAT/National Merit Scholarship Qualifying Test is a standardized test administered by the College Board and National Merit Scholarship Corporation in the United States.This test is offered by the College Board....
, as well as on the SAT-9. Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, and Webb and Dowling reported IMP students performed significantly better on statistics questions from the Second International Mathematics Study, on mathematical reasoning and problem solving tasks designed by the State of Wisconsin, and on a quantitative reasoning test developed by a university to administer to entering students.