Interactive Mathematics Program

Last updated

The Interactive Mathematics Program (IMP) is a four-year, problem-based mathematics curriculum for high schools. 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 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. IMP was published by Key Curriculum Press in 1997 [1] and sold in 2012 to It's About Time. [2]

Contents

Curriculum

Designed in response to national reports pointing to the need for a major overhaul in mathematics education, [3] [4] [5] the IMP curriculum is markedly different in structure, content, and pedagogy from courses more typically found in the high school sequence. [6]

Controversy

Nearly every one of these distinctive characteristics has generated controversy and placed the IMP curriculum right in the middle of the “math wars,” 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 calculators, blocks, guesswork, and group activities and they shun things like algorithms and repeated practice. The new programs are shy on fundamentals and they also lack the mathematical depth and rigor that promotes greater achievement.” [8] 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….” [9]

Criticism often includes anecdotal evidence including stories of school districts that have decided to discontinue or supplement use of the IMP curriculum [10] and of students who did not feel they had been prepared adequately for college. [11]

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. [12] Kramer reported that grade 12 IMP students in his study performed better on all areas of mathematics tested by the NAEP test, [13] 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. [14]

See also

Related Research Articles

<span class="mw-page-title-main">Mathematics education</span> Teaching, learning, and scholarly research in mathematics

In contemporary education, mathematics education—known in Europe as the didactics or pedagogy of mathematics—is the practice of teaching, learning, and carrying out scholarly research into the transfer of mathematical knowledge.

A cognitive tutor is a particular kind of intelligent tutoring system that utilizes a cognitive model to provide feedback to students as they are working through problems. This feedback will immediately inform students of the correctness, or incorrectness, of their actions in the tutor interface; however, cognitive tutors also have the ability to provide context-sensitive hints and instruction to guide students towards reasonable next steps.

Principles and Standards for School Mathematics (PSSM) are guidelines produced by the National Council of Teachers of Mathematics (NCTM) 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. It is the primary model for standards-based mathematics.

Founded in 1920, The National Council of Teachers of Mathematics (NCTM) is a professional organization for schoolteachers of mathematics in the United States. One of its goals is to improve the standards of mathematics in education. NCTM holds annual national and regional conferences for teachers and publishes five journals.

In elementary arithmetic, a standard algorithm or method is a specific method of computation which is conventionally taught for solving particular mathematical problems. These methods vary somewhat by nation and time, but generally include exchanging, regrouping, long division, and long multiplication using a standard notation, and standard formulas for average, area, and volume. Similar methods also exist for procedures such as square root and even more sophisticated functions, but have fallen out of the general mathematics curriculum in favor of calculators. As to standard algorithms in elementary mathematics, Fischer et al. (2019) state that advanced students use standard algorithms more effectively than peers who use these algorithms unreasoningly. That said, standard algorithms, such as addition, subtraction, as well as those mentioned above, represent central components of elementary math.

The Independent School Entrance Examination (ISEE) is an entrance exam used by many independent schools and magnet schools in the United States. Developed and administered by the Educational Records Bureau (ERB), the ISEE has four levels: the Primary level, for entrance to grades 2–4; Lower level, for entrance in grades 5–6; Middle level, for entrance in grades 7–8; Upper level, for entrance in grades 9–12. All levels consist of five sections: Verbal Reasoning, Quantitative Reasoning, Reading Comprehension, Mathematics Achievement, and a 30-minute essay. The ISEE can be seen as a parallel to the Secondary School Admission Test, or SSAT. It is currently administered by Measurement Incorporated.

<span class="mw-page-title-main">Core-Plus Mathematics Project</span> High school mathematics program

Core-Plus Mathematics is a high school mathematics program consisting of a four-year series of print and digital student textbooks and supporting materials for teachers, developed by the Core-Plus Mathematics Project (CPMP) at Western Michigan University, with funding from the National Science Foundation. Development of the program started in 1992. The first edition, entitled Contemporary Mathematics in Context: A Unified Approach, was completed in 1995. The third edition, entitled Core-Plus Mathematics: Contemporary Mathematics in Context, was published by McGraw-Hill Education in 2015.

Mathematically Correct was a U.S.-based website created by educators, parents, mathematicians, and scientists who were concerned about the direction of reform mathematics curricula based on NCTM standards. Created in 1997, it was a frequently cited website in the so-called Math wars, and was actively updated until 2003.

Traditional mathematics was the predominant method of mathematics education in the United States in the early-to-mid 20th century. This contrasts with non-traditional approaches to math education. Traditional mathematics education has been challenged by several reform movements over the last several decades, notably new math, a now largely abandoned and discredited set of alternative methods, and most recently reform or standards-based mathematics based on NCTM standards, which is federally supported and has been widely adopted, but subject to ongoing criticism.

Investigations in Numbers, Data, and Space is a K–5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, United States. The curriculum is often referred to as Investigations or simply TERC. Patterned after the NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. As opposed to referring to textbooks and having teachers impose methods for solving arithmetic problems, the TERC program uses a constructivist approach that encourages students to develop their own understanding of mathematics. The curriculum underwent a major revision in 2005–2007.

MathLand was one of several elementary mathematics curricula that were designed around the 1989 NCTM standards. It was developed and published by Creative Publications and was initially adopted by the U.S. state of California and schools run by the US Department of Defense by the mid 1990s. Unlike curricula such as Investigations in Numbers, Data, and Space, by 2007 Mathland was no longer offered by the publisher, and has since been dropped by many early adopters. Its demise may have been, at least in part, a result of intense scrutiny by critics.

Integrated mathematics is the term used in the United States to describe the style of mathematics education which integrates many topics or strands of mathematics throughout each year of secondary school. Each math course in secondary school covers topics in algebra, geometry, trigonometry and functions. Nearly all countries throughout the world, except the United States, normally follow this type of integrated curriculum.

In the United States, math wars are debates over modern mathematics education, textbooks and curricula that were triggered by the publication in 1989 of the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM) and subsequent development and widespread adoption of a new generation of mathematics curricula inspired by these standards.

Thomas "Tom" Albert Romberg was Professor Emeritus of Curriculum and Instruction at the School of Education, University of Wisconsin–Madison, and former director of the National Center for Improving Student Learning and Achievement in Mathematics and Science, Wisconsin Center for Education Research.

Singapore math is a teaching method based on the national mathematics curriculum used for first through sixth grade in Singaporean schools. The term was coined in the United States to describe an approach originally developed in Singapore to teach students to learn and master fewer mathematical concepts at greater detail as well as having them learn these concepts using a three-step learning process: concrete, pictorial, and abstract. In the concrete step, students engage in hands-on learning experiences using physical objects which can be everyday items such as paper clips, toy blocks or math manipulates such as counting bears, link cubes and fraction discs. This is followed by drawing pictorial representations of mathematical concepts. Students then solve mathematical problems in an abstract way by using numbers and symbols.

Connected Mathematics is a comprehensive mathematics program intended for U.S. students in grades 6–8. The curriculum design, text materials for students, and supporting resources for teachers were created and have been progressively refined by the Connected Mathematics Project (CMP) at Michigan State University with advice and contributions from many mathematics teachers, curriculum developers, mathematicians, and mathematics education researchers.

Reform mathematics is an approach to mathematics education, particularly in North America. It is based on principles explained in 1989 by the National Council of Teachers of Mathematics (NCTM). The NCTM document Curriculum and Evaluation Standards for School Mathematics (CESSM) set forth a vision for K–12 mathematics education in the United States and Canada. The CESSM recommendations were adopted by many local- and federal-level education agencies during the 1990s. In 2000, the NCTM revised its CESSM with the publication of Principles and Standards for School Mathematics (PSSM). Like those in the first publication, the updated recommendations became the basis for many states' mathematics standards, and the method in textbooks developed by many federally-funded projects. The CESSM de-emphasised manual arithmetic in favor of students developing their own conceptual thinking and problem solving. The PSSM presents a more balanced view, but still has the same emphases.

<span class="mw-page-title-main">Mathematics education in the United States</span> Overview of mathematics education in the United States

Mathematics education in the United States varies considerably from one state to the next, and even within a single state. However, with the adoption of the Common Core Standards in most states and the District of Columbia beginning in 2010, mathematics content across the country has moved into closer agreement for each grade level. The SAT, a standardized university entrance exam, has been reformed to better reflect the contents of the Common Core. However, many students take alternatives to the traditional pathways, including accelerated tracks. As of 2023, twenty-seven states require students to pass three math courses before graduation from high school, while seventeen states and the District of Columbia require four. A typical sequence of secondary-school courses in mathematics reads: Pre-Algebra, Algebra I, Geometry, Algebra II, Pre-calculus, and Calculus or Statistics. However, some students enroll in integrated programs while many complete high school without passing Calculus or Statistics. At the other end, counselors at competitive public or private high schools usually encourage talented and ambitious students to take Calculus regardless of future plans in order to increase their chances of getting admitted to a prestigious university and their parents enroll them in enrichment programs in mathematics.

Mathematics education in the United Kingdom is largely carried out at ages 5–16 at primary school and secondary school. However voluntary Mathematics education in the UK takes place from 16 to 18, in sixth forms and other forms of further education. Whilst adults can study the subject at universities and higher education more widely. Mathematics education is not taught uniformly as exams and the syllabus vary across the countries of the United Kingdom, notably Scotland.

<span class="mw-page-title-main">Gary Bitter</span> American educational technology researcher

Gary Bitter is an American researcher, teacher, and author focusing on educational technology. He is Professor of Educational Technology and past Executive Director of Technology Based Learning and Research at Arizona State University. He was a founding board member of the International Society for Technology in Education and served as its first elected president. He is the co-author of the National Technology Standards (NETS) which have been used extensively as a model for National and International Technology Standards.

References

  1. ↑ Wu, H. "Review of IMP" (PDF).
  2. ↑ "Press". Key Curriculum Press Release. Archived from the original on 2012-11-07.
  3. ↑ Everybody Counts: A Report to the Nation on the Future of Mathematics Education, Mathematical Sciences Education Board, National Research Council, 1989
  4. ↑ Reshaping School Mathematics: A Philosophy and Framework for Curriculum, Mathematical Sciences Education Board, National Research Council, 1990
  5. ↑ Science for all Americans, American Association for the Advancement of Science, 1989
  6. ↑ Introduction and Implementation Strategies for the Interactive Mathematics Program: A Guide for Teacher-Leaders and Administrators, Key Curriculum Press, 1997
  7. ↑ "What is Common Core Math: Its Difference from Traditional Math". Brighterly. Retrieved 2023-04-23.
  8. ↑ Archived 2011-11-28 at the Wayback Machine Mathematically Correct, www.mathematicallycorrect.com
  9. ↑ Allen, F: “A Critical View of NCTM Policies with Special Reference to the Standards Reports” on mathematicallycorrect.com, last retrieved April 7, 2010
  10. ↑ "Does kid's math have go to basics?”
  11. ↑ Datta, S: “Interactive Mathematics Program: Manifesto on an Experimental Concept Gone Awry” on mathematicallycorrect.com, last retrieved April 7, 2010
  12. ↑ Merlino, J. and Wolff, E: Assessing the Costs/Benefits of an NSF “Standards-Based Secondary Mathematics Curriculum on Student Achievement, Philadelphia, PA: The Greater Philadelphia Secondary Mathematics Project, 2001
  13. ↑ [ permanent dead link ] Kramer, S: “The Joint Impact of Block Scheduling and a Standards-Based Curriculum on High School Algebra Achievement and Mathematics Course Taking” (doctrinal dissertation), University of Maryland, 2003 [DEAD LINK]
  14. ↑ Webb, N. and Dowling, M: “Comparison of IMP Students with Students Enrolled in Traditional Courses on Probability, Statistics, Problem Solving, and Reasoning,” Project Report 97-1, University of Wisconsin – Madison, Wisconsin Center for Education Research, 1997
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.