Investigations in Numbers, Data, and Space

Investigations in Number, Data, and Space is a K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts, USA. The curriculum is often referred to as Investigations or simply TERC. Patterned after the heavily debated NCTM standards for mathematics, it is among the most widely used of the new reform mathematics curricula. It is also one of the most protested against by groups of parents and some mathematics experts who object that students using this curriculum receive no direct instruction in traditional arithmetic methods. Investigations is supported by research which purports that "children in the Constructivist group were the most successful"^{[citation needed]}. Rather than memorizing and practicing the same methods taught to their parents, students are guided develop their own constructivist mathematical understanding. The curriculum underwent a major revision in 2005 - 2007.

^[1]

History

Investigations was developed between 1990 to 1998. It was just one of a number of equally controversial "reform mathematics" curricula initially funded by a National Science Foundation grant. The goals of the project caused opposition to the curriculum from critics (both parents and mathematics teachers) who objected to the emphasis on conceptual learning instead of instruction in specific methods for basic arithmetic.

The goal of the Investigations curriculum is to help all children understand the fundamental ideas of number and arithmetic, geometry, data, measurement and early algebra. Unlike traditional methods, the original edition did not provide student textbooks to describe standard methods or provide solved examples. Instead, the design of the curriculum directed teachers to discourage or omit entirely the introduction of most standard computational methods such as multiplication tables, lowest common denominators or long division. Instead, students were guided to develop their own invented algorithms through writing, cutting, pasting, interviewing and playing games.

Some school districts and states stopped using Investigations and adopted more traditional mathematics texts such as Saxon Math in response to very low test scores, which many have blamed on adoptions of texts such as Investigations.

In response to criticism, Investigations released its second edition for 2006 that focuses its core values of teaching for understanding. The revised version has further emphasis on basic skills and computation, though the initial edition was based largely on the idea of abandoning instruction of basic skills such as regrouping and memorization of math facts. It is also easier for teachers to use since the format is more user friendly^{[citation needed]}, though some districts have abandoned the second edition as well in favor of textbooks that teach traditional arithmetic methods.

Research

A variety of measures of student achievement and learning including state-mandated standardized tests, research-based interview protocols, items from research studies published in peer-reviewed journals and specially constructed paper-and-pencil tests have been used to evaluate the effectiveness of Investigations

The TERC website claims that students who use Investigations, among other things, "do as well or better than students using other curricula." To support the assertion that children do better when they are not taught traditional arithmetic, Anne Goodrow of Tufts University compared subtraction strategies of students taught traditional methods with those who used constructivist methods with Investigations curriculum. A "constructivist" student subtracting 9 from 28 recognizes that 8 minus 9 is negative one, even though the concept of negative numbers is not covered in the text. The negative number is then added to twenty to make 19, rather than using the borrowing strategy which confused the traditionally taught student.^[2] The author concluded that "although they did not receive instruction in the use of the standard algorithms, the children in the Constructivist group were the most successful at both two-digit addition and subtraction." The study however did not explain that negative numbers are traditionally not introduced until after the elementary grades, while regrouping was taught to all 2nd and 3rd graders as is familiar to their parents in all cultures prior to the adoption of constructivist curricula, while most parents are unfamiliar with the use of negative numbers in basic arithmetic. For division, the teacher manual states the notation for long division is no longer used in mathematics. Any notation may be used to denote the remainder as long as it is not the letter "R" which has historically been taught as standard.

In actual practice, the advantages have been less clear cut. In the Ridgewood Public School System, TERC has been introduced into two of the village's elementary schools. Contrary to the claims made on the TERC website, math scores on statewide standardized tests for students in these elementary schools have declined ever since the introduction of TERC. Supporters of TERC point to the high math scores of the district as a whole but conveniently omit the fact that the other four elementary schools in the village do not use TERC.

Criticism

Investigations initially was commercially successful. But parents and math educators have criticized its lack of traditional arithmetic content, of decimal math, of multiplication tables, and of a traditional textbook; its incompatibility with high-school and international mathematics methods; its complex homework assignments; its high cost (a concern mainly of home-schooling parents); and other factors.

A common complaint is that the curriculum does not teach any of traditional arithmetic methods familiar to those taught in other nations and to parents with as little as an elementary-school education.

Investigations is among the texts most often deemed especially poor results of the reform mathematics approach.^{[citation needed]} Parents have said that the curriculum harms their children's education.^{[citation needed]}

Complaints are that pupils spend much time coloring and circling and that many basic arithmetic skills, such as regrouping, long division, and computing a mean, are not taught or are explicitly discouraged by the teacher instructions.

A common parent complaint is that there is no recognizable arithmetic and that homework is frequent and very time-consuming, with some tasks requiring help from family members and considerable cutting, pasting, and coloring, whereas a traditional worksheet may take little time.

Another common parent complaint is that the math program does not teach the traditional math algorithms and makes it difficult for the parents to help children with their homework. Such algorithms are introduced only when students happen upon them and demonstrate them to the class.

Non-traditional materials and content

• Student materials included in the 2002 Grade 5 package for TERC Investigations: 4 rolls of adding machine tape; 36 blank 5/8" cubes; 1,000 stickers for blank cubes; 200 1-cm cubes; 16 transparent blank spinners; 4 450-piece sets of power polygons; 4 buckets of square color tiles (400 per bucket); 1,000 Snap(TM) cubes; 1 set of elementary bar mass set-Ohaus; 4 graduated measuring prisms (2-cm x 5-cm x 21-cm); 4-liter measuring pitcher (calibrated 100 ml - 1,000 ml); 4 spectrum school balance (includes 7-piece mass set); 4 sets standard measuring pitchers (3 pitchers: quart, pint, cup per set); 10 measuring tapes; 12 meter/yard sticks.
• The total package for Grade 5 is listed at $1,388.42, and within that total the cost of the just mentioned student materials, for a class of 32, is $817.00^[3]
• In the original edition, there was no multiplication table presented. Instead, students were instructed to color in multiples of numbers on a 100s chart, or to draw and count tally groups.
• There is no formal presentation of decimal addition. Students are instructed to use colored pencils on 10,000 grid chart rather than the standard method.
• Students are not instructed to compute an average by "adding up the items, and dividing by the number of items" because it is judged to be too complex for students of some groups to compute. Instead, the teacher is given a chapter on different ways to compute the median.*
• Students who demonstrate knowledge of a standard method of calculation must still invent at least one other method of calculation.
• Students are asked to compute the volume of a rectangular solid. They are not allowed to use or be told the standard formula of length multiplied by width and height, which is the formula given on standardized tests such as the SAT.

Parody

The textbook series has been parodied by the on-line cartoon series "Weapons of Math Destruction", including one panel of a student declaring that they can't finish their homework because they have run out of glue, or writing two different ways to determine if 13 is even or odd, and explaining the answer.

Adoptions

An incomplete listing of school districts that have adopted TERC materials

• Lake Washington School District
• Bellevue School District adopted it for 10 years, dropped in favor of Math Expressions as "outdated and inefficient" for 2008.^[4]
• Stillwater School District
• Ridgewood Public Schools
• Seattle School District. Dropped in favor of Everyday Mathematics in 2007-08.
• Reading City Schools (Cincinnati, OH)
• Frederick County Public Schools (Maryland)

External links

• Pearson / Scott Forseman website for curriculum
• A collection of links to reviews of and commentaries of TERC: Investigations in Number, Data, and Space, Bas Braams, Elizabeth Carson, and NYC HOLD
• Critical "Mathematically Correct second grade review"
• "Math Education: An Inconvenient Truth", M.J. McDermott, Q13 FOX KCPQ-TV
• "Beyond TERC National" message board for concerned citizens
• STOP Taking Excessive Risks with our Children

Notes

1. ^ [1] Jan Mokros, Susan Jo Russell and Karen Economopoulos, Beyond Arithmetic (Dale Seymour Publications, White Plains, NY, 1995), p. 74.]
2. ^ Modes of Teaching and Ways of Thinking Anne Goodrow TERC/Tufts University
3. ^ [2] Reviews of TERC
4. ^ Bellevue Reporter March 22, 2008