Investigations in Numbers, Data, and Space

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Investigations in Number, Data, and Space is a complete K-5 mathematics curriculum, developed at TERC in Cambridge, Massachusetts. Investigations is both one of the most popular new standards-based mathematics curricula among districts, and most protested against by groups of parents and some mathematics experts, patterned after the heavily debated NCTM standards for mathematics.

Although an initial commerical success with federal programs helping to pay for a widespread adoption without a formal public debate process, increasing numbers of educational institutions are discarding it as an instructional failure as it is nearly always supplemented with traditional mathematics materials. This is neccesary because, in line with controversial studies which claim that it is harmful to teach standard arithmetic to elementary school children, it did not teach any of traditional arithmetic methods familiar to those taught in other nations, or to parents with as little as an elementary school education, a serious problem addressed in a later edition.

Its goal was to help all children understand the fundamental ideas of number and arithmetic, geometry, data, measurement and early algebra. But many of these concepts are unfamiliar not only to parents, but also teachers and professional mathematicians who have never seen such an approach to mathematics before. As with other "standards-based" curricula, it was distinguished by the complete lack of presentation any standard computing methods, and a lack of congruence with any other standards-based mathematics series, as they were all developed using completely different alternative approaches to computation.

1 Basic Skills Added
2 Abandonment
3 Research
4 Critical Reviews
5 Parody
6 Adoptions
7 External Links
8 Notes

[edit] Basic Skills Added

In response to shrill criticism, Investigations has now released its second edition for 2006 that has included its core values of teaching for understanding. Recognizing the mistake of omitting basic skills from the curriculum, it now has a strong emphasis on basic skills and computation. It is also easier for teachers to use since the format is more user friendly. Many teachers who have felt the need to supplement the original curriculum will find the second edition ideal. ^[1] Supporters concede it was weak on algorithms and the basic facts, and parents couldn't help the kids because there was no textbook. The new edition includes a handbook for students and families. This book is referenced by lesson for use for activities and homework.

[edit] Abandonment

The original version remains widely used by thousands of youngsters with its problems unremedied, and its critics largely reject the NCTM standards entirely as a mistake. Many school districts and states have already abandoned Investigations in favor of traditional mathematics texts such as Singapore Math or Saxon Math in response to very low test scores, which many have blamed on adoptions of texts such as Investigations. In November 2005, Utah lawmakers ordered a study of the math curriculum in response to complaints about texts such as Investigations. As a result, Investigations has been eliminated from a process which will select one traditional mathematics method and one standards-based mathematics text. It is scheduled to be removed from classrooms by the fall of 2007 in the Alpine School District, where it was already degraded to less than half of the mathematics instruction content.

The Dale Seymour imprint, which was the initial publisher of Investigations has also abandoned Investigations in favor of selling Modern Curriculum Press, which is traditional mathematics, not aligned with the NCTM standards. It covers all traditional grade level math topics with short, simple investigation-free explanations of methods, has worksheets which take only minutes to complete alone rather than all night with the rest of the family. It is inexpensive enough for homeschool families, an environment for which Investigations is completely impractical. The original edition of Investigations had no student textbook. Its teacher's manual is a series of several softcover books which take up significant shelf space. Even advocates of Standards-based Education Reform such as Washington State's state superintendent Terry Bergeson have consented to an independent evaluation of programs like Investigations.

Connected Mathematics, another highly criticized math program built around the NCTM standards is the Junior High School follow-on to this series.

[edit] 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

Quoting from the TERC website, the studies of Investigations in Number, Data, and Space® indicate that:

Investigations students do as well or better than students using other curricula in straight calculation problems involving basic facts and the whole number operations.

Investigations students have a better understanding of number and number relationships than students working with more traditional programs.

Investigations works equally well with students at different achievement levels in mathematics.

Students who use Investigations achieve greater accuracy on word problems and on more complex calculations than students in comparison classrooms.

Students in schools fully implementing Investigations outperform students in schools not using Investigations (or other NSF-funded elementary mathematics curricula) on a the MCAS high stakes standardized test administered in Massachusetts.

[edit] Critical Reviews

Investigations, also known as TERC has also been one of the most frequently cited as being an especially poor standards-based mathematics texts, and the object of popular protest as harmful to their children's education. Complaints are that children spend a lot of time coloring and circling, and many basic arithmetic skills such as regrouping, long division, or computing a mean are either not taught, or explicitly discouraged by the teacher instructions.

Some unusual 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^[2]

A common parent complaint is that there is no recognizable arithmetic, and homework is frequent and very time consuming, with some tasks requiring considerable cutting and pasting and coloring, and the assistance of parents or other family members. By contrast, the "drudgery" of a worksheet only takes a few minutes.
A second grade unit on addition provides sheet music for the song Happy Birthday. Investigations places a high value of multiculturalism, so it also instructs the teacher to ask students to sing it in their own language, though no words for any other language are provided. Elementary school teachers who are not music teachers mostly cannot, and are not expected to be able to read sheet music. There is no instruction on traditional regrouping methods.
There is no muliplication table presented. Instead, students are instructed to color in multiples of numbers on a 100s chart, or to draw and count tally groups, an extremely inefficient method of computation.
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 used in industry in organizations such as NASA or Boeing.
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.
A white paper contrasting the standard borrowing method against "invented" methods shows that a second grade student who uses the standard method introduces an error, while a student who deeply thinks about the process uses the property of negative numbers gets the correct answer. Investigations does not introduce negative numbers in the second grade, and it is a concept not traditionally introduced until after elementary school.
The teacher is instructed that the notation for long division is "no longer used by mathematicians". The teacher is also instructed that the student may use any notation for remainder except for the letter "R" (which is the traditional usage).
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.

[edit] 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.