## Reviews of TERC: Investigations in Number, Data, and Space

### Basic Information and Introduction

Investigations in Number, Data, and Space is a K-5 curriculum developed by TERC Inc., Cambridge, MA, and marketed through Pearson Scott Foresman (and previously by Scott Foresman – Addison Wesley and by Dale Seymour). The TERC Investigations Project Director is Susan Jo Russell and the project web site is www.terc.edu/investigations/. Pearson Scott Foresman has a Teacher Resources page for the Investigations curriculum.

TERC: Investigations in Number, Data, and Space is marketed (in 2002) as whole classroom units. The curriculum does not come with traditional student textbooks and workbooks. Instead, each year of the curriculum is sold as a box full of material: teacher guides for the year and for individual units, posters, overhead transparencies, manipulatives, work sheets, and assorted gadgets.

As an example of the composition of TERC Investigations, here is the list of student materials included in the Grade 5 package (valid in 2002). 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.

### Content Reviews

2008 TERC Math vs. 2008 National Math Panel Recommendations, by Bill Quirk, April, 2008. Bill Quirk reviews the most recent edition of TERC’s Investigations in Number, Data, and Space in the context of the report of the National Mathematics Panel which emphasizes the critical role of the K-7 curriculum in preparing students for traditional algebra. Key points of Bill Quirk’s critique (explained in more detail in the review) include the following.

*TERC’s nonstandard computational methods are substituted for the standard methods that children need to master to prepare for algebra.**TERC confuses children by claiming to offer several “strategies” for each operation. […]**TERC no longer claims that students “invent” these methods. Now they are “constructed” and “named” with the assistance of the teacher. Apparently every class chooses the same names. They’re really “standard” TERC 2008 names, but not standard elsewhere.**Generally speaking, the TERC computational methods are cumbersome, inefficient, and only work for carefully selected simple problems. They seriously mislead children because they attempt to avoid the concepts of carrying, borrowing, and common denominators.**Traditionally, children first experience the power of automaticity as they migrate up the elementary math learning curve. But there is no possibility for automaticity with the TERC 2008 methods. By attempting to suppress carrying, borrowing, and common denominators, TERC eliminates the keys to automaticity for basic arithmetic. Conscious thought is regularly required for both TERC method selection and TERC method execution. TERC’s authors are openly proud of this. They believe that maximum conscious thought indicates maximum conceptual understanding. They fail to recognize that automaticity at lower learning levels helps to maximize the effectiveness for conscious thought at higher learning levels.*

Mathematically Correct Second Grade Review of TERC [then Dale Seymour] Investigations in Number, Data, and Space. Some observations and conclusions: “Poor focus, lots of child centered discovery activities and no meaningful mathematical content. […] [T]he authors accept that some children, at the end of second grade, will still add and subtract by drawing pictures and counting, or by counting back and forth on a `100 chart.’ […] With the exception of some discussion of counting by 2’s, 5’s and 10’s, multiplication is not obviously introduced. […] This program is totally dedicated to discovery learning and away from mastery, depth, or any skill or understanding… There is nothing to recommend about this program.”

Mathematically Correct Fifth Grade) Review of TERC Investigations. Excerpts: “This program received the lowest rating of Mathematical Depth of the fifth-grade programs in this review. […] The quality of presentation for this program also received the lowest rating among the fifth-grade programs reviewed. The lack of a student text by the fifth grade contributes to this as it leaves students without such resources as a glossary or the opportunity to review prior instruction independently. […] Although there is a fairly reasonable number of student worksheets, the actual work expected is severely limited in depth and scope and is unlikely to support mastery of content.”

Mathematics Program Reviews Comparative Summary for Second Grade and likewise Comparative Summary for Fifth Grade, by Mathematically Correct. The previously cited MC program reviews of TERC Investigations are part of a comparative review of eight mathematics programs for both 2nd and 5th grade. For both grades two of the eight programs (Everyday Mathematics and TERC Investigations) are deemed to fall far short of the Mathematically Correct review criteria, and in both cases the Investigations in Number, Data, and Space curriculum is rated unambiguously the worst of all that were reviewed.

TERC Hands-On Math: The Truth is in the Details. An Analysis of Investigations in Number, Data, and Space by Bill Quirk. This is a detailed analysis of the mathematics in TERC’s Fifth Grade teaching materials. Bill Quirk writes: “But math is a vertically-structured knowledge domain. Learning more advanced math isn’t possible without first mastering traditional pencil-and-paper arithmetic. This truth is clearly demonstrated by the shallow details of the TERC fifth grade program. Their most advanced `Investigations’ offer probability without multiplying fractions, statistics without the arithmetic mean, 3-D geometry without formulas for volume, and number theory without prime numbers.”

TERC Hands-On Math: A Snapshot View, by Bill Quirk. This is a condensation of the previous reference.

Do NCTM Standards-Based programs prepare students for calculus? by Stanley Ocken, CUNY (June, 2001). The article focusses on the TERC Investigations K-5 curriculum and contrasts the style of mathematics found there with the mathematics that students will experience in college. Professor Ocken concludes that “[…] current efforts at reform are moving in precisely the wrong direction, by de-emphasizing the critical role played by symbol manipulation and algebraic fluency. Instead, curricular reform should acknowledge the importance of these skills and seek innovative and effective methods of helping students develop their proficiency in arithmetic and algebra. Educators and theorists must awaken to the reality that every calculus course requires its students to enter with a substantial reservoir of formal skills.”

Investigations In Number, Data, and Space (TERC) by Wilfried Schmid, Harvard University (June, 2001). Opening remarks at the NYC HOLD math forum at NYU. “A TERC teacher doesn’t explain, and a TERC teacher doesn’t teach! I don’t want to be misunderstood: group learning and discovery learning are parts of the tool chest of every accomplished teacher, but it is folly to turn these techniques into an ideology. If we mathematicians had to re-discover mathematics on our own, we would not get very far! And indeed, TERC does not get very far. By the end of fifth grade, TERC students have fallen roughly two years behind where they should be.”

A Partial List of my Objections to the TERC Investigations Curriculum, by Thomas Parker, Professor of Mathematics at Michigan State University. Professor Parker concludes: “TERC students will hit a wall, probably at the end of middle school. They are not being given the grounding needed to understand the abstractions of high school algebra and geometry. Their options for careers in science and engineering are being closed off by their elementary school program.”

### Additional commentary and local activism

Investigations Math Summary, by Oak Norton. “The core problem we face in Utah is low state education standards, especially for math. Investigations math and the set of curricula like it that encourage personal discovery of math facts are receiving a strong push into our schools by the state board. However, these curricula are all being condemned by hundreds of college professors and Nobel Laureates. They see what’s happening to our youth and are trying to avert a complete disaster in the future.” This web page is in connection with a petition to restore a rigorous math curriculum in Utah. There is also a summary flyer.

‘Innovative’ Math, but Can You Count?, by Samuel G. Freedman, The New York Times, November 9, 2005. Concerning the Math Wars over TERC Investigations and Connected Mathematics Program in Penfield, NY.

Presentation of a Mathematics Petition to Penfield (NY) Board of Education. “We, the undersigned, state that the Investigations, Connected Math, and Core Plus Math programs, recently implemented in the Penfield School District, do not teach the fundamental math skills that children must know to succeed in furthering their education. We therefore ask that a traditional math program be offered as a choice for all Penfield students.” The petition was signed by 671 Penfield residents 18 years of age or older. See alsoParents Concerned With Penfield’s Math Programs and the NYC HOLD summary page Controversy over Mathematics in Penfield, NY, Public Schools.

Mathematical unknowns. A Boston Globe editorial highly critical of TERC and the “constructivist” approach to teaching, Nov 8, 2004.

Somerset Elementary School Parents Concerned about TERC Curriculum. Letter to Bellevue (WA) superintendent Dr. Mike Riley, Jan 22, 2003.

An Open Letter to the Friends School of Baltimore community about their mathematics program, by W. Stephen Wilson (March, 2002). This letter is a plea for mathematics content in general, with special focus on TERC Investigations as this is the school’s K-5 mathematics program.

Damage to Mathematics Education by the NSF Education and Human Resources Directorate, by Wilfried Schmid, May 7, 2002. Email letter to Representative Nick Smith (Chairman, House Subcommittee on Research) and Representative Sherwood Boehlert (Chairman, House Committee on Science). The letter discusses the support for TERC Investigations as representative of the extreme approach towards education that has been consistently pushed by the NSF EHR Directorate.

2+2=5: Fuzzy Math Invades Wisconsin Schools, by Leah Vukmir (WiI, Winter 2001). The President of Wisconsin parent activist group PRESS (Parents Raising Educational Standards in Schools) describes parent reaction to the introduction of the TERC Investigations in Number, Data, and Space curriculum into a Wisconsin School District. Ms. Vukmir’s article also places the TERC curriculum in the context of the NCTM Standards and the NSF’s active sponsorship of constructivist mathematics curricula through staff development programs.

Making Education Fun, Creative – And Impossible, by Stephen M. Hollister (September 23, 2000). An Op-ed in the Providence Journal concerning the introduction of TERC Investigations in a local school.

New Battles in the Math Wars, by Wilfried Schmid. The Harvard Crimson, May 04, 2000.

Teach Utah Kids. Web site of a parent group in Alpine school district, Utah, concerned about curriculum. Their main concern is TERC Investigations in grade school and Connected Mathematics Project in middle school. Note especially their News Articlespage.

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