TERC 2008 misdirects students and fails to provide the "foundations of algebra"

In Uncategorized on April 24, 2008 at 12:29 pm


A major objective of elementary math education is to provide the foundations for algebra, the gateway to higher math education. Although we call it “elementary math,” K-5 math content is quite sophisticated and not easy to master. But constructivist math educators believe that concrete methods, pictorial methods, and learning by playing games are the keys to a stress-free approach. This is the approach found in the second edition of TERC’s Investigations in Number, Data, and Space (TERC 2008). Unfortunately, as we will explain below, TERC has achieved their “easy to learn” objective by eliminating the content that’s necessary for later success in algebra. What is this necessary content? That question has been at the heart of the “math wars” debate. For many years opposing sides have failed to communicate. But a 4-year search for common ground has now reached consensus. The March 2008 Final Report of the National Mathematics Advisory Panel (NMP 2008) clearly identifies the “Critical Foundations for Algebra.” The primary purpose of this paper is to show how TERC 2008 misdirects students and fails to provide the “foundations of algebra” K-5 math content identified in NMP 2008.

The complete set of TERC 2008 5th grade materials, provided by NYCHOLD, served as the primary source for this paper. The reader will find a much more limited view by clicking on TERC 2008 Curriculum by Content and following links to PDF documents. Some of these links will be given in context below.

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  1. My daughter, now a 9th grader, spent the last three years at BF where she received solid Bs in math each grading period. On a hunch, we had her tested in basic Math skills last summer to see if she was prepared for high school-level math. We were shocked to discover that she knew virtually nothing. Thanks to the combination of a poor curriculum, lazy teaching and grade inflation that didn’t identify obvious problem areas, she will never catch up. She doesn’t now, nor will she ever, attend RW public schools. From my experience, I think I can state confidently that the biggest challenges for change are in the middle schools, where the brains of smart kids are allowed to turn to mush.

  2. No pain, no gain as they say. Regina B. please crawl out from under that desk of yours and slay the evil you’ve launched on out town.

  3. I wonder how our middle schoolers would do taking a math test given to the average child in the Netherlands, Singapore, India or japan.

    I would guess they would do rather poorly, don’t you?

    Time for Ridgewood to get it’s act together.

  4. Conclusions from the same source:

    Faced with TERC 2008? A Compact Guide for Parents

    The major objective of this paper has been to arm parents with the specific information needed to effectively oppose the implementation of TERC 2008. Short of that, this information should help parents achieve maximal class time for the mastery of standard arithmetic. Remember the following points when you communicate with those who control your child’s math education.

    NMP 2008 is very clear about the foundations of algebra. Mastery of standard arithmetic is essential.

    Mastery isn’t possible without practice. TERC provides no practice for standard arithmetic.

    Suggest that Singapore math materials be used as a supplement. Singapore textbooks and workbooks are great for practice and the textbooks offer a clear, child-friendly development of elementary math ideas. And they’re reasonably priced!

    The National Council of Teachers of Mathematics (NCTM) is now clear about the fundamental importance of standard arithmetic. In their 5th Grade Focal Points, they say that 5th grade students should develop fluency with “the standard algorithm for dividing whole numbers” (long division). Also, they should learn to “represent the addition and subtraction of fractions with unlike denominators as equivalent calculations with like denominators” (convert to a common denominator). And they “should develop proficiency with standard procedures for adding and subtracting fractions and decimals.”

    TERC knows this! The 5th grade NCTM Focal Points are found on page 109 of the TERC 2008 5th Grade Implementation Guide for Teachers. TERC offers a table that indicates where these topics are (supposedly) covered in TERC 2008.

    TERC promotes the weaker “fluency” for single digit number facts. You want your child to know these facts automatically, without conscious thought. You want instantly known, not quickly figuring it out.

    TERC promotes “mental math” methods and the use of calculators. They offer one “general” whole number computational strategy for addition, subtraction, and multiplication. Relative to the standard algorithms, TERC’s alternative methods more openly reveal underlying place value details. The price for this “transparency” benefit is significantly reduced computational efficiency. The TERC alternatives also reduce the need for carrying and borrowing. But TERC is not satisfied with reducing the need, they want elimination of the need. The price for this “total avoidance of carrying and borrowing” benefit is significantly reduced generality. TERC must carefully limit to special case problems to achieve this objective. As we’ve noted above, TERC doesn’t want to admit the special case limits, so we get the suppression of the embarrassing carrying and borrowing details. We also see borrowing avoided by the premature introduction of negative numbers and integer arithmetic. Somehow these advanced concepts are easier than the important concepts of carrying and borrowing.

    On page 74 of the TERC 2008 5th grade Teacher’s Guide for Unit 7, a “Math Note” includes this quote: “just as students may use standard algorithms for other operations, they may use long division to solve division problems.” Key point: TERC says that students may choose to use the standard algorithms for all operations. TERC also says that each student should choose their own computational methods. This primacy of personal choice philosophy was also promoted in TERC’s first edition, but teachers were then advised how to discourage choosing a standard algorithm. With TERC 2008, the attempt to discourage may still be present, so parents should make sure that their child can explain carrying and borrowing. Have them ready to explain for simple problems, such as 28 + 14 and 54 – 27.

    TERC misleads students when they they attempt to suppress the concept of common denominator and when they suggest the use of a calculator to convert 1/4 to 0.25.

    TERC dwells on concrete and pictorial methods. At most, such methods may be helpful to demonstrate an idea, but they have no long term value. Children need to move to abstract level, sooner rather than later.

    TERC emphasizes the use of calculators. But easily acquired calculator skills will not help when it comes to learning algebra.

    Bill Quirk is a graduate of Dartmouth College and holds a Ph.D. in Mathematics from the New Mexico State University. He co-authored The State of State Math Standards 2005, a report published by the Fordham Foundation. For more of Bill Quirk’s essays, please visit wgquirk.com.

  5. 833, 1125 and 1127 then why did you vote for brogan and goodman ? You get what you vote for perhaps the fuzzy math clouded your judgement

  6. Thank you 8:23 for sharing your story. Maybe its time for more of us to do the same. The carefully gathered, expertly presented research did little to sway those who believe there is no problem with the math. Maybe if a line of people got up at a meeting and presented flesh and blood case stories of children the system has failed people would begin to sit up and take notice

  7. It’s not just about TERC!!! Get this through your head. BF is failing. GW is failing. Where do most of the kids who go to these places attend high school? Sooner or later RHS will implode under the weight of the remedial education programs necessary for
    9th graders. And then we’ll be in bigger trouble.

  8. Both BF and GW have recently abandoned more traditional math programs for Connected Math (CMP). CMP is the constructivist-type middle school curriculum designed to dovetail with the TERC and Everyday Math curricula used in grade schools. I suspect this is a big reason for the downturn some are reporting.

  9. Easy approaches make learning math hard
    Forget real-world examples. Teaching abstract concepts works best
    By Julie Steenhuysen
    updated 5:28 p.m. ET, Thurs., April. 24, 2008
    CHICAGO – Frustrated math students may have a good excuse — some of the teaching methods meant to make math more relevant may in fact be making it harder to understand, U.S. researchers said on Thursday.

    They said students who were taught abstract math concepts fared better in experiments than those taught with real-world examples, such as story problems.

    Adding extraneous details makes it hard for students to extract the basic mathematical concepts and apply them to new problems, they said.

    “We’re really making it difficult for students because we are distracting them from the underlying math,” said Jennifer Kaminski, a research scientist at Ohio State University, whose study appears in the journal Science.

    The findings cast doubt on the widely used practice among elementary and middle schools in the United States and elsewhere of using friendly, concrete examples to teach abstract math concepts.

    For example, a teacher might use a bag of colored marbles to explain probability, or teach a formula about distance with the classic example of two trains departing from different cities and traveling at different speeds.

    “The danger with teaching using this example is that many students only learn how to solve the problem with the trains,” Kaminski said.

    To find out the best methods of teaching basic math concepts, the researchers conducted several experiments using college students in which some students were taught concepts using basic symbols, while others were taught with concrete examples.

    For example, they studied different approaches at teaching the basic mathematical property of commutativity — that you can switch up the order of elements and still get the same answer, as in 3 + 2 or 2 + 3 equals 5.

    Some students learned the concepts using generic symbols. Others were taught with concrete examples such as pictures of measuring cups filled with liquid, or slices of pizza or tennis balls in a container.

    While all of the students were able to master these concepts easily, the students who first learned math concepts using abstract symbols were better able to transfer that learning to other problems when tested.

    That is not to say story problems should disappear. Kaminski said story problems offer a good way to test whether a student has mastered the abstract concept.

    “Story problems aren’t out, but they are probably not the way we want to go about introducing concepts or problem solving,” she said in a telephone interview.

    “That would be best done through symbolic math.”

    Copyright 2008 Reuters. Click for restrictions.
    URL: http://www.msnbc.msn.com/id/24299980/

  10. Duh!

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