New Math? Fuzzy Math? Fluffy Math!

[BuddhaRhubarb]

What is the typical US math curriculum like?

For me, it was the basics for 1st-5th grade.  Pre-algebra and geometry for 6th-8th with Algebra 1/2, Geometry, Algebra 3 and Trigonometry courses through high school.

Sounds about the same as we had.

[Pishtaco]

That second example is how I do it too. And I like the idea of encouraging making estimates.

[Ed Anger]

Yep, Catholic or private school is looking better and better in about 4 years.

[DisturbedPervert]

The second is ok if you're doing it in your head. 

[PDH]

I had calculus in high school, and I tested out of the first semester of university calc...  Then I went into history.

[CountDeMoney]

That second example is how I do it too. And I like the idea of encouraging making estimates.

Fag.  2 + 2 = 5 does not deserve a ribbon.  Asshole.

[Pishtaco]

That second example is how I do it too. And I like the idea of encouraging making estimates.

Fag.  2 + 2 = 5 does not deserve a ribbon.  Asshole.

My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.

[Iormlund]

I'm all for making concepts the prime target in maths.

I've met an awful lot of engineers that were able to memorize definitions and solve equations well enough to get their degree, yet can't solve problems in the real world.
I don't fucking care if you can ace an exam, if you are unable to create something new, you are worth nothing. I don't know if you can train kids for that, but it's certainly worth considering.

[garbon]

I had calculus in high school, and I tested out of the first semester of university calc

[The Brain]

Major Characteristics of TERC's Program: Investigations in Number, Data, and Space

   1. TERC insists on the ongoing use of hands-on tools (manipulatives, "models," and calculators).
          * They say concrete tools must always be available and regularly used.
          * TERC strongly rejects the idea that children must eventually migrate from hands-on to abstract thinking.
   2. TERC rejects the need for memorization and practice.
          * They say that student's familiarity with single-digit number facts must "grow out of lots of experience with constructing these facts on their own."  BA, Page 72   (emphasis added)
                             [Please click on  References for the meaning of the BA code.] There's no additional gain in conceptual understanding associated with the task of trying to "construct" one more basic number fact.
              o o TERC doesn't think it's possible to understand memorized information. But knowledge must first be loaded into the brain before it can connected to other knowledge and "understood."  Explicit memorization is sometimes the most efficient way to get it there.
                o TERC fails to understand that it's often desirable to move to automatic use of knowledge. The mind must be free to think at higher levels of complexity, without consciously revisiting underlying details. For example, the key idea of the standard algorithms is that multi-digit calculations are reduced to multiple single-digit calculations.  If children don't have instant recall of the single-digit number facts, they aren't equipped with the essential pre-knowledge for easily carrying out multi-digit computations.
   3. TERC fails to clearly define terms.
          * They regularly state: "We don't ask students to learn definitions of new terms."
          * They offer some "definitions," typically using multiple undefined terms to "define" a new term.
          * They favor "natural language" and "personal language."
   4. TERC emphasizes "familiar numbers."
          * The  "landmark numbers" are 5, multiples of 10, and multiples of 25.
                o Landmark number are also known as anchors.
          * The "familiar fractions" are limited to proper fractions with denominator equal to 2, 3, 4, 5, 6, 8, 10 or 12.  Thus 7 and 11 are not familiar denominators.  Perhaps TERC is opposed to gambling.
                o Note: 12 is included because it's needed for TERC's clock face method for adding fractions.
          * TERC doesn't believe in defining terms, so you won't find the preceding definitions in TERC materials.  This is what they appear to mean by these phrases.  We welcome their clarification.
          * Although TERC rejects explicit memorization of basic single-digit number facts, they expect students to remember many non-basic facts about landmark numbers and familiar fractions.
   5. TERC omits standard formulas.
   6. TERC emphasizes estimation and many right answers.
          * They suppress the concepts of precision and accuracy.
   7. TERC proudly rejects standard computational methods.
          * No standard algorithms for multi-digit computation.
          * No standard methods for operations with fractions and decimals.
          * No general methods for calculating with numbers.
          * TERC emphasizes special case methods involving landmark numbers and familiar fractions.
   8. TERC attempts to directly teach their shallow and misleading content.
          * They claim to offer a "constructivist" approach where students discover math as they play games and carry out investigations.  But they provide thousands of pages of teaching instructions and recommended scripts that identify the content they expect kids to "discover."
                o Thousands of pages for the teacher, but no text for the student.

Even the TERC manifesto doesn't seem to like it.

[The Brain]

I don't know which is the best way to teach math. As long as radically new methods are thoroughly tested before they are deployed all should be well.

I will however observe that the "teaching sciences" seem to be totally out of control. At least in Sweden students are several years behind their parents and grandparents when it comes to math. What used to be high school math has crept up into university courses etc. In other fields performance is usually increasing over time instead of decreasing. But in teaching? No.

[CountDeMoney]

That second example is how I do it too. And I like the idea of encouraging making estimates.

Fag.  2 + 2 = 5 does not deserve a ribbon.  Asshole.

My doctoral thesis was about the circumstances under which n+n can appear to be the same size as n, for n a suitably large number.

We're not talking doctoral theses here, Good Will Cunting, we're talking elementary level mathematics.  A 9 year old doesn't need to learn that n + n = "not really".   At their level, they need to know mathematics has a right answer, and a wrong answer, not an almost right answer.

[grumbler]

Even the TERC manifesto doesn't seem to like it.

I haven't seen the "TERC Manifesto" but Bill Quirk doesn't seem to like TERC! 

[grumbler]

That second example is how I do it too. And I like the idea of encouraging making estimates.

Indeed.  Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success.  If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.

Having said that, I am not a fan of TERC itself.  There are plenty of other programs that teach estimation and real-world problem solving that don't go as far as TERC from the need to actually memorize some aspects of arithmetic.

[CountDeMoney]

Indeed.  Estimation is not only a higher-level thinking skill (and thus useful in its own right) but essential to actual math success.  If one sticks to the CountDeHeadInTheSand method, students cannot recognize when they have reached mpossible andswers unless the teacher tells them.

4th graders aren't given problems with impossible answers.  And what's with all this "higher-level thinking"  and Pishtaco's PhD bullshit, anyway?  Can we all wait until they at least reach puberty before we teach them higher-level math already?