**Welcome to Cogitatus2**

*"Study hard enough to become Smart enough."*

*Some content on this page has been removed and reposted on Cogitatus3.*

*Click Cognitatus3*

**When education cowers to activism, racism, and radicalism, you are no longer talking about education.**

**You're talking about indoctrination!**Today, much of education is

**not**about teaching kids to read, write, do arithmetic or about achievement, merit, and excellence. Government schools advocate equity, diversity, identity, and inclusion. They are strongly supported by teacher unions, schools of education, federal and state departments of education, school boards, and others, including the

**media**. I believe education has gone down the rabbit hole, an

**abyss.**

*Commonly, there seems to be an*

**inverse relationship**between excellent academics and equity. The "equity" reformers have been dumbing down the curriculum for decades. 5-4-21

**✍️****The difference between school math and university math is proof, says**Ian Stewart

**.**We need to change from

**why**to how, explains Stewart, a mathematician, who writes,

*"*At

**school**, we learn

**how**to solve equations or find the area of a triangle; at the

**university**, we learn

**why**those methods work and prove that they do." Students are novices and need to grasp the how not "understanding" the why.

*Novices should not be doing proofs until college.*(Ian Stewart:

*Letters to a Young Mathematician*, 2006) 5-4-21

**---------**

**Trust the science. Follow the science.**

**Trust the media?**

**Really?**

*I never trust the media's narrative.*

**Science doesn't prove things right!**

**testable hypotheses**, then there is no way to show whether you are actually right or wrong," points out Youyang Gu, a superstar data scientist. Richard Feynman lectured students about confirmation bias and fudging the data to make it fit

**a narrative or political agenda.**

**Note:**

**-----------**

**Cognitive Science Summary**

*Linking new stuff to old stuff.*Cool!

**It's true!**The more I know, the more I can learn, the faster I can learn it, the better I can think and solve problems. WOW, isn't cognitive science great? Linking new content to old content in long-term memory is the backbone of Learning Science.

**Have educators or their leaders gone mad?**

**WOKE**

**Asian American**New Yorkers is the Department of Education's ill-disguised effort to

**eliminate merit test-based admission**to the city's eight highly selective high schools," writes Bob McManus for Fox News. Asian Americans, he says, "won 54% of this year's freshman seats." In contrast, only 5% (Hispanic) and 4% (African Americans) won seats. The elimination of merit is insane. These people are radicals and promote utopian ideas. In my opinion, the DOE ought to be thrown into the backyard along with the rest of the trash, like Critical Race Theory or Action Civics.

**Note:**I see the same thing in

**science textbooks**that promote an agenda, which is indoctrination, not science.

**The function of science is not to prove things right.**

*Science textbooks often state a correlation, even a theory, as fact.*

**1. Gone Mad 1**

**action civics**and

**Critical Race Theory**out of K-12," writes Stanley Kurtz. Teachers should focus on reading, mathematics, science, literature, history, and writing, not

**indoctrinating**students to be activists and militants by interpreting everything through the race prism. The problem starts in schools of education, explains Charles Buck, where "critical pedagogy is

**propaganda**attempting to pass as instruction." Stanley Kurtz points out that the government is "set to push critical race theory on U.S. schools." He writes, "The new Biden rule favoring education grants that push Critical Race Theory is a disaster for this country." (Click Kurtz)

**2. Gone Mad 2**

**cancel accelerated math**courses before grade 11 and call it

**equity**? Yet, this is what the Virginia Department of Education proposes, to rework the math pathway to one way. Why can't education focus on

**academics**? Everything seems to be about race, identity, and equity.

**Equity**is not the same as fairness, points out Thomas Sowell.

**Parents are furious**at the proposal for one math pathway for K-10! Such

**nonsense**drives parents out of the public school system.

**Understanding**(My understanding of understanding)

This whole thing about understanding disturbs me. **I don't understand understanding **because, like **creativity, it is a vague, nonspecific term and difficult to measure. **If you can't measure something, then what is it? A teacher said, "Yesterday when I was going over the problem **(-12ab) + 4ab** ... The kids said, 'Can you just work the problem?' They don't want to understand math; they just want the procedure and move on." (Comment: Combining like terms is a simple task. How does the teacher define understanding? I don't know. Did the teacher link combining like terms to prior knowledge? Kids are novices, not experts.)

Well, that's what Issac Newton did with his calculations (a.k.a **calculus**). **He moved on!** *He used the procedures even though he didn't understand why they worked.* Why? The calculus just worked! It agreed with experimental observations. That was good enough, but it took another 200 years "to hammer out the formal details," explain Klein and Bauman. (Limits)

**Note:** For novices, the act of performing or applying procedures implies some level of "understanding" that is difficult to quantify or explain. It is a **functional understanding**. Novice: At first, I "understand" something when I perform or apply it. For example, **3 x 4** = 4 + 4 + 4 or 12 is useful at first, but 345 x 876 needs "something more sophisticated" than repeated addition, says Ian Stewart, mathematician. "Mathematics builds new ideas on old ones." Stewart *(Letters to a Young Mathematician*, 2006, also points out the **practice does not cause talent, **but it can *improve performance*.

The next time a teacher says they stopped teaching long division because kids won't understand it, **Think, Newton**. Students can learn to do it and apply it, even if they don't completely understand it. How do you think students learn arithmetic, algebra, trig, and calculus? (With perfect understanding? Right?) The idea of division is easy and can be taught in 1st grade as intuitive division. The understanding of the standard algorithm takes repeated practice and time. To do the **standard algorithm for multiplication,** you should memorize basic **number facts**, such as 3 x 7 = 21 or 8 x 7 = 56, no later than the 3rd grade. (Half in the 2nd grade.) In short, children will not learn much algebra when they don't know basic arithmetic. My **Teach Kids Algebra** program fused algebra ideas to traditional arithmetic. *Hence, the importance of memorizing math facts that support basic arithmetic (e.g., standard algorithms) was emphasized. *

We are told that not understanding math stuff will result in poor algebra scores. It's mostly nonsense. Being able to perform arithmetic or algebra on paper indicates that the student has acquired some understanding, which is a functional understanding. I did not understand arithmetic, algebra, precalc/trig, or calc as well as I do today at age 78, yet, in college, I could apply the procedures correctly in chemistry and physics. Understanding grows slowly and is intertwined with the **mechanics of procedures** such as the standard algorithms and other operations such as "taking the opposite, finding the reciprocal, taking a root, and raising to a fractional power," etc. **You will not understand addition unless you can do sums efficiently, **in your head, or on paper by using standard algorithms based on place value. And you cannot do division of fractions without finding **reciprocals**, a mini functional procedure.

**Note:** "Symbolic reasoning and **calculations with symbols** are central in algebra." (California 1997 Algebra Content Standards) When symbolic manipulations are marginalized, it's "pretend" math, not algebra.

** ✍️ **Marxist radicals have taken over education at the local, state, and federal levels.

*The only way to close gaps, they say, is to lower content standards and eliminate excellence.*No child gets ahead. The radicals have redefined achievement as privilege, says Thomas Sowell.

**These are terrible ideas!**"Equalizing down, by lowering those at the top" is a crazy idea, a "

**fallacy of fairness,"**not equity, explains Sowell in his book of essays and his latest book below.

Credit: EmB |