“One of the most salient features of our culture is that there is so much bullshit. Everyone knows this… But we tend to take the situation for granted… (the bullshitter) does not care whether the things he says describe reality correctly. He just picks them out, or makes them up… (Bullshitters) continue making assertions that purport to describe the way things are but that cannot be anything except bullshit.” ~ Princeton professor emeritus, Harry Frankfurt, 2005 Bestseller, On Bullshit

“[The] erroneous assumption is to the effect that the aim of public education is to fill the young of the species with knowledge and awaken their intelligence, and so make them fit to discharge the duties of citizenship in an enlightened and independent manner. Nothing could be further from the truth. The aim of public education is not to spread enlightenment at all; it is simply to reduce as many individuals as possible to the same safe level, to breed and train a standardised citizenry, to put down dissent and originality.” ~ H.L. Mencken, 1924

Think Nice’s brilliant 5-minute artistic frame for Professor Frankfurt (although there’s likely more to climate change than he mentions [and here, here]):

Stephen Colbert’s 2005 two minutes on truthiness as *bullshit*’s brother (embedding forbidden by Comedy Central).

This 12-part series addresses an overarching fact about public education: its design of intentional curricular lies of omission and commission to keep our children and the general public powerless, relatively stupid, and controlled work animals.

Importantly, I do not blame education professionals working in good-faith effort to produce high-quality learning from our children; public education exists in a matrix of control for ongoing empires that I’ll explain in detail within the series’ sections. That said, anyone truly educated in one’s field gradually discovers that public education is a ridiculous substitute for what’s most important to teach and learn. This is *Emperor’s New Clothes* obvious when pointed to, with this paper’s content including factual assertions that no counterarguments exist outside of shallow and misleading bullshit.

The 12 sections (links to be added as the series progress):

** US public education: Bullshit to train stupefied work animals**:

** ****

**Mathematics so-called ‘real-world’ problems are lie-conceived trivial puzzles condescending to professionals; totally failing to count what’s most important in quality, money, time (5 of 12)**

Let’s consider just three examples to prove that public education mathematics is bullshit. As a credentialed mathematics teacher, I will attempt to model math’s ethical use. Therefore, to begin, please review our definition of *bullshit* if that’s helpful to clearly grasp what we’re discussing.

Our three examples:

- The definition of mathematics.
- ~99% of adults never use algebra, trigonometry, or calculus at work or home.
- Fundamental text lies that their problems are “real-world.”

Let’s also consider three questions about our topics, that I’ll revisit with you at the end of this section:

*What does it mean that the term mathematics is not given a definition in our children’s texts, with its importance clearly communicated?**What does it mean about the choice of mathematics classes of algebra, trigonometry, and calculus when ~99% of adults (and children) never use it at work or home?**What is the intention of text authors to claim “real-world” problems when even the most cursory analysis demonstrates these authors didn’t look in the real world but prefer puzzles almost all humans find no value in solving?*

**Example 1:**

**What in the x is the definition of mathematics?!**

The two algebra texts I have at home do not have a definition of *mathematics*, do not list it the glossaries, and do not have it on their indexes. That is, students are introduced to their algebra course without context as to what mathematics is, and why it’s important to learn. These two texts also do not define *algebra*, nor list it in their glossaries or indexes.

On its face, this omission is inexcusable.

*Prima facie* data show that something important is missing from public education of algebra as up to half the students fail this class in urban high schools. And, in this revealing *NY Times* article titled, *Is algebra necessary?*:

- Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math.
- a typical faculty report: “failing math at all levels affects retention more than any other academic factor.”
- A national sample of college transcripts found mathematics had twice as many F’s and D’s compared to other subjects.

At the relatively low-performing high school where I teach in Northern California, over 50% of students fail algebra the first time they take the class (my fail rate is typically less than 10%, and ~5% at this school).

Importantly, completing math requirements in order to graduate is connected to lifetime work earnings: **trade school and college graduates earn ~ one-to-two million more dollars** over their careers compared with students who do not earn those skills. This means that if you add total job income until age 65, a person who invests in well-paying trade school skills (plumber, carpenter, auto mechanic, etc.) or college will earn on average over a million dollars compared to a person with only a high school education.

The profession of mathematics currently has no clear definition. Perhaps they need at least one to present to public school children. At least these text authors should be honest enough with students, families, and our communities of the *reasons why* they don’t provide even a definition of the academic area or the course title.

The omission of this usual practice to define what one is working on seems to be bullshit. This becomes especially clear when contrasted with an obvious overview something like:

“**Mathematics is the language of reality.** Science is the study of reality, with public school emphasis on biology (Life), chemistry (elements composing reality), and physics (mass, motion, energy). Public school mathematics begins two of its branches: algebra (math’s structural language) and geometry (shape). The big picture is for human understanding of reality, which includes its mathematical structures expressed algebraically. That is, we want to fully understand nature’s designs. To combine your two branches with two further areas of mathematic consideration as an overview for what we’re trying to do:

*Algebra is the language of shape*. Childhood education uses algebra to communicate straight and curved lines’ positions and degree of curvature (slope at any given point). Calculus, the pinnacle high school math course, is an algebraic language of slopes within curves, and areas and volumes within defined sections of simple shapes.*Geometry is the study of shape*. Childhood education studies simple shapes’ algebraic expressions, 2-dimensional areas, and 3-dimensional volumes. Trigonometry is a geometric use with historic grounding in astronomy to mathematically express our place in the larger reality.*Mathematical analysis could be defined at your level as the study of change*. That is, if we expand our view for math’s use to understand 1, 2, and 3 dimensions of measurable reality*over time*(which at beginning levels we can start thinking as a 4th dimension of reality), to what use is mathematics to describe and understand the world we apparently live in: a 3-dimensional reality in motion? Calculus can be considered an introduction to mathematical analysis.*Number theory*expands the type of “counting” you’ve learned to ask fundamental and essential question if we want to know reality:*how does nature count? What does nature count?*

So, **what is mathematics, and what is it good for? **In humanity’s quest to understand nature/reality, algebra is our attempt to decode reality’s mathematical structure, geometry is our study of nature’s shapes, with further areas of study that consider how we can mathematically express reality within the concept of time AND to look for what nature is counting and how she counts!

If we get good at this, we can decode the algebra of nature, like the equations for an octopus, a strawberry plant, and the DNA instructional language to regrow a human arm (as we know exists in the mathematical and geometric DNA for some animals).

Pause for a moment and reflect that DNA can be precisely described in its mathematical sequencing and 3-D geometrical form.

The benefits of mastering mathematical language seem to include tapping into the “free energy” of reality (planets never get “tired” of orbiting a star, nor electrons orbiting a nucleus), and what a founder of calculus (Sir Isaac Newton) spent half his life to discover: how mathematics can be applied to “add or subtract” from one element to achieve another (alchemy). If we can communicate this math into matter, we can imagine the potential of what Sir Isaac concluded was possible: matter replicators as in *Star Trek *to construct whatever we wish to communicate.

If science is the study of reality, and mathematics is reality’s language, a full understanding of both opens nature for our full embrace of its design with optimal engagement of our relationship within reality.”

Although the above definition could inspire students, you’ll never see anything like it in the current *bullshit* environment meant to conceal ongoing illegal rogue state empire, as we’ve discussed in this series (and this series if you’d like more).

My definition for public school students:

Mathematics:the language of reality to improve performance.

Does this definition match how most people use math? Let’s look at our next example.

**Example 2:**

**~99% of adults never use algebra, trigonometry, or calculus at work or home**

Whenever an adult comes into my teaching classroom of math, I ask as politely as I can if he/she can recall anytime in Life where algebra, trigonometry or calculus was needed to solve a real-world problem.

To date, only one adult said yes: a school counselor to help construct student class programming. All other adults have answered they can’t recall such a time ever in Life. Most need assistance to not be embarrassed in making this admission, with my students trained to see if they notice any fear of the adult to answer such a simple question. Most adults are both embarrassed *and* afraid; we’ll consider possible reasons why in this section.

I’ve never needed algebra, trigonometry, or calculus in my real-world life outside of doing these problems with students at a desk, on 2-D paper, without any of us then using that work to produce or perform anything.

I’ve never witnessed another human being using that advanced math to solve any real-world problem. Perhaps I wasn’t paying attention. My father was a mechanical engineer who said he used a few formulas. My wife is a computer systems engineer who says she never uses these particular math skills. I do know a few rocket scientists who work at JPL, but we’ve never needed advanced math in our interactions.

How about you?

My students are challenged to understand the purpose of a year-long class when in the history of my teaching no student has ever reported using algebra, trig, or calculus, ever needing it, or ever seeing anyone else needing or using those skills.

I ask my students what they think this means that they’re meant to learn a subject that from their life experience they’ve never seen necessary. The most common answer after genuine reflection: *This math must be bullshit.*

Although it takes a while in the art and science of communication, I tell my students of a few instructors of math teachers:

- John Bennett at a TED talk who concludes that algebra and higher math courses should not be required because of the obvious disconnect between course content and the real-world life of students that show 99%+ will not ever use higher math content. This translates to our 2,000 student high school to only 20 students. He does conclude, as I do, at present this path is necessary for monetary benefits.
- An instructor of math teachers I observed (no video I could find) as the only one who told the truth regarding the typical student question: “When will I ever use this (algebra, trig, calculus)?” Our answer: “Probably never.” This instructor’s follow-up is that the abstract math we teach is similar to the benefits of weight-lifting for a sport: a non-direct exercise that improves real-life skills.
- These two TED talk math instructors (here, here) who highlight research that mathematics as taught causes a dumbing-down and math anxiety for more people than it helps. That is, public school math instruction harms more people than it helps to count what’s most important in life, and interact with reality in confidence to quantify and upgrade real-world performance. Combined with our statistic that only ~20 of our school’s students will use this type of math, perhaps it should be an elective class.

I tell my students that they use math multiple times every day to keep track of reality, and to improve their performances. This usually involves basic counting to tell us how much of something exists, but not algebra and higher math content. The everyday counting using math includes work, money, time, and hobbies. Mastery of math allows creativity and power to:

- Observe and creatively apply basic statistics to measure performance, with intent to upgrade measurable performance.
- Move a countable amount of work to zero powerfully and efficiently so we have more free time at our creative command.
- Count money to successfully plan for the future, and live intelligently in the present.
- Play more enjoyably and successfully by understanding basic statistics (such as baseball batting average, soccer team winning percentage, how much of something must be accomplished to move to the next level of a video game, etc.).

The good news about math is that real-world applications for most adults is exactly what’s described above, and exactly what people of all ages practice in life. It’s as simple as understanding a school grading scale (90% = A, 80% = B, etc.).

Again, my father was a mechanical engineer, my wife is a computer systems engineer, my older brother does research in psychology, and my younger brother and I teach math. All of us agree that math teaches clear thinking to solve real-world problems, *and* none of us can recall one single instance we’ve solved a real-world problem using calculus, trigonometry, algebra beyond calculating a percentage, or geometry beyond making a scaled drawing to represent 3-D reality fairly accurately (certainly never anything like the *Tangent-secant circle theorem *or other geometric proofs).

That said, we all do use these skills, and see that most people would want them:

- Work until a problem is completely solved.
- Accept our human brain’s condition to be confused, and then take a problem one step at a time by drawing pictures and/or talking our way through the problem with someone.
- Use math to play more effectively by knowing how to add “points on the scoreboard.”

Precisely: science and engineering use math formulas relating to their area of study to understand how those realities function. If students proceed in those directions, they’ll be among the few using the math we now study, at least as a foundation to measure performance.

The stated purpose for mathematics in the California State Framework, Introduction, pg. 2:

Mathematics impacts everyday life, future careers, and good citizenship. A solid foundation in mathematics prepares students for future occupations including the fields of business, medicine, science, engineering, and technology. Students’ understanding of probability and the ability to quantify and analyze information enables them to interpret economic data, participate in political discussions, and make wiser personal financial decisions. Mathematical modeling is a tool for solving everyday problems, making informed decisions, improving life skills (i.e., logical thinking, reasoning, and problem solving), planning, designing, predicting, and developing financial literacy.

Connected to this purpose for math, I took an economics course at Harvard from Richard Murnane, who conducted research to answer the question, “What are the most important skills a student can learn that is most-linked to earning work promotions?” The answer he found: 1) Understand and speak the statistics that measure the business’ performance, 2) Be able to write a brief on aspects of the business, 3) Be able to speak a brief on the same. All three of these skills are founded upon math to measure performance, with the goal of improvement.

In my particular classroom, we also consider this definition, given algebra appears from our real-world observations as a type of desk puzzle disconnected from what ~99% of us see performed in the real-world:

algebra:counting, but there’s something you don’t know that you have to count.

We also consider math as a language, and as any language when you can point to the thing and say the right word, you have a good chance of understanding what is asked. We also consider algebra as puzzles that become easy when one can point to the symbolic language and say what the puzzle is asking us to perform.

Importantly, this abstract math can be translated into powerful applications if, and only if, the student has that intention. For example, consider the example of Abraham Lincoln; considered one of the most powerful writers and speakers in human history. He is remarkable for communicating much with few words, as in the Gettysburg Address. Abe credited his ability to demonstrate facts from his study of geometry; specifically from the most famous textbook in history: Euclid’s *Elements*. From a biography of Lincoln, Abe explains using the powerful skill found in geometry to *demonstrate* why an idea is factually accurate:

“In the course of my law reading I constantly came upon the word

demonstrate. I thought, at first, that I understood its meaning, but soon became satisfied that I did not. I said to myself, What do I do when Idemonstratemore than when Ireasonorprove? How doesdemonstrationdiffer from any other proof? I consulted Webster’s Dictionary. They told of ’certain proof,’ ’proof beyond the possibility of doubt’; but I could form no idea of what sort of proof that was. I thought a great many things were proved beyond the possibility of doubt, without recourse to any such extraordinary process of reasoning as I understooddemonstrationto be. I consulted all the dictionaries and books of reference I could find, but with no better results. You might as well have definedblueto a blind man. At last I said,–Lincoln, you never can make a lawyer if you do not understand whatdemonstratemeans; and I left my situation in Springfield, went home to my father’s house, and stayed there till I could give any proposition in the six books of Euclid at sight. I then found out whatdemonstratemeans, and went back to my law studies.”

** Therefore**, in consideration of public education teaching of mathematics as bullshit distraction from real-world skills: this non-defined subject that is the greatest cause of education dropouts contains content ~99% of humans never use and never apply outside of on-paper and at-desk puzzles, yet is required in most schools for students to memorize from one chapter to the next, and one year to the next. Of course, students and adults forget this math content almost immediately with a reality that a school’s non-math teachers and almost all parents would fail the higher math assessments we give our children because such course content isn’t used, isn’t important, and isn’t fun enough to practice in our real lives.

Keeping in mind our definition of bullshit, public education of math is somehow lies of omission and commission to obfuscate reality and debilitate children from creative power.

This is most clearly demonstrated in our next section.

Paradoxically, students report that this context for teaching and learning mathematics is the most helpful they’ve received in their education, with reports of relief to finally receive the truth, calmness to view and solve these on-paper desk problems for the relatively easy puzzles they are, and renewed enthusiasm to engage in what’s important to learn for genuinely improved lives.

To consider the math skills learned from public education do not transfer well into other ways of thinking, experience this for yourself in this 3-minute test:

**Example 3:**

**Tragic-comic unreal word problems claiming to be “real-world”**

We’ll consider just three examples from current texts, and student written responses of their conclusions after a year of studying an entire text that now is often over 1,000 pages. Please take a moment to consider the purpose of over 1,000 pages on these subjects, and to the extent students might be buried in this bullshit.

In my classes, we invest time for each section to carefully consider text authors’ claims that they present “real-world” problems, with an assessment question for student analysis of a text word problem.

**First:** from Algebra 1’s Module 22 quiz on *Using square roots to solve quadratic equations*:

Consider this claimed “real-world problem” on page 1038:

“A person standing on a second-floor balcony drops keys to a friend standing below the balcony. The keys are dropped from a height of 10 feet. The height in feet of the keys as they fall is given by the function h(t) = 16 t^{2}+ 10 , where (t) is the time in seconds since the keys were dropped. The friend catches the keys at a height of 4 feet. Find the elapsed time before the keys are caught.”Please self-express with at least three reasons why this is or is not “real-world.”

Let’s apply some analysis to what extent the text’s five expert authors and dozens of consultants/reviewers claim is “real-world.” In our class, we look at one such word problem together, students have another to do either on their own or with teams for a practice quiz, then a third on their own for an assessment. From my observations and student responses, ~99% conclude these types of math problems are not at all applicable to their interests and issues.

Student responses for this word problem included these observations:

- Does this person live in a mini Lego home? What second-floor balcony is only 10 feet off the ground when a person is standing on it?
- What is the point of doing this puzzle when the answer is like, “Maybe one second for keys to fall six feet?” How will this help me, and why should we care? All of these are the same: nobody cares what fraction of a second it takes.
- None of these math-hole authors ever did this, ever saw anyone solve this, and nobody thinks to answer something like this. This is a waste of time.
- A real problem is ending poverty or making sure everyone has health care. This is a distraction from what’s important to study.

**Second:** from Algebra 1’s Module 21 practice quiz on *Factors to solve quadratic functions:*

Consider this claimed “real-world problem” on page 993:

“A rectangular Persian carpet has an area of(x^{2 }+ x – 20)square feet and a length of(x + 5)feet. The Persian carpet is displayed on a wall. The wall has a width of(x + 2)feet and an area of(x^{2 }+ 17x + 30)square feet. Find the dimensions of the rug and the wall if(x = 20 feet).”Please self-express with at least three reasons why this is or is not “real-world.”

Student responses for this word problem included these observations:

- A real person would just measure the rug and wall. Nobody would invent an algebra puzzle to do this.
- I solved this puzzle and got a rug 25 feet by 16 feet. Does this real person live in a mansion? Hey – something real would be how to hold a rug that big on the wall. It’s going to be really heavy.
- Rugs go on the floor, not on walls.
- Who the function cares to do this problem to put a fake rug on a fake wall? The authors never saw this in the real world, and lie that it’s real.

**Third:** from Geometry’s Module 18 quiz on *Volume formulas*:

Consider this “problem” on page 952:

“Right after Cindy buys a frozen yogurt cone, her friend Maria calls her, and they talk for so long that the frozen yogurt melts before Cindy can eat it. The cone has a slant height of 3.9 in. and a diameter of 2.4 in. If the frozen yogurt has the same volume before and after melting, and when melted just fills the cone, how much frozen yogurt did Cindy have before she talked to Maria to the nearest tenth of a fluid ounce?”Please self-express with at least three reasons why this is or is not a “real-world scenario.”

Student responses for this word problem included these observations:

- What, Cindy’s too stupid to talk and eat at the same time?
- Does Cindy have super powers to balance the cone without spilling? So she’s just holding this filled to the top instead of throwing it out? Nobody does this.
- People buy frozen yogurt on sizes for what they want. They don’t measure to the nearest tenth of a fluid ounce. WTF (What the Function)?
- People care about real work or real problems like ending the stupid wars. Nobody would ever solve this problem in the real world.

For the final exam, I asked students their personal conclusions after a year’s consideration of such problems. Although I welcome such a response, to date no student has defended the text’s problems as real, with less than 1% finding them helpful in their overall learning. A few of their responses for why such claims of “real-world” word problems are in their texts:

“To keep us stupid and not think about real problems because they still want to have wars for resources and keep us all as work animals to have a majority of the money.”

“The “real world problems” that they give us is just a bunch of BS to keep us ignoring all the real world problems that they are causing to happen. They keep the real world problems just for them because if other people are wise enough they’ll get exposed to a big argument to the whole nation of why they are not doing anything to fix the problems.”

“These problems are not really real world problems. They are just stupid and unimportant questions. I feel people give these questions out because they don’t want us to be smart enough to figure out the real world problems which are the facts that the people in charge are stealing and killing from from others for themselves.”

“They are calling them “real-world” problems to maintain us distracted while they jack other places and kill people so kids won’t speak up because they don’t know what’s wrong around them. They manipulate people or even laugh at us because while they make money we are over here solving some dumb questions.”

“It’s complete bullshit that they waste our time with this, and they claim it’s real world? Wasting our time is one thing but lying to us and misleading us by claiming we will use this in real life instead of teaching us something that is actually useful is fucked up. They’re not even close to real world.”

These two students referenced a previous quiz problem that claimed a sporting goods store sold supplies for “cheese rolling.” We researched “cheese rolling” and watched this 2-minute video to verify there isn’t a market for such supplies. After watching the video, many students concluded the text authors are making fun of students with such “problems,” and “educating” them to be like Homer Simpson or SpongeBob:

“Those “real world” problems seem to be a distraction so you wouldn’t know when to actually use math. These problems are only teaching you to solve ridiculous questions that will never happen. The purpose of giving these “real world” problems is so they can cheese roll us.”

“We’re being cheese-rolled because or so we are distracted from the actual real-world problems. They don’t keep us updated on the homeless, all the behind-the-counter deals going on and all the millions of innocent people dying in Syria/Iraq as we speak.”

I also conclude that the purpose of public education is to cheese roll our students into tumbled lives of work and psychopathic entertainment of heartless “leaders” for ongoing empires. These ridiculous “problems” are insulting to those of us doing work in the real world, and stupefy our children from the purpose of creating value in reality. When asked, students overwhelmingly agree that the most important areas of life to apply math are topics that can help the most people living their real lives. They want a nice place to live, fulfilling time with friends and family, creative and valuable work, peace and cooperation, and to be inspired with a future that gets better and better.

The text so-called “real-world” problems are as real as Santa Claus and the Easter Bunny. Perhaps if the text devolved further to “document” those exploits, brainwashed supporters would argue:

- Ok, Santa isn’t real
*per se*, but students learn real-world skills and thinking by doing these problems! They learn about charity and being jolly, for example. - Some people work with animals, in cold climates, have night shifts or seasonal work, and have to travel a lot. That’s important for children to learn.
- We should be tolerant of fat people. Santa is a great model to teach this lesson. You should also have a well-engineered roof to hold extra weight.
- Regular chimney cleaning is important (this can be extended to any maintenance).
- Engineering is important for Santa’s sleigh. We can use parabolic equations for flights, and to calculate how long it would take Santa to drop from different chimney heights.
- Diversity in the work place is usual (little people in Santa’s workshop), artisan work has its place, and students should understand deadlines when work
*must*be completed. - Red isn’t always a gang color. Saying “Ho” isn’t always an insult. We should avoid knee-jerk reactions.

Math can, and should, help quantify what our real conditions are and provide a scoreboard for genuine upgrades. Those of us who respect real-world work do not waste time, do not hide the biggest problems, and do not lie about the real world.

But what about your conclusions? Our three reflective questions:

*What does it mean that the term mathematics is not given a definition in our children’s texts, with its importance clearly communicated?**What does it mean about the choice of mathematics classes of algebra, trigonometry, and calculus when ~99% of adults (and children) never use it at work or home?**What is the intention of text authors to claim “real-world” problems when even the most cursory analysis demonstrates these authors didn’t look in the real world but prefer puzzles almost all humans find no value in solving?*

******

*Note: **I make all factual assertions as a **National Board Certified Teacher** of US Government, Economics, and History, with all economics factual claims receiving zero refutation since I began writing in 2008 among **Advanced Placement Macroeconomics** teachers on **our discussion board**, public audiences of **these articles**, and **international conferences** (and **here**). I invite readers to empower their civic voices with the strongest comprehensive facts most important to building a brighter future. I challenge professionals, academics, and citizens to add their voices for the benefit of all Earth’s inhabitants.*

**

Carl Herman is a National Board Certified Teacher of US Government, Economics, and History; also credentialed in Mathematics. He worked with both US political parties over 18 years and two UN Summits with the citizen’s lobby, RESULTS, for US domestic and foreign policy to end poverty. He can be reached at Carl_Herman@post.harvard.edu

*Note:** **Examiner.com has blocked public access to my articles on their site (and from other whistleblowers), so some links in my previous work are blocked. If you’d like to search for those articles other sites may have republished, use words from the article title within the blocked link. Or, go to** **http://archive.org/web/**, p**aste the expired link into the box, click “Browse history,” then click onto the screenshots of that page for each time it was screen-shot and uploaded to webarchive. I’ll update as “hobby time” allows; including my earliest work from 2009 to 2011 (blocked author pages: **here**, **here**).*