After falling down the rabbit hole and entering the garden, Alice encounters The Mad Hatter, The Dormouse, and The March Hare having a tea party. The tea party is characterized by switching places on the table at any given time, making short, personal remarks, asking unanswerable riddles and reciting nonsensical poetry. The encounter with these three characters is confusing. They contradict Alice at every turn, correcting her with confusing arguments that have their own strange logic.
During the seemingly nonsensical conversation, the Hatter asked Alice: “Why is a raven like a writing-desk?”
After some further conversation, attention was again turned to the riddle.
“Have you guessed the riddle yet?” the Hatter said, turning to Alice again.
“I haven’t the slightest idea,” said the Hatter.
Alice finally became frustrated and remarked: “At any rate I’ll never go there again!” said Alice as she picked her way through the wood. “It’s the stupidest tea-party I ever was at in all my life!”
Alice’s Adventures in Wonderland, Chapter VII: A Mad Tea-Party
You may be asking yourself what the mad tea party has to do with mathematics. I have been keeping up with some of the different ways and methods to teach mathematics, e.g., Common Core Standards, Singapore Math and Vedic Maths. All of the information on each of these methods is like the conversation that Alice had with the Hatter – confusing! Each teaching method has their pros and cons (see below), but some problems arise especially when first introduced, the parents are not told about the change and they are not taught the new method.
For example, Mr. Incredible gets exasperated trying to help his son with math homework. His son, Dash, holds up the textbook titled “New Math for Life” and tells his dad that he is doing the math wrong and he should do the math “this way.” Mr. Incredible yells, “Math is math!” This scene (see Videos below) strikes a chord with many parents because their children are learning to do math in ways that are unfamiliar to them. When they try to help, their kids exclaim that they aren’t doing math correctly. Parents ask, “If this method worked for me all my life, how could the method suddenly be wrong?”
Too many people think they know what is the right way to teach mathematics in K-12, but it turns out their way is like the question “Why is a raven like a writing-desk?” There is no answer. Each says that their way is the best. And many times the selected way is chosen to ensure federal and state funding of the school system which, in turn, demands standardized testing and causes teachers to teach for testing purposes. Frustrating for teachers and parents! I went through this with two of my children when they were in school.
I am not sure that there is a definitive answer to the problem because of the way that schools are currently funded, organized and the processes they use to teach. Also, the diversity of ways that math is taught in different schools, school districts, states, and in public and private institutions.
Note what one teacher stated about teaching school today1:
We have lots of bosses. Department heads. Principals. Deans. Superintendents. School boards. Vice chancellors. Boards of trustees. We also have people who think they’re our bosses, aka parents who show up at school board meetings to tell us “what your real job is.” They rant about mask mandates and critical race theory, even though they have no idea what that is. None of them teach. They have no idea what we do.Jessica Wildfire
All of them feel like they can tell us how to run our classes. They spend their time thinking about how to make us “better.” That usually comes in the form of more rules and micro-management.
My recommendation, that worked for me, is found in the editorial “Would you tell me, please, which way I ought to go from here?” I also stress throughout this website that I am a fan of the teaching philosophy of physicist Richard Feynman, and I urge each person to consider using The Feynman Technique in their studies.
Common Core Standards
What Are the Pros of Common Core?
- The standards of Common Core are internationally benchmarked.
This means that students who can meet the standards of Common Core will be able to compete on a global scale in terms of their education. The United States has fallen behind other developed nations in regards to education quality, so having Common Core standards meet or exceed the same standards that other countries use can make the US become more competitive.
- It creates professional consistency.
Before Common Core, many states in the US were able to set their own educational standards. Expectations could be very different from state to state, which meant teachers and other educators would need to learn new standards if transitioning to a different classroom or job in a different state. Common Core creates consistency in state standards, eliminating this issue almost entirely.
- Common Core allows districts to share costs.
With Common Core state standards implemented, it becomes possible for all districts in each state where it has been approved to save money on common tasks. Creating tests, scoring tests, and other grading issues are brought to the same standards, allowing each district in multiple states to share these costs instead of forcing a state-by-state standard that would limit cost-sharing to in-state districts only.
- It allows students with high mobility to receive a consistent education.
In the past, when students lived in families with high mobility, such as a military family, their education could be inconsistent due to the different standards in different states. For the states that have adopted Common Core standards, the studies of high mobility students match up better on a school-by-school basis, creating more consistency in the educational opportunities for them.
- It covers multiple skills in one package.
Much of the focus on Common Core tends to involve mathematics, but multiple skills are covered by these standards. Many of the standards evaluate multiple skills within each question, allowing for a greater development in critical thinking and problem-solving. Reading, writing, and other key subjects are still required and evaluated.
- Common Core allows for individualized educational opportunities.
Before Common Core, it was common for higher grades in the K-12 educational system to grade “on a curve.” This meant that students were compared to one another instead of being graded on their own individualized merits. Common Core standards make it possible for the teachers of a student to track their individualized progress throughout the year with greater detail, allowing for customized plans to be developed that can address any potential deficiencies right away.
- It creates more definition within learning expectations.
Students who are in a Common Core program have a better understanding of what they are learning and why they are learning it. Although the method of creating this understanding may seem confusing, especially to those who were taught within a different system, it does create faster opportunities to achieve a true understanding of each skill. In terms of education, an understanding is a better achievement than rote memorization.
- It has created a network of professional development for teachers and educators.
Teachers and educators are all essentially teaching the new curricula throughout the United States. This has led to a new network of collaboration and professional development that didn’t exist before. Some entrepreneurial teachers have even created business opportunities out of curricula development that others can implement in their classrooms.
- Learning is now based on empirical methods.
In the past, it was simply good enough for a student to come up with the correct answer. A smart enough student could look up the answer from a different source, write it down, and get their grade. With information access at its highest levels in history, Common Core forces students to do more than find the correct answer. They must also be able to show how they arrived at their specific answer and then be able to appropriately defend it.
What Are the Cons of Common Core?
- It forces teachers to focus on student performance and accountability.
Learning should be an individualized process, which is what Common Core attempts to address. The only problem is that it doesn’t address this from a teaching standpoint. Teachers are often graded on the test results their students are able to achieve. This grading can affect their salary, their placement within a school district, or even their employment and they have no control over which students they will have each year.
- This causes teachers to teach for testing purposes.
Because teachers are forced to produce testing results, it takes them away from the time they’d spend creating educational results. Students using Common Core standards are often taught the skill of meeting the standard instead of being taught practical educational skills. This makes it seem like students are performing as they should when there really could be several educational deficits present.
- It leaves students with special needs behind.
All students are tested under the same generalized standards under Common Core. This means a student with a specific learning disability or other special need is treated the same as a student who is in the district’s gifted and talented program. Although this provides a certain sense of equality between students, it also eliminates some of the individualization in testing that was present in prior educational standards.
- Common Core has caused teachers and educators to retire.
The extensive changes to the educational system that Common Core caused drove many of the most experienced teachers and educators into retirement or a different career. This isn’t because of the changes to how certain reading or mathematics concepts are taught. It’s also because many of the state standards that have been implemented are very broad and vague.
- Because of somewhat vague standards, some states have experienced educational declines.
Some states in the past had very rigid and high educational standards for their students. By adopting to the Common Core standards, they are forced to reduce the quality of their education in order to create more consistency on a national level. The goal of Common Core was to create an “average” between states, so those with low standards were raised, but at the expense of other states.
- It has forced textbooks to update due to standards changes.
The price of textbooks is one of the highest costs that a school district faces. Common Core standards forced an almost complete update to a district’s textbooks because it changed how skills were taught. All materials and curricula had to meet the new standards, which meant almost every district had a large expense to convert to this new system.
- Many of the assessments that are required in Common Core happen online.
This means school districts must have a certain level of technology incorporated into the classroom environment. The adoption of these standards forced some school districts to invest heavily into computers and other technologies that would allow students to access the internet just so they could be evaluated in their progress.
- It has created an environment of high stakes testing.
Students can over-perform in the classroom, but under-perform on the testing standards and be considered an “inferior” student. Because each student is judged on their testing performance and not on their actual educational skills that are used every day, their placement into future classes, college majors, and even vocational opportunities could be at-risk if they aren’t good test takers. Because the standards have become more consistent state-by-state, this issue is only going to become worse as more information becomes available.
- The results of Common Core are not showing fast progress.
Although the adoption of Common Core standards has been relatively quick, the outcomes being seen from this switch have not be as fast to arrive. Between parents who do not support these standards and teachers who may not wish to implement them, along with students who struggle to understand them, the expected results have not been as anticipated.
Gaille, Louise. 2017. “18 Big Common Core Pros And Cons”. Vittana.org. https://vittana.org/18-big-common-core-pros-and-cons.
In 1965, physicist Richard Feynman wrote in the essay, New Textbooks for the “New” Mathematics:
If we would like to, we can and do say, ‘The answer is a whole number less than 9 and bigger than 6,’ but we do not have to say, ‘The answer is a member of the set which is the intersection of the set of those numbers which are larger than 6 and the set of numbers which are smaller than 9’ … In the ‘new’ mathematics, then, first there must be freedom of thought; second, we do not want to teach just words; and third, subjects should not be introduced without explaining the purpose or reason, or without giving any way in which the material could be really used to discover something interesting. I don’t think it is worthwhile teaching such material.
“New Math – Wikipedia”. 2021. en.wikipedia.org. https://en.wikipedia.org/wiki/New_Math#Criticism.
Singapore Math is popular with homeschoolers, private schools, and public schools alike—and for good reason. Research into the pedagogy of countries whose students excel in math, like Singapore and Japan, has found these countries’ use of diagrams in teaching math can provide a valuable bridge between early and advanced learning stages and encourage intuitive problem-solving skills.
Some benefits of Singapore Math include the following:
- It asks for students to build meaning to learn concepts and skills instead of rote memorization of rules and formulas.
- It aligns with the Common Core State Standards Initiative.
- It covers fewer topics in a year but in an in-depth way that ensures students have a foundation to move forward without needing to relearn concepts.
- Textbooks and workbooks are simple to read with clear and concise graphics.
- Textbooks are sequential, building on previously learned concepts and skills, which offers learning acceleration without additional work.
Despite the number of pros to Singapore Math and some research suggesting that it is superior to traditional U.S. textbooks, some schools find that the method is not easy to implement.
Some drawbacks of Singapore Math include the following:
- It aligns with the Common Core State Standards (yes, this can be a pro and a con, depending on whom you ask).
- It may not work well for a nomadic student population. Many students move in and out of school districts, which isn’t a big problem when the math programs are similar. However, since Singapore Math is sequential and doesn’t re-teach concepts or skills, using the program could potentially set these students up for failure whether they’re moving into or out of a district using it.
- It has less of a focus on applied mathematics than traditional U.S. math textbooks. For instance, Everyday Mathematics, a curriculum developed by the University of Chicago, which came out around the same time as Singapore Math, emphasizes data analysis using real-life, multiple-step math problems. On the other hand, Singapore Math’s approach is more conceptual and ideological.
- It requires extensive and ongoing teacher training, which is neither financially nor practically feasible in some school districts and not always practical for homeschooled children.
- Supplies are consumable and must be re-ordered for every classroom every year, which can put a financial burden on already strained school budgets and homeschoolers alike.
“Is Singapore Math Right For Your Student?” 2022. Verywell Family. https://www.verywellfamily.com/singapore-math-pros-and-cons-620953.
What are the benefits of Vedic maths?
Some of the benefits of Vedic maths are listed below:
- Calculations become easy and short.
- We can do simplifications in less time.
- Students undergo less mental stress. We can easily verify the results obtained by sutra-based methods with routine procedures.
- The possibility of committing errors by students using these sutras is negligible.
- The use of sutras helps students to improve their knowledge and interest in the subject of mathematics.
- Vedic maths helps to solve complicated problems using mental calculations.
“What Are The Benefits Of Vedic Maths? – Maths Q & A”. 2022. BYJU’s. https://byjus.com/questions/what-are-the-benefits-of-vedic-maths/.
Some of the disadvantages of Vedic Maths are:
- No general rule: Rules for Vedic maths are meant for some particular problems only.
- Too Many rules: For any operation like multiplication you will find too many rules which is applied for different types of problems as mentioned in point 1. This creates confusion.
- Need More mental calculations: Solving Problems with Vedic methods needs more mental calculations.
- Not easy to cross check: Since in Vedic maths you will find the algorithms only it becomes difficult to cross check the answers.
- Need to remember: Rules / Algorithms for solving problems are difficult and you have to remember them. and its very difficult.
Kumar, Vinay. “What Are The Disadvantages Of Vedic Maths?” 2022. Quora. https://www.quora.com/What-are-the-disadvantages-of-Vedic-maths.
1 Wildfire, Jessica. “I’M A Teacher. I’M About To Quit.”. 2021. Medium. https://jessicalexicus.medium.com/im-a-teacher-i-m-about-to-quit-f7afd11109dd.
Alice’s Adventures In Wonderland
“A Math-Free Guide To The Math Of Alice In Wonderland”. 2022. Gizmodo. https://gizmodo.com/a-math-free-guide-to-the-math-of-alice-in-wonderland-5907235.
“Alice’s Adventures In Wonderland”. 2022. Matrix Wiki. https://matrix.fandom.com/wiki/Alice%27s_Adventures_in_Wonderland.
“Alice In Wonderland’s Hidden Satire”. 2022. magellantv.com. https://www.magellantv.com/articles/alice-in-wonderlands-hidden-satire-math-slips-down-the-rabbit-hole.
⭐ “Alice’s Adventures In Algebra: Wonderland Solved | New Scientist”. 2022. newscientist.com. https://www.newscientist.com/article/mg20427391-600-alices-adventures-in-algebra-wonderland-solved/.
Take the chapter “Advice from a caterpillar”, for example. By this point, Alice has fallen down a rabbit hole and eaten a cake that has shrunk her to a height of just 3 inches. Enter the Caterpillar, smoking a hookah pipe, who shows Alice a mushroom that can restore her to her proper size. The snag, of course, is that one side of the mushroom stretches her neck, while another shrinks her torso. She must eat exactly the right balance to regain her proper size and proportions.
While some have argued that this scene, with its hookah and “magic mushroom”, is about drugs, I believe it’s actually about what Dodgson saw as the absurdity of symbolic algebra, which severed the link between algebra, arithmetic and his beloved geometry. Whereas the book’s later chapters contain more specific mathematical analogies, this scene is subtle and playful, setting the tone for the madness that will follow.
“Alice’s Adventures In Wonderland: Motifs | sparknotes”. 2022. sparknotes. https://www.sparknotes.com/lit/alice/motifs/.
“Chapter VII: A Mad Tea-Party – Alice-in-wonderland.net”. 2022. Alice-in-wonderland.net. https://www.alice-in-wonderland.net/resources/chapters-script/alices-adventures-in-wonderland/chapter-7/.
⭐ Danim, Rachel. “Alice In Wonderland: A Satire On Math”. 2021. Medium. https://medium.com/@connectrachelfilms/alice-in-wonderland-a-satire-on-math-a85f6ab6af42.
Charles Dodgson was a conservative mathematician and logician who did not accept the new math that was flooding in during his lifetime. Therefore, he took to his pseudonym, (Lewis Carroll) and rewrote his nursery tale, Alice’s Adventures Underground, turning it into a satire. The original Alice’s Adventures in Wonderland was written for Alice Liddell and had no real meaning — it was just an imaginary world of madness.
“The Hidden Math Behind Alice In Wonderland”. 2022. maa.org. https://www.maa.org/external_archive/devlin/devlin_03_10.html.
“The Mad Tea Party”. 2022. Alice In Wonderland Wiki. https://aliceinwonderland.fandom.com/wiki/The_Mad_Tea_Party.
Common Core Standards
“Controversial Common Core, What You Should Know Before Taking Sides”. 2022. ThoughtCo. https://www.thoughtco.com/common-core-state-standards-3194603.
“Everything You Need To Know About The Common Core”. 2014. Vox. https://www.vox.com/2014/10/7/18088680/common-core.
“New Math: An Explainer For Millennial Parents”. 2022. Parents. https://www.parents.com/kids/education/math-and-science/new-math-method-explained-for-millennial-parents/.
“The Common Core Is Today’s New Math – Which Is Actually A Good Thing”. 2015. The Conversation. https://theconversation.com/the-common-core-is-todays-new-math-which-is-actually-a-good-thing-46585.
Isbrucker, Asher. “What Happened to ‘New Math’?” 2021. Medium. https://medium.com/age-of-awareness/what-happened-to-new-math-eeb8522fc695.
“New Math – Wikipedia”. 2021. en.wikipedia.org. https://en.wikipedia.org/wiki/New_Math.
“Singapore Math Review – The Smarter Learning Guide”. 2022. The Smarter Learning Guide. https://smarterlearningguide.com/singapore-math-review/.
“What Is Singapore Maths? Or Should We Say Singapore Math? | MNP Blog”. 2013. Maths — No Problem!. https://mathsnoproblem.com/blog/teaching-maths-mastery/singapore-math-singapore-maths/.
“Why Is Singapore Maths So Popular Overseas? | theAsianparent”. 2018. theAsianparent – Your Guide To Pregnancy, Baby & Raising Kids. https://sg.theasianparent.com/why-is-singapore-math-so-popular-overseas.
Middleton, Kenneth. 2022. “Vedicmaths.Org – What Is Vedic Mathematics?”. vedicmaths.org. https://www.vedicmaths.org/introduction/what-is-vedic-mathematics.
“Vedic Maths (Vedic Mathematics) – Sutras, Tricks, Examples”. 2022. BYJUS. https://byjus.com/maths/vedic-maths/.
“Vedic Math | Origin | Applications | Importance”. 2022. cuemath. https://www.cuemath.com/learn/mathematics/arithmetic-vedic-math/.
⭐ I suggest that you read the entire reference. Other references can be read in their entirety but I leave that up to you.
“Why is a raven like a writing-desk?”
Edgar Allan Poe wrote on both.
Waggoner, Ben. “Why Is A Raven Like A Writing Desk?”. 2022. Quora. https://www.quora.com/Why-is-a-raven-like-a-writing-desk-5/answer/Ben-Waggoner-1?ch=10&oid=303880403&share=34736a92&srid=uLYie&target_type=answer.
Lewis Carrol said that when he wrote the riddle, he had no answer in mind. But he later came up with the answer that both can produce a few notes, but they’re very flat. He also said that they are nevar put with the wrong end in front. (The joke is that nevar is raven spelled backwards—i.e. a raven is nevar put with the wrong end in front.)
Others have pointed out that a raven is like a writing desk because Edgar Allen Poe wrote on them. (Recall that “to write on” is a somewhat archaic way of saying “to write about.) Someone else pointed out that they both stand on their legs, conceal their steals, and ought to be made to shut up. (The pun is that ravens steal things and hide them, and writing desks would have had a compartment for steel pen nibs, back when those were in use. Steals = steels, get it?)
Someone else pointed out that a writing desk is a rest for pens and good for writing books, and a raven is a pest for wrens and good for biting rooks. It has also been noted that they are both used to carri-on de-composition.
Katz, Johan. “Why Is A Raven Like A Writing Desk?”. 2022. Quora. https://www.quora.com/Why-is-a-raven-like-a-writing-desk-5/answer/Johan-Katz?ch=10&oid=107422035&share=587a05e6&srid=uLYie&target_type=answer.
The answer is because they both have a black quill. This answer makes less sense in modern times as we use other writing instruments. A black quill was dipped in ink for writing while a raven has one in its wing.
T, Wayne. “Why Is A Raven Like A Writing Desk?”. 2022. Quora. https://www.quora.com/Why-is-a-raven-like-a-writing-desk-5/answer/Wayne-T-7?ch=10&oid=223722966&share=75d85ab9&srid=uLYie&target_type=answer.
‘… In 1976 Carroll admirer Denis Crutch pointed out that in the 1896 preface quoted above, the author had originally written: “It is nevar put with the wrong end in front.” Nevar of course is raven spelled backward. Big joke! However, said joke didn’t survive the ministrations of the proofreaders, who, thinking they understood the author’s intentions better than the author, changed nevar to never in subsequent editions. …’