Showing posts with label Teaching. Show all posts
Showing posts with label Teaching. Show all posts

Monday, April 01, 2024

Trivium and Quadrivium

The reason I've always been captivated by the Trivium and Quadrivium is almost certainly that these ancient western educational models happen to coincide with six main interests of mine: math, music, astronomy/cosmology, logic, writing, and debate. 

Moreover, philosophy, another one of my main interests, was considered such an obvious part of classic liberal arts training that it wasn't included in the list of subjects for either the Quadrivium or Trivium.

From the Wikipedia article on Quadrivium:

"From the time of Plato through the Middle Ages, the quadrivium (plural: quadrivia[1]) was a grouping of four subjects or arts—arithmetic, geometry, music, and astronomy—that formed a second curricular stage following preparatory work in the trivium, consisting of grammar, logic, and rhetoric. Together, the trivium and the quadrivium comprised the seven liberal arts,[2] and formed the basis of a liberal arts education in Western society until gradually displaced as a curricular structure by the studia humanitatis and its later offshoots, beginning with Petrarch in the 14th century. The seven classical arts were considered "thinking skills" and were distinguished from practical arts, such as medicine and architecture."

One has to wonder what our society would look like if schools prioritized these essential subjects in grades K-12.

St. Ann Classic Academy is a school trying to implement such a curriculum.

For an excellent book on the Quadrivium, try Quadrivium: The Four Classical Liberal Arts of Number, Geometry, Music, & Cosmology. 

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Thursday, February 01, 2024

Teachers are Quitting

It seems our schools are always in trouble for this reason or that one. 

This was not at all the case when I was a boy in the 1960’s. California public schools, K-College, were unquestionably the best in the world, and all were levels were free or very low cost. So it’s especially hard for boomers like myself to see the kite hit the ground like this.

As a private academic coach for more that 45 years, I’ve tried to figure out what went wrong. I still don’t know, after all these years.

And now, a sobering new trend is emerging. Teachers are leaving K-12 schools in droves.

The reasons are many and various. But what I hear over and over again is that they boil down to several core issues: low salary, poor mental health, toxic work cultures, unsupportive administrations, lack of respect inside and outside school, lack of authority in the classroom, and out of control students and parents.

I have no answer, but I do have suggestions. At a minimum:

Pay teachers like doctors, require the same achievement, give them the same respect inside and outside schools, and weed out poor teachers (the Finnish approach); give teachers back-up they need and deserve within schools hierarchies; return classroom authority to teachers; allow sensible grading and disciplinary procedures, including compassionately but unapologetically holding back students who don’t meet grade level standards; a teacher-aid in every classroom; effective protection against parent-zillas think their little Johnny can do no wrong; make it unnecessary for teachers to buy learning supplies their students need; and provide enough public funding to pay for all this, realizing that doing so is less expensive than not.

For further information, I recommended the following:

I quit teaching for better mental health: former teachers share the jobs they got after teaching

Why Teachers Quit: Lack of respect, abominable working conditions, and more.

After Teaching For 11 Years, I Quit My Job. Here's Why Your Child's Teacher Might Be Next.

I quit my job as a teacher after 6 years to work in tech sales. I make $20,000 more ...and am so much happier now.

Teachers Who Quit Are Sharing The Moment They Realized It Wasn't For Them

Why Teachers Quit + Top Signs Quitting Teaching Is The Right Move

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.


Wednesday, March 01, 2023

lizardpoint

Lizardpoint is a wonderful all-around early learning site for people of all ages. Students can use lizardpoint to learn geography, flags, world leaders (current and past), art, and math.

The site is great for adults as well as for children.

Sections on geography help students master finding countries and provinces, naming their capitals, topographical features, airport codes, and more.

The section on art features quizzes on major western artists and their most well-known works, fine art terminology, and important movements.

Math offerings include on-screen and downloadable/printable worksheets (with answer sheets) for arithmetic operations, decimals, percents, and fractions.

Quizzes on trivia, important definitions, and more round out learning activities presented.

New stuff is added regularly, collected in What's New.

Like Freerice.com, lizardpoint can be addicting, but in a good way. These two educational sites keep interested students learning and growing while having fun.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Monday, August 01, 2022

Get a Head Start

A head start in life is a great advantage, and nowhere is this more clear than in the educational realm.

For example, any parent with a good high school education can teach his or her child to read at a very early age. See: Teach Your Child to Read in 100 Easy Lessons.

Likewise, any child who can draw stick figures with a crayon can learn to form letter shapes.

Simple mathematical concepts can be taught as soon as a child can count. Counting objects is the first step in acquiring "number sense," a visceral feel for numbers essential to mastering mathematics. The goal of all early math education should be the development, strengthening, and maintenance of number sense, along with the ability to do accurate mental and paper/pencil calculations and estimates. These aims should be ardently pursued and achieved in grades K-6.

Parents can work with eager children at home to provide them an early start. My own daughter was reading at age four, mastering math facts at five, operating with negative numbers at six, typing at seven, and doing algebra at eight.

Not all parents are professional academic tutors, as I am. Still, it doesn't take much forethought for most parents to provide their children a leg up in their schooling.

For those who wish to have professional guidance, I offer private consulting for parents of young children. In addition to providing general information about schools, early education, and tutoring at home, I help parents design and implement individualized, age-appropriate academic head start plans tailored to each child's particular needs and interests. You can contact me here for more information about this unique service.

An good head start is a great gift, one of the best parents can offer their children.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, July 01, 2022

Mad Minute

Mastery of the basic facts of arithmetic is the first step toward mathematical fluency, and is a central early academic goal. 

A "Mad Minute" is a simple, daily exercise for elementary school students striving to memorize their basic math fact "tables." Mad Minute worksheets contain several dozen questions using the same operation (addition, subtraction, multiplication, or division), and are an excellent way to provide kids with daily practice.

To complete an exercise, students are given one minute to answer as many questions as they can. Each correct answer earns one point. After the minute is over, the number of correct answers is counted and written atop the page. Speed, therefore, is essential to a high score. However, students stop earning points after the first mistake! So accuracy is even more important. 

[Note: Mad Minutes introduce and reinforce two very important rules in studying mathematic – speed is important but accuracy is even more important – and are therefore doubly beneficial.]

Mad Minutes should be assigned at home each day (one for each operation, if possible, according to the student's current ability).

Mad Minute exercises are also great ways to track progress, since each completed exercise acts as a current assessment of mastery. Students might enjoy recording their scores in a 2-column table, and visualizing them using a 2-D chart with dates along the horizontal axis and scores along the vertical – an excellent way to introduce the concept of numbers as data. You can find large-format graph paper here and here.

Mad Minute books, providing multiple worksheets for each operation, have been around for decades. Click here to buy the latest on amazon.

Free downloadble/printable basic number fact worksheets, along with online drills and simple games, plus more worksheets and drills covering advanced work with operations, decimals, percents, and fractions, and simple mental exercise games like Make a Match and Find It, can be found on lizardpoint.com here.

Hint: Downloaded files are easier to work with, since workbooks eventually fill up and need to be re-purchased. Mad Minute exercise files, on the other hand, like those available on lizardpoint, can be printed over and over again, as needed.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, June 01, 2022

The Great American Bathroom Books

Imagine a single-volume guide to a classic liberal arts education. You get essentially that in The Great American Bathroom Books, Volume 2.

Containing two-page thumbnails of all-time great written works, readers get a taste of famous titles without having to invest hours in the process. Single-sitting synopses are well-organized and well-written. Think of each as a summary of a summary, a shortened "Cliff Notes." 

Volumes 1-3 include main plot points, central themes, and condensed analysis of classic works of literature, important novels and plays, and popular recent non-fiction titles. All but Volume 3 are out of print. Read the second volume, first.

But a good used copy on amazon here or eBay here.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, April 01, 2022

PreK-12 Curricula

Public and private schools vary greatly in quality, and parents ought to take responsibility for ensuring each child is learning what he or she needs to learn at every stage.

There's a vast ocean of teaching guides and materials available online. Few parents are professional teachers or education experts, and those without such training or experience will find it difficult to separate wheat from chaff. Those looking to monitor the education of their children or who want to teach or tutor their children at home will need help in their efforts.

For such parents, having access to a reliable curriculum guide is essential. Two that I've found useful are the ones found at IXL and World Book.

The IXL platform is used in schools all over the nation, and a paid IXL account may be worth the investment for your family, given the breadth and depth of their PreK-12 course offerings, excellent learning materials, and sterling reputation.

The Core Knowledge Foundation, headed by E. D. Hirsch, author of the acclaimed Core Knowledge book series, provides free curriculum materials for grades 1-8. I'm a big fan of Core Knowledge Books, and recommend them highly. Based on the excellence of these publications, I'm confident the curriculum materials prepared by the Core Knowledge Foundation will be of similar quality. Interested parents can check them out here.

An excellent resource for teaching young children to read is the phonics-based Teach Your Child to Read in 100 Easy Lessons. I used this book to teach my own daughter (eager learner) to read at age four. Each lesson takes about 20 minutes to complete, and can be broken up into two parts for kids without lengthy attention spans. The method of instruction is so simple that any parent with a good high school education can implement it easily.

Nowadays, it's quite important to carefully monitor what's taught (and how it's taught) in school. Gone are the days when parents can safely take these things for granted.

Fortunately, there's a lot parents can do to ensure their children actually receive a high quality education.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Tuesday, February 01, 2022

Freerice

At
freerice.com students of all ages can learn everything from basic arithmetic to art history, world geography, anatomy, and English grammar and vocabulary, while earning grains of rice to donate to the United Nations' World Food Program (WPF).

"Rice" is used as a metaphor for donations generated by users of the site that sponsors then fulfill. Each correct answer stores 10 grains of virtual rice for donation to the WFP. Sponsors then give the monetary equivalent of all rice collected to the WPF to fund its charitable work around the globe.

From the site:

"The United Nations World Food Programme (WFP) is the 2020 Nobel Peace Prize Laureate. We are the world’s largest humanitarian organization, delivering life-saving food assistance in emergencies and working with vulnerable communities to improve nutrition and build resilience."
Freerice is a great way to learn while helping others in need throughout the world. The site generates billions of "rice grains" each year, a total of 224 billion to date! Caring students get smarter while making the world a better place in a concrete way."

For anyone who loves learning, it's hard to imagine a better way to have fun.

FAQ here.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, December 01, 2021

Coaching v. Tutoring

Academic Coaching is a specialty in the field of private practice education.

How has academic coaching evolved? What's the difference between ordinary tutoring and professional academic coaching? When is it wise to hire an expert, despite the higher cost?

The purpose of this article is to clarify the distinction between ordinary tutoring and academic coaching and help answer these salient questions.

Historically, private tutoring was the way most education happened, the primary means by which critical knowledge and skills were passed from one generation to the next.

Whether the subject matter is hunting mammoths, learning Latin, sewing a dress, playing piano, passing the bar exam, or mastering basic algebra, nothing beats one-on-one private instruction with an engaging, expert private teacher. Indeed, it's been said that the best possible educational setting is "yourself, Aristotle, and a log."

[Continue reading here.]

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, October 01, 2021

Mathematical Logic

The trunk of the tree of mathematics divides into two main branches: applied mathematics, and pure mathematics.

Applied mathematics is concerned with calculation. Getting the right answers. Building things. Making sure the probe lands safely on Mars, that the bridge can withstand high winds, that revenue will exceed expenses. Utilitarian math.

I've always been interested in pure mathematics: the study of numbers, purely, for no other reason. Useless math, in other words. Math for the sake of math, only. Utterly non-utilitarian math.

The purest of pure math is logic, the foundation of mathematics. Mathematical logic is "meta-mathematics," the software running the machine, the engine under the hood.

One my favorite undergrad courses was an upper-division class in mathematical logic. Not long ago, I decided to take out some old textbooks, and summarize what I'd learned decades ago. The result was a set of simple notes for doing "Truth-Tree" proofs, one my favorite class activities.

You'll find the notes here.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Wednesday, September 01, 2021

Secret Sauce

Standardized testing is an inescapable fact of academic life.

Unfortunately, many students receive low scores simply because they lack the necessary test-taking know-how, preparation tools, practice habits, or skilled instruction required to maximize scores on tests like the SAT and ACT.

Nowhere is this more evident than on the math sections of such tests.

Of course, mathematical ability is the best predictor of success on any math test, and many tutors use an entirely content-based approach in an attempt to quickly increase standardized test math scores. In most cases, however, this is a fool’s errand.

[Continue reading here.]

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Saturday, May 01, 2021

Toy Box Subscriptions

New parents often wonder what kinds of toys to buy for their infants and toddlers.

When given a choice, little ones seem find everyday objects the most fascinating. Kitchen items are a favorite source of amazement: bowls, cups, pots and pans, silicon cupcake moulds, ice cream scoops, etc. Balls, plain wooden blocks, fabric, toilet paper tubes, and small boxes are other examples of free or low-cost toys that babies love.

Remember to assiduously avoid anything sharp, pointed, small enough to fit all the way inside a young child’s mouth, or painted (unless you know the paint is safe). Remember, until infants are a year old or so, everything goes in the mouth.

Nevertheless, it’s nice to find some fine educational toys to add to the mix. Researching the best options for baby at each age of development can be a chore, however. Fortunately, regular delivery of curated selections of age-appropriate toys is now possible through various subscription services. One of the best of these is Lalo.

Rooted in the Montessori early learning model, boxes of educational toys picked for specific age groups can be purchased individually or through a subscription model. With minimal effort, busy parents can check this task off their to-do list and give themselves more precious family time.

You’ll find other top offerings in Best Baby Toy Subscriptions of 2024 published by U.S. News.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Monday, February 01, 2021

Cart Before Horse

Students in marginalized groups are not doing well in math, and this is hampering upward mobility. But the solution provided in the recently adopted California Mathematics Framework (CMF) doesn’t serve the laudable goal of improving mathematical fluency in under-represented populations. 

In a 11/29/21 article by Joe Hong in Cal Matters, Tom Loveless, a retired math education expert puts it in a nutshell: “The way you get social justice in mathematics is to teach the kids math … not by dressing up mathematics in social justice.”

In the original draft of the CMF, central author and instigator Jo Boaler actually went so far as to write that mathematical talent isn't a thing, that it doesn't exist. Of course, to say such a thing is nuts. It's ridiculous. Nevertheless, differentiated advanced instruction for gifted students was condemned, at best, in early drafts of the CMF. Palo Alto parent Avery Wang makes the point clear. “Holding back high achievers makes them achieve more? That’s exactly the same philosophy that’s being promoted in the math framework.”

But this is the inevitable, illogical conclusion of woke ideology in math education, and woke ideology, generally: “Our personal differences are of central importance, but despite real differences, we should all achieve equally.”

The CMF is the culmination of a decades-long crusade within math education circles to teach math “constructively" by "discovery” and make math “more relevant” and “more fun." As a long-time member of the National Council of Teachers of Mathematics, a trade group for math educators that took a leading role in promoting constructivisism the late 1980s, I’ve watched this movement gain steam in recent decades.

Music Theory is not “Music Appreciation.” Those are two entirely different courses. Likewise, “Precalculus” and “Recreational Mathematics” are utterly dissimilar in purpose, method, and scope.

In the article, Michael Malone, parent and math tutor, puts it well: “They’re changing math to make it math appreciation. A part of math is learning things that are not authentic to life.” He then opines that the CMF “does a disservice to historically marginalized student groups by offering them a simplified version of math that fails to prepare them for the challenges of a career in science, tech, engineering or math.” Finally, Malone correctly concludes: “Math is gonna be hard for students who don’t enjoy it as much.”

[Thank you, Captain Obvious.]

In a separate Cal Matters article, UC professor Svetlana Jitomirskaya expresses her exasperation by the decision of the authors of the CMF not to seek much input from from STEM experts who naturally have first-hand awareness of the level of mathematical maturity and training incoming undergrads must have. “The process should have definitely involved STEM faculty from top CA universities with direct knowledge of what is needed for success as STEM majors,” she emailed. “It is absurd this was not done.” 

Jitomirskaya further criticizes the CMF for emphasizing “exploration at the expense of skills development,” and says there’s a “mountain of evidence that similar ideas have consistently failed when implemented at scale, and a rigorous approach — teaching students to back up answers with logic — is the only method known to decrease the [mathematics achievement] gap.”

This has been my own experience as a professional math educator for 45+ years. Sure, it would be nice if each student could reinvent the wheel, and in an ideal world, constructivism would be the best approach to take in teaching mathematics. In a very small class with a genius teacher, highly motivated and gifted students, and two math periods a day, constructivism could play a key role and be an important and highly productive part of the mix. But how many American math classrooms does this describe? As the professor points out, the constructivist idea doesn't scale. It's good in theory, bad in practice. Although both are important ideally, in reality, acquiring mathematical skill is more important than discovering mathematics.

Citing CMF-styled math exercises, Professor Jitomirskaya shows how these problems are illogical, poorly formed, and could introduce "a wrong idea of what it means to solve a problem — something that college professors struggle to undo."

Jitomirskaya states “It is irresponsible to make the entire state a laboratory for very controversial educational theories ..." and concludes that "Social justice, while desirable and necessary, will not come about by abandoning mathematical rigor."

I couldn't agree more. If one is concerned about upward mobility, getting good grades in math isn't what counts. What does count is having genuine mathematical skill and intuition, which cannot be developed simply by watering-down curricula so that struggling students are able to show better marks on their report cards. Masking problems doesn't make them go away. Pretending students are accomplished isn't helpful, and it isn't compassionate. Eventually, the rubber will actually hit the road. Again, quoting Tom Loveless: "The way you get social justice in mathematics is to teach the kids math."

Whatever one thinks of the "social justice" movement, math is still math and chemistry is still chemistry. The derivative of 6x^2 and the atomic weight of boron have nothing to do with “diversity, equity, and inclusion.”

If we're smart as a society, we'll make sure the horse precedes the cart.

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Copyright © 2006-present: Christopher R. Borland. All rights reserved.

Friday, May 01, 2020

Episodic Memory vs. Semantic Memory

Memory is mysterious.

Why do we recall some facts and not others? These event but not those?

How does human memory work?

What can we do to optimize memory in various situations and settings?

30-year primary teacher Clare Sealy has written a fascinating acting article in Education Next contrasting Episodic Memory with Semantic Memory and discussing the implications in educational settings.

The article begins:

When we look back on our own school days, our strongest memories are probably a mix of big occasions—field trips, plays, and sports days alongside more personal events tinged with strong emotion. Things that happened that were really funny or sad, or that made us feel excited, interested, exhilarated, or angry. We don’t tend to remember vividly, if at all, actually learning the substance of math or English or design technology. We might remember amusing anecdotes from lessons gone awry, or still bristle at past injustices — “but I wasn’t talking” — or have a vague impression of sitting in the science lab, with fleeting snippets of memories of this or that experiment. All of which leads to us making the entirely reasonable hypothesis that if we want students to remember what we teach them, then we need to make our lessons more like the spectacular one-off special events, or, at the very least, involve something specially selected because it’s exciting and possibly unusual. Memorable events, in this view, should form the template for creating memorable lessons.

As reasonable as this seems, this is a myth. It is a myth because human memory works in two different ways, both equally valid but one of which is much better at enabling us to transfer what we have learnt to new contexts. This transfer is an essential prerequisite for creativity and critical thinking.

The two forms of memory are known as episodic and semantic memory. Episodic memory is the memory of the ‘episodes’ of our life—our autobiographical memory. This takes no effort on our part, it simply happens. We don’t have to try consciously to remember what happened yesterday. Those memories just happen automatically. But there is a downside. Episodic memory is “easy come, easy go.” If you try to remember what you had for lunch yesterday, you will probably remember. If you try to remember what you had for lunch a year ago today—unless that happened to be some very significant date and some particularly noteworthy lunch—you will have no idea.

Semantic memory, on the other hand, involves much harder work. We have to expend effort to create semantic memories. This is the kind of memory we use when we consciously study something because we want to remember it. Unlike episodic memory, it does not just happen. The upside, however, is that the effort involved results in a long lasting memory.

Have you ever been in a course where you have really enjoyed listening to the speaker, found the subject matter interesting and the presenter amusing and engaging. Yet when you try to explain to someone the next day what the course was about, all that is really left is a vague impression of your emotions during the day, tinged with the odd snippet of content? You know the course was really good yet can’t really explain what it was actually about beyond the most general of assertions.

[Continue reading here.]