# June 2015

## Math: Not So Formal!

In the fall of 1929 I made up my mind to try the experiment of abandoning all formal instruction in arithmetic below the seventh grade and concentrating on teaching the children to read, to reason, and to recite – my new Three R’s. And by reciting I did not mean giving back, verbatim, the words of the teacher or of the textbook. I meant speaking the English language. I picked out five rooms – three third grades, one combining the third and fourth grades, and one fifth grade.– Louis P. Benezet, describing his innovative program in 1929.

Allegedly, formal math teaches children how to think logically. In practice, for most children, it teaches how to grope for the “right formula” – and to then misapply it.

Benezet wrote three articles, combined here: Benezet: Informal Beats Formal Math.

These articles recount his experiences with a variety of classes, some of which use the traditional formal method of math instruction; others use the new Three R’s: Read, Reason, and Recite. Students in the informal classes – most of whom were learning English as a second language – had richer vocabularies and stronger mathematical reasoning skills They had incorporated math understanding into their language; it became second nature to them.

Benezet encountered much resistance. He took his critics around, and posed a problem to several fifth grade classes:

A pole is stuck in the mud at the bottom of a pond. There is some water above the mud and part of the pole sticks up into the air. One−half of the pole is in the mud; 2/3 of the rest is in the water; and one foot is sticking out into the air. Now, how long is the pole?”

Traditionally-taught students floundered – they tried various operations at random, without actually understanding the relationships – half plus one half equals one whole, for example.

The informally-taught children – who spent four years learning how to express themselves and to reason – homed more directly into the correct approach:

One−half of the pole is in the mud and 1/2 must be above the mud. If 2/3 is in the water, then 2/3 and one foot equals 3 feet, plus the 3 feet in the mud equals 6 feet.

Teach the facts, or the concepts? I’ll go with the concepts every time. Benezet, Correa, and many others have come to similar conclusions: students who understand what they are doing, and can articulate why it works, are much more confident and correct when reasoning about math problems, especially those much-dreaded “word problems.”

The difference is so marked that we should not even be having this debate, nearly 100 years after Benezet’s results – but we still do.

New word: state-spreaders, AKA statists – people who violently claim more than their share, whenever they can get away with it.

Aided and abetted by: statheists, people who believe that the state is the solution to most or all problems, praise be to the state forever and ever, amen.

## Steal Not Thy Child’s Time

My then-wife and I homeschooled two children until they reached ages 12 and 14. I’m also proud and delighted to be a grandfather, that my daughter has been home- or un-schooling her children (seven, aged 1-13 years), and that my son is very engaged with the education of his own.

Unlike most dads, I initiated the discussion of home education. My wife, having a degree in elementary education, balked at the very idea of teaching our own. She had been trained to plan and prepare, to have formal structure, and so forth – a complex task which would daunt any one person.

I view education from the perspective of the student; I ask not “how to teach,” but how to learn most productively. During 11 years of Catholic school – skipping grade 8 – I often felt that my time was being stolen from me; I wanted something better for my own – not merely in terms of “quantity of stuff learned,” but qualitatively different.

Like the top fifth of entrants, I was already above First Grade level in reading and arithmetic. The most effective way to progress would have been to actually read, to play with new ideas and interesting and challenging math problems. This is precisely what we were not allowed to do.

Instead, we spent 40 minutes or so waiting for a turn to read two lines from a “See Dick Run” book. Far better to use the same time to read interesting books at our own pace – which is what my homeschooled grandchildren do.

With math, we drilled and killed our way through textbooks, page by boring page. This is a horrendous waste of children’s time.

Lately, researchers have been discovering the value of the time spent by that top third or so outside of school. I know what I was doing outside of school – independent reading, playing with math, and otherwise teaching myself. Researchers – such as those at Reading is Fundamental – are often bewildered that children – even at the bottom of the SES rankings – often learn and improve substantially over the course of the summer, with just the slightest bit of assistance – self-chosen books, in this instance.

My wife, the degreed educator, insisted that our son go to a “gifted” first grade class at a nice suburban school. The teacher was respected by our neighbors. We actually had to push to obtain admission; the test administrators balked because his art skills, in their minds, were not quite up to snuff.

Two weeks later, he came home and asked “What is 5-7?”

“She says it’s too complicated.”

“What do you think?”

“I know that 7-5 is 2, and 7-7 is zero. So is 5-5, anything minus itself is zero. I think 5-7 must be something else, but I don’t know what it is.”

Anybody who can articulate all that is ready to advance. I briefly explained the idea of negative numbers, using a thermometer diagram to illustrate; turned the diagram on its side, making it a number line, and explained how to think of negative numbers as growing to the left versus the right, and subtraction as moving the opposite direction from addition. He understood immediately. I made sure he learned how to add and subtract all combinations of positive and negative numbers.

A few days later, I come home from work, he’s doodling on his paper, and there’s a number line. This is his own initiative, his own “work.” I asked a few questions, and he’s got the concepts perfectly, in every particular. This took minutes, not days, weeks, or months. I never had to repeat the lesson. It stuck, because it was his question; he was interested.

My wife, observing this, had an epiphany. Our son could learn without complicated textbooks and plans and so forth – a lot more rapidly than at his “gifted” class. We began homeschooling, which continued until our children were 12 and 14 years of age. They had little trouble adapting to formal education. They had some gaps (and what student does not?), but had outstanding mathematical intuition, and rapidly mastered new material.

My wife and I divided our labors; Under no circumstances was she to teach math. I was (and remain) devoted to what I call “organic learning,” and some call “unschooling,” inspired by John Holt. It was my desire to work with the nature of my children, rather than against it. Instead of “begin at page 1,” my children and I had many “random” conversations which where suited to their abilities and interests – sometimes about everyday math, sometimes about more abstract ideas such as binary arithmetic, and we conversed about myriads of non-math topics. We played many games which exercise math skills. Both became skilled mental calculators.

I must stress the role of frequent conversations, often initiated by my children. At age 3, my son asked “What is gwabbity?” (he had overheard the word “gravity” in a conversation). I could have said “gravity is what makes things fall down,” but that seemed too simple, given his state of knowledge at the time. So I went to the whiteboard, writing down the formula $F = g \frac {m_1 m_2} {r^2}$, and began to talk and draw. In a few minutes, he learned the word “mass,” had a loose idea of its meaning, was reminded that the earth is a really really big ball, was informally introduced to the idea of using vectors to represent force, and a few other ideas. I fudged very little, and built a framework which was close to what he’d want to know as his knowledge of math and physics grew.

To further illustrate the potential, let us move forward about 30 years, to a conversation with my 2nd-generation home-schooled grandson, aged 6.

I asked him to think about adding the integers from 1 to 100. The obvious but slow method: add 1 and 2, add 3, add 4, and so on. 99 additions. $1+2+3+...+100$

Or, one could write the numbers down as 1 2 3 … 50, and then write the 2nd half in reverse order:

$\begin{tabular}{ r r r r r} 1 & 2 & 3 & ... & 50 \\ +100 & +99 & +98 & +... & +51\\ \end{tabular}$

My grandson interjected “each pair adds to 101. There are 50 pairs. 5050.”  That was fast.

Could he generalize? What is the sum of the even numbers, from 2 to 100? He pondered for a few seconds, and replied “2550” – which is correct. This problem stumps most high school students. At age 8 or 9, he tested at the 18th grade equivalent in math. Does he have good math genes? Is he something of a prodigy? Yes – but a prodigy who could race at own his speed, unhindered by a governor.

And that is why we teach our own. We don’t want to hold them back, nor let schools steal their time.

From the “in other news, water is wet” file:

## Summer Reading Loss Reversed When Students Get Books to Keep

On average, 80 percent of low-income children lose ground in reading proficiency over the summer.  Reading is Fundamental (RIF) wanted to cut that percentage in half. They did even better. How?

RIF distributed books which children could take home. They allowed the children to make choices. And they encouraged both children and parents to read.

## And, to the surprise of researchers, 57 percent significantly improved their reading skills between the end of one school year and the start of the next.

Seriously? Professional Educational Researchers, if your a priori bias does not imagine, let alone encourage,  students learning during the summer – that is, with little to no direct input from professional educators – you need a very strong dose of humility. It is quite possible that you are doing education wrong. You may be working against the nature of children and their parents.

It is the learners, not you, who are essential to learning. It is they who must do the heavy lifting.

A side note: the RIF Report is an example of How Not To Write. It jumbles together many things which are only sort-of-related, and it uses acronyms – such as STEAM – without explanation.  Via web search, I conclude that STEAM is STEM+A; that is, Science, Technology, Engineering, Math + Arts. Adding the Arts may a) be easier and cheaper than finding teachers who actually understand STEM, and b) unduly dilute the focus on STEM. But that’s another topic; consider this paragraph as almost a throwaway.

Summary: if we parents do our part, our children – the real stars of the learning process – can do theirs. Inexpensive books are available at thrift stores, garage sales, and flea markets. Put them to use! And if you are reading-challenged? Read, read, and find a coach!

## Libertarian Party of California Convention, April 1-3. Jerry Jewett on “The Cost of Liberty”, April 21. Libertarian Party of Los Angeles County Convention, April 23.

All of the events below will be held at Raffaello Restorante (see Home page) except the booth at street fairs and the conventions and conference.  For the 2016 national, state and local Libertarian Party conventions, and the 7th Annual Southern California Libertarian Party Regional Conference please see below.

Our dinner meetings are held on the third Thursday of each month except December.  We do not have a meeting in December because people are involved in the holidays.  Some of the other regions may have meetings and parties; check their websites at the L. A. News Rag (http://www.lanewsrag.com)

April 1 – 3, 2016, Libertarian Party of California annual convention will be held at the LAX Hilton.  Go to http://www.lpcevent.com/ for full information.

April 21, 2016, Jerry Jewett will speak on “The Cost of Liberty” at the South Bay Libertarian dinner meeting.  Among other examples, Jewett will compare the regions of Somalia governed by the state’s law with that nation’s  ungoverned regions.  He will examine how stateless societies function in modern times–the lost comforts of a state regulated society vs. the benefits in freedom.

April 23, 2016, the Libertarian Party of Los Angeles County will hold their annual convention from 1 to 4 p.m. at The Reef Restaurant, 880 Harbor Scenic Drive, Long Beach, CA 90802, 562-435-8013.  The meal choices are steak, chicken, salmon, and vegetarian (pasta).  Salad, desert, and coffee or tea are included, sodas and alcohol are not but can be ordered from the bar.  The cost for the event is \$40.  Please make the check out to “Libertarian Party of L.A. County” and send it to Jonathan Jaech, 3200 East 3rd Street, Los Angeles, CA 90063.  On line registration is available at http://www.eventbee.com/v/lplactreas/event?eid=151248484 .

May 19, 2016, Rodney Schaerer will give “a comparison of Father Martin Luther to modern libertarianism and an argument that Father Luther was an libertarian and the Libertarian Party should consider establishing Father Luther as a party icon.”

May 27 – 30, 2016, National Convention of the Libertarian Party will be held in Orlando, Florida.  Go to http://www.lp.org/event/lp-2016-national-convention for details.

July 13 – 16, 2016, Freedom Fest will be held at Planet Hollywood in Las Vegas.  I have been to a number of these and have always found them worthwhile.  Go to http://freedomfest.com for more information.

July 21, 2016, Dave Schrader on “The Libertarian Youth Movement – What’s Happening?”  Can we count on younger people to understand the basics of libertarianism and avoid the seduction of socialism?  It looks like a mixed story, and this talk will focus on some of the positive efforts underway to educate and activate youth.  We’ll survey encouraging data points from leading organizations like Young Americans for Liberty and Students for Liberty.  We’ll also take a look at issues that appeal to youth, like the topics in the book “Disinherited: How Washington Is Betraying America’s Young”.  Dave Schrader is a long-standing Region 66 member who frequently give talks on a variety of topics at LP regional events.  His last talks were “Empires and Their Demise – Is the USA Next”, and “Civil Rights in the Civil War”.

## Imagine No Guns? No Thanks

In a world without guns, the young and strong, and those who have time to master other weapons, utterly dominate the weak and defenseless. Is it better to arm the few against the many, or the many against the few? The answer depends, in large part, on whether you believe that the many prefer peace, or Hobbesian warfare.

Carlisle E. Moody has published a working paper, Firearms and the Decline of Violence in Europe: 1200-2010, which tends to support the latter hypothesis.

Abstract

Personal violence has declined substantially in Europe from 1200-2010. The conventional wisdom is that the state’s monopoly on violence is the cause of this happy result. I find some evidence that does not support this hypothesis. I suggest an alternative hypothesis that could explain at least some of the reduction in violence, namely that the invention and proliferation of compact, concealable, ready-to-use firearms caused potential assailants to recalculate the probability of a successful assault and seek alternatives to violence. I use structural change models to test this hypothesis, and find breakpoints consistent with the invention of certain firearms.

## Things Parents Can Do

The Economic Policy Institute recently released a report:  Five Social Disadvantages That Depress Student Performance (Why Schools Alone Can’t Close Achievement Gaps).

The EPI being what it is – a think tank which promotes government solutions – it behaves as if it has a hammer and everything is a nail. Leaving that aside, there are many valuable lessons to be learned.

Parenting practices that impede children’s intellectual and behavioral development: Lower-social-class parents [tend to] engage in fewer educationally supportive activities with young children, such as reading aloud or playing cognitively stimulating games. Lower-social-class parents also [tend to] exert more direct authority and offer children fewer choices in their daily interactions, leaving them less prepared for “critical thinking” when school curricula expect it.

Parents’ failure to engage in educationally supportive activities is associated with children’s poorer academic and behavioral outcomes.

Why add the editorial phrase “tend to?” Because we are not automatons; some folks in lower SES levels do behave differently. Poor socioeconomic circumstances need not be your child’s destiny. As a parent, you can make choices. And, frankly, some high-SES parents do make bad choices.

The report continues:

There are well-validated programs that can offset these effects. High-quality early childhood care and education centers provide intellectually stimulating environments that disadvantaged children may miss at home.

Does the EPI understand economics? It is true that high-quality early childhood care and education centers do provide intellectually stimulating environments. Why do we not already have an abundance of such institutions? Because the supply of high-quality caregivers is not unlimited. It isn’t easy to create high-quality centers, and they surely do not fall from trees.

The poorly-performing parents of today already went to educational facilities which were approved by, funded by, and usually provided by government agencies. Why, in twelve years, did they not learn to be better parents?

Perhaps we’re looking for help in the wrong places. Instead of asking “what can government institutions do,” let us ask “what can parents do – and how can neighbors, relatives, and other folks aid in this process?”

The five things listed by the EPI are:

• parenting practices that impede children’s intellectual and behavioral development
• single parenthood
• parents’ irregular work schedules
• exposure to and absorption of lead in the blood.

The first is directly under your control, and is where my experience and knowledge might be most useful.

What can parents take away from this report? It helps if you

• play with children, not sports
• talk with/listen to children

An interesting finding: “Patrick Sharkey, for example, has shown that the quality of the neighborhood where a child’s mother was raised has a bigger influence on the child’s achievement than the quality of neighborhood where the child was raised. ”

This suggests that my frequent remarks about the importance of a family culture of educational support – reading to children, playing with them, interacting with them – apply even when family fortunes rise and fall. The 30 million word research by Hart and Risley suggests a similar idea: young children benefit from heavy verbal interaction, as opposed to directive speech, which tends to dominate lower-SES households.

The report includes a table of the differences in “number of books” owned by various households. People with higher SES rank tend to have more books, on average. White people tend to have more, on average. The differences are not huge – 34 on the low corner of the grid, 145 at the high end.

Individual differences can be much greater – if you’ve ever visited a professor or other bibliophile, you’ll know that they often own thousands of books. Back when I was both young and poor, I was already a bibliophile with thousands of books – most of which were acquired cheaply at flea markets, garage sales, and discount stores. It’s a matter of choice whether your child grows up with many books or only a few, and it is certainly a matter of choice whether you read to your children or not.

The number of books owned is one of the most reliable indicators of whether your child will do well academically. But books themselves are not magical talismans; you’ll have to actually read and talk about books frequently, before your child comes to the conclusion that reading is valuable.

Another quote from the report:

By age 6, white children have typically spent 1,300 more hours engaged in conversations with adults than black children. Six-year-olds from affluent families have spent 1,300 more hours in indoor and outdoor recreation, churches, businesses, and other non-school, non-home, and non-caretaker settings than children from low-income families. Differences are greater still (1,800 hours) between children of parents with less than a high school education and children of college graduates. This gives children of high-income and highly educated families more background knowledge, the most important predictor of later academic achievement.

I stipulate that the research on which this statement is based is probably correct, but ill-focused and not as useful as it could be. I’m fairly sure that there is nothing about “being black” which necessitates this result. I argue that it is cultural. (see Sharkey and Hart and Risley, above.) Most importantly, it is a choice; something over which you have control.

If you are unemployed (as mentioned in the report), you have to spend time looking for work, of course. But are you truly spending 40 hours plus travel time, every week? I certainly did not. I had more time to spend with my children, when unemployed. I spent that time reading to them and otherwise interacting with them. This does not require “being rich” or “having white skin” – it’s just a choice, which was easier for me because it reflected choices made by my parents when I was young, and my conscious choice to be involved with my children.

Now, I grant that life is tougher when you’re poor – I’ve been there! And it’s tougher when you’re a minority; I’m not blind to the external pressures. But the only thing we can really change is our own behavior, and we do have a lot of influence on our own children; let us use that to best effect.

There’s a lot more in this report – I encourage parents to read it critically – but my summary: if you want to make a difference in your child’s cognitive skills, much earlier is much better than later. As for how to intervene:  reading, conversing, and playing. There’s a tag cloud to the right; (scroll up) you may find “30 million words” and other tags to be of interest.