Archive for the ‘College Education’ Category

The New Math: Part II – Three Reasons Why It’s NOT Working in So Many Schools

September 5, 2013

My students come to me for math tutoring because they continue to flounder with the “new math” curriculum.  For a complete description of what is being taught and how it feels for students, see Part I of this series.  Part I – The New Math:  Why We Have It

If expert mathematicians have redesigned the curriculum, why aren’t the results better?

Expert mathemeticiansEinstein

I believe it’s because the experts aren’t taking into account the developmental stages of most students, and because they really aren’t aware of the problems most classroom teachers are faced with.

The new math teaching methods are mainly designed to create:

1.)  the ability to work in cross-disciplinary teams;

2.)  understanding (now viewed as even more important than being able to compute); and

3.)  innovative and divergent math thinkers–the three characteristics increasingly required of white-collar jobs in industry today.

Yet the new math curriculum is failing to achieve these goals.  Let’s take a look at WHY, by seeing how these things actually play out in most classrooms.

How These Three Goals Actually Work Out in Classrooms:

1. Creating an ability to work in cross-disciplinary teams. The idea is clearly that “putting students in groups to solve problems” will create this ability. However, there are TWO IMPORTANT REASONS why this is not happening in most classrooms. The first reason is BULLYING, and the second reason is STUDENT ATTITUDE and LACK OF MATURITY.

cross-disciplinary teams

Middle-school, when most students are first put into math-solution groups, is the age of the MOST EXTREME BULLYING (although bullying starts in Kindergarten). Students are usually left to sort themselves into groups, and usually, in-crowd friends choose each other, while the remaining students are randomly forced into groups with students who regularly bully them. This same situation continues in many high-school classes, and is sometimes worst of all in the smallest schools where there is only one math class per grade.

It takes an extremely effective teacher who can give groups precise tasks, direction, and rewards based on individual effort to get a group to make effective progress. Generally what happens is one of several things. The students don’t understand what they are doing at all and therefore have no idea (or motivation) even to try. They end up wasting time and talking about non-math-related matters. Or, at best, one or two students do understand and do the work, while the others loaf and do nothing, but coast on the group grade (if there is one), having not done the work, and not understanding the work that was done by the others. Or, those who are friends in the group use the hour as a social time, while the unwanted group members spend the time staring at their papers, feeling excluded, and just wasting the whole hour.

Requirements for effective group work are:  1.) being in a group with others you like or respect, and others who like or respect you; 2.) Having enough background in the subject, that when given A SPECIFIC TASK, all the individuals in the group can work on it;  3.) Being able to effectively subdivide tasks; and 4.) Having individual accountability for one’s contributions to the group. Most teachers do not have either sufficient time or experience to be effective in all these ways and rely on immature students who are not willing/able to these things themselves (as an adult work group would be able to do).

2.  Creating understanding of WHY methods work, rather than merely learning computational solutions.  This is an admirable goal, but it is not being correctly implemented at the proper ages, in the proper stages, or in the proper ways.

understanding the new math

Mental maturity, and ability to deal with abstract concepts arrives at different times for different students.  Abstract thinking arrives for a very few students in the lower elementary grades, for a few more students in the upper elementary grades, for about half of students by middle school, and for at best two-thirds of students by high school and early adulthood.  For some people, it never arrives at all.  Having taught a great variety of math topics over the years, some students grasp one topic at a young age, but don’t grasp another until many years later, if at all.  Since every student has a unique profile of what they grasp or don’t grasp, this is the origin of the “spiral curriculum,” where each year, many topics are introduced, and each year, the math texts cut slightly deeper into each topic (assuming the school is still using math texts).

Let us take telling time as an example.  A few students are able to grasp telling time well in kindergarten, while others, no matter HOW much time is spent in the classroom in grades two and three, just cannot grasp it until fifth grade.  Then suddenly, something “clicks.”  Their brain has arrived at the right level of mental maturity.

Unfortunately, today’s curriculum introduces so many topics that few are actually mastered.  Thus, many students move up through the grades NEITHER understanding, NOR being proficient in calculating.  Most students need and WANT to become proficient at calculating and getting the right answer in the elementary grades.  This builds their confidence.  They also want to know in what situations they might use those skills (which gives learners motivation, and is often an area neglected by teachers).  Those who do not become proficient at calculating lose confidence in themselves and are certainly even LESS likely to be open to any discussions of “understanding.”

A current controversial topic in the math field is whether students need a certain amount of proficiency before they can understand “why” things work.  After two decades of experience teaching math at the elementary and middle-school levels, I come down hard on the side that it IS necessary.  Young elementary students can appreciate that a correct answer can be found through several different methods, but it is a waste of precious class time AT THAT AGE to spend a lot of time on WHY (an abstract concept which despite the weeks spent on it does not actually increase their understanding) instead of on developing proficiency and thereby building students’ confidence and excitement about learning more.

It was not the intent of the math experts, I am sure, in revising math curriculum, to have students wind up being neither able to understand, NOR be able to calculate!  Their intent was to WIDEN the curriculum to INCLUDE more understanding.  But with only four-to-five hours a week (at best) of classroom time to teach math per week,  at least half of the available time is being taken up with “understanding” (which is not being understood by the majority of students), and not enough time for most students to become proficient at calculating.  Those who do become proficient are generally having additional support from parents and tutors.  Furthermore, homework has been greatly reduced from a decade ago (approximately cut in half) which means that more students than ever before are not mastering basic procedures.  When students get into middle school and one-third of them still cannot determine the answer to 3 x 8 without consulting their calculators, it is highly unlikely they will gain any “higher understanding.”

3.  Creating innovative and divergent math thinkers.  Criticisms of the past were that students were memorizing times tables and learning to calculate, but not understanding what those calculations meant; students were unable to take even a simple story problem and know which calculations to perform.

innovative and divergent thinkers

After two decades in the classroom, I can easily see this problem did not stem from memorizing or calculating.  This problem stemmed from teachers throughout school not teaching children how to TRANSLATE between English words, and math language.  In most cases, elementary teachers are not math majors.  In fact, most became elementary teachers because they are math-phobic!  They teach the calculations, and generally skip all the story problems (as did I when I first began to teach math).  Yes, it is partly a time problem, but the REAL problem is that most teachers are afraid they will not be able to explain to students how to do story problems, because they never learned themselves! Speaking as someone who did not learn this skill myself until I was an adult, I see that this is the number one area that students need the MOST help with.  I find myself wondering if students in India, China, and Japan are getting this sort of help from a young age, while students in the West are not?

Rather than wasting precious elementary time on esoteric math subjects, and making “arrays” for WEEKS in order to “understand” multiplication, students would be much better served learning to calculate, and having DAILY GUIDED PRACTICE on particular types of story problems, both in order to recognize types of problems, and to be able to readily understand how to translate the English language into MATH language.

What the math “experts” who design curriculum are not realizing is that showing students all the different possible ways to solve every type of math problem does NOT create the “divergent” innovative thinkers they are looking for.
As for math majors, sometimes (not always), those who were brilliant in math are unable to explain it clearly to those who are having trouble, because the teachers never experienced those same troubles themselves.  Sometimes (not always) teachers who were not good math students are able to master math, and are far better at figuring out where and why students are “stuck.”  Lucky children with difficulties have those teachers!  The very first requirement for becoming a divergent thinker is self-confidence in one’s own abilities.  This comes from being sure that one knows at least ONE way to get the right answer every time, even if one knows that other ways do exist.  The main thing is to MASTER at least one method.

Beyond competence, creating divergent thinkers is more of a personality-trait question.  This question has more to do with motivation and stimulating interest, and comes from the sort of child who always asks, “Why?”  Most children don’t ask why, and most don’t care about why.  To create more innovative, divergent thinkers, every teacher in every classroom, in every subject, needs to challenge ideas and get students excited about learning.  And yes, teachers need to be “entertaining,” too! Innovative thinkers aren’t usually innovative in just one area (such as math).  Most innovative thinkers draw their ideas from multiple sources and synthesis of ideas from multiple disciplines.  Students need help becoming competent, and beyond that, to be inspired enough to pursue their own interests in a self-directed way.  Curriculum which forces students to calculate by many different methods fatigues many students and actually de-motivates them from further self-directed learning.

It is difficult for a new or average teacher to overcome these difficulties.  Hopefully with time and experience, Western society will adjust to the new math curriculum, but I am afraid it will be later, rather than sooner.

–Lynne Diligent

The NEW Math:  Part I – WHY We Have It

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The NEW Math: Part I – WHY We Have It

September 5, 2013

Test Anxiety

“PLEASE, can you help me, Mrs. D.?  We are having a math test TOMORROW and I don’t understand anything!”  This has been the most common complaint I have from my sixth- and seventh-grade tutoring students (ages 11-13).  Whether the topic involves geometry, equations, story problems, or even more basic calculations, nearly all my students (excellent students, too) are having the same dilemma.

If you are a parent or educator who has wondering for years (as I have) WHY we HAVE the new math, this post will explain it clearly.  (Part II explains why the new math is not working in many schools.)

 The New Math Style

The new math style in some schools appears to be, “The teacher doesn’t explain—he or she merely facilitates ‘groups’ while students (hopefully) just teach themselves.”  Like many people, I have felt confused for several years about the new style of math teaching.  Instead of presenting a lesson, giving students guided practice, and then sending them home to do independent practice (homework), the new style, which my tutoring students are experiencing, seems to be, “Don’t follow a text book (even if they are available).  Instead, just find some seemingly random problems off the internet (seemingly without any overall coherent plan of units), tell students to put themselves into groups, and pass out the photocopies.  Tell the students, ‘See if you can find some solutions to these problems.  Do this for three or four days, then tell students, “We will be having a test on Friday.’ “

Imagine middle-school students with these feelings being asked to get into a group and work on random problems.  It is not likely to go well.

Imagine middle-school students with these feelings being asked to get into groups and work on random problems. It is not likely to go well.

Of course parents’ reaction to this is panic.  Eighty percent of the children are LOST with this approach. Those who can afford it are rushing to math tutors, who teach the children by traditional methods what they should have learned in school.  Those who cannot afford it have children who fail.

Let us look at a “hammer” analogy.  Instead of saying, “Let’s learn how to use a hammer and see if we can get a good result with the nail pounded in correctly,” the new approach effectively asks, “Let’s learn why the hammer was developed, and how and why it works in theory….but don’t waste your time becoming competent in using one!”

hammer nailing into a board

Next, students are given a national or state test consisting of pounding nails into a board, which of course they FAIL!   Meanwhile, the “experts” lament that they are unable to do it!  

This is exactly what has happened with math education.  Teachers using “traditional” methods have been drummed out of education (mostly retired), while younger teachers have all been trained to use the “new” methods.  

WHERE did this approach ever come from?

I finally found the answer I’d been searching for, in a MOOC (FREE online course offered through Coursera, taught by world-renowned British mathematician Keith Devlin of Stanford University, Fall 2013, called Introduction to Mathematical Thinking.)

Keith Devlin

Keith Devlin

Devlin explains that in the job market, there is a need for two types of mathematical skills.  He describes Type 1 skills as being able to solve math problems that are already formulated, and it’s just a matter of calculating the correct answers.

carpenter measuringmachinist measuringloan officers

Type 2 skills involve being able to “take a new problem, say in manufacturing, identify and describe key features  problem mathematically, and use that mathematical description to analyze the problem in a precise fashion.”

aircraft designBoeing CEO

“In the past,” Devlin says, “there was a huge demand for employees with Type 1 skills, and a small need for Type 2 talent.”  In the past, education produced many Type 1 employees and a few Type 2 employees.  However, in today’s world, the need for Type 2 thinkers has greatly expanded.  Not only do scientists, engineers, and computer scientists need to think this way, but  new business managers also need to, in order to be able to understand and communicate with math experts and make decisions based upon properly understanding those experts.  So the “new math” curriculum is an attempt by the “experts” to produce many more Type 2 thinkers; yet, it is FAILING to do so.

Prior to the late 1800s, math was viewed as “a collection of procedures for solving problems.”  In the late 1800s a revolution occurred among mathematicians which shifted the emphasis from calculation to understanding.  The new math of the 1960s was the first attempt to put this shift into the classroom, and the results were not successful.  I see the current shifts to put new math into the classroom as the second attempt, which is different from the 1960s attempt (children are not studying various bases these days), yet no more successful in reality.  Part II of this series will explain the three reasons WHY this is happening.

 –Lynne Diligent

The New Math:  Part II – Why It’s NOT Working in So Many Schools

Marijuana Use, Then and Now, on College Campuses in Colorado

November 26, 2012


 I live overseas in North Africa, but my home state in America is Colorado.  Colorado is one of the two states which just voted to make marijuana legal.

Yesterday at home, I was sorting through some old boxes and came across the letters I had received while in high school and college.  Most were now moldy, and I was reading through them one last time before tossing them all these years later.

2011 Boulder annual “420 Pot-Smoking Rally” on the University of Colorado campus

To my surprise, in letters from 1973, I had a friend at the University of Colorado in Boulder, who said, “If you don’t smoke grass, there is nothing to do on the weekends.”  He wasn’t a smoker, but implied most people around him were.

In another letter, from my boyfriend, who was a serious student at the University of Northern Colorado in Greeley,  said, “I went to a party this weekend where there was only supposed to be beer.  But when I got there, there was a pile of marijuana at least three inches high.  Everyone was rolling cigarettes (with the marijuana) and passing them around.  I passed five (marijuana cigarettes) by to other people, but I didn’t try them myself.   Everyone was stoned.”

Mass exhale of marijuana smoke on the University of Colorado at Boulder campus in 2010, at the annual “420 Pot-Smoking Rally.”

I know a student currently at the University of Northern Colorado.  I asked her what the reaction was on campus to the new law.  She told me all the college students voted for it, and many were running around shouting, “Yay!” with their arms in the air after hearing that the new law passed.  But I don’t think everyone is using it.  The student I know told me that she’s been to a couple parties where she smelled the marijuana smoke in the air, but didn’t actually see any marijuana.

I’m sure I must have been around people who used drugs, but I never associated closely enough with them to know that they really were, other than some cousins I had who used marijuana during the hippy era.  I also attended a couple of parties (in Cape Girardeau, Missouri) where I smelled the marijuana smoke in the air, but never actually saw the product myself.   I used to hear during the 1980s that one or two people I knew in business were using cocaine, but I didn’t know whether to believe it or not.

Interestingly, I’ve lived in North Africa for twenty years, and I hear that tourists are always offered marijuana in the souk.  Yet it’s never happened to me.  My husband (a local) says it’s because, “You don’t look like the type of person who would want it,” which is true!  But with it happening to so many others, I felt a little disappointed that I’d never even been asked, or approached.

I don’t know what the percentage of marijuana users in U.S. colleges was then, or is now, but I’m going to guess the percentages were/are similar.  I’m going to guess that back then, 30-40% of people tried it once, and that maybe 15-20% of people might have been regular users in college (and far fewer once they got out of college).

Legal marijuana clinic in Colorado, prior to marijuana being legalized for everyone.

I’m going to guess that with this new law, maybe 60-70% of youth may try it once, and maybe 30% might turn into regular long-term users.  In April, 2012, a marijuana-smoking rally at CU Boulder attracted 10,000 participants.  But it should be remembered that Boulder has 30,000 students, which means that 2/3 did not attend.

I predict it will be a novelty for a generation, and as health problems start to show up in regular users (such as happened with tobacco cigarettes), people will try to quit, and it will become thought low-class to be a pot-smoker, as has happened today with cigarettes.

–Lynne Diligent

Do Cat Thieves Give Clues to the Origins of Criminality in Humans?

November 12, 2012

Here in  North Africa, I watch the neighborhood animals, who belong to no one, and make their rounds in the same places daily.  We have a lot of street animals, and cats often jump in to our house through the windows (other people’s houses, too), in search of food. Some of them can get quite aggressive, especially with our own cats.  Our cats feel they have to go outside and “defend the yard” every time they see a cat jump in over the garden wall.  Of course they go absolutely wild if a neighborhood cat jumps into our house.

I began to think about these intruders as thieves, because that’s what they would be considered, if they were humans. It’s easier for them to steal food than it is for them to hunt for it themselves in an urban environment.

It’s also easier (than working) for human thieves to do the same–either because they are lazy, or their environment didn’t give them other reasonable options, or because they are more greedy than others (white collar criminals?). I wonder how much of this laziness/greediness could be genetically determined, or if it is somewhat genetically programmed into all of us.  In fact, scientists are now finding evidence of this (see HERE and HERE).

My observation of cats in the neighborhood has lead me wonder whether ALL cats would be thieves if they weren’t fed by their owners.

Therefore, what keeps ALL humans from becoming thieves? Rather than asking the question who is likely to become a criminal (in human society), perhaps we should seek to understand this question  by asking instead, what KEEPS people from taking the easy route of becoming a thief/criminal? Instead of asking who cheats and why, maybe we should be asking, “Why doesn’t EVERYONE cheating/lying/stealing? What keeps those of us who are law-abiding citizens, so?”

I wonder if the answer lies in the environment.  Instead of saying that the environment causes criminality, perhaps the reverse is actually closer to the truth.  Perhaps we would all be criminals, except for if we have a positive environment which, as we are raised, gives us POSITIVE REWARDS (such as RESPECT or ADMIRATION) for becoming law-abiding citizens.  Those who grow up in impoverished environments (or cultural environments) where they never experience these rewards, are unlikely to become honest and law-abiding.

What do others think?

WHY Parents and Teachers Need to Watch the Same Television Shows as Students Do

February 17, 2012

As a parent or teacher (even outside of America, and regardless of your religion or lifestyle), have you tried to instill proper values and behavior in your own children or students, yet watched while the following values and behavior appeared instead?  Have you wondered where this has been coming from?

  • Requesting a bulldog
  • Popularity of sushi
  • Proliferation of fake ID’s and even younger high school students attempting to use them
  • Underage drinking, even at home parties, where parents leave and let children party alone
  • Obsession with champagne
  • A sudden interest in learning Burlesque dancing
  • Requesting or attempting underage driving
  • Obsession with Ivy League colleges
  • Teenage obsession with wearing only “designer” dresses
  • Thinking it’s not normal for parents to make a “curfew” time
  • The idea that even young teenagers “go where they want, and do what they want,” and that “their parents give them the freedom to do so just like adults;”  they TELL their parents what they are doing, rather than ASK them.
  • Girls (even young girls) acting in a sexually aggressive manner toward boys (girls insisting that they both take off clothes)
  • Girls thinking that it’s normal to date older men secretly without their parents knowing about it
  • Thinking that normal parents just go to bed, and “don’t wait up for their high school children who come home late.”
  • Sassy, angry attitude toward any parents who question any of the above assumptions!
  • The idea that “success” in life equates ONLY to how much money you have, and how “glamorous” you appear to others!
  • Honesty, dependability, responsibility, and/or service to humanity are unfashionable, boring, stupid, and undesirable
  • Kindness to others is “out;” while “one-upsmanship” and rude “put-downs” at the expense of others are “in”
  • An expectation that life is supposed to be one continuous “party”

Any parent or teacher who is having trouble understanding teenage values and behavior today should IMMEDIATELY watch the three television series Beverly Hills 90210 ; Gossip Girl; and 90210 (a different show than Beverly Hills 90210).   Even watching a couple of episodes of each show will give you an idea of where this culture is coming from.  (Click on these titles for direct links to the series which should work worldwide.  Make sure to start with Season 1, Episode 1.)    These new values are coming directly from television.

Unfortunately, teenagers are now watching these shows WORLDWIDE.  Some are watching on the internet, in English (especially with the global rise in study of English, it is now accessible).  But in most countries, these shows are now dubbed in local languages, and right on the television.  Not only is American culture changing, but world culture is assuming that these TV shows represent traditional American values (which they most assuredly do NOT).

The people who made these shows recognized that they are FANTASIES of how teenagers WISH their lives were.  That’s what makes them fun to watch.  However, unfortunately, the children who grew up watching these (without any input from their parents) grew up assuming that this is what they WOULD be able to do as teenagers, and now, the upper middle classes ARE DOING it. Some of the middle class parents don’t know that their children are behaving this way.  Among more conservative families, parents should BEWARE if their child asks to spend the night with another family, because they are often going out, or even sneaking out to nightclubs.  It doesn’t help that the full age of majority in many countries is 18, rather than 21.

I live in the Middle East, and throughout our region, this is exactly how most teenagers are behaving.  The emphasis in our region is all on appearances to create the impression with others that you are rich (even if you are not).  Most of those who are rich turn their children (even girls) loose with plenty of money and the family chauffeur (usually driving an expensive, black, four-wheel-drive vehicle) for the weekend.  They certainly don’t wait up for their children to come home at night.  Most of the kids have fake ID’s and go to night clubs (which don’t even open until 11).  Their age is clear, but they just slip $20 to the doorman, who lets them in.

Father Knows Best

In the past couple of years, I’ve read a number of articles where generations following the baby boomers are now criticizing the work ethic of baby-boomers (born 1946-1960) and wondering where this work ethic came from.  It’s very clear to me now.  It came directly from TELEVISION (as well as from our parents, and from society in general).

Shows during the 1950s and 1960s (and even into the 1970s) showed children working hard, being kind, taking responsibility, and most importantly, GETTING RESPECT FROM OTHERS FOR DOING SO.  Some of these shows were Father Knows Best, Leave It to Beaver, The Rifleman, The Waltons, and Little House on the Prairie.   In contrast, teenagers who behave this way today don’t get any respect from others.  Instead, they get “USED BY OTHERS” (in the words of a teenager I tutor).  Today, it’s showing-off and acting in accordance with the list above that gets a teenager respect from other teenagers.

–Lynne Diligent

Why A College Degree Does NOT Slow Brain Aging

January 23, 2012

The idea currently being promulgated by aging researchers that a college degree itself increases mental capacities later in life by at least a decade is just plain WRONG.

A Sharper Mind, Middle Age and Beyond (New York Times, January 2012) summarizes some of the latest aging research and states, “For those in midlife and beyond, a college degree appears to slow the brain’s aging process by up to a decade, adding a new twist to the cost-benefit analysis of higher education — for young students as well as those thinking about returning to school.

Having been a teacher for a decade in America and two decades in Africa, I’d say something else is at work here, skewing the statistics. This research has simply put the cart before the horse.

It’s no doubt true that exercising mental capacities maintains a better level of brain functioning, it is NOT the college degree which is creating the improvement.   It is that higher-functioning people (and more wealthy people) tend to be the ones who complete their college degrees!

Having lived in Africa for two decades as a teacher, I’ve had plenty of opportunity to observe many people who were illiterate, many who left their education at all sorts of different levels, and many college graduates.

What happens is that those who have learning disabilities, listening and/or attention problems, intelligence deficits, or other problems which prevent them being successful in learning tend to drop out all along the educational path.  It is the higher-functioning people who go on to complete their education.  If a researcher comes along later and says, “These people are higher-functioning later in life because they earned a college degree,” the whole premise is wrong.  Those people are higher-functioning because they always were higher-functioning.

In America, we are now trying to push everyone into college.  Having a college degree will not give everyone the benefit of an extra decade of a higher-functioning brain.  I know some people in America who struggled mightily to get through college in six years, who in spite of their degree, don’t like to read (because they had learning disabilities to start out with).  It is not a person’s college degree which keeps their brain active.  It is their PERSONALITY.

 

Furthermore, I have known certain people who never learned how to read or write who enjoy conversing on current events; who follow active hobbies, crafts, dancing, or sports; who read, write, or blog; who take a course or who teach something to others; or who regularly participate in social activities or weekly luncheon clubs.  All of these things can keep one’s brain active.

Study, or a college degree is just one type of activity.  The aging researchers quoted in the article linked to above are just being far too narrow in their focus.  College-educated people have already self-selected themselves into a group which has high cognitive functioning.

It’s not the college degree that keeps one’s brain from atrophying.  It’s the personality, the interest, the spark for life.

–Lynne Diligent