Archive for the ‘Teachers’ Category

Teaching Cursive Part 7 (of 25): How to Teach Correct Forward Slant

January 8, 2016


Turn the paper while writing in order to get properly slanted cursive.

Turn the paper while writing in order to get properly slanted cursive.


Correct positioning for left-handed writers to obtain the forward slant.

Correct positioning for left-handed writers to obtain the forward slant.


This post is both for parents and for teachers who may be called upon to teach cursive, but need help with how to teach the correct slant.  For examples of correct slant, see this post.

The way to get a slant is to TURN THE PAPER (or notebook). Instead of having the paper directly upright in front of you, rotate it about 45° COUNTER-CLOCKWISE, so that the upper right corner is in the 12:00 position (and lower left corner is in 6:00 position). Then write normally on the page, and the writing will have the proper slant.

The paper should be turned on an angle to write for one’s entire life–it is the correct way–it is not something one does while learning as a child, and later on reverts back to using a straight paper.  No one can write with a proper forward slant if the page is not turned on the desk

A helpful hint for teachers and parents is to cut a thin strip of paper (I used to use a 1/8th-wide strip cut from red construction paper, but any paper will do) and tape it to the desk or table where your student is working. The bottom edge of his paper should rest on that line. As a third-grade teacher, I taped these red lines on each desk before the first day of school. (I also did it when I taught Kindergarten for three years.) How did I get the idea? My own teachers did it when I was a child.

Line taped on edge of desk for slanted cursive writing.

Line taped on edge of desk for slanted cursive writing.

If you would like to try the taped line method (highly recommended), here is how to put it in the right position:

Steps for Correctly Positioning the Taped Line on the Desk

It’s important to WATCH your own children or students work, for several weeks or months, until they develop the habit automatically. It feels very awkward at first since they have most likely learned incorrectly. They might need constant reminding every two or three minutes at first.  As a teacher, it was easy for me to keep constant watch in the classroom and remind students all day long, “Turn your papers,” or “Papers on the red line.”

How to Move the Paper Up and Down While Writing

Once students start writing, there will naturally be some students whose writing is not slanted enough, and others whose writing is too slanted.  At that point, tell those individual students to habitually turn their papers more, or less–whatever is required–in order to arrive at the correct amount of slant.

 How to Adjust Student Papers Later On

My hope is that these instructions will help parents and teachers understand how to teach cursive slant with excellent results.

Teaching Cursive Part 6 (of 25): WHY Correct Cursive Slant Is Important in American Writing

January 7, 2016

Cursive Slant in American Writing

Why is cursive slant still important?  American society still makes judgments about people based on their handwriting, and slant is one of the strongest criteria used.   Most people make these judgments subjectively and subconsciously every day.  However, employers and bank officers are just two examples of those in the power structure who employ professional handwriting analysts to make judgments about prospective employees and about people applying for loans.

In the photo above, I have written out some examples of various slants, as well as how they are perceived.  As a teacher, when I introduce cursive writing, I actually write samples like this on the chalk board to show them to students, and explain what people might think about others based on the slant of their handwriting.  So I encourage them right from the very first day that our goal is to try for an average forward slant, shown in the last example in the photo above.

One other example did not fit on the page, so here it is:

Variable slant

Our slant, like other aspects of our handwriting, will change from day-to-day, but we should generally try for a correct forward slant.  This can be obtained by turning the writing paper 45° counterclockwise (subject of the post following this one, Part 7).

Countries and cultures, when compared with one another, also tend to have typical characteristics.  For example, British “reserve” as compared with American “friendliness with strangers” can be seen in typical handwriting slants from each culture.  Vertical, or even backslanted writing is more common in British culture than in American.  If we move to North Africa, we find people generally suspicious and distrustful of others, and as expected, backslanted writing (in Western languages) is most common of all.

If you are from outside the United States, you should be all right using the slant which is most common in your own culture, and no one will judge you negatively.  But if you are living or working in America, you should be very aware of this and of the impact it could have on your personal life or career with any of the undesirable slants discussed above.

My next post will explain, with photos, how to position the paper to get a correct forward slant.

In case anyone has had trouble reading the cursive in the photo, here is a typed version:

Cursive Slant for American Writing

In American culture:

A vertical slant is not considered desirable; you are judged to be too logical, too cold, and without feeling.

A backslant is to be avoided at all costs; you are judged to be  emotionally suppressed, possibly with some kind of ecret emotional trauma in your background, difficult to approach,and someone who maintains a shell around themselves.

This is too much forward slant; these people are judged as being far too emotional, of making all of their decisions based on feelings.

This is the minimum acceptable forward slant.

This is an average/normal forward slant, which is considered most desirable in America.  This slant, to Americans, indicates a balanced person who uses good judgment between logical decisions and emotion in their decision-making.

A variable (frequently changing) slant indicates moodiness, instability, and a frequently changing picture of oneself, as well as trouble making decisions.


How Can Parents and Students Find a Good Tutor?

August 3, 2015

Good tutor

When looking for a tutor, start by asking individual teachers and other parents at your own school if they can recommend someone.  Ask other parents, first, because sometimes they know of current tutors that the school doesn’t.  Sometimes students don’t want anyone at school to know that they are being tutored, which is why parents sometimes know of more tutors than schools do.  Numerous individuals in schools know of good people, so don’t just limit yourself to asking only one teacher, or one administrator.  If you don’t find someone through other parents, ask the librarian, the administrator, and all the teachers near the grade level of your child–a couple grades up, and a couple grades down.  If that doesn’t work, try asking neighbors and work colleagues who have children.  Don’t forget to ask people with older children, as previous tutors may still be available, but current school personnel may no longer know them.  If you are an expat, ask other expats in your community.

The most important things in finding a tutor for your child are that:

1.)  The student likes the tutor, and that they are able to develop a personal connection; otherwise, no matter how knowledgeable the tutor, it just doesn’t work with your child.

2.)  The tutor understands that what you want is better grades, but also for your child’s skills to improve.  It has to be a combination of both to work out.

3.)  The tutor also functions as a cheerleader/coach for your child, as many students in need of tutoring have lost confidence in themselves.  A good tutor, who the student connects with, can help replace that confidence, while helping your child master the skills he or she is having trouble with.  This is why it’s so important that they like each other and have a good relationship.

4.)  The tutor needs to be just a little more on your child’s side, than on the school’s side.  Sometimes, the problem with tutors who are also teachers at the same time is that there is a fine line between helping a student overcome difficulties and helping them improve their grades, vs. helping too much, and crossing over into doing it for them.  Tutors who are also teachers sometimes don’t go far enough, while sometimes tutors go too far.  A personal recommendation from other pleased parents or pleased teachers can go far in finding a tutor that strikes the right balance to really help your child.

–Lynne Diligent

Why Reading Levels Continue to Decline–PART I (of 2)

April 30, 2015

Students who still can't read

The problem of students who are unable to adequately read their grade-level textbooks is not new; the problem starts in early elementary school and only gets worse as students move up in grade levels.  Unfortunately, the rise of the internet in the past twenty years has only exacerbated the problem.

Let’s look briefly at the pre-internet reading situation in middle-class schools and above (poor schools have additional problems which will not be treated in this particular article).  Looking back, the most important function of the school library was to be filled with books to be used for school research projects which were at the correct reading levels for students.

Primary School Libraries

Not only were grade-level books provided, but there were plenty of below-grade-level books on every topic available to readers who were still below grade-level.  For example, a middle-school student with a lower reading level could still find good primary-level books on any research topic assigned. There used to be hundreds of books available through publishers, on every conceivable topic, for school libraries and public libraries to choose from.  Bookstores made them available to the general public.

Today, funding priorities are focused less on providing new books for the school library–partly because of the explosion of new topics and knowledge in our modern world, and also because of the explosion of information on the internet.  Now funding must be divided between  books, and new library computers.

The market for children’s non-fiction has plummeted since 2005.  Sales to both libraries and bookstores have dropped substantially. Therefore,  fewer nonfiction books for children are being written and published.  Publishers and booksellers decided to drop most nonfiction, and focus primarily on children’s fiction–for which there does continue to be a market.

Desirable Non-Fiction Book Topics

 The lack of nonfiction is particularly damaging for boys.  They tend to prefer autobiographies, nonfiction, newspapers, and realistic topics. Ever since 2005, as the internet has become more powerful, children’s nonfiction has declined.  This decline is preventing many boys from developing as readers. National standards in Britain and America drive the decline even further, “…as the strictures of the national curriculum have driven many publishers to stop producing anything very original, and how many books on Vikings and rainforests do we really need?”

Starting in middle school–most commonly Grade 6 and above–teachers now direct students to the internet for research, instead of to school libraries. One reason is that science classes are now often researching topics which are not even available in books in the school libraries–things such as genetics, and various types of cells–and this is happening in Grades 6, 7, and 8.

Students are now being asked to research obscure people for reasons of diversity in the classroom, rather than famous people.  This means that the information can only be found on the internet.  Students are now expected to use the internet for all research.  This is now true even in elementary school.  Students may be assigned reports on animals, for example.  Perhaps there are perfectly good books in the school library at the right reading level; however, it has now become “too much trouble” to even check , when one can “just look it up online.”

Using online sources creates a much worse problem–aside from the problem of whether a source is reliable, biased, or incomplete–that is, the problem of reading level!

Below is reading sample from a Grade 5 science text which more than half of students (even in good schools) might find too difficult to read without the teacher’s help.  Why?  Because students are now used to reading only fiction in reading class.  They are not used to the vocabulary in non-fiction; nor are they used to reading expository sentences..

Levers text


Not only have student reading levels declined in real terms, but the sources students are now attempting to use are usually written at far too high of a level for their age.  Students in middle school and high school usually go first to Wikipedia (and are often specifically told to do so by their teachers, particularly in international schools that have much less access to English-language printed material).  Unlike school library books or school text books of old, vocabulary is not controlled for difficulty.  Sometimes the articles are poorly written, and written by scholars who are just trying to impress other scholars with their difficult vocabulary.

Below is a section of what one of my 7th-graders attempted to read for a report on glial cells last year, using Wikipedia.  Most students now need adult help to translate and explain what they are trying to read.  To a poor reader, this may as well be in Chinese:

Glial cells text from Wikipedia

Those students who can afford it hire private tutors.  My students show up and say, “I have a project or report due next week on glial cells (or guard cells, or an obscure historical figure).  Can you help me?”  Students arrive knowing nothing about the topic, and are expected to research on line, and write a report listing their sources.  So, together we look on line and usually find very scholarly articles, which I, as an excellent reader in my 60s with a graduate degree and decades of experience teaching, sometimes have trouble understanding!  So we pull out little snippets of information from various articles, which I explain in plain English and then mark our source.  Even many Wikipedia articles are written by scholars, seemingly just in order to impress other scholars!

Hiring a private tutor

I learned a great trick years ago when I was in a professional writers’ group.  If you need good, concise information on an area or a subject, one of the best ways to find it is to go directly to children’s books, where you can find the information thoroughly distilled and written in clear, easy English.  I use this same strategy now and show students how they can search on the internet using the search terms “my topic + explained for children.”  It doesn’t always work, but it often does.  Sometimes we arrive at a website where something has been clearly explained at a reading level appropriate for middle-school students.

The thing which most excited me about the internet when it first began, especially as an overseas teacher with little access to English-language reading materials, was its potential as a world library at our fingertips.  Sadly, much of this potential is being lost for two reasons.  First, children are not developing adequate non-fiction reading abilities to function in society.  Second, most of what is available on the internet is written at far too high of a level for students to be able to benefit from it.

In most American schools, for the past several decades, the textbook has been seen by teachers as only one resource of many for classroom use.  In fact, years ago, over-reliance on the textbook was almost seen as the mark of a lazy teacher, within the teaching profession.  Unfortunately, the current result of this attitude has now led to teacher over-reliance on the internet, with students who are unable to understand either their textbooks OR the internet!  I personally have come around 180° to the view that students would be better served if they learned and discussed in class everything which is in the textbook.  Now, however, there is a new problem!  Many schools are now moving entirely away from textbooks as a way to save money, and teachers are mostly downloading random worksheets from the internet. Unfortunately, it is students who are again losing out on their education.

Part II of this series will discuss what parents, schools, and teachers can do to address these problems.

–Lynne Diligent

Why the Flipped Classroom Has Gone Too Far

April 20, 2015


Flipped Classroom

The flipped classroom is just not appropriate for all subjects, all of the time.  This educational fad has gone way too far, and is being used for the wrong reasons.  Most importantly, it runs into problems when teachers attempt to use it as a time-saving device in order to cover more material, because only a small percentage of students’ reading levels are actually up to grade level.

While the flipped classroom sounds like a new idea, it is actually an old idea.  Several decades ago, it was called preparation–a good name–in Britain, although I am not aware of any specific name for it in America.  It often consisted of reading a selection in a text book before arriving in class, for example, so that one could better benefit from a lecture.

The flipped model works extremely well for math classes.  As an elementary teacher, I would look each day at the following day’s homework section.  I would give about fifteen minutes of instruction and guided practice specifically on what my third graders needed to complete that day’s homework. We did not waste time in class doing homework.


I expected all children arrive in class with their homework complete, in order to be ready for the most important part of the lesson, learning from mistakes.  Right or wrong, they all got nice, big A‘s on the homework for completing it in pencil (including showing all work and carry numbers or cross-outs).  If they did not show their work, or if the work was either undone, or incomplete, they got a large, red F.  Within a short time EVERY child arrived daily with homework done.  We then put pencils away, and got out ink pens which we called “marking pens.”  Each child corrected their own paper.  There was no incentive to erase wrong answers, because the child already had an A, just for completing the homework.  We spent the following 30 minutes going over the problems missed by the largest numbers of students, working them on the board.  Students learned so much when they could see where they went wrong.  In most cases, we found errors such as subtracting the ones place, while adding the ten’s place, in the same problem–or, in forgetting to add in carry numbers, things like that.  In math class, the flipped classroom works fantastically.

Using the flipped classroom as a time-saving device runs into trouble in subjects which require a lot of reading for two reasons.  One reason is that in many good schools, students are feeling overwhelmed with the amount of homework, leading them to take ineffective shortcuts.  Using Spark Notes, and similar services, just do not engage student interest, and students miss the benefit of the literature.

The most important reason the flipped classroom runs into trouble is that students’ reading levels are just not up to grade-level standard in terms of being able to read either text books, or literature, on their own.

This problem is not new.  It was widespread in the 1970s and 1980s.  Secondary teachers in Colorado at that time were required to take Reading in the Content Area.  It was a course designed to help secondary teachers help students who were unable to read their textbooks adequately.  Because of the decline in book reading and adequate reading instruction, together with the rise in technology, in 2013,  more than two-thirds of students in the United States were now below reading level for their grade.

4th Graders Who Scored Below Profient Reading 2013

Unfortunately, today, most students, even some of the best students are not even attempting to read literature (or their history, or science, text books).  Most are attempting to find the film online.  Poor readers who attempt to read Spark Notes have trouble understanding even that, and certainly no one finds Spark Notes inspiring.

Many secondary English teachers (including elementary reading teachers, and secondary science and history teachers) are now assigning reading for homework, in order to cover more material and just have discussion in class.  The problem with this is that two-thirds of students are either not able to read effectively, and do not even attempt to read because of feeling overwhelmed.

So what do teachers need to do in order to combat these problems effectively?

First, they need to read the book (or text book section) themselves, in the mindset of a student, thinking about vocabulary which many students may not know, and noting it down.  They need to think about the major ideas and how those ideas relate to life today.

Next, they need to introduce the book or reading selection with a short, inspirational talk, that will make students feel like they can’t wait to read more!  They need to talk about and explain vocabulary (whether it is old-fashioned language or science terms) before students start to read.  History teachers need to think about the problems they are teaching about in a historical context and how those problems relate to life in the world somewhere today. Introduce the similar problems and questions of today and how they are being dealt with in the modern world, then look at the same questions in how they are being dealt with in the novel, or in history, or in the science text book.  Discuss what could happen in the future with the same issues.

Rather than starting a unit with reading the text book or novel, start the unit with a discussion of the students’ life questions about the issues which will arise in the reading selection  Here are three examples:


History:  While studying various political decisions of Roman Emperors, first discuss similar problems in the modern world.  Open with a question, “What do you think about when you hear of an apartment building collapse that kills people because of shoddy building practices?  What should be done?”  Or, “What’s it like to be stuck in rush-hour traffic?  What would it be like if the highway were also clogged with pedestrians, donkey carts, and horse-drawn carriages all at the same time, and it happened four times a day instead of two times a day?”  Then, “Now let’s see how they dealt with these same problems in ancient Rome.”

Rhett loves Scarlet, while Scarlet loves Ashley and uses Rhett!

Rhett loves Scarlet, while Scarlet loves Ashley and uses Rhett, in Gone with the Wind

Literature:  “How many of you have ever had the experience of being in love with someone, only to have that person be in love with a different, third person?”  Then, “The problem of love triangles is universal throughout human history, and that’s what this novel is about.”

Science (Astronomy):  “Does alien life exist on other planets, or in other galaxies?  What do various current scientists think about this, and why?  Which planets and stars are most likely for this?  What kinds of planetary conditions are thought to be necessary?  Could we actually travel to other stars or planets, and how long might it take?”  Then, “Now let’s turn to the text book and begin reading together about the planets.”

Lastly, MUCH more time needs to be devoted to in-class reading (even in high school).  If teachers are concerned about embarrassing some students reading aloud, or if there are poor oral readers, students benefit greatly (even in high school) from the teacher reading aloud well (and adding in inflections and pauses), while they follow along.  It also gives everyone a chance to stop and discuss various points, such as how they feel about actions characters take, or what situations they find themselves in.

Teachers need to inspire and motivate students, and help students to see connections that they would not see on their own.  If the teacher is excited about the material, he cannot help but communicate that love and excitement to the students.

–Lynne Diligent



Education Inflation and the Future of Jobs

March 14, 2015

Education Inflation These days, the only jobs not requiring a college degree, or some kind of post-high school training or certificate course are in manual labor, or the very lowest rung of service positions.  These include fast food, waitressing, and retail sales and stocking.  The lucky few who are both hard workers and happen to get noticed, can still work their way up into management from the inside, but the percentage of people able to do this is fairly low, compared to the number of workers.

Yet, a college education is no guarantee of a job, and becoming even less so as more people become college educated.  Furthermore, 73 percent of college graduates in the United States now end up working in a different field from what they studied.

Many of the jobs now requiring college degrees used to require only high school degrees in the 1950s.  Why, then, are college degrees required now for jobs such as insurance adjuster, salesperson of insurance or office equipment, higher-levels of office assistants, and most office jobs, even though many of these jobs pay relatively low white-collar salaries? Why are employers requiring college degrees, without caring too much what subject the future employee has a degree in?  The reason is that they feel it is indicative of the person’s quality.  It’s proof to an employer that they will hire someone with sufficient reading, writing, and critical thinking ability.  It weeds out the people who can’t make it through college because of weak reading/writing abilities.  Good reading/writing abilities are a good indication of good thinking abilities and adequate arithmetic skills for use in everyday life business situations.

In the 1950s, a high school degree was indicative of the good skills which a college degree indicates today.  Now that most people graduate from high school, many people seem to have that piece of paper, but still haven’t mastered basic arithmetic in order to be able to do business math, and cannot read, write, think, or speak, at the level employers require in a white-collar office setting. Before I had a college degree, I worked as an executive secretary (and had taken courses in a secretarial school to be able to do so).  Later, when I was in a management position in a bank, and was hiring an executive assistant, I asked for a typing speed of 70 words per minute as one of the hiring qualifications.  Why?  It was not because we had a lot of things to type; it was because excellent typing skills are the best indicator that a potential assistant really has good skills in all areas. Similarly, a college degree is the best current indicator to an employer that they are hiring someone who has the general  reading, writing, critical thinking, intelligence, and public presentation abilities that they want.  Now a graduate degree is usually required to get a higher-paying job in a specialized field.  The one exception to this might be in any type of engineering.

What we are really fighting today is the process of technology advancing to take over higher-and-higher level jobs.  First we saw low-wage manual labor taken over by robots.  Next we saw most former middle-class jobs outsourced to third-world countries as their workers became educated–for example, our lower-level legal research formerly performed by new lawyers, now being outsourced to India.  Accounting work, such as tax returns, are now being outsourced over the internet to trained accountants in India.  In both cases, their foreign salaries are far less than would have been paid in America.  Now there is talk of replacing fast-food service workers and restaurant service workers with robotic solutions.  Some of these are already being tried out in Asia.

A computer-scientist friend of mine from Silicon Valley claims very convincingly that it is only a matter of time before all jobs are taken over by computers.  He claims that it is only a matter of time before computers will be able to repair themselves and no longer require humans to do so.  He further claims that even scientific research no longer need humans, as the way to solve a problem is to throw a lot of research at one area, trying many things until a solution is found.   He points out that computers are far more efficient at doing this than humans.  I always imagined that Hal, the computer, in 2001:  A Space Odyssey, could never be a reality, but my friend insists this is not nearly as far off as people think. If my friend is right, then we can look forward to a world without work, where all work is done by machines.

Unfortunately,in a capitalist world, this might be an unattractive future for many people, as how will they live, or get money to live?  The European socialist model might work better in a world without work, as machines produce, and the benefits from that are divided among all.  Different countries, capitalist or socialist, might take different paths toward dealing with the future problem of a world without work.  This is a frightening prospect, indeed. Will some countries of the world divide ever further, in a world without work, between haves and have-nots, while others create socialist utopias?  Or will the countries of the world divide between those who can afford computers and robots to do work, while those without robots employ humans as the lowest-wage slave labor?

–Lynne Diligent

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

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

Students Mourn Never Learning Cursive

April 3, 2013
Cursive - the new undecipherable secret code script!

Cursive – the new undecipherable secret code script!

Cursive was taught in my school until four years ago.  When I left, the school discontinued it as a regular subject.  Now those students are in upper elementary and early middle school, and can neither read nor write in cursive writing.

Among my tutoring students, several of them have expressed to me their sadness that their older brothers and sisters can read and write in cursive, and they cannot.  Still being in the first few classes not to learn cursive, they feel babyish and incompetent.  Perhaps in subsequent years, this embarrassment will disappear when none of the new students  have older brothers and sisters who know cursive, when they don’t.  In another six or seven years, no one will know it, and it will seem normal to upcoming students.  It’s only those in these transition years who will feel the loss.  But they will feel it for the rest of their lives.

How many adults remember the childhood feeling of waiting to learn “grown-up” writing, or scribbling to other young friends (at the age of five or six) on a paper and bragging, “I know how to write in cursive?”  Of course, at that age, no one knew, so your friends believed you, because they couldn’t read it, either!

When I tutor these students, I have to slow down and print (much more time-consuming).  Of course these students also will never be able to read historical documents or even old family letters. Furthermore, most European and Latin American countries don’t teach printing at all–they teach only cursive script starting at the age of five.  I feel this bodes poorly for a future globalized world.

I’d be happy to teach cursive to these students (being an expert cursive teacher), but that is not what I’m being paid to tutor in–we generally spend the time on math, science, reading, and writing. Furthermore, teaching cursive at an older age can be done, but it is not generally enjoyable as it is for children.  It makes children feel grown-up, and they enjoy learning it.

–Lynne Diligent