One of my former tutoring students posted this recently on Instagram as some homework that they are currently being given at the end of Grade Six (age 11-12). His comment was about hating homework.

Thank goodness I did not have to teach in this manner when I taught in an overseas American School. About three years ago (well after I left and started a tutoring business), the school I taught in revamped to the new “Common Core” curriculum, which apparently de-emphasizes calculations, and where students are required to spend more than 50% of their time explaining reasons why things are done–in English words. Yet, many students are still unable to add, subtract, multiply, or divide correctly, even by the end of elementary school.

In my own 30 years’ experience teaching–it’s not that I OBJECT to students knowing the reason why something will work–however, my personal conclusion is that many students have trouble in primary math because of:

1. Brain maturation issues. A few students can master time and problems with time, place value and what each place means relative to each other, etc., at the time it is first taught (age 7); but most are not able to really get it until about age 10, no matter how much time is spent on these subjects at a younger age.

2. Needing individualized help. Some students need what seem like simple processes broken down into much smaller steps; followed by putting those smaller steps back together, to get to mastery. One teacher in a full classroom may have time difficulties doing this for students who need this extra help.

3. Concrete vs. abstract thinking. Young students are mostly concrete thinkers who do better at younger ages (in my opinion) with concrete math tasks. The worksheets like in the picture above now start in Grade 2 (age 7). Some students just don’t have the abstract thinking abilities required for these tasks at this age; in some cases, they don’t have the language ability in English, if they speak more than one language (as all students in overseas schools do).

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.

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.

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, 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 motivatestudents, 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.

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.

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?

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?

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.

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.

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.

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.

“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 IIexplains 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 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!”

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

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.

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.”

“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.

When I started teaching elementary school (as a second career in 1995), I was very surprised to find all the new textbooks now referring to the centigrade scale as the Celsius scale. Of course they are the same thing, but I wondered why the textbooks were now using this term when I had never heard it growing up. Now, I know why.

The short answer is that people continue to call a thing by the same name they, themselves, learned while growing up. Most adults, and just about everyone in academia through the 1980s, grew up hearing “centigrade” and continued to use that term with their own students throughout high school and university.

The new name, “Celsius,” disturbed me ever since I began hearing it in the mid-1990s; but now that I know there was an actual reason for the name change, it no longer bothers me. A unit of measurement, called a “grade,” was actually in use. Therefore, in 1948, the Conference General de Pois et Measures (in France) decided to change the name of the scale to “Celsius.”

The International System of Units

A second reason for the change in name was that the Conference General de Pois et Measures decided that “All common temperature scales would have their units named after someone closely associated with them; namely, Kelvin, Celsius, Fahrenheit, Réaumur and Rankine.”

The change in elementary-school textbooks began to take place around 1968, and during the 1970s, as districts began to replace their former textbooks. In the meantime, parents, scientists, and college professors continued to use the name they had grown up with. Only students born in the 1970s and later would have grown up calling the scale “Celsius.” (I continue to catch myself saying “centigrade” to my own students.)

In England, the BBC Weather did not begin using the term Celsius until 1985, and the word centigrade continues to to be commonly used in England, according to some sources.

Swedish Astronomer Anders Celsius (1701-1744)

The centigrade scale was known as such from 1743-1954. In 1948, the scale was renamed the Celsius scale, after the Swedish astronomer Anders Celsius (1701-1744) who developed a SIMILAR scale (but not actually the same scale). Interestingly, Celsius’ original scale was the reverse of today’s scale; “0” indicated the boiling point of water, while “100” indicated the freezing point of water.

Swedish Zoologist and Botanist Carolus Linnaeus(1708-1777)

The Swedish zoologist and botanist, Carolus Linnaeus (1707-1778), remembered for giving us the basis of taxonomy (classification of living things into genus and species), reversed Celsius’ original scale so that “0” indicated the freezing point of water, while “100” indicated the boiling point. As the older generations retire and pass away, the new name change will become universal. It seems to take about three generations for a name change to really become universally accepted in society.

In this shocking short video, originally written about on Brian Rude’s Blog, an adult woman in her 20s doesn’t have a clue how to go about figuring out an answer to the following question. “If we are in a car traveling at 80 mph, how long will it take us to go 80 miles?”

Having taught elementary and middle-school math for twenty years, I can categorically state that this is NOT just a question of the girl “not having paid attention in math class” as some of the commenters on YouTube stated. This is a THINKING problem which needs to be addressed, either through private tutoring (with the right tutor) or through an elementary or middle-school math class taught at a level to deal with this problem (taught by a teacher who understands these thinking difficulties).

Over many years, I have discovered that TEACHING MATH IS LIKE TEACHING DRAWING SKILLS. Now, let me explain.

We all know of people who seem to have a natural ability as artists. Those without this natural, seemingly inborn, ability stand continually in awe of those who have it. We wonder how these natural artists are able to take pencil to paper and draw something that actually approximates reality, while we, ourselves, are stuck drawing stick figures, even as adults. This happened to me. Then, in my 20s I had an opportunity to take a short, six-session drawing course from a fantastic instructor who understood that drawing is a SKILL which CAN BE TAUGHT. In TWO HOURS, I went from drawing stick figures to drawing quite realistic portraits, and so did my other classmates.

How is this possible? I remember the feeling exactly. What happened was the teacher was able to show all of us a DIFFERENT WAY OF SEEING. Our art teacher was able to TRICK our left brain hemispheres into turning off, and our right brain hemispheres into taking over, using clever and skillful exercises. It is actually a different physical feeling. She then showed us how to call up this state at will, and continued showing us precise drawing techniques used to improve perspective, and the like. Now I can draw quite adequately whenever necessary.

As someone who suffered severe math disability as a child–but overcame as an adult– (not in calculating, but in understanding any sort of real-world problem), I can immediately recognize the problem of the girl in this video. She is trying to draw upon her real-world experience, but cannot recognize what is right in front of her.

Just as in drawing, there are people who seem to have a natural, inborn ability with understanding math. But I doubt that more than a third of people fall into this category.

I would say the average person acquires usable math ability through regular math classes; however, at least a quarter of normal-intelligence students are NOT able to acquire it through normal math classes. Most times these students get through school and end up not able to use ordinary arithmetic that would help them in their daily lives. Shouldn’t THIS be the foremost goal of math education? These students need a DIFFERENT KIND of help; they need help in SEEING MATH PROBLEMS IN A DIFFERENT WAY.

Speaking of myself, who overcame math anxiety problems only in adulthood, the feeling was exactly like what I described in my art class. The shift didn’t happen in an hour (it happened over a couple of years); but once it happened, it changed my life. Students with these problems ideally need to be taught by someone who has suffered with the same sorts of problems, and who has overcome them. Most math instructors don’t understand the unique problems of students who aren’t thinking in the same way other students are. The problem is a lack of CONCEPTUAL understanding. The girl in the video understands she can run seven miles per hour. But she clearly has no comprehension of what the term “miles per hour,” in an of itself, ACTUALLY MEANS.

Here is another example of a lack of conceptual understanding. When I was in my first semester of college, I signed up to take Principles of Accounting and found myself completely lost conceptually, as to what debits and credits were. When I asked the teacher, she told me, “Debit is the left side of the ledger, and credit is the right side of the ledger.” But that did not help me conceptually understand what I was doing. Now, years later, I have my own business, and do my own bookkeeping, and do understand. If she had explained it like this, I would have understood:

“Accounting is like organizing–making a place for everything, and having everything in it’s place. Each account is like a separate cupboard. When you have an expense, you must think, ‘What kind of expense is this? Which cupboard does it belong in? When you put something INTO a cupboard, it’s a CREDIT. When you take it OUT of the cupboard, it’s a DEBIT.’ “

In other words, people with math comprehension problems need things explained in a VERY CONCRETE manner. Not every teacher is able or willing to do that when students get beyond second or third grade. But do it, they must, if they expect their students to succeed. After two or three years of practice with situations given in word problems explained as in my accounting example above, students will find they are able to begin to reason abstractly and understand explanations that previously went right over their head, as with the girl in the video.

This is why we need tracking to be brought back in math classes. If the teacher gives this sort of explanation for the students who need it, the more advanced students will generally make fun of those students. This bores the advanced students, and yet still keeps the lower-level students from being able to even hear the appropriate explanations.

To those who say tracking is unfair to lower-level students, I would pose the question, “What good is studying calculus, geometry, or even algebra, if one cannot make sense of the simplest math questions one faces every day in counting change, in measuring, in cooking, and in doing daily tasks?” An enormous number of students are passing through school and taking advanced math classes, yet still have no idea how to do these basic tasks, and are unable to figure out how to go about discovering the answers to important questions in their daily lives.

“Thinking back to literature tutoring days, there’s a fine line between helping students, and doing the work for them. Students and parents are happiest only if the tutor crosses it. How do you handle such situations?” a fellow tutor asked me.

This is the tutor’s most crucial dilemma, in a nutshell.

Most successful long-term tutors have also been teachers. As teachers, we want students to benefit from doing their own work. However, as tutors, we have to remember who we are working for, if we wish to stay employed.

Most students who choose to use a tutor are not reading the required books in school anyway. Few students are. These days, tutors or not, I’m finding that upwards of 90 percent of students are just watching the movie, and a few students are going to Spark Notes and reading those notes, or taking those quizzes. (Few actually read the Spark Notes well, and even fewer bother to take their quizzes.)

As a tutor, what I’m really being paid for is to make sure my students get good grades. Parents are willing to shell out money for this, but not so much for someone who tells students that they must read on their own and who does not coach non-reading students for their tests. So, what is a tutor to do?

Formerly as a teacher, I prided myself on getting all of my students to LOVE reading for pleasure, and to become truly interested in whatever subject we were studying. Presently as a tutor, I pride myself on getting my non-reading students to read SOME, and to APPRECIATE what we are reading or studying.

I use all sorts of techniques to achieve these aims. I sometimes rewrite books that use difficult language, to tell the story in simpler language. I read these simpler rewrites with my students, and once they understand, they are sometimes motivated to read the original. Sometimes they are unable to read the original, but at least they read SOMETHING, and learned about the story, and are able to pass a test asking them about the story. We discuss the story and how we feel about it as we read it (even if it is in its easier version), and the students gain an appreciation for the piece of literature.

Is this acceptable?

As a tutor, I cannot take the same attitude I would take as a teacher. As a tutor, I am coming from the perspective that students are not reading, and are not going to read. If I can get them to read ANYTHING (even if I have to “spoon-feed” it to them), they are reading more than they would if they were not coming to me. If I can get them to APPRECIATE the story, they are appreciating it far more that if they were not coming to me. If they are PASSING THE TEST, they are learning far more than if they were not coming to me.

Should we spoon-feed pupils?

So yes, I DO cross that “line” as a tutor, but I try to do it stealthily, where I sneakily make the student work and understand more than he planned to do before he came to me!

This same dilemma exists in helping with writing assignments, with math homework, and with everything else that a tutor does As a tutor, I try to help lighten the students’ burden, while at the same time actually teaching the student on a one-to-one basis, in a way which would be impossible in a full classroom. For example, I often do math homework problems on individual white board along with the student. Then we compare answers. If they are the same, we move ahead. If they are different, we go back through the problems step-by-step to see where we diverged. I feel students learn more this way.

I would like to hear about how others deal with this dilemma. If you are a tutor, where do you draw the line? If you are a teacher, what are your thoughts? If you are a parent, what are your feelings?

As a teacher (or even homeschooler), have you ever considered how adding filmmaking capabilites could enhance your teaching abilities with students?

The only materials you need to do so are a computer with high-speed internet connection, and a simple point-and-shoot digital camera with video capabilities (although higher levels of video cameras or those with more manual controls are always a plus).

Filmmaker Luke Holzmann now offers a free, online, 36-week course to all who are interested. A brief description of the course and simple materials needed (which most of us already have) can be found HERE.

Filmmaker Luke Holzmann

Many teachers, students, and adults are interested in filmmaking, but most don’t have a clue where to start if they are not actually in school especially for this purpose. Check out this exciting course, either to enhance your career skills, or as an enjoyable hobby.