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).

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.