Why Tracking Needs to Be Brought Back in Math Classes

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.

–Lynne Diligent

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21 Responses to “Why Tracking Needs to Be Brought Back in Math Classes”

  1. edthinktank Says:

    A major problem with tracking is that the most able teachers will usually prefer the group composed of the most able students. To make this work well, excellent teachers need to be interested in teaching the lowest level. A problem with that is the ridiculous expectations of administrators for students that have been socially promoted for years and the administration’s perpetual failure to effectively deal with disruptive students.

    • Lynne Diligent Says:

      Yes, you are right on both counts. It is less socially prestigious for a teacher to teach the lowest level, so it does take a really dedicated teacher to do so (being one of those dedicated teachers who would be willing to do so, myself). You are also right about the expectations of administrators and the cumulative effects of social promotion.

    • Kris Says:

      The idea of the most able teaching the most able may be changing at least in some places. In my school we often hear “the neediest students need to be taught by the best teacher” at our intervention meetings.

      • BHuskie Says:

        I think it might be more accurate to say that we need to put the right teacher in the right class. I find that the term “best teacher” is problematic in that teachers themselves are their own greatest promoters. Also, by which criteria do you judge a teacher to be “best”? Engagement? I can keep a class engaged with books with little to no literary merit. Standards? In my district, if you expect me to hold that line, expect a casualty rate like Omaha beach. Passing rate? That’s literally a key stroke; basically “social promotion”, but I prefer to think of it as promotion based on what they “did”, and not on what they “know”. Likability? It’s helpful in the classroom, but I can’t say that makes you a good or bad teacher, necessarily. The problem I’ve seen is that certain teachers get tagged as “good” or “the best”, because they are good at what they do, and usually those are the upper track teachers, who have more work in regards to grading and planning, but who have an easier time getting results. Then those same teachers, by the logic “neediest kids–>best teachers”, get stuck doing what is essentially a completely different job, it takes them several years to catch their breath and reassess their entire program (often reassess why they didn’t just become a dentist).

        If anything, the most “academic” teachers…the brainiest…ought to stick with the higher tracks (the AP and honors and the like). Putting those teachers in remedial isn’t going to help anyone. The teachers with the most patience and empathy ought to be in the lower tracks. Not to say some teachers aren’t “good”, and some aren’t “bad”…it’s just that, in my experience, there are very few truly bad teachers, and the teachers who are very good are good at what they do, not necessarily at whatever they touch.

        As far as tracking goes, the very idea that we’re moving teachers that we perceive as the “best” to the students with the least ability is a flawed rationale, even if there were such a thing as “best” teacher. What about the higher achieving kids? They get a second rate education and the neediest are pulled up to Ds and Cs? To that end, we should bring back aptitude tests and seriously expand vocational classes (like, to the point where kids leave with valid certifications or close to it), especially in low achieving rural and urban schools. In this way we work to both teacher, and student strengths, without spending too much time on weaknesses.

      • Lynne Diligent Says:

        BHuskie, the criteria I would use for “best teacher” is those who are most INTERESTED in teaching that lower level. I personally would sign up for it because I’ve found I’m very good at getting through to that level. I have a lot of patience and enjoy finding myriad ways to get through to students. I would much prefer this to teaching an honors course or something like that. I would say that any teacher who is interested in teaching the lower level will find a way to do a good job of it. It’s not about the “best” teacher. It’s about the best student-teacher combination for those students to learn.

  2. Lynne Diligent Says:

    From LinkedIn: By E.T.: “Very revealing video (amusing too) but tracking is only one part of the solution. I have seen many examples where schools have easily identified and competently tracked individuals and groups students over a number of years – the bigger problem I see is not the willingness or ability of schools to track but their failure to really commit resources to close the control loop and not just address, but actually resolve, the under-performance that they have put so much effort into identifying and tracking. I am tempted to say that compiling and distributing spreadsheets seduces some people into thinking that the problem is being managed – management means “closing the loop” and actually doing something to ensure that the next time students are measured that there has been a change in the right direction. IMHO primary schools generally have little excuse for passing on students to high schools with poor reading, comprehension and writing skills – not after 6 or 7 years in a primary school.”

  3. Lynne Diligent Says:

    From LinkedIn: By E.T.: “Unfortunately the blog post doesn’t logically deduce that a lack of tracking is at the fault – the post is incoherent, touching on various issues such as the problems of teaching mixed ability classes, teaching for understanding, the quality of teaching, etc Actually, if you analyse what she says, she deserves more credit than some might initially give her, she does try to relate the question to what she feels she really does know – that she can run a mile in 7 minutes – she does not comprehend what “miles per hour” means as a mathematical term but it wouldn’t take much teaching to move her from where she is, with her understanding of 1 mile in 7 minutes to grasp that she would run 2 miles in 14 minutes and then round that up to 2 miles in 15 minutes and go on to 4 miles in 30 minutes to 8 miles in an hour – good teaching should do that – start from where the student really is, not just in terms of their understanding of concepts but in terms of their understanding of the words they use – we help them with understanding concepts but we also have to teach them the right language to use, to be able to talk about these concepts.”

  4. Lynne Diligent Says:

    From LinkedIn, by K.L.: “The initiative to push for higher levels of math and science means algebraic concepts are taught starting in elementary school. This has left us with some students who have not learned times tables or basic concepts of math before they are moved into an abstract level. They soon give up on math because it doesn’t make sense to them.”

  5. Danaher M Dempsey Jr Says:

    A few elementary schools in Seattle, WA are using “Walk to Math”. In this grouping plan Math classes are taught at the same time everyday and students walk to the classroom where students of similar skills and ability are being taught.

    Around 1990 I taught in a cross graded 7th 8th middle school. We had a group of 64 – 7th and 8th graders – who ranged in skill level from SpEd to 8th grade Algebra.

    We had two teachers and a full time instructional assistant. Classes were on alternating days for 97 minutes. We used a lot of in class flexible ability grouping. Annual testing showed our program to be very effective and discipline problems were very few.

    We blended active learning using a lot of lessons from Visual Mathematics (Math Learning Center materials from Oregon) in whole group instruction with small group instruction from traditional textbooks using direct instruction (remember ITIP from Madeline Hunter?)

  6. BHuskie Says:

    Good post…and I agree.

  7. makethea Says:

    Reblogged this on makethea.

  8. makethea Says:

    I really do not agree with any form of tracking. In this case, specialized schools need to be developed, since it is obviously clear that not every student has the potential to be a professional in STEM.

    I support areas that students are excellent in, not areas they are forced in. If it is not math, it is not math. Parents and teachers need to find another fit for their students.

    Tracking shall not be the answer. No student wants to feel manufactured.

    • BHuskie Says:

      Are you arguing for both no tracking, and more tracking, at the same time? Are you saying that instead of “remedial math”, for instance, that students should just not take math, if they aren’t good at it?

      • makethea Says:

        I am not sure what you mean by more tracking. In this case, I am not referring to specialized schools as tracking schools. There are specialized schools for arts, fashion, trade, etc.

        If students do not perform well in math, and math is not their strongest suit, then a career in math will be horrific for them. I am sure students generally know how to count and to compute basic arithmetic, especially if money is involved.

        But, advanced math such as calculus, statistics, etc. requires more than “remedial math.” Honestly, students who take “remedial math” are far behind than other students who have surpassed the basics in math.

        Students have to take math to know whether or not they have the mental capacity for it. Additional training does not hurt if the students choose it. My comment above refers to students who prefer to do something other than math. Of course, everything in life involves math, and math has many forms. Math does not always consists of numbers.

        Referencing the video of the woman, this women may not know conversion of metric units because of not being properly taught in basic math. Then, again, a learning disability can be the cause. Too many factors can interfere with the learning process.

  9. Dan Umbarger Says:

    My understanding is the tracking arose because of the court system which said, in effect, that to group students because of ability and/or background you were depriving students of “behaviorial an academic models of excellence” which, according to the judges, was against the law. Of course the same judges allow Pre-AP and AP class sections because those students have a legal right to be challenged. So the result is that average students are shouldering the entire responsibility of being “behaviorial and academic role models of excellence” for the weaker students.

    Of course when you throw intense administrative and parent pressure to socially promote then that is where the whole thing goes up in smoke. Many really good teachers know that the current system is a set-up for failure and either leave teaching, go to private schools, or go into teaching AP, Pre-AP or Computer Science where the stated goals are more obtainable. I worked in a school where the co-head of the Math Department of a 4A school had certification in elementary ed but she could talk “edu-geese” which ingratiated her to “educrats” and in general well thought of by the system.

    Dan Umbarger

  10. Lynne Diligent Says:

    From LinkedIn: L.T. • “I too have seen this insane acceleration of concepts down into elementary. They are not developmentally ready for algebra. When kids have their times tables down cold, and can do fractions and percents, send them to algebra but not before!”

  11. Lynne Diligent Says:

    From LinkedIn: S.S. • “insane acceleration” indeed! Cover the curriculum because the quarterly test developed by administrators means teachers need to be on page 127 by Nov etc….Not only do the basics not get truly mastered by any but the most able, but in the push for science and math prep for college, our students NEVER get any basic business math necessary to real world survival or to the possibility of their ever starting their own business without relying on outsiders for accounting basics. Our local high school completely dropped their business dept, in an economy full of very small businesses (landscapers, property managers, carpenters, roofers etc). So sad.”

  12. Lynne Diligent Says:

    From LinkedIn: K.N. • “When are teachers going to say enough is enough and start educating the public, explaining in simple terms why what is happening in the classroom is not promoting quality education.

    As a former teacher, I am saddened by the lack of quality education our students get because the testing companies have pulled the greatest financial rape on our educational programs. Who is the winner? The states and the testing companies, who rake in millions of dollars each year. The losers are our children, who, unfortunately are not allowed to learn not only by text, but by problem solving and critical thinking. All have gone out the window for the glorified “fill in the bubble”.

    One example of poor education was what happened here in D.C. on Tuesday. I wanted to bring my grandson to watch the shuttle as it flew around D.C. before landing at Dulles. There is nothing more educational than to experience something like this. What did the school do? They scheduled a SOL test on that day, and the students were stuck in the classroom taking the stupid test, instead of experiencing a live science event. For those parents who pulled their children out of school to experience the event, I pat them on the back. For those schools who did not take the opportunity to do a REAL teaching moment, “Shame on you”

    It is time that teachers start screaming at the top of their lungs about what is happening in the classroom. NEA and AMERICAN FEDERATION OF TEACHERS aren’t doing their job, so it is left up to you to do it. When is enough going to be enough?”

    • Lynne Diligent Says:

      Thankfully, Karen, teaching in an international school overseas, we haven’t yet become subject to all this testing! I agree it totally takes away from real learning time.–Lynne

  13. Mike Byster Says:

    I believe one of the biggest reason so many children and adults have difficulty in math is that many teachers really never learned themselves how to teach math in a fun and cool way. The same exact kids that struggle learning their multiplication tables can memorize hundreds of sports statistics if they love sports or memorize dozens of songs consisting of thousands of words if they love music. When something is fun or cool it is so much easier to learn than something that is boring. A big key to why I learned to love math is because I had a couple of special teachers that would always play math games like “Around the World” or “Buzz” with the class and almost every kid really enjoyed it and did well. When the ABC news show “20/20” did a feature story about me and my company Brainetics (www.brainetics.com), they were amazed at what kids who learned Brainetics could accomplish with their minds. But, what amazed the crew just as much was how much fun the kids were having doing math. I told them that if the kids were not having fun while they learned they would not be able to accomplish the incredible things they were able to do with their minds. I realize sometimes it is really challenging, but if you are able to make something fun, kids will flourish in that environment.

    Mike Byster

  14. Mari Adkins Says:

    I’m dyslexic and dyscalculiac. I didn’t know about the dyscalculia until I was 27 years old. All through school, I made straight As and failed every math class I ever took. Everyone told me that I was just being lazy and not living up to my full potential. I have a wonderful therapist who gave me a diagnosis of true ADD three years ago. I’m one of those people who, as you described, need very concrete, clear descriptions of what, how, and why I’m doing – and I need clear, concise directions and explanations. (Both of my sons are the same way, for the record.)

    If I’d known all these things in 1975 and there had been a way to help me and I’d gotten help, my world today would be a drastically different place. As it is, I need a calculator for the simplest math; simple algebra brings me to tears*; and I’m not able to balance my own checkbook – I have to use a special Excel spreadsheet my husband made me for that (it does everything for me). *If I’m having a bad day, even someone giving me a telephone number will cause me confusion. Instead of ten numbers, I’ll basically hear what amounts to the voice of the teacher from The Peanuts.

    My world would be a better place if I could find someone who could teach me basic math in a way that I could understand and actually use it.

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