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Ababsolutum/iStockHigh school math should be more practical, more engaging, and without tracking systems that place some students — often low-income, African-American or Latino — in less challenging classes that leave them unprepared for college, according to a report released last week by the National Council of Teachers of Mathematics.
The 126-page report, “Catalyzing Change in High School Mathematics,” was compiled over 18 months by high school math teachers, mathematicians, college professors and school district leaders. It also includes feedback from 200 public comments.
“If you look at the last three decades of national K-8 scores, the trend has been positive. But the trend in high school math has been flat,” said Matt Larson, president of the council. “This is about ensuring that each high school graduate is prepared to use math to understand the world around them and has an appreciation for the important role math plays in society.”
According to the Nation’s Report Card, high school math scores have remained stagnant since the 1970s, with only about 25 percent of 12th-graders scoring at or above proficient.
The council recommended that schools eliminate tracking, in which students — usually beginning in middle school — are placed in math classes that are either honors, general or basic-level math. Those placed in less challenging classes tend to stay on that track through high school and graduate less prepared for college math, the report states.
The council also suggests eliminating “teacher tracking,” in which the most experienced and effective teachers are assigned to higher-level math classes and less experienced teachers are sent to lower-level classes.
“Teacher tracking increases isolation and burnout for early career teachers, reduces collaboration and does not take into account expertise and need when assigning courses,” according to the report.
The report suggests that all high school students take four years of math, including algebra, geometry and either advanced math such as calculus or practical math such as statistics, financial literacy or data science. Schools would have flexibility as to how those courses would be structured.
The goal, Larson said, is for students to enjoy math and learn real-life concepts they’ll use throughout their lives.
“We hope students will come to understand the beauty of mathematics and see that it’s no different than history or literature or art,” Larson said. “It’s embedded in nearly every aspect of our lives. That’s why it’s essential that people understand it.”
Kyndall Brown, executive director of the California Mathematics Project at UCLA, said the council’s report “is right on time and expresses the challenges that students and high schools are facing. We really do need to rethink how to get more students through the mathematics pipeline at high school.”
Too many low-income, African-American and Latino students are shortchanged by math tracking, he said. They’re not only poorly prepared for college math, but they’re not learning the practical math skills they need in the workplace and life, he said.
African-American 12th-graders scored on average 30 points lower than their white peers on the 2015 National Assessment of Educational Progress math exam, while Hispanic students scored 22 points lower.
“Math tracking is a huge problem,” he said. “It’s the reason we have the current outcomes we have, with fewer low-income and students of color scoring proficient.”
Mark Ellis, a math education professor at Cal State Fullerton, said the council’s report should spur schools to change the way they structure math courses. Some districts, including San Francisco Unified, have already ended math tracking, and hopefully more will follow suit, he said.
But eliminating tracking isn’t the sole solution, he said. Improved curriculum and more engaging teaching will also help improve high school math education, he said.
“While many are focusing on the idea of de-tracking, for me that is one change that is part of a larger systemic effort to improve outcomes,” he said. “It also means working with curriculum, instructional practice, course placement and sequencing and policy to help to move the needle with respect to student engagement in and success with high school mathematics.”
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John Bachta 3 years ago3 years ago
I have taught high school mathematics for 19 years. I have taught every math course except Statistics at every level and am a big advocate of tracking. My honors classes contained honors students. I was able to teach them college level material and expected and got college level effort. My students were very well prepared for college and usually scored 4's and 5's on the AP exams. If you abolish tracking and put unprepared and … Read More
I have taught high school mathematics for 19 years. I have taught every math course except Statistics at every level and am a big advocate of tracking. My honors classes contained honors students. I was able to teach them college level material and expected and got college level effort. My students were very well prepared for college and usually scored 4’s and 5’s on the AP exams.
If you abolish tracking and put unprepared and unmotivated students into the honors classes you must slow down the class. This hurts the true honors student. I was fortunate enough to teach in a school that racked for math. It was up to me to modify the level of instruction to meet the ability level of the student. Everyone came away with a solid understanding of the basics but the honors students, the ones who might actually use the advanced math in college and beyond, were not deprived of the best education that I could provide.
Society must admit that certain students have developed a better understanding of abstract math…just as certain students have a superior athletic ability. It is the teacher’s responsibility (and that is why teaching mathematics well is so difficult) to get the most out of every student. Putting all students into the same math class is not the way to do it.
Vincent L Taylor 3 years ago3 years ago
One of the problems I faced as a student is the fact that people tend to jump to conclusions regarding students which is wrong. I recently attended a lecture at Excel Mathematics where I learned that math is an evolving process and it cannot be conquered in a day.
Kelli 3 years ago3 years ago
My question would be if we eliminate math tracking, especially in middle school, how does my advanced learner continue to advance? My son is pretty darn bored with 4th grade math right now (and this is a kid who does math for fun at home) I figured once he starts middle school next year and gets a homogeneous math class he might be challenged.
Cialix 4 years ago4 years ago
I completely agree that teacher tracking is a problem. But let's look at the root of the problem as a whole. If kids are supposedly doing well in elementary and middle schools, then start failing in high school, then perhaps the real problem lies in elementary and secondary schools. Each grade's responsibility is to prepare students for the next year or the next level of math. I have talked to many adults freshly out of … Read More
I completely agree that teacher tracking is a problem. But let’s look at the root of the problem as a whole. If kids are supposedly doing well in elementary and middle schools, then start failing in high school, then perhaps the real problem lies in elementary and secondary schools. Each grade’s responsibility is to prepare students for the next year or the next level of math. I have talked to many adults freshly out of school that can not calculate simple math without using a calculator. And middle school children are worse. The ones that can do the math can’t even tell you why the way they are solving the problem works. Which helps show that they don’t understand numbers and how they work. Math is one of the most , if not the most important subject in school.
We should be looking at other countries with strong math scores and see what it is that they are doing right that we are not doing. Most engineers in America are foreign born. Why is that? We simply need to revamp our entire system when it comes to teaching math. And teacher tracking doesn’t even make sense. Where is the logic? The best teachers should be helping the kids that struggle the most. And moreover there should be a better standard for hiring teachers in the first place.
Michael Morad-McCoy 4 years ago4 years ago
As someone who has earned a Ph.D. in Counselor Education and who is the father of a musically gifted high school student, I couldn't agree more that current requirements in high school and college math are hugely irrelevant to the vast majority of adult activities (both professional and academic). My kid just hit the middle of Algebra I and is now having to calculate decay rates?!?! While the concept of decay rates is, in some … Read More
As someone who has earned a Ph.D. in Counselor Education and who is the father of a musically gifted high school student, I couldn’t agree more that current requirements in high school and college math are hugely irrelevant to the vast majority of adult activities (both professional and academic). My kid just hit the middle of Algebra I and is now having to calculate decay rates?!?! While the concept of decay rates is, in some disciplines, important, how many people actually NEED to do the calculations? I teach counseling, I teach research, and this calculation leaves me totally flummoxed. I don’t understand why American education is mired in these esoteric ideas of literacy. I was taught algebra and geometry and have hardly ever used them. But I was given NO education in financial literacy and that lack has played a huge role in my actual lived life. And, fortunately, I learned some economic theory in college and find that SO much more important in being an informed citizen making important decisions about voting than anything I ever learned in algebra. We really need to rethink these ideas that, if you look at the history, are more about the anti-communism paranoia of the 1950s than anything that is supported by any actual research.
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Ruth Tekell 4 years ago4 years ago
Math, including decay rates (a very good real world application) teaches you how to think about everything more clearly. Most students in k-12 don’t know that they’re not going to ever need math. Learning math well only opens doors and minds. Not learning math closes doors. These kids are going to be faced with overwhelming science and engineering challenges as their entire planet begins to collapse under their feet, quite literally. The least we can do is get them prepared.
Anonymous 5 years ago5 years ago
If there is no tracking for math, how about eliminating tryouts for sports and music? Regardless of your abilities, you’ll be guaranteed a spot on the varsity team and the honor band.
John 5 years ago5 years ago
As a teacher who taught high school math at an inclusion school, that is, no tracking, the results were a failure. Simply, who do we teach to — the lower level students, or the higher level students? At the end, I was teaching to the middle which benefited no one — lower levels still didn’t get and expressed their frustrations by acting out, and the higher levels were bored, unchallenged, and similarly frustrated. … Read More
As a teacher who taught high school math at an inclusion school, that is, no tracking, the results were a failure. Simply, who do we teach to — the lower level students, or the higher level students? At the end, I was teaching to the middle which benefited no one — lower levels still didn’t get and expressed their frustrations by acting out, and the higher levels were bored, unchallenged, and similarly frustrated.
Maybe for different subjects inclusion classes may work, but math where you build upon basic knowledge, it cannot be taught to students of varying levels in one class successfully.
My question to those who think that by having lower level math students mixed in with high achieving math students will somehow automatically transform them — have you ever taught in such a classroom? Yes, diffentiation works, but only so far when levels are not chasms.
There is no silver bullet solution. And inclusion classes for math is definitely not the answer!
Dan Phu 5 years ago5 years ago
Schools approach teaching algebra by long methods which all learners will walk down on the path to solve algebraic equations longer than otherwise needed. It clouds kids' intuition to see father ahead in the problem. It takes longer to finish each problem and increase possibility of errors. Then when algebraic equations become complicated, schools introduce Least Common Denominator to simplify equations. This just pull kids back from doing real algebra by detouring … Read More
Schools approach teaching algebra by long methods which all learners will walk down on the path to solve algebraic equations longer than otherwise needed. It clouds kids’ intuition to see father ahead in the problem. It takes longer to finish each problem and increase possibility of errors. Then when algebraic equations become complicated, schools introduce Least Common Denominator to simplify equations. This just pull kids back from doing real algebra by detouring rather than facing algebra head on. As a result, Algebra becomes a fragmented mathematical tool which kids need to learn much more to make up for the shortfall and they also need useless memorization to make algebra work.
After 12 years of math education, you can see kids mostly only able to solve algebraic equations from left toward right. It is very much like kids fight with only left hand and leave the right hand and 2 legs unused. How do you expect them to win ? It is very sad to see math end up this way.
Xela 5 years ago5 years ago
Please give and example of how you would get rid of tracking. What would this path look like?
Natalie 5 years ago5 years ago
For how long are we going to sacrifice our high-achieving students to the altar of political correctness? We all know that de-tracking means that students who need to move faster through the curriculum will not get a chance to do so. De-tracking will only result to more families pulling their high performing kids to homeschooling or private schools while forcing kids who have no interest in math into more challenging classes that they are not prepared to take.
Dennis 5 years ago5 years ago
This sounds similar to the Integrated Math plan of a couple decades ago where we mixed together the content of traditional high school math courses. It didin't help because moving the content around is a horizontal move that really doesn't change things. You have to wonder if textbook publishers aren't behind it --or maybe it's just the need to do something and not knowing what to do. About ceasing to "track" students … Read More
This sounds similar to the Integrated Math plan of a couple decades ago where we mixed together the content of traditional high school math courses. It didin’t help because moving the content around is a horizontal move that really doesn’t change things. You have to wonder if textbook publishers aren’t behind it –or maybe it’s just the need to do something and not knowing what to do. About ceasing to “track” students and teachers, no where in the NCTM executive summary do they address why tracking is so popular in the first place. And about elementary grades showing steady improvement, at the school district I’m at, something like 30% of grade school students are competent at math. This is just another report that’ll go nowhere.
Jon 5 years ago5 years ago
I wonder how having semester-long courses vs year-long courses affect math scores which have remained "flat." I know that when I was in high school, we had year-long math and now a lot, if not most, have semester-long courses. I teach high school to students that are 2 years behind and to students that are "on grade level." And there is a huge difference between the two group of students. So I don't see how … Read More
I wonder how having semester-long courses vs year-long courses affect math scores which have remained “flat.” I know that when I was in high school, we had year-long math and now a lot, if not most, have semester-long courses.
I teach high school to students that are 2 years behind and to students that are “on grade level.” And there is a huge difference between the two group of students. So I don’t see how you can get rid of tracking (making informed decisions using data) when there is clearly a difference in ability levels. Middle school tracks and scores are positive, high School tracks and scores remain flat does not give an argument to get rid of tracking.
I feel there is way more to it then just getting rid of tracking. For example, students have a lot more opportunity to get involved in extra curricular activities in high school. Jobs, clubs, sports, relationships, etc. I do believe there needs to be an overhaul but more for the students at risk of dropping out of high school, not the ones who are going to college.
Paul 5 years ago5 years ago
Sometimes I have to shake my head at the NCTM, even though I was a proud member when I taught. If you want people to read your important report, make it free instead of selling it for $39.50! A Web search turned up a free public review copy, but that was only a draft, and judging by the stern warning in the watermark, it will probably be removed as soon as the NCTM realizes it's … Read More
Sometimes I have to shake my head at the NCTM, even though I was a proud member when I taught. If you want people to read your important report, make it free instead of selling it for $39.50! A Web search turned up a free public review copy, but that was only a draft, and judging by the stern warning in the watermark, it will probably be removed as soon as the NCTM realizes it’s still accessible.
I strongly agree with ending tracking for math students – and for their teachers. Bravo to the NCTM for bringing up the latter! This is one of the first published sources to admit that newcomers are assigned to teach the courses that incumbents can’t be bothered with.
“All Algebra, All the Time”
At one East Bay middle school, I was assigned to teach all five algebra sections. I arrived with much more teaching experience than the typical university internship credential holder – and a stronger math education than the incumbents in the department – but I still found it puzzling that they would expect a relative newcomer to be able to improve on years of terrible results, when they had not been able to. Algebra I was a mandatory Grade 8 course in the district, and for years only 6% or so of students at the school demonstrated proficiency, on the old CST. (The principal and the department head were surprised that I had looked up the school’s test results for my interview.) My seasoned colleagues cherry-picked the courses that were pleasant to teach (Grade 6 Math) or attracted high-performing students (Grade 8 Geometry).
I do take issue with the phony dichotomy between “advanced” math, ostensibly calculus, and “practical” math, ostensibly statistics and personal finance. Does this distinction appear in the NCTM document? If it does, it’s an insidious form of tracking.
Statistics is quite sophisticated, and financial math would be, too, if topics like EMV, NPV, and amortization were taught, and if the major application were financial modeling (which would fit perfectly with the habits of mathematical practice in the Common Core), not balancing one’s checkbook.
Finite math is likewise undervalued in US public education. (At least it was offered as an optional Grade 13 course in Ontario, Canada, where I grew up.) Topics such as number bases other than ten, Boolean algebra, set theory, and first-order logic tie directly into computer science, digital electronics, and introductory philosophy.
The notational discipline learned in a discrete math course would even serve our “advanced” friends, with their fancy, continuous math! Say what you will about 1970s “new math,” but being able to talk in terms of a “solution set”, instead of “the answer,” becomes quite useful when a student realizes that quadratic equations have zero, one or two roots, and that solutions of a rational equation are expressed by exclusion (all numbers except these few) rather than inclusion.
Calculus is not the only worthy “advanced” high school math course!
This brings me to my last point: the State of California should mandate four years of high school math. For what has recently been confirmed as the world’s fifth-largest economy, mandating just two years of high school math is an embarrassment. More and more districts are adopting the University of California’s A-G course requirements as local graduation requirements. I disagree with this, because in practice it means that students who meet state but not local requirements are deprived of high school diplomas, or that teachers of locally-required courses are expected to pass everyone.
A statewide four-year math mandate, coupled with worthwhile third- and fourth-year options in addition to Algebra II and Calculus (or a “drive-by” year of AP Statistics), would be fair. The big problems are staffing (teachers at all levels tend to have poor math preparation) and money (some of you will remember the old “second year of high school science” graduation requirement, found by the courts to be a reimbursable state mandate).
el 5 years ago5 years ago
I appreciate the thought, but I'm wondering if there's data that shows that putting kids in more challenging math classes increases their success. If students are placed in lower level math classes because they are already having difficulty with math, giving them the equivalent of the honors curriculum seems unlikely to change that. Kids in our current system show significantly different ability in math by 9th grade and it's probably a disservice to all of … Read More
I appreciate the thought, but I’m wondering if there’s data that shows that putting kids in more challenging math classes increases their success. If students are placed in lower level math classes because they are already having difficulty with math, giving them the equivalent of the honors curriculum seems unlikely to change that. Kids in our current system show significantly different ability in math by 9th grade and it’s probably a disservice to all of them to have them take the same classes at the same rate.
Instead, I think there’s real value in rethinking the high school math progression – the discussion in an earlier article to replace intermediate algebra with statistics makes sense to me – and maybe to build some electives that are math-based. Data science is an excellent choice and could be a terrific way to develop an appreciation for math in students who haven’t found its appeal. Computer programming also can lean on math, especially graphical type work that is also fairly rewarding.
I do think it’s a disservice to kids to have no math or math-related class in their senior year, whether it’s a practica/appliedl class like financial literacy or construction math or a theoretical class like calculus.
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Ruth Tekell 4 years ago4 years ago
I think there are studies, reported by Texas Education Agency that show kids who take AP courses in high school perform better in college. I just saw that today, but I didn’t read the whole article because I was looking for something else. Maybe you could find it with a bit of research