Two math pathways in high school?

Most community college students don’t need Algebra II, but do need mastery of middle-school math, concludes What Does It Really Mean To Be College and Work Ready?, a recent report by the National Center on Education and the Economy. In his Top Performers blog, NCEE’s Marc Tucker explains why he supports Common Core Standards, which require Algebra II content, but doesn’t think Algebra II should be  graduation requirement.

Algebra II prepares students to take calculus, which fewer than five percent of U.S. workers will use on the job, writes Tucker. Why require it of everyone?

Some students, including many who will go on to STEM careers, should study Algebra II and beyond, including, if possible, calculus.  But many others, going on to other sorts of careers, should study the advanced mathematics that is appropriate for the kind of work they will do.  Homebuilders, surveyors and navigators might need geometry and trigonometry, whereas those going into industrial production or public health might want to pursue statistics and probability.  We argued not for lowering the standards but for creating pathways through advanced mathematics in high school that make sense in terms of the kind of mathematics that may be most useful to students when they leave school and enter the workforce.

Phil Daro, who headed the team that wrote the Common Core State Standards (CCSS) for mathematics, also co-chaired the NCEE study’s math panel. Daro writes that the Common Core math standards include “college ready” and STEM goals. The lower “college ready” standards are not as rigorous as a traditional Algebra II course, though they are “more demanding than the NCEE study found was necessary for success” in community college.

 In writing the CCSS, we were charged with articulating one set of standards for all students that would be sufficient preparation for 4-year college programs.  . . . we could not customize different standards for different students with different destinations.  The principle behind this is social justice, but it has a cost.  One could argue that it would be better to have the common standards end earlier, and specialized standards start sooner.

Indeed, my own view is that there should be two mathematics pathways to college readiness that split after grade 9: one for students with STEM ambitions and one for students with other ambitions.

To avoid “social justice risks associated with different pathways,” Daro suggests making both pathways qualify for college admission without remediation.

By 10th grade, students would have to decide whether to take the easier non-STEM path or tackle college-prep math courses that keep the door open to a career in engineering, math and hard sciences.

Now, many students wander through years of middle-school and college-prep math without understanding what they’re doing. If they’re assigned to remedial math in college, the odds are they won’t earn a degree or a job credential. Is that social justice?

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  1. I think we’d be much better off if the HS-grad/work/CC ready path included real algebra, geometry and a semester/year of consumer-style basic econ, finance and stats (which kids on the accelerated/honors/college-prep path could take in MS). Pretending that all HS kids can/should take math beyond geometry leads to mass-fail scenarios like the one currently in MoCo, MD. Better to do the basics and do them well than pretend that “all” should go beyond that.

    Those kids aspiring to a non-elite 4-year college should be expected to take algebra II and probably pre-calc, somewhat depending on college requirements. Those aspiring to very competitive/elite colleges and/or STEM fields should have AP calc BC (STEM could go beyond), because those colleges use calc as a screening tool.

    Those kids going into voc ed (which I think should be more available and better advertised) should take the kind and amount of math dictated by the specific field; (cosmetology and admin assistance don’t need more, technical fields do), and incorporated into that coursework.

    BTW, there’s a great little story, “Children of the Corn”, in the archives of National Review Online; basic economics in action. Sorry for the digression, but it’s something even MS kids can understand.

  2. I meant to add the the math problem, like most of the ed problems, needs to be fixed in ES. If ES doesn’t ensure the proper foundations of all the subjects, the kids will struggle thereafter and far too many will fail. Getting a proper education shouldn’t depend on parents’ out-of-school efforts, as is far too often the case. We need to go back to proper curriculum and proper instruction.

  3. Ann in L.A. says:

    Regardless of whether bifurcating the math curriculum is a good idea, we need to have every kid take at least one semester of a serious statistic course.

    It is the most-important, least-taught class in schools. Everyone–everyone–needs some background in statistics. Every newscast, every newspaper, every business, etc. uses statistics on an almost-daily basis. Not being able to understand that “_______ doubles your risk of cancer!!!!!” doesn’t mean anything if the risk started out as 1/100,000,000 and doubles to 1/50,000,000. People need to have some idea how to approach the statistics that they hear every day.

    Statistics isn’t a part of the normal math sequence, but it should be.

    • Genevieve says:

      What level of math do students need to have before they take statistics for the statistics class to make sense.
      I didn’t take statistics until after I had taken Calculus. While my background with proofs and derivations was very helpful in understanding how statistical methods worked, I would think a solid grounding in algebra would be sufficient. I wonder whether people would understand statistics without an understanding of algebra.

      • A basic statistics course requires a knowledge of basic algebra (mode/mean/variance/std deviation, etc), now you could teach an applied stats class (i.e. for non-majors), but it does require a basic working knowledge of algebra in order to get it.

        If you don’t know the basics of MDAS, you’re gonna have trouble in stats.

  4. I took lots of stats in grad school, but I don’t think all HS students need anything more than good “consumer-type” stats, geared to understanding, not calculation.

    • Richard Aubrey says:

      Took an intro stat class for non-majors in college. It was an experimental class in terms of the methodology of teaching. I think we were all given courtesy Ds. Ran into the prof later on and introduced myself by remarking I’d been in that/his class. He flinched and said he’d hoped we were all gone by then.
      However, while chi square remained a mystery, the mysteries of lying with statistics were no longer mysteries.
      Hugely important for citizens.

  5. cranberry says:

    Who will teach the statistics classes? How many years will it take to refresh all American math teachers’ knowledge of statistics? How does one require a 15 year veteran to fit in continuing education courses in statistics?

    The first step would be to persuade leading colleges to accept statistics courses as equivalent to calculus courses in college admissions. Once that mountain’s been moved, one can move to required teacher retraining.

    The report in this post points out many students don’t master middle school math. Until they master middle school math, statistics will be just as incomprehensible to them as calculus.

  6. Roger Sweeny says:

    What a high school statistics should be depends on what the purpose of the course is.

    Possibility 1.) Like a high school calculus course, it is, for most students, a meaningless hoop to jump through in order to get into a selective college. Most of the students will have forgotten most of it by the time they enter the selective college but it will serve as a signal, “See, I’m smart enough and driven enough to take this hard course and get a decent mark in it. I can do well during four years on your campus.” In this case, the course should be an abridged version of a college statistics course, given by math teachers. Such a course will also be useful for the minority of students who expect to pursue something like it in college.

    Possibility 2.) The purpose of the course is to make students aware of “the use and abuse of statistics.” The emphasis of the course is on what various statistics actually mean–and don’t mean! Many teachers will use parts of Darrell Huff’s “How to Lie with Statistics.”

    In that case, the course should not be like a college statistics course. It should focus on examples and not on math. It needn’t be taught by a math teacher.

    Of course, schools could give both. Even have a semester of Possibility 2 required of all students, followed by a semester of Possibility 1 open to students with good math grades (or a “parental override”: Students with bad math grades can take the course if the parent sees a guidance counselor and signs a form saying (in the nicest way possible), “Your son/daughter was not recommended for this course. He/she realizes it will be hard. If he/she doesn’t do well, don’t blame us.”).