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Have there been any major content (not pedagogical) changes in the basic US high school mathematics curriculum since the mid-1990's? More specifically, if I wanted to become a tutor of high school math today as someone who learned his secondary-level math skills back in the 1990's, would a review of my previous curriculum provide a decent foundation, or would there be skills or concepts that young people are learning that I would likely never have heard of?

As a background, I completed US high school mathematics (up through basic Calculus) in the 1990's. Back then, there was a heavy focus on hand-drawing graphs, along with some level of acceptance of black-and-white 8-bit Z80 graphing calculators as an aid to comprehension. I later completed university level coursework (at least through Linear Algebra) in the early 2000's. My understanding is that students nowadays are drawing fewer hand-graphs and using more and more technical modeling technology, but does this primarily represent changes in pedagogy, or are there concepts that high schoolers are learning today that would not have been covered in the 1990's?

I'm not asking about becoming a full classroom teacher (which would obviously require a strong foundation in modern pedagogy). I'm looking for something along the lines of "Oh, nearly every Algebra II class nowadays covers Smooran's Theorem of Transdynamic Coordination, but it was first discovered in 2008 so you probably never studied it.", or something slightly weaker. I'm not asking about general pedagogical changes like online discussion boards or video chat that we really didn't have access to.

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    $\begingroup$ The only thing that seems to have been developed in my lifetime (a little older than you) that is in use in US math classes is box-and-whisker plots for statistics. Beyond that, if you've had a semester of Statistics nothing should flat-out surprise you except the tech itself $\endgroup$ – Matthew Daly Sep 13 '19 at 16:57
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    $\begingroup$ Yeah, in the traditional curriculum there is definitely more emphasis on stats-type problems, but Smooran seems not to have made it in there yet. Some may also be doing more discrete stuff or even multivariate, but that probably wouldn't be the norm. Tutor away! $\endgroup$ – kcrisman Sep 13 '19 at 20:28
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    $\begingroup$ One example. I think using star $*$ for multiplication (even outside computer programming) is a lot more common now than in 1990. $\endgroup$ – Gerald Edgar Sep 14 '19 at 14:44
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    $\begingroup$ @GeraldEdgar I would say that's part of pedagogy, not content. A content difference would be, say, if there's a new model of what multiplication means, and students are expected to demonstrate an in-depth knowledge of the mechanisms of that model rather than figure out some way to multiply 443x by 832xy. Notation changes come and go - I remember that the big "thing" back then for multiplication was transitioning from the x to a single centered dot, which of course was on nobody's keyboard (but then, we were hand-writing almost all of our math assignments anyway so it didn't really matter). $\endgroup$ – Robert Columbia Sep 14 '19 at 14:46
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    $\begingroup$ Little has changed since mid-1990s, when NCTM and its minions like Western Michigan University and Michigan State University upended school math with its integrated, group-based, calculatory-heavy, geometry-thin math. Statistics was made a part of the program at that time. The latest Common Core edition of Core-Plus Mathematics suggests finding roots of a quadratic equation by doing solve(p*(50-p)=500,p) on a graphing calculator just like the 1995 edition did instead of teaching the algebraic method, so nothing new. Well, maybe using Desmos instead of a $100 calculator. $\endgroup$ – Rusty Core Sep 17 '19 at 15:52
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I gave an earlier answer [to a rather different question] in which I pointed to the Regents Exam Archives. One approach that you could take would be to look over a few tests from the 1990s as compared to now to see whether you sense disconnects. Of course, the Regents are rather geographically specific; so, I am not sure how well this will apply to your specific situation.

Others have commented a bit about the inclusion of some topics from Statistics (e.g., into Algebra II). You may find relevant questions to this end by looking, specifically, at the Algebra II Regents.

The major shift that I have seen as pertains to the Common Core State Standards is the declaration of a focus on mathematical modeling. This is a feature of CCSS that contrasts with earlier policy or curricular documents, but, candidly, I am not aware of large-scale shifts by US K-12 institutions towards meaningfully teaching the content knowledge that would be necessary to support math modeling. You can look into some of the resources developed by COMAP, but I would be surprised if you encountered students who are taking classes that broach topics like voting, scheduling, cake cutting, or required the relevant content knowledge.

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    $\begingroup$ Almost everybody in STEM claims they do modeling, but almost nobody actually does. It's a very high-level intellectual skill, and probably beyond the cognitive level of almost all high school students, unless it's a class whose student population is heavily selected. $\endgroup$ – Ben Crowell Sep 14 '19 at 22:37
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The most profound shift that the Common Core introduced is scattering statistics into the standards across most of the grade levels. For instance, in my state (New York), high school freshmen are expected to know how to calculate linear regressions from a two-column table and discuss the degree of correlation between the two factors. Also, upperclassmen should be able to take data from a normally-distributed variable and express a 95% confidence interval for it. I would venture to say that a reasonable and motivated person could pick up everything in an afternoon from watching Khan Academy videos.

Beyond that, though, there is a shift in the gray area between content and pedagogy. That is, we are often less interested in calculating the answer (especially when we can get tech to calculate it for us) and now more interested in correctly interpreting the answer and applying it to make decisions.

For instance, consider a table showing for each of $n=10$ students the amount of time a student spent studying for a test and the grade they got on the test. The first part of the question asks us to calculate the correlation coefficient $$r=\frac{(n\Sigma x_iy_i)-\Sigma x_i\Sigma y_i}{\sqrt{n\Sigma x_i^2-(\Sigma x_i)^2}\sqrt{n\Sigma y_i^2-(\Sigma y_i)^2}}$$ and then interpret the meaning of $r$. In our day, the first part would have been worth 8 points and the second worth 2. Nowadays those would be reversed and the students would probably never even see the formula. On the other hand, one would expect the student would at least understand and agree with the following response.

Based on a correlation coefficient $r=-0.96$, the data suggests a strong negative correlation between time spent studying for a test and the grade on that test. However, it cannot be concluded from this data that the studying is the cause of the test grade. A controlled experiment would need to be conducted to establish causality.

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    $\begingroup$ high school freshmen are expected to know how to calculate linear regressions from a two-column table Huh? By hand, using least-squares? That's nuts. If I wanted to do that by hand, I would first have to take 15-20 minutes to work out the relevant theory. And after I had done that, I certainly wouldn't waste time carrying out the numerical part of the calculation on a four-function calculator. $\endgroup$ – Ben Crowell Sep 14 '19 at 22:39
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    $\begingroup$ @BenCrowell What I meant is that they are expected to know how to enter the table into a graphing calculator and generate the equation for the line of best fit and the correlation coefficient. $\endgroup$ – Matthew Daly Sep 14 '19 at 22:57
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I've notices that rigid motion transformations, rotations, translations, and reflections, is getting more attention now in geometry.

Ive seen that topics from John Tukey's "Understanding Robust and Exploratory Data Analysis" have made it into the classroom.

I saw one class where they were teaching voting theory, which I had no idea how to do.

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Some years ago, I did stumble on a book of exam of my grand-father, and was stunned by the problems: they were on subjects totally different as of today.

Two examples:

  • A tree of height 20 feet has a circumference of 3 feet. There is an arrowroot vine which winds seven times around the tree and reaches the top. What is the length of the vine? [Answer: 29 ft.]
  • A wooden log is encased in a wall. If we cut part of the wall away, at a depth of 1 inch, the width of the exposed log measures 1 foot. What is the diameter of the log? [Answer: 37 in.]

Of course these are variants of the 15th problem of the Jiuzhang suanshu.

enter image description here

Now, as for your question:

  • Yes, I would have been able to solve these questions and train someone to do so.
  • No: I would not have been able to invent the appropriate type of problems to prepare someone for the exam.
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  • $\begingroup$ The answer to the first problem cannot be correct. 7 times the circumference of the tree is about 130 feet. $\endgroup$ – Steven Gubkin Sep 16 '19 at 16:09
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    $\begingroup$ @StevenGubkin had me looking at the edit history. $7 \times 3 = 21$ and $20^2 + 21^2 = 29^2$. $\endgroup$ – shoover Sep 16 '19 at 19:20
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    $\begingroup$ Oh I misread. Thought the radius of the tree was 3 feet. $\endgroup$ – Steven Gubkin Sep 17 '19 at 0:12
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I am going to give an answer that will probably bore people to death; I am going to give an Australian perspective. Disclaimer: the Australian mathematics school curriculum has had enormous changes from the 1970's onward. Australian states also have huge differences in methods of assessment. The following will not be representative of all maths education in Australia. [yes we say maths, not math]. I am also going to oversimplify some things to make it easier to explain.

I completed high school in 1992. Problem solving was not a main part of the curriculum. It did happen. But it was an extension activity. Either in a problem solving competition such as the Westpac maths competition. Or as an extension class for brighter kids.

I am not a maths teacher. My only involvement since 1992 was in 2008; I did some volunteering to help kids with their maths and English. The kids brought some of their school maths problems along. I found that problem solving has changed completely; it's now taught as a main part of the curriculum to all kids from late primary school [US elementary school?]. I had a girl who was 11 at my table and her school problem solving task was harder than anything that I had been set in my 80's/90's school life! I don't think that I could, or should, ever teach maths to any kids. I don't think that I could ever bridge such a change in problem solving emphasis. I'd be useless to kids. They need someone who has had problem solving as part of being educated; that could never be me. I doubt if I could be retrained. That's not even considering the computer aspects of problem solving in maths. In my day it it was rare to write a computer program to solve a maths problem. [actually it's more complex than that because in the 1970's maths in Australia did a better job of teaching computers for maths than it did in the 90's.But that is a whole other discussion.] Kids would want help with computer programs in maths. Again, I'd be useless.

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    $\begingroup$ Could you give examples of problems brought to you, like the one the 11 year old girl had? $\endgroup$ – Rusty Core Dec 6 '19 at 18:12

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