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When we have discussions about which technology to include in our classrooms today, we are often somewhat conflicted with many standard arguments and worries being presented on both sides. To help inform this discussion, I'm looking for sources that chronicle math educators' opinions about the adoption of the scientific calculator in the math classroom.

I would be very interested in seeing things like:

  • even-handed discussions of pros and cons written in the 1970s United States, or similar transition periods in other places
  • "pro-calculator"/"anti-calculator" statements from professional organizations from a time when calculators were just becoming widespread
  • rants from angry instructors or students written during a transition

I am not interested in anecdotes from instructors or students who saw the transition happen first-hand unless you can refer to notes or writings that illustrate what you were thinking at that time.

For example if anyone has access or links to the sources mentioned below (from "A Brief History of Calculators"), I would love to see them:

In 1975, the National Advisory Committee on Mathematical Education (NACOME) issued a report on calculators, suggesting that those in eighth grade and above should have access to them for all class work and exams. Five years later, the National Council of Teachers of Mathematics (NCTM) recommended that “mathematics programs [should] take full advantage of calculators … at all grade levels.”

Thank you!

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    $\begingroup$ I'll point at out that at my institution the transition is ongoing right now. Our math department consensus is for no-calculators for remedial courses, but the higher university administration has demanded in the past year that calculators be allowed on those final exams. $\endgroup$ – Daniel R. Collins Aug 23 '17 at 16:53
  • $\begingroup$ Can you clarify the term "scientific calculator"? Do you mean a basic one, that can do basic arithmetic, powers, square roots, etc. and not much more, or are you talking about calculators that already include a little CAS in them, that, for example, are able to plot the graph of a function, compute maxima, minima, and much more? As far as I know, most schools and even universities still only allow the first kind (in Germany, might be different in the US). $\endgroup$ – Dirk Aug 24 '17 at 9:06
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    $\begingroup$ @DirkLiebhold: Usually "scientific calculator" means that you've got scientific notation, plus stuff like exponential, logarithmic, and trigonometric functions (but not graphing or CAS). en.wikipedia.org/wiki/Scientific_calculator $\endgroup$ – Daniel R. Collins Aug 24 '17 at 13:22
  • $\begingroup$ By using the word "scientific," I guess I am just trying to distinguish the transition "should there be calculators" from the transition "should graphing calculators be allowed or just basic ones." This was probably not maximally clear. $\endgroup$ – Chris Cunningham Aug 24 '17 at 16:33
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Googling "NACOME" 1975 calculators seemingly leads to the report that you mention:

Hill, S. (1975). Overview and analysis of school mathematics, grades K-12 (NACOME Report). In Washington, DC: National Advisory Committee on Mathematical Education, Conference Board of the Mathematical Sciences. Link (pdf).

The section on Calculators begins on PDF 40 (just after the section on Computers). You may also link chase using google scholar to see who cited this report, and then who cited them.

Specifically, five citations of the NACOME report can be found here, after which you can click through the "Cited by" to find lots more. For example, clicking through the 1977 piece by Bell leads here, and clicking through the 1980 piece by Roberts leads here. And so on, and so forth.

As a final note of interest, you may find that Zalman Usiskin shares in your curiosity, as remarked in the recent(ish) interview:

Karp, A., & Roberts, D. L. (Eds.). (2014). Leaders in mathematics education: Experience and vision. Springer. Link (google books).

From pp. 180-181:

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[edited 25AUG, see comments]

Chris:

[Not meant to be a putdown, just some basic instruction in how to search.] Here is a Google Scholar search with certain keywords and restricted to 1950 to 1980. You can consider to open it through 1990 or later (see anecdote). You can add or remove keywords. If you want to make the search more restrictive, put the keywords "teacher" or "reaction" in quotes (that makes the search require them.)]

http://scholar.google.com/scholar?q=calculator+math+education+teacher+reaction&hl=en&as_sdt=1%2C47&as_ylo=1950&as_yhi=1980

Here is first paper I found that hits your needs (first page of Google Scholar window):

http://onlinelibrary.wiley.com/doi/10.1111/j.1949-8594.1980.tb09656.x/full

I would consider to open up the search a little later into post 1980 (calcs really weren't in many math classes before then...experiments sure, but not wide pattern of use.) Would also consider to just read some of the reports on efficacy and then skim them to look for teacher reaction...since that is more your interest than efficacy.

[Anecdotal segue, but it is to frame discussion at least:

You need to be careful to distinguish use of calculators in science number crunching and in math class. The former was very rapidly introduced and noncontroversial. The latter was very slow and remains controversial--like ask yourself, do kids have a hard time learning to punch buttons so they need to practice it--it was not a problem in chem class to use it for stoichiometry. I went to school in the 70s and 80s and scientific calculators were VERY fast in introduction into the sciences. There was zero controversy about replacing slide rules or log tables (I never used a slide rule, but I used log tables and was just a couple years past routine use of slide rules.)

I personally don't remember any controversy about calculators in math class either...as it just wasn't done. I went to a competitive grad school in the late 1990s (in the hard sciences) and I don't recall seeing calculator use in undergrad or upper grad courses and many difficult algebra manipulations were all done by hand (e.g. Jackson E&M, Tinkham superconductivity...lots of Bessel function craziness). I remember being forced to use Maple once, but it was to learn how to make that beast print and set up a complex phase diagram and associated diffyQs and a numerical solver. Not because of needing the CAS. I suspect a lot of physicists still expect and get manipulation (see comments to this effect on Physics Forum) and there are many colleges where calculators are not used in a normal calculus class (most of the problems don't have arithmetic number crunching like chemistry and they want you to learn the methods of integration and manipulation and the like, not have a CAS do it for you.)]

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  • $\begingroup$ Thank you; my research skill for math education articles is very undeveloped and I readily admit that lack of skill. $\endgroup$ – Chris Cunningham Aug 24 '17 at 16:43
  • $\begingroup$ In the question, I tried to be as clear as possible that I wanted sources of opinion and policy that were written at a time when calculator adoption was just getting started. So neither the 2012 nor the 1999 articles you have linked answer my question right now. I was hoping some educators might know what would be enlightening 1970s or earlier writings on the topic (for the US) or other time periods for other countries. The primary thing I am looking for is writing from a certain time period. $\endgroup$ – Chris Cunningham Aug 24 '17 at 16:49
  • $\begingroup$ Chris, I suggest picking a few appropriate journals and looking through their tables of contents for the years you're interested, such as Mathematics Teacher and Arithmetic Teacher (or whatever it changed it's name to) and School Science and Mathematics and College Mathematics Journal and Mathematical Gazette. On average, what you'll get will be slanted slightly toward pro-calculator usage. To counteract this, look at letters to the editor in Notices of the Amer. Math. Soc. and, even better, do some newspaper searches (ask a librarian). $\endgroup$ – Dave L Renfro Aug 25 '17 at 14:26
  • $\begingroup$ Also, you'll find very pointed opinions expressed in some book reviews (Amer. Math. Monthly and Math. Mag. are two that come to mind), but finding these will take a lot searching. But if you have access to JSTOR, it might worth trying --- search for reviews of various high school level and early college level textbooks. Maybe use an appropriate time interval search with one or more of the words/phrases such as "algebra", "college algebra", "trigonometry", "precalculus", etc. along with the word "calculator". $\endgroup$ – Dave L Renfro Aug 25 '17 at 14:36
  • $\begingroup$ See also Sarah Banks; A Historical Analysis of Attitudes Toward the Use of Calculators in Junior High and High School Math Classrooms in the United States Since 1975. (Of course, look at her references, not just her synthesis.) "This study found similar attitudes and reactions by parents and educators toward calculator usage in contrast to the opinions and mandates of organizations such as the NCTM, the College Board, and local school board administrations. Parents and educators were strikingly more hesitant and concerned regarding the effects of calculators than educational institutions." $\endgroup$ – guest Aug 29 '17 at 15:51
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I want to preface the response with the fact that calculators are not in wide use in high schools in the United States of America. I also think that we should not use calculators anymore now that we have access to tools like Jupyter notebooks and languages like R and Python with substantial libraries that crush anything possible on a handheld calculator. Further, nobody I've met carries a graphing calculator around with them except math students and teachers. When people grow up they use computers to solve these problems and it's about time we did the same in the mathematics classroom.

The article Usiskin is referencing in his answer comes from the NCTM's History of School Mathematics, a two volume set that has some relevant articles including a history of technology in the mathematics classroom. Here's a link to the books on Amazon. (https://www.amazon.com/History-School-Mathematics-Volumes/dp/0873534719) There is also the Ackerberg Hastings text on technology in the mathematics classroom.(https://jhupbooks.press.jhu.edu/content/tools-american-mathematics-teaching-1800%E2%80%932000)

In terms of research that discusses the use of calculators, you may be interested in the volumes edited by M. Kathleen Heid on technology in mathematics education that include a variety of works dealing with calculators. (https://www.amazon.com/Research-Syntheses-M-Kathleen-Heid/dp/1931576181)

The NCTM has many different articles across their journals that have taken on calculators and have published position papers on the issue and give these references as support:

  • Ellington, A. J. (2003). A meta-analysis of the effects of calculators on students' achievement and attitude levels in precollege mathematics classes. Journal for Research in Mathematics Education, 34, 433–463.

  • National Council of Teachers of Mathematics. (2015). Strategic use of technology in teaching and learning mathematics: A position of the National Council of Teachers of Mathematics. Reston, VA: Author.

  • National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA: Author.

  • Reys, B. J., & Arbaugh, F. (2001). Clearing up the confusion over calculator use in grades K–5. Teaching Children Mathematics, 8, 90–94

If you are interested in the computing work rather than calculators you might find the Seymour Papert or James Kaput work interesting. Also, there are even early FORTRAN courses from the SMSG (a group in the 'new math' of the 50's and 60's) that tried to introduce computing in elementary, middle, and high school classrooms.

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