[net-gold] Can the Cognitive Impact of Calculus Courses be Enhanced?: Response to Dubinsky
- From: "David P. Dillard" <jwne@xxxxxxxxxx>
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- Date: Sun, 5 Jan 2014 20:50:22 -0500 (EST)
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Date: Sun, 5 Jan 2014 16:55:41 -0800
From: Richard Hake <rrhake@xxxxxxxxxxxxx>
Reply-To: Net-Gold@xxxxxxxxxxxxxxx
To: AERA-L@xxxxxxxxxxxxxxxxx
Cc: Net-Gold@xxxxxxxxxxxxxxx
Subject: [Net-Gold] Can the Cognitive Impact of Calculus Courses be Enhanced?:
Response to Dubinsky
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If you reply to this long (152 kB) post please don't hit the reply button,
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appear in your reply down to a few relevant lines, otherwise the entire
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The ABSTRACT reads:
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ABSTRACT: In response to my post "Can the Cognitive Impact of Calculus
Courses be Enhanced?" [Hake (2013)] at <http://bit.ly/1loHgC4> (2.7 MB),
Ed Dubinsky (2013) at <http://bit.ly/JRB9Km> of the RUME (Research in
Undergraduate Math Education) list made 6 points which I have abbreviated
below and to which I respond in this post:
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1. "I agree with most of what you wrote."
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2. "As far as I know, 'UME Trends' has not been archived. . . . the
articles are historically important because they represent a major turning
point in the mathematical community towards undergraduate education."
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3. "I think more has gone on in MER during the last 20 years than is
indicated in your piece. There is a special interest group SIGMAA ON RUME,
which stands for Special Interest Group of the MAA on Research in
Undergraduate Mathematics Education."
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4. "I think we who work in RUME must acknowledge our debt to Physics
Education Research."
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5. "I am not quite as enthusiastic about CCI as you are. . . . . How are
you going to keep the educational community from using CCI to 'teach to
the test' and even to cheat?"
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6. "I wonder what you have to say about the C4L calculus reform project
that we developed at Purdue and was funded by the NSF Calculus Reform
movement?"
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In response to my post "Can the Cognitive Impact of Calculus Courses be
Enhanced?" [Hake (2013)] veteran Math Ed Researcher (MER) Ed Dubinsky
(2012) of the RUME (Research in Undergraduate Math Education) list made 6
points which I copy below (slightly edited; my comments inserted at ". . .
. . .[[comment]]. . . . .").
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1. Dubinsky (2013) wrote: "I enjoyed this article . . . .[["Can the
Cognitive Impact of Calculus Courses be Enhanced?" (Hake, 2013)]]. . . . .
and I thank you for sending it. I agree with most of what you wrote."
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Thanks for your thanks. None of the traditionalist math warriors of
Math-Teach with archives at <http://bit.ly/eOTrs1> responded to my post,
but I suspect they do NOT agree with most of what I wrote. [G.S. Chandy
(2013) of the Math-Teach list seemed to agree with most of what I wrote,
but he is the polar opposite of a traditionalist math warrior.]
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2. Dubinsky (2013) wrote: "I very much regret that, as far as I know, 'UME
Trends' has not been archived. It ran from 1987 to 1993 and in those days
there was not the practice of putting everything on line. I know that
hard copies exist. I have a full set of hard copies of the issues (it is
bound, given to me by the MAA). I wish someone would put them on line,
but I know of no plans to do so. . . . . [[I think that the MAA should be
urged to put the UME Trends articles online.]]. . . . . . . I think they
are historically important because they represent a major turning point in
the mathematical community towards undergraduate education. . . . .[[I
emphatically agree]]. . . . It came to an end, as I recall, because the
MAA wanted to expand 'FOCUS' and incorporating several of the features
(and some of the staff) of 'UME Trends 'was part of that."
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3. Dubinsky (2013) wrote: "I think more has gone on in MER during the
last 20 years than is indicated in your piece. There is a special
interest group SIGMAA ON RUME, which stands for Special Interest Group of
the MAA on Research inUndergraduate Mathematics Education. It holds an
annual conference of papers on RUME. . . . . .[[See e.g., "Conference on
Research in Undergraduate Mathematics Education, 27 Feb – 11 March 2014,
Denver, CO" online at <http://bit.ly/1lg7JVh>]]. . . . . . . . and works
to foster research and help mathematicians who want to switch their field
of research to RUME.
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SIGMAA ON RUME used to publish an occasional volume, RCME or Research in
Collegiate Mathematics Education and is trying to get the MAA to support a
journal dedicated to RUME. The latter is not succeeding, but I think it
is for a good reason. When I switched from research in mathematics to
research in RUME, most math ed journals were not interested in publishing
papers in RUME as opposed to K-12 research. For some it was an explicit
policy. This is one of the reasons we started RCME.". . . . . . .
.[["See, e.g., "Issues in Mathematics Education Book Series online at
<http://bit.ly/1iDNiSo>, which includes (a) "Published Volumes in the CBMS
Issues in Mathematics Education Series" at <http://bit.ly/1kjkd0l>; (b)
"Editorial Policy and Information for Authors" at <http://bit.ly/JSApF0>,
and (c) "Editorial Policy for Research in Collegiate Mathematics Education
Volumes" at <http://bit.ly/1ey1tDx>.]]. . . . . . . . . .
.
Today, however, I think just about every math ed research journal is
perfectly willing to publish articles in RUME. One indication of what I
see as a 'sea change' is that I was recently asked to be an Associate
Editor of the "Journal of Mathematical Behavior". . . . . . . . . .[[See
<http://bit.ly/19Ija5N>.]]. . . . . . . . . I believe that, in part, it
was because the journal wants to increase the number of papers focussing
on RUME. So I am not sure we are so needful of, or ready for, a journal
specifically devoted to RUME. I think that first, we must determine that
there will be a sufficient number of high quality papers to justify such a
step. Nevertheless, I think it is fair to say that RUME is flourishing and
it is doing so in the mathematical community (most mathematics departments
today either have or would like to have faculty who specialize in RUME)
with not total, but growing, acceptance."
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4. Dubinsky (2013) wrote: "I think we who work in RUME must acknowledge
our debt to Physics Education Research. This not only came before RUME
but provided many ideas that helped form a foundation for RUME. Physics
was the leader and I hope that RUME will live up to that example."
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Dubinsky's comment is consistent with "Teaching in a research context"
[Wood & Gentile (2003)] published in "Science" – see the signature quote.
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5. Dubinsky (2013) wrote: "I am not quite as enthusiastic about CCI as you
are. I agree with its power as assessment, but I don't see how it has
been or is going to be a powerful force for enhancing the cognitive impact
of calculus courses. This concern applies to any form of testing,
especially by multiple choice questions. How are you going to keep the
educational community from using CCI to 'teach to the test' and even to
cheat?
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The tendency to treat any concrete form of assessments in this way was
called by Piaget 'the American Problem.' The current American frenzy for
testing substantiates his view. . . . . . . [[According to Zachary Stein
(2007), what Piaget called "the American problem" was the tendency of
Americans to try to speed up childrens' cognitive development. I think the
problem which concerns Dubinsky is better set forth by the laws of
Dunkenfield and Campbell – see e.g., "Dukenfield's Law & Campbell's Law"
[Hake (2010)] and the signature quotes.]]. . . . . . . .
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[According to Wikipedia:
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(a) at <http://bit.ly/19Y2yRV>: "William Claude Dukenfield (January 29,
1880 – December 25, 1946), better known as W. C. Fields, was an
American comedian, actor, juggler, and writer. Fields' comic persona was
a misanthropic and hard-drinking egotist, who remained a sympathetic
character despite his snarling contempt for dogs, children, and women."
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(b) at <http://bit.ly/12eZL7I>: "Donald Thomas Campbell (November 20, 1916
– May 5, 1996) was an American social scientist. He is noted for his work
in methodology. He coined the term "evolutionary epistemology" and
developed a selectionist theory of human creativity.]
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In "Interactive-engagement vs traditional methods: A six-thousand-student
survey of mechanics test data for introductory physics courses" [Hake
(1998a)] I considered various systematic errors, among them 'teaching to
the test' and test-question leakage, that might negate my conclusion that
"The conceptual and problem-solving test results strongly suggest that the
classroom use of IE (Interactive Engagement) methods can increase
mechanics-course effectiveness well beyond that obtained in traditional
practice." Therein I wrote "Considering the elemental nature of the FCI
questions, for IE courses both the average <<g>>48IE = 0.48 ± 0.14, and
maximum <g> = 0.69 are disappointingly low, and below those which might be
expected if teaching to the test or test-question leakage were important
influences. . . . . . In the broadest sense, IE courses all 'teach to the
test' to some extent if this means teaching so as to give students some
understanding of the basic concepts of Newtonian mechanics as examined on
the FCI/MD tests. However this is the bias we are attempting to measure.
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And in "Re: pre-to-post tests as measures of learning/teaching" [Hake
(2008)] I wrote "Since pre/post testing in the courses surveyed in Hake
(1998a,b) was FORMATIVE, not summative, "Campbell's Law" [Campbell (1976),
Nichols & Berliner (2005, 2007)] is unlikely to have raised its ugly head.
In fact, the use of pre/post testing to gauge the effectiveness of
high-school and undergraduate courses in promoting students' conceptual
understanding has succeeded in part because it is strictly formative:
both teachers' 'action research' and education researchers' scientific
research is carried out to improve classroom teaching and learning, NOT
to rate instructors, students, or institutions. Thus it's "formative" as
defined by the Joint Committee on Standards for Educational Evaluation,
JCSEE (1994):'Formative evaluation is evaluation designed and used to
improve an object, especially when it is still being developed.'
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6. Dubinsky (2013) wrote: "I wonder what you have to say about the C4L
calculus reform project that we developed at Purdue and was funded by the
NSF Calculus Reform movement? You reference most of the material
describing that program (but not much of the research into its
effectiveness) but you don't say anything about it. I think this project
is an exception to many of the points you make in your article. I say
"exception" rather than "counter example" because I think overall, what
you say about Calculus Reform is on the mark. But I would be very
interested to know your views on C4L."
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In "Can the Cognitive Impact of Calculus Courses be Enhanced?" [Hake
(2013)] I referenced "Assessing the Effectiveness of Innovative
Educational Reform Efforts [Schwingendorf (1999)] and "A longitudinal
study of the C4L calculus reform program: Comparisons of C4L and
traditional students" [Schwingendorf, McCabe, & Kuhn (2000).] For the
latter reference I failed to indicate that the article is online as a 172
kB pdf at <http://bit.ly/1i7QQcV>. The abstract reads [bracketed by lines
"SMK-SMK-SMK-. . . . ."]:
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SMK-SMK-SMK-SMK-SMK-SMK-SMK-SMK-SMK
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This paper presents the results of a longitudinal statistical study in
which comparisons are made between students who were taught introductory
calculus courses using the Calculus, Concepts, Computers and Cooperative
Learning (C4L) pedagogical methodology and students taught in the
traditional way (TRAD). Two basic, related, questions considered in this
study are:
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(a) Which program, C4L or TRAD, provides a student with a better
understanding of the required calculus concepts?
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(b) Which program, C4L or TRAD, better inspires students to pursue further
study in calculus or, more generally, mathematics?
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The results of this study favor the C4L program over the TRAD program. On
the one hand, for example, it is found the C4L students earn higher grades
in calculus courses; in fact, almost half a grade higher, on average, than
the TRAD students. On the other hand, for example, it is found the C4L
students are as prepared as the TRAD students, but not more so, for
mathematics courses beyond the calculus program. After some discussion of
the C4L program, the paper describes the statistical model used to perform
the comparison between the two teaching methods and then presents the
results of this sta- tistical analysis. This paper reports on one phase of
the evaluation of the C4L calculus program, a quantitative evaluation
based on a statistical model which is similar to that used in some health
studies (e.g., studies on the relationship between second-hand smoke and
cancer) and industrial studies (e.g., studies of the effects of the notion
of Total Quality Management as related to productivity and employee
satisfaction) which are observational in nature. The other phase of the
C4L evaluation involves qualitative research studies involving both C4L
and TRAD students.
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SMK-SMK-SMK-SMK-SMK-SMK-SMK-SMK-SMK
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Considering the above, I agree with Dubinsky that the C4L program is an
exception to the usual "Lack of Evidence of Improved Student Learning"
[Section "E" of Hake (2013).]
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Richard Hake,
Emeritus Professor of Physics,
Indiana University;
LINKS TO:
Academia <http://bit.ly/a8ixxm>; Articles <http://bit.ly/a6M5y0>; Blog
<http://bit.ly/9yGsXh>; Facebook <http://on.fb.me/XI7EKm>; GooglePlus
<http://bit.ly/KwZ6mE>; Google Scholar <http://bit.ly/Wz2FP3>; Linked In
<http://linkd.in/14uycpW>; Research Gate <http://bit.ly/1fJiSwB>; Socratic
Dialogue Inducing (SDI) Labs <http://bit.ly/9nGd3M>; Twitter
<http://bit.ly/juvd52>.
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"Physics educators have led the way in developing and using objective
tests to compare student learning gains in different types of courses, and
chemists, biologists, and others are now developing similar instruments.
These tests provide convincing evidence that students assimilate new
knowledge more effectively in courses including active, inquiry-based, and
collaborative learning, assisted by information technology, than in
traditional courses." - Wood & Gentile (2003)
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If a thing is worth winning, it's worth cheating for." - Dunkenfield's Law
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"The more any quantitative social indicator is used for social decision
making, the more subject it will be to corruption pressures and the more
apt it will be to distort and corrupt the social processes it is intended
to monitor." - Campbell's Law
REFERENCES [All URL's accessed on 05 Jan 2014; most shortened by
<http://bit.ly/>.]
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Campbell, D. T. 1976. "Assessing the impact of planned social change," in
G. Lyons, ed., "Social research and public policies: The Dartmouth/OECD
Conference, " Chapter 1, pp. 3-45.; online as a 201 kB pdf at
<http://bit.ly/L35QtF>.
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Chandy, G.S. "Re: Can the Cognitive Impact of Calculus Courses be
Enhanced?" online on the OPEN! Math-Teach archives at
<http://bit.ly/JRB9Km>. Post of 31 Dec 21:53 –0500 to Math-Teach.
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Dubinsky, E. 2013. "Re: Can the Cognitive Impact of Calculus Courses be
Enhanced?" online on the OPEN! RUME archives at <http://bit.ly/JRB9Km>.
Post of 30 Dec 19:54:18–0500 to RUME.
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Hake, R.R. 1998a. "Interactive-engagement vs traditional methods: A
six-thousand-student survey of mechanics test data for introductory
physics courses," Am. J. Phys. 66: 64-74; online as an 84 kB pdf at
<http://bit.ly/9484DG> . See also the crucial but generally ignored
companion paper Hake (1998b).
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Hake, R.R. 1998b. “Interactive-engagement methods in introductory
mechanics courses,” online as a 108 kB pdf at <http://bit.ly/aH2JQN>. A
crucial companion paper to Hake (1998a). Submitted on 6/19/98 to the
“Physics Education Research Supplement” (PERS) of the American Journal of
Physics, but rejected by its editor on the grounds that the very
transparent, well organized, and crystal clear Physical-Review-type data
tables were "impenetrable"!
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Hake, R.R. 2008. "Re: pre-to-post tests as measures of learning/teaching"
online at the OPEN AERA-J archives at <http://bit.ly/1kkrpte>. Post of
28 Jan 2008 17:33:48-0800 to AERA-L and several other discussion lists.
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Hake, R.R. 2010a. "Dukenfield's Law & Campbell's Law," online on the OPEN!
AERA-L archives at <http://bit.ly/9FWI9n>. Post of 14 Aug 2010
20:52:11-0700 to AERA-L, Net Gold, and various other discussion lists.,
See also Hake (2010b).
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Hake, R.R. 2010b. "Dukenfield's Law & Campbell's Law #2," online on the
OPEN! AERA-L archives at <http://bit.ly/1ezRCgg>. Post of 22 Aug 2010
15:31:31-0700 to AERA-L, Net Gold, and various other discussion lists.
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Hake, R.R. 2013. "Can the Cognitive Impact of Calculus Courses be
Enhanced?" An update of 26 Dec 2013 of an invited talk of 24 April 2012,
Department of Mathematics, University of Southern California, online as a
2.7 MB pdf at <http://bit.ly/1loHgC4> and as ref. 70 at
<http://bit.ly/a6M5y0>. The abstract and link are being transmitted to
various discussion lists and are also on my blog "Hake'sEdStuff" at
<http://bit.ly/1jXolD6> with a provision for comments.
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Nichols, S.L & D.C. Berliner. 2005. "The Inevitable Corruption of
Indicators and Educators Through High-Stakes Testing," Arizona State
Univ., Education Policy Studies Laboratory, online at
<http://bit.ly/fwzB3X> (1.7 MB). See also Nichols & Berliner (2007).
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Nichols S.L. & D. Berliner. 2007. "Collateral Damage: How High-Stakes
Testing Corrupts America's Schools." Harvard Education Press, foreword by
Nel Noddings, publisher's information at <http://bit.ly/JVP6a6>.
Amazon.com information at <http://amzn.to/fi57g7>, note the searchable
"Look Inside" feature.
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Stein, Z. 2007. "Addressing the American problem by modeling cognitive
development," online as a 70 kB pdf at <http://bit.ly/Ktu83F>.
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Schwingendorf, K.E. 1999. "Assessing the Effectiveness of Innovative
Educational Reform Efforts," in MAA (1999); in Gold, Keith, & Marion
(1999) online at <http://bit.ly/1e6ShtL>, pp. 249- 252. Schwingendorf
wrote: "This study explains the creation of a calculus reform program, its
objectives, and philosophy and provides an in-depth comparison of
reform-trained students with traditional students. The ‘Calculus,
Concepts, Computers and Cooperative Learning,’ or C4L Calculus Reform
Program is part of the National Calculus Reform Movement. The initial
design of the C4L program began in 1987 under the leadership of Ed
Dubinsky and Keith Schwingendorf on the West Lafayette campus of Purdue
University."
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Schwingendorf, K.E., G.P. McCabe, & J. Kuhn. 2000. "A longitudinal study
of the C4L calculus reform program: Comparisons of C4L and traditional
students," in Research in Collegiate Mathematics Education IV [Dubinsky et
al. (2000)] at <http://bit.ly/MNQbwI>. . . . . . [[added on 05 Jan 2014:
online as a 172 kB pdf at <http://bit.ly/1i7QQcV>]]. . . . . ..
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Wood, W.B., & J.M. Gentile. 2003. "Teaching in a research context,"
Science 302: 1510; 28 November; online as a 213 kB pdf
<http://bit.ly/SyhOvL>, thanks to Ecoplexity <http://bit.ly/152aFQ9>.
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