Abstract
K-12 mathematics education has undergone many changes over the past decades, sometimes driven forward by mathematicians, sometimes by mathematics educators. Those two groups have often disagreed, but we are now in a more cooperative period in which experts on both sides seem to agree more and argue less. But in reaching this rapprochement, we have left out another group of experts who offer valuable perspectives and fresh ideas—the K-12 mathematics teachers themselves. In doing so, we not only miss the opportunity to draw on different expertise but also inadvertently demean the teaching profession itself.
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Notes
- 1.
Perhaps the most famous and frequently cited economist is Eric Hanushek at the Hoover Institute. Here is a typical paper from Hanushek (Hanushek, 2011):
“Most analyses of teacher quality end without any assessment of the economic value of altered teacher quality. This paper begins with an overview of what is known about the relationship between teacher quality and student achievement. Alternative valuation methods are based on the impact of increased achievement on individual earnings and on the impact of low teacher effectiveness on economic growth through aggregate achievement. A teacher one standard deviation above the mean effectiveness annually generates marginal gains of over $400,000 in present value of student future earnings with a class size of 20 and proportionately higher with larger class sizes. Replacing the bottom 5–8% of teachers with average teachers could move the U.S. near the top of international math and science rankings with a present value of $100 trillion.”
- 2.
The most notable recent such paper was by three Harvard economists: Chetty, Friedman, and Rockoff (2014).
An excerpt from the abstract is illustrative:
“Using school district and tax records for more than one million children, we find that students assigned to high-[Value Added] teachers are more likely to attend college, earn higher salaries, and are less likely to have children as teenagers. Replacing a teacher whose VA is in the bottom 5% with an average teacher would increase the present value of students’ lifetime income by approximately $250,000 per classroom.”
- 3.
For example, the distinguished Hoover Institution at Stanford University publishes research that is frequently cited. The Hoover Institution currently lists eight distinguished fellows with “expertise in education” (http://www.hoover.org/fellows?expertise=638). Half of those eight are economists; two others are political scientists.
- 4.
Much of the popular reaction to the Common Core State Standards illustrate this point. In dozens of postings, parents complain about the new mathematics standards, often unaware of what the standards actually say. Frequently, they cite their credentials as engineer or business executive, giving them expert status. (“Her husband, who is a pipe designer for petroleum products at an engineering firm, once had to watch a YouTube video before he could help their fifth-grade son with his division homework.”) This was described by Motoko Rich in a New York Times article on June 29, 2014, “Math Under the Common Core has even Parents Stumbling.” Similarly, on July 29, 2012, the New York Times published a prominent essay “Is Algebra Necessary?” by Andrew Hacker (http://www.nytimes.com/2012/07/29/opinion/sunday/is-algebra-necessary.html). The author is a professor political science who other than twice teaching an experimental course in mathematical literacy has no credentials in mathematics education whatsoever. The article drew national attention.
- 5.
The International Commission on Mathematical Instruction (ICMI) was established at the Fourth International Congress of Mathematicians in 1908. The original aim was to support the “widespread interest among mathematicians in school education” (http://www.mathunion.org/icmi/icmi/a-historical-sketch-of-icmi/). The eminent mathematician Felix Klein was its first president; Hans Freudenthal was the eighth.
- 6.
PĂłlya (1958)
- 7.
Coburn (1821) (An 1884 reprint can be found at https://archive.org/details/intellectualari00colbgoog).
- 8.
Grouws (1992).
- 9.
Willoughby (1967).
- 10.
Ibid. p 7.
- 11.
Ibid. p 11.
- 12.
- 13.
An illustration of this point of view can be found in Mathews (1996).
- 14.
An illustration of this point of view can be found in Andrews (2001).
- 15.
Schumacher (1978).
- 16.
Tom Lehrer: http://curvebank.calstatela.edu/newmath/newmath.htm.
- 17.
In his 1997 State of the Union address, President Clinton proposed a voluntary national mathematics test to be given to students in the eighth grade. The Department of Education formed a Mathematics Committee in order to gauge the feasibility of such a test, and the Committee held hearings at various locations around the country. Individuals and groups were invited to testify at those hearings, including representatives from both the mathematics and the mathematics education communities. The ideas mentioned here were presented at those hearings—along with many others. The dramatic divergence of views about mathematics education was sobering. The test was eventually abandoned. See Bass (1998).
- 18.
Wu (2014)
Also see Wu’s “Mathematical Education of Teachers, Part I: What is Textbook School Mathematics?” Posted on February 20, 2015 on the AMS Blog (http://blogs.ams.org/matheducation/2015/02/20/mathematical-education-of-teachers-part-i-what-is-textbook-school-mathematics/)
- 19.
Ball, Ferrini-Mundy, Kilpatrick, Milgram, Schmid, and Schaar et al. (2005)
- 20.
Math for America is a program that offers 4-year fellowships to outstanding math and science teachers, who come together in a scholarly community to work on both content and pedagogy. In 2016, the program in New York City has approximately 1000 teachers; another 900 are in a similar program in the rest of New York State, with another 300 in other cities.
- 21.
For example, US News holds an annual conference on STEM education (http://usnewsstemsolutions.com/). In 2015 the conference had more than 50 speakers—CEOs from major corporations, university deans, heads of nonprofits, and a single classroom teacher. It also included many panels, and of all the panelists there was a single teacher among them. This is typical of major national education conferences.
- 22.
Wu (2011)
A perceptive and engaging article that makes many valid points but containing a number of unsubstantiated generalizations about teachers. For example:
“At the moment, most of our teachers do not know the materials of the three grades above and below what they teach, because our education system has not seen to it that they do.” (p 381)
- 23.
Teacher educators sometimes intentionally downplay the expertise of practicing teachers. For example, the following passage appears in Thames and Bal (2013):
“Another impediment to progress is the inclination to persist with outdated and refuted ideas about teacher quality, especially with respect to content knowledge …. The focus tends to be on teacher quality, particularly when it comes to teachers’ inadequate content knowledge. However, the issue is not teacher quality, but teaching quality.” (p 34)
- 24.
Here is a small sample of major reports, all of which are unabashedly critical of US education and US teachers:
-
A Nation at Risk. 1983. Report from the National Commission on Excellence in Education. http://www2.ed.gov/pubs/NatAtRisk/index.html
-
Rising Above the Gathering Storm. 2007. Report from Committee on Science, Engineering, and Public Policy; National Academy of Sciences and National Academy of Engineering. http://www.nap.edu/catalog/11463/rising-above-the-gathering-storm-energizing-and-employing-america-for
-
Rising Above the Gathering Storm, Revisited: Approaching Category 5. 2010. Report from Members of the “Rising Above the Gathering Storm” Committee; National Academy of Sciences; National Academy of Engineering; Institute of Medicine. http://www.nap.edu/catalog/12999/rising-above-the-gathering-storm-revisited-rapidly-approaching-category-5
-
U.S. Education Reform and National Security. 2012. Report from the Independent Task Force on U.S. Education Reform and National Security chaired by Joel Klein and Condoleezza Rice, http://www.cfr.org/united-states/us-education-reform-national-security/p27618
-
- 25.
The assertion of this paragraph—that practicing teachers have expertise that both overlaps and compliments that of mathematicians and mathematics educators—is regularly challenged by (some) mathematicians and educators. This itself illustrates the teacher’s dilemma: When they are not viewed as experts, they are marginalized in policy making, both education and professional. This makes it hard to find examples of teachers’ expert influence on policy. Nonetheless, the participation of teachers in discussions about major recent initiatives to expand computer science, extend the introduction of algebra in earlier grades, and build coherent curricula based on the Common Core amply illustrate their actual and potential expertise.
One recent example stands out. In a recent op-ed (“Wrong Way to Teach Mathematics” Feb 27, 2016) in the New York Times, the political scientist Andrew Hacker wrote to denounce the usual mathematics requirements for high school graduation (http://www.nytimes.com/2016/02/28/opinion/sunday/the-wrong-way-to-teach-math.html). He urged eliminating almost all mathematics requirements and eliminating a common curriculum. He promoted a light-weight quantitative literacy, criticizing more standard (high school) courses in statistics. Hacker elaborated on these ideas in his book, The Math Myth and Other STEM Delusions, 2016, New York: The New Press. While these ideas have been debated in many venues, the mathematics and mathematics education community has been relatively ineffective in addressing them. Many prominent educators and writers have sympathized with Hacker, dismissing the reactions of the mathematics community as self-interested. Teachers themselves have addressed the issues most effectively, both the details and the tenor of his proposals. For example, see the blog posts of two highly accomplished mathematics teachers:
- 26.
The development process for the Common Core State Standards is described in detail at http://www.corestandards.org/about-the-standards/development-process/. This describes teacher involvement as follows:
“Teachers played a critical role in development
The Common Core State Standards drafting process relied on teachers and standards experts from across the country. Teachers were involved in the development process in four ways:
-
1.
They served on the Work Groups and Feedback Groups for the ELA and math standards.
-
2.
The National Education Association (NEA), American Federation of Teachers (AFT), National Council of Teachers of Mathematics (NCTM), and National Council of Teachers of English (NCTE), among other organizations were instrumental in bringing together teachers to provide specific, constructive feedback on the standards
-
3.
Teachers were members of teams states convened to provide regular feedback on drafts of the standards.
-
4.
Teachers provided input on the Common Core State Standards during the two public comment periods.”
For mathematics, the Work Group consisted of 51 individuals: exactly 2 of them were practicing teachers. The Feedback Group consisted of 22 individuals: exactly 1 of them was a practicing teacher.
-
1.
- 27.
Wingert, Pat. 2014. “When Teachers Need Help in Math.” Atlantic, October 2
http://www.theatlantic.com/education/archive/2014/10/when-teachers-need-help-in-math/381022/
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Ewing, J. (2018). Who Are the Experts?. In: Li, Y., Lewis, W., Madden, J. (eds) Mathematics Matters in Education. Advances in STEM Education. Springer, Cham. https://doi.org/10.1007/978-3-319-61434-2_8
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