All Teachers Can Learn Mathematics (PD needed)
All Students Can Learn Mathematics From Teachers Who Know Mathematics
Collected by Jerome Dancis (Univ. of Maryland)
1. “R U 4 teachers knowing Arithmetic?” (a report of mine) (www.math.umd.edu/~jnd/R_U_4_Teachers_know_Arith.html)
includes: “As Secretary of Education Arne Duncan said (May 11, 2009 at Brookings Institution): So I agree we can use a ton of these resources to send teachers back to schools and universities to get the endorsement [and] to get the content and the knowledge they need to be able to teach.”
This report is background for the 40+ mathematicians public letter, "RACE TO THE TOP AND K-12 MATHEMATICS EDUCATION at www.math.umd.edu/~jnd/RTTTPublicLetter.html Excerpts:
“We agree with U.S. Secretary of Education Arne Duncan's statement: ‘... it is hard to teach what you don't know. When we get to 6th, 7th, and 8th grades, we see a lot of students start to lose interest in math and science ... because their teachers don't know math and science’. For the United States to remain competitive, every part of K-12 mathematics education in this country must be strengthened: curriculum, textbooks, instruction, assessments, and, above all, the preparation and continuing professional development of those who teach mathematics and science, regardless of grade level and the kind of school in which they teach.”
“Recommendation 1. ... The rigorously researched [National Mathematics Advisory] Panel‘s 2008 report advises that teacher preparation programs and licensing tests for all K-8 mathematics teachers should fully address the foundational topics in arithmetic (including fractions, decimals, and percents), geometry, measurement, and algebra that are spelled out in the Panel's report. Middle school teachers should know more than teachers in early grades. ... “
“Recommendation 5. The U.S.D.E. should fund content-rich professional development programs for current K-8 mathematics and science teachers, coaches, and supervisors, and for elementary and middle school principals. ... “
2. Math PD needed for writers of NAEP and state math assessments. “Quoting the NAEP Validity Study: Five percent of NAEP items were found to be seriously flawed mathematically at Grade 4, and 4% were designated seriously flawed at Grade 8. ... For marginal items, NAEP had 28% at Grade 4 and 23% at Grade 8, ... “ There are similar rates for flawed and marginal items on the sample of state exams. (From a slide in Wilfried Schmid’s presentation at the 2009 CBMS Forum, “The National Mathematics Advisory Panel (NMP) [andNAEP]”. This slide may be access from www.cbmsweb.org/Forum2/Panels.htm)
Question: How much additional Math content PD is needed for Mathematics and science supervisors and coaches and for writers of state and NAEP math and science assessments?
3. The inadequate preparation in Mathematics of future elementary school teachers by 67 of the 77 colleges surveyed, is documented in the National Council on Teacher Quality (NCTQ) report, “No Common Denominator: The Preparation of Elementary Teachers in Mathematics by America's Education Schools [NOT]”, (June 2008). It is at
4. Math content certification requirements for high school math teacher.
In my state of Maryland (MD), the subject content certification requirement for a high school teacher is 36 college credits in the subject (at least 12 credits in junior-senior level courses) – teacher’s choice. Then the teacher must pass the Praxis II exam.
A fully certified MD high school math teacher need NOT have taken a Geometry course in high school or college. Same for probability and statistics, even though 40% of the Grade 9 and 10 state math test is on data analysis and probability. Passing this test is a HS graduation requirement; there is a loophole.
Writing and speaking mathematics rigorously. Most important, a fully certified MD (and likely most states) high school math teacher need NOT have taken a college math course, which teaches mathematical rigor. One that includes instruction on how to write and speak mathematics coherently, clearly, comprehensively, logically, accurately and precisely without being cryptic, vague, ambiguous, or obscure as well as how to distinguish a correct mathematical argument from an incorrect or incomplete mathematical argument.
Prospective high school math teachers use graphing calculators on Praxis II exam, so NO need for them to be able to graph y = x by hand. Also, the syllabus for the Praxis II High School math exam omits knowing why (-1)(-1) is defined as +1, something the Common Core syllabus expects grade 7 students to be able do. Access info on all Praxis exams at
5. “All Purpose Science Teacher [NOT]” (September, 2010) One can be a fully certified high school science teacher without ever taking a physics course.
6. Teachers rarely used mathematical proofs was noted, some years ago, by math education professor, Guershon Harel. He wrote: "During the last two years, I have worked intensively with junior-high and high-school inservice teachers. One of the most robust behavior I see with these teachers is the absolute reliance on pictures and patterns. Almost in all problems I give to the teachers, their first approach is to attempt to solve them by numeric patterns or by drawing pictures. Once the teachers observe a "pattern" (from two or three cases) or draw a picture, they derive the final conclusion empirically or perceptually. There are almost no attempts to support and supplement their empirical and perceptual reasoning with algebra.
7. "Racial Equity Requires Teaching Elementary School Teachers More Mathematics" in the Notices of the AMS, February, 2005, Volume 52, Number 2 or at
8. The ten myths exhibited in my report, “[Common] Missteps in Mathematics Books” should be taught as being wrong, not mis-taught as correct mathematics. This report appeared in the section “Fallacies, Flaws, and Flimflam” of The College Mathematics Journal (November 2008).
9. President’s Council of Advisors on Science and Technology (PCAST) report (Sept. 2010):
RECOMMENDATION 2. “TEACHERS: RECRUIT AND TRAIN 100,000 GREAT STEM TEACHERS OVER THE NEXT DECADE WHO ARE ABLE TO PREPARE AND INSPIRE STUDENTS” (www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-stemed-execsum.pdf)
“The most important factor in ensuring excellence is great STEM teachers, with both deep content knowledge in STEM subjects and mastery of the pedagogical skills required to teach these subjects well.“
“The Federal Government should set a goal of ensuring over the next decade the recruitment, preparation, and induction support of at least 100,000 new STEM middle and high school teachers who have strong majors in STEM fields and strong content-specific pedagogical preparation, by providing vigorous support for programs designed to produce such teachers.”
10. We need to break this: Cycle: Low Learning of Math by Students
--> Low Knowledge of Math of Math Teachers
--> Low Learning of Math by Students
--> ... --> ... -->&nbssp; ... --> ...
For middle school, this is the report at http://usteds.msu.edu and is the first article at: