** 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.
ÒR U 4 teachers knowing Arithmetic?Ó **(a report of mine) **(**www.math.umd.edu/~jnd/R_U_4_Teachers_know_Arith.html)

includes: ÒAs 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.Ó

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:

ÒWe agree with U.S.
Secretary of Education Arne Duncan's statement: Ô... 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 scienceÕ. 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.Ó

**ÒRecommendation 1.** ... The rigorously researched [National Mathematics Advisory]
PanelÔs 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. ...
Ò

** ÒRecommendation 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. ... Ò

**2. Math
PD needed for writers of NAEP and state math
assessments.**
ÒQuoting 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, ... Ò There are similar rates for flawed and marginal
items on the sample of state exams.
(From a slide in Wilfried SchmidÕs presentation at
the 2009 CBMS Forum, ÒThe National
Mathematics Advisory Panel (NMP) [andNAEP]Ó. 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, ÒNo Common Denominator: The Preparation of Elementary Teachers in
Mathematics by America's Education Schools [NOT]Ó, (June 2008).
It is at

*www.nctq.org/p/publications/reports.jsp*

**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) – *teacherÕs
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

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

www.ets.org/praxis/prepare/materials

**5. ÒAll Purpose Science Teacher [NOT]Ó** (September, 2010) One can be a fully certified high
school science teacher *without* *ever* taking a physics course.

(www.nctq.org/p/publications/docs/NCTQ_All_Purpose_Science_Teacher.pdf)

**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

www.ams.org/notices/200502/fea-kenschaft.pdf

**8.** The
ten **myths** exhibited in my report, Ò**[Common] Missteps in Mathematics Books**Ó
should be taught as being *wrong*, not *mis*-taught as
correct mathematics. This report
appeared in the section ÒFallacies,
Flaws, and FlimflamÓ of __The College Mathematics Journal__ (November
2008).

**9.** PresidentÕs
Council of Advisors on Science and Technology (PCAST) report (Sept. 2010):

RECOMMENDATION 2. ÒTEACHERS:
RECRUIT AND TRAIN 100,000 GREAT STEM TEACHERS OVER THE NEXT DECADE WHO ARE ABLE
TO PREPARE AND INSPIRE STUDENTSÓ (www.whitehouse.gov/sites/default/files/microsites/ostp/pcast-stemed-execsum.pdf)

ÒThe 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.Ò

ÒThe
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.Ó

**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**

**--> ... --> ...
--> ... --> ...**

For
middle school, this is the report at http://usteds.msu.edu
and is the first article at:

http://sboe.dc.gov/sboe/frames.asp?doc=/sboe/lib/sboe/Dancis_Common_Core.pdf