I really like what this teacher has to say about children needing to derive formulas instead of just being taught them and I like how he integrates physics with math.

# Category: Math

## Algebra in Wonderland?

Someone sent me a link to this NY Times story about how Alice in Wonderland was really a story about math. Who knew?

http://www.nytimes.com/2010/03/07/opinion/07bayley.html?pagewanted=all

## A Letter to U.S. Secretary of Education Arne Duncan

This letter was posted, in August, 2009, to the RACE TO THE TOP comments section of the federal government website. (http://www-users.math.umd.edu/~jnd/RTTTPublicLetter.html)

Underlining is mine. Signatures have been removed to shorten the post. You can view them at the link above. It’s a who’s-who of math professionals.

**RACE TO THE TOP AND K-12 MATHEMATICS EDUCATION:**

**A Letter to U.S. Secretary of Education Arne Duncan**

**Introduction**

If a first grade teacher read at the fifth grade level, we’d be outraged. But what if she had only third or fourth grade mathematics skills and lacked the conceptual understanding needed for teaching mathematics? Unfortunately, this is the reality for all too many licensed K – 8 teachers in this country. According to a recent report by the National Council on Teacher Quality, the current training that prospective K-8 teachers receive in the vast majority of this country’s education schools assures that this appalling situation will continue unchanged.

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.

Teachers’ mathematical knowledge is particularly important in K-8, since students’ mathematical foundations are built there. The first priority must be rigorous mathematics courses for **prospective **teachers of elementary and middle school children, followed by state-approved licensing tests that fully assess their knowledge and conceptual understanding of elementary mathematics. We must radically upgrade the mathematical content of their professional development programs as well.

**Recommendation 1.** The United States Department of Education should fund only those states that present a plan to implement the recommendations of the National Mathematics Advisory Panel in mathematics courses or programs for prospective or current teachers of mathematics and science in K-8 and on their licensing (certification) tests. The rigorously researched 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. Other professions have state licensing requirements, whose purpose is to protect the public from practitioners without entry-level knowledge and skills. Good grades from law school do not exempt aspiring lawyers from having to pass state bar exams. Clearly the education of K-12 students should be considered as important to safeguard as the interests of a lawyer’s clients.

What are needed are serious **college mathematics courses**. The Massachusetts Department of Education’s guidelines for the mathematical preparation of elementary and special education teachers are a step toward describing the content of such courses. The courses must cover the core material that we should expect teachers to know in order to prepare our children to compete successfully in the world economy and to help their students avoid remedial coursework if and when they enter college.

**Recommendation 2.** The programs funded by the U.S.D.E. should require instructors of the mathematics courses for aspiring or current K-8 mathematics and science teachers, coaches, and supervisors to hold a Ph.D. in mathematics or a mathematics-dependent field (or at least be closely supervised by someone holding such a degree). All prospective K-8 mathematics and science teachers, coaches, and supervisors should be required to pass a solid test on the core mathematical material (especially arithmetic) for licensing. Mathematics supervisors and coaches should be required to have at least the mathematics qualifications of those they supervise.

**Recommendation 3.** The U.S.D.E., as part of the provision in Title II of the Higher Education Act, should require each state to report publicly by institution the pass/fail rates for all prospective elementary and special education teachers on a mathematics licensure test as demanding as the 40-item test now required in Massachusetts. This recommendation is fully supported by the report of the National Council on Teacher Quality documenting the inadequate preparation in mathematics of future elementary school teachers in 67 of the 77 colleges/universities surveyed.

**Recommendation 4.** The states funded by the U.S.D.E. should be required to align the courses in mathematics pedagogy taken by prospective K-5 teachers with the new mathematics coursework, as outlined in Recommendation 1. Current methods courses too often focus only on demonstrating how to teach very low level mathematics content.

**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. It should not fund professional development programs that do not have a significant arithmetic component.

Close cooperation between teachers in the field, mathematicians having an active interest in K-12 mathematics education, and mathematics educators, together with the active help of government and the business community, can turn our mathematics outcomes around, but time is of the essence.

**References**

National Council on Teacher Quality. (2008). *No common denominator: The preparation of elementary teachers in mathematics by America’s education schools*. NCTQ: Washington, DC: www.nctq.org/p/publications/docs/nctq_ttmath_exec_summ_20090208042841.pdf

National Mathematics Advisory Panel. (2008). *Foundations for Success: Final Report of the National Mathematics Advisory Panel.* U.S. Department of Education: Washington, D.C. www.ed.gov/about/bdscomm/list/mathpanel/report/final-report.pdf

**We, the undersigned, support this letter: (see link at top)
**

## Math Update

Howdy folks,

I’ve been buried with projects, one of which is getting Mathino ready for purchase as quickly as possible so those of you that want it for Christmas can get it. It’s really a fantastic game (since I didn’t create it I can say that :)).

There’s been a bit of stuff lately that has come out, some more important than others and where my time is short I will just summarize the highlights and give you links to the information.

Oak

************************

**********************

In this classic “news” report by The Onion, just substitute “reform” for “Montessori” and “math” for “dentisty” and you’ll get a good laugh over the insanity of constructivism.

**Montessori School Of Dentistry Lets Students Discover Their Own Root Canal Procedures**

***************************

A couple weeks ago, the U.S. Chamber of Commerce released a new report on educational innovations in each state entitled “Leaders and Laggards”. Not many states faired well, but Utah was near the bottom of the heap with poor school management, staffing (removing ineffective teachers), pipeline to postsecondary, and technology. We did get an ‘A’ for data and a ‘B’ for finance, but overall a ‘D’ rating.

**************************

**NCTQ report recommends Colorado adopt Singapore Math**

***************************

Latest outrages:

**Achtung! Prosecutor says only jail deters homeschooling**

## Free Honors Coordinate Geometry Book

Curtis Blanco has put together a coordinate geometry book that is free for use. If you are homeschooling or looking for additional geometry problems for a class, you can get it here. Updates are being made on a regular basis so check back periodically.

http://www.constructorscorner.com/Corners/Corners_files/Honors_Coordinate_Geometry.pdf

## One Step Ahead of the Train Wreck

A great article from Barry Garelick on the insanity of Everyday math and the virtues of Singapore math.

http://ednews.org/articles/one-step-ahead-of-the-train-wreck.html

What exactly is the attraction of reform math? I still haven’t figured out why so many “educators” are so blind to this method of teaching and the results it’s producing. Two year colleges are being hit especially hard with the number of students requiring remedial math. Utah is no exception, but here’s some hard figures from another community college:

http://www.math.umd.edu/~jnd/Remedial.Math.Problem.htm

The numbers of students needing remediation went from 63% in 1999 to 71% today. One eighth of the PGCC budget is allocated to remediation.

## Impressive Math Lesson Videos

Someone recently sent me a link to the Khan Academy’s site. This person has over 800 videos on YouTube teaching various math courses. The videos aren’t too long, but the amount of them is quite impressive. If your child is struggling with a concept, see if there isn’t something on this page they can review to get up to speed.

Not only does he cover tons of math subjects, he also has a lot on finance including some analysis on the Geithner and Paulson plans.

## National Standards are Dangerous

There are certain appealing aspects to having national standards, such as looking at a country like Singapore or Japan that has very high standards and achieves great things through them. However, within the United States, we have already seen tendencies from those in power to dictate down to the local level things that are “best” for us when in fact they’ve been proven wrong over and over again. This article by Laurie Rogers is an excellent summary of some of the issues.

http://ednews.org/articles/national-standards-national-curriculum-dangerous.html

## “No Common Denominator”

Two reports by the National Council on Teacher Quality (NCTQ) do a fantastic job of showing just where education colleges are failing students who want to become teachers, and then our children who are taught by these teachers. One report was released in June 2008 for mathematics preparation of teachers entitled “No Common Denominator–The Preparation of Elementary Teachers in Mathematics by America’s Education Schools.” The second, released in May 2006, is on reading and is titled “What Educations Schools Aren’t Teaching About Reading and What Elementary Teachers Aren’t Learning.”

The math report examined 77 schools around the country and Utah State University was the only college in Utah that was examined, and also received a failing mark for teacher preparation.

This August, thanks to a grant by a generous donor, a report will be revealed that examines all 8 major colleges in Utah. I understand that only 1 college has received a passing mark, while 3 would pass if they required more courses of elementary education students, and 4 fail completely.

The links below will take you to the math and reading reports, but the gist of them was to give a few standards for teachers and development of a proper education base before they go off to teach impressionable minds. The math report details 5 standards as follows:

1) Teachers must acquire a deep conceptual knowledge of math focused on

1. numbers and operations,

2. algebra,

3. geometry and measurement, and — to a lesser degree —

4. data analysis and probability.

2) Higher entry standards into the program with teachers demonstrating mastery of geometry and algebra 2 at the high school level

3) Must demonstrate a deeper understanding of math than what they must teach to children

4) Elementary content courses must emphasize numbers and operations and student teaching must focus on delivery of math content

5) Math content delivered to teachers should be done within the purview of a MATH DEPARTMENT

The entire math report is 28 pages and contains some other interesting things should any of you wish to look over it. I am eager for the report in August and can’t wait to see how <cough>BYU</cough> fares. I’m not expecting it will be the lone passing school in the state.

The reading report is also great and tells us what we already knew, that phonics and explicit instruction work best. Sorry whole language constructivism. You lose again.

## Stop TERC

An excellent new site has popped up recently that is a great resource for those fighting Investigations math. Check it out here:

Loads of resources in one giant white paper. Produced by people in Frederick County, Maryland, this site is a great topical view of the problems with TERC.