Links for Portland Parents of Talented and Gifted Children


Mathematics Instruction in Portland


Materials approved by the Oregon State Board of Education for 2009-15

About Singapore Math


go to other mathematics links on this page




Mathematics Links


State-Adopted Instructional Materials for Mathematics, 2009-2015

Category 2 Mathematics, Grades K-5/6

Carolina Biological Supply Co., Math Out of the Box, c. 2009

HMH Supplemental Publishers, Inc., Saxon Math, c. 2008

Houghton Mifflin Harcourt School Publishers, Math Expressions, c. 2009

Kendall/Hunt Publishing Co. Math Trailblazers, c. 2008

Macmillan/McGraw-Hill, Math Connects, c.2009

Pearson Scott Foresman, Investigations in Number, Data, and Space, c. 2008

Pearson Scott Foresman, enVisionMATH, c. 2009, Inc. Earlybird Kindergarten Mathematics Standards Edition and Primary Mathematics Standards Edition, c. 2008

The Math Learning Center, Bridges in Mathematics, c. 2007, 2008

Wright Group/McGraw-Hill, Everyday Mathematics, Third Edition, c. 2007, 2008


Category 3 Mathematics Education, Grades 6-8

Glencoe/McGraw-Hill, Math Concepts and MathScape, c. 2009 & 2007

HMH Supplemental Publishers, Inc., Saxon Math, c. 2007

Holt McDougal, Holt Mathematics, Holt Algebra 1, McDougal Littell Pre-Algebra, MathThematics, Algebra Readiness and Math Intervention, c. 2007 & 2008

Pearson Prentice Hall, Connected Mathematics, c. 2009

Pearson Prentice Hall, Prentice Hall Mathematics, c. 2008

SMc Curriculum, Oregon Focus on Math, c. 2008

Wright Group/ McGraw-Hill, The University of Chicago School Mathematics Project, Pre-Transition Mathematics, Grade 6, Transition Mathematics, Grade 7, Algebra, Grade 8, c. 2009 & 2008



Sites related to the "math wars" or mathematics education


NEW With Fractions, Common-Core Training goes beyond "Invert and Multiply" by Liana Heitin for Education Week, August 12, 2014.  Blog article links to the presentation M106 in the Maryland College and Career Readiness Conference (below).


Mathematic [sic] Sessions from the College and Career Readiness Conference at the University of Maryland


NEW Alberta Education Shrugs Off Concerns: an article from the Edmonton Journal, February 16, 2014.  At the bottom of the story, there is a set of links to earlier stories on the introduction of "conceptual math" curricula into Alberta.


Paul L. Morgan, George Farkas, Steve Maczuga, "Which Instructional Practices Most Help First-Grade Students With and Without Mathematics Difficulties?" Published online first in Educational Evaluation and Policy Analysis, June 25, 2014

Youtube presentation by co-author Paul L. Morgan:

News release:


Full Text: 

"Right and wrong methods for teaching first graders who struggle with math" from the "Education by the Numbers" blog on the Hechinger Report website:

[From the Blog post]

"First grade teachers facing a class full of students struggling with math were more likely to turn to music, movement, and manipulative toys to get their frustrated kids engaged, finds a new study in the journal Educational Evaluation and Policy Analysis. Yet researchers found these techniques did not help—and in some cases hindered—learning for the students having the most difficulty..."


"Skill-based Sorting in an Era  of College Prep for All"  by Elaine M. Allensworth and Takako Nomi Recommended. A research review by the University of Chicago Consortium on Chicago School Research, March 2014.  This brief summarizes the results of ten separate studies of Chicago's "Algebra for All", Double dose Algebra and College Prep for All.  Nor surpisingly, the study finds that results are mixed: the authors found that how schools sort students is as important as the content students are exposed to.

Below are two of the more striking conclusions:

"Average test scores are higher when classes are sorted by skills due to large benefits for high-skilled students’ learning gains. ...
A universal curriculum with unsorted class-rooms can increase, rather than diminish, inequities by race and income if teachers are unable to differentiate instruction and maintain classroom control."


World Class Standards For Preparing Teachers of Mathematics, William Schmidt, Nathan Burroughs, Leland Cogan
Working Paper, Center for the Study of Curriculum & The Education Policy Center,  Michigan State University, 2013

The worst-performing teacher-preparation programs are producing about two-thirds of all American middle-school math teachers. Moreover, If American math teachers were to have the same background as teachers in Taiwan, they would have to be recruited from the top quarter of American 8th. graders. College courses taken by nearly all middle school teachers in the most successful countries included beginning Calculus, Calculus, Multivariate Calculus, Differential Equations, Linear Algebra and Probability.



Achievement Effects of Four Early Elementary School Math Curricula:  Findings for First and Second Graders, by Roberto Agodini,  Barbara Harris, Melissa Thomas (Mathematica Policy Research, Inc) and Robert Murphy, Lawrence Gallagher (SRI International), Institute of Education Sciences,  U.S. Department of Education  October 2010


What's Wrong with the New Math Curriculum? a post by Karen Smith, a parent in Maryland


More Oregon students are getting math class, By Betsy Hammond, The Oregonian November 07, 2009, 7:50PM
"Oregon math teachers have moved middle schoolers far enough ahead in math that the typical eighth-grader now can do math at nearly the same level as many high school sophomores.
Middle school students in every racial, ethnic and income group show greater mastery of mathematics -- including algebraic reasoning, statistics and geometry -- than they did three years ago.
Educators attribute much of the progress to Oregon's embracing a national recommendation to drastically scale back the number of math topics covered in each grade. ......"


 Report of the National Mathematics Advisory Panel


 Education Panel Lays Out Truce In Math Wars Effort to Fix 'Broken' System Sets Targets for Each Grade, Avoids Taking Sides on Method By JOHN HECHINGER for the Wall Street Journal March 5, 2008; Page D1

"A presidential panel, warning that a "broken" system of mathematics education threatens U.S. pre-eminence, says it has found the fix A laserlike focus on the essentials. The National Mathematics Advisory Panel, appointed by President Bush in 2006, is expected to urge the nation's teachers to promote "quick and effortless" recall of arithmetic facts in early grades, mastery of fractions in middle school, and rigorous algebra courses in high school or even earlier. Targeting such key elements of math would mark a sharp departure from the diverse priorities that now govern teaching of the subject in U.S. public schools."


Final Report on the National Survey of Algebra Teachers for the National Panel,  September 27, 2007. Recommended


Most Algebra teachers felt their students' preparation was "weak" and the skill areas of greatest concern were rational numbers, word problems and study habits.  A slight majority of the teachers consider a lack of ability grouping to be a moderate or serious problem--and teachers in schools that did not offer ability grouping were more likely to consider this a serious problem (See Research Question 11)


National Council of Teachers of Mathematics, Focal Points  The new grade-based skills recommended by the NCTM

Common Denominator: The Preparation of Elementary Teachers in Mathematics by America's Education Schools, June 2008
American students' chronically poor performance in mathematics on international tests may begin in the earliest grades, handicapped by the weak knowledge of mathematics of their own elementary teachers. NCTQ looks at the quality of preparation provided by a representative sampling of institutions in nearly every state.

Content Review of CPM mathematics by Wayne Bishop, Department of Mathematics and Computer Sciences, California State University, Los Angeles:

 "Much of Volume 1 actually detracts from developing algebraic competence. Almost all of the mathematical content is at the level of the Grade 7 standards or below, e.g., the equations to be solved all are, but the activities are still very time consuming and sometimes frustrating. The worst of all, however, is not teaching the power of algebra itself. Unit 4: 123 is TOOL KIT CHECK UP and it is mandated that it contain Guess and Check tables, and "cups and tiles to model solving equations."  This is not algebra and it is not college preparatory math, no matter what it calls itself. Eventually, Volume 2 starts teaching some algebra but it is too little and too late."


Adding it up: Helping Children Learn Mathematics,  Mathematics Learning Study Committee: Jeremy Kilpatrick, Jane Swafford, and Bradford Findell, editors, Center for Education, Division of Behavioral and Social Sciences and Education, National Research Council.  Recommended.

"In comparison with the curricula of countries achieving well on international comparisons, the U.S. elementary and middle school mathematics curriculum has been characterized as superficial, “underachieving,” and diffuse in content coverage. ...Students invariably spend considerable time on topics they encountered in the previous grade.26 At the beginning of each year and of each new topic, numerous lessons are devoted to teaching what was not learned or was learned inadequately the year before. Because the curriculum is consequently so crowded, depth is seldom achieved, and mastery is deferred. ... The massive amount of review created by the inadvertent de facto curriculum set by textbooks wastes learning time and may bore those students who have already mastered the content. Such constant review is also counterproductive. It is much easier to help students build correct mathematical methods at the start than to correct errors that have been learned and practiced for a year or more."


The Brookings Institution released a review of the NAEP tests that concluded American tests are years behind the level of math included in the Singapore texts--partly because all the arithmetic used whole numbers.  Tom Loveless, the author of the review also concludes that American students lost ground in the 1990s and many do not have the math skills they need to be successful later.

  See his speech Trends in Math Achievement: The Importance of Basic Skills summarizing this work at at


"Youngsters who have not mastered whole number arithmetic by the end of 4th grade are at risk of later becoming remedial students in mathematics. Half of the nation's nine year olds missed the multiplication and division items on the trend NAEP the last time the test was given.

A similar concern can be raised about the performance of thirteen and seventeen year olds. Their level of proficiency on computation skills remains unacceptably low. Look closely at fractions. Proficiency with fractions is critical in preparation for algebra. In 1999, only about half of thirteen and seventeen year olds could compute accurately with fractions on the NAEP. Students who leave eighth grade not knowing how to compute with fractions enter high school as remedial math students. Students who leave high school lacking proficiency with fractions are inadequately prepared for college mathematics. On the most recent trend NAEP, both age groups were less proficient at computing with fractions than in 1982, twenty years ago."


See also on the use of calculators in testing

and: on the NAEP/Singapore



Julie E. Riordan and Pendred E. Noyce, The Noyce Foundation:  "The Impact of Two Standards-Based Mathematics Curricula on Student Achievement in Massachusetts"

"Since the passage of the Education Reform Act in 1993, Massachusetts has developed curriculum frameworks and a new statewide testing system. As school districts align curriculum and teaching practices with the frameworks, standards-based mathematics programs are beginning to replace more traditional curricula. This paper presents a quasi-experimental study using matched comparison groups to investigate the impact of one elementary and one middle school standards-based mathematics program in Massachusetts on student achievement. The study compares statewide standardized test scores of fourth-grade students using Everyday Mathematics and eighth-grade students using Connected Mathematics to test scores of demographically similar students using a mix of traditional curricula. Results indicate that students in schools using either of these standards-based programs as their primary mathematics curriculum performed significantly better on the 1999 statewide mathematics test than did students in traditional programs attending matched comparison schools. With minor exceptions, differences in favor of the standards-based programs remained consistent across mathematical strands, question types, and student sub-populations.
Journal for Research in Mathematics Education 2001, Vol. 32, No. 4, 368–398


" Flaws in the Evaluation Process" an article by Mark Clayton that appeared in the Christian Science Monitor in 2000,  explains that the Department of Education's evaluation of the Connected Math project relied on research on the curriculum's effectiveness that was conducted by the authors of the project or their associates.  This is part of a multi-article series in the CSM on American Mathematics instruction.  The other  articles (listed in the sidebar) are no longer available through the original links, but they were re-printed by NYC Hold and the series can now be found at



The Relationship Between Using Saxon Middle School Math and Student Performance on Texas Statewide Assessments April 2005. A report commissioned by Harcourt Brace from PRES associates.  Finds a slight benefit for non-gifted students in the Saxon series.


Conference Summary:" Does Two plus Two Still Equal Four: What should our children know about math?"  Sponsored by the American Enterprise Institute for Public Policy Research

 "Some of my ideas about mathematics programs" by W. Stephen Wilson, professor of mathematics at Johns Hopkins University.  Includes his comments on what students must know to be prepared for college mathematics



 "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education" by H. Wu from the American Educator.  This article is especially valuable for its discussion of the fundamental concepts embedded in common mathematics algorithms such as performing division of fractions by inversion and multiplication.



 "Another Everyday math horror story"

  The Fordham Report on State Mathematics Standards:

An Appraisal of Math Standards in 46 States, the District of Columbia, and Japan by Ralph A. Raimi and Lawrence S. Braden. A scathing series of comments on various state mathematics curriculum standards by two well-qualified individuals. Raimi is professor emeritus of mathematics at the University of Rochester and former chairman of the math department (and graduate dean) at that institution. Braden has taught mathematics and science in elementary, middle, and high schools for many years in Hawaii, in Russia, and now in New Hampshire, at St. Paul's school. He is a recipient of the Presidential Award for Excellence in Science and Mathematics Teaching. He holds a bachelor's degree in mathematics from the University of California and an M.A.T. in mathematics from Harvard. [from the website]. Oregon received a "D" from these authors.

The report is written in rather formal English and requires some patience but their comments deserve serious consideration by our state and local policymakers. Recommended.

League of Women Voters report on math education in California

The Education Committee of the Los-Altos-Mountain View League of Women voters has prepared a presentation entitled "Algebra And The New California High School Exit Exam: Will Our Children Be Prepared?" It contains numerous links to other reputable sources and seems to be the closest thing available to an unbiased history of the California math conflicts. Recommended.

2+2, Mathematically Correct website maintained by critics of "whole math"

GTAforum: the entire saga of an attempt by Montgomery County Public Schools (MCPS) to gain teacher training tied to the Connected Mathematics Program. Includes letters, newspaper articles both for and against. The opposition was led by the Gifted and Talented Association of Montgomery County (GTA).

Math Forum From Swarthmore, provides a generally positive view of "math reform." also provides a Discussion list and many other links

"Math wars" from the McNeil/Lehrer news hour. Contains many references to Oregon. A typical News Hour report, with all sides represented

Parents Skilled at Math protest new Curriculum article from the L.A. times. Despite its title, a relatively balanced discussion of the California "math wars"

The Politics of California School Mathematics: The Anti-Reform of 1997-99  By Jerry P. Becker and Bill Jacob.  From the Phi Delta Kappan. A criticism of the views and actions of the "whole math" opponents by two professors of education.

NEW: Where's the  Washington State advocacy group

See also: "Middle School Math Comparison for Singapore Mathematics ......" below


 A few of my favorite mathematics links

( These are not related to the math wars.)


NEW Abacus: the Art of Counting with Beads


NEW Algebasics.  A straightforward introduction to Algebra with narrative and examples


American Mathematical Society


AMSER Math Links:  From the Scout Report's Applied Math and Science Education Repository, the section for Mathematics


Dave's Short Trig Course A Short Course in Trigonometry


Dr. Mike's Math Games


Euclid's Elements


NEW Explore the math twitter blogosphere  created, according to the homepage by a "cohesive gaggle of obsessed math teachers"



Harvard Math Circle: website created by a group that started math enrichment classes in Cambridge


Historical Activities for the Calculus Classroom: a set of problems that challenged mathematicians in the past with illustrations and solutions

History of Mathematics website: From Clark University. Not as well organized as it might be, but a storehouse of information, including biographies of over 1,000 mathematicians.

Hoagies Kids and Teens Math  Links a very entertaining collection of math contests, games, and child-friendly sites from the Hoagies site for gifted children.  Recommended

The Integrator

Internet Resources in Mathematics: From Langara College in British Columbia, a very large, well organized collection of sites that have been reviewed and annotated. Recommended. Note especially the pages for "resources, lists, and catalogues--General" which is a very large set of resources organized by topic.

NEW Kathy Shrock's Guide for Educators. Straightforward list of Math websites

NEW The KnotPlot site

NEW Life of Fred: a series of mathematics textbooks popular with home-schooling families.  Fred encounters problems in his life and then used mathematics from arithmetic to calculus to solve them.  Contains some mild Christian references.

MacTutor History of Mathematics from St. Andrew's University.  Includes an Index of Famous Curves, Birthplace Maps, Biographies, Mathematical Societies, timelines and so on.  Well-organized and informative.

Mathcasts: A collection of demonstrations of math operations from elementary school through calculus.  Requires the latest version of the Macromedia Flash Player.

Mathematical Association of America Classroom Capsules collection of material issued by the MAA in printed form, now online

Mathematical Fiction compiled by  Alex Kasman, Associate Professor in the College of Charleston Department of
Mathematics, listed by category (e.g. mystery, fantasy, children's books).

Mega-Math:  A colorful and entertaining introduction to such topics as knot theory, the four color theorem etc .

NEW Mathematical Imagery  A great collection of links to math images but the one for the Visual Mathematics Journal (the bottom on the left) is LOADED with objectionable pop-up ads.  The others seem fine.


NEW Napier's bones. From the Mathematical Association of America, a site about Napier and a demonstration of how his "bones" functioned .


Online Teachers Resource Network in Australia, Math Links


The Opinionator: Entertaining math blog from the New York Times, aimed at the "common reader" (i.e. not math specialists)


The Pacific Institute for the Mathematical Sciences at the University of British Columbia offers a host of appealing mathematical webpages.  Select "Education" to find copies of their newsletter "Pi in the sky" which offers a wide range of math articles, problems and activities including cartoons  Topologists might want to install their Knot

Mathematical Fiction

Plus Magazine  From Great Britain.  Lively and enjoyable.  Don't miss their article on the Parliamentary debate on the quadratic equation in issue 29.


Sphere Eversion a cool 20 minute video on topology:


Wolfram MathWorld created and edited by Eric W. Weisstein.  See also the section called MathWorld Classroom

Zona Land


About Singapore Math

Singapore (the country) astonished educators by the very high performance of its students in the TIMSS (Third International Math and Science) tests--the international equivalent of NAEP in 1995 and again in 1999. Some people wondered what they were doing right and decided to take a look at the curriculum they were actually using in Singapore schools. Singapore students are taught in English. A company here in Oregon City decided to make these books available to American families and they have become very popular with TAG families and homeschooling families across the country. A few school districts have experimented with the series and have had very good results.


The Singapore Primary Math series is one of many different approaches to math that are on the list of materials approved for adoption by the State of Oregon


It was also approved by California

I am not associated in any way with the Singapore math books--I don't know anyone in the company and have read only one of the books all the way through. If you want to learn more about it, go to the company site at


They also offer a very limited set of news articles on the site. My understanding, however, is that Singapore math is not simply a "back to basics" approach but also teaches thinking skills.

It's hard to find unbiased stories about Singapore Math. I have been following the saga of its use in Montgomery County, Maryland because I know someone there. It was adopted on a pilot basis in 2001.  An article about the pilot appeared in the Washington Post on October 17, 2001--see



 The principal supporters of the program were TAG parents who were frustrated by the district's slow math curriculum.
A study by the school district's own evaluation staff found that students in the Singapore pilot program schools significantly outperformed students in control programs after two years
And then....the Superintendent dropped the program on the grounds that it was inadequately aligned with the state curriculum standards

    See also the testimony of John Hoven which provides a detailed comparison of the work expected of American students (as evidenced by the questions on the National Assessement of Educational Progres, NAEP) and that routinely expected in Singapore "Testimony of John Hoven On Behalf of The Center for Education Reform"  This testimony was given in 2001.

and "Miracle Math" by Barry Garelick, an article on the Montgomery County story


Wikipedia article


For the use of Singapore Math in the Ingenuity program in Baltimore see


"Middle School Math Comparison for Singapore Mathematics, Connected Mathematics Program (CMP) and Mathematics in Context, a Summary (Including Comparisons with the NCTM Principles and Standards 2000"  A summary of the November 2000 report submitted to the National Science Foundation by the Department of Applied Mathematics University of Washington.


Finds that the best match with the NCTM standards is in the CMP and that the Singapore series fails to teach "higher order thinking skills" and relies on knowledgeable teachers.  However, it also includes the following comments:
 "The Algebra level in CMP and MIC appear to be almost two grade levels lower than in the Singapore materials.  ... It is also our prediction that students wishing to take calculus before the end of their 12th grade year are likely not to be on track to do so after completing 8th grade CMP or MIC, but would be ready to do so after completing Singapore s SL2.  We are not advocating that calculus in high school should be a goal for all students, but if this is the desired goal for certain students, the proper supplementation of CMP and MIC at an accelerated pace cannot be ignored.  Moreover, we are skeptical about the possibility of maintaining the interest of high-end students while progressing at the pace necessitated by the discovery process, if care is not taken to individualize these discoveries for the students" (pp. 43- 49)




Making Math Lessons as Easy as 1, Pause, 2, Pause by Winnie Hu in the New York Times, Sept. 30, 2010

...In contrast to the most common math programs in the United States, Singapore math devotes more time to fewer topics, to ensure that children master the material through detailed instruction, questions, problem solving, and visual and hands-on aids like blocks, cards and bar charts. Ideally, they do not move on until they have thoroughly learned a topic. Principals and teachers say that slowing down the learning process gives students a solid math foundation upon which to build increasingly complex skills, and makes it less likely that they will forget and have to be retaught the same thing in later years. And with Singapore math, the pace can accelerate by fourth and fifth grades, putting children as much as a year ahead of students in other math programs as they grasp complex problems more quickly....


Singapore math a success so far in Fayette Co. By Jim Warren, Lexington Kentucky Herald Leader

.....Polly Anna Cox taught a calendar math lesson to her fifth-grade class at Liberty Elementary School, one of nine Fayette County schools that instituted a full Singapore math curriculum this year. Cox says she is teaching math at a "much higher level now."... Participating students are using a textbook called Math in Focus, which essentially is identical to the text used by about 80 percent of elementary students in Singapore, a tiny Asian city-state whose kids have been hitting the ball out of the park on international math assessments since the late 1990s. Fayette County is hoping for similar results.


At L.A. school, Singapore math has added value  By Mitchell Landsberg Los Angeles Times Staff Writer March 9, 2008

"Here's a little math problem. In 2005, just 45% of the fifth-graders at Ramona Elementary School in Hollywood scored at grade level on a standardized state test. In 2006, that figure rose to 76%. What was the difference?

If you answered 31 percentage points, you are correct. You could also express it as a 69% increase.

But there is another, more intriguing answer The difference between the two years may have been Singapore math.

At the start of the 2005-06 school year, Ramona began using textbooks developed for use in Singapore, a Southeast Asian city-state whose pupils consistently rank No. 1 in international math comparisons. Ramona's math scores soared.

"It's wonderful," said Principal Susan Arcaris. "Seven out of 10 of the students in our school are proficient or better in math, and that's pretty startling when you consider that this is an inner-city, Title 1 school.",1,2133870.story?track=rss&ctrack=1&cset=true


Scarsdale looks to Singapore for the new math
By Swapna Venugopal Ramaswamy • The Journal News • October 9, 2008
SCARSDALE -- Dylan Cadalzo's third-graders watched intently as he placed brightly colored number discs under four columns marked 1,000s, 100s, 10s and 1s on the classroom's whiteboard.
"How much does that make?" Cadalzo quizzed the Edgewood School class, and almost immediately several hands competed for his attention.
The answer: 6,342.
"Now, how much more do you have to add to make it 6,442?" the teacher asked.
"Hundred," answered Hannah Dong, as she proceeded to add a red disc to the 100s column.
Though using math manipulatives - concrete objects that can be moved and used to represent abstract concepts - is not new to the class, it will increase in emphasis this year, as the Scarsdale school district adopts Singapore math in kindergarden through fifth grade, replacing Trailblazers, used in the district for a decade.
The textbook series, written by the Ministry of Education of Singapore, is called Primary Mathematics, and Scarsdale is the first public school district to use it in New York as its core curriculum.