2008 WA State High School Mathematics Review Comparison: Looking at Mathematical Soundness

NOTE: To fully understand the dramatic difference between the WA High School Math Program Soundness Reviews presented by Strategic Teaching (WA SBE) and OSPI (Initial Report) all reviews linked below should be read.

This document is a side-by-side comparison of mathematical reviews completed for WA High School Math Programs.

High School Mathematics Curriculum Study
Prepared for WA State Board of Education by Strategic Teaching with requested reviewers:

Dr. Guershon Harel and Dr. W. Stephen Wilson
Review of Mathematical Soundness of High School Curriculum Materials
completed for WA Office of Superintendent of Public Instruction by:

Dr. James R. King and Dr. George W. Bright
1. Online Report Links1. Complete ST High School Mathematics Report
High School Mathematics Curriculum Study

2. Dr. Harel, Ph.D. Mathematics
A Review of Four High-School Mathematics Programs

3. Dr. Wilson, Ph.D. Mathematics
WashingtonState HighSchoolMathTextReview
1. Complete OSPI High School Mathematics Initial Report
2008 High School Mathematics Core Comprehensive Materials Review & Recommendations Report Initial Recommendations

2. Dr. King, Ph.D. and Dr. Bright, Ph.D. (p. 87-107 of above report)
Mathematical Analysis of Top-Ranked Programs
Review of Mathematical Soundness of High School Curriculum Materials
James R. King, Ph.D. and George W. Bright, Ph.D.
2. Accessibility to Online ReportsThese three reports readily available on the WA SBE website home page.

These documents are still on the SBE website but they may have been archived by now.
This report was imbedded in the 2008 Mathematics Instructional Materials Review Initial Recommendations Report (Algebra1/Algebra2: p. 89-93 and Geometry: p. 94-103 and Integrated: p. 104-107)

This report is difficult to locate on the OSPI website. (Under Instructional Materials Review > Mathematics). The “Soundness Review” by Bright and King was recently pulled out and posted as a separate document by the Initial HS Recommendations Report.
3. ReviewersWA SBE hired two independent mathematicians to complete individual, detailed reports analyzing the mathematical soundness of the four high-school mathematics programs:

Guershon Harel, Ph.D. Mathematics is a professor of Mathematics at UC San Diego. A graduate of Ben-Gurion University Israel, he has taught at Purdue and Northern Illinois as well. He specializes in cognition and epistemology of mathematics and their implications on curricula and teacher education. Widely published, Dr. Harel brings an international perspective to the review of math curriculum. Dr. Harel has managed to remain neutral in the reform debate.

W. Stephen Wilson, Ph.D. Mathematics is a professor of Mathematics at John's Hopkins University. A graduate of MIT, he has taught at Oxford, Kyoto, Princeton, and is widely published. He served as Senior Advisor for Mathematics: Office of Elementary and Secondary Education, U.S. Department of Education in 2006, and has written extensively concerning issues of reform mathematics.
OSPI hired two known individuals:

George Bright, Ph.D. Mathematics Education (Retired) most recently worked for Dr. Terry Bergeson as her special assistant on mathematics. A graduate of the College of Education at UT Austin, Dr. Bright was a long time professor in the college of education at University of North Carolina. He is well known in the NCTM community and has been a vocal advocate and author of inquiry-based reform mathematics. He was part of the assessment team which authored the "Connected Mathematics Project 2" for middle school math.

James King, Ph.D. Mathematics from the University of California at Berkeley has been teaching at the University of Washington since 1975 and specializes in teacher preparation courses. He is author of Geometry Through the Circle with The Geometer's Sketchpad, Key Curriculum Press. Dr. King has been a vocal advocate in Washington promoting NCTM inquiry based mathematics programs.
4. Curriculum VitaeThere is an extensive Curriculum Vitae for both Dr. Harel and Dr. Wilson in the Strategic Teaching Report: High School Mathematics Curriculum Study of March 11, 2009 (see p. 30-44).A Curriculum Vitae for either Dr. Bright or Dr. King was absent. In fact, there was not even a short note about Dr. Bright or Dr. King in the Initial Recommendations Report (see the Mathematical Analysis of Top-Ranked Programs p. 87-107).

NOTE: Greta Bornemann has stated that the Curriculum Vitae for both Dr. Bright and Dr. King would be included in the Final 2008 Mathematics Instructional Materials Review & Recommendations Report available in late April 2009.
5. Conflict of Interest
It should be noted:

Dr. James King is the author of:
Geometry Through the Circle 
with The Geometer's Sketchpad® Version 3
ISBN: 978-1-55953-048-4 | 201 pp.

NOTE: This resource is available as an Educator’s resource and is published by Key Curriculum Press. See Dr. King’s website. The link for “My Books and Papers” has links for the two resources he has had published through Key Curriculum Press.

The Geometer’s Sketchpad® is referenced on the Discovering Math Program Website.

Key Curriculum Press publishes the Discovering Math Program.

NOTE: There are numerous references to Dr. James King on The Geometer’s Sketchpad® resource site within the Key Curriculum Press website. For example:
See: Geometry Tuned On
a. Bibliography

b. Preface
6. Statement of DisclosureThere are no known connections to WA OSPI by Drs. Harel or Wilson.

There was not a Disclosure of Potential Conflicts of Interest in the ST Report, however, I am sure that Linda Plattner (Strategic Teaching) would provide this information if requested.

NOTE: WA SBE requested that a mathematician review the (2008 K-8 Curriculum Review for Mathematics) programs to determine whether or not each is mathematically sound. ST mathematician, W. Stephen Wilson, Ph.D., reviewed key topics and their development across grade levels.
It is known that Dr. Bright has had close ties with WA OSPI due to his employment at OSPI through 2008 and Dr. King has ties with Key Curriculum Press. There should be a Disclosure of Potential Conflicts of Interest in this report.


The research team for this evaluation consists _______. ___________ has financial interests that could be affected by the findings from the evaluation. This study’s members, which were convened by the WA OSPI to provide advice on key features of the 2008 High School Math Programs, have financial interests that could be affected by the evaluation’s findings.
7.Organization of ReviewNot only were there two independent reviews submitted for the same core content categories, but there was a synthesis of these two reviews presented in the Strategic Teaching Report: High School Mathematics Curriculum Study of March 11, 2009. Findings were presented on p. 3 in chart form.Although it is not clear in the High School Initial Report, Greta Bornemann (OSPI) confirmed that:

a. Dr. Bright reviewed Algebra & Algebra 2.

b. Dr. King reviewed Geometry.

NOTE #1: Dr. Bright did NOT review the Geometry materials and Dr. King did NOT review the Algebra materials.

There was only 1 person reviewing the Algebra 1 & 2 materials.

There was only 1 person reviewing the Geometry materials.

NOTE #2: It is unclear who completed the Integrated Review as that question has not been asked at the time of this writing.
8. Example of the Degree of ReviewBoth Dr. Harel and Dr. Wilson submitted very detailed review reports.

Example: Discovering Math Program

a. Dr. Harel (p. 10-15 = 6 pages of review)

b. Dr. Wilson (organized differently = 6 ½ pages total)
Dr. Bright and Dr. King submitted very limited review reports.

Example: Discovering Math Program

a. Dr. Bright (p. 89 = 1 page of review)

b. Dr. King: Discovering Geometry was NOT REVIEWED as it was ranked #6 overall. King reviewed the top 4 Geometry Programs: Holt, McDougal Littell, Glencoe, & Prentice Hall

NOTE: See p. 13 of 2008 High School Mathematics Core Comprehensive Materials Review & Recommendations Report Initial Recommendations for a ranking of Geometry Programs.
9. Review FormatThese mathematical program reviews were written in an analysis format. Specific examples are referred to from the textbooks. Each mathematician notes strengths and weaknesses of math programs within the core content areas reviewed.

The mathematical review presentation was professional, structured, and thorough. It is important to note that a common analysis framework was present in the Wilson-Harel study.

Example: See Dr. Harel’s Independent Review
a. Topics were defined and articulated why they were included
b. Procedure for analysis was stated
c. Criteria was stated (ex. see Harel report p. 2 & 3)
d. Definitions included (ex. see Harel report defining the difference between holistic and contrived problems)
e. Text references are provided (ex. see Harel report p. 4)
f. Specific examples from the book are cited.

NOTE: The detailed approach to mathematical analysis by both Harel and Wilson is specific and comments are directed toward the actual mathematical core content.
The OSPI mathematical program reviews were written in essentially a book report format. The comments are general and not specific and the format follows a summary format where lessons are cited where topics can be found. The Bright-King report repeats the standards for a majority of this document. There is very little in the way of mathematical analysis.

The attributes found in the Strategic Teaching/Harel-Wilson Reviews could not be found in the OSPI/Bright-King Review.

Example: Discovering Algebra/Advanced Algebra
Dr. Bright’s review of Discovering Algebra is one-page long (3 paragraphs dedicated to Algebra 1 and 1 paragraph dedicated to Advanced Algebra). After making broad statements such as, “The development of critical ideas earlier in the context of many different functions should help students develop rich cognitive understanding that can be retained permanently.” (p. 89 Initial Report), he ends his one-page review of Discovering Algebra by concluding: “By the end of the Advanced Algebra course, students should be quite ready to move on to pre-calculus.”

NOTE: One wonders how a focus on citing where content can be found constitutes a basis for determining mathematical soundness.
9a. Additional Notes on
OSPI Algebra 1 & 2 Review

Algebra 1 & 2
Dr. Bright makes the following statements that reflect a small grain of analysis.

1. We were looking for evidence that materials provided opportunities for students to develop mathematical understanding that would be rich and deep, as opposed to compartmentalized.

2. Understanding domain/range, developing skill at moving among representations of functions, and identifying the role that parameters play are all important ideas.

The analysis itself indicates the author was not analyzing whether the mathematics was mathematically correct in its development in terms of convention, properties, theorems and foundation... for example: They are not answering the question "Is the mathematics correct?" Rather they are answering questions of “What is the methodology being used?” and “Is the methodology balanced for skills and concepts?” It is basically just an enriched alignment overview of a set of quadratic and function Performance Expectations.

There is no expected detail, only generalities, as compared to a very crisp and professional framework of analysis in the Wilson-Harel Reviews.
9b. Additional Notes on OSPI Geometry Review
Additional Notes on Geometry Review:
This is the framework used by Dr. King. Notice it is somewhat more developed than Dr. Bright’s Algebra (a non-mathematician) framework.

1. What is called for is a set of theorems stating properties of parallelograms. What is needed for this are the basic theorems about angles formed by parallels and a transversal, along with the angle sum theorem for polygons and some congruence theorems for triangles. In the reviews that follow, these topics will be referred to as the standard parallelogram theorems.

Dr. King actually does an adequate job in his analysis. Looking for postulate development to usable theorems, etc... There are points that can be nit-picked, but he essentially sees the same things that Wilson and Harel saw in the overlapping texts. He is less detailed and softer, but actually quite consistent with Wilson-Harel in the traditional analysis
9c. Additional Notes on OSPI Integrated Review

In general the Algebra Review portion by Dr. Bright is again very vague and does not answer the question of mathematical correctness. Notably, the Geometry Review of the Integrated sounds much more like Dr. Bright's voice than Dr. King's voice. Much talk about cognitive methods and appropriateness, but little if any about the correctness of the geometry. Whether postulate geometry is correctly established and developed is entirely sidestepped. This does not sound like Dr. King's analysis of traditional material at all. This is the voice of a methodology major, not a mathematician.

NOTE: Who specifically reviewed the Integrated textbook components is not clear and was not a questioned clarified at the time of this writing.

Approach to Mathematical Review
ST Approach (p. 9)

Dr. Harel and Dr. Wilson selected state content standards as a lens to assess the programs. More specifically, ST’s review focused on three selected topics that are covered in each program in order to determine how well the topics fare with respect to the reviewer’s criteria for mathematical soundness.

ST Report articulates differences in what types of problems the two mathematicians consider to be good math problems. (p. 10-11)
Bright/King Approach (p. 87-88, 94)

On p. 87 it states that they looked for “evidence** of mathematical soundness; that is mathematical correctness and coherent development of ideas.” Then in the next paragraph, “No review is likely to represent all possible views. We were looking for evidence** that materials provided opportunities for students to develop mathematical understanding that would be rich and deep*, as opposed to compartmentalized.”

*The terms ‘rich and deep’ are not defined. This phrase is often used by those biased in favor toward reform math.
**The evidence found to justify mathematical soundness seems to be in the form of where the various Performance Expectations are located.
11. The High School Discovering Math Program: Algebra, Geometry, & Advanced AlgebraQ. Why is the Discovering Math Program mathematically unacceptable?

1. Discovering often side steps the use of formal algebra. Consequently, students do not gain the fluency they will need and they do not learn to appreciate the power of the general form. (see ST Report, p. 4)
2. Discovering places more emphasis on the study of graphs rather than the study of quadratic functions. It does not help students build an understanding of the structure of algebra. (p. 4)
3. In Discovering, the proof itself looks valid, but it is based on almost 700 prior pages of inductive geometry. (p. 5)

NOTE: In Wilson’s report (p. 22) he makes a statement about the High School Text Discovering Geometry:

“This is a highly unsatisfactory geometry text.”
Q. Why should the Discovering Math Program be questioned?

A. It was not included in the Geometry Review due to the 6th place ranking.

In addition, there was only a one-page summary of Algebra/Advanced Algebra Performance Expectation location.

How can a one-page summary (the totality of the OSPI Math Review for this High School Math Program) constitute a mathematical analysis on this particular high school math program
Request #1: Textbooks
Q. Has Superintendent Dorn or Deputy Asst. Superintendent Burke physically viewed any of the following textbooks:
Prentice Hall
McDougal Littell

Please look at a side-by-side comparison to see why parents are so concerned with the lack of clarity/precision/organization of the Discovering Algebra/Geometry/Advanced Algebra textbooks.
Request #2: Online Textbooks
After viewing the Holt, Prentice Hall, and Discovering online textbooks, Holt and Prentice Hall online textbooks are superior to the Discovering online textbooks.

Two Examples from the Online Textbook:
1. Neither the chapters nor the lessons in the Table of Contents have titles. So a person would have to 'guess' what chapter might contain Quadratic Functions. Holt and Prentice Hall provide very detailed online Table of Contents and Chapters for quick perusal of topics.

2. The layout of the Holt and Prentice Hall online text is excellent. Holt has online tutorials that come with each and every lesson.

Textbooks not viewed online as of 4-19-09:
McDougal Littell

2008 WA State High School Mathematics Review Comparison: Looking at Mathematical Soundness - Mathematically Sound Foundations

To download a pdf of the above WA Textbook Review Results table click here.

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