Selecting a Math Program Achieving World-Class Standards

1. A Joint Publication of FrederickEducationReform.com StopTERC.com In consultation with The American Math Forum Selecting a Math Program Achieving World-Class Standards

2. Who are these organizations? • FrederickEducationReform.com • Local grassroots organization founded by parents • Provides information on current issues affecting schools in our district through public comment, letters to the editor, participation on local radio talk shows, and maintaining reports and presentations on a user friendly website • Moderates local education discussion forum • Supports continued improvement of our schools and school choice through public charter schools

3. Who are these organizations? • StopTERC.com • Founded by Adamstown resident, Jerry Jongerius • Sheds light on the Frederick County Public School (FCPS) system’s decision to adopt an elementary “fuzzy math” program called Investigations, a program that leaves elementary students below grade level and lacking in basic content knowledge and skills • Documents steps taken to bring the shortcomings of the Investigations program to the attention of the local Board of Education and the Board’s responses • Expanded to include additional online “watchdog” role

4. Who are these organizations? • American Math Forum • a nonpartisan private activity promoting informed thought and action in American K-12 mathematics education reform and advocacy in schools, districts and states across America • Founded by Elizabeth Carson of NYC HOLD NATIONAL, today’s flagship website for the mathematics education advocacy community • Supports systemic improvements in the quality of mathematics education in our nation’s schools • Advocate programs and policies that help all students achieve success in school mathematics courses, that prepare all students for the broadest options in high school math and science courses, and that give them the opportunity to advance into mathematics based college courses and careers

5. Why did we create this publication? • Background: In response to the need to implement the Common Core Standards, FCPS has established a task force which will investigate and recommend new math texts and materials to align with the initiative. Our local board will eventually approve both the curriculum and the instructional materials. • Purpose: This publication is intended to help our local district, and others like it, select good math programs by providing information, guidelines, and research that will improve the selection process. • The presentation is divided into three sections: • Achieving World-Class Standards • Characteristics of a Strong Selection Process • Summary

6. What are world-class standards? • The National Math Panel found that the best math standards… • Teach a smaller number of topics taught to mastery • Focus on the topics needed for algebra • Proceed from simpler topics to more sophisticated • Make logical connections between the topics • Though the Common Core standards are a significant improvement over Maryland’s previous math standards, many experts hold California’s 1997 math standards in higher regard.1 • We hope school systems will aim for the best possible standards, will make adjustments to the Common Core to achieve that goal. 1 http://www.edexcellence.net/publications-issues/publications/the-state-of-state.html

7. What does great math teaching look like? In her excellent book, “Knowing and Teaching Elementary Mathematics”, Dr. Ma defines excellent teaching as teaching that is based on PUFM—a Profound Understanding of Fundamental Mathematics. PUFM is a quality that teachers must have so they can pass it on to their students. “Teachers’ knowledge plays a very important role in how textbook contents are selected and interpreted.”1 “In China, teaching a course is considered to be like acting in a play. Although an actor has to know a play very well and can interpret it in an original way, he or she is not supposed to write (or rewrite the play)…A thoughtfully and carefully composed textbook carries wisdom about curriculum that teachers can “talk with” and that can inspire and enlighten them”.1 1 “Knowing and Teaching Elementary Mathematics”, page 148

8. How do the best systems support math? In contrast to the American schools, where textbooks are regarded as “just a resource”, textbooks in China play a central role in both teacher and student learning. U.S Schools of education typically require minimal and insufficient math coursework to obtain a degree in education.1 Teacher professional development includes content training and a balanced approach that includes direct instruction, individual and group work, practice, and exploratory learning.2 1 “Not Good Enough: A Content Analysis of Teacher Licensing Examinations,” Thinking K-16, Vol. 3:1, Spring 1999, p. 9, available at www2.edtrust.org/NR/rdonlyres/5F7B8FCA-2400-47DE-9C40-AC948D934836/0/k16_spring99.pdf (accessed November 17, 2005 2 http://www.cs.nyu.edu/faculty/siegel/ST11.pdf

9. Characteristics of a Strong • Textbook Selection Process • #1 The selected program(s) must contain the content, rigor, focus, and coherence called for in a college preparatory set of content standards • #2 Valid, reliable research is valued more than closely held beliefs • #3 Participants in the decision-making must have strong math backgrounds • #4 Participants must understand the “math wars” • #5 Cognitive science is fully considered • #6 Participants recognize that balanced approaches are not truly balanced if they compromise content • #7 Professional development addresses areas in which teachers may lack knowledge • #8 Selection is not limited to just one program • #9 A pilot program is designed, conducted and ultimately implemented with fidelity • #10 Post selection, implementation is monitored heavily and problems which may arise are handled in a timely manner

10. #1The selected program(s) must contain the content, rigor, focus, and coherence called for in a college preparatory set of content standards. • The primary consideration for selecting a math program should be that it has the right emphasis on important content. • Ultimately, the content to look for in the K-12 progression is that math needed to prepare students to pass a college entrance exam. • The committee should develop a list of topics that it expects to be covered, along with specific criteria for each topic and its placement in the overall sequence. • Example: Fractions • When fractions are introduced, are students shown a full range of examples (1/4 and 5/4) to avoid the misconception that fractions always have a smaller numerator? • Does the program explain how to convert fractions into decimals by dividing the numerator by the denominator?

11. #1The selected program(s) must contain the content, rigor, focus, and coherence called for in a college preparatory set of content standards. • Pedagogical considerations are important, but committees should first remove all programs from consideration that lack the right emphasis on important content. • Once programs with the appropriate content and opportunity to master that content are selected, teachers will bring their own personality and enthusiasm to the task of teaching the material. • Committees which start with the premise that the selected textbook must carry labels such as constructivist, student-centered, inquiry-based or reform math are often left with content poor activity books rather than texts which provide a solid foundation for students in mathematics.

12. #2Valid, reliable research is valued more than closely held beliefs • Committees should identify large scale studies that compare the math programs under consideration and look at objective data to determine their relative performance. (Be careful as most education studies are small scale, qualitative in nature, and address a single topic or theory about teaching, instead of overall program performance.) • During committee discussions, all members should try to back up any assertion they make with research, and should develop a habit of asking each other, “What research supports that idea?” • We strongly recommend that the committee members invite outside experts in math research to consult with them regarding the validity of studies or refer to the National Academies Press.

13. #2Valid, reliable research is valued more than closely held beliefs • While a common default, committees need to avoid falling back on the beliefs, opinions, and experiences of the members to guide their decision-making. • Beliefs, opinions, and experiences can be reasonably expected to play some role in decision-making, but the results of reliable research should be given far greater weight. • What works in education is not a matter of philosophy. It is a matter of evidence.

14. #3Participants in the decision-making must have strong math backgrounds • Committee members should include a diversity of expertise, including those with a major or minor in mathematics or have the equivalent knowledge, knowledge of the prerequisite college preparatory content needed in grades 6-12, knowledge of the math needed for undergraduate STEM majors, classroom teaching expertise at elementary and middle school levels, experience in standards and program analysis and adoption, and knowledge of international comparative analysis of programs and teaching approaches. • A district committee will likely include individuals whose strength is not in mathematics. These individuals, while bringing their ability to review applicable studies and ask pertinent questions, may not have the expertise to fully participate in the analysis of the content required for the selection of the best mathematics programs. Their specific expertise should be used appropriately.

15. #3Participants in the decision-making must have strong math backgrounds • Districts should include various stakeholders on the committee, such as parents, strong in math, who have children currently in the system or recently graduated from the system. They will have familiarity with current offerings and their shortcomings. • We strongly encourage committees to intentionally seek out knowledgeable community members with a diversity of opinion about mathematics education. A debate will lead to a better decision than selecting members who are known to be in agreement with each other. • Forming a committee whose members lack knowledge of math will ultimately lead to a disconnect between what parents and colleges expect and the outcomes that programs recommended by such a committee can deliver.

16. #4Participants must understand the “math wars” • We recommend that participants read (or be provided with a fair summary of) Jeanne Chall’s “Academic Achievement Challenge,” Diane Ravitch’s “Left Back: 100 Years of Failed School Reform,” or E.D. Hirsch’s book “The Schools We Need” to better understand the long history of the math wars. • We also recommend reading Dr. Klein’s excellent essay that focuses on the math wars starting with the 1980s at http://www.csun.edu/~vcmth00m/bshm.html • It is important that committee members have this knowledge so they have a historical perspective on their decision and will recognize the similarities today’s math programs have to previous fads and movements in education.

17. #4Participants must understand the “math wars” • Those following the current status of public education often misunderstand the “math wars;” limiting the characterization of them to a debate about pedagogy, or even more simply, a debate between the value of rote memorization and deep conceptual understanding. We need to understand the debate is ultimately about content. • Advocates of more progressive pedagogy have argued that elementary mathematics should de-emphasize arithmetic, while advocates for traditional math want to retain the emphasis on arithmetic. • The “math wars” are secondarily about pedagogy, but the primary issue to focus on is getting the content right. • Understanding the nature of the math wars—and avoiding the trouble-causing factors—can help districts avoid the controversy poor choices will ensure.

18. #5Cognitive science is fully considered • We recommend that committee members read Dr. Daniel Willingham’s book “Why Don’t Students Like School,” which explains common misconceptions about how students learn. This book is aimed at educators and the general public. http://www.danielwillingham.com/about.html • Committees should be aware that some programs (such as the Connected Mathematics Project (http://connectedmath.msu.edu/ pnd/theory.shtml) claim to be based in cognitive science, but use that phrase as window dressing to support a trendy pedagogy. We strongly recommend review of Robert Siegler’sImplications of Cognitive Science Research for Mathematics Education at http://www.psy.cmu.edu/~siegler/NCTM.pdf. • Siegler, R. S. (2003) Implications of cognitive science research for Mathematics education. In Kilpatrick, J., Martin, W. G., & Schifter, D. E. (Eds.), A research companion to principles and standards for school mathematics (pp. 119-233). Reston, VA: National Council of Teachers of Mathematics.

19. #5Cognitive science is fully considered • Many committees never question their underlying assumptions about teaching and learning, which influence their decision making. For example, it is common for committees to assume that “drill and kill” decreases student interest, that appealing to learning styles increases student achievement, and that “rote memorization” should be de-emphasized in favor of “deep conceptual understanding.” • Cognitive science shows that extensive practice is necessary for learning, that appealing to learning styles does not provide an advantage, and that “understanding is remembering in disguise.”1 1 “Why Don’t Students Like School”, Dr. Daniel Willingham

20. #6Participants recognize that “balanced” approaches are not truly balanced if they compromise content • The right goal is to find the most effective programs. • Programs that are the most effective may often appear the most “traditional” because they place the right amount of emphasis on arithmetic. • Rather than select a program based on its placement along the continuum of progressive to traditional approaches, as may occur when valuing consensus over program content, pick programs based on having the right content and evidence of effectiveness. • The balance struck must be what serves children best, not what serves the adults involved in the process best. Content must not be compromised.

21. #6Participants recognize that balanced approaches are not truly balanced if they compromise content • Some committees are formed after a district has selected an ineffective program (such as TERC). To recover from a program that is at the progressive end of the spectrum, committees often seek to find a program that is a “balance” between constructivist and traditional math pedagogies, so as to appear fair instead of reactionary. • While there is a necessary balance in teaching approaches, aiming for the middle for the sake of being in the middle may remove effective, traditional programs from consideration prematurely. • Seeking a balance often leads to choosing programs like Everyday Mathematics, which lack important content and advocate an ineffective pedagogy.

22. #7 Professional development addresses areas in which teachers may lack knowledge • Regardless of which program is selected, teachers may need extensive professional development to implement it well. • Programs that provide more teacher support (such as Saxon Math and Connecting Math Concepts) will be easier to implement than programs that expect teachers to have a high level of mathematical knowledge (such as Singapore Math). • We recommend that math committees consider the ease of implementation as a part of their evaluation criteria, and provide extensive professional development. Current task force is reviewing “connection (vs. conflict) with prior professional development for elementary math teachers.” • According to the National Council for Teacher Quality, 87% of education schools do not adequately prepare elementary teachers to teach math.

23. #7Professional development addresses areas in which teachers may lack knowledge • Even the best program will get less than stellar results unless the gap in teacher knowledge (both content and pedagogy) is addressed. • In the book “Knowing and Teaching Elementary Mathematics” by Dr. Liping Ma, she explains the significant differences between Chinese teachers’ understanding of math and that of their American counterparts. The book is based upon her dissertation for her Ph.D. at Stanford. She was encouraged to make these findings accessible to teachers, parents, and those concerned about the state of mathematics education in book form. • "Liping Ma's work has given me hope about what can be done to improve mathematics education.  She illustrates what 'profound understanding of fundamental mathematics' is for elementary school teachers and has some useful suggestions about what we can do to help more teachers acquire this knowledge." -- Richard Askey, John Bascom Professor of Mathematics, Univeristy of Wisconsin-Madison

24. #8Selection is not limited to just one program • There are advantages and disadvantages to all commercially available math programs. • Choosing a single program may not be the best choice. • The advantages of a single program include consistency across the system, a volume price discount, a shared language and approach that facilitates teachers sharing best practices, and the ability to focus the school system’s resources on fixing the faults of a single program instead of multiple programs. • The disadvantage is that one program may not fit all students due to differences in pacing and approach.

25. #8Selection is not limited to just one program • We recommend that the committee examine research supporting each program under review, and investigate the pros and cons of having only a single program available to teachers and students. • In a system with more than one math program option, committees should avoid the mistake of only giving strong math content to above average students. Content and high expectations are important for all ability levels.

26. #9A pilot program is designed, conducted and ultimately implemented with fidelity • As a part of the selection process, we strongly recommend that the system pilot several programs to determine their performance with students of different achievement levels. • Even after a program(s) have been selected, the system should continue to systematically pilot lesson plans that have been developed to address the shortcomings of the selected program(s). • We recommend that school systems consider having the implementation of the pilot program facilitated and reviewed by an outside research organization to maintain objectivity and gain access to additional expertise.

27. #9A pilot program is designed, conducted and ultimately implemented with fidelity • Many school systems select their math program based on surveys of the opinions and feelings of teachers and administrators who used the programs during a pilot. • Student achievement data should be the primary consideration when evaluating program effectiveness. • A valid pilot should meet high standards of research, including random assignment, the existence of a control group, accounting for differences in student demographics and achievement levels, and teacher experience.

28. #10Post selection, implementation is monitored heavily and problems which may arise are handled in a timely manner • Instead of waiting until parents and teachers complain (or even call for a program’s removal) actively seek out negative information and address it. • Avoid dismissing concerns in an effort to bolster public support. In the long run, public support and trust will grow when schools are honest about shortcomings and demonstrate a real commitment to address them. • Prior to choosing a program, visit other sites that have implemented it and learn what the common implementation issues are and how they were addressed.

29. #10Post selection, implementation is monitored heavily and problems which may arise are handled in a timely manner • Math programs exist in complex host environments called schools. The performance of even the best program is limited by things external to the program itself: training, leadership, evaluation and improvement procedures, community support, and so on. These variables must be addressed for successful implementation. • It is inevitable that problems will arise due to these factors in addition to faults with the program itself. How these are addressed by decision-makers will affect students directly and should be addressed in a timely manner.

30. Summary Achieving world-class standards will require making adjustments to the Common Core. Textbooks should be regarded central to the mathematics program, not “just a resource”. The selection process must be done well for systems to choose solid books. Most teachers will need extensive professional development to develop the “Profound Understanding of Fundamental Mathematics” needed to teach math well. While ambitious, these goals are achievable with sustained, systematic effort. We encourage those with questions to contact our groups at our web sites.