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Math Adoption Q & A
Last updated on April 27, 2009

Additional Q & A

The purpose of this Question and Answer Section Regarding Everyday Math is to provide the community with responses to the questions and issues that have been raised regarding the recommendation to the board that it adopt Everyday Math for grades K-5 for the 2009-2010 school year.  It is important to note the process here.  By board policy, staff makes a recommendation regarding the instructional materials to be used by teachers and students to the board.  The board then makes the final decision regarding these materials and must approve instructional materials.

In the case of this math adoption, the board will have this item on its April 14 agenda for discussion.  At this point it is scheduled to be brought back for board action at the April 28 meeting.

Staff has also planned a K-5 Parent Math Evening to learn about the Everyday math Program, including sessions on components of the materials, the use of technology, and the home-school connection.  This evening is from 7:00 to 8:30 p.m. at Nixon Elementary School at 1711 Stanford Avenue.  Childcare and live Spanish translation will be available.  If you have any questions, please contact Ginni Davis at 329-3709 or via email at


  1. How do our students perform in math on rigorous standardized assessments and compare to peers in the state, country, and world?
  2. What are our goals for students in math, and why do we believe math is so important?
  3. What did we learn from teachers and parents in our strategic planning process last spring, and what are we aiming to improve in our K-12/K-5 math program/instruction?
  4. Can you describe the math adoption process in PAUSD?
  5. Why was McGraw Hill / SRA Real Math not piloted? (revised on April 27, 2009)
  6. Why are we adopting and buying new math materials for grades K-5 and grades 6-8?
  7. Why is it important to have one publisher for K-5 grades/teachers?
  8. How does a textbook fit into our math program/curriculum?
  9. What are the strengths and weaknesses of Everyday Math (EDM)?
  10. How will we address the challenges of Everyday Math?
  11. District staff has spent extensive time developing extension/support materials to complement the K-5 text adopted 7 years ago.  What extension or support materials will need to be replaced to extend and supplement the Everyday Math units?  
  12. How will Everyday Math support the goal of student mastery of basic facts and standard algorithms?
  13. How can parents help support their children?
  14. Explain what the spiraling philosophy is and how PAUSD will integrate it into the elementary math program.
  15. What is the PAUSD philosophy on the use of calculators in elementary school?
  16. How do the language skills of young students impact their ability to learn math using Everyday Math (EDM)?
  17. How will we evaluate the effectiveness of Everyday Math (EDM)?
  18. How will the District provide staff development for the Everyday Math program in 2009-10 and going forward?
  19. What math training will be available for new teachers, teachers new to the District, and substitute teachers?
  20.  What are some districts in California that have adopted Everyday Math?
  21. What online support is available for parents and students to help with homework?
  22. How will 5th grade concerns be addressed?
  23. Why did the California State Board of Education approve the Third Edition of Everyday Math (EDM) when the previous edition was not approved?
  24. What are the main points from teachers who piloted and recommend Everyday Math (EDM)?
  25. What is Everyday Math's (EDM) response to concerns about their program?
  26. To learn more about Everyday Math (EDM) and other essential pedagogical background materials for the Math Adoption Committee and Elementary Math Network, please see


1. How do our students perform in math on rigorous standardized assessments and compare to peers in the state, country, and world?

As PAUSD student data supports, our students compete at top academic levels nationally in math.  Disaggregated data is available on the CDE website; in Board reports, PAUSD SARCs and Single Plan reports; and more. 

The District uses MARS and CST results as the primary metrics for assessing student progress. The figures below summarize three years of available California Standards Mathematics and MARS aggregate performance data. PAUSD students’ math achievement based on these metrics significantly exceeds that of their grade level peers in the county and the State for CSTs, and in the MAC for the MARS.

STAR Program CST Math Results
Percent of Students at Proficient and Advanced Levels
Grades 3 and 5

County 3/5
State 3/5


MARS Results
Percent of Students Meeting or Exceeding Standards
(Meeting standards and Exceeding Standards are the highest two of the four scoring levels)
Grades 3 and 5

MAC 3/5

The data clearly illustrate the large percentage of third and fifth grade students who have “Met” (Level 3) or “Exceeded” (Level 4) standards over the past three years, as measured by the MARS. An additional 20-30% [more] [of] PAUSD students reached or exceeded standards than in the Mathematics Assessment Collaborative (MAC) overall.

SAT Comparisons: Top CA High Schools
(grade 12 enrollments greater than 200)

Class of 2007
Monta Vista
Mission S.J.
Univ. (Irvine)
San Marino


SAT Comparisons: Class of 2008

Mean Scores



SAT Percentile Ranks

PAUSD: 25th Percentile
California: 75th Percentile
National: 75th Percentile
PAUSD: 50th Percentile

Note: A student who received a PAUSD average score (661) ranked above the 88th percentile nationally!

Crosstabulation: MARS Performance Level versus STAR CSTs Mathematics Performance Level:
Grade: 2
MARS Performance Levels California Standards Tests (CSTs) Math Performance Levels
1 2 3 4 5 Total



































Grade: 3
MARS Performance Levels California Standards Tests (CSTs) Math Performance Levels
1 2 3 4 5 Total



































Grade: 4
MARS Performance Levels California Standards Tests (CSTs) Math Performance Levels
1 2 3 4 5 Total



































Grade: 5
MARS Performance Levels California Standards Tests (CSTs) Math Performance Levels
1 2 3 4 5 Total



































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2. What are our goals for students in math, and why do we believe math is so important?
Our goals, as stated in the PAUSD Vision Statement, for students in math are to provide an exceptional math program that supports every student developmentally, in achieving mastery and confidence at each individual’s highest level.  Math academic learning is crucial for building conceptual, procedural, and mathematical reasoning competencies as referenced by the National Mathematics Advisory Panel Report, 2008 ; Adding it Up, National Research Council, 2001; California State Standards, 2007; and Everybody Counts, National Research Council,1989.
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3. What did we learn from teachers and parents in our strategic planning process last spring, and what are we aiming to improve in our K-12/K-5 math program/instruction?
What we learned from teachers and parents in our strategic planning process helped determine the following goals:

A1.1  Improve K-12 curriculum articulation, coordination, and alignment to meet needs of the full range of   students
A1.2  Expand curricular, instructional, and assessment support; and staff training to increase the breadth and depth of learning for all students
A1.3  Communicate a K-12 vision for the appropriate use of specific instructional strategies by curriculum areas

As part of our efforts to improve the K-12 math instruction as determined in the strategic plan, there is a critical need to align instructional practices supported by high quality materials and targeted assessment.  In addition, to implement a strong math program teachers need professional learning that is at once focused and sustainable, and embedded in the implementation of daily instruction.

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4. Can you describe the math adoption process in PAUSD?  

The Math Adoption Committee was formed in September 2008. In planning and organizing the work of the math adoption, co-facilitators and district administrators reviewed the California State Board of Education Policy. Guidelines for Piloting Textbooks and Instructional Materials.  (California Constitution, Article IX, Section 7.5. Education Code Sections 6006060062, 60200-60206, 60400-60411, 60450-60453) The guidelines include specific recommendations for a structured and monitored pilot process to be helpful to school districts and school sites as they consider the adoption of instructional materials.

The formal adoption committee process began with an overview of the official PAUSD Board Policy and charge statement for the role of the committee to review State-adopted materials and submit a recommendation to the PAUSD Board of Education.  The group also reviewed PAUSD documents such as the Vision and Mission, the Strategic Plan, and the curriculum standards in agreeing upon the Criteria for Evaluation of the nine state-approved instructional materials for grades K-5.

On October 6, the group met at the Santa Clara County Office of Education and applied the pre-established criteria in a comprehensive review by each grade level looking at review sets from each publisher. The following table summarizes the initial results of the analysis.








Houghton Mifflin



































MacMillan McGraw Hill














Everyday Math














Key:  N = no                 Y= Yes              M= maybe

Based on these results, the committee came to consensus that Saxon, Houghton Mifflin, McGraw Hill, and Sadlier would not be considered any further. It was also clear that we wanted to further review Everyday Math (EDM) and SRA Real Math.  The committee deliberated at length whether or not to continue to review Singapore Math at the next meeting. Strengths, including the bar model with all operations; strong lesson design and instructional strategies; simple layout and manageable materials; step-by-step sequencing; and a pictorial glossary were cited.  However, the list of strikes against the program, including very limited available professional development help from company for a program that will require intense teacher preparation to implement, also included a lack of the following: suggestions to support facilitation of mathematical discourse; means to identify, inform, or correct students’ misconceptions; hands-on opportunities; a parent communication piece; support for students working at different paces/modalities; multiple strategies; or Spanish-translated materials.  The comparison of pros and concerns swayed the committee to vote against moving the program to the next level.  After additional discussion and an ensuing electronic vote the committee agreed to invite four publishers to present at its meeting on October 17, 2008:  SRA Real Math, enVision Mathematics/Investigations, Everyday Math, and Harcourt.

Upon being invited to present to the PAUSD committee, the SRA representative informed our planning team that SRA Real Math had not had much success in California in the first year of the adoption process and the company had decided to pool their resources and focus on the Language Arts Adoption. Only after a great deal of discussion were we able to get a review set of materials and a copy of their PowerPoint presentation, which was made available to the committee on October 16.

After listening to the presentations and spending additional hours analyzing the materials, the committee voted to pilot three programs: Everyday Math, SRA Real Math, and enVision supplemented by Investigations. However, the SRA representative reported that he would not be able to provide the materials for piloting due to a company policy decision.  By the time the committee met on November 3 to plan the classroom piloting procedures, the group decided to only pilot Everyday Math and enVision/Investigations, realizing that long-term commitment and support for SRA in the extended life of the adoption would be challenging and unreliable.

Additional committee findings from the piloting period and further analysis of the materials are available from the minutes of the Committee’s meetings on January 28, February 24, and March 16.  It was only after extensive review and analysis of the materials and the findings collected from the piloting period that the committee voted to recommend adoption of Everyday Math.
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5. Why was McGraw Hill / SRA Real Math not piloted? (revised on April 21, 2009)

At the Santa Clara County Office of Education, the committee looked at McGraw Hill / SRA and liked the mathematics in the program. Wedecided to review it further and have the publisher make a presentation to the committee. However, when we contacted the local rep, we were unable to secure a presenter. And only after a great deal of discussion were we able to get a review set of materials and a copy of their powerpoint presentation. The rep had to go around picking up materials from districts that had reviewed their materials and decided not to adopt them. The rep told us that due to financial considerations the company was backing away from supporting the adoption of their program. He stated that they had not had much success in CA in the first year of the adoption process and so the company decided to pool their resources and focus on the Language Arts Adoption.

At the October 16th meeting, one of the TOSAs shared the powerpoint presentation with the committee and the committee spent the afternoon using the criteria form to further evaluate the program. The committee did think it was worthy of us piloting. However, when the rep was notified of our wishes to pilot, he stated that he didn’t think he could get us materials for piloting. The company was not allowing him to send us materials.

Furthermore, the rep wasn’t completely sure of the support we would receive from the company if we were to adopt the program. On the issue of availability of consumables for the life of the adoption, he stated that he wasn’t sure. Nor was he clear on the professional development that would be offered to us. When a TOSA spoke to the vice president of sales for McGraw Hill / SRA about the situation, she stated, “As an officer of a company representing both Everyday Math and Real Math, I made the decision that Everyday Math with proven success throughout the country would be a better fit in Palo Alto. Ross (the rep) asked to pilot Real Math in Palo Alto, but I felt sure that Everyday Math would provide more rigor and be more challenging for the students in Palo Alto. Though Real Math has excellent instruction, many don’t understand how the program was designed. Because of this, there is not much documentation and data to support the effectiveness of the program. I am delighted to know that your committee saw the value, but I felt sure that they would see the same in our other program, Everyday Math.”

CA Districts That Have Adopted McGraw Hill / SRA Real Math:

API for 2008
Number of Students
Coalinga-Huraon Joint Unified
Di Giorgio Elementary
Gustine Unified
Lincoln Unified
Mendota Unified


Oakdale Joint Unifed
Pleasant Valley Elementary
Ready Springs Union

CA Districts That Piloted SRA but Chose Another Program:

API for 2008
Number of Students

McGraw-Hill for K-2
enVision for 3rd - 5th

Bonny Doon
McMillan McGraw-Hill
Everyday Math


San Juan
Houghton Mifflin

During the last adoption cycle, Los Altos School District used McGraw Hill / SRA Explorations and Applications, a series that is no longer on the State adopted materials list. They are currently piloting enVision and Houghton Mifflin and hope to have a final decision in late March, early April.
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6. Why are we adopting and buying new math materials for grades K-5 and grades 6-8?

California requires school districts to adopt materials in grades K-8 from the State adoption list every seven years. The materials currently in use in grades K-5 (California Math) are no longer on the State adopted list, therefore we had to select a new textbook series.  The Holt Course 1, Course 2, and Algebra textbooks have been recommended as core materials for grades 6-8. Understanding that no set of materials is complete within itself, the committee also recommended continuing the use of Connected Mathematics as supplementary materials.
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7. Why is it important to have one publisher for K-5 grades/teachers?

The PAUSD Strategic Plan (A1.1 above) specifies the need for an articulated curriculum used consistently across the district. The use of one core set of materials is more likely to address this need.  Currently, Palo Alto uses Scott Foresman’s California Mathematics.  In the last adoption, the committee also recommended using the Scott Foresman Investigations series, which incorporates inquiry-based activities to develop conceptual understanding. The district invested significant resources to develop joint usage curriculum guides (K-5) for the two programs. California Mathematics isno longeron the State list, but the committee did consider enVision, a new program by the same company, which could also be used in tandem with an updated version of Investigations.  After piloting these materials and careful consideration, the committee preferred Everyday Math as detailed in the committee process minutes.

Everyday Math is balanced and comprehensive. It uses a consistent, research-based approach to mathematics instruction so students and teachers become familiar with daily routines, lesson structures, terminology, models, manipulatives, and other resources.  Having one program will be an advantage for facilitating new teacher training and continued professional development.  The proposed implementation plans include time and resources for teachers to collaboratively reflect on the program’s strengths and weaknesses, aimed at ensuring that the best instruction is available to PAUSD students.
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8. How does a textbook fit into our math program/curriculum?

The math textbook serves as a resource for planning and implementing quality instruction.  As stated in the District Mission, teachers will “utilize a variety of instructional practices and curriculum, valuing conceptual understanding, problem solving, critical thinking and mathematical fluency.”  PAUSD students and teachers are held accountable to the District standards.  The textbook is not the sole reference for what is taught or how it is taught.  Teachers, following the Vision and Mission of the District will use the adopted materials to guide them in planning and implementing lessons.
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9. What are the strengths and weaknesses of Everyday Math (EDM)?

After carefully reviewing state-adopted materials, including extensive piloting in K-5 classrooms, the following strengths and concerns for Everyday Math were identified:



Math Content


  • Consistent format and use of models to build understanding of concepts across grade levels
  • Thorough and in-depth exposure to standards
  • Deliberate connections between strands
  • Spiral review offers opportunity to revisit previous topics in a deeper way
  • Activities provide opportunities for rich mathematical discourse
  • Some reading materials have a high level of academic language
  • Classrooms may need additional materials (e.g., manipulatives, calculators, attribute blocks) to effectively implement curriculum


Content Delivery to Students


  • Engaging and challenging for students
  • Math Message is a good, well-designed introduction to each day’s lesson
  • Multiple components for each lesson
  • Hands-on, real-world applications of math
  • Models bring depth to the program
  • Art, literacy, science, music connections
  • Games used to build concepts and practice facts and skills
  • Student reference book: usage is taught at beginning; good tool
  • Rich mathematical vocabulary, (inc. Home Links)
  • Spiral format may feel confusing as teachers and students first adapt to the program
  • Re-teaching may be necessary during transition period to cover models and concepts not learned in a previous grade
  • Standard algorithms are included as add-on projects in some grade levels


Teacher Support

Professional Development & Implementation

  • Teacher-friendly in explaining set-up, daily routines, lesson, classroom structure
  • Teacher reference and guide good for new teachers to understand concepts
  • Extensions easy and natural
  • Depth when developing concept with different models, embedded differentiation and accessibility for a range of learners
  • Appropriate and ongoing assessments
  • Home link booklets provide follow-up connecting homework to class
  • Workbook pages easy to use
  • One single complete teacher manual also provided on a CD and electronic interactive tools available online for teachers and students
  • District-wide implementation needs to be standardized with accountability
  • Teachers will need time for in-service to be comfortable with program format
  • Needs strong professional development, including pedagogy
  • Requires attention to adequate transition to sixth grade as per PAUSD expectations
  • Need more practice for some skills


This list is representative of the evidence that informed the committee recommendation and the concerns are further addressed in the proposed implementation and professional development plan that would ensue if the materials are approved by the PAUSD Board.  The elementary adoption committee decided on a final recommendation through the questions and the final analysis as described above. 
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10. How will we address the challenges of Everyday Math?

a. The program requires professional development for teachers in order to effectively teach with it.

Sustained professional development, as called for in Adding It Up (National Research Council Report, 2001), is a key component in any successful program.  We believe this challenge presents an excellent opportunity for a sustained focus on K-5 mathematics for all elementary school teachers. 
PAUSD will commit to a 2-year focus on math professional development, as outlined in the attached Implementation Plan.  In Year 2 and going forward, teachers new to the district will participate in sustained training over the course of their first 2 years in the district through the BTSA/PAR New Teacher Workshops, led by “teachers on special assignment” (TOSAs) and classroom master teachers.

b.   We will assess gaps in the curriculum in relation to expected student progress in concepts and skills.

Fifth Grade will not implement the program in Year 1.  Instead, all 5th grade teachers will participate in publisher-supplied training in the materials, piloting selected units.  Using a study group/classroom research model that includes doing sample lessons in their own rooms, as well as lesson observations and debriefings with K-4 teachers and coordinating with the 6th grade Math IS teachers, 5th grade teachers will identify areas that need additional or alternative materials and create a grade level curriculum guide.  In Year 2, all teachers at 5th grade will implement the updated curriculum. 
All other grades will implement in Year 1, using time designated in the Implementation Plan to review student work, assess student progress and recommend adaptations.  Special attention will be paid to successfully transitioning students from the previous curriculum to EDM through lesson modification.  Curriculum Guides will be developed to provide clear communication to all teachers about best practices, core experiences and vocabulary (including instruction and practice in the traditional US algorithms at 5th grade), and necessary assessments. 

c.   The spiraling curriculum may be confusing for teachers to implement at first. 

Piloting teachers noted initial disequilibrium with jumping into a program that relies on students having previous experiences with the program in earlier grades or during the year.  Many teachers had to read materials very carefully, making use of the scaffolding portions of each lessons or leaving out references to material they had not yet covered.  Most piloting teachers did comment that as they continued to use the materials, the spiraling did make sense and was a desirable aspect of the program.  The District will need to invest in professional development from teachers experienced in implementing the program in classrooms, as recommended by the publisher and other local districts that have already adopted the program.  Part of the continued professional development will be establishing teacher networks within and across schools focused on implementing the program.  These networks have proven very useful in past implementations in literacy and science, so the blueprints are already established within the District professional community.
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11. District staff has spent extensive time developing extension/support materials to complement the K-5 text adopted 7 years ago.  What extension or support materials will need to be replaced to extend and supplement the Everyday Math units?  

The PAUSD Curriculum Guides were specific to California Math and Investigations, so they will not be used with the upcoming adopted materials.  Everyday Math provides a cohesive Teacher Guide at each grade level, available in hard copy and electronically, to help teachers use the materials to differentiate instruction.  A guide for 5th grade teachers will be developed by a team of teachers and TOSAs over the 2009-10 school year.  Built into the professional development for the 2009-10 school year will be time and resources for teachers to reflect on the curriculum strengths and weaknesses, to record what kinds of additional resources have been identified, and to share their experiences and expertise.  As is being done in other curricular areas, teachers identifying topics needing more depth or practice will be supported by TOSAs, as well as colleagues across the district, in finding and using additional sources of materials.  For example, in the current Science adoption implementation, teachers are making use of grade level email lists to share information and ideas.  TOSAs will continue to use the District internal website to provide a catalog of identified resources.  They will also incorporate best practices and year-long scope and sequence modifications into future trainings for new teachers.
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12. How will Everyday Math support the goal of student mastery of basic facts and standard algorithms?

Everyday Math uses non-standard algorithms and student-invented algorithms to boost conceptual understanding of mathematical number sense, place value, and properties, but does not dismiss the value or importance of standard, paper-and-pencil algorithms.  The third edition of EDM met the conditions set forth by the California State Board of Education by adequately addressing the state standards for mathematics.  Palo Alto teachers and curriculum specialists will collaborate to ensure that the EDM materials are used to promote a balance between conceptual understanding, computational efficiency, calculation strategies (including the standard algorithms), and basic facts mastery.  These are important Palo Alto mathematics standards and will be monitored by regular assessment tools.  Reporting on the progress towards mastery in basic facts and computation at the different grade levels will continue to be provided regularly to parents using our Progress Report Forms.  For more information on our current standards and mastery benchmarks, see the Chart of Excerpted Standards for PAUSD Mathematics Curriculum.

Everyday Math Background on Algorithms
An algorithm is a step-by-step procedure designed to achieve a certain objective in a finite time, often with several steps that repeat or “loop” as many times as necessary.  The most familiar algorithms are the elementary school procedures for adding, subtracting, multiplying, and dividing, but there are many other algorithms in mathematics. Knowledge and accurate applications of algorithms in computational proficiency for standard operations in addition, subtraction, multiplication, and division are critical foundations for mathematics.  Traditionally, the core of mathematics has been seen as this arithmetic understanding and fluency.  While still an essential part of our standards, the role of algorithms in elementary mathematics has shifted.  While conventional skills in paper-and-pencil calculation are still important, due to the widespread use of calculators and computers in school and in the employment sector, preparing workers for complicated computations by hand is a less important goal of school mathematics today.  The new demands in our global economy call for the mathematics curriculum to adapt so that students are still required to master basic algorithms for computation, but instruction must also focus on problem solving, estimation, mental arithmetic, geometry, and data analysis (NCTM, 1989).

EDM recognizes that traditional algorithms have advantages, as they are generally efficient and can help students understand both the decimal number system and the underlying operations.  Traditional algorithms also provide common vocabulary and foundation for further development of mathematical ideas.  Andy Isaacs, principal author of the EDM Third Edition offers the following assurances regarding the EDM materials:

  • EDM does not restrict itself to "small and nice numbers."  The exact opposite is the case.  Multiplication of multi-digit numbers is not omitted.  Students are not left on their own to re-invent 2000 years of mathematics.
  • Children do learn how to perform calculations with pencil and paper.  Some of the ways they learn have been used for centuries.  The long division algorithm used in the program, for example, first appeared in Greenwood's Arithmetiks in 1729.  The lattice method for multiplication is even older.
  • Children are expected to master the basic facts.  Practice is provided throughout the program.
  • Both division of fractions and long division are included in the program.

Additional Research that informs PAUSD vision/mission in regards to algorithms:

Background information on the research foundations for use of varied algorithms in Everyday Math

Bibliography for research on computation

Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School, by Thomas P. Carpenter, Megan Loef Franke, Linda Levi, © 2003 Heinemann
“Learning mathematics involves learning ways of thinking. It involves learning powerful mathematical ideas rather than a collection of disconnected procedures for carrying out calculations. But it also entails learning how to generate those ideas, how to express them using words and symbols and how to justify to oneself and to others that those ideas are true.”
 “The procedures we use to add, subtract, multiply, divide and compare numbers are based on a small number of fundamental properties of number and number operations, and much of algebra is based on the same basic properties. When students clearly understand these properties and how they apply to the mathematics they learn, they have acquired the basis for understanding arithmetic and algebra. As children learn arithmetic, they implicitly use a number of these fundamental properties.”

Adding It Up: Helping Children Learn Mathematics, Mathematics Learning Study Committee, Center for Education, National Research Council, © 2001, National Academy Press.
Executive Summary – Recommendations
“The integrated and balanced development of all five strands of mathematical proficiency (conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition) should guide the teaching and learning of school mathematics. Instruction should not be based on extreme positions that students learn, on one hand, solely by internalizing what a teacher or book says or, on the other hand, solely by inventing mathematics on their own.”
“Learning to use algorithms for computation with multi-digit numbers is an important part of developing mathematical proficiency. Algorithms are procedures that can be executed in the same way to solve a variety of problems arising from different situations and involving different numbers. Children can and do devise algorithms for carrying out multi-digit arithmetic, using reasoning to justify their inventions and developing confidence in the process. A variety of instructional approaches (using physical materials, special counting activities, and mental computation) are effective in helping students learn multi-digit arithmetic by focusing on the base-ten structure and encouraging students to use algorithms that they understand.”

Foundations for Success: Final Report of the National Mathematics Advisory Panel, © 2008 U.S. Department of Education
Main Findings & Recommendations - Learning Process
"10) To prepare students for Algebra, the curriculum must simultaneously develop conceptual understanding, computational fluency, and problem solving skills. Debates regarding the relative importance of these aspects of mathematical knowledge are misguided. These capabilities are mutually supportive, each facilitating learning of the others. Teachers should emphasize these interrelations; taken together, conceptual understanding of mathematical operations, fluent execution of procedures, and fast access to number combinations jointly support effective and efficient problem solving."

"11) Computational proficiency with whole number operations is dependent on sufficient and appropriate practice to develop automatic recall of addition and related subtraction facts, and of multiplication and related division facts. It also requires fluency with the standard algorithms for addition, subtraction, multiplication, and division. Additionally it requires a solid understanding of core concepts, such as the commutative, distributive, and associative properties. Although the learning of concepts and algorithms reinforce one another, each is also dependent on different types of experiences, including practice."

Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction, Catherine Twomey Fosnot & Maarten Dolk, © 2001 Heinemann (Also Young Mathematicians at Work: Constructing Multiplication and Division)
                “Algorithms—a structured series of procedures that can be used across problems, regardless of the numbers—do have an important place in mathematics. After students have a deep understanding of number relationships and operations and have developed a repertoire of computation strategies, they may find it interesting to investigate why the traditional computation algorithms work. …[Traditional algorithms] should not be the primary goal of computation instruction. Using algorithms, the same series of steps with all problems, is antithetical to calculating with number sense. Calculating with number sense means that one must look at the numbers first and then decide on a strategy that is fitting—and efficient…By abandoning the rote teaching of algorithms, we are not asking children to learn less, we are asking them to learn more. We are asking them to mathematize, to think like mathematicians, to look at numbers before they calculate, to think rather than to perform rote procedures.”

Elementary School Mathematics: Teaching Developmentally, John A. Van De Walle, ©1990, Longman
“…it is still true that pencil-and-paper holds a dominant place in the curriculum. There is, however, a long overdue trend toward viewing the algorithms with a different perspective. In that past, it was true that computational proficiency was a required skill in our society. We taught computations because it was necessary for everyday living… Today, computations with [large] numbers are virtually never required of us, thanks to the readily available calculator.
An extreme reaction might to be to delete pencil-and-paper computations from the curriculum. That would be a mistake. Some simple computations will always be done with pencil and paper when that is convenient. But perhaps more important than a utilitarian view of the algorithms is the effect that understanding them can have on other aspects of a more modern curriculum. A strong conceptual approach to the algorithms developed through the use of base ten models and discussion—and avoiding a premature rush toward mastery—can have a beneficial effect on computation taken more broadly. Pencil-and-paper computation; mental computation; estimation; and use of calculators--all of these forms of computation, with whole numbers, decimals, and fractions, can and should be interrelated. Understanding and use of one helps and contributes to the understanding and use of the others.”

Teaching Student-Centered Mathematics, Volume 2, Grades 3-5 (Volume 1, Grades K-3), John A. Van De Walle & LouAnn H. Lovin, ©2006, Pearson Education, Inc.
“With today’s technology, the need for doing tedious computations by hand has essentially disappeared. At the same time, we now know that there are numerous methods of computing that can be handled either mentally or with pencil-and-paper support. In most everyday instances, these alternative strategies for computing are easier and faster, can often be done mentally, and contribute to our overall number sense.
“…The primary goal for all computation should be students’ ability to compute in some efficient manner—not what algorithms are used. That is the method of computing is not the objective; the ability to compute is the goal.”

About Teaching Mathematics: A K-8 Resource, Second Edition, Marilyn Burns, ©2000, Math Solutions Publications
“The advantage of algorithms is that they provide reliable ways to compute and, therefore, simplify potentially difficult calculations. It is important for children to understand that algorithms are procedures that have been invented by people to carry out calculations that are done repeatedly. It is important for them to learn how algorithms are based in the structure and logic of our number system.”
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13. How can parents help support their children?

The home-school connection is very important.  The District Implementation Plan outlines parent night informational meetings throughout the year in 2009-2010. These will be a combination of district-led and site-based, using resources developed by the Math TOSAs and Math Adoption Committee members. Parent outreach must include background in the philosophy and expectations of the PAUSD elementary math program as well as information about what to expect to see both in the classroom and coming home. Everyday Math (EDM) materials include a Student Resource Book both in hardcopy and accessible through a password-protected website. New to the current addition, this on-line version of the Student Resource Book provides animated, narrated tutorials in algorithms, in addition to a glossary. 
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14. Explain what the spiraling philosophy is and how PAUSD will integrate it into the elementary math program.

Spiraling refers to having students be introduced to a topic, concept, or skill, practicing it, and then returning to practice the skill again after a period of time.  Often when the topic, concept, or skill is revisited, it is presented with a new layer of depth or complexity so that students’ understanding of the material is deepened or skills mastery is developed.  The spiral may happen during a school year, or over a span of grade levels.  Many of the curricula on the state’s approved list of math materials have spiraling materials as components to their programs as cognitive science research supports this approach.  “Long-term retention is best served if assignments on a particular skill are spread out in time rather than concentrated within a short interval.”1   Research also shows that  “short periods of intensive review are better than long periods, and that games provide effective review.”1   An extensive bibliography on the research behind the spiraling curriculum is available.

As Palo Alto teachers have known and implemented in their math programs already, students need to continue to practice skills and revisit Big Ideas repeatedly over time, coalescing new learning with prior knowledge.2  By bringing the topic to the forefront throughout the year, students gain mastery and deepen understanding through repeated practice, moving from concrete to pictorial to abstract.  In the Everyday Math program, as well as in PAUSD standards, students are expected to master grade level standards.  As recommended by the National Research Council, the program’s spiraling structure provides repeated exposure and practice over time that develops the five attributes of mathematical proficiency: ”
1) conceptual understanding (comprehension of mathematical concepts, operations, and relations)
2) procedural fluency (skills in carrying out procedures flexibly, fluently, and appropriately)
3) strategic competence (ability to formulate, represent, and solve mathematical problems)
4) adaptive reasoning (capacity for logical thought, reflection, explanation, and justification)
5) productive disposition (habitual inclination to see mathematics as sensible, useful, and worthwhile, coupled with a belief in diligence and one’s own efficacy).”3  

Ongoing in-class assignments and tests, including daily work, chapter tests, basic facts assessments, MARS tasks, and STAR results will provide feedback on a student’s mathematical progress, which teachers will use in planning instruction.

According to the National Mathematics Advisory Panel, “A focused, coherent progression of mathematics learning, with an emphasis on proficiency with key topics should become the norm… Any approach that continually revisits topics year after year without closure is to be avoided.”4  What can get misrepresented by providing a limited picture of a math program is that teachers and students are not held accountable, or given the tools they need, to become proficient in the skills and concepts outlined by our standards.  This is not true.  The EDM curriculum is divided into topic chapters that focus on developing a set of related concepts over a series of consecutive lessons.  At the end of each chapter, there is a chapter assessment.  Student progress toward mastery of math skills and concepts is assessed and, unlike in traditional textbooks, the curriculum provides embedded, continued practice once the unit is finished.  Teachers will use their discretion to provide any additional time or practice with a concept or skills, based on their observations of student work, just as they always have.  Teachers will use a revised District Basic Facts Assessment system to keep students and their families informed throughout the school year about progress toward mastery.

1 M. Suydam, 1985 ERIC digest (ED 260891) on the role of review in math instruction
2J. Van de Walle and L. Lovin, Teaching Student-Centered Mathematics, Pearson, 2006
3 Adding It Up, National Research Council, 2001, p. 116

4 Foundations for Success: The Final Report of the National Mathematics Advisory Panel, U.S. Department of Education, 2008, p. 22
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15. What is the PAUSD philosophy on the use of calculators in elementary school?

Students will learn how to do computations without calculators. Calculators will not change the expectation of teachers to hold students accountable for knowing their basic facts and how to compute.

Based on research that has shown calculator use can enhance cognitive gains in the areas of number sense, conceptual development and visualization, the National Council of Teachers of Mathematics (NCTM) recommends the integration of calculators into mathematics programs for all grade levels.  Many researchers have studied the effects on how students learn.  “Calculators can have useful role even in the lower grades, but they must be used carefully so as not to impede the acquisition of fluency with basic facts and computational procedures.“ Reaching for Common Ground in K-12 Mathematics Education, Ball, Ferrini-Mundy, Kilpatrick, Milgram, Schmid, and Schaar, 2005.

From the Teacher Reference Manual from Everyday Math (EDM), “The preponderance of evidence from these studies suggests that the proper use of calculators can enhance students’ understanding and mastery of arithmetic, promote good number sense, and improve problem-solving skills and attitudes toward mathematics.”

“Three summaries of this research are:

  • Research on Calculators in Mathematics Education by Ray Hembree and Donald  J. Dessart;
  • A Meta-Analysis of Outcomes from the Use of Calculators in Mathematics Education by Brian A. Smith;
  • A Meta-Analysis of the Effects of Calculators on Students’ Achievement and Attitude Levels in Precollege Mathematics Classes by Aimee J. Ellington”

“The Smith and Ellington studies also conclude that calculator usage does not hinder the development of paper-and-pencil skills.  Ellington recommends that calculators be used by children in Kindergarten through Grade 2 for experimenting with arithmetic concepts in problem-solving contexts.”

“Both teacher experience and educational research show that most students develop good judgment about when to use and when not to use calculators.”  EDM supports students’ need to learn how to decide when it is appropriate to solve an arithmetic problem by estimating or calculating mentally, by using paper-and-pencil, or by using a calculator.  The evidence indicates that students who use calculators are able to choose appropriately.” 

In the Everyday Math program, emphasis is placed on using the calculator as a tool for learning mathematics. In kindergarten, for example, calculators add a visual dimension to oral counting routines as children count forwards and backwards by 1s, 2s, 5s, and 10s.  Seeing the numbers on the calculator display as they count helps children learn written number sequences. (Activity 5.5) Furthermore, entering +2 on the calculator when counting by 2’s, reinforces the notion that when you count by 2’s you are actually adding 2 (not just skipping a number).  (Activity 6.14)
In first and later grades, students play a calculator game called Beat the Calculator. This game challenges students to develop an automatic recall of the basic facts, and demonstrates why it is better to develop quick mental math skills instead of always relying on a calculator.  The program also includes a number of calculator games that are designed to provide practice with place value and problem-solving skills.

In fifth grade, students are learning about Exponents.  Study Link 7.1 has students complete a table showing the exponential notation, base, exponent, repeated factors and standard notation for a set of numbers.  Students are allowed to use a calculator on this lesson. 

The following example illustrates how a calculator enhanced a student’s understanding of exponents, divisibility and problem solving.  Given 262,144 in standard notation, students are asked to write the exponential notation for it.  While a student could solve this by doing the prime factorization and get 218 for the answer, they can also use a calculator to discover that there are several different answers, including 86 and 49.  A student can use the calculator to explore what number, multiplied by itself a certain number of times, with give you 262,144.   If students know the divisibility rule for 4, they know that 262,144 is divisible by 4 and can use the calculator to investigate how many times you will need to multiple 4 to get 262,144. 

Everyday Math also recognizes that it isn’t always appropriate to use a calculator. These lessons are clearly marked with the "no calculator" sign: No Calculator  

Referring back to Study Link 7.1, the practice problems at the bottom of the page are computational in nature in which mental math can be easily used to solve the equations, and thus no calculators are allowed. 

Furthermore, the teacher in the classroom always has the choice to limit calculator use on activities.  For example, there is a “teaching option” that allows students to play High Roller with a calculator.  However, this is at the teacher’s discretion.   A teacher may feel this isn’t appropriate and thus not give students this optional adaptation. 

Teachers and math curriculum specialists will collaborate to determine the best use of EDM lessons that incorporate calculators to ensure that they are in tandem with PAUSD standards and goals for developing student mathematical proficiency.  It is important to remember that the textbook isn’t the program; it is a resource used by teachers to create a quality program.
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16. How do the language skills of young students impact their ability to learn math using Everyday Math (EDM)?

Academic language is the language used to teach a discipline.  Mastery of academic language is essential for all students.  In math, examples include “estimate,” “square,” and “equals.”  Content area coaches (TOSAs) have been working together on this topic for the past 2 years, with the literacy/science content focus at the heart of this year’s science adoption professional development.  This effort will continue in the area of literacy/math content integration.  No matter which math resource teachers use, be it EDM materials or supplementary materials, students will need instruction in braiding together thinking, language and mathematics.  EDM is language-rich.  In the program’s English Learners Handbook, teachers are provided with specific strategies and modifications for all young students, regardless of their first language.  These modifications and strategies will be a key component of the continued professional development and family outreach with the PAUSD math program.

In terms of the home-school connection and how students’ families can help at home with the math/literacy connection, each student will have access to the online Student Resource Book, which provides audio narration of the entire book as well as live links to glossary definitions of vocabulary words.
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17. How will we evaluate the effectiveness of Everyday Math (EDM)?

As described in the timeline/implementation plan, we will monitor the results of EDM implementation as follows:

  • Demonstrated mastery on formative assessments
  • Standardized summative assessment
  • Teacher and parent feedback on surveys
  • Evaluation of ongoing professional learning
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18. How will the District provide staff development for the Everyday Math program in 2009-10 and going forward?

There are dedicated professional development funding sources specifically for implementation and support of new textbook adoptions.  In particular, this math adoption will have at a minimum a two-year support plan as well as sustained opportunities to continue differentiated math professional learning.  Due to the constraints of available time for teachers to learn and collaborate, there will need to be many different options for making that time available.  We have developed a proposal that includes a menu of ongoing collaborative learning opportunities for teachers.
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19. What math training will be available for new teachers, teachers new to the District, and substitute teachers?

We have a robust two-year new teacher support program in math, as well as other content areas, for beginning teachers and teachers who are new to Palo Alto.  Substitutes will also be welcome to attend.  The content is focused on PAUSD math standards, curriculum, assessment, and instructional strategies to promote learning that meets the range of student needs.
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20. What are some districts in California that have adopted Everyday Math?

  • Belmont-Redwood Shores
  • Berkeley
  • Brisbane    
  • Burlingame
  • Emeryville
  • Glendale Unified                          
  • Hillsborough                                
  • Jefferson Elementary
  • Menlo Park
  • Palos Verdes (not yet Board approved)
  • Piedmont                                    
  • Portola Valley
  • San Francisco
  • Saint Helena Unified                    
  • San Mateo-Foster City
  • San Rafael                                 
  • Saratoga     K-2 enVision / 3-5 Everyday Math
  • St. Helena
  • West Contra Costa
  • Woodside
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21. What online support is available for parents and students to help with homework?

  • Family Letters describing each unit available in English and Spanish
  • Support for home /study links (homework)
  • Computation Explanations:  This section provides examples demonstrating how to use a variety of algorithms included in Everyday Math.  It also includes research basis, explanations, information, and advice about basic facts and algorithm development.
  • My Reference Book and Student Reference Books are online.  They bring interactivity to the texts in order to facilitate student learning at school and in the home.

      *     Audio narration of the entire book for reading support
      *     English and Spanish versions which provide significant ELL support
      *     Hundreds of "Show Me" animations highlight key elements
      *     "Try Me" interactive tools that allow students to control and experiment with the concepts being taught
      *     Live links to glossary definitions for vocabulary words within the text

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22. How will 5th grade concerns be addressed?

We are preparing a 2-year timeline for 5th grade teachers to determine the best supplemental materials to use with the core program to create the best bridge between 4th grade and 6th grade math instruction.

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23. Why did the California State Board of Education approve the Third Edition of Everyday Math (EDM) when the previous edition was not approved?

The previous edition of EDM was a national program.  The current (third) edition is a California edition that is fully aligned with the California Math Standards.

In addition, the following changes have been made to the EDM program to improve it (according to a presentation by Hillsborough staff which have been teaching the program for 9 years):

  • Increased emphasis on writing both in lessons and assessments
  • Easily identifiable assessment of target skills for each lesson
  • Quick access to enrichment, re-teach and activity adjustment strategies.  Enrichment is true enrichment.
  • Self assessment and reflection opportunities for each unit
  • Math boxes are integral and redesigned to allow for more revisiting of concepts and looking ahead.  On average, 2 boxes are review, 2 boxes are on concepts currently being learned, and 1 box previews what is coming up next.  Student reference book pages are annotated to help refer a student to where they can find help on a problem.
  • Online Resources – games, student reference book and family resources
    • Family Resources include a section with tutorial videos to complement algorithm handbook
    • Reference book has a symbol students can use to have the text read aloud to them.
    • There are “show me” videos to help explain a concept or algorithm
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24. What are the main points from teachers who piloted and recommend Everyday Math (EDM)?

This program is not a radical change from the way we are teaching math now.  On the contrary, of the programs we reviewed, we feel Everyday Math is the closest match to support our philosophy, goals, and instructional strategies.  We are particularly impressed with the development of problem solving and logical thinking skills and opportunities for teaching the academic range of students.  The effectiveness of EDM has been validated by extensive research including independent studies by the National Academy of Sciences (2004) and the Institute of Education Sciences (2006).  We have reviewed many of the critiques of EDM found on the internet and provided by community members and are well aware of the reported shortcomings of this program.  We do not expect any program to meet all our needs, but feel we can adapt and supplement this program when necessary to best educate our students.

We plan to use Everyday Math as our core program, but expect to make adjustments and supplement as needed.  Significant time is allowed for teachers to supplement or expand on skills that may not be covered to provide student mastery.  We will not be “locked in” to something we can’t adjust, nor will we hesitate to tailor our instruction to meet the needs of our students.  We will, however, gain a wealth of new activities and tools to reach our many diverse learners.
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25. What is Everyday Math's response to concerns about their program?

Below is the response from Bob Burch from Everyday Math.

1. I think the success of districts that used an earlier edition of EDM is important, because they used an edition that was not tied securely to the math standards at that time, and yet they exceeded state averages. (Please see the attached). There are no studies as yet that involve the 3rd edition since it has been available for 18 months. Nevertheless, the program has been carefully built using mathematical research and annual classroom studies for almost 30 years. As importantly, EDM is the only program that is actually written by U of Chicago professors who have degrees in both mathematical research and education. The authors typically span editions, grade levels, and content strands, whereas traditional programs use development houses, and authors in name only, authors that change substantially from edition to edition. It is the only curriculum that has a genuine research base under it.

2. Let me aggregate some of the items below. Teachers have a choice of traditional or alternative algorithms. Long division is included. Our algorithms are based on extensive classroom studies, and allow children to take a path to understanding that allows for individual differences. Teachers, for example, don’t have to teach how to deal with “mistakes” in some traditional models; EDM avoids them.

3. EDM was developed to eliminate differences between gender and demographics. It is used in New York City, Philadelphia, Chicago, and Reno, suburban districts, diverse districts with substantial Title I schools and poverty levels, and by about 50% of the California Association of Independent Schools.

4. There is substantial practice in EDM—the Math Journals, the Home and Study Links workbooks, the Teachers Assessment Assistant that generates tests, games, and so on. However, we believe that both students who do and don’t understand a concept can be identified quickly. There is clearly an important difference between a problem and a repetitive exercise that simply replicates correct or incorrect answers. EDM believes and supports practice and the automaticity of facts, but also offers time to develop problem-solving skills when a child needs to rely on information to solve a question that they don’t automatically know. Finally, we typically think of practice in terms of pencils and paper. The aural and verbal practice in EDM is extensive, and enables children to use their minds to solve problems. The Games are an important part of each child’s conceptual development, and allow children to develop number sense.

5. The spiral that is carefully articulated in the program allows children different options/methods to grow number sense and problem-solving skills. Part 2 of each lessons focuses on topics that have been covered in other places; Part 3 offers Differentiation for all classes of students.

6. Calculators are recommended for use to expand understanding, not eliminate it. They are used to calculate larger numbers. If you are standing on the floor of the NY Exchange, you are unlikely to use a pencil and paper to calculate the value of 32000 shares at $17.85 a share. You will rely on the strategies that you find in EDM to estimate orders of magnitude.

Longitudinal Study of Everyday Math
General Changes from Second and Third Editions of Everyday Math
California "Waivered District" Test Data

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26. To learn more about Everyday Math (EDM) and other essential pedagogical background materials for the Math Adoption Committee and Elementary Math Network, please see:

  • Adding It Up: Helping Children Learn Mathematics, Mathematics Learning Study Committee, Center for Education, National Research Council, © 2001, National Academy Press.
  • Math Matters, Chapin and Johnson, Math Solutions, 2006.
  • Teaching Student-Centered Mathematics, Van de Walle and Lovin, Pearson, 2006
  • Young Mathematicians at Work (series), Fosnot and Dolk, Heinemann, 2001.
  • Knowing and Teaching Elementary Mathematics:  Teachers’ Understanding of Fundamental Mathematics in China and the United States, Li Ping Ma, 1999.
  • Lesson Study:  A Handbook of Teacher-Led Instructional Change,  Catherine Lewis, 2002.
  • Everybody Counts,  Mathematical Sciences Education Board and the Board of Mathematical Sciences, 1989.
  • Making Sense, Hiebert, Carpenter, et al., Heinemann, 1997.
  • Thinking Mathematically: Integrating Arithmetic and Algebra in Elementary School,  Carpenter, Franke, and Levi, © 2003 Heinemann.
  • Learning & Teaching Geometry K-12: 1987 Yearbook ,  Lindquist, Mary Montgomery, © 1997, National Council of Teachers of Mathematics.
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Should you have questions or concerns, contact Ginni Davis or at (650) 329-3709

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