# What Parents Need to Know About Changes in Mathematics Education

## Learning Benefits

To a great extent, mathematics curriculum and instructional practices in the United States have changed very little since the early 1900s. There have been some attempts at changing mathematics curriculum and instructional practices, from "New Math" in the 1960s to the "Back to the Basics" movement in the late 1970s and early 1980s. However, mathematics instruction has been largely a system of teaching children how to *do* math, rather than how to understand and use math.

In 1989, the National Council of Teachers of Mathematics (NCTM) released the Curriculum and Evaluation Standards for School Mathematics, sometimes referred to as the NCTM Standards. The Standards was the first document to stress problem solving, communication, connections, and reasoning as integral parts of mathematics education.

In 2009, the Common Core State Standards for Mathematics were introduced and subsequently voluntarily adopted by forty-five states, the District of Columbia, four territories, and the Department of Defense Education Activity. The Common Core State Standards (CCSS) have established a set of clear, concise, rigorous, and relevant standards for mathematics education. The adoption of the CCSS marks a dynamic shift in mathematics instruction for students in kindergarten through 12th grade.

In most mathematics classrooms, instruction is shifting from traditional skills-based learning to a process of constructing understanding and meaning of mathematics as a language to understand the world and solve real-world problems. The shift involves less emphasis on memorization and greater emphasis on conceptual understanding, reasoning, and problem solving.

Schools use numerous math programs, instructional approaches, and curricular addenda that may have parents questioning the quality of their child's math education, and may leave them exclaiming, "I don't understand my child's math homework!" Fear not! The following information will provide you with a greater understanding of some of today's most popular mathematics programs. It may not be able to help you with your child's homework, but it will provide you with insight into how today's mathematics is preparing your child for tomorrow's opportunities.

**enVisionMATH ©2011** (Grades K - 6)

*Program Goal: *

• enVisionMATH seeks to help students develop a conceptual understanding of math through problem-based instruction, small-group interaction, and visual learning with a focus on reasoning and modeling.

*Program Highlights:*

• enVisionMATH is a core curriculum for students in kindergarten through sixth grade.

• enVisionMATH develops math concepts through interactive and visual learning.

• The program includes access to interactive digital courseware.

• Instructional design of the program is based upon Dr. Grant Wiggins' concept of "Understanding by Design.".

• Student assignments are based upon data-driven differentiated instruction.

• enVisionMATH is aligned with the Common Core State Standards.

*Program Development:*

• Scott Foresman-Addison Wesley enVisionMATH ©2011 was designed based on the most current research in mathematics education.

• Research on the effectiveness of the enVisionMATH program in increasing student achievement has been validated by the Department of Education's What Works Clearinghouse.

• Published by Pearson, Lebanon, IN.

**Everyday Mathematics**® (Grades Pre-K - 6)

*Program Goal: *

• Everyday Mathematics provides students with opportunities to build conceptual understanding, computational fluency, and real-world problem-solving skills that will enable them to become lifelong mathematical thinkers.

*Program Highlights:*

• Everyday Mathematics is a core curriculum for students in pre-kindergarten through sixth grade.

• Students are presented with opportunities to learn concepts and practice skills using a variety of representations.

• Everyday Mathematics focuses on real-life problem solving.

• Students are encouraged to explore different ways of solving problems and taught how to communicate their mathematical thinking.

• Everyday Mathematics is aligned with the NCTM Standards and the Common Core State Standards.

*Program Development:*

• Everyday Mathematics was developed by the University of Chicago School Mathematics Project (UCSMP) based on 10 years of research in mathematics education.

• Published by McGraw-Hill School Education, Columbus, OH.

**Excel Math** (Grades K - 6)

*Program Goal: *

• Excel Math seeks to develop higher-order thinking skills, build mathematical proficiency by introducing new concepts while reviewing previously-taught concepts, and to build confidence through immediate feedback on each student's progress.

*Program Highlights:*

• Excel Math is a core curriculum for students in kindergarten through sixth grade.

• Excel Math incorporates a sophisticated process of introduction, reinforcement, and assessment that leads to mastery and long-term competency.

• New topics are introduced, while previous math concepts are reviewed.

• Excel Math uses consumable Lesson Sheets to eliminate tedious copying of problems out of a textbook.

• Excel Math is aligned with the Common Core State Standards.

*Program Development:*

• Excel Math was originally developed by Janice Raymond and has been used and refined for over 35 years.

• Published by AnsMar Publishers Inc., Poway, CA.

**GO Math! **(Grades K - 6)

*Program Goal: *

• GO Math! seeks to provide students with the opportunity to build a strong foundation of conceptual understanding and procedural fluency.

*Program Highlights:*

• GO Math! is a core curriculum for students in kindergarten through sixth grade.

• The program includes a comprehensive offering of print and online components to support students, teachers, administrators, and parents.

• GO Math! is available as a consumable textbook or as an electronic textbook.

• The program includes a financial literacy component for grades 3-6.

• The program places a strong emphasis on developing 21st-century skills.

• GO Math! was written specifically to support the Common Core State Standards for Mathematics with a focus on depth of instruction.

*Program Development:*

• GO Math! program's design was based on a balance between research expertise and practical experience from among the program's authors.

• Published by Houghton Mifflin Harcourt, Orlando, FL.

**Investigations in Number, Data, and Space for the Common Core** (Grades K - 5)

*Program Goal:*

• Investigations provides students with the opportunity to build a deep understanding of mathematics through a strong emphasis on mathematical thinking and reasoning in addition to learning basic arithmetic skills.

*Program Highlights:*

• Investigations is a core curriculum for students in kindergarten through fifth grade.

• Investigations utilizes collaboration and communication of mathematical ideas with peers to build fundamental understandings of mathematics.

• Students are encouraged to explore problems and develop their own strategies for solving them.

• Investigations utilizes a strong interactive and hands-on approach to learning mathematics.

• The Common Core State Standards for Mathematical Practice are deeply embedded into every Investigations lesson.

• Investigations is aligned with the Common Core State Standards for Mathematical Content.

*Program Development:*

• Investigations in Number, Data, and Space for the Common Core was designed by TERC in Cambridge, Massachusetts.

• Published by Pearson, Lebanon, IN.

**Math Connects **(Grades Pre-K - 5)

*Program Goal: *

• Math Connects provides opportunities for students to build their understanding of mathematical concepts, and it provides abundant practice to master critical mathematical skills.

*Program Highlights:*

• Macmillan/McGraw-Hill Math Connects is a core curriculum for students in pre-kindergarten through fifth grade.

• The pre-k -5th grade program continues with Glencoe's Math Connects for grades 6-8.

• Math Connects is a bounded, non-consumable textbook.

• All concepts within the program are presented within a strong problem-solving environment.

• Math Connects is aligned with the Common Core State Standards.

*Program Development:*

• Macmillan/McGraw-Hill Math Connects was designed based on the most current research in mathematics education.

• Published by McGraw-Hill School Education, Columbus, OH.

**Math-U-See** (Grades K - 12)

*Program Goal: *

• Math-U-See uses manipulatives to illustrate and teach math concepts. Mathematical understanding is built by using a multi-sensory, mastery-based approach suitable for all levels and learning styles.

*Program Highlights:*

• Math-U-See is a core curriculum for students in kindergarten through 12th grade.

• Math-U-See is an explicit, structured, systematic, and cumulative program using multi-sensory teaching techniques.

• Math-U-See continuously reviews and integrates topics and concepts that were presented in previous levels.

• The curriculum does not designate specific grade levels, so that students of any age can work at their own ability levels.

• The program offers co-op online classes for secondary level courses.

• The program is used by many homeschooled students.

• Math-U-See is aligned with the Common Core State Standards for Mathematical Content.

*Program Development:*

• Math-U-See was designed by Steve Demme.

• Published by Math-U-See, Lancaster, PA.

**McGraw-Hill My Math** (Grades K - 8)

*Program Goal: *

• McGraw-Hill My Math is personalized for the way students learn and is individualized to maximize their success. The program seeks to move students from learning abstract concepts to learning concepts they can apply.

*Program Highlights:*

• McGraw-Hill My Math is a core curriculum for students in kindergarten through eighth grade.

• The program is deliberately designed to provide a consistency and continuity of instruction from kindergarten through 8th grade, ensuring a smooth transition from elementary to middle school mathematics.

• McGraw-Hill My Math is a consumable program.

• Each student interacts with the text in multiple ways throughout each learning cycle.

• The program features personalized vocabulary, student-created examples, online games, and downloadable apps.

• McGraw-Hill My Math is aligned with the Common Core State Standards.

*Program Development:*

• McGraw-Hill My Math was designed based on the most current research in mathematics education.

• Published by McGraw-Hill School Education, Columbus, OH.

**Saxon Math** (Grades K - 12)

*Program Goal:*

• Saxon Math provides students with the opportunity for mastery and retention of mathematical concepts and skills through the incremental introduction of new topics accompanied by a continuing spiral review of previously learned material.

*Program Highlights:*

• Saxon Math is a core curriculum for students in kindergarten through 12th grade.

• Saxon Math is a kit-based program at the primary levels and transitions to a hard bound text at the intermediate levels. Manipulatives, activities, and technology are incorporated throughout.

• Saxon Math systematically distributes instruction, practice, and assessment throughout the year as opposed to grouping related concepts into units or chapters.

• At the primary level, all new concepts are developed through hands-on activities. Students move from the concrete to the pictorial to the abstract.

• At the intermediate and middle grade levels, daily lessons introduce new concepts and skills, incorporating real-world problem solving and applications of mathematics.

• Saxon Math is aligned with the Common Core State Standards.

*Program Development:*

• Saxon Math was designed by John Saxon.

• Published by Houghton Mifflin Harcourt, Orlando, FL.

**Singapore Math**® (Grades K - 12)

*Program Goal:*

• Singapore Math promotes mastery of mathematics through a consistent and strong emphasis on problem solving and model drawing, along with a focus on in-depth understanding of essential math concepts and skills.

*Program Highlights:*

• Singapore Math is a core curriculum for students in kindergarten through 12th grade.

• Instructional time is devoted to mastering essential math skills. The assumption is made that after a concept or skill has been taught, it is mastered.

• Singapore Math utilizes pictorial models to transition students between concrete mathematical experiences and abstract representations. Models include bar models, ten frames, arrays, and place value charts.

• Singapore Math utilizes the "bar model" method to solve multi-step word problems.

• In Singapore Math, students are deliberately taught the "whys" of mathematical rules as opposed to mere memorization of those rules.

• Singapore Math is aligned with the Common Core State Standards.

*Program Development:*

• Singapore Math was designed by the Curriculum Development Institute of Singapore.

• Published by Singapore Math Inc., Oregon City, OR.

**T.A.I. Mathematics** (Grades 3-8)

*Program Goal: *

• T.A.I. Mathematics seeks to improve computation success through individualized instruction and cooperative learning.

*Program Highlights:*

• The program integrates cooperative learning and individualized instruction in fundamental math concepts and operations.

• Students progress on an individual basis, while working with peers to achieve team goals.

• Students are assigned to 1 of 13 student books based on a placement test.

• Students work in mixed-level, competitive teams.

• Students check one another's work.

• Students give and score practice tests, certifying that team members are ready to move on to the next level.

• Teachers maximize their time spent working with small groups and individuals.

• T.A.I. Mathematics is aligned with state standards.

*Program Development:*

• T.A.I. Mathematics was developed based on over 15 years of research of cooperative learning instructional processes at Johns Hopkins University.

• Published by Charlesbridge Publishing, Watertown, MA.