As states and local districts adopt more rigorous standards, our nation’s students must be prepared to face these greater challenges in order to keep pace. A strong foundation is essential for later success in mathematics, and adequate preparation is essential to their future success. According to the 2015 National Assessment of Education Progress (NAEP) Mathematics test, 60 percent of America's fourth graders are not proficient in mathematics. The NAEP data also reveals that 67 percent of eighth graders are not proficient in mathematics (National Center for Education Statistics, 2015). More students in the U.S. need to be proficient in mathematics in order to be successful in algebra. The National Mathematics Advisory Panel’s Final Report (2008) has established that fluency with fractions and other basic arithmetic concepts and skills are critical foundations for algebra. If students are struggling with the acquisition of these foundational skills, it is essential to provide the supports necessary for them to become proficient in these areas.
Success in the Early Stages of Instruction Will Lead to a Greater Likelihood of Success in the Future
Children struggle with mathematics for a number of reasons such as language, learning disabilities, and a simple lack of adequate prior exposure. English learners, for example, can struggle with understanding the mathematical concepts and vocabulary (Frederickson & Cline, 2002). Learning disabilities are a pervasive challenge in our nation’s classrooms. Between five to eight percent of school-aged children have some form of a learning disability which affects their ability to learn mathematics (Geary, 2004). One percent of school-aged children experience a math disability not associated with any other learning disability, and two to seven percent experience serious math deficits. Although these challenges can be significant, they can also be addressed especially if done so early with adequate supports for both teachers and students.
Another factor affecting the classroom is the adoption of more rigorous standards. The effects of increasing rigor also impact teachers who report changes in the way they deliver instruction. In addition, teachers report a greater need for support, especially those working with students who are one or more grade levels behind (Bay-Williams, Duffett & Griffith, 2016). Support can take several forms such as professional development and advances in technology and infrastructure.
Results from a recent national survey show that educators are more optimistic about using new technologies that enhance instruction and perform differentiated instruction. The survey also indicates that approximately 97 percent are using some form of digital technology in their classroom, and many have seen these benefits in the form of increasing student engagement and achievement (HMH, 2015).
The National Council of Teachers of Mathematics (NCTM®) Principles to Actions (2014) outline the importance of teaching and learning, tools and technology, coherent curriculum, assessment, and professional development as key components to creating “systematic excellence” in schools. In addition, the National Mathematics Advisory Panel recommends that math curricula for elementary and middle school be a coherent progression of key topics with an emphasis on proficiency. For many students, especially those who struggle, meeting these goals presents a challenge when they only receive a typical 50-minute daily session dedicated to math instruction. Moreover, many students require instruction that is specifically designed to target key misconceptions and to focus on the most critical foundational mathematical concepts.
This Research Foundations document describes a program that addresses many of these challenges and is based on decades of research used to inform its development. The document will outline and connect the eight guiding principles of Do The Math with supported research. Examples from the program will be used to demonstrate how these guiding principles impact the way students learn mathematics. Finally, a set of studies pointing to the program’s efficacy in improving student academic outcomes are summarized.
Since its inception almost 10 years ago, Do The Math has fostered student engagement in math and provided support for teachers in thousands of classrooms across the United States.
A Long History of Turning Research into Practice
Do The Math was initially published in 2008. The program is based on nearly 50 years of research and experience by Marilyn Burns working with teachers and students in the classroom. Marilyn Burns, along with a team of Math Solutions® instructors with extensive classroom teaching experience, created the lessons in Do The Math. They discussed, wrote, debated, tested, rewrote, and refined the lessons to ensure that the content, pacing, and scaffolding were on target to meet the needs of struggling students. She continues to teach regularly in classrooms, finding the experience essential for developing and testing new ideas and materials. The program was initially intended to provide math intervention for students who had fallen behind, yet many teachers reported using the modules in a wide variety of settings including whole-class instruction. The lessons are effective for building all students’ understanding, skills number sense, and engaged them with the mathematical practices.
Do The Math shifts the focus of instruction from simply covering content to uncovering essential math content (Burns, 2014). With this new focus the challenge of the teacher is not about finding better ways to explain new content but rather finding better ways of asking students to make sense of what they are learning for themselves (Burns, 2014). This shift from telling to asking is infused throughout all of the modules that comprise the Do The Math program.
The modular design of Do The Math provides flexibility, allowing for the program to be implemented in small-group settings to support struggling students, or in whole-class settings to build numerical understanding and reasoning skills. This flexibility also allows for it to be used in a variety of settings such as classrooms, resource rooms, extended day, and after school programs. The program can be used to supplement on-grade level instruction as well as an intervention for students who are multiple grade levels behind. The program aligns to Response to Intervention (RTI), a national framework for instruction and intervention.
The current version of Do The Math retains the core research principles from the original program and expands and enhances them with the use of lessons learned and the effective leveraging of current technologies. Now available for all tablets, the new Do The Math experience provides teachers and students with easy access to all lessons, interactive visual models, and games to engage and challenge learners within and beyond the walls of the classroom. Students have the flexibility to explore, make mistakes, and have fun with the range of tools and games designed to build their fluency and understanding of key concepts. Teachers can refine their instructional practices using a library of point-of-use resources designed by Marilyn Burns and Math Solutions.
Building upon the effective uses of technology, Do The Math’s HMH Teacher Central® is a new tablet-ready digital experience that provides teachers with virtual tools, games, and professional learning resources right at their fingertips. In addition, with the new HMH Student Central™, all of the students’ favorite games and hands-on materials are now available digitally to provide additional practice. ProgressSpace™ is another digital feature that offers an online assessment and reporting tool.
Do The Math rebuilds critical mathematical foundations for understanding by:
Designed to support struggling students in Grades 1–5+, Do The Math is organized into 13 scaffolded modules that focus on whole numbers and fractions. Each module contains 30 lessons. Students receive an assessment every fifth lesson to monitor progress. Additionally, students take a beginning- and end-of- module assessment to monitor growth.
Addition and Subtraction
Number Core supports students’ success by rebuilding the foundations of Numbers and Operations. Students develop mental representations of quantity using the benchmark number of 5 and then 10, learn to think flexibly about how to compose and decompose numbers, and build facility with figuring sums to 20.
ADDITION & SUBTRACTION A: ADDITION WITH SUMS UP TO 100
Addition & Subtraction A builds a foundation for addition using two of the big ideas of mathematics:
These big ideas help students to build place-value understanding and make sense of meaning behind the addition facts and calculations involving regrouping.
ADDITION & SUBTRACTION B: SUBTRACTION WITH NUMBERS UP TO 100
Addition & Subtraction B reinforces subtraction and addition as inverse operations. The major emphasis of this module is on helping students recognize the three meanings of subtraction in real-world contexts: take- away, missing part, and comparison. Students also learn three ways to compute differences between numbers from 0 to 100, and how to flexibly apply these strategies to solve contextual problems involving subtraction.
ADDITION & SUBTRACTION C: NUMBERS GREATER THAN 100
Addition & Subtraction C applies and extends the big ideas, concepts, and skills developed in earlier modules to calculations with greater numbers. Students use place value and explore the open number line to solve word problems with addition and subtraction involving numbers up to 999,999.
MULTIPLICATION A: BASIC CONCEPTS
Multiplication A provides visual and contextual models to help students understand the meaning of multiplication—a major building block for students that requires a shift from thinking additively to thinking multiplicatively.
MULTIPLICATION B: FACTS THROUGH 12 X 12
Multiplication B uses array models to represent the basic facts and show how the Commutative Property reduces the number of facts to learn. Applying the big idea that numbers can be decomposed to splitting array models lays the foundation for the Distributive Property and provides students with strategies for multiplying.
MULTIPLICATION C: FACTORS GREATER THAN 12
Multiplication C uses patterns; place value; and the Commutative, Associative, and Distributive Properties to help students make sense of and develop skills for multi-digit multiplication.
DIVISION A: BASIC CONCEPTS
Division A focuses on the idea that division is the inverse operation of multiplication, eliminating the need to memorize division facts. Computational methods for solving a division problem are introduced contextually and concretely to help students understand the two meanings of division—sharing and grouping.
DIVISION B: FACTS THROUGH 100÷10
Division B applies understanding of the inverse relationship between multiplication and division to help students calculate quotients and remainders for two-digit numbers divided by two-digit divisors, and to solve word problems.
DIVISION C: DIVIDENDS TO 1000
Division C extends to dividing two- and three-digit dividends by two-digit divisors, engages students in exploring divisibility, and provides experiences with solving contextual problems involving greater numbers.
FRACTIONS A: BASIC CONCEPTS
Fractions A provides students with concrete models that develop understanding of the meaning of fractions as equal parts of a whole. Teaching with fraction strips to model combining unit fractions, comparing fractional quantities to the benchmarks of ½ and 1, and identifying equivalent fractions is essential to help students give meaning to the abstract ideas of fractions.
FRACTIONS B: EQUIVALENCE AND COMPARISON
Fractions B develops six strategies for comparing and ordering fractions using reasoning with the support of fraction strips. Students extend their understanding of fractions of a whole to fractions as parts of sets, and learn to rename fractions as equivalent fractions.
FRACTIONS C: ADDITION AND SUBTRACTION
Fractions C extends students’ understanding of fractions to adding and subtracting fractions and using concrete models only to verify answers. Students use number sense to compute fractional sums and differences mentally, and use benchmark fractions to make estimates.
Do The Math provides teachers and students with easy access to all lessons, interactive visual models, and games to engage and challenge learners within and beyond the walls of the classroom. Students have the flexibility to explore, make mistakes, and have fun with the range of tools and games designed to build their fluency and understanding of key concepts. The program can flexibly adapt to a range of locally available technology including all tablets. ProgressSpace and its reporting functionality allow the teacher to monitor student understanding of key concepts periodically throughout a module. Teachers can also gauge student growth in their understanding through the use of pre- and post-module assessments.
For The Teacher
The Teacher Bookcase contains all the teaching materials and professional resources needed for clear instructional guidance and lesson planning.
The Teacher Guide provides all the information needed for lesson planning, monitoring student progress, and using both the Classroom Materials and mTools effectively.
PROFESSIONAL LEARNING GUIDE
The Professional Learning Guide from Math Solutions provides a comprehensive overview of the program architecture and instructional strategies.
HMH TEACHER CENTRAL FOR DO THE MATH
This new tablet-ready digital experience provides teachers with mTools, games, and professional learning resources right at their fingertips.
The Annotated WorkSpace provides clear representations of model student answers to help teachers provide timely progress monitoring.
Read alouds provide engaging children’s literature to support the instruction throughout the program.
For The Student
The WorkSpace® is designed to support students’ transition to independent work and to help teachers monitor students’ progress and understanding. The WorkSpace provides clear representations of model student answers to help teachers provide timely progress monitoring.
CLASSROOM MATERIALS BOX
The Classroom Materials Box provides hands-on resources and manipulatives that support and extend student learning throughout the modules.
HMH STUDENT CENTRAL
With HMH Student Central, all of the students’ favorite games and interactive visual models are now available digitally to provide additional practice.
mTools allow teachers and students to use visual models to better understand foundational mathematical concepts and differentiate instruction on interactive whiteboards and tablets.
About Marilyn BurnsMarilyn Burns is one of the most highly respected mathematics educators in the United States today. Over almost 50 years, she has educated children, conducted countless in-service workshops, written more than a dozen children’s books and numerous articles in professional journals, and created more than 20 professional development resources for teachers and administrators. In 1984, Marilyn founded Math Solutions Professional Development, an organization dedicated to the improvement of math instruction. She has received a number of awards, including the Glenn Gilbert National Leadership Award, given by the National Council of Supervisors of Mathematics, and the Louise Hay Award for Contributions to Mathematics Education, given by the Association for Women in Mathematics.
Marilyn Burns, along with a team of Math Solutions instructors with extensive classroom teaching experience, created the lessons in Do The Math. They discussed, wrote, debated, tested, rewrote, and refined the lessons to ensure that the content, pacing, and scaffolding were on target to meet the needs of struggling students. She continues to teach regularly in classrooms, finding the experience essential for developing and testing new ideas and materials.
About The Coauthors
VICKI BACHMANwas a primary classroom teacher in Iowa City, Iowa, for more than 20 years and was most recently a math consultant for Grant Wood Area Education Agency in Cedar Rapids, Iowa. A Math Solutions in-service instructor, Vicki is the author of First Grade Math: A Month-to-Month Guide.
JANE CRAWFORDis a recipient of the Presidential Award for Excellence in Teaching Mathematics, a Math Solutions consultant, and the author of Math by All Means: Money; she also taught in the Kalispell School District in Montana for more than 10 years and has a master’s degree in curriculum and instruction.
EUNICE HENDRIX-MARTINis a teacher at Carrillo Elementary School in Carlsbad, California, and has been teaching for 37 years. She is a curriculum developer and a conference presenter and has been a consultant for Math Solutions. Eunice has also authored math educational resources through Stenhouse.
LEO KOSTELNIKis a K–8 principal, has been a classroom teacher in Grades 1–12, as well as a mentor teacher and professional development presenter.
MELODY RANDELhas over 20 years of classroom teaching experience at the elementary, middle school, and university levels, and has been a Math Solutions consultant for over 17 years. She has a particular interest in the areas of teaching English learners and using differentiated instruction. She is one of the authors of the Math Reasoning Inventory® (MRI).
SUSAN SCHARTONhas over 30 years of experience teaching at the elementary and university levels and is currently a Math Solutions consultant. She completed her EdD in Teaching and Learning in 2007. Her book, Teaching Number Sense, was published in 2005.
MALLIKA SCOTTis the cofounder of S&S Math Services, has been a classroom teacher in Grades 2–8 as well as a math coach, mentor teacher, professional development presenter, and conference speaker.
DANIELLE WEILLhas over 18 years of experience teaching at the upper elementary and middle school levels. She is currently a 6th grade teacher and math leader at her school in California, in addition to working as a Math Solutions consultant. She worked closely with Marilyn Burns during the development of the Teaching Arithmetic: Introducing and Extending Fractions books.
MARYANN WICKETTis a former elementary classroom teacher and mathematics staff developer in San Marcos Unified School District in San Marcos, California, and is a recipient of the Presidential Award for Excellence in Science and Mathematics Teaching. She is also a workshop leader, conference speaker, and Math Solutions consultant.
LYNNE ZOLLIis a classroom teacher in Grades 1–6 and has also been a mentor teacher, professional development leader, and conference speaker. Lynne has served as a grant writer and written Math Solutions professional books.
In the years since the original release, Do The Math has been proven to be successful in addressing the key challenges that American students face.
The program’s instructional design applies what is known about reaching a wide variety of students who struggle with math to help them achieve proficiency with arithmetic concepts and skills.
Do The Math incorporates the following guiding principles:
Teaching for understanding describes an approach to mathematics instruction in which the teacher: 1) demonstrates and provides clear models of thinking through solving a problem or learning a skill, 2) supports students to understand connections and articulate relationships, 3) provides extensive practice with timely feedback, and 4) encourages students to verbalize their thinking. Teaching for understanding is accomplished through explicit, intentional instruction that addresses the diverse needs of students.
How Do The Math Delivers
Do The Math supports teaching for understanding through the use of explicit instruction intentionally designed to model mathematical thinking, connect concepts to their mathematical representations, and introduce appropriate language. In Do The Math, explicit instruction does not mean to imply “teaching by telling.” When learning requires understanding of logical mathematical processes, it is essential that the explicit instruction presents carefully sequenced experiences through which the students develop concepts, learn skills, see relationships, and make connections. However, when students are required to learn social conventions, such as vocabulary and mathematical symbols, the explicit instruction imparts the necessary and appropriate information.
Scaffolding is the systematic process of analyzing the content and partitioning it into small manageable chunks for the purpose of planning and delivering instruction that facilitates students’ learning. Scaffolded content is at the heart of planning instruction for struggling students. Research shows that scaffolding content to inform instruction benefits all students, and particularly students with learning disabilities.
How Do The Math Delivers
Do The Math focuses on the basics of Numbers and Operations with lessons that build accuracy, efficiency, and understanding. All lessons have been carefully designed and sequenced to align with the scaffolding of the content, and then paced to ensure student success.
Multiple strategies are essential to ensure that all students build number sense, develop skills, deepen their mathematical understanding, and make connections. Using multiple strategies such as modeling, engaging in discussions, and viewing and creating visual representations to teach mathematics ensures that students have a deep understanding of each skill and concept, rather than a shallow or incorrect notion.
How Do The Math Delivers
In Do The Math, lessons engage students with concepts and skills in multiple ways using concrete manipulative materials, games that reinforce concepts and provide practice, selected children’s literature that offers a context for mathematical concepts and skills, and visual representations to help students represent their thinking.
Do The Math is focused on developing the early habits of mind necessary to foster the ongoing progress toward mathematical proficiency. Building these skills is fundamental in developing students into mathematical thinkers. Students must be able to persevere, reason abstractly, use mathematics to model and solve real-world problems, and strategically apply mathematical and practical tools.
How Do The Math Delivers
In Do The Math, students are asked to solve real world problems that are presented in ways that are accessible to them. When solving these problems, they are asked to represent them in multiple ways both mathematically and with the use of concrete and digital manipulatives. In order to accomplish this successfully, students must draw from prior knowledge and communicate their ideas mathematically when working in pairs and independently when applying their reasoning individually.
When students voice their mathematical ideas and explain them to others, they extend and deepen their understanding of the mathematics. Using classroom routines such as “think, pair, share” encourages students to interact and to take responsibility for their own learning as they discuss their thinking. Expressing math knowledge verbally to a partner is particularly valuable for many students who are developing English language skills.
How Do The Math Delivers
In Do The Math, student interaction is built into the program.
Independent student work is most effective when it provides students opportunities to use their developing conceptual understanding and number sense, and is connected to previously learned concepts and skills. Regular practice is essential, and intervention students typically need more practice. Independent work, such as practice, provides students opportunities to strengthen and reinforce their learning as they connect new understanding to existing knowledge.
How Do The Math Delivers
In Do The Math, independent student work is an essential part of every lesson. The written practice in the WorkSpace is always similar to what students experienced during the lesson. The practice is carefully sequenced so that no new knowledge or skill is required in order for the student to be successful. Practice is supported through visual directions on the WorkSpace pages for those students who need a point-of-use reminder of the steps involved.
Teaching students correct mathematical language gives them the tools to articulate their mathematical thinking coherently and precisely. Students incorporate the new vocabulary into their own language as they explain their thinking to each other or in whole-group settings. Explicitly teaching vocabulary and then using the words frequently in class discussions benefits all learners and encourages them to use the words when they are explaining their reasoning to each other.
How Do The Math Delivers
In Do The Math, vocabulary is introduced after students experience and develop a firm understanding of the mathematical concept so that they can anchor the word in their understanding. The meaning of a key vocabulary word is explicitly taught using the routine of see it, hear it, say it, write it, and read it. The word is recorded on a math vocabulary chart with examples so that students may refer to it as needed. Students read the meaning in their own student glossaries and record the meaning with an example in their WorkSpace. Students hear the word used frequently by the teacher and naturally begin to incorporate it into their own explanations as they talk to their partners and share their reasoning with the whole group.
Probing students’ internal reasoning processes reveals both their grasp of foundational concepts as well as their misconceptions. Do The Math provides guidance for teachers to assess students’ understandings during instruction and immediately address misconceptions. This allows teachers to differentiate instruction for all students: those who need additional help and those who are ready for a challenge.
How Do The Math Delivers
In Do The Math, lessons are carefully built on scaffolded content with attention to the common misconceptions of students who are in need of intervention. Ongoing assessment and suggestions for differentiation are integral to the program.
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