Math Expressions

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We get students started on the right path in Pre-K, but that's just the beginning. It's also about looking beyond numbers to understand how and why they work, and learning to ask the questions that lead to a thoughtful, informed approach to solving problems. </p> <p class="intro" style="margin-bottom: 0;text-align:left;"">Based on research funded by the National Science Foundation (NSF), <em>Math Expressions</em> is a proven Pre-K–6 curriculum that helps children make sense of math by exploring, discussing, and demonstrating their understanding of key concepts. In busy, active lessons, students learn how to look deeper and choose their own path to the answers—skills that will take them far beyond the math classroom. </p> <div class=" button-row" style="margin: 0 auto 40px auto;"> <div class="intro" style="display: inline-block; margin-bottom: 0; margin-right: 20px; padding: 0;"> Jump to...</div> <a href="#overview" style="margin: 0 15px;">Overview</a> <a href="#research" style="margin: 0 15px;">Research & Results</a> <a href="#author" style="margin: 0 15px;">Author</a> </div> <div class="centerit bottommargin"><a class="btn" href="https://learning.heinemann.com/math-expressions-contact-us">Contact Sales</a> <a class="btn" href="https://learning.hmhco.com/math-expressions-dse">Request a Sample</a> <a class="btn" href="https://samplers.heinemann.com/math-expressions-overview">Download Overview</a></div> <hr /> <p class="intro"><strong>Looking deeper produces exceptional results</strong></p> <div class="flex-container bottommargin"> <div class="three-columns-flex centerit small-text"> <img src="icon_01.png" alt="" /><br /> <strong>Every lesson integrates mathematical<br /> processes and practices.</strong> </div> <div class="three-columns-flex centerit small-text"> <img src="icon_02.png" alt="" /><br /> <strong>Students use authentic examples to<br /> make sense of mathematics.</strong> </div> <div class="three-columns-flex centerit small-text"> <img src="icon_03.png" alt="" /><br /> <strong>Schools see an average gain of<br /> 12–15% on state tests.</strong> </div> </div> <div class="clearit"></div> <div class="flex-container two-column-blocks topmargin"> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">A Yearlong Study of Success</p> <p>Students from eight schools across four states showed "statistically significant" improvement.</p> <p> When children understand math, they're not relying on memorization. They're relying on themselves. Dr. Karen Fuson's comprehensively researched approach to teaching math is based on the way children actually learn and is used across the country because it raises student achievement. </p> </div> </div> <div class="two-columns-flex" style="flex: 1;"> <img src="results.png" alt="bar graph of successful results" /> </div> </div> <hr class="stripe" /> <a name="overview" class="anchor"></a> <h2 class="textcenter">Overview</h2> <h3 class="sansheader">How to think about math</h3> <p>The deep conceptual understanding that's the hallmark of the program leads to strong skills fluency and the ability to make generalizations within and among mathematical strands. As students grow and learn to think critically, teachers develop their own richer understanding of math through detailed instruction and embedded support.</p> <div class="clearit"></div> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <img src="kids3.png" alt="Math Expressions Grade K" /> </div> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left"><em>Math Expressions</em> is based on NSF-funded research.</p> <p><strong>Contextual Learning</strong><br /> Students develop an understanding of mathematics through real-world situations and visual supports.</p> <p><strong>Multiple Strategies</strong><br /> Students learn multiple ways to solve problems, including algorithms based on reasoning.</p> <p><strong>Manageable Instruction</strong><br /> Teaching materials embody a "learn-while-teaching" style.</p> </div> </div> </div> <div class="clearit"></div> <div class="clearit"></div> <hr /> <h3 class="sansheader">Student Experience</h3> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">Student technology builds understanding, practice, and problem solving.</p> <ul class="bullet-list"> <li>Award-Winning Matific delivers friendly and entertaining animated characters who help build confidence that inspires mastery and fluency with encouraging instructions and motivational feedback as students improve, make progress, and earn rewards.</li> <li>Games in the online Math Activity Center develop fluency in math facts and operations.</li> <li>Students build concrete and pictorial relationships with digital manipulatives.</li> </ul> </div> </div> <div class="two-columns-flex" style="flex: 1;"> <img src="Matific-Picture.png" alt="ipad example" /> </div> </div> <div class="clearit"></div> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <img src="desk.png" alt="Math Expressions Grade K" /> </div> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">Lessons build understanding through active inquiry. </p> <p><strong>Coherence <br /> </strong>Students make connections between key topics both within and across grades.</p> <p><strong>Discourse</strong> <br /> Math Talk gives students the chance to ask questions and use their MathBoards to explain and justify their solutions.</p> <p><strong>Practice</strong> <br /> The online Student Activity Book gives young learners the tools to explore and deepen their understanding of key math concepts.</p> </div> </div> </div> <div class="clearit"></div> <hr /> <h3 class="sansheader">Teacher Experience</h3> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <img src="teacher1.png" alt="Teacher Lesson" /> </div> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left"><em>Math Expressions</em> facilitates learning while teaching.</p> <ul class="bullet-list"> <li>Professional development, classroom demonstration, and daily routine videos are at point of use in the Teacher Edition. </li> <li>Lessons include teaching and inquiry notes, visual models, and suggestions for Math Talk. </li> <li>Mathematical processes, practices, and learning progressions are featured in every lesson. </li> <li>Formative assessment reporting helps group students for instruction and identifies appropriate differentiation resources. </li> </ul> </div> </div> </div> <div class="clearit"></div> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">Differentiated support to encourage all students.</p> <p><strong>Differentiated Instruction <br /> </strong>The Math Activity Center supports every child with Practice, Re-teach, and Challenge resources for each lesson.</p> <p><strong>Adaptive Practice<br /> </strong>Customize instruction with the Personal Math Trainer<sup>®</sup> Powered by Knewton™, an online personalized learning and assessment system with real-time reporting and adaptive practice.</p> </div> </div> <div class="two-columns-flex" style="flex: 1;"> <img src="kids1.png" alt="Kids working on ipad" /> </div> </div> <div class="centerit"> <script src="https://fast.wistia.com/embed/medias/m11a3kbe77.jsonp" async></script> <div class="wistia_responsive_padding" style="padding: 56.25% 0 0 0; position: relative;"> <div class="wistia_responsive_wrapper" style="height: 100%; left: 0; position: absolute; top: 0; width: 100%;"> <div class="wistia_embed wistia_async_m11a3kbe77 videoFoam=true" style="height: 100%; position: relative; width: 100%"> <div class="wistia_swatch" style="height: 100%; left: 0; opacity: 0; overflow: hidden; position: absolute; top: 0; transition: opacity 200ms; width: 100%;"> <img src="https://fast.wistia.com/embed/medias/m11a3kbe77/swatch" style="filter: blur(5px); height: 100%; object-fit: contain; width: 100%;" alt="" aria-hidden="true" onload="this.parentNode.style.opacity=1;" /> </div> </div> </div> </div> </div> <p class="intro-left">Math Expressions classrooms are collaborative</p> <p>Hear from a teacher about how Math Talk engages his class.</p> <div class="clearit"></div> <hr /> <h3 class="sansheader">Matific</h3> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">Delivering powerful and informative educational technology, <a href="https://heinemann.com/matific">Matific</a> personalizes learning paths to support adaptive engagement for active learning. </p> <ul class="bullet-list"> <li>Wrapped in a fun journey of discovery, a carefully curated and rigorous 5-point pedagogy designed by educational experts from leading universities is fully aligned into a robust curriculum of topics and skills.</li> <li>Multimedia activities bring learning to life with real-world problems through student agency and adventure driven by challenging responsiveness and rewards.</li> <li>Easy to assign digital and printable activities provide teachers formative feedback and real-time insight to inform instruction and monitor progress.</li> </ul> </div> </div> <div class="two-columns-flex" style="flex: 1;"> <img src="Matific-Picture2.png" alt="Matific Image 2" /> </div> </div> <div class="clearit"></div> <hr /> <h3 class="sansheader">Math Expressions in Spanish</h3> Expresioñes en matemáticas brings the proven curriculum of Math Expressions—in Spanish! Ideal for English learners, or students in Spanish immersion programs, Expresioñes en matemáticas is designed to help students develop content language and literacy skills while building deep conceptual understanding of mathematics. <ul class="bullet-list" style="padding: 20px 0 0 50px;"> <li><strong>Built on a Solid Foundation of Research</strong></li> <p style="padding-left: 20px;">For twenty-five years, Dr. Karen Fuson, Professor Emerita of Education and Psychology at Northwestern University, researched effective methods of teaching and learning mathematics. Results from her research indicated students using the approaches featured in Math Expressions achieved higher rate than students using other programs.</p> <li><strong>Instruction that Supports Language Development</strong></li> <p style="padding-left: 20px;">Expresioñes en matemáticas instruction starts at the students’ level and continually elicits their thinking; provides visual and linguistic supports to move them rapidly to understanding; and ends with extended fluency practice and application while continuing the emphasis on understanding and explaining.</p> <li style="padding-top: 10px !important;"><strong>Available in Both Print and Digital</strong></li> <ul class="bullet-list" style="list-style-type: square; padding-left: 40px;"> <li>Consumable Student Book with cut-out vocabulary cards, paper manipulatives, fluency checks, a glossary, and more</li> <li>Homework and Remembering Book that includes daily lesson homework and mixed daily review</li> <li>Digital Student Access with virtual manipulative tools, online assessments, adaptive homework support, and more</li> <li>Extensive suite of print and digital teacher resources: Teacher Edition, assessment guide, reteach, practice and enrichment activity masters, Math Activity Center with gameboards, math readers, and activity cards</li> </ul> </ul> <hr /> <div class="clearit"></div> <div class="centerit"> <script src="https://fast.wistia.com/embed/medias/vtaasxxnj2.jsonp" async></script> <div class="wistia_responsive_padding" style="padding: 56.25% 0 0 0; position: relative;"> <div class="wistia_responsive_wrapper" style="height: 100%; left: 0; position: absolute; top: 0; width: 100%;"> <div class="wistia_embed wistia_async_vtaasxxnj2 videoFoam=true" style="height: 100%; position: relative; width: 100%"> <div class="wistia_swatch" style="height: 100%; left: 0; opacity: 0; overflow: hidden; position: absolute; top: 0; transition: opacity 200ms; width: 100%;"> <img src="https://fast.wistia.com/embed/medias/vtaasxxnj2/swatch" style="filter: blur(5px); height: 100%; object-fit: contain; width: 100%;" alt="" aria-hidden="true" onload="this.parentNode.style.opacity=1;" /> </div> </div> </div> </div> </div> <p class="intro-left">Making teachers' lives easier by changing the learning landscape </p> <p>Hear what Dr. Fuson thinks about early learning in mathematics and how it can help close the equity gap.</p> <hr /> <h3 class="sansheader">Early Learning Resources</h3> <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <img src="sample1.png" alt="Sample" /> </div> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p class="intro-left">Classroom Structures Support Understanding and Math Talk</p> <ul class="bullet-list"> <li>Students use colorful manipulatives and shape puzzle mats to develop a deep understanding of number and geometry concepts. </li> <li>Fun games and puzzle cards engage students and get them excited about mathematics. </li> <li>Daily routines include learning the count word sequence and relating to number symbols and quantities through patterns, fingers, and actions. </li> <li>Students take turns as student leaders, building confidence over time. </li> </ul> </div> </div> </div>  <div class="flex-container two-column-blocks bottommargin"> <div class="two-columns-flex" style="flex: 1;"> <div class="wrapper"> <p>Research tells us that students who start kindergarten with a high level of math understanding do better in both math and reading after kindergarten. With that in mind, we developed <em>Math Expressions</em> Early Learning Resources to provide early learners with the understanding they need to confidently take the first and subsequent steps of their mathematics journey. </p> <p><strong>Grounded in Research</strong><br /> Students will benefit from teaching-learning paths and structured, repetitive experiences as recommended in “Mathematics Learning in Early Childhood: Paths toward Excellence and Equity.”</p> <p><strong>Rated as Strong by ESSA</strong><br /> <em>Early Learning Resources</em> is based on the same ESSA strong foundation and research as the rest of <em>Math Expressions</em>, making it an ideal transitional program for pre-kindergarten early learners. </p> <p><strong>Focused on Numbers and Geometry<br /> </strong>Research guidelines led to a strong focus on numbers and geometry, content areas that are particularly important in early math instruction.</p> <p><strong>Hands-On<br /> </strong>Playful activities help children see, discuss, and use mathematical structures, building understanding and fluency gradually and systematically.</p> </div> </div> <div class="two-columns-flex" style="flex: 1;"> <img src="kids2.png" alt="Kids Collaborating" /> </div> </div> <hr /> <p class="intro-left">Instructional Content</p> <p>The instruction keeps students constantly moving forward while providing teachers with explicit support. Learn more about Dr. Fuson's approach through the samplers below.</p> <div class="centerit topmargin"> <div class="three-columns"> <a href="/mathexpressions/HNM_WF279369_MX_MathExpressions_2018_National_Sampler.pdf"><img src="/mathexpressions/Sampler-2018Program.png" alt="" /> <p>2018 Program Sampler</p> </a> </div> <div class="three-columns"> <a href="/mathexpressions/HNM-WF274796_MX274796_2018_CC_Sampler.pdf"><img src="/mathexpressions/Sampler-CCSSProgram.png" alt="" /> <p>CCSS Program Sampler</p> </a> </div> <div class="three-columns"> <a href="/mathexpressions/HNM-WF274712_MX_2018_Pre-K_Sampler.pdf"><img src="/mathexpressions/Sampler-EarlyLearning.png" alt="" /> <p>Early Learning Sampler</p> </a> </div> </div> <div class="centerit topmargin"> </div> <div class="clearit"></div>  <hr class="stripe" /> <h2 class="textcenter">Outcomes</h2> <div class="outcomes"> <img src="1.png" style="float: left;" alt="1" /> <p class="slider " aria-expanded="false" id="1q" aria-controls="1a" tabindex="0" role="link"><span class="rspv-up-arrow" role="img" aria-label="collapsed icon" style="margin: 0;"></span><span class="large-text">Deepen mathematical understanding</span></p> <p style="display: none;" class="internal" id="1a" aria-labelledby="1q" aria-hidden="true" tabindex="-1"> Students develop an understanding of the concepts behind the math and build connections between concrete, pictorial, and abstract relationships. </p> </div> <div class="outcomes"> <img src="2.png" style="float: left;" alt="2" /> <p class="slider " aria-expanded="false" id="2q" aria-controls="2a" tabindex="0" role="link"> <span class="rspv-up-arrow" role="img" aria-label="collapsed icon" style="margin: 0;"></span><span class="large-text">Develop critical-thinking skills</span> </p> <p style="display: none;" class="internal" id="2a" aria-labelledby="2q" aria-hidden="true" tabindex="-1">Students learn to ask questions and use the answers to devise thoughtful, informed approaches to solving problems.</p> </div> <div class="outcomes"> <img src="3.png" style="float: left;" alt="3" /> <p class="slider " aria-expanded="false" id="3q" aria-controls="3a" tabindex="0" role="link"> <span class="rspv-up-arrow" role="img" aria-label="collapsed icon" style="margin: 0;"></span><span class="large-text">Enhance teacher effectiveness</span> </p> <p style="display: none;" class="internal" id="3a" aria-labelledby="3q" aria-hidden="true" tabindex="-1"> Teachers use the program's extensive, lesson-by-lesson support to supplement and deepen their own mathematical understanding. </p> </div> <div class="outcomes"> <img src="4.png" style="float: left;" alt="4" /> <p class="slider " aria-expanded="false" id="4q" aria-controls="4a" tabindex="0" role="link"> <span class="rspv-up-arrow" role="img" aria-label="collapsed icon" style="margin: 0;"></span><span class="large-text">Increase student participation</span> </p> <p style="display: none;" class="internal" id="4a" aria-labelledby="4q" aria-hidden="true" tabindex="-1">Math Talk classrooms create lively, collaborative environments where children share their ideas and solutions and listen respectfully to the ideas of their classmates.</p> </div> <div class="outcomes"> <img src="5.png" style="float: left;" alt="5" /> <p class="slider " aria-expanded="false" id="5q" aria-controls="5a" tabindex="0" role="link"> <span class="rspv-up-arrow" role="img" aria-label="collapsed icon" style="margin: 0;"></span><span class="large-text">Improve student performance</span> </p> <p style="display: none;" class="internal" id="5a" aria-labelledby="5q" aria-hidden="true" tabindex="-1"> Students learn to effectively communicate their mathematical understanding verbally and in writing. </p> </div> <div class="clearit"></div> <div class="button-row"><a class="btn" href="https://learning.heinemann.com/math-expressions-contact-us">Contact Sales</a></div> <hr class="stripe" /> <div class="clearit"></div> <a name="research" class="anchor"></a> <h2 class="textcenter">Research & Results</h2> <p class="intro">The research driving <em>Math Expressions</em> gives students a full understanding of concepts behind the math and the tools to effectively express what they've learned. Learn more about what's behind the program and its impact on students across the country.</p> <div class="centerit"> <a href="https://www.edreports.org/reports/overview/math-expressions-2018"><img src="/mathexpressions/EdReports-HMH.png" /></a> <h3 class="sansheader">"All-Green" Rating from EdReports</h3> <p><em>Math Expressions</em> Grades K-5 has been rated as Meets Expectations at Gateways 1, 2, and 3 by EdReports.</p> </div> <hr /> <h3 class="sansheader">Strong ESSA Rating</h3> <p><em>Math Expressions</em> received a Strong ESSA rating based on the distinctive amount and quality of professional learning teachers receive.</p> <p> <a class="btn text-center" href="/mathexpressions/ESSA_Evidence_Overview_021424.pdf">ESSA Evidence Criteria for Math Expressions</a></p> <hr /> <h3 class="sansheader">Foundational and Efficacy Research</h3> <p><em>Math Expressions</em> is based on the results of the NSF-funded Children's Math Worlds research project, a 10-year study led by Dr. Fuson.</p> <div class="res-summary topmargin"> <h4 class="sansheader"><strong><em>Math Expressions</em>: Research Evidence Base</strong></h4> <ul class="mx"> <li><strong>Report Type</strong>: Research Evidence Base</li> <li><strong>Grade Level</strong>: Elementary, Middle</li> </ul> <div><a href="https://www.hmhco.com/research/math-expressions-research-evidence-base" target="_blank"><strong>Read & Download the Report</strong> <img src="/shared/index_files/new-window.png" alt="Document opens in a new window."></a></div> </div> <div class="res-summary"> <h4 class="sansheader"><strong>US Department of Education Institute of Education Sciences (IES): Achievement Effects of Four Early Elementary School Math Curricula: Finding for First and Second Graders (Year 2)</strong></h4> <ul class="mx"> <li><strong>Report Type</strong>: Efficacy Study, Publication from External Organization, Study Conducted by Third Party</li> <li><strong>Grade Level</strong>: Elementary</li> <li><strong>District Urbanicity</strong>: Urban, Suburban</li> </ul> <div><a href="https://www.hmhco.com/research/us-department-of-education-institute-of-education-science-ies-achievement-effects-of-four-early-elementary-school-math-curricula-finding-for-first-and-second-graders-year-2" target="_blank"><strong>Read & Download the Report</strong> <img src="/shared/index_files/new-window.png" alt="Document opens in a new window."></a></div> </div> <div class="res-summary"> <h4 class="sansheader"><strong><em>Math Expressions</em>: Impact Study, Grades 2 and 4</strong></h4> <ul class="mx"> <li><strong>Report Type</strong>: Efficacy Study, Study Conducted by Third Party </li> <li><strong>Grade Level</strong>: Elementary</li> <li><strong>Region</strong>: Midwest, West</li> <li><strong>District Urbanicity</strong>: Suburban, Rural</li> </ul> <div><a href="https://www.hmhco.com/research/math-expressions-impact-study-grades-2-and-4" target="_blank"><strong>Read & Download the Report</strong> <img src="/shared/index_files/new-window.png" alt="Document opens in a new window."></a></div> </div> <div class="clearit"></div> <div class="centerit topmargin bottomargin"> <div class="three-columns"> <a href="/mathexpressions/Math-Expressions-2018-CC-Problem-Solving-Author-Paper.pdf"><img src="/mathexpressions/Research-ProblemSolving.png" alt="" /> <p>Problem Solving in <em>Math Expressions</em></p> </a> </div> <div class="three-columns"> <a href="/mathexpressions/Math-Expressions-2018-Common-Core-Math-Talk-Author-Paper.pdf"><img src="/mathexpressions/Research-AMathTalkCommunity.png" alt="" /> <p>A Math Talk Community</p> </a> </div> <div class="three-columns"> <a href="/mathexpressions/WF598389_MX_2018_CC_NBT_Author-Paper_FO_HR.pdf"><img src="/mathexpressions/Research-CCSSNumberAndOperationsInBaseTen.png" alt="" /> <p>CCSS Number and Operations in Base Ten (NBT)</p> </a> </div> </div> <div class="clearit"></div> <div class="centerit topmargin"><a class="btn" href="https://www.hmhco.com/research/library?sort=&programs=Math%20Expressions"> Explore More Research <img src="/shared/index_files/new-window-wht.png" alt="Document opens in a new window."></a></div> <hr class="stripe" /> <a name="author" class="anchor"></a> <h2 class="textcenter">About the Author</h2> <p class="intro">Dr. Karen Fuson, is a leading voice in math education today</p> <p><strong>Dr. Karen Fuson</strong>, Professor Emerita at Northwestern University, has studied how children understand math ideas for more than 50 years. She designs teaching materials based on how children learn and understand, along with working in schools to help teachers support every child.</p> <div class="clearit"></div> <hr class="stripe" /> <h2 class=" textcenter">Related Insights and Resources </h2> <div class="flex-container cards bkg-cards"> <div class="three-columns-flex components js "> <div style="padding-top: 8px; text-align: center;" class="thumbnail"> <img src="https://s3.amazonaws.com/prod-hmhco-vmg-craftcms-public/hnm/images/_transforms/_large/MX_BlogHeaders-7.jpg" alt="" /> </div> <div class="wrap"> <div class="card-title"> <p><strong>Why Inquiry-Based Math Counts on a Helping Community in the Classroom</strong></p><p>Building confidence with math learning and teaching, establishing a helping community in the classroom empowers ALL students to learn mathematics through shared responsibilities. </p> </div> <p class="text-center"> </p> <div class="wrap2"> <div class="clearit"></div> <hr /> <div class="button-row text-center"> <a href="https://blog.heinemann.com/why-inquiry-based-math-counts-on-a-helping-community-in-the-classroom" class="btn" target="_blank" aria-label="Read more about Why Inquiry-Based Math Counts on a Helping Community in the Classroom. 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They just need many experiences solving, discussing, and writing word problems. </p> </div> <p class="text-center"></p> <div class="wrap2"> <div class="clearit"></div> <hr /> <div class="button-row text-center"> <a href="https://blog.heinemann.com/building-meaningful-mathematical-thinking-for-english-language-learners" class="btn" target="_blank" aria-label="Read more about Building Meaningful Mathematical Thinking for English Language Learners. 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Math Expressions