enVision Mathematics Pennsylvania Grades 6-8

enVision® Mathematics © 2024 for grades 6-8 is the only middle grades math program that combines problem-based learning and visual learning to deepen students’ conceptual understanding. enVision is used by classrooms across the country and around the world. The latest enVision is even better with new digital Let’s Investigate! lessons which provide students with opportunities to take ownership of deeper exploration into problem-based learning. Ensure successful implementation with the comprehensive teacher support based on the 5 Practices.

enVision packs a unique one-two punch. Lessons start with Problem-Based Learning (PBL), where students must think critically about a real-world math problem, evaluate options, collaborate, and present solutions. This is followed by Visual Learning to solidify the underlying math concepts. It’s the best way to help kids better understand math ideas.

The program is made up of the following program components:

• Teacher’s Edition - Available in digital or print, the Teacher’s Edition includes wrap-around pages that provide direct instruction and teaching suggestions to engage students. The Interactive Teacher’s Edition online features annotation models and downloadable lesson resources.
• Student Edition - Interactive Student Edition—available in digital or print write-in format.
• enVision Digital - enVision digital courseware on Savvas Realize® includes robust digital tools that give teachers flexibility to use a digital, print, or blended format in their classrooms. Teachers can customize the program to rearrange content, upload their own content, add links to online media, and edit resources and assessments. All program resources, including personalized practice, remediation, and assessments are available in one location for easy lesson planning and presentation Students will use technology to interact with text and activities, and they can write directly in their digital Student Edition to make interaction with text more meaningful. Students will engage in activities that will inspire conceptual understanding, classroom discourse, and build their mathematical thinking skills, while learning to formulate and defend their own opinions.

The learning model in the enVision program—problem-based learning, visual learning, and data-driven differentiated instruction—has been researched and verified as effective. Core instruction used for every lesson has been shown to be effective for developing conceptual understanding.

enVision Mathematics features comprehensive differentiated instruction and intervention support to allow access for all students. The program’s balanced instructional model provides appropriate scaffolding, differentiation, intervention, and support for a broad range of learners, and is designed to facilitate conceptual understanding of mathematics for students at a range of learning levels.

Comprehensive, built-in differentiation resources support all levels of learners, including those with learning disabilities and ELLs, through personalized, adaptive learning. The program meets a variety of student needs and provides Response to Intervention (RtI) during each lesson, at the end of each lesson, at the end of each Topic, and any time as indicated in the Teacher’s Edition. A description of RtI tiered instructional resources for the program is included in the Teacher’s Program Overview for each grade. The following are examples of tiered instructional support found online for each lesson.

Tier 1 ongoing Intervention includes the following resources that can be used during the lesson:

• Prevent Misconceptions. During the Visual Learning Example, a remediation strategy is included to address a common misconception about the lesson concept.
• Error Intervention (If... Then...). During Practice & Problem Solving, error intervention identifies a common error and provides remediation strategy
• Reteaching Set. This set is provided before independent practice to develop understanding prior to practice.
• MathXL for School: Practice & Problem Solving, during the lesson, includes personalized practice for the Practice & Problem Solving portion of the lesson, along with Additional Practice or Enrichment; auto‐scored with on‐screen help, including Help Me Solve This and View an Example tools, tutorial videos, Math Tools, and one‐click animated glossary access.

Tier 2 strategic intervention includes the following resources that can be used at the end of the Lesson:

• Intervention Activity. This supports teachers working with small groups of struggling students.
• Reteach to Build Understanding. This provides guided reteaching as a follow‐up to the intervention activity.

Tier 3 intensive intervention instruction is delivered daily outside of the core math instruction, often in a one‐to‐one situation. The Math Diagnosis and Intervention System can be used for this purpose, for example.

• Variety of Instructional Strategies
• Multisensory instruction is provided in online Solve & Discuss It!/Explore It!/Explain It! activities that include audio, Visual Learning
• Animation Plus, Virtual Nerd videos, interactive MathXL for School: Practice & Problem Solving, Additional Practice, and Enrichment, online digital math tools, and online math games.

The authorship team is made up of respected educational experts and researchers whose experiences working with students and study of instructional best practices have positively influenced education. Contributing to enVision with a mind to the evolving role of the teacher and with insights on how students learn in a digital age, these authors bring new ideas, innovations, and strategies that transform teaching and learning in today’s competitive and interconnected world.

• Dr. Robert Q. Berry, III is an Associate Professor at the University of Virginia in the Curry School of Education with an appointment in Curriculum Instruction and Special Education. A former mathematics teacher, he teaches elementary and special education mathematics methods courses in the teacher education program at the University of Virginia. Additionally, he teaches a graduate level mathematics education course and courses for in-service teachers seeking a mathematics specialist endorsement.
• Zachary Champagne taught elementary school students in Jacksonville, Florida for 13 years. Currently he is working as an Assistant in Research at the Florida Center for Research in Science, Technology, Engineering, and Mathematics (FCRSTEM) at Florida State University.
• Dr. Randall Charles is Professor Emeritus in the Department of Mathematics at San Jose State University, San Jose, California. His research interests have focused on problem solving with several NCTM publications including Teaching and Assessing Problem Solving, How to Evaluate Progress in Problem Solving, and Teaching Mathematics Through Problem Solving. In recent years Dr. Charles has written and talked extensively on Big Ideas and Essential Understandings related to curriculum, teaching, and assessment.
• Francis (Skip) Fennell, PhD, is emeritus as the L. Stanley Bowlsbey professor of education and Graduate and Professional Studies at McDaniel College in Maryland, where he continues to direct the Brookhill Institute of Mathematics supported Elementary Mathematics Specialists and Teacher Leaders Project. A mathematics educator who has experience as a classroom teacher, principal, and supervisor of instruction, he is a past president of the Association of Mathematics Teacher Educators (AMTE), the Research Council for Mathematics Learning (RCML), and the National Council of Teachers of Mathematics (NCTM).
• Eric Milou is a Professor in the Department of Mathematics at Rowan University in Glassboro, NJ. He is an author of Teaching Mathematics to Middle School Students. Recently, his focus has been on approaches to mathematical content and the use of technology in middle grades classrooms.
• Dr. Jane Schielack is Professor Emerita in the Department of Mathematics and a former Associate Dean of Assessment and PreK-12 Education in the College of Science at Texas A&M University. A former elementary teacher, Dr. Schielack has pursued her interests in working with teachers and students to enhance mathematics learning in the elementary and middle grades. She has focused her activities for improving mathematics education in two main areas: teacher education and professional development and curriculum development.
• Jonathan Wray has involvement and leadership in a number of organizations and projects. His interests include the leadership roles of mathematics coaches/specialists, access and equity in mathematics classrooms, the use of engaging and effective instructional models to deepen student understanding, and the strategic use of technology in mathematics to improve teaching and learning.

enVision Mathematics is designed to achieve a coherent progression of mathematical content within each course and across the program, building lesson to lesson. Every lesson includes online practice instructional examples as the progression of topics builds, allowing students additional practice with these skills and to develop a deeper conceptual understanding.

At the beginning of every topic, teachers are provided with support for the focus of the topic, how the topic fits into an overall coherence of the grade and across grades, the balance of rigor in the topic, and how the practices enrich the mathematics in the topic. Carefully designed learning progressions achieve coherence across grades:

Coherence is supported by common elements across grades, such as Thinking Habits questions for math practices and diagrams for representing quantities in a problem. Coherence across topics, clusters, and domains within a grade is the result of developing mathematics as a body of interconnected concepts and skills. Across lessons and standards, coherence is achieved when new content is taught as an extension of prior learning—developmentally and mathematically. (For example, Solve & Share at the start of lessons engages students in a problem-based learning experience that connects prior knowledge to new ideas.)

Look Back! and Look Ahead! connections are highlighted in the Coherence part of Topic Overview pages in the Teacher’s Edition.

The Topic Background: Rigor page shows teachers how the areas of rigor will be addressed in the topic, and details how conceptual understanding, procedural skill and fluency, and application builds within each topic to provide the rigor required.

On the first page of every lesson, the Lesson Overview includes sections titled Focus, Coherence, and Rigor. The Rigor section highlights the element or elements of rigor emphasized in the lesson, which may be one, two, or all three. Features in every lesson support each element, but the emphasis will vary depending on the standard being developed in the lesson. The core instructional model features support for conceptual understanding, procedural fluency, and application during both instruction and practice, as described below.

• Problem-Based Learning
  Step 1 Problem-Based Learning supports coherence by helping students connect what they already know to a problem in which new math ideas are embedded. When students make these connections, conceptual understanding emerges. Students are given time to struggle to make connections to the mathematical ideas and conceptual understandings. They can choose to represent their thinking and learning in a variety of ways. Physical and online manipulatives are available.
• Visual Learning
  Step 2 Visual Learning further develops understanding of the lesson ideas through classroom conversations. The Visual Learning Example features visual models to help give meaning to math language. Instruction is stepped out to help students visually organize important ideas. Students perform better on procedural skills when the procedures make sense to them. Procedural skills are developed through careful learning progressions in the Visual Learning Example.
• Assess and Differentiate Step 3 Assess and Differentiate features a Lesson Quiz and a comprehensive array of intervention, on-level, and advanced resources for all learners, with the goal that all students have the opportunity for extensive work in the state standards. Leveled practice with scaffolding is included at times. Varied problems are provided and math practices are identified as appropriate. Higher Order Thinking problems offer more challenge. Students have ample opportunity to focus on conceptual understanding and procedural skills and to apply the mathematics they just learned to solve a range of problems.

At the start of the school year, schools have the opportunity to implement norm-referenced and validated assessments to identify students’ strengths and areas for growth. The new award-winning Math Screener and Diagnostic Assessments and Growth work directly with the enVision Mathematics course on Savvas Realize to inform instruction and provide robust student data. As a result of the Diagnostic assessment, teachers are armed with flexible instructional recommendations personalized to every student.

enVision Mathematics portrays diverse individuals and groups in a variety of settings and backgrounds. The program has been reviewed and approved for unbiased and fair representation. 

Our educational materials feature a fair and balanced representation of members of various cultural groups, including racial, ethnic, and religious groups; males and females; older people; and people with disabilities. The program integrates social diversity throughout all of its lessons, and includes a balanced representation of cultures and groups in multiple settings, occupations, careers, and lifestyles. 

We strive to accurately portray diverse groups within our society as well as diversity within groups. Our programs use language that is appropriate to and respectful of our cultural diversity. We involve members of diverse ethnic and cultural groups in the concept development of our products as well as in the writing, editing, illustration, and design.