In November 2005, further focus groups were held in California, Illinois, New Jersey, and Texas for the purpose of eliciting feedback on various items, such as the Tables of Content organization, TE and SE packaging, and TE and SE prototypes. This additional feedback allowed the enVisionMATH team to further refine the prototype. Additionally in November 2005, math technology surveys and focus groups were done in California, Texas, and several other states and included more than 100 teachers at grades 1 and 4. The goal was to obtain insights into existing practices and future interest in computer resources for math instruction. This information was incorporated into the development of the digital path.
Field testing was then conducted to provide anecdotal feedback during the final stages of the development of enVisionMATH. Three teachers—two from grade 1 and one from grade 4—from Texas taught one topic using prototypes from the new math program. Feedback was provided in the forms of daily lesson logs, discussions with Pearson staff, and a post sample lesson testing survey. This feedback was used in the final revision to the enVisionMATH prototype before the program was published in 2007.
enVisionMATH Instructional Design
The 2011 enVisionMATH program is a research-based instructional model designed to make mathematics more accessible to a wide range of students. Through interactive learning and problem-based activities, students are able to build their own understanding of concepts and skills before the formal representation of ideas occurs.
Gagne and Driscoll (1988) found that the learning of skills typically requires the explicit prior development of simpler component skills (prerequisite skills). The use of the Daily Spiral Review sections ensures that students are accessing prior knowledge. The development of skills acquisition and conceptual understandings are an important component of enVisionMATH. Ball (2001) states that mathematics needs to be developed with a clear sense of the big mathematical ideas that support each of the skills students are expected to develop. In order to communicate clear lesson objectives, a Problem of the Day introduces each portion of the enVisionMATH lesson.
Visual representations drive concept and skill development and each lesson contains a student “visual learning band” which incorporates a dynamic presentation of the objective and essential understanding of the lesson. enVisionMATH author Stuart Murphy concludes, “Visual learning strategies can make a profound difference in a student’s depth of understanding about mathematics” (Murphy, 1997, p. 5).
One example of a visual strategy incorporated into the program is using bar diagrams to solve word problems—problems that “too many students continue to be unsuccessful at solving!” (Charles, 1997, p. 1). Bar diagrams provide a visual representation to show how quantities are related in a word problem and help a student to see relationships and connect those to operation meanings (Charles, 1997). Indeed, Nickerson (1994) found that the ability to use bar diagrams is integral to mathematics thinking and learning.
Jitendra et al. (1999) found that each lesson should provide an adequate number of practice exercises on the new skill. Guided Practice and Independent Practice within each lesson provide ample practice for enVisionMATH users. Further, timely, frequent assessments throughout assist teachers in individualizing instruction, which is supported by the large range of differentiated instructional resources provided to teachers. Technology alternatives allow the print version to come alive through motion and sound. Teacher explanations and Center Activities reinforce, deepen, and extend learning.
The enVisionMATH program is organized into 20 individual content topics, rather than longer, broader chapters. Each topic contains from four to nine lessons and develops one or more related content standards in depth. enVisionMATH was developed so that all of the lessons in the program can be taught prior to the end-of-year state/ district testing.
To accomplish the goals of the enVisionMATH program, resources were carefully designed to meet the needs of all students. Cognitive research on multiple intelligences (Gardner, 1991) indicates the need for children to experience a variety of pedagogical methods. enVisionMATH uses a variety of representations to help students understand mathematical concepts. Some of the ancillary materials included with the program and used by participating teachers include the following:
Interactive Homework Workbook
Interactive Math Series Big Book (K–2)
Math Diagnosis and Intervention System
Individual Student Manipulative Kits
Teacher Overhead Manipulative Kits
Center Activities Kits
Visual Learning Bridge Transparencies
MathStart readers by Stuart Murphy (K–2)
World Scape readers (3–6)
ExamView® Assessment Suite
It should be noted that several built-in components of the enVisionMATH program, such as the Math Diagnosis and Intervention System (MDIS), are designed to aide teachers in providing intensive or Tier 3 intervention. The MDIS and other program tools help teachers provide individual instruction and intervention to students below level.
enVisionMATH Summative Research
Pearson strongly believes that its programs should be proven through scientific research to increase student achievement. As such, it contracted with independent research group PRES Associates, Inc., to conduct a longitudinal study of its enVisionMATH curriculum materials. The study commenced in 2007–08 with second- and fourth-grade students, following them into third and fifth grades in 2008–09. This report summary presents the evaluation design and methods, an assessment of program implementation, student performance results, and a discussion of findings.
Study Design and Research Questions
The purpose of this study was to evaluate and assess the effectiveness of the enVisionMATH curriculum in helping students attain critical math skills and to document the teachers’ implementation of the enVisionMATH program. The study employed a longitudinal randomized, controlled trial (RCT) design with the random assignment of teachers to treatment and control groups. That is, teachers within each participating school were randomly assigned to use either enVisionMATH materials or their current school math curriculum. This study design was utilized in order to address all quality standards and criteria described in the What Works Clearinghouse (WWC) Study Review Standards (2008). Specifically, the study addressed the following overarching evaluation questions:
Do students in treatment groups demonstrate significant learning gains in math during the study period?
How does the math performance of students in treatment groups compare to that of students using other