New Review: BFW’s Mathematical Models with Applications

[Source: BFW Publishing]

[Source: BFW Publishing]

Bedford, Freeman, & Worth’s Mathematical Models with Applications: Texas Edition is a comprehensive high school mathematics course available in print format. Content emphasizes concepts presented in Algebra I and Geometry in order to prepare students for Algebra II; all prerequisite topics for Algebra II are addressed. Instruction emphasizes the development algebraic, graphic, numeric, and geometric reasoning, as well as the use of functions to model real-world applications. Learning List recently published a review of this course.

The first part of the course focuses on algebra and the use of linear equations and functions. Concepts in geometry are presented at naturally occurring points throughout algebra instruction. The course’s latter chapters separately address personal finance, data analysis, and probability. Throughout instruction students learn to identify the relevant elements of a real-world problem, represent them symbolically in a mathematical model, and explain their reasoning in written and spoken formats.

Each chapter includes four types of lessons: (1) Activities, (2) Investigations, (3) Regular Lessons, and (4) Review and Practice. Activities are hands-on experiments that introduce topics and allow students to work collaboratively to collect and analyze data and answer related questions. Investigations are guided discovery activities in which students work with peers to analyze and solve real-world problems (e.g., create a function to help a business price its T-shirts). Regular Lessons provide direct instruction in key concepts. Each chapter includes one Review and Practice (RAP) lesson that reviews previously learned skills.

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What’s the Difference? Comprehensive vs. Supplemental Materials

20150327 21st wordleRecently, Learning List’s reviewers were confronted with an interesting question: How do we characterize materials as comprehensive or supplemental? Generally speaking, we understood that a comprehensive product would address all, or nearly all, of the standards for a particular grade and subject area, and a supplemental product would focus on a particular set of standards. However, our reviewers found that some materials that were designed to for supplemental instruction (e.g., test preparation resources) addressed nearly all of the standards for a given course. This prompted us to examine our thinking about what the labels “comprehensive” and “supplemental” mean in terms of instructional materials.

To clarify our understanding, we looked to how some states and districts define these terms. For example, California defines comprehensive, or “basic”, instructional materials to be “instructional materials that are designed for use by pupils as a principal learning resource and that meet in organization and content the basic requirements of the intended course (Educ. Code § 60010.a). In California, supplementary materials are materials that provide more complete coverage of a subject in a course, address diverse learning needs, and support the use of technology in the classroom (Educ. Code § 60010.l). Similarly, Carroll County Public Schools in Maryland defines comprehensive materials as “the primary source of instruction for students in a course” (emphasis in the original) and supplemental materials as “those items used to extend and support instruction and address the needs of all learners.”

Both definitions of comprehensive materials clarify that a comprehensive material is one that supports instruction for a course’s full curriculum and is provided for all students. Such materials would include broad, deep discussions of content; remediation and enrichment activities; formative and summative assessments; as well as teacher resources. Although neither definition specifies that a comprehensive resource must address 100% of the standards for a course, it seems reasonable that a “principal learning resource” or a “primary source of instruction” would need to be highly aligned to standards. Both definitions of supplemental materials indicate that supplemental resources are not designed to be the sole instructional resource for a course. Instead, supplementary materials complement, enrich, or extend the content of comprehensive resources. It seems reasonable that supplemental products will vary in terms of their alignment to standards. Some products may focus on a narrow set of standards, while others, such as test preparation resources, may provide a brief review of all standards.

[Source: Learning List]

[Source: Learning List]

Learning List’s Fill in the Gap™  tool helps educators identify supplemental materials that will extend content and address gaps in comprehensive resources. For each product in Learning List’s database that is not 100% aligned to standards, the Fill in the Gap tool suggests other products that address the missing standards. Suggested products may include both comprehensive and supplemental materials that address the missing standards. This allows educators identify the particular product or combination of products that meets the needs of their students.

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New Review: Jarrett Publishing’s World Geography

[Source: Jarrett Publishing]

[Source: Jarrett Publishing]

Jarrett Publishing’s Mastering the TEKS in World Geography is a supplemental test preparation resource for the STAAR end-of-course exam in world geography available in print format. Content provides complete coverage of the high school world geography TEKS. Instruction addresses physical, human, and political geography, as well as globalization. Learning List has recently published an alignment report and editorial review of this resource.

The first unit of Mastering the TEKS in World Geography addresses test taking, geography, and problem solving skills. Test taking instruction provides guidance in answering different types of questions (e.g., multiple choice, data analysis) and introduces the three-step “E-R-A” strategy: (1) Examine the Question, (2) Recall What You Know, and (3) Apply What You Know. Instruction in geography skills teaches students how to use and interpret different types of maps (e.g., thematic, historical, political). Instruction in problem solving outlines a set of steps to help students make informed decisions.

Video Courtesy of Jarrett Publishing

[Source: Jarrett Publishing]

Subsequent units cover physical, human, and political geography; geographic change(s) over time; and issues in globalization. Each chapter begins by identifying the TEKS and geographical terms addressed in instruction. Chapter openers list the “Important Ideas” students will learn and pose several essential questions to guide students’ thinking. Chapters include application exercises in which students apply their learning to new situations and “Acting as an Amateur Geographer” activities in which students complete short research projects.

Chapters end with Study Cards, “Checking Your Understanding” questions, and Concept Maps that help students prepare for the STAAR test. Study Cards summarize the key concepts and vocabulary covered in the chapter. Students are encouraged to illustrate the back of each card with a picture that visually represents the concept or term. Study Cards support student review individually and in groups. “Checking Your Understanding” presents a set of practice questions formatted to reflect the STAAR end-of-course exam.

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