Does the instruction in Math Advantage provide an opportunity for students to learn the benchmark ideas and skills?

Numerous sightings were analyzed to determine the instructional criteria ratings for Math Advantage. The following chart provides a typical example of the sightings that were analyzed to determine each criterion rating. Looking at these sightings will provide a picture of the overall instructional guidance provided in the textbook.

TYPICAL SIGHTING CHART pdficon.gif (224 bytes)(Adobe PDF document)

The graph below depicts major strengths and weaknesses in the overall instructional guidance provided by Math Advantage. It does so by showing the average score Math Advantage received on each of the 24 instructional criteria, across all six of the benchmarks used for the evaluation.

INSTRUCTION HIGHLIGHTS CHART pdficon.gif (224 bytes)(Adobe PDF document)


Overall, analysts rated Math Advantage as unsatisfactory in helping students achieve the number, geometry, and algebra benchmarks used for the evaluation. The following describes the seven instructional categories and their criteria and summarizes the analysts’ justification for their ratings for Math Advantage.


Instructional Category I

Identifying a Sense of Purpose
Part of planning a coherent curriculum involves deciding on its purposes and on what learning experiences will likely contribute to achieving those purposes. Three criteria are used to determine whether the material conveys a unit purpose and a lesson purpose and justifies the sequence of activities.

All chapters present a unit purpose through a set of objectives and a unit project, and the lesson purpose is stated on the opening page of each lesson; however, the effectiveness is inconsistent from one benchmark to another. The material addressing the algebra benchmarks does not provide a unit or lesson purpose. The same is true for material dealing with number ideas and skills. Material addressing the geometry benchmarks does a better job of providing a purpose for chapters and activities. In all cases, the rationale for the activity sequence must be inferred from the way activities are clustered.


Instructional Category II

Building on Student Ideas about Mathematics
Fostering better understanding in students requires taking time to attend to the ideas they already have, both ideas that are incorrect and ideas that can serve as a foundation for subsequent learning. Four criteria are used to determine whether the material specifies prerequisite knowledge, alerts teachers to student ideas, assists teachers in identifying student ideas, and addresses misconceptions.

For the most part, the material explicitly states prerequisite knowledge or skills in a variety of ways. However, for some benchmarks, such as the number concepts and algebra graph concepts, prerequisite connections must be inferred. Possible misconceptions and some ways for helping teachers identify these ideas are noted in Troubleshooting sections and Common Error Alerts, but there are few strategies or suggestions to teachers for dealing with these misconceptions.


Instructional Category III

Engaging Students in Mathematics
For students to appreciate the power of mathematics, they need to have a sense of the range and complexity of ideas and applications that mathematics can explain or model. Two criteria are used to determine whether the material provides a variety of contexts and an appropriate number of firsthand experiences.

A great variety of contexts are given for all the benchmarks except for number concepts. Students gain experience with a range of real-world contexts through investigations, teacher demonstrations, and discussions. The text is strong in including activities that promote firsthand experiences for geometry skills and ideas. There are some suggestions for firsthand activities for all benchmarks through Learning Labs and Idea Files; however, most lessons do not engage students in firsthand experiences.


Instructional Category IV

Developing Mathematical Ideas
Mathematics literacy requires that students see the link between concepts and skills, see mathematics itself as logical and useful, and become skillful at using mathematics. Six criteria are used to determine whether the material justifies the importance of benchmark ideas, introduces terms and procedures only as needed, represents ideas accurately, connects benchmark ideas, demonstrates/models procedures, and provides practice.

Math Advantage is inconsistent in building a case for the importance and validity of mathematics ideas. Although real-world applications are referenced, the mathematics content is sometimes de-emphasized, and the teacher must clarify and make the connections for students. The material does an effective job of introducing terms and procedures in conjunction with experiences and presenting accurate and comprehensible representations of mathematics ideas. For most benchmarks, there are clear connections among benchmark ideas. Overall, procedures are clearly demonstrated in the student text, although teacher commentary is weak. Practice is included throughout the material in a variety of situations, although most practice involves familiar tasks with little application.


Instructional Category V

Promoting Student Thinking about Mathematics
No matter how clearly materials may present ideas, students (like all people) will devise their own meaning, which may or may not correspond to targeted learning goals. Students need to make their ideas and reasoning explicit and to hold them up to scrutiny and recast them as needed. Three criteria are used to determine whether the material encourages students to explain their reasoning, guides students in their interpretation and reasoning, and encourages them to think about what they’ve learned.

The material provides opportunities for students to express and attempt to clarify their ideas about the benchmarks; however, there is little evidence throughout the material that students have opportunities to justify or interpret their thinking or get feedback from others. Most of the material addressing the benchmarks, particularly the number and algebra skills and concepts, is weak in guiding student interpretation and reasoning. The material does not identify opportunities for students to think about what they’ve learned nor make suggestions to teachers on how to encourage this.


Instructional Category VI

Assessing Student Progress in Mathematics
Assessments must address the range of skills, applications, and contexts that reflect what students are expected to learn. This is possible only if assessment takes place throughout instruction, not only at the end of a chapter or unit. Three criteria are used to determine whether the material aligns assessments with the benchmarks, assesses students through the application of benchmark ideas, and uses embedded assessments.

Math Advantage is most effective in the alignment of assessment items or tasks with benchmark ideas. Assessment tasks are weak in requiring application of number and algebra equations concepts. While there are application level assessment tasks for some benchmarks, tests are primarily multiple choice items at the comprehension and knowledge levels. There is no evidence that the text effectively and routinely includes embedded assessment as part of the instructional design.


Instructional Category VII

Enhancing the Mathematics Learning Environment
Providing features that enhance the use and implementation of the textbook for all students is important. Three criteria are used to determine whether the material provides teacher content support, establishes a challenging classroom, and supports all students.

There is little evidence of resources to help teachers improve their understanding of mathematics content or for creating an environment that welcomes curiosity, creativity, and healthy questioning for any of the benchmarks. Attention to diversity is evident in pictures including women, minorities, and persons with disabilities; however, there are no references to contributions by these groups to mathematics-related fields. There are suggestions in ancillary materials for modifying instruction for students with special needs.

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