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

Numerous sightings were analyzed to determine the instructional criteria ratings for Mathematics Plus. 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 Mathematics Plus. It does so by showing the average score Mathematics Plus 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 Mathematics Plus 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 Mathematics Plus.


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.

Mathematics Plus provides a purpose at the beginning of the chapters and lessons in the teacher’s edition, implying that the teacher is to relate the purpose to the students. The purpose of the chapters and lessons is not made explicit to the students. The material seems to have a rationale, although it is unstated, for the overall sequence of the lessons; the sequence reflects the stated purpose of the chapter. The format is consistent throughout each textbook.


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.

There are only infrequent attempts to make the teacher aware of prerequisite knowledge or skills. For the number and geometry skills, the prerequisite knowledge is more apparent. Through Error Alerts, minimal support is given to help the teacher identify students' commonly held ideas or misconceptions, but these often don’t provide sufficient explanation of the difficulty students have with understanding ideas. Suggestions and assistance for addressing student misconceptions are in the teacher notes section accompanying each lesson.


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.

Mathematics Plus provides numerous activities that address benchmark ideas about number and geometry and provides a variety of contexts and firsthand experiences. Manipulative activities include drawing activities using graphing paper in the algebra-related exercises; protractors, rulers, compasses, geoboards, and pattern blocks are used in the geometry lessons. Some activities call for the use of a calculator or computer for extended practice. Other than activities using graph paper, few hands-on experiences are provided in addressing algebra graphing and equations concepts.


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.

With the exception of the criterion "justifying the importance of benchmark ideas," the text adequately develops the mathematical ideas in the sampled benchmarks. Mathematics Plus only implicitly communicates the importance or validity of the mathematical concepts or skills. Terms and procedures are introduced appropriately and with accuracy and without undue use of extraneous mathematics vocabulary. Representation of ideas and demonstration of the use of skills and knowledge are accurate and comprehensible. Connections are made between ideas through the use of numerous examples and activities. Practice is present throughout the lessons including word problems that require detailed responses that go beyond a numerical or one-word answer.


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.

Mathematics Plus rarely encourages students to explain their reasoning. The "What Did I Learn?" section provides questions about the lessons within the chapter, but the students are not given the opportunity to develop their own ideas or reflect on their understanding. They are only asked direct and mostly routine questions about the lesson. When students are asked to express ideas, there are few opportunities for students to receive explicit feedback on clarifications and justifications.


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.

The text contains numerous assessment items and tasks that are aligned and on target with the benchmark ideas; however, assessment items that require application of benchmark concepts and skills are not as numerous, and embedded assessment is not widely used in the lessons.


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.

A section at the end of the textbook called Alternate Teaching Strategies does not focus on teacher content understanding that might help improve instruction or on teaching specific benchmark ideas. The few activities that do prompt student creativity are not consistent enough to promote a sense of exploration and individual development. The material avoids stereotypes and contains relevant illustrations of the contributions of women and minorities in mathematics.

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