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

Numerous sightings were analyzed to determine the instructional criteria ratings for Middle School Math. 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 Middle School Math. It does so by showing the average score Middle School Math 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 Middle School Math 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 Middle School Math.


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.

Middle School Math identifies and maintains a sense of purpose by providing a chapter overview that is clear and interesting and asking the teacher to convey the purpose to the students through a chapter project; however, these projects are sometimes only related to the topic and not the substance of a benchmark idea. The lesson purposes are communicated to students by "You’ll Learn" comments and instructional prompts called "Where are we now?" and "Where are we going?" Lesson Links allow students to recall what they have learned earlier and how it relates to the present lesson. These components tend to be broad statements and are not particularly helpful in the lessons that present the algebra benchmarks.


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.

The "Where are we now?" questions and the Lesson Links statements found at the beginning of each lesson are not explicit enough to be very helpful in addressing prerequisite knowledge or skills. The notes that remind students of prior knowledge are not sufficient to determine if students actually have that knowledge. A few relevant misconceptions are mentioned in the text in the Error Prevention and Meeting Individual Needs sections, but the hints and suggestions are inconsistent in alerting the teacher and helping to address commonly held ideas.


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.

The material engages students with a variety of contexts and firsthand experiences. For the number concept ideas, the text uses grid models, drawings of shaded rectangles and circles, measuring tools, rulers, and polygon blocks. A smaller variety of contexts are used in developing the ideas in the number skills benchmark. The geometry activities include computer applications (drawing), geoboards, grid paper, measuring, and building of geometric models. There are a variety of firsthand activities and applications for algebra graphing, including writing stories to accompany graphs, plotting points on a coordinate plane of a classroom, and performing experiments. There are fewer activities of this type for the algebra equation benchmark.


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.

The material presents a reason for learning benchmark ideas with an exploration activity found at the beginning of each lesson. Terms and procedures are introduced in conjunction with experiences and with symbolic, pictorial, and graphical examples that are accurate and, for the most part, comprehensible to students. The algebra equation ideas are somewhat abstract and lack connection with informal activities. Connections among benchmark ideas are mainly at the topic level or only implied in general activities under the heading "Check Your Understanding." The sequence of activities, examples, and questions provide for clear demonstration of procedures and skills; however, commentary on these is not provided. Practice and application are appropriate except for the algebra equations, which provide skill-based practice that is not focused on benchmark concepts


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.

Middle School Math provides few opportunities for students to express their thinking about the benchmark ideas. The exploration activities and Critical Thinking sections allow some opportunities for students to express their ideas, but there are no provisions for feedback by students or teachers. The material does a satisfactory job in guiding interpretation and reasoning about number skills but does not accomplish this for any of the ideas in the other benchmarks. The Check Your Understanding exercises are the only attempt to provide students with an opportunity to think about what they’ve learned, but the exercises do not have students assess their progress, think about how their ideas have developed, or revise their initial ideas about benchmarks.


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.

Assessment items are aligned with the benchmark ideas; however, the tasks for algebra benchmarks miss the mark and are mainly focused on skills rather than concepts. The chapter assessments do provide applications in addition to simple use of computation, but more applications are provided for number ideas than for geometry or algebra ideas. Embedded assessments are found in Practice and Check Your Understanding questions, but there are few suggestions for modifying instruction based on the results of these assessments.


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.

Teacher Talks and In-Service Workshops sections attempt to contribute to teacher content learning but are too general to be very helpful. The chapter projects provide the only opportunities for students to be creative. These projects are somewhat separated from the day-to-day work and are stronger in chapters dealing with geometry ideas than with number or algebra ideas. Middle School Math provides for diverse needs through inclusion, extension, and challenge activities as well as through a multilingual handbook.

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