Does the instruction in Middle Grades 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 Grades 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 Grades Math. It does so by showing the average score Middle Grades 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 Grades 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 Grades 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 Grades Math only implicitly provides a sense of purpose. There are no clear real-world applications in the text that would help to provide a sense of purpose and make the material appear more interesting. In each lesson, a What's Ahead section states the purpose of lessons to the student as well as to the teacher but does not relate it to the purpose of the chapter. There is no apparent rationale for the overall sequence of the activities or lessons.


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 Flashbacks segments sometimes state prerequisite ideas or skills that students should know, but few prerequisites are stated for the number concepts and algebra benchmarks. Teachers may be alerted to students’ commonly held misconceptions in the Error Alerts and Think and Discuss sections, but the text does not always clarify the nature of the misconceptions. Suggestions from the Connecting to Prior Knowledge section can be used as potential assessments of student ideas, but there is little guidance on probing student responses. The Error Alerts and Think and Discuss sections attempt to address student misconceptions that are relevant to the benchmark ideas, but there are no questions that would help students progress from their initial 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.

Middle Grades Math includes experiences in a variety of contexts related to some of the benchmark ideas. Activities involve topics such as science, physics, music, cooking, and money. A more limited variety of contexts are presented for the number and the algebra equation concepts. Hands-on experiences include manipulatives such as geoboards, fraction bars, calculators (scientific and fraction), protractors, compasses, and computer software applications. Some experiences are not appropriately sophisticated for the intended age range and not effective in helping students to understand more formal procedures or symbolic representations.


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.

A section at the beginning of each chapter attempts to provide a reason for learning the mathematics, but it is not always well aligned with benchmark ideas. Middle Grades Math often introduces terms before students have experiences with the concepts. The representations of ideas are accurate and mostly comprehensible, although there is not always sufficient variety. Only a few relevant connections are made among particular benchmark ideas. The text provides adequate demonstrations of benchmark skills and concepts that are comprehensible, although they sometimes lack commentary or justification. The number of practice activities and tasks is appropriate, and the activities are applicable to the ideas of the benchmarks; however, they are mostly routine and sometimes lack variety and in-depth 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.

Middle Grades Math provides few opportunities for students to express ideas. Even though students are often asked to explain their answers, the focus is not on clarifying or justifying their ideas. The material does not provide teachers with suggestions for feedback regarding student ideas. The Work Together activities only sometimes ask students to explain their reasoning. A few opportunities for students to think about what they’ve learned are provided in ongoing assessments in which students work in pairs and note agreements and disagreements.


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.

Only a few assessment items are aligned with the specific ideas of the selected benchmarks. Assessment is mainly limited to the test and cumulative review at the end of the chapter. The Student Self-Assessment Surveys and other similar activities are good embedded assessment tasks that have the potential to allow the teacher to obtain information about the students' knowledge; however, there are no suggestions as to how to use this data to help students or modify instruction.


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 bibliography lists reading materials for teachers and students but does not address specific skills or particular ideas. Middle Grades Math attempts to help teachers create a challenging classroom environment through its Work Together section, but there is little evidence that the material provides occasions for the students to take risks or ask questions. The material supports all students by avoiding stereotypes or language that might be offensive to a particular group. In the Work Together section, the material attempts to connect mathematical ideas to various people (both mathematicians and non-mathematicians) and cultures.

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