Does the instruction in Middle Grades Math Thematics 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 Thematics. 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 Thematics. It does so by showing the average score Middle Grades Math Thematics 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 Thematics as satisfactory 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 Thematics.


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.

Each module, or set of lessons, begins with a stated theme that weaves throughout, addresses the content, and concludes at the end of the module. The section overview connects the theme with the math content to be studied in the module. Module topics are interesting, comprehensible, and motivating. Students have the opportunity to think about and discuss the purpose throughout the module. The Teacher’s Resource Book gives a clear discussion of how lessons and activities are intended to flow, how they are connected, and how they proceed from one to the other.


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.

Prerequisite information is available throughout the text and teacher’s information, but no explicit reference is made to guide teachers or students in using it to learn benchmark ideas. There are a number of sections in the Teacher’s Resource Book that alert teachers to commonly held ideas. Some list specific skills with which students may have difficulty and suggest what the teacher can do to help. There are a few examples in which Middle Grades Math Thematics explicitly addresses commonly held ideas with activities and strategies; however, there is not clear evidence that the material explicitly helps students challenge their common misconceptions with correct 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.

For most of the sampled benchmarks, Middle Grades Math Thematics provides many experiences in a variety of contexts. One exception is found in material addressing the graphing benchmark. There are many activities involving graphing but little variety among these activities. Students gain first-hand experiences working with a wide range of manipulatives (student-made and purchased), models, lab activities, games, etc., which are relevant to the benchmarks. There are some missed opportunities for making mathematical connections, however, especially in material related to the number and algebra benchmarks.


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.

One of the goals of the material seems to be to show the utility of mathematics. Problems posed at the beginning of each module justify the content and the purpose of the lessons that follow. Vocabulary is introduced with a written definition, then expressed in several forms and used in application problems. Vocabulary is taught with an emphasis on understanding not just memorization. The mathematics is represented in an accurate and comprehensible manner. Representations for developing geometry benchmarks are clearer for the skill benchmark than for the concept benchmark. Justifications of procedural skills are found in the teacher commentaries and in examples boxes. There are many opportunities to practice the benchmark ideas using familiar as well as nonroutine problems. The application problems require students to use numbers from tables and charts; the questions are interesting and comprehensible.


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 many opportunities for students to express, justify, clarify, and represent their ideas about the benchmarks. The material provides for feedback, but few suggestions are made to the student or the teacher on how to use responses to diagnose errors or further develop students’ ideas about the benchmarks. Questions do not always help to gauge progress on or encourage revision of specific ideas but tend to be more open-ended. The final project at the end of each unit does provide some opportunity for students to think about the ideas presented in the unit, get feedback from peers, and revise their ideas accordingly.


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.

Middle Grades Math Thematics includes a number of assessment tools both in the Teacher’s Resource Book and in the student text that are content-matched to the benchmarks. Extensive assessment is included in the chapter review pages, which test every concept taught. Alternative assessments, especially module projects, are an excellent source of novel assessments. Standardized and regular chapter tests are more traditional and procedural in nature. Assessment is embedded throughout the material in student practice pages; however, suggestions for probing students’ understanding and diagnosing future instructional needs are minimal and not aligned with benchmark ideas.


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.

References to build teacher content understanding are not annotated and provide minimal information on specific content. However, for the most part, the material does a satisfactory job of enhancing the learning environment. Middle Grades Math Thematics is effective in helping teachers to create opportunities for students to express creativity, take risks, reflect, and challenge ideas through a variety of activities. A wide variety of cultures are represented in pictures, scenarios, and printed form; however, references to contributions of women and minorities to mathematics-related fields are limited. The Teacher’s Resource Book addresses gifted, second language, and visual and tactile learners, among others.

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