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

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


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.

Every section within each unit begins with a listing of mathematical goals for each lesson in that section. At the end of each section, assessment activities return to the purpose. The purpose of each activity is found in a number of places throughout the material; however, the material does not generally prompt the teacher to convey the purpose. The sequence of activities outlined in the student’s and teacher’s books clearly describes mathematics goals and the systematic unit activities designed to achieve those goals.


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.

MathScape provides a list of prerequisites at the beginning of each unit in the teacher’s guide. A supplemental book called Hot Words, Hot Topics provides ways to address student understanding and skills. Notes from teachers who piloted the program offer suggestions for addressing various issues. A detailed pre-assessment at the beginning of each unit helps teachers determine student difficulties.


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 variety of contexts are used to develop the benchmark concepts and skills. Each unit is filled with firsthand experiences manipulating, exploring, discussing, and representing ideas along with various other approaches. The lessons open with exploratory activities, direct instruction, and problem-solving situations that apply skills and concepts from earlier lessons, continue with individual or group practice or extension of opening ideas, and close with a writing assignment for student reflection.


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 importance and validity of the benchmark ideas are developed using real-world contexts that continually involve students in developing understanding. Terms and procedures are introduced in conjunction with applications or examples. While representations are accurate and comprehensible, there are not a consistently appropriate variety of representations. Connections among benchmark ideas are strongest in material addressing the geometry and algebra benchmarks. Demonstrations are an integral part of each lesson’s activities. MathScape provides ample practice of skills at the end of each lesson as well as throughout the lessons in the form of writing letters, solving problems, making presentations, and creating objects.


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.

There are numerous opportunities for students to express themselves but inconsistent instances for students to receive feedback. Teacher notes provide some guidance on using student responses and often suggest questions that can be useful in guiding student understanding. Writing prompts help guide students’ thinking toward generalizations. A student self-assessment criteria sheet provides a way for students to monitor their skills and think about what they’ve learned after each phase in a unit.


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 tasks are available that align with all of the sampled benchmarks. The use of an entire lesson at the end of each section as an assessment provides opportunities for application of skills and ideas and not just brief responses. Assessment is embedded throughout the material and teachers are provided with assessment rubrics for each lesson.


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.

In the teacher’s edition, each section begins with an explanation of mathematics content. Numerous approaches to motivate students are provided along with many ways to express ideas and knowledge and many avenues for all students to be successful. The material avoids stereotypes and offensive language but does not make explicit reference to the contributions of women, minorities, and persons with disabilities. Opportunities are provided to challenge high-level students, but no other special need is addressed. While there are only a few specific suggestions to modify instruction for special needs, the nature of the material is likely to be accessible to a variety of learning styles and abilities.

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