Algebra Textbooks Evaluation
Instructional Criteria
The criteria for making judgments about instruction were derived from research
on learning and teaching and on the craft knowledge of experienced educators.
Sources included Chapter 13, "Effective Learning and Teaching,"
of Science for All Americans; Chapter 15, "The Research Base,"
of Benchmarks for Science Literacy; Research Ideas for the Classroom:
Middle Grades Mathematics, (Owens, 1993); and Handbook of Research
on Mathematics Teaching and Learning, (Grouws, 1992). From these and other
sources, 24 criteria—arranged into seven categories—were selected
to serve as a basis for the instructional analysis. (Read
about the curriculum analysis procedure in detail)
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.
I.1 Conveying Unit Purpose
I.2 Conveying Lesson Purpose
I.3 Justifying Sequence of Activities
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.
II.1 Specifying Prerequisite Knowledge
II.2 Alerting Teacher to Student Ideas
II.3 Assisting Teacher in Identifying Ideas
II.4 Addressing Misconceptions
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.
III.1 Providing Variety of Contexts
III.2 Providing Firsthand Experiences
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.
IV.1 Justifying Importance of Benchmark Ideas
IV.2 Introducing Terms and Procedures
IV.3 Representing Ideas Accurately
IV.4 Connecting Benchmark Ideas
IV.5 Demonstrating/Modeling Procedures
IV.6 Providing Practice
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.
V.1 Encouraging Students to Explain Their Reasoning
V.2 Guiding Interpretation and Reasoning
V.3 Encouraging Students to Think about What They've Learned
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.
VI.1 Aligning Assessment
VI.2 Assessing through Applications
VI.3 Using Embedded Assessment
Category VII: Enhancing the Mathematics Learning
Environment. (Because the criteria included in Category VII were not
scored numerically, ratings for them are not displayed on the summary charts
elsewhere on this web site. A summary of analysts' comments will be provided
in the narrative report for each textbook.) 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.
VII.1 Providing Teacher Content Support
VII.2 Establishing a Challenging Classroom
VII.3 Supporting All Students
Continued: Idea Sets Used to Evaluate Algebra Textbooks
