**Does the instruction in ***Mathematics
Plus* provide an opportunity for students to learn the benchmark ideas and skills?Numerous
sightings were analyzed to determine the instructional criteria ratings for *Mathematics
Plus*. 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 (Adobe PDF document)
The graph below depicts major strengths and weaknesses in the overall instructional
guidance provided by *Mathematics Plus.*** **It does so by showing the average
score* Mathematics Plus* received on each of the 24 instructional criteria, across
all six of the benchmarks used for the evaluation.
INSTRUCTION HIGHLIGHTS CHART (Adobe PDF document)
Overall, analysts rated *Mathematics Plus *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* Mathematics Plus.*
**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.
*Mathematics Plus* provides a purpose at the beginning of the chapters and lessons
in the teacher’s edition, implying that the teacher is to relate the purpose to the
students. The purpose of the chapters and lessons is not made explicit to the students.
The material seems to have a rationale, although it is unstated, for the overall sequence
of the lessons; the sequence reflects the stated purpose of the chapter. The format is
consistent throughout each textbook.
**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.
There are only infrequent attempts to make the teacher aware of prerequisite knowledge
or skills. For the number and geometry skills, the prerequisite knowledge is more
apparent. Through Error Alerts, minimal support is given to help the teacher identify
students' commonly held ideas or misconceptions, but these often don’t provide
sufficient explanation of the difficulty students have with understanding ideas.
Suggestions and assistance for addressing student misconceptions are in the teacher notes
section accompanying each lesson.
**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.
*Mathematics Plus* provides numerous activities that address benchmark ideas about
number and geometry and provides a variety of contexts and firsthand experiences.
Manipulative activities include drawing activities using graphing paper in the
algebra-related exercises; protractors, rulers, compasses, geoboards, and pattern blocks
are used in the geometry lessons. Some activities call for the use of a calculator or
computer for extended practice. Other than activities using graph paper, few hands-on
experiences are provided in addressing algebra graphing and equations concepts.
**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.
With the exception of the criterion "justifying the importance of benchmark
ideas," the text adequately develops the mathematical ideas in the sampled
benchmarks. *Mathematics Plus* only implicitly communicates the importance or
validity of the mathematical concepts or skills. Terms and procedures are introduced
appropriately and with accuracy and without undue use of extraneous mathematics
vocabulary. Representation of ideas and demonstration of the use of skills and knowledge
are accurate and comprehensible. Connections are made between ideas through the use of
numerous examples and activities. Practice is present throughout the lessons including
word problems that require detailed responses that go beyond a numerical or one-word
answer.
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.
*Mathematics Plus* rarely encourages students to explain their reasoning. The
"What Did I Learn?" section provides questions about the lessons within the
chapter, but the students are not given the opportunity to develop their own ideas or
reflect on their understanding. They are only asked direct and mostly routine questions
about the lesson. When students are asked to express ideas, there are few opportunities
for students to receive explicit feedback on clarifications and justifications.
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.
The text contains numerous assessment items and tasks that are aligned and on target
with the benchmark ideas; however, assessment items that require application of benchmark
concepts and skills are not as numerous, and embedded assessment is not widely used in the
lessons.
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 section at the end of the textbook called Alternate Teaching Strategies does not
focus on teacher content understanding that might help improve instruction or on teaching
specific benchmark ideas. The few activities that do prompt student creativity are not
consistent enough to promote a sense of exploration and individual development. The
material avoids stereotypes and contains relevant illustrations of the contributions of
women and minorities in mathematics. |