**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 (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 (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. |