|Does the instruction in Middle
Grades Math provide an opportunity for students to learn the benchmark ideas and
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
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
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
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
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
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 theyve learned are provided in ongoing assessments in which students work in pairs and note agreements and disagreements.
Instructional Category VI
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
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.