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

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


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 in Context conveys the purpose to students at the beginning of each unit, and students have the opportunity to think about the purpose throughout the unit activities. Goals are listed, and the steps to achieve the goals are provided to the teacher. The material does not convey or prompt the teacher to convey how the lessons and activities are connected and does not engage students in thinking about what they have learned and what they need to do next; however, notes throughout the sections refer back to previous lessons or modules, and students are reminded of previous knowledge.


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.

In each of the units, prerequisites are identified and, on most pages, suggestions are given to alert the teacher to students’ commonly held ideas. The Hints & Comments section tells teachers how a student may respond to certain tasks, but there is no consistent advice on addressing these. The text alerts the teacher to commonly held students ideas and suggests general strategies for addressing them; however, it does not provide questions, tasks, or activities at the site of the alert, only in prior or future units. Activities focus on conceptual underpinnings before introducing a formula, so common misconceptions are addressed before they become operative, which decreases the need to correct misconceptions.


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.

The use of real world contexts is the central strategy and approach throughout all of the units. Many different types of applications and topics, such as sports, entertainment, construction, science, and environmental news, are employed in investigations that develop and practice the mathematical ideas in the sampled benchmarks. A heavy emphasis is placed on the use of hands-on experiences and data collection to teach the benchmark ideas. Investigations use data collection, measurement, and manipulative materials. Data are graphed, summarized, and expressed in a variety of ways to explore connections and relationships.


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.

Mathematics in Context makes a case for benchmark ideas and clearly explains their validity and importance. Summaries at the end of each section make connections and reiterate the importance of benchmark ideas by providing realistic experiences. Mathematical terms are used in context but are not always formally defined in the student pages. The material uses a wide variety of representations, such as diagrams, models, graphs, and drawings, to make the ideas clear for students. Connections among benchmark ideas and among unit topics are provided in the Unit Focus and Connections sections. Concepts are often developed through an inductive process that models the way a symbol or expression represents a concept or procedure. A variety of practice problems and exercises are available within the activities and at the end of units. Instead of using drill exercises, the material provides practice experiences that include computations derived from discussions, work done in groups, and problem solving.


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.

Students have many opportunities to share their reasoning orally and in writing. Usually, the teacher is encouraged to discuss student solutions and guide student work. Teachers are directed to probe student work and ask students to re-think their reasoning and convince others about the usefulness of their methods. The text contains few questions that encourage students’ own reflections or suggestions to help students think about what they’ve learned.


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 assessment problems and exercises on concepts and skills require the application of benchmarks and provide good alignment with learning goals. Assessment items and tasks are provided at the end of each unit that are appropriate and aligned with the benchmarks. Writing is a key focus for assessment. The only suggestions to teachers for modifying assessments for students with special needs are found in extension problems. Many assessment ideas are embedded throughout the activities, especially for the number benchmarks. Assessments include notes to teachers that give ideas on how to probe student thinking, but suggestions for addressing difficulties are located in hands-on activities rather than assessment items.

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.

Background information that is provided about the mathematics is helpful and useful for developing teacher knowledge. The format of Mathematics in Context is designed to promote creativity and curiosity and to encourage discussion. The material provides a variety of ways for students to express ideas, such as by writing, drawing pictures, creating tables, and using hand gestures, and encourages students to bring material in from home and to make everyday connections. Pictures are mainly illustrations and include middle school boys and girls of various ethnic backgrounds; however, activities have few illustrations showing the contributions of mathematicians, women, or minorities. There is little in the way of explicit suggestions for alternative formats or ways to modify activities for students with special needs.

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