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

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


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.

Heath Mathematics Connections is inconsistent in identifying a unit purpose. In some units it is clearly stated in either the teacher commentary or student text, while in others it is not evident. Each lesson includes a stated objective in both the teacher’s and the students’ materials; however the objective does not encourage students to think about the purpose of the activity or its connection to other activities or to prior or subsequent learning. Although there is no stated rationale for the sequence of activities, skills and ideas build upon one another within lessons and, in some cases, from one lesson to the next.


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.

Prerequisite knowledge is only implied in the material, with the exception of lessons addressing the geometry skills and the algebra graph benchmarks. When prerequisites do occur in previous lessons, the text does not point out where they can be found. The Common Error sections in some lessons alert the teacher to possible misconceptions, but there are few instances in which a strategy is suggested for teachers to help students clarify or explain their ideas. The Math Log and Think sections attempt to stimulate students to think about the concepts, but they fall short of having students make predictions about or explain the concepts. Little support is provided for eliciting student ideas, and there are no probing questions to identify students’ preconceived 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.

Most firsthand activities in this material are built in as alternate approaches, not as part of the structured lesson. There are a few meaningful activities in the main student text, and the Teacher’s Activity Bank is a source for firsthand experiences, but most are considered optional to the lesson. While there are some activities that provide real-world contexts such as those dealing with recipes, sales, and mileage, they are few in number and are not organized effectively so as to be integral to the other learning activities.


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.

Each lesson begins with an effort to motivate students, but the justifications for the importance of the mathematics are often too general to be relevant or convincing to students and are not always developed further through the lesson. Vocabulary that is listed in the introduction is not always developed in the lesson. In some cases, terms are introduced without sufficient explanation of their meaning or a context with which to associate them. Representations of mathematical concepts, procedures, and relationships are accurate but sometimes confusing for students. There is inconsistent evidence of connections among benchmark ideas and development of those connections. Throughout the material, there are examples in the teacher commentary of modeling and demonstration of skills or the use of knowledge. The materials include good activities for practicing ideas and skills, but the activities are almost exclusively drill and offer virtually no context for the problems.


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.

Providing students with opportunities to explain their reasoning appears to be a low priority for Heath Mathematics Connections. There are suggestions for ways that teachers can encourage students to share their thinking but a sufficient number of specific examples are not given. If teachers have students writing in math logs every day, students will have the opportunity to think critically about concepts and come up with their own ideas; however, there is little guidance for the teacher on how to give explicit feedback regarding responses or how to diagnose misconceptions. The material doesn't encourage students to reflect on their progress or give students opportunities to revise ideas. Only rarely are students asked to reflect on their questions. All monitoring of student learning is teacher-directed.


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.

There tend to be more assessment opportunities for skills benchmarks than for concepts benchmarks. For the skills benchmarks there are a wealth of assessment tasks that are closely content-matched to the benchmark ideas, but there are a very limited number of assessment tasks that require application of skills or concepts. An exception is the material addressing the algebra equation concepts benchmark. This material has a sufficient number of assessment tasks that focus on knowledge, comprehension, and application of benchmark ideas. Heath Mathematics Connections does provide assessment tasks as part of the instructional strategy; however, it does not include guidance to students on how to further understand benchmark ideas nor suggestions to teachers about how to probe for understanding or how to use embedded assessment to make instructional decisions.


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.

The material does not provide information that will help teachers improve their understanding of mathematics and its applications. There is a bibliography of resources for each lesson, but it is not annotated. There are few opportunities for students to express curiosity or creativity. The In-Text Inservice section describes best practices for teaching, but most resources fail to identify strategies for challenging students’ ideas and assumptions. The material avoids offensive language and stereotypes and includes photos and pictures that show diverse cultural populations. Each chapter begins with an overview that includes general suggestions for working with various special populations such as those who speak limited English and those who are gifted and talented.

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