Integrated Mathematics, Science, and Technology (IMaST) Program Characteristics

Each text includes the full student text of each activity followed by teaching suggestions. Each of the activities in the Teacher's Edition is prefaced with information to help the teacher organize instruction of that activity. This introductory material summarizes what students will be doing; provides a detailed, itemized equipment and materials list; and provides background information and/or suggestions for preliminary or accompanying activities for use in helping to initiate, reinforce, or extend concept development. Careers related to the activity's subject matter are also included in this introductory material. A section entitled, Cyberspace Connections, provides key search terms that have been included at the end of each learning cycle as a guide for you and your students to complete further research about the concepts using the Internet. The Teacher's Edition also includes activity assessments (and accompanying rubrics outlining grading criteria) for each activity.

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Problem solving is used as a key instructional technique throughout the IMaST program. As students work to explore and solve the situations and problems presented to them in the activities, they develop strong critical thinking skills such as predicting, hypothesizing, planning, controlling variables, analyzing, interpreting, and assessing. Problem solving becomes second nature to students in the IMaST program.

Although each discipline has its own problem-solving approach, there are strong relationships among them. Teachers are naturally more familiar with, and usually prefer, the terminology associated with their own field. On the other hand, in an integrated program such as IMaST, common problem-solving terminology leads to much less confusion among students. Therefore, a generalized description of problem solving was developed by the IMaST Design Team and incorporated into each of the modules. This approach is referred to by the acronym "DAPIC" - Define, Assess, Plan, Implement, and Communicate.

• Define

  Stating the problem clearly in a sentence or two often helps to identify just what the problem is and may even suggest a possible solution. This statement (or question) identifies matters involving doubt, uncertainty, or difficulty as well as the limitations related to specific need or opportunity. It defines what the student wants or needs to know. Although the problem can be identified by the teacher, it is most often identified by the student from experience.

• Assess

  In this stage, conditions surrounding the problem are evaluated. Any and all information that can be used to develop a good solution must be gathered. Examples of relevant information might include learning what barriers or difficulties exist or learning what solutions have been tried in the past, but failed, and then investigating why they failed. This information may come from research, or it can be obtained through experimentation. The goal is to learn as much as possible about the problem before developing a plan.

• Plan

  At this stage, a number of alternative solutions to the problem are suggested and analyzed. This may mean using an experimental design in which variables are controlled in order to determine the best (or most workable) solution for the particular situation. Then, a plan for putting this solution into effect must be developed.

• Implement

  The plan is carried out. Data are systematically collected and analyzed according to the plan; modifications to the plan are made as the need arises.

• Communicate

  The results are analyzed, conclusions are reached, and the results are shared with others. This takes the form of written or oral reports, predicting consequences, and even identifying new problems to solve.

The DAPIC problem-solving process has no definite starting point or order. It is not a series of steps that must be followed in the same order each time. In fact, careful observation of successful problem solvers reveals that they often use a non-linear approach. Although some students may choose to solve problems by going through the stages in linear order, more flexibility is often required. For example, a problem may occur while assessing, developing, or implementing a plan. Likewise, communication may be necessary at any stage of the problem-solving process. The DAPIC model allows for all of these variations. However, students should be encouraged to define and redefine, if necessary, the problem as soon as possible. This process will help students prioritize their actions.

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In response to research supporting Constructivist learning theory, a learning cycle is used throughout the curriculum.

• Exploring

  During this phase, students are directed to manipulate objects, test materials or products, observe carefully, collect data, and/or make general observations. Sometimes they are asked to make predictions, which can act as useful indicators of student understanding.

  During the Exploring phase, the teacher circulates among the students to observe, guide, and monitor their progress. The teacher is a facilitator during the Exploring phase, not the dispenser of knowledge.

• Getting the Idea

  This is a reflective stage that is usually accomplished as a structured class discussion. During the discussion, students share the data collected and problems encountered during Exploring. Often this involves pooling data to form a class data set. The discussion should allow as much student interaction as possible and lead the students to arrive at or construct the desired idea or concept for themselves. The teacher uses key questions to coax the class toward the concept or idea of the lesson. These key questions are designed to aid students to:

  1. Organize and explain discrepancies in class data
  2. Discuss ideas and explanations for the observed phenomena
  3. Suggest things to consider.

• Applying the Idea

  In this phase, students are asked to apply the concept, generalization, or idea developed in Exploring and Getting the Idea to a new situation. In this section, students supply evidence that they have internalized the idea, met the objectives, and understood the concept. The students accomplish these goals by experimentating with new variables, completing written exercises (e.g., questions, problems, or reports), developing new designs, making projects, and/or reading assignments.

• Expanding the Idea

  This phase is similar to the Applying the Idea stage. Questions, problems, activities, and/or situations presented in this phase require students to extend the concept to new situations. This phase is designed to cause students to connect the concept to daily life, to other disciplines, and/or to a global context. This section may also show new aspects of the concept.

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Learning Cycle Phase	Teacher's Role	Student's Role
Exploring	Gathers materials Keeps students on task Provides safety and skills instructions Asks questions Promotes journal writing as needed	Interacts with materials Designs and builds Collects and records data Makes predictions
Getting the Idea	Leads class discussion Questions students Corrects misconceptions Supplies terms Builds sets of class data	Compares data Answers questions Forms generalizations Writes in journal
Applying the Idea	Supplies materials Assures safe practice Keeps students on task Corrects lingering misconceptions	Applies concepts, principles, and laws Designs and makes projects Conducts experiments Solves problems
Expanding the Idea	Makes sure resources are available Asks questions to help students make connections with broader contexts	Expands concepts to more general or global situations through reading, research, and journal writing

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Group work is often justified by the fact that, as adults, students will, in nearly every circumstance, be expected to work with others. A more compelling reason is that research shows learning can be enhanced through a social process. While many of the learning activities in the IMaST curriculum are designed for students to work together in teams, the organization of these teams is left to the teacher. Some teachers prefer highly structured teams with clearly defined roles for each member of the team. Other teachers have more success with a loosely organized arrangement. However, it must be noted that field testing has shown that it is important to be directive in the establishment of the teams so that, over time, each student learns to work with everyone in the class.

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Rather than merely use a knowledge-based format to assess students' learning, the IMaST program assesses students' learning and understanding by evaluating how well students can apply the knowledge and skills they have developed to new situations. Student behavior—the things students can do, say, illustrate, or write—is viewed as evidence that learning has occurred. Concepts and skills are assessed at both the individual and group levels through completion of assignments that reflect students' abilities to reason, communicate (orally, graphically, and through modeling), and solve problems. This authentic assessment weds the knowledge, skills, and attitudes outlined in the lessons' objectives to the instructional method used in the classroom.

To assess discipline-specific skills, processes, and content, the Teacher's Resource Binder includes an activity assessment, along with a rubric outlining grading criteria, at the end of each activity. Each IMaST assessment activity is a problem-based performance measure of both content and process skills that relate to that activity's objectives. With slight modifications, these activity assessments may be used for either individual or team learning. In some cases, the Applying phase has been used to assess students' internalization of the concepts and skills. When the Applying has been designed for this role, rubrics and further instructions have been provided in the assessment section of the teacher edition.

The end-of-module assessment measures student success. This module assessment incorporates content and processes from all three disciplines—mathematics, science, and technology. This Module Assessment includes an encompassing authentic activity and a portfolio assignment.

For the portfolio, each student writes a key concept essay that focuses on the module's key concepts. For each of the key concepts, students summarize the investigations they conducted in relation to that concept and what they learned from their investigations. Students attach to this essay samples of journal sheets (as well as samples of design sketches, graphs, tables, etc., that they may have developed in addition to those on journal sheets) that substantiate the main ideas in their essay. Thus, the portfolio consists of the essay and the chosen substantiating materials. A rubric outlining criteria for evaluating students' success in developing their portfolio is included in the Teacher's Resource Binder.

Generic forms have been provided at the end of the teacher edition to assess students' use of the DAPIC process. This form could be used at any time during the module when students are engaged in the DAPIC process.

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There are two pathways for the implementation of the IMaST Program. First, a teacher may wish to enhance instruction with a learning cycle or two to address a particular concept. Perhaps other teachers will join her/him and an interdisciplinary unit of instruction can occur. As the teachers become more familiar with the content and pedagogy, more learning cycles can be incorporated, ultimately replacing the traditional instructional materials and methodologies.

The second pathway for the implementation of the IMaST program is to initiate systemic reform. This is seldom possible. In some situations, however, such as the creation of a STEM Academy, full implementation serves as the answer to a multitude of questions. To realize the full potential of the IMaST program, full implementation by the mathematics, science, and technology/engineering instructors is necessary. Every one of the 16 books is utilized in order. Shared planning time assures that each teacher is on schedule and the integration is being optimized.

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The integration of learning occurs in the lives of the students as students move from one discipline to the next. This requires the teachers to plan the instruction in ways to provide for integration, as well as to make changes in the program to accommodate the learning needs of students. It is obvious, then, that it is essential that the teachers using IMaST materials work together as they facilitate learning through the use of IMaST activities. For this reason, it is suggested that the cooperating teachers have a common planning period each day.

In classrooms that are not self-contained, team planning periods may initially be used to review the activities in the module to decide how they relate and support each other. Team members must also make decisions regarding at which point to facilitate the activities in each teacher's own discipline. Team planning sessions are also a time to compare notes on progress.

In addition to the pace of instruction, team planning must include matters such as the possibilities for sharing equipment and supplies, the assignment of students into teams, the scheduling of common events, such as field trips, preparing for and conducting public relations activities (such as an open house for parents), and classroom management strategies.

Experience has shown that anticipation is key. Teachers should anticipate the materials needed, behavior of students as they are assigned into teams, and how one's own activities relate to the activities going on in the other disciplines. This kind of anticipation will go a long way in helping to create an overall environment that provides a natural context for students to see connections among the disciplines, as well as to see the relevance of their learning to real life.

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Activities throughout the IMaST program involve students in hands-on learning. The materials and tools used in these activities are those commonly found in schools or, for the most part, can be purchased locally at a reasonable cost. The program does not require specialized equipment beyond what is typically found in the mathematics, science, and technology education laboratories in traditional programs.

The equipment and materials needed for the various sections of each activity are listed in the Teacher's Resource Binder at the beginning of each activity. These Equipment/Materials listings should be reviewed in advance to make sure that sufficient supplies of all needed equipment and materials will be readily available for each student or team. It should be noted that the Equipment/Materials listing often suggests simple, readily available, and economical substitutions or alternatives for some of the suggested materials. Additionally, teachers may develop their own creative substitutions or alterations.

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