Classroom Instruction that Works: Research-Based Strategies for Increasing Student Achievement by Robert J. Marzano, Debra J. Pickering, and Jane E. Pollock identifies 9 categories of instructional strategies that have been shown through research to be effective in the classroom. They base their conclusions on meta-analyses done by researchers at Mid-continent Research for Education and Learning. It is important to realize that there is much overlap in the strategies and the good techniques in one strategy are often used to advantage to enhance the learning effectiveness of other strategies. Below we list the strategies employed in this web activity. The strategies are listed in order of effectiveness as rated by the average effect size (achievement in standard deviation units).
Identifying Similarities and Differences: The concept of spatial dimension can be grasped better using the strategy of Indentifying Similarities and Differences. By doing the GPS activity, which is two dimensional, and learning geometry associated with two dimensions and then researching how a GPS works in three dimensions, students can gain a better understanding of dimension. Students should be asked to identify the similarities and differences they see between two and three dimensions.
Summarizing and Notetaking: Students should take notes as they do their research on how a GPS works. An effective note taking structure is to use the left side for notes in text, perhaps an outline, and the right hand sides for drawings and other graphical aids that help organize and clarify their observations. Finally, a summary can be written along the bottom as the groundwork that holds the structure together (download an MSWord version of the note taking structure). For the most effective use of this technique, have your students discuss and compare their notes and summaries.
Reinforcing Effort and Providing Recognition: Reinforcement students positively when they correctly identify the Norbert and Zot place. The very best reinforcement and recognition comes from parents, teachers, and other students.
Homework and Practice:You should assign researching how a GPS works as homework. The students can get practice in geography each time they follow Norbert and Zot to a new location.
Nonlinguistic Representations: This activity is replete with nonlinguistic representations such as graphics and animations. If the students deconstruct the Squeak project to find out how it works and construct a modified project using the graphical tiles, they will be working with nonlinguistic representations of ideas (programming commands) and mathematics (arithmetic). The natural integration of these representations enhances the learning experience.
Cooperative Learning: Setting up cooperative learning groups is the recommended way to maximize student learning in this activity. Five defining elements of cooperative learning are: positive interdependence, face-to-face promotive interaction, individual and group accountability, interpersonal and small group skills, and group processing. Reciprocal Teaching is a research-based strategy that can be used effectively with cooperative groups. The four phases are summarizing, questioning, clarifying, and predicting. If you assign groups to research how a GPS works, they can divide the task into parts (satellites role, transmitting and receiving signals, the computer in the GPS, geometry, etc.) or they could each work independently and come back later as a group. Then through discussion the team members can summarize, question and clarify. Students could be asked to predict the geometry of a GPS in a one dimensional world and could be challenged to think of four dimensions, but that would be much harder. A good resource for that would be the book Flatland by Edwin Abbot and students would enjoy reading the story, which has interesting political and social dimensions.
Setting Objectives and Providing Feedback: Objectives that are set shouldn't be too narrowly focused or learners tend to miss too much related material. For this activity a good objective would be to understand the difference between two and three dimensions. Feedback on exams or projects has been shown to enhance learning and the best form is an explanation as opposed to just being given the correct answer. Students could offer feedback to other students through discussions explaining what they found in their research. If you give your students a test on the activity, research shows that the optimal time is one day after exposure to the material.
Generating and Testing Hypotheses: Both inductive (abstracting a principle from a set of specific observations) and deductive (using a principle to predict a specific result) reasoning can be used to advantage to promote learning. Deductive reasoning activities have been shown to be more effective, but it depends on the circumstance. The division into inductive and deductive is often blurred and the concepts are most valuable when considered as two extremes of reasoning. You should encourage your students to predict what would be required to have a GPS in a one dimensional world and ask them to refine their predictions as they discuss them with their group members. Some questions might be: Would it still make sense to talk of being somewhere on Earth? What would Earth be? Where would the satellites be? How many satellites would you need to find your location anywhere along a line? There isn't just one correct answer to these questions, depending on how you define Earth. A fun book to read to help your students think about this problem is Flatland by Edwin Abbot. Students could progress from a more deductive approach to a more inductive approach. It has also been shown valuable for students to explain their hypotheses and predictions.
Cues, Questions, and Advance Organizers: These strategies all take advantage of students' prior knowledge and are good ways to start a lesson. As you give cues and ask questions, keep in mind that higher-order questions are more effective and students are more interested in things they already know something about. For example, if your focus is geometry, a good starting question would be "What is a circle?" Remember that it is important to wait after asking your questions to give the students time to collect their thoughts before they respond - you will have a much better discussion. Advance organizers are a way of giving your students a brief "heads up" before starting a topic - they aren't outlines or summaries. Research shows the most effective advanced organizers are expository, followed closely by skimming. In this case a story involving Norbert and Zot with a discussion of space and geometry followed by brief definitions of theorem, dimension, point, circle, sphere, etc. would be in order. If your focus is geography, you could come up with a similar plan.