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: Your students can use the strategy of Indentifying Similarities and Differences by noting the similarities and differences for their data and plots for hours from 7 to 11 AM and 1 to 5 PM. This is a good lesson in the importance of symmetry in mathematics.
Summarizing and Notetaking: Students should take notes as they make their observations and take their data. 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. In this case the graphical aids could be data tables and plots. 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). This method of notetaking would be effective in this activity if students put all their observations together on the same sheet or group of sheets. For the most effective use of this technique, have students discuss and compare their notes and summaries.
Reinforcing Effort and Providing Recognition: Reinforce students positively as they explore and make progress on their observations and discussions and as they begin to understand and organize their data by plotting and using the power of mathematics. Have the students present their data and analysis so you and the class can recognize their good work. If some groups of students are capable of going on to the more advanced challenges, have them make presentations to the rest of the class. The very best reinforcement and recognition comes from parents, teachers, and other students.
Homework and Practice: You should assign reading about the Earth, Sun and sundials. Students should tabulate their data and plot their data on graph paper. When they are finished with the challenges you choose to do, assign as homework a brief paper summarizing their data and analysis. Very high achieving students could be assigned the Squeak challenge to make the sundial more accurate.
Nonlinguistic Representations: This activity is replete with nonlinguistic representations such as graphics and simulations. Students will learn more from nonlinguistic actions as they explore the sundial simulation. If the very high achieving students try the Squeak Challenge and deconstruct the Squeak project to find out how it works, 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 work on on the challenges, it is important for each student to contribute ideas. When working on the challenges, the team members can compare, summarize, analyze, question, clarify and learn mathematics together through discussion.
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 how the shadows are related to the daily motion of the Sun across the sky. Students could offer feedback to other students through discussions explaining their data and analysis. If you give your students a test on the activity, research shows that the optimal time is one day after exposure to the material. 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.
Generating and Testing Hypotheses: Both inductive (abstracting a principle from a set of specific observations) and deductive (using a principle to predict or obtain 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. This activity offers an excellent opportunity for students to reason both inductively and deductively and compare the two processes. When students try to explain their data in terms of the daily motion of the Sun across the sky, they will be reasoning inductively. Students would use deduction when they use their data plots to predict shadow directions for different hours of the day and then check to see if their predictions are correct. It has also been shown valuable for students to explain their reasoning and analysis, which they could do as homework or in class or both if time permits. Part of the assignment could be to compare the processes of induction and deduction.
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, a good starting question would be "How could you use the Sun to tell time?" 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. Don't worry if they don't get the correct answers, those are hard questions. The important thing is that your students are challenged to think. 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. In this case a story involving Norbert losing his watch and needing to know the time would be appropriate.
