According to Motani and Garg (2002), a successful learning environment is one in which students and teachers interact easily, continuously and without any inhibitions. In this type of learning environment, student learning is not left to chance; rather, teachers know whether their students understand intended concepts. The key to this success is the implementation and use of an instantaneous feedback system. Instantaneous feedback enables teachers to intervene immediately when students misunderstand a concept or principle which is important in meeting the learning objective. A teacher may have to adjust a teaching strategy, provide different examples or offer alternative explanations. In making these adjustments, teachers show that they recognize and appreciate that previous attempts at teaching the concept or principle were not effective. Furthermore, making adjustments in teaching instantaneously with the aim of reaching all students, and especially less successful students, leads to improved learning for all students (Guskey, 2003).
Mathematics teachers can use several strategies to get and give feedback about how well students are learning material that is being taught. Motani and Garg (2002) observe that there are electronic and non-electronic mechanisms for getting feedback. Non-electronic mechanisms may include class discussions, cooperative group work, board-work, seat-work or answering questions that are posed orally. While these interactive strategies are effective, a major shortcoming is that at any particular time, only a subset of the students in the class are actively providing information to the teacher about their learning and are receiving feedback from the teacher. Class discussions are a good example of how an interactive strategy can work for some, but not all students. Silverthorn (2006), a professor or physiology, noted, “There was always a group of students, usually sitting at the front of the room, who would answer questions and talk to me as if we were chatting in my office, while the remainder of the class sat passively at the back [of the room] and listened and took notes” (p. 136). The students who sat at the front of the room benefited from the verbal interactive exchange with the professor. The students in the back of the room did not benefit from the exchange of information about their learning with the professor. Therefore, in order to engage more students in the interactive activities in the class, Silverthorn (2006) suggests that professors employ more student-talk, less teacher-talk and more class time for problem-solving activities.
Even when teachers employ interactive assessment strategies such as assignments or examinations to determine what and how much students have learned, care must be taken so that these strategies are effective in improving student learning. One reason that care must be taken is because the feedback to students from teachers is often delayed – that is, the feedback to students does not occur during the instruction. When students respond to questions on an assignment or examination, they may not get feedback for several days or weeks. Thus, by the time they receive feedback, they may have moved on to “learning” new content. If understanding of the new content is dependent on understanding of the old content, and if there were misunderstandings of the “old” content that were not addressed immediately when it was presented, then the cumulative effect of misunderstandings coupled with no corrective feedback could put students at risk of under performance or even failure. A second reason is that students generally focus on doing what is necessary to get the highest grade possible on an assignment. Strategies used by students in this
context may result in very little learning. Should either of the above scenarios exist, the goal of improved student learning would be compromised.
Over the last 25 years, technological advances have provided opportunities for creating interactive mathematics learning environments using electronic mechanisms. Some examples of electronic mechanisms are personal response systems (PRS) and personal data assistants (PDA). These e-mechanisms allow interaction between fellow students and students and teachers and enable teachers to provide instantaneous or immediate feedback. For example, the PRS allows students to respond privately (and anonymously) to questions posed by the teacher during instruction. The student responses are collected, analyzed, summarized and displayed as a histogram. The teacher is able to use the results to make adjustments in teaching in real time and correct any misunderstanding of concepts or principles among students. “Low tech” strategies that accomplish similar interactive learning objectives as the “high tech” PRS and PDA are colored flash cards and quiz games. Notably though, PRS and PDA provide students who would otherwise be reluctant participants in an open interactive classroom with a safe and non-threatening way to participate in classroom activity and still provide the teacher with information about their learning that will ultimately help themselves and others maximize learning of intended instructional objectives.
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