Three workshops were held over the course of the first term. These modeled inquiry-based instruction for students, pedagogy that facilitated collaboration between groups of students who did not know each other, and use of technology for instructional purposes, including hands-on instruction of tools on a large richly textured Web site, The Math Forum .
This workshop began with introductions of faculty working with the IIT project and the two Math Forum staff members who would be working with the students and faculty during the Fall portion of IIT.
Prior to the workshop, students had been asked to access, answer, and submit their answer to the Elementary Problem of the Week (ElemPoW), a nonroutine challenge problem posted on The Math Forum each week. Each of the six types of Problems of the Week on the Math Forum site are designed to provide students with individualized mentoring that will enhance their mathematical thinking. An extension of students mathematics instruction, these problems are typically built into the existing curriculum, assigned as extra credit, or undertaken as independent mathematical enrichment. Each week, a new problem is posted. To receive credit for submitting an answer, students must not only submit an answer but an explanation of their solution strategies within the week that the problem is posted. Mentor teachers respond to each submission by acknowledging students work, engaging the students in discussing their answers, and encouraging students to revise and resubmit their answer when their work is incomplete or inaccurate. Following posting of the problem and the period in which students submit and resubmit answers, a solution page that summarizes a variety of accurate solutions tot he problem is posted. These problem and solution pages are then archived and made available to everyone.
Following introductions, students worked were organized in small groups to discuss their submissions and revisions to the ElemPoW they had been assigned. The composition of the small groups was designed to allow students with differing backgrounds to get to know each other; and to position at least one person in the group who had been able to submit or resubmit an accurate solution to the problem.
Following small group discussion, the students gathered as a larger group and used information from their small group discussions to compile descriptors of what an effective answer to the PoW might consist.
Students were then asked to pair off in groups of 2, such that they would work with a person they had not known when they entered the workshop. They were first introduced to the PoW "office" area. This is a location on the Math Forum site where mentors compose responses to students who submit answers to the PoW each week. One of its particularly useful features is that it is possible to pull up a students past submissions and the mentors responses, and use these to inform the development of a response in terms of the kinds of encouragement and skill development that that a student is judged to need.
Following the introduction to the office area, the college students were asked to work together to respond, or "mentor", a student on his or her work with a problem (although this response was not sent directly to the student but instead was picked up by the Math Forum staff members who gave the college students feedback on their responses. The college students were asked to revise their responses, resubmit them to the Math Forum staff and then they were sent on to the student who had submitted the response.)
As homework, the college students were asked to respond to three students about their submission before the next workshop. This process involved the college students writing out a response and the Math Forum staff members writing back to them about the response and ways in which it might be developed in order to most effectively "mentor" a given student.
The second workshop was focused on the language used to interact with students online. The students were grouped in two groups, those who currently were in the classroom as student teachers, and those who were students. Each discussion was facilitated by a Math Forum staff member. They opened with a discussion of the mentoring process in which the college students had been involved. They compiled a list of key elements of mentoring, i.e., use of age appropriate language, accurate spelling and grammar, clear and concise responses to students submissions, acknowledgement of effort, issues of when to push, encouragement and respect for pupils as learners. They also talked about the links between the use of these mentoring techniques in classrooms as well as on the Web, and the strengths and weaknesses of an online service such as the ElemPoW.
Following the discussion in two groups, the college students came together as a whole group and worked with transcripts of online interactions between pupils and mentors. The students were encouraged to consider: things the mentor was doing, was not doing, and suggestions they might make to the mentor. The discussion also introduced the college students to error analysis: considering what the student understood and what he or she still needed to learn. The college students worked together to review a solution page for the problem on which theyd been working with students. The solution page underscored the range of possible solution strategies for the problem and identified difficulties that had emerged for those who had submitted answers.
The assignment for the third workshop included mentoring 5 additional PoW submissions and creation of a solution page that highlighted students solution strategies and the difficulties they encountered.
The third workshop began with detailed small group discussion around the solution page on which the students had worked. Students were grouped based on the content area in which they were or would be teaching and the age student with whom they were or would be working. The grouping permitted student to focus on concerns specific to their discipline and age group with respect to the mentoring process and their sense of what an effective solution and mentored response to a problem in their discipline would consist.
Following the small group discussions, the group met together as a whole group and talked about the relation between technology and inquiry-based pedagogy, i.e., the Web provides access to primary sources, adds a dimension to written text, is loved by kids, provides fast access to research material which allows questions to be kid driven, kids get to control aspects of learning, and the classroom can be extended to the larger community.
Students then worked together with the same small group with whom they had worked at the outset of this workshop to review six sites in their content areas (drawn from a sample of content areas) and together with others in their group designed an inquiry-based lesson. The focus of this assignment was two-fold. It introduced students to other sites and it encouraged the students to consider how teachers might build the use of a site into their classes.
The third workshop closed with an overview of the work that would be undertaken during the following term as part of the IIT project.
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