VPEM
- The primary goal of the Videocases for Preservice Elementary Mathematics (VPEM) Project (NSF-0837031) was to develop a collection of videocases to be used in elementary mathematics preservice courses and to conduct an exploratory study of the extent to which these cases enhance preservice teachers' learning of the mathematical knowledge needed for teaching. The videocases were developed using video and interview data of K-5 classrooms from a prior National Science Foundation (NSF) project (NSF-0242704). To date, we have developed nine videocases and accompanying facilitator guides to be used in mathematics content courses for preservice teachers. Each videocase includes the following:
- One or more 2-15 minutes video clips - the video clips depict children working on a mathematics problem individually or in small groups, or children answering the teacher's questions during a whole group discussion.
- A transcript of the video clip(s) - the video clip(s) are transcribed by individual turns, and each line of the transcript is assigned a line number. Pictures of artifacts, manipulatives or work samples generated or used by children in the video are also included in the transcripts.
- A set of focus questions - there are four different types of focus questions designed to focus preservice teachers' attention on particular aspects of children's thinking in the video clips:
- Questions about children's thinking or understanding. For example, what do students in Part 1 seem to understand about the task? Cite evidence from the transcript.
- Questions about mathematics content. For example, in Part 1, what is Student 2 referring to when she says, "that number" (line 66)? How would you represent "that number" in the strategy you used to solve the task?
- Questions about extending children's idea or strategy. For example, how can you use Student 5's strategy to determine the number of eye squares?
- Questions about mathematical tasks of teaching. For example, what does the teacher have to manage mathematically in this discussion? Why do you think so?
- A facilitator guide - the facilitator guides are designed to support instructors in facilitating preservice teachers' discussion of the videocase, including answers to focus questions, and strategies and questions to use to extend the discussion of the video clip(s).
In addition to focusing on core elementary mathematics topics (e.g., fraction operations, place value), the VPEM curriculum was also designed to develop PSTs' ability to engage in certain mathematical tasks of teaching. For example, analyzing children's errors, mapping representations to underlying mathematical ideas, and choosing and developing useable definitions are considered tasks of teaching that draw on teachers' mathematical knowledge for teaching. In other words, such tasks of teaching require considerable specialized content knowledge on the part of teachers. Thus, the VPEM curriculum is designed to not only focus on children's engagement with core elementary mathematics content, but also to highlight the ways in which particular tasks of teaching are manifest in the classroom. Table 1 includes brief descriptions of the nine videocases, including mathematical topic and mathematical tasks of teaching foci.
- For more information about the VPEM Project or for inquiries about using the videocases, please contact amcastro@uic.edu.
Videocase Title | Mathematics Topics | Mathematical Tasks of Teaching |
---|---|---|
Finding Patterns | Algebra | Evaluating the plausibility of children’s claims Asking productive mathematical questions |
Counting Strategies | Meaning of addition, subtraction; Addition, subtraction problem types | Evaluating children’s mathematical explanations Asking productive mathematical questions |
Understanding Place Value | Counting; Place value | Analyzing children’s thinking |
Modeling Double-Digit Subtraction | Subtraction algorithm | Linking representations to underlying mathematical ideas |
Debating Remainders | Division; Remainder interpretation | Evaluating children’s mathematical arguments Asking productive mathematical questions |
Student Errors with Multiplication & Division Algorithms | Place value; Standard, alternative multiplication & division algorithms | Analyzing children’s errors |
Pattern Block Fractions | Relationship between improper fractions and mixed numbers | Analyzing children’s thinking Analyzing children’s errors |
Why is 1/20 not equal to 20%? | Relationship between percentages and | Analyzing children's errors Linking representations to underlying mathematical ideas |
Making Predictions Using Multiple Solution Strategies | Fractions; Liner functions | Evaluating children's mathematical explanations |
Table 1. VPEM videocase design overview