Peer Review

Encouraging Mathematical Thinking, Discourse around a Rich Problem

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Content Quality:

Effectiveness:

Ease of Use:

Overview:: These webpages are a videopaper that opens a conversation about the use of
discourse as the basis for encouraging students' mathematical thinking in
classrooms and for supporting professional grown. This site is part of the Math
Forum. It includes video clips, written documentation, and a discussion
forum.
Type of Material:: Lecture/presentation, web multimedia
Recommended Uses:: The presentation would be a useful addition to a mathematics methods class or an
inservice presentation for teachers. It can be used in conjunction with other
experienced mathematics educators and while studying research-based approaches.
Technical Requirements:: Computer system capability of playing video and audio.
Identify Major Learning Goals:: To provide practitioners and preservice teachers with an illustration of the
connection between research and practice culled from discussions of research
articles and chapters, classroom practice and videotapes of classroom teaching.

To encourage the use of discourse to promote mathematical thinking and
professional growth.
Target Student Population:: Mathematics teachers and preservice teachers.
Prerequisite Knowledge or Skills:: Teachers or preservice teachers need to be familiar with the standards-based
approach to mathematics teaching, as espoused by the National Council of
Teachers of Mathematics. Middle school/high school mathematics teaching
prerequisites and familiarity with accessing multimedia on the Internet.

Rating:
Strengths:: The material presented is an excellent blend of research and practice. It is
presented in such a way that educators can view a lesson, read about it, and
then respond in a threaded discussion.

The creators of this site are wise to investigate the "student work" on these
investigations and share those with the visitors. Some of the discussions
posted are limited in mathematical depth.
Concerns:: Internet access via modem may mean very long download times for video clips. The
site suggests that those with dialup connections to the Internet should avoid
the video clips. The site is interesting without them, however, and readers can
still participate in the threaded discussion that is ongoing.

Some of the links are no longer working. Some of the transcripts are unclear.
It would be helpful if the transcripts could stand alone, or at least be
clarified (i.e. "Is that right?" -- is WHAT right?") Students need to learn to
express ideas precisely. The transcripts chosen do not always model this.

Rating:
Strengths:: This site would be a great addition to an online course in mathematics methods.
It allows students to view a teacher in action, read about her motivation and
the research that backs her approach, and then comment and ask questions about
the lesson. It is an excellent example of practice/research in action.

The authors would be wise to revisit the examples of discussion for precise
language and for pedagogy which helps readers to create more in-depth
discussion. For example, questioning by asking "Everybody agrees?" isn't a very
effective technique for assessing student knowledge or for instructing about a
particular concept.
Concerns:: The written material is lengthy. For those who have difficulty reading on the
computer screen, it would be a large amount of material to print. The site is
truly enhanced by the classroom video clips and would not be as successful
without them.

Unfortunately sometimes the multimedia is used as a substitute for precise
language. In the discussion of the volume of Cylinder 1 and Cylinder 2, the
students say "it" is "bigger." The teacher should be prompting the students to
indicate what "it" is, what "bigger" is.
Some of the links can lead the reader away from the lesson as well. ("We chose
this Experiment with Volume"--Experiment with Volume is a link.)

Rating:
Strengths:: The site can be tricky to navigate. However, there are buttons which allow one
to return to the videopaper after viewing clips or contributing to discussion.

The problems from Cynthia Lanius' website are not always quoted as written on
the original site, and lose some of the mathematical precision in the
translation.
Concerns:: The video clips preclude the use of many educators with only dialup access.Some
links are not working.

Other Issues and Comments:: This is a scholarly approach to mathematics education. Included in the site are
reflections by all the participants in the BRAP (Bridging Research and
Practice) team.
Creative Commons: