Mathematics Education in the Middle Grades Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations: Proceedings of a National Convocation and Action Conferences (2000) / Chapter Skim
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Teaching Issues in the Middle Grades
Teaching Issues in the Middle Grades
Pages 61-94
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From page 61... ...
What tools and strategies wait make a difference in how middle grades students learn mathematics? USING VIDEO OF CLASSROOM PRACTICE AS A TOOL TO STUDY AND IMPROVE TEACHING Nanette Seago, Project Director, Video Cases for Mathematics Professional Development, Renaissance Project.
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From page 63... ...
These frame the design, development and formative evaluations of my current work: iNational Science Foundation; (ESI #9731339~; Host Institutions: San Diego State University Foundation, West Ed 2I would like to acknowledge my colleagues Judy Mumme, Deborah Ball and her research group at University of Michigan, Magdalene Lampert, Deidre LeFevre, Jim Stigler, Joan Akers, Judy Anderson, Cathy Carroll, Gloria Moretti, and Carole Maples for their on-going help in thinking about these ideas. 3Ioan Akers is the formative evaluator of the VideoCases Project; Deidre LeFevre is a graduate student of Magdalene Lampert and Deborah Ball at the University of Michigan and is using the developmental process of our project to research the impact of different forms of video case facilitation on teacher engagement and learning around issues of pedagogy, student learning, and mathematical content.
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From page 64... ...
Educational researchers can use this work across multiple and varied contexts to research why and how teachers learn from professional education experiences whether it is using video or other practice-based materials such as student curriculum, student work, or written cases. Teaching is thinking, intellectually demanding work.
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From page 65... ...
How does one use individual student thinking and alternative approaches to further the collective mathematical learning of the whole class? Does a teacher stop and pursue every chil(l's thinking, always, in USING VIDEO OF CLASSROOM PRACTICE every lesson?
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From page 66... ...
· Balancing between individual student and whole class mathematical thinking and learning analyzing and deciding · Building a mathematical story · Budgeting time · Learning about students Abler · Figuring out what to do tomorrow based on today · Analyzing student work · Learning about students PURPOSES FOR USING VIDEO When most people think of the purpose for using video with teachers, they think of models, exemplars, or illustrators of a point. The question this poses is one worth researching.
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HOW DO WE USE VIDEO TO PROMOTE TEACHER LEARNING? What might it mean to plan anti orchestrate professional education that is guided by analytic and educative purposes?
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From page 68... ...
THE CONTENT OF THE VIDEO The Cindy video clip lesson begins with Cindy posing the problem, If you lined up 100 equilateral triangles in a row i_ (shared edges) , what would the perimeter be?
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Nick may have USING VIDEO OF CLASSROOM PRACTICE Figure 3. Cincly Lesson 1 .
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What appears to be the teacher thinking anti reasoning for the (recisions around each student's thinking? For what mathematical learning goals would she seize in(livi(lual student thinking, when would she not?
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USING VIDEO OF CLASSROOM PRACTICE · Learn about the uncertainty in teaching. These video segments offer the opportunity for participants to learn about the uncertainties involved in a complex practice (McDonald, 1992)
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While this may be very (lifferent from the way in which the facilitator connects to this video case, reaching the participants means the facilitator has an understand ing of where the participants will enter the video case. Some entry points into the Cindy video include: student thinkingspecifically Lindsey and plus 4; teacher questioning specifically all of the questions Cindy asked in the segment; the role of the table in furthering/ hindering student learning; classroom environment; and the role of mathematical understanding in teacher decisionmaking around student thinking.
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Figuring out how to use evaluative statements as entries into analysis is something for which strategies are not USING VIDEO OF CLASSROOM PRACTICE yet wall-defined. Comparing this to analyzing student thinking is helpful.
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From page 74... ...
It is helpful to recognize this up front anc} to plan for at least two viewings the first to get out on the table the things they will pay attention to anyway en c} the seconc} to focus using a particular lens. Asking that viewers choose incliviclual stuclents to follow en c} figure out their apparent thinking along with the apparent teacher decisions anc} possible reasoning arounc} that thinking is a helpful task in learning to focus.
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USING VIDEO OF CLASSROOM PRACTICE Eisner, E.W.
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He noted that the teacher had navigated through measurement and the topic of unit and that some students moved past symbolic patterns to use geometry to solve the problem. There was also some mathematical tension because using T+2 to find the perimeter seems on the surface to conflict with the fact that the perimeter increases by increments of 1.
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She commented that it strikes her as particularly unhelpful in professional development to talk about good questioning techniques absent a content base. The teacher has to have the ability to hear students and to keep an eye on where she is going with the (liscussion.
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When the students spoke, you TEACHING ISSU could not hear which is typical because in U.S. classrooms it is often not required that everyone hear student responses.
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The students respon(le(1 strongly to descriptions of "typical" American and Japanese classrooms and suggested they would like an opportunity to share their ideas about what is possible. Hence, they applied and were invited to present at the 1998 annual meetings of the National Council of Teachers of Mathematics anti the National Council of Supervisors of Mathematics in Washington, DC.
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From page 80... ...
How can we tell when learning is happening? · What tools and strategies wait make a difference in how middle grades students learn mathematics?
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From page 81... ...
example of what ~ call ineffective ques tioning by a well-intentioned teacher. This type of questioning leads a student to a certain way of thinking instead of having them figure it out on their own.
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From page 82... ...
What questions and/or activities might have prompted the mathematical thinking that I~in(lsay, Joel, anti Kyle (remonstrate in their examples? LINDSAY VISUAL MODELS Working with models for mathematics i(leas helps me have a better un(lerstan(ling of mathematics concepts which lea(ls to confidence anti success in mathematics.
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From page 83... ...
They help me produce work more efficiently, and give me a better understanding of mathematics concepts because ~ can actually "see" the why behind a concept. Most importantly, these mo(lels enable me to be confident in myself as a mathematics student and know that ~ really (lo have an inner mathematician.
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From page 84... ...
F 4 I t A $ _ ~ ~-r ~$ 11~ ~ 0~ ~ _ t~4 -~_0 ~.~v-;l-,~411~-~4^,~S.~. ~ TEACHING ISSUES been working on in class....
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From page 85... ...
, I ~J ~s.- ,- ~. r KYLE MATHEMATICAL TRUST Learning mathematics is a journey.
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From page 86... ...
~ ~ _- ~$ ~ r -- - ,~ ~ ~I; ~- ~ Al 56 8~ ~-~ ~·~ ~ ~ ·~-( I 1 4. ~_~ _ ~ i, ~_ ., i ~ -0 ^- =^ -~ ~ ~ ' ~ ~~ ' i: : ~>_ _ _ _ Lam _ ~ _ tam ~ ~ ~- ~ ~ ~ ~ ~ ' - ~ ~I Fatal _~J ~,nauat_S~E-~-._ TEACHING ISSUES
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From page 87... ...
What is meaningful context? If one agrees that these students provide evidence that it is possible to cultivate interest in serious mathematical content, what are the instructional practices that are most influential in cultivating such interest?
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TEACHING ISSU · As Erica pointed out, teaching that focuses on how students think about mathematics has a powerful influence on students' learning as well as their views of themselves as mathemati cians. It also provides the teacher rich information about the extent to which students un(lerstan(1 anti are able to integrate mathematical ideas and processes into their own way of thinking.
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From page 89... ...
Had these students written their papers even a year earlier, some students would have expressed doubts about how and what they were learning (they kept close tabs on activity in their peers' more traditional cIassrooms S T U D E N T P E R S P E C T I V E S the media, and even some mathematics teachers, told them they would never learn what they needed to know) ; there would have been more disequilibrium about certain mathematical i(leas that are described with confidence here; their parents may have expressed doubt due to the uproar about mathematics reform in the local news; and their teacher would have been a little less secure in her conviction to main tain high expectations, trusting everyone's (lisequilibrium was a sign of new learning about to occur.
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From page 90... ...
Chattin pointed out that it is hard for adults to recognize just how serious middle grades students are. Hyman Bass described himself as a university mathematician "infected" with observing elementary teaching and thinking about how students learn mathematics.
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From page 91... ...
She framed her remarks around the conjecture that this teacher had PANEL RESONSE TO FOREMAN STUDENT VIDEO actively held and communicated high expectations for students. She said that teachers can move children if they hold expectations that students can learn and (lo not take refuge in "Most (or my)
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From page 92... ...
The answers to the first question clearly reflected the middle school philosophy, with an emphasis on a safe learning environment where students work in a social caring classroom and learning mathematics is treated as a social activity. There was strong support for student-centered classrooms and reinforcement of student ideas and work.
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From page 93... ...
Students who un(lerstan(1 can apply mathematics to solve problems and have the ability to revise their thinking based on their investigations. What tools anti strategies will make a difference in how middle grades students learn mathematics?
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From page 94... ...
The initial ten TEACHING ISSU dency to criticize can overtake the discussion. There was concern that viewers might not recognize good teaching.
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