Technology Investigations for Middle School. Mary C. Enderson Middle Tennessee State University Janet M. Walker Indiana University of Pennsylvania. Outline of session. Connections to NCTM Principles and Standards Focal Points Presentation of: GSP Investigations Digital Imagining
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Technology Investigations for Middle School
Mary C. Enderson
Middle Tennessee State University
Janet M. Walker
Indiana University of Pennsylvania
Connections to NCTM Principles and Standards
Closing thoughts and reactions
Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning (Ch.2).
Students can learn more mathematics more deeply with the appropriate and responsible use of technology. They can make and test conjectures. They can work at higher levels of generalization or abstraction. In the mathematics classrooms envisioned in PSSM, every student has access to technology to facilitate his or her mathematics learning.
Focal Points have the potential to guide the thinking of the profession in the development of the next generation of curriculum standards, textbooks, and tests. This work may assist in the creation and eventual development of new models for defining curriculum, organizing instruction, developing materials, and creating meaningful assessments that can help students learn critical mathematical skills, processes, and ways of thinking and can measure and communicate what students know about the mathematics that we expect them to learn.
Models for Addition of Integers
Models for Multiplication
Models for Intermediate mathematics
Outside Looking In
Borrowed from InterMath, which is a Georgia statewide internet-based project with the goal of designing and implementing a series of workshops and ongoing support programs that feature contemporary applications of technology and mathematics pedagogy in the middle-grades.
OUTSIDE LOOKING IN:
Can you determine the sum of the three exterior angles?
Would this relationship hold for all triangles? Explain your reasoning.
How would your response change if you were investigating a quadrilateral or pentagon? How about any polygon? Explain your reasoning.
GSP files (Outside1-1, 2, 3)
Background (will refer to later when presenting use of video clips)
GSP: Investigate golden ratio by golden rectangle (Golden1-1,2,3)
Move into investigating the Fibonacci numbers by way of spreadsheets (later in presentation).
One way in which teachers can connect mathematics to contexts outside of the classroom is through the concept of digital imaging; the process of taking a digital picture and then superimposing some type of mathematical function on top of that picture.
Rectangular digital imaging examples
Polar digital imaging examples
I. Use a video clip to help “set up” an activity (in this case investigating the golden ratio):
(NOTE: There are also some good YouTube videos for golden ratio)
II.Encouraging Mathematical Thinking (Math Forum) – video clip of teachers “setting up” a problem for students to investigate.
Two ways of looking at the same paper model.
Which holds more?
What occurs when one has a constant perimeter. A constant area?
Ways of using technology
Methods of questioning students’ understanding
Making attempts to plan for using the technology in instruction and assessment
Mary C. Enderson
MTSU-Math Sci. Dept.
P.O. Box 34
Janet M. Walker
233 Stright Hall
Indiana, PA 15705