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 Digital Microscope Video Clips Spreadsheets Closing thoughts and reactions
Principles and Standards for School MathematicsWhat about Technology? 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 What do they say? 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.
Geometer’s Sketchpad Investigations Models for Addition of Integers Models for Multiplication grouping area scaling Models for Intermediate mathematics fractions grouping multiples integers coordinate system
More Geometer’s Sketchpad Investigations 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. Golden ratio
http://intermath.coe.uga.edu/ 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)
Outside Looking In Findings: • Response to questions – “explain your reasoning” • Student write up for investigations • Power of extensions – how pieces in mathematics connect with each other.
Golden ratio by way of GSP 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).
Digital Imaging 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
Digital Microscope • QX5 Digital Microscope • Paperclip • Needle • Leaf of a weed • Safety pin • Pens/pencils Examples
Video Clips I. Use a video clip to help “set up” an activity (in this case investigating the golden ratio): http://discoveryeducation.com/video-in-the-classroom/golden-ratio.cfm (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? Volume of cylinder
Volumes by way of spreadsheet • Use Excel (or any other spreadsheet software) as a tool to organize tables and graphs. • Data represented in table format, graphical format, and function format. • Spreadsheet has capability to handle large numbers • EXCEL file: CylinderVol • Movie clip (aha – if time).
Fibonacci by way of spreadsheet • Look at the Fibonacci sequence • Look at patterns in the data • Look at it graphically • Refer to Excel file Fib1 (Sheet 1,2,3,4)
Closing thoughts and reactions Ways of using technology Methods of questioning students’ understanding Making attempts to plan for using the technology in instruction and assessment
Contact Information Mary C. Enderson MTSU-Math Sci. Dept. P.O. Box 34 Murfreesboro,TN 37132 email@example.com Janet M. Walker IUP-Math. Dept. 233 Stright Hall Indiana, PA 15705 firstname.lastname@example.org