My Comrade, Technology Pam Losinski Michigan State University Masters of Arts in Educational Technology CEP 805-Learning Mathematics with Technology

Overview Success in today’s classrooms demands assistance from technology. Teacher Student Technology Student Teacher Student Technology

Objective I Technology needs to be readily available for education. Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning. -NCTM’s Technology Principle

The Argument Allow teachers the ability to determine appropriate technology for their classrooms.

Instances of Technology at QMS Calculators –Scientific to TI-83 graphing calculators Computers –Teacher desktops –LCD projectors –Document Cameras –Computer lab equipped with 30 student desktops –Laptop carts equipped with 24 laptops, wireless printing capabilities Data Collection Devices –CBR and CBL

Blocked Technology at QMS Internet Resources –Online Communities –Course Management Sites Programs & Simulations available for download

Northwest Regional Educational Laboratories “Computers make possible experiences and representations that cannot take place in the real world, providing new experiences and improved understanding.”

Objective II Networking within Quincy Middle School’s Mathematics Department will provide students with the most effective education possible.

Existing Networking Department Meetings –Teachers gather once a month –Agenda sent via prior to meeting –Minutes recorded and posted on middle school collaborative drive Web Based Bookmark Manager –Collection of math websites available to entire department, annotated for easy searching

Proposed Networking Teachers prepare brief presentations to introduce new technology.

A Sample Presentation SimCalc “Research and development in technology and curriculum dedicated to democratizing access to the Mathematics of Change and Variation, including ideas underlying Calculus.”

SimCalc: Curricular Vision To democratize access to the big ideas of mathematics To democratize access to the big ideas of mathematics

SimCalc Project believes that technology provides essential means to restructure this curriculum in order to: / Democratize access to important and powerful ideas. / Build much more longitudinal coherence between early and later years. / Focusing on the growth of big ideas, and their roots in everyday human experience. / Crack the formalism barrier by providing multiple ways of working with mathematical ideas, using the full range of human linguistic, visualization and cognitive capacities. / Increase efficiency by teaching several important ideas simultaneously. / Make room for more modern mathematics, moving out of the 19 th century and into the 21 st. / Democratize access to important and powerful ideas. / Build much more longitudinal coherence between early and later years. / Focusing on the growth of big ideas, and their roots in everyday human experience. / Crack the formalism barrier by providing multiple ways of working with mathematical ideas, using the full range of human linguistic, visualization and cognitive capacities. / Increase efficiency by teaching several important ideas simultaneously. / Make room for more modern mathematics, moving out of the 19 th century and into the 21 st.

SimCalc: Sack Race Performance Activity / Focus: / Slope as a rate of change / Positive Slope / Negative Slope / Zero Slope / Systems of Equations / Intersection of Linear Equations / Focus: / Slope as a rate of change / Positive Slope / Negative Slope / Zero Slope / Systems of Equations / Intersection of Linear Equations

/ Students manipulate Actor A and B to simulate a sack race that ends in a tie / PDF links: / Introduction Introduction / Teacher Instructions Teacher Instructions / Student Instructions Student Instructions / Students manipulate Actor A and B to simulate a sack race that ends in a tie / PDF links: / Introduction Introduction / Teacher Instructions Teacher Instructions / Student Instructions Student Instructions SimCalc: Sack Race Performance Activity

SimCalc: Sample Race Actor A, Big Red, and Actor B, The Green Giant, both start off strong as the race gets underway. Unfortunately, at 4 seconds into the race, Actor B gets sidetracked when he sees a friend standing beside the path. Not wanting The Green Giant to lose the race, he quickly reminds him to “keep running!”. Distracted, The Green Giant starts running back toward the starting line. Realizing his mistake, he quickly turns around and runs as fast as he can to catch up to his rival, Big Red. As his poor physical condition gets the best of him, he slows slightly, but still manages to finish the race in a tie with Big Red.

Classroom Follow Up / Presentations of individual graphs & stories / Discussion of slope / When they equal? / What that means? / What positive/negative slope means for the racers. / Presentations of individual graphs & stories / Discussion of slope / When they equal? / What that means? / What positive/negative slope means for the racers.

Michigan Grade Level Content Expectations / Sixth Grade Standards / A.PA Solve applied problems involving rates, including speed, e.g., if a car is going 50 mph, how far will it go in 3 1/2 hours? / A.RP Understand that relationships between quantities can be suggested by graphs and tables. / A.RP Represent simple relationships between quantities using verbal descriptions, formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches. / Seventh Grade Standards / A.PA Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.* / A.RP Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. / Eighth Grade Standards / A.FO Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions. / A.FO Solve linear inequalities in one and two variables, and graph the solution sets. / Sixth Grade Standards / A.PA Solve applied problems involving rates, including speed, e.g., if a car is going 50 mph, how far will it go in 3 1/2 hours? / A.RP Understand that relationships between quantities can be suggested by graphs and tables. / A.RP Represent simple relationships between quantities using verbal descriptions, formulas or equations, tables, and graphs, e.g., perimeter-side relationship for a square, distance-time graphs, and conversions such as feet to inches. / Seventh Grade Standards / A.PA Recognize when information given in a table, graph, or formula suggests a directly proportional or linear relationship.* / A.RP Represent directly proportional and linear relationships using verbal descriptions, tables, graphs, and formulas, and translate among these representations. / Eighth Grade Standards / A.FO Solve simultaneous linear equations in two variables by graphing, by substitution, and by linear combination; estimate solutions using graphs; include examples with no solutions and infinitely many solutions. / A.FO Solve linear inequalities in one and two variables, and graph the solution sets.

Additional Ideas for Networking from CEP 805 National Council of Teachers of Mathematics –Connections between math and technology The Jasper Series Geometers Sketchpad –An alternative from Cabri Geometry

Sources