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Technology Use for CMP3
and BeyondKevin A. Lawrence, Michigan State University [email protected] Twitter: @kalawrence9 & @ipadmath
Nicholas J. Gilbertson, Michigan State [email protected]
About us Kevin Lawrence
PhD student (3rd year) in Mathematics Education (PRIME) at Michigan State University
Taught H.S. math and physics for six years (IN) Interested in technology use by teachers and students, student transition from K-12 to collegiate math
Nic Gilbertson PhD student (5th year) in Mathematics Education (PRIME) at Michigan State University
Taught M.S. & H.S. math for seven years (WI, OR, IL) Interested in technology use, classroom discussions.
Types of Technology Discussed
Would not require one-to-one student access Whole-class inquiry & discussion Focus on conjecturing, justification, and sense making
Includes math specific and non-math specific technologies Math Specific
• GeoGebra• Desmos
Non-Math Specific• Spreadsheets• Screencast Apps
Graphing Calculators
The Good The Bad The Ugly
Graphing Calculators
The Good More available for one-to-one use in some schools (compared to newer technologies)
Graphing Calculators are math-specific technologies
Accepted technologies within the math teaching communities
Graphing Calculators
The Bad Easiest (and most common) use is entering in symbolic representation for the production of:• Tables• Graphs
Doesn’t work well in problem-based scenarios that present a representation other than symbolic:• Raw data• Graphs
Representational Translations (Janvier, 1987)
To
From
Situations,
Verbal
Tables Graphs Formula
(Symbolic)
Situations,
Verbal
Measuring Sketching Modeling
Tables Reading Plotting Fitting
Graphs Interpretat
ion
Reading off Curve
Fitting
Formula
(Symbolic)
Parameter
Recognition
Computing Sketching
Graphing Calculators
The Ugly• Students may use the calculator output as the authority– Unaware of input errors and effect on other representations (tables, graphs, etc.)
– Technology masks the mathematical characteristics that are emphasized outside of calculator use (shapes of graphs of particular function families).
CCSSM Standard for Mathematical Practice CCSS.Math.Practice.MP5 Use appropriate tools strategically. Mathematically proficient students consider the available tools when
solving a mathematical problem. These tools might include pencil and paper, concrete models, a ruler, a protractor, a calculator, a spreadsheet, a computer algebra system, a statistical package, or dynamic geometry software. Proficient students are sufficiently familiar with tools appropriate for their grade or course to make sound decisions about when each of these tools might be helpful, recognizing both the insight to be gained and their limitations. For example, mathematically proficient high school students analyze graphs of functions and solutions generated using a graphing calculator. They detect possible errors by strategically using estimation and other mathematical knowledge. When making mathematical models, they know that technology can enable them to visualize the results of varying assumptions, explore consequences, and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources, such as digital content located on a website, and use them to pose or solve problems. They are able to use technological tools to explore and deepen their understanding of concepts.
We are not here to devalue the use of graphing calculators.
Technology > Graphing Calculators Not all tasks should dictate the same technologies to be used
GeoGebra
GeoGebra
Free download at geogebra.org
Some limitations compared to Geometer’s Sketchpad
Many improvements in the past few years
GeoGebra
One main affordance: help see relationships between continuous variables.
Two Examples Nets of Prisms Area and Perimeter of Triangles
GeoGebra – Area and Perimeter
GeoGebra – Nets of Prisms
Desmos – Free Online Graphing Calculator Desmos.com and iPad app Similar display on any platform (computer, mobile, app)
Save to Google Doc (not yet on iPad) Pros:
Enter either equation or data (tables) View equation, table, and graph at the same time Sliders for equations provide dynamic change in graphs and tables!
Can import picture to sit behind the coordinate grid.
Desmos
Given raw data as coordinates, find the function that matches Test different types of function families with the use of sliders
Allows the user to test different values See changes that occur when changing the value of parameters (how the graph moves/adjusts)
Desmos – Exponential Growth
Situation/verbal Symbolic Table Graph
Desmos – Exponential Decay
Table (incomplete?) Symbolic Graph
Spreadsheets
Spreadsheets
From Variables & Patterns (ACEs 1-3, Inv. 4)
1. Extend the pattern
2. Write an equation (or expression) that helps describe how to find the number of toothpicks for any shape number
iPad Apps
There are many math apps that are available on iPads and other mobile devices.
There are many apps that are not math specific that can be used for effective communication within the mathematics classroom.
Use of interactive white boards on tablets allows for students to verbalize their thoughts while writing their work in real time by creating a video.
Great for capturing students interpretations of graphs.
Video can be shared in various ways (url links, embed codes, social media, within apps, etc.)
iPad AppsEduCreations ShowMe ScreenChomp
Ask3 Explain Everything TouchCast
Example of a Screencast
http://www.educreations.com/lesson/view/cmpusers14/17503779/?ref=link
Thank you!
Twitter: @connectedmathfacebook.com/connectedmathematicsproject
Kevin A. Lawrence, Michigan State University [email protected] Twitter: @kalawrence9 & @ipadmath
Nicholas J. Gilbertson, Michigan State [email protected]
