1. CHAPTER 7 Using Technological Tools to Teach Mathematics
Elementary and Middle School Mathematics Teaching Developmentally
Ninth Edition
Van de Walle, Karp and Bay-Williams
Developed by E. Todd Brown /Professor Emeritus University of Louisville

2. What are Mathematical Technologies?
digital content assessed via computers
calculators and other handheld or tablet devices
computer algebra systems
dynamic geometry software
online games
recording devices
interactive presentation devices
spreadsheets
communicative and collaborative tools- i.e. Web 2.0
synchronous and asynchronous collaboration- i.e blogs,
wikis

3. Technological, pedagogical & content knowledge
TPACK framework
Pedagogical content knowledge (PCK) is the intersection of mathematics content knowledge with the pedagogical knowledge of teaching and learning (Shulman, 1986), a body of information possessed by teachers that the average person, even one strong in mathematics, would not likely know. TPACK describes the infusion of technology

4. Examples of Technology-Supported Activities
Consider and Make Sense of New Information Gain information from a student or teacher demonstration or presentation Screencasting (Doceri, Educreations, Explain Everything, Jing, Show Me QuickTime) Document camera, digital camera, interactive whiteboards, presentation applications (Keynote, PowerPoint, Prezi) video (Animoto, YouTube, School Tube)
Practice Various Techniques Scientific/graphing calculators, spreadsheets, WolframAlpha XtraMath, AAAMath, FASTT Math. Math XL, iFlash, computation apps on handheld/tablet devices Virtual manipulatives, brainteaser websites

5. When to Use a Calculator
When students are exploring patterns, conducting investigations, testing conjectures, solving problems and visualizing solutions
TRY THIS ONE
Find the decimal equivalent of 8/9, 7/9, 5/9.
Does a pattern emerge?
In this activity using the calculator supports Standards for Mathematical Practice 8 (seek regularity in repeated reasoning)
Discuss how calculators can improve student attitudes and motivation.

6. Graphing Calculators Students can visualize concepts as they make real-world connections with data.
Statistical functions allow students to examine means, medians, and standard deviations
Graphs for data analysis are available, including box plots, histograms, and—on some calculators—circle graphs, bar graphs, and pictographs.
Random number generators allow for the simulation of a variety of probability experiments. Functions can be explored in three modes: equation, table, and graph. Because the calculator easily switches from one to the other and because of the trace feature, the connections between these modes become quite clear.

7. Appropriate and Strategic Use of Digital Tools
E-tools or virtual manipulatives are designed for student interaction that extends beyond the textbook or a tutor
Concept instruction- best used when students control the program on the large display screen along with teacher-guided discussion and analysis
Problem solving- DreamBoxLearning is an example of adaptive, individualized online program aligned with Common Core and NCTM standards
Drill an reinforcement- free online math fact, fluency programs help students pre-assess and keep track of progress

8. Selecting Appropriate Digital Content
Teachers need to be well informed about content to evaluate the merits
Gather information through journals and websites and use critical questions when considering;
How will students be challenged to learn better than opportunities without digital access?
How are students likely to be engaged with the content?
How easy is the tool or resource to use?
What controls or assessments are provided for the teacher?
Is the digital resource equitable in its consideration of age, gender, culture ?

9. Discerning Internet Resources
Authority- a reputable educational institution or organization Content- materials should add depth to your information Objectivity- site should not reflect a biased point of view
Accuracy- information should be free or errors Currency- site should be current and frequently visited Audience- site should be accessible by all learners