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

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

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

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

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.

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.

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

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 ?

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