1. Fathom – Dynamic Software Deeper understanding and perception of mathematical concepts

2. What you can do with Fathom Drag the data Drag and drop to build new graphs and tables Take control of your graphs Use formulas with a purpose Build data simulations Use sliders Investigate the data Import data Finish the assignment – explanations, processes and conclusions

3. Fathom - continued Enter data and make a graph Use the context menu to find commands Make basic objects such as case tables, graphs, and summary tables Select cases in order to explore data Add a movable line on a graph Filter data Rescale and reorder axes Create a simple summary table

4. Fathom - continued Illustrate the concept of a best fit line Plot and adjust functions Make and manipulate a histogram Work with units Take a sample from a collection, repeat the process and change the sample size Download and analyze US Census data

5. US Census data - activity Choosing cases –Years/states/metropolitan/people/sample size Choosing attributes –Year and location/person-ethnicity-family- income-travel/household basic-economic- dwelling

6. Importance in Fathom Make better predictions Can manipulate data Perception and clearer understanding Study of demographics make easier for business to speculate with greater degree of accuracy Ideas for future exploration

7. Fathom Software Promotes –Exploration –Investigation –Discovery Leads to deeper understanding

8. Polya – 4 phases of mathematical problem solving Understand the problem Devise a plan to solve the problem Carrying out the plan Examine the obtained solution

9. Shoenfeld – 6 stages Reading Analyzing Exploring Planning Implementing Verifying

10. Novice Problem Solver

11. Semi-Novice/Expert Problem Solver

12. Conclusions Deeper understanding brings about better learning Fathom software allows individuals a deeper understanding and perception of mathematical concepts Based upon the work of Polya and Schoenfeld students spend little time as a novice problem solver reading the problem and most of the time exploring

13. Conclusions - continued As an individual becomes a semi-novice/expert problem solver he/she transitions back and forth through the different stages and spends more time reading and understanding the problem before searching for solutions Fathom – Dynamic Software allows individuals the opportunity to explore, investigate and discovery which will allow the individual the opportunity to transition between the phases of problem solving with better perception and become a semi-novice/expert thinker. This will lead to a deeper understanding of mathematical concepts