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What Does Conceptual Understanding Mean Florence S. Gordon fgordonnyit Sheldon P. Gordon gordonspfarmingdale

CUPM Curriculum Guide. . All students, those for whom the (introductory mathematics) course is terminal and those for whom it serves as a springboard, need to learn to think effectively, quantitatively and logically. Students must learn with understanding, focusing on relatively few concepts but treating them in depth. Treating ideas in depth includes presenting each concept from multiple points of view and in progressively more sophisticated contexts..

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What Does Conceptual Understanding Mean Florence S. Gordon fgordonnyit Sheldon P. Gordon gordonspfarmingdale

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    1. What Does Conceptual Understanding Mean? Florence S. Gordon fgordon@nyit.edu Sheldon P. Gordon gordonsp@farmingdale.edu

    2. CUPM Curriculum Guide

    3. CUPM Curriculum Guide

    4. AMATYC Crossroads Standards

    5. NCTM Standards

    6. Associates Degrees in Mathematics

    7. Bachelor’s Degrees in Mathematics

    8. The Needs of Our Students

    9. Voices of the Partner Disciplines CRAFTY’s Curriculum Foundations Project

    10. Curriculum Foundations Project

    11. What the Physicists Said

    12. What Business Faculty Said

    13. What the Engineers Said

    14. Conceptual Understanding

    15. What Does the Slope Mean?

    16. Responses in Traditional Class

    17. Responses in Traditional Class

    18. Responses in Reform Class

    19. Responses in Reform Class

    20. Responses in Reform Class

    21. Understanding Slope

    22. Further Implications

    23. Further Implications

    24. Developing Conceptual Understanding

    25. Should x Mark the Spot?

    26. Should x Mark the Spot?

    27. Should x Mark the Spot?

    28. Some Illustrative Examples of Problems to Develop or Test for Conceptual Understanding

    29. Identify each of the following functions (a) - (n) as linear, exponential, logarithmic, or power. In each case, explain your reasoning. (g) y = 1.05x (h) y = x1.05 (i) y = (0.7)x (j) y = x0.7 (k) y = x(-˝) (l) 3x - 5y = 14

    30. For the polynomial shown, (a) What is the minimum degree? Give two different reasons for your answer. (b) What is the sign of the leading term? Explain. (c) What are the real roots? (d) What are the linear factors? (e) How many complex roots does the polynomial have?

    31. Two functions f and g are defined in the following table. Use the given values in the table to complete the table. If any entries are not defined, write “undefined”.

    32. Two functions f and g are given in the accompanying figure. The following five graphs (a)-(e) are the graphs of f + g, g - f, f*g, f/g, and g/f. Decide which is which.

    33. The following table shows world-wide wind power generating capacity, in megawatts, in various years.

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    35. Biologists have long observed that the larger the area of a region, the more species live there. The relationship is best modeled by a power function. Puerto Rico has 40 species of amphibians and reptiles on 3459 square miles and Hispaniola (Haiti and the Dominican Republic) has 84 species on 29,418 square miles. (a) Determine a power function that relates the number of species of reptiles and amphibians on a Caribbean island to its area. (b) Use the relationship to predict the number of species of reptiles and amphibians on Cuba, which measures 44218 square miles.

    36. The accompanying table and associated scatterplot give some data on the area (in square miles) of various Caribbean islands and estimates on the number species of amphibians and reptiles living on each.

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    40. Building Conceptual Understanding

    41. Building Conceptual Understanding

    42. Recognizing Conceptual Understanding

    43. Recognizing Conceptual Understanding

    44. Recognizing Conceptual Understanding

    45. Recognizing Conceptual Understanding

    46. Recognizing Conceptual Understanding

    47. Conclusion

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