Heather Fisher & Alex MacDonald With Marina Milner-Bolotin Proudly supported by TLEF Thursday, February 28, 2013 SyMETRI Meeting Math & Science Teaching and Learning through Technology Proudly supported by TLEF

Question Title Blocks and a Pulley m2m2 m1m1

Question Title Two blocks are connected via a pulley. The blocks are initially at rest as block m 1 is attached to a wall. If string A breaks, what will the accelerations of the blocks be? (Assume friction is very small and strings don’t stretch) Question Title Blocks and a Pulley II m2m2 m1m1 A B Why are the assumptions above important?

Comments Answer: E Justification: None of the above answers is correct. Consider two blocks as one system: one can see that the system has a mass of (m 1 +m 2 ), while the net force pulling the system down is m 1 g. Therefore, applying Newton’s second law, one can see that the acceleration of the system must be less than g: Some people think that the acceleration will be g. They forget that the system consists of two blocks (not just m 1 ) and the only pulling force is m 1 g. Thus the system is NOT in a free fall. Compare this questions to the previous one to see the difference. Comments Solution

Objectives Assist teacher-candidates through four platforms: Within their B. Ed Methods courses (as learners) Developing personal teaching style Providing resources for teacher-candidates (as teachers) Creating a stronger connection to the UBC Community

Activity

Logical reasoning If m and p are positive integers and (m + p) x m is even, which of the following must be true? (A) If m is odd, then p is odd. (B) If m is odd, then p is even. (C) If m is even, then p is even. (D) If m is even, then p is odd. (E) m must be even.

Question Title A.24 m 2 B.76 m 2 C. 100 m 2 D. 124 m 2 E.Not enough information What is the area of the figure below? Question Title Area 10 m 6 m 4 m 10 m

Comments Answer: B Justification: The easiest way to find the area is to imagine a 10 m by 10 m square and subtracting a 4 m by 6 m rectangle. Comments Solution A = 10 m x 10 m – 4 m x 6 m = 76 m 2 Alternatively, the shape’s area can be found by dividing it into 2 rectangles and adding the areas together. 10 m 6 m4 m 6 m 10 m

Logical reasoning In the figure below, a square is inscribed in a circle with diameter d. What is the sum of the areas of the shaded regions, in terms of d ?

1.Which questions generated the most productive discussion? Why? 2.How do you think clickers supported/hindered problem solving? How did clickers affect class dynamics? 3.Were there multiple ways to solve the problems? How were multiple interpretations dealt with? 4.What level of understanding did each question address (ex. conceptual understanding, application, recall, etc.)? How did students engage with each type of question? 5.What did the teacher do to support the students during the activity? What could have been done differently? Were all students supported? Discussion

Next Steps Resources SMARTboards Primary Grades Outreach Faculty and community awareness

Beatty, I., Gerace, W., Leonard, W., & Defresne, R. (2006). Designing Effective Questions for Classroom Response System Teaching. American Journal of Physics, 74(1), 31–39. CWSEI Clicker Resource Guide: An Instructors Guide to the Effective Use of Persnal Response Systems (Clickers) in Teaching. (2009, June 1). Lasry, Nathaniel. (2008). Clickers or Flashcards: Is There Really a Difference? The Physics Teacher, 46(May), Milner-Bolotin, Marina. (2004). Tips for Using a Peer Response System in the Large Introductory Physics Classroom. The Physics Teacher, 42(8), Mishra, P., & Koehler, M. J. (2007). Technological pedagogical content knowledge (TPCK): Confronting the wicked problems of teaching with technology. In Society for Information Technology & Teacher Education International Conference (Vol. 2007, pp. 2214–2226). Retrieved from Resources

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Appendix

Logical reasoning If & is defined for all positive numbers a and b by Then 10 & 2 =

Question Title Ratios in a Bag of Candy The ratio of red to green to blue candies in a bag of candy is 2 : 3 : 4. Jeremy eats 1 red, 1 green, and 1 blue candy. Does the ratio of red to green to blue candies change? A.Yes B.No C.Not sure –

Comments Answer: A Justification: The ratio of red to green to blue candies will change. After removing 1 of each color: 2 – 1 = 1 red candy 3 – 1 = 2 green candies 4 – 1 = 3 blue candies The ratio 2 : 3 : 4 is not the same as 1 : 2 : 3. In most cases, only multiplying or dividing the terms in a ratio will result in an equivalent ratio. Comments Solution

The Unit Circle A circle with radius 1 is drawn with its center through the origin of a coordinate plane. Consider an arbitrary point P on the circle. What are the coordinates of P in terms of the angle θ? x y θ 1 P(x 1,y 1 ) Press for hint P(x 1,y 1 ) 1 θ x1x1 y1y1 x y

Solution Answer: C Justification: Draw a right triangle by connecting the origin to point P, and drawing a perpendicular line from P to the x- axis. This triangle has side lengths x1, y1, and hypotenuse 1. P(x 1,y 1 ) 1 θ x1x1 y1y1 x y Therefore, the point P has the coordinates (cos θ, sin θ). The trigonometric ratios sine and cosine for this triangle are: