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“Active Learning Strategies Inside and Outside the Mathematics Classroom” Julie Miller Daytona State College

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Goals for today: Outline the use of preliminary activities to help students prepare for class Discuss the use of video lecture outside of class Create a Camtasia video from start to finish

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The Need for Change… From 2000 – 2004, enrollment in developmental mathematics at DSC steadily decreased The college collected data from past, present, and future students regarding primary obstacles to success The college identified and interviewed students who had begun their math sequence, but then dropped out of school

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Survey Results… Students in developmental math overwhelmed by the amount of time to complete their math sequence. The mean amount of time that students spent on math homework per week was less than 1.6 hr. Students who tried to study at home said they got “stuck” and frustrated.

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What We Did… Class meets for 8 weeks, 4 days per week for 1½ hours per day. Lecture is condensed to 20 minutes at the beginning of the period. Students work on mandatory assignments for the remaining part of class. These are graded daily. Implemented a mandatory lab. (Immersion) (Minimize passive part of learning) (Active Learning) Class time + Lab time = 7+ hours of active practice

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Attendance… 29 Students

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Completion Rates… 2005 – 20062006 – 20072007 – 2008 Completers MAT0002 Prealgebra 1049 / 2161 (48.5%) 1602/ 2270 (70.6%) 1774 / 2464 (75.2%) MAT0024 Introductory Algebra 926 / 1959 (47.3%) 1700 / 2564 (66.3%) 1665 / 2849 (58.9%) MAT1033 Intermediate Algebra 1282 / 2226 (57.6%) 1722 / 2883 (61.5%) 2034 / 3810 (56.1%) MAC1105 College Algebra 1459 / 2465 (59.1%) 1701 / 2723 (62.5%) 1899 / 3119 (61.8%) Total 4716 / 8811 (53.5%) 6725 / 10,440 (64.4%) 7372 / 12,142 (60.7%) New Course Delivery

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Strategies to Save Class Time… Use preliminary worksheets for discovery Use video content outside of class This leave more time in class for group work and hands-on practice

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Introduction to Complex Fractions 1.Add: 2. Subtract: 3.Divide: 4.Simplify the complex fraction by using the order of operations: 5.Simplify the complex fraction by using the order of operations: Problem 1 Problem 2 Problem 3

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6.Multiply: 7. Multiply: 8.Simplify the complex fraction by multiplying numerator and denominator of the “big” fraction by the LCD of all individual fractions. That is, = = 9.Simplify the complex fraction by multiplying numerator and denominator of the “big” fraction by the LCD of all individual fractions. That is, = = … Problem 6 Problem 7 = 39 = -4

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Multiplying Radical Expressions Square each expression. 1. (a + b) 2 2. (a – b) 2 3. (a + 5) 2 4. (5w – 4) 2 5. 6. 7.

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Multiplying Binomials Puzzle Complete the table. Show all work on a separate sheet of paper. BinomialsProduct (x + 4)(x + 5) (y + 1)(y + 3) (2p – 3)(p + 1) (7w + 4)(w – 8) x 2 + 7x + 12 y 2 + 8y + 15 2x 2 + 7x + 5 3z 2 + 10z + 8 (3x – y)(5x + 4y)

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Squaring Binomials Puzzle Complete the table. Show all work on a separate sheet of paper. BinomialsProduct (x + 4) 2 (y + 1) 2 (2p – 3) 2 (7w + 4) 2 x 2 + 10x + 25 y 2 – 6y + 9 4x 2 + 20x + 25 25w 2 – 90w + 81 (10t + 7w) 2

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Multiplying Conjugates Puzzle Complete the table. Show all work on a separate sheet of paper. BinomialsProduct (x + 3)(x – 3) (y + 2)(y – 2) (2x – 5)(2x + 5) (3t – 8)(3t + 8) t 2 – 16 x 2 – 4 25c 2 – 1 36d 2 – 25 (4m + n)(4m – n)

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Creating a Function “Repertoire” xy -3 -2 0 1 2 3 1. y = x2. y = x 2 xy -3 -2 0 1 2 3

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Creating a Function “Repertoire” xy -3 -2 0 1 2 3 3. y = x 3 4. y = |x| xy -3 -2 0 1 2 3

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Creating a Function “Repertoire” xy -3 -2 0 1 2 3 5. y =6. y = xy -3 -2 0 1 2 3

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Future Possibilities… Create a library of lecture videos for students to watch for homework. Do practice problems in class where the instructor can help. (Reverse the role of lecture and homework)

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What is Camtasia? Screen capture software that allows the user to record, edit, and share screen video content.

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Applications for Recording… PowerPoint TI-Smartview (graphing calculator emulator) Tablet (write lectures directly on screen) Flash Maple Excel Other…

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Lecture Video Using Tablet PC Record lecture videos. Post videos and accompanying PDF file for notes. Students watch videos for homework with accompanying worksheet. Video library available for students who miss class or need reinforcement.

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Video Homework

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Other Video Applications Graphing Calculator Videos PowerPoint Videos Videos to summarize course policies iPod videos

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Contact Information… Julie Miller: millerj@DaytonaState.edu

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EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x2 5 9 8x28x2 += 9 3x 8x 2 3x + 5 2 12x 3 2 Rewrite fractions using LCD,

EXAMPLE 3 Add expressions with different denominators Find the sum 5 12x 3 9 8x28x2 5 9 8x28x2 += 9 3x 8x 2 3x + 5 2 12x 3 2 Rewrite fractions using LCD,

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