A Design Experiment of a Deeply Digital Instructional Unit and Its Impact in High School Classrooms

Transcription

1 A Design Experiment of a Deeply Digital Instructional Unit and Its Impact in High School Classrooms A. J. Edson Michigan State University The 3rd CSMC Interna/onal Conference Chicago, IL November 8, 2014

2 Moving Towards Deeply Digital Curricula Flexible, highly interactive digital instructional resources offer a promising, but thus far underdeveloped, alternative to conventional print materials. Currently, [w]hile the programs offered features identified as transformative there were many features that did not take full advantage of the digital medium (Choppin, Carson, Borys, Cerosaletti, & Gillis, 2014, p. 11). Materials with characteristics that leverage the affordances of present and emerging digital technologies to improve student learning and related teacher practices are commonly referred to as deeply digital instructional materials (Dorsey, 2011). 2

3 Transition to College Mathematics & Statistics Transition to College Mathematics and Statistics Print and Digital Deeply Digital Unit 3

4 Key Features of Transition to College Mathematics & Statistics Problem-based, inquiry-oriented, and technology-rich approach to mathematics and statistics Student-centered investigations promoting active learning, teamwork, and communication Real-world applications and mathematical modeling provide contexts for developing and connecting important mathematical content and mathematical practices Curriculum-embedded software, TCMS-Tools, supports student inquiry, mathematical modeling, and problem solving 4

5 Binomial Distributions and Statistical Inference Lesson 1: Binomial Distributions Investigation 1: Rules of Probability and Binomial Situations How can rules of probability help you analyze a binomial situation? Investigation 2: The Binomial Probability Formula How can you find the probability of getting a specified number of successes x in a binomial situation with n trials and probability p of success on each trial? Investigation 3: Statistical Significance How can you use technology to find out whether the number of successes in a binomial situation is statistically significant? Lesson 2: Sample Surveys Investigation 1: Trustworthy Surveys What are the characteristics of a trustworthy survey? Investigation 2: How Surveys Can Go Wrong What are the characteristics of an untrustworthy survey? Lesson 3: Margin of Error From Sample to Population Investigation 1: Variability from Sample to Sample How far is the proportion of successes in a random sample likely to be from the proportion of successes in the population from which it was taken? Investigation 2: The Margin of Error How can you estimate the sampling error when you do not know the proportion p of successes in the population? Investigation 3: Interpreting a Confidence Interval How is a 95% confidence interval computed and how should it be interpreted? Lesson 4: Looking Back 5

6 Research Context Purpose To (re)design, iteratively develop, test, and evaluate a deeply digital instructional unit focusing on binomial distributions and statistical inference from Transition to College Mathematics and Statistics (Hirsch, et al., 2015). Design Experiment (Brown, 1992; Collins, 1992, 1999; DBRC, 2003) Involving iterative cycles of (re)design, development, and testing of the digital materials for students whose intended college program of studies did not require calculus Context Conducted within a one-to-one, fourth-year high school mathematics classroom that contained two interactive whiteboards connected to a single audio system. Data Classroom observations and digital artifacts, student and teacher interviews, student surveys and assessments 6

7 Overall (Re)design and Development Process Iteration I Print Materials* Iteration II Prototype Lesson** Iteration III Deeply Digital Unit Acknowledgements: *Ann Watkins in developing the print version of the unit **James Laser in coding the initial shell for the digital unit 7

8 Digital Design Features Digital Design Features 8

9 Example Problem from the Print Unit Example Audio Clip and Related Launch Questions 9

10 Digital Design Features Digital Design Features 10

11 Example Problem from the Print Unit Example Snapshots of TCMS-Tools 11

12 Digital Design Features Digital Design Features 12

13 Example Problem from the Print Unit Example of Scroll-Over Definitions and Glossary of Key Terms 13

14 Digital Design Features Digital Design Features 14

15 Example Problem from the Print Unit Example of Digital Collaborative Notebooks 15

16 Example Problem from the Print Unit Example of Digital Collaborative Notebooks 16

17 Digital Design Features Digital Design Features 17

18 Example Problem from the Print Unit Example Problem from the Print Unit 18

19 Example Problem from the Deeply Digital Unit Example Problem from the Deeply Digital Unit 19

20 Example Problem from the Deeply Digital Unit Example Problem from the Deeply Digital Unit 20

21 Some Results Related to the Learner-Controlled Scaffolding Students solved complex and more open-ended problems. Groups used the learner-controlled scaffolding in different ways when they had difficulties on a problem. The prompts help those who are stuck on a particular problem, by having these prompts available they help those to get on the right path, without giving away the answer. For example, collectively, groupmates would use the learner-controlled scaffolding, discuss their thinking about the problem, and then write their thinking in the digital collaborative notebooks. For other groups, one or two groupmates used the learner-controlled scaffolding in their group and then incorporated the idea of prompt into their group discussion. Students used the learner-controlled scaffolding as a prompt for reflecting on their thinking. For instance, If you have done the problem and not sure if you have done it right, then click on that and make sure that it still makes sense using the new context of the prompt. 21

22 References Brown, A. L. (1992). Design experiments: Theoretical and methodological challenges in creating complex interventions in classroom settings. The Journal of the Learning Sciences, 2(2), Choppin, J., Carson, C., Borys, Z., Cerosaletti, C., & Gillis, R. (2014). A typology for analyzing digital curricula in mathematics education. International Journal of Education in Mathematics, Science, and Technology, 2(1), Collins, A. (1992). Toward a design science of education. In E. Scanlon & T. O'Shea (Eds.), New directions in educational technology (pp ). New York, NY: Springer. Collins, A. (1999). The changing infrastructure of education research. In E. C. Lagemann & L. S. Shulman (Eds.), Issues in education research: Problems and possibilities (pp ). San Francisco, CA: Jossey-Bass. Design-Based Research Collective. (2003). Design-based research: An emerging paradigm for educational inquiry. Educational Researcher, 32(1), 5-8. Dorsey, C. (2011). Perspective: Defining a deeply digital education. Retrieved from Hirsch, C.R., Hart, E.W., Watkins, A.E., Ritsema, B.E., with Fey, J.T., Keller, B.A., Walker, R.K., & Laser, J.K. (2015). Transition to college mathematics and statistics. Columbus, OH: McGraw-Hill School Solutions. 22