Skip to Main Content
 

Global Search Box

 
 
 
 

Files

File List


Smucker Dissertation 7.14.pdf (5.37 MB)

ETD Abstract Container

Abstract Header

Preservice Secondary Mathematics Teachers’ Approaches to Probabilistic and Stochastic Problem Solving Using Computer Simulations

Smucker, Karoline
http://orcid.org/0000-0003-2133-8521
http://rave.ohiolink.edu/etdc/view?acc_num=osu1657653985717453

Abstract Details

2022, Doctor of Philosophy, Ohio State University, EDU Teaching and Learning.
Probabilistic simulations have long served as instructional tools in statistics and probability education. With advances in technology, computer simulation environments where large quantities of data can be collected and analyzed have been suggested as venues for problem solving in contexts involving both known and unknown probability distributions. This research used task based interviews to examine how four secondary preservice mathematics teachers approached seven probabilistic and stochastic contexts which included designed computer simulation environments. The interviews included tasks involving both known and unknown probability distributions. Participants’ problem solving and stochastic modeling practices were considered, along with the role the simulations may have played in their approaches. This research proposes an empirically grounded model for problem solving with simulations in stochastic contexts based on participants’ tendencies. Results suggest that participants’ problem solving varied based on whether the task involved a known or unknown distribution. When tasks involved known distributions, the simulations were used primarily to confirm or test mathematical ideas from outside the simulation. In contexts involving unknown distributions, participants used the simulation environment to investigate empirically and provide approximations and inferences. Prior experience in statistics and probability played a key role in problem solving outside the simulation, and included mathematizing the contexts using distributions, lists, charts, and formulas. In the simulation environments, participants worked mathematically with the data using calculations, proportions, counts, and graphs. Data collection in the simulation environments tended to be iterative, with participants testing, evaluating, and refining ideas over several rounds, though the amount of data which they considered to be necessary to draw conclusions varied significantly based on context.
Azita Manouchehri (Advisor)
Jan Nespor (Committee Member)
Arnulfo Perez (Committee Member)
354 p.
Educational Technology; Mathematics Education; Statistics; Teacher Education; Teaching
Statistics Education; Probability Education; Preservice Teachers; Simulation Technology; Problem Solving

Recommended Citations

Citations

  • Smucker, K. (2022). Preservice Secondary Mathematics Teachers’ Approaches to Probabilistic and Stochastic Problem Solving Using Computer Simulations [Doctoral dissertation, Ohio State University]. OhioLINK Electronic Theses and Dissertations Center. http://rave.ohiolink.edu/etdc/view?acc_num=osu1657653985717453

    APA Style (7th edition)

  • Smucker, Karoline. Preservice Secondary Mathematics Teachers’ Approaches to Probabilistic and Stochastic Problem Solving Using Computer Simulations. 2022. Ohio State University, Doctoral dissertation. OhioLINK Electronic Theses and Dissertations Center, http://rave.ohiolink.edu/etdc/view?acc_num=osu1657653985717453.

    MLA Style (8th edition)

  • Smucker, Karoline. "Preservice Secondary Mathematics Teachers’ Approaches to Probabilistic and Stochastic Problem Solving Using Computer Simulations." Doctoral dissertation, Ohio State University, 2022. http://rave.ohiolink.edu/etdc/view?acc_num=osu1657653985717453

    Chicago Manual of Style (17th edition)

osu1657653985717453
340
© 2022, all rights reserved.
This open access ETD is published by The Ohio State University and OhioLINK.