Student Knowledge on Period, Frequency, and Angular Frequency
Explore how students grasp concepts of period, frequency, and angular frequency in physics with a focus on hierarchies in knowledge and mastery levels. Discover the preliminary skills related to determining these key elements.
Download Presentation
Please find below an Image/Link to download the presentation.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author. If you encounter any issues during the download, it is possible that the publisher has removed the file from their server.
You are allowed to download the files provided on this website for personal or commercial use, subject to the condition that they are used lawfully. All files are the property of their respective owners.
The content on the website is provided AS IS for your information and personal use only. It may not be sold, licensed, or shared on other websites without obtaining consent from the author.
E N D
Presentation Transcript
Modeling Student Understanding of Period, Frequency, and Angular Frequency Nicholas T. Young Andrew F. Heckler The Ohio State University 1
Introduction Period: T Wan et al (2016) Frequency: f Angular Frequency: Oscillations Ambrose (2007) Tongnopparat et al (2014) Waves Kryjevskaia et al (2012) Wittman (2003) Rotations Rimoldini and Singh (2005) 2
Research Goal Goal: Search for possible hierarchies in student knowledge regarding finding the period, frequency, and angular frequency from various representations Skill A Skill B (Hierarchical Relation) Skill A Skill B 3
Reasons for Hierarchy Graphical Representation Mathematical Representation ? ? = 2cos(? 3? +? 4) To find angular frequency: 1. Find period 2. Use ? =2? To find period: 1. Find angular frequency 2. Use ? =2? ? ? 4
Methods Pilot Studies/ Interviews Spring 2014 Introductory, algebra- based physics students N=590 Online, 30-item multiple choice test Student Difficulties/ Question Refinement Mock Recitation Sessions Online Essential Skills Training Spring 2017 Hierarchies 5
Sample Questions What period is depicted in the following graph? The equation ? ? = 7cos(2? describes the motion of a mass on a spring. What is the frequency of this motion? 5? + 3) Graphical Question Equation Question A harmonic oscillator has a frequency of Hz. What are the angular frequency and the period? Calculation Question 6
Mastery Find f from Graph Not mastered 163 203 Mastered 13 211 Find T from Graph Not mastered Mastered Finding f from graph Finding T from graph T=1/f Not mastered 116 48 Mastered 189 237 Not mastered Mastered =2 /T Applying =2 /T Applying T=1/f 7
Initial Results Find f from ? ? = cos 2??? (17%) Find T from ? ? = cos(2? (23%) T?) Find or f from ? = 2?? (28%) Find from graph (24%) Find using ? ? = cos(??) (33%) Find T or using ? =2? ? (48%) Find f from graph (38%) Find T or f using ? =1 ? (72%) Find T from graph (70%) No skills (5%) Figure 1: Preliminary hierarchy of skills related to determining the period, frequency, and angular frequency. Percentage of students who demonstrated mastery of each skill is indicated. 8
Limitations Exploratory description No measure of goodness of fit Cannot account for random errors 9
Item Tree Analysis Van Leeuwe (1974), Schrepp (2003), Unl & Sargin (2010) Two skills j and i: j -> i j -> i number of counterexamples: bji 0 number of counterexamples: bji 1 ... number of counterexamples: bji L Hierarchy 0 Hierarchy 1 j -> i Hierarchy L L is between 0 and the number of students, N, in data set, D Compute diff( L, D) for L=0, 1, 2, .... N 2 ???? ?,? ??? ??? ? ? Expected Counterexamples Observed Counterexamples Select hierarchy with lowest diff( L, D) value Use DAKS package (Unl & Sargin 2010) 10
Revised Hierarchy Figure 2: Hierarchy of skills related to determining the period, frequency, and angular frequency generated from item tree analysis 11
Conclusions Can be modeled as multi-level hierarchy T=1/f and finding period are essential 12
Funding/Questions Questions? A poster will be presented at the 9:15-10 session (E34) on this work. Funding for this project provided by the Center for Emergent Materials: an NSF MRSEC under award number DMR- 1420451. 13
