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El. knyga: Large-Scale Studies in Mathematics Education

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  • Formatas: PDF+DRM
  • Serija: Research in Mathematics Education
  • Išleidimo metai: 05-May-2015
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319077161
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Large-Scale Studies in Mathematics EducationDidesnis paveikslėlis
  • Formatas: PDF+DRM
  • Serija: Research in Mathematics Education
  • Išleidimo metai: 05-May-2015
  • Leidėjas: Springer International Publishing AG
  • Kalba: eng
  • ISBN-13: 9783319077161
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In recent years, funding agencies like the Institute of Educational Sciences and the National Science Foundation have increasingly emphasized large-scale studies with experimental and quasi-experimental designs looking for 'objective truths'. Educational researchers have recently begun to use large-scale studies to understand what really works, from developing interventions, to validation studies of the intervention, and then to efficacy studies and the final "scale-up" for large implementation of an intervention. Moreover, modeling student learning developmentally, taking into account cohort factors, issues of socioeconomics, local political context and the presence or absence of interventions requires the use of large data sets, wherein these variables can be sampled adequately and inferences made. Inroads in quantitative methods have been made in the psychometric and sociometric literatures, but these methods are not yet common knowledge in the mathematics education community. In fact, currently there is no volume devoted to discussion of issues related to large-scale studies and to report findings from them. This volume is unique as it directly discusses methodological issue in large-scale studies and reports empirical data from large-scale studies.
Why Mathematics Education Needs Large-Scale Research
1(16)
James A. Middleton
Jinfa Cai
Stephen Hwang
What Is Meant by "Large Scale?"
3(1)
Sample Size
3(9)
Purpose of the Study
5(2)
Generalizability and Transportability of Results
7(1)
Type and Complexity of Data Analysis
8(4)
Summary
12(1)
References
13(4)
Part I Curriculum
A Lesson for the Common Core Standards Era from the NCTM Standards Era: The Importance of Considering School-Level Buy-in When Implementing and Evaluating Standards-Based Instructional Materials
17(28)
Steven Kramer
Jinfa Cai
F. Joseph Merlino
Background
18(5)
Method
23(10)
Achievement Measures
23(1)
Will-to-Reform Scale
24(3)
Comparison Schools
27(3)
Statistical Model
30(3)
Results
33(6)
Overall Treatment Effects
33(1)
Buy-in Effects
34(3)
Effects of Will-to-Reform Subcomponents
37(2)
Discussion
39(2)
References
41(4)
Longitudinally Investigating the Impact of Curricula and Classroom Emphases on the Algebra Learning of Students of Different Ethnicities
45(16)
Stephen Hwang
Jinfa Cai
Jeffrey C. Shih
John C. Moyer
Ning Wang
Bikai Nie
Background
46(3)
The LieCal Project
46(1)
Algebra Readiness
47(1)
Conceptual and Procedural Emphases
47(2)
Method
49(3)
Sample
49(1)
Assessing Students' Learning
49(2)
Conceptual and Procedural Emphases as Classroom-Level Variables
51(1)
Quantitative Data Analysis
51(1)
Results
52(5)
State Standardized Tests
53(1)
Student-Level and Curriculum Cross-Sectional HLM Models
53(2)
Student-Level, Classroom-Level, and Curriculum HLM Models
55(2)
Discussion
57(1)
References
58(3)
Exploring the Impact of Knowledge of Multiple Strategies on Students' Learning About Proportions
61(14)
Rozy Vig
Jon R. Star
Danielle N. Dupuis
Amy E. Lein
Asha K. Jitendra
Theoretical Background
62(2)
Method
64(4)
Participants
64(1)
Intervention
65(1)
Measures
65(2)
Strategy Coding
67(1)
Results
68(4)
Strategy Use at Pretest
68(2)
Relationship Between Strategy Profile and Posttest Performance
70(1)
Discussion
70(2)
References
72(3)
Challenges in Conducting Large-Scale Studies of Curricular Effectiveness: Data Collection and Analyses in the COSMIC Project
75(20)
James E. Tarr
Victor Soria
The COSMIC Project
75(1)
Results of the COSMIC Project
76(2)
Issues Related to Collection and Analysis of Student Data
78(8)
Lack of a Common Measure of Prior Achievement
78(3)
Composition of Student Sample
81(5)
Issues Related to Collection and Analysis of Teacher Data
86(1)
Issues Related to Modeling Student Outcomes
87(3)
Conclusion
90(1)
References
91(4)
Part II Teaching
Turning to Online Courses to Expand Access: A Rigorous Study of the Impact of Online Algebra I for Eighth Graders
95(38)
Jessica B. Heppen
Margaret Clements
Kirk Walters
Overview
95(3)
Background and Rationale
98(4)
Significance of Algebra I
98(2)
Use of Online Courses to Expand Offerings
100(1)
Prior Research on Online Course Effectiveness
101(1)
Study Design and Methodological Considerations
102(4)
Goals and Research Questions
102(1)
Study Design
103(3)
Analytic Methods
106(1)
Study Sample
106(6)
School Recruitment
106(2)
Description of Participating Schools
108(1)
Description of Students in Participating Schools
109(3)
Measures
112(3)
Implementation Measures
112(1)
Outcome Measures
113(2)
The Online Algebra I Course: Course Content, Online Teachers, and On-Site Proctors
115(3)
Course Content
116(1)
Online Teachers
117(1)
On-Site Proctors
118(1)
Implementation Findings
118(5)
Online Course Activity
118(2)
On-Site Proctors
120(1)
Online Course Completion Rates
121(1)
Course Content in Control Schools: Treatment Contrast
121(1)
Summary of the Implementation Findings
122(1)
Impact Findings
123(5)
Impacts on Algebra-Ready Students' Algebra Scores and High-School Coursetaking
123(2)
Impacts on Algebra-Ready Students' General Math Achievement and Non-Algebra-Ready Students' Outcomes
125(3)
Conclusions and Future Directions
128(2)
Limitations of the Study and Future Research Directions
129(1)
References
130(3)
A Randomized Trial of Lesson Study with Mathematical Resource Kits: Analysis of Impact on Teachers' Beliefs and Learning Community
133(26)
Catherine C. Lewis
Rebecca Reed Perry
Background on Lesson Study
134(2)
Method
136(8)
The Study Design and Conditions
136(3)
Measurement of Teachers' Beliefs and Teacher Learning Community
139(1)
Measurement of Teachers' and Students' Fractions Knowledge
140(1)
Data Collection
141(2)
Data Analysis
143(1)
Results
144(7)
Discussion
151(2)
Conclusions
153(1)
Appendix: Scales to Measure Teachers' Beliefs and Teacher Learning Community
154(1)
References
155(4)
Conceptualizing Teachers' Capacity for Learning Trajectory-Oriented Formative Assessment in Mathematics
159(20)
Caroline B. Ebby
Philip M. Sirinides
Conceptual Framework: Learning Trajectory-Oriented Formative Assessment
160(1)
The TASK Instrument
161(7)
Scoring Rubric
166(1)
Ongoing TASK Development
167(1)
Large-Scale Field Trial Results
168(3)
Descriptive Statistics
168(2)
Instrument Properties
170(1)
Pathways Analyses
171(3)
Building Capacity for Effective Mathematics Instruction
174(1)
References
174(5)
Part III Learning
Using NAEP to Analyze Eighth-Grade Students' Ability to Reason Algebraically
179(30)
Peter Kloosterman
Crystal Walcott
Nathaniel J.S. Brown
Doris Mohr
Arnulfo Perez
Shenghi Dai
Michael Roach
Linda Dager Hall
Hsueh-Chen Huang
The NAEP Assessments
180(2)
NAEP Framework and Scoring
181(1)
Access to NAEP Data
182(1)
What Can NAEP Tell Us About Students' Algebraic Reasoning Skills?
182(15)
Method
184(6)
Results
190(7)
NAEP as a Database of Student Understanding
197(1)
Themes in the Algebra Data
197(1)
Conceptual, Logistical, and Methodological Issues in the Use of NAEP Data
198(5)
Analyses Are Limited by the Data Available
199(1)
Access to Secure NAEP Data
200(1)
Using Statistical Software with NAEP Data
201(1)
What Does It Mean to Say That a Certain Percentage of Students Answered an Item Correctly?
202(1)
Limitations on Analyses by Demographic Subgroup
202(1)
Looking Forward
203(3)
Subscales for Specific Mathematics Skills
203(1)
Psychometric Issues
204(2)
References
206(3)
Homework and Mathematics Learning: What Can We Learn from the TIMSS Series Studies in the Last Two Decades?
209(26)
Yan Zhu
Homework Is an Important Issue Inside and Outside of Academia
209(2)
Effects of Homework Are Inclusive
211(2)
Changes in TIMSS Investigations About Homework from 1995 to 2011
213(1)
Is There a System-Level Homework Policy Available?
214(1)
How Often Do Students Receive Homework in Mathematics from Teachers?
215(2)
How Much Time Do Students Spend on Mathematics Homework?
217(3)
What Types of Mathematics Homework Do Teachers Assign?
220(3)
What Mathematics Homework-Related Activities Were Carried Out in Classes?
223(4)
How Much Were Parents Involved in Students' Homework?
227(2)
Summary and Conclusions
229(3)
References
232(3)
Effect of an Intervention on Conceptual Change of Decimals in Chinese Elementary Students: A Problem-Based Learning Approach
235(30)
Ru-De Liu
Yi Ding
Min Zong
Dake Zhang
A Conceptual Change Approach to Explain Children's Difficulties with Decimals
236(1)
Existing Interventions for Teaching Decimals
237(2)
Problem-Based Learning and Self-Efficacy
239(1)
Method
240(7)
Design
240(1)
Participants and Setting
240(1)
Dependent Measures
241(1)
Coding and Scoring
242(1)
Procedures
243(4)
Treatment Fidelity
247(1)
Results
247(6)
Pretreatment Group Equivalency
247(1)
Quantitative Measure of Students' Conceptual Change in Decimals
247(2)
Students' Self-Efficacy and Academic Interest
249(1)
Qualitative Measure of Students' Conceptual Change in Decimals
250(1)
Students' Computation Errors
250(2)
Analysis of Relations Between Whole Number and Decimal Computation
252(1)
Discussion
253(3)
PBL and Improvement in Computation Skills
253(1)
Effects on Enhancing Students' Self-Efficacy and Academic Interest
253(1)
Effects on Enhancing Students' Metacognition
254(1)
Effects on Conceptual Change in Decimals
254(2)
Limitations and Conclusions
256(4)
Appendix 1 Teaching Scripts for Teaching New Decimal Division
257(1)
Appendix 2 Teaching Scripts for Reviewing Previous Contents (Decimal Division Error Clinic)
258(1)
Appendix 3 PBL Procedure
258(1)
Appendix 4 Treatment Fidelity Checklists
259(1)
Appendix 5 Sample Problems from the Curriculum
259(1)
References
260(5)
A Longitudinal Study of the Development of Rational Number Concepts and Strategies in the Middle Grades
265(28)
James A. Middleton
Brandon Helding
Colleen Megowan-Romanowicz
Yanyun Yang
Bahadir Yanik
Ahyoung Kim
Cumali Oksuz
Introduction
265(3)
Longitudinal Analysis
266(1)
Issues in Mapping Students' Growing Knowledge
267(1)
Method
268(5)
Setting and Participants
268(1)
Data Collection Procedures: Interviews and Classroom Observations
269(2)
Assessment of Students' Rational Number Performance
271(2)
Results
273(11)
Comparison of Performance of Sample to a National/International Sample
273(1)
Comparison of Performance at Different Grade Levels
274(1)
Describing Students' Mathematics Achievement over Time
275(2)
Interview Results
277(4)
Summary of Interview Data
281(3)
Discussion
284(3)
Conclusions
285(1)
Commentary on the Issue of Scale in Intensive Interview and Observational Methods
286(1)
References
287(6)
Part IV Methodology
Measuring Change in Mathematics Learning with Longitudinal Studies: Conceptualization and Methodological Issues
293(18)
Jinfa Cai
Yujing Ni
Stephen Hwang
Two Longitudinal Studies Examining Curricular Effect on Student Learning
293(1)
Conceptualizing and Measuring Change in Student Learning
294(2)
Analyzing and Reporting Change
296(6)
Analyzing and Reporting Change Quantitatively
297(2)
Analyzing and Reporting Change Qualitatively
299(2)
Analyzing and Reporting Change Beyond the Grade Band
301(1)
Interpreting Change in Mathematics Achievement
302(3)
Equivalence of Student Sample Groups
302(1)
Initial Conceptual Model
303(2)
Conclusion
305(2)
References
307(4)
A Review of Three Large-Scale Datasets Critiquing Item Design, Data Collection, and the Usefulness of Claims
311(24)
Darryl Orletsky
James A. Middleton
Finbarr Sloane
Introduction
311(4)
Education Longitudinal Study of 2002
312(1)
National Assessment of Educational Progress
313(1)
Trends in International Mathematics and Science Study
314(1)
Sampling Issues
315(1)
Validity
316(14)
Statistical Validity
318(2)
Internal Validity
320(4)
Construct Validity
324(5)
External Validity
329(1)
Conclusions on Validity
330(1)
Discussion: Usefulness
330(2)
References
332(3)
Methodological Issues in Mathematics Education Research When Exploring Issues Around Participation and Engagement
335(28)
Tamjid Mujtaba
Michael J. Reiss
Melissa Rodd
Shirley Simon
Background
335(1)
The Context of This Study
336(1)
Introduction to Findings
337(24)
Multi-level Findings: Intention to Participate in Mathematics Post-16 Amongst Year 8 Students
340(5)
The Emergence of the Importance of Teachers via Qualitative Work
345(6)
Deconstructing What Our Original Constructs Actually Measured: Perceptions of Mathematics Teachers, Mathematics and Mathematics Lessons
351(6)
Multi-level Re-analysis to Explore the Importance of Students' Perceptions on Intended Post-16 Mathematics Participation (Using Items from the Survey Rather than Constructs)
357(4)
Methodological Conclusions
361(1)
References
362(1)
Addressing Measurement Issues in Two Large-Scale Mathematics Classroom Observation Protocols
363(10)
Jeffrey C. Shih
Marsha Ing
James E. Tarr
Methods
364(2)
Observational Protocols
364(2)
Analysis
366(1)
Results
366(3)
Lessons (CLE)
366(1)
Lessons and Raters (MQI)
367(2)
Discussion
369(1)
References
370(3)
Engineering [ for] Effectiveness in Mathematics Education: Intervention at the Instructional Core in an Era of Common Core Standards
373(32)
Jere Confrey
Alan Maloney
The Process of "Engineering [ for] Effectiveness"
373(4)
Intervening at the Instructional Core
377(1)
Curricular Effectiveness Studies
378(15)
Case One Single-Subject vs. Integrated Mathematics (COSMIC Study)
379(6)
Case Two Comparing Effects of Four Curricula on First- and Second-Grade Math Learning
385(5)
Case Three The Relationship Among Teacher's Capacity, Quality of Implementation, and the Ways of Using Curricula
390(3)
Overall Conclusions from the Three Cases
393(4)
Engineering [ for] Effectiveness: Summary and Recommendations
397(4)
Steps in a Strategic Plan to Strengthen the Instructional Core in Relation to Curricular Use, Implementation, and Outcomes
400(1)
References
401(4)
The Role of Large-Scale Studies in Mathematics Education
405(12)
Jinfa Cai
Stephen Hwang
James A. Middleton
Benefits of Large-Scale Studies in Mathematics Education
406(4)
Understanding the Status of Situations and Trends
406(1)
Testing Hypotheses
407(1)
Employing Sophisticated Analytic Methods
408(2)
Pitfalls of Large-Scale Studies in Mathematics Education
410(2)
Resources and Time
410(1)
Complexity of Authentic Research Settings
411(1)
Methodology
411(1)
Looking to the Future
412(1)
References
413(4)
Index 417
James A. Middleton is Professor of Mechanical and Aerospace Engineering at Arizona State University. Prior to these appointments, Dr. Middleton served as Associate Dean for Research for the Mary Lou Fulton College of Education at Arizona State University and as Director of the Division of Curriculum and Instruction. He received his Ph.D. in Educational Psychology from the University of Wisconsin-Madison in 1992, where he also served in the National Center for Research on Mathematical Sciences Education as a postdoctoral scholar for 3 years. Jims research interests focus in the following areas where he has published extensively: Childrens mathematical thinking; Teacher and Student motivation in mathematics; and Teacher Change in mathematics. He has served as Senior co-Chair of the Special Interest Group for Mathematics Education of the American Educational Research Association, and as chair of the National Council of Teachers of Mathematics Research Committee.

Jinfa Cai is a Professor of Mathematics and Education and the director of Secondary math education at the University of Delaware.  He is interested in how students learn mathematics and solve problems, and how teachers can provide and create learning environments so that students can make sense of mathematics.  He received a number of awards, including a National Academy of Education Spencer Fellowship, an American Council on Education Fellowship, an International Research Award, and a Teaching Excellence Award. He has been serving on the Editorial Boards for several international journals, such as the Journal for Research in Mathematics Education.  He was a visiting professor in various institutions, including Harvard University.  He has serves as a Program Director at the U.S. National Science Foundation (2010-2011) and a co-chair of American Educational Research Associations Special Interest Group on Research in Mathematics Education (AERAs SIG-RME)(2010-2012).  He will be chairing a plenary panel at the ICMI-12 in Germany in 2016.

Stephen Hwang is currently a post-doctoral researcher working with Jinfa Cai in the Department of Mathematical Sciences at the University of Delaware. His research interests include the teaching and learning of mathematical justification and proof, the nature of practice in the discipline of mathematics, the development of mathematical habits of mind, and mathematics teacher preparation.
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