WWW.THESIS.DISLIB.INFO
FREE ELECTRONIC LIBRARY - Online materials, documents
 
<< HOME
CONTACTS



Pages:     | 1 |   ...   | 100 | 101 || 103 | 104 |   ...   | 121 |

«PROCEEDINGS OF THE 15TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION EDITORS STACY BROWN SEAN LARSEN KAREN MARRONGELLE ...»

-- [ Page 102 ] --

With this project we seek to fill a gap in the knowledge that exists about how mathematics faculty members new to teaching with inquiry-based learning [IBL] methods learn to use these approaches. Specifically, we seek to produce accounts of the process of learning to teach using IBL from faculty who are new to the method and contrasting that process with faculty who consider themselves advanced users of IBL. At the undergraduate level, inquiry-based learning in mathematics finds its roots in views of R. L. Moore of the University of Texas. Moore believed students should build their own understanding and work through the course material individually. As peer collaboration and group work have come to be valued (National Council of Teachers of Mathematics [NCTM], 2000), Moore’s insistence on individual work has fallen out of favor. Instructors have adapted Moore’s values with time, and now, dubbed IBL, the method refers to a spectrum of instructional styles that allow students to work in small groups, consult outside resources, or pose and seek answers to their own questions. Present in all IBL classrooms, however, is an emphasis on student presentations and active student participation with very limited lecturing (Coppin, Mahavier, May, & Parker, 2009). A growing body of research has been documenting the positive impact of IBL methods on students’ gains in the cognitive and social domains (Hassi, 2009; Laursen & Hassi, 2009, 2010; Laursen, Hassi, & Crane, 2009; Laursen, Hassi, Crane, & Hunter, 2010). In particular, Laursen and colleagues (Laursen, et al., 2010) report that students in IBL courses report higher cognitive gains than students in non-IBL courses, in terms of mathematical thinking, understanding of concepts, and application of mathematical knowledge. Students in IBL courses, and in particular future teachers, reported higher cognitive gains about teaching. Given that lecturing is a predominant model of instruction in college mathematics classrooms (Lutzer, Rodi, Kirkman, & Maxwell,

2007) we asked: How do faculty learn to teach with these new methods? What kinds of concerns 15TH Annual Conference on Research in Undergraduate Mathematics Education 507 do they have? And how do resources such as experience, other colleagues, books, or conferences and workshops help them in developing a better sense of what it means to use IBL methods in teaching mathematics?

The literature on teacher learning to teach mathematics is extensive at the K-12 level, but is more limited in the post-secondary level. Investigations at the post-secondary level suggest a developmental path in the process of learning to teach (Nardi, Jaworksi, & Hegedus, 2005;

Nyquist & Sprague, 1998). Nyquist and Sprague (1998) suggest that teaching assistants’ concerns, discourse, and relationships with students and colleagues progress through a series of stages. Initially, teaching assistants focus on themselves (“Will my students like me?”) and on their own survival; next, they worry about managing discussions or handling classroom participation; and in later stages, they start to focus on students’ understanding and learning outcomes. These shifts from concerns about the self, to concerns about managing teaching, and finally to concerns about students’ learning and understanding, determine a path that we might expect as instructors teach with a new method. Nardi and her colleagues (2005) worked with tutors at the University of Oxford over an 8-week period doing individual interviews in which they were prompted to reflect on aspects of their teaching. The researchers identified four stages of pedagogical awareness—naïve and dismissive, intuitive and questioning, reflective and analytic, and confident and articulate (p. 293)—which, they propose, reveal a spectrum of awareness about students’ difficulties, strategies to overcome those difficulties, and selfreflection about teaching practices. Because they claim that instructor awareness can feed into other teaching formats (p. 293), we could anticipate comparable stages of awareness as teachers face a new instructional method for the first time. Other accounts of teaching with inquiryoriented curriculum (Marrongelle & Rasmussen, 2008; Speer & Hald, 2008; Stephan & Rasmussen, 2002) point at specific dilemmas that instructors face, in particular navigating the need to stay away for lecturing and moving toward more discussion-based classes. This literature is informative and allows us to think that there might be common concerns faculty have when they start teaching using IBL methods, and that these concerns may change and evolve as faculty teach other IBL courses.

Methods There are two primary sources of data collected over a one-year period: on-line teaching logs filled every other week and three interviews with faculty, at the beginning of the year, half way through, and the end of the year. In the pilot phase of the study, we worked with four instructors, all new to the method, having been through one week-long workshop the previous summer.

The on-line teaching logs request information on time spent on various types teaching activities (homework review, lecturing, large-group discussion, small group work, student presentations, assessment, class preparation, mathematical content, and pacing); challenges faced and concerns about these activities, solutions found to resolve these challenges, and resources used. The initial interview seeks to get baseline information about their understanding of IBL, what are necessary and sufficient conditions for a successful IBL course, and their anticipated learning goals for the students. The intermediate interview seeks to get information on the students, the curriculum, the instruction, and their assessment practices; in addition we explicitly ask instructors to tell us what they have learned about themselves, the students, teaching, and mathematics through teaching with IBL. The interview also asks for information on specific entries in the logs. The 508 15TH Annual Conference on Research in Undergraduate Mathematics Education final interview asks a combination of questions from the initial interview (e.g., their understanding of IBL) and the intermediate interview (e.g., students, curriculum, assessment).





The log data have been analyzed by finding themes across all the comments (N=36) submitted by the four instructors over a one-year period, attending first to the type of teaching activity. The themes were then used to code across the comments and refined into five categories: Student preparation, motivation, and engagement; Coverage; Rigor; Difficulty of the material; and Student Learning. We are currently analyzing the interview data.

Findings The instructors most frequently reported concerns about Student Preparation, Motivation, and Engagement with the material (14/36). For example they mentioned that the students would come to class with incomplete homework or with no evidence of having worked on some of the assignments (e.g., “The only challenge was in the most recent class when none of the students had a proof of Euler's Theorem.” Instructor 4). Instructors were concerned that student motivation waned towards the end of the term, presumably due to other commitments the students had (e.g., “My students are starting to feel the end of the semester, and they all seem quite worn down. I'm worried that their lack of enthusiasm will have a detrimental effect on their ability to keep being productive in the class.” Instructor 1) or that they appeared, at times, to be less engaged than they should be (e.g., “well overall, it is good, but I guess before spring break, their mind were somewhere else.” Instructor 3). Coverage, (8/36) was a concern shared by all instructors. As the method relies on students’ discovering the material, this theme is not unexpected, of course, and the instructors tended to compare time with their experience with non-IBL courses (e.g., “We didn't get to the division algorithm until day 5, and usually this is covered by day 2 when I'm lecturing!” Instructor 1). Departments were mentioned as a source of the pressure to cover the material (e.g., “pressure from the department to reach a level of content (namely reach the fundamental theorem of calculus), at this point it seems impossible unless I switch to a lecture format.” Instructor 3). But the pressure also came from the time that it takes to go through the discovery process (e.g., “I designed this course for prospective secondary math

teachers to end with the proof of the three impossible constructions of Euclidean geometry:

doubling the cube, squaring the circle and trisecting the angle. Everything was set up to get us there; it ties into the course we've taken in math history, and the 2-quarter sequence in geometry.

And, we aren't going to make it. It's a disappointment to me.” Instructor 2). Rigor and Difficulty of the material were each mentioned with the same frequency (6/36). Rigor referred to instructors’ dissatisfaction that the students were not learning to be careful in writing proofs (e.g., “Students were getting a little too informal in class, particularly when it came to giving proofs by induction. I struggled with how to get them to write out formal proofs by induction.” Instructor 1). Instructors also mentioned the difficulty of the content or assignments as a challenge (“The material that we are currently covering is a notch or two up in difficulty from what we have been doing all semester.” Instructor 4), which tied to students’ waning interest in some cases, led to disengaged classes. Finally, the two comments that we classified as Student Learning referred to the areas of assessment. Instructor 2 showed concern that in spite of designing a test that was quite similar to the homework assigned, students’ scores were around 78% with 2 students failing. This instructor adds: “I was disappointed to see scores as low as they were when the students weren't asked to do anything that was significantly new.” Instructor 4 showed concern about finding ways to assess students’ knowledge using other means beyond homework and presentations. We took these comments as referring to student earning because 15TH Annual Conference on Research in Undergraduate Mathematics Education 509 they appear to indicate worry about the measures we use (through assessments) of what students know.

Discussion It is interesting that these instructors voice concerns that are focused on whether students like them or the method but more about managing instruction: keeping students engaged, ensuring that they are prepared for class, regulating the difficulty of the material and the rigor of students’ productions, and handling pressures to cover material. It is less evident that the instructors worry about students’ learning. Although not definitive, this analysis gives us information about what types of concerns to expect from the larger sample. Up to now we have collected 131 teaching logs from a new sample of 28 instructors and we are in the process of analyzing these to identify trends over time and trends by instructors' experience.

Questions for the audience

1. What types of questions could be added to the logs so that student learning can become more visible? 2. We propose a developmental path but other possible interpretations are viable. What could be other frameworks that could be used to analyze these data?

References Coppin, C. A., Mahavier, W. T., May, E. L., & Parker, G. E. (2009). The Moore Method: A pathway to learner-centered instruction. Washington, DC: The Mathematical Association of America.

Hassi, M.-L. (2009). Empowering undergraduate students through mathematical thinking and learning. Paper presented at the 15th International Conference of Adults Learning Mathematics, Lancaster, PA.

Laursen, S., & Hassi, M.-L. (2009, January 5-8). Inquiring about inquiry: Progress on research and evaluation studies of inquiry based learning in undergraduate mathematics at four campuses. Paper presented at the Joint Mathematics Meetings of the MAA and AMS, Washington, DC.

Laursen, S., & Hassi, M.-L. (2010). Benefits of inquiry based learning for undergraduate college mathematics students. Paper presented at the Annual meeting of the American Educational Research Association, Denver, CO.

Laursen, S., Hassi, M.-L., & Crane, R. (2009, July 16-18). First findings from evaluation studies of the IBL Mathematics Projects. Paper presented at the 12th Annual Legacy of R. L.

Moore conference, Austin, TX.

Laursen, S., Hassi, M.-L., Crane, R., & Hunter, A.-B. (2010). Student outcomes from Inquiry Based Learning in mathematics: A mixed method study. Paper presented at the Joint Meeting of the Mathematical Association of America and the American Mathematical Society, New Orleans, LA.

Lutzer, D. J., Rodi, S. B., Kirkman, E. E., & Maxwell, J. W. (2007). Statistical abstract of undergraduate programs in the mathematical sciences in the United States: Fall 2005 CBMS Survey. Washington, DC: American Mathematical Society.

510 15TH Annual Conference on Research in Undergraduate Mathematics Education Marrongelle, K., & Rasmussen, C. L. (2008). Meeting new teaching challenges: Teaching strategies that mediate between all lecture and all student discovery. In M. Carlson & C.

L. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 167-177). Washington, DC: Mathematical Association of America.

Nardi, E., Jaworksi, B., & Hegedus, S. (2005). A spectrum of pedagogical awareness for undergraduate mathematics: From 'tricks' to 'techniques'. Journal for Research in Mathematics Education, 36(4), 384-316.

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics. Reston, VA: Author.

Nyquist, J. D., & Sprague, J. (1998). Thinking developmentally about TAs. In M. Marincovich, J. Protsko & F. Stout (Eds.), The professional development of graduate teaching assistants (pp. 61-88). Bolton, MA: Anker.

Speer, N., & Hald, O. (2008). How do mathematicians learn to teach? Implications from research on teachers and teaching for graduate student professional development. In M. Carlson & C. L. Rasmussen (Eds.), Making the connection: Research and teaching in undergraduate mathematics education (pp. 305-317). Washington, DC: Mathematical Association of America.

Stephan, M., & Rasmussen, C. L. (2002). Classroom mathematical practices in differential equations. Journal of Mathematical Behavior, 21, 459-490.

–  –  –



Pages:     | 1 |   ...   | 100 | 101 || 103 | 104 |   ...   | 121 |


Similar works:

«SACS Preparation Division of Student Affairs Upward Bound Program REQUIREMENTS: • The institution provides student support programs, services, and activities consistent with its mission that promote student learning and enhance the development of its students.Responses: 1. Describe how your unit’s mission, services and activities are consistent with the mission of the University. The mission of the North Carolina State University Upward Bound (UB) Program is to provide participants, without...»

«for immediate release steven.swartz@boosey.com tel 212/358-5361 fax 212/358-5306 New York celebrates Steve Reich@70 Composer’s birthday is marked by a unique collaboration among Brooklyn Academy of Music, Carnegie Hall, and Lincoln Center Celebration includes two U.S. premieres and one NY premiere, anchoring a year of international festivities “There’s just a handful of living composers who can legitimately claim to have altered the direction of musical history and Steve Reich is one of...»

«Vibrant and Viable Places New Regeneration Framework 11 March 2013 Photos on pages 4, 9, 13, 17, 22 and 43 © Crown copyright (2011) Visit Wales Printed on recycled paper Print ISBN 978 0 7504 9175 4 Digital ISBN 978 0 7504 9177 8 © Crown Copyright 2013 WG17660 Contents 1. Executive summary 4 2. Foreword – Minister for Housing, Regeneration & Heritage 7 3. Context – What has changed and where we are now? 9 4. Our definition, vision and outcomes 13 5. Our principles and approaches 17 6. Our...»

«Adjusting Journal Entry Investigation Audit No. 14-023 UNT Michelle Finley, CIA Chief Internal Auditor April 16, 2014 WHY THE INVESTIGATION WAS PERFORMED An investigation was performed as a result of complaints received from the Texas State Auditor’s Office (“SAO”) and UNT Compliance hotline in September 2012. The complaints were similar and expressed concerns related to journal entry #0000213745. The adjusting journal entry was recorded to UNT’s general ledger on August 1, 2012, and...»

«UNITED NATIONS OFFICE FOR OUTER SPACE AFFAIRS United Nations Treaties and Principles on Outer Space and related General Assembly resolutions UNITED NATIONS UNITED NATIONS TREATIES AND PRINCIPLES ON OUTER SPACE Text of treaties and principles governing the activities of States in the exploration and use of outer space and related resolutions adopted by the General Assembly UNITED NATIONS New York, 2008 ST/SPACE/11/Rev.2 UNITED NATIONS PUBLICATION Sales No. E.08.I.10 ISBN 978-92-1-101164-7...»

«1 Divorce and Remarriage I Corinthians 7:10-24 – September 21, 2014 We come now to one of the key passages in Scripture about divorce and remarriage. Divorce and remarriage are so common in our society that it is easy to become dull to what the Bible actually says. Add to that the many interpretations on remarriage among evangelicals, godly men and women, and you have a quagmire of opinions. The one thing I DO NOT WANT TO DO TODAY is to diminish the seriousness of the marriage covenant and...»

«LAKE CENTRAL HIGH SCHOOL 2016 2017 STUDENT HANDBOOK AND CALENDAR 8400 Wicker Avenue, St. John, Indiana 46373 219-365-8551 Fax 219-365-7156 Property of: Address: _ Phone #: _ Email: In case of emergency, please notify: Name: _ Phone #: TABLE OF CONTENTS Administration Regulations Guidance Student Internet/On-Line Access Policy.29 Athletics Secondary Student Rules for Internet Use.29 Introduction Student Social Security Requirement Lake Central Mission Lake Central High School Dance Policy.31...»

«Train the Trainer toolkit Train the Trainer | Toolkit 1 Train the Trainer | Toolkit  Contents Train the Trainer toolkit Section 1: Training 1.1 Advisory/support groups for trainers of supported employees. 6 1.2 Assistive technology 1.3 Session plan – example 1.4 Training checklist 1.5 Training notebook – example layout 1.6 Training plan 1.7 Computer-based training Section 2: Assessment and evaluation 2.1 Assessment record – sample 2.2 Assessment task/activity samples 2.3 Evaluating...»

«DANIELI & C. – OFFICINE MECCANICHE S.p.A. Headquarters: Buttrio (UD), via Nazionale 41 Fully paid-up share capital of euro 81,304,566 Tax and Registration Number with the Register of Companies of Udine: 00167460302. ****** REPORT ON CORPORATE GOVERNANCE AND OWNERSHIP STRUCTURE 2014/2015 FINANCIAL YEAR In accordance with article 123-bis of Legislative Decree n.58 dated February 24, 1998 Approved by the Board of Directors on September 24, 2015 (traditional model of administration and control)...»

«PRESUPUESTO 2010 DETALLE EXPLICATIVO DEL PRESUPUESTO DE INGRESOS OPERACIONES CORRIENTES. El presupuesto de ingresos de la Universidad de Málaga clasifica en sus capítulos 3º al 5º los ingresos por operaciones corrientes. El importe de los ingresos por operaciones corrientes alcanza para el año 2010 la cifra de 236.907.354 euros, lo que supone el 83,76% del total de los ingresos inicialmente presupuestados. Los ingresos aplicables a cada nivel de desagregación son los que se describen en...»

«IN THE UNITED STATES DISTRICT COURT FOR THE EASTERN DISTRICT OF PENNSYLVANIA ZURICH AMERICAN INS. CO. : CIVIL ACTION : :v. : : : RITE AID CORPORATION : NO. 04-1759 MEMORANDUM OPINION November 23, 2004 PRATTER, District Judge. I. INTRODUCTION The substance of this case involves a petition filed pursuant to the Federal Arbitration Act (the “FAA”) to vacate, modify or correct an arbitration award regarding an insurance coverage dispute and a cross-petition to uphold the arbitration award....»

«The Unshackled Organization FACING THE CHALLENGE OF UNPREDICTABILITY THROUGH SPONTANEOUS REORGANIZATION BY JEFFREY GOLDSTEIN PUBLISHER'S MESSAGE B Y NORMAN BODEK PRODUCTIVITY PRESS PORTLAND, OREGON An invitation to colleagues and friends from Stewart Mennin. The Unshackled Organization, an invaluable book on leadership, is out of print. The author, Jeffrey Goldstein, a friend and colleague, has generously given permission for me to share a pdf version with you. He has written many other...»





 
<<  HOME   |    CONTACTS
2017 www.thesis.dislib.info - Online materials, documents

Materials of this site are available for review, all rights belong to their respective owners.
If you do not agree with the fact that your material is placed on this site, please, email us, we will within 1-2 business days delete him.