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



Pages:     | 1 |   ...   | 97 | 98 || 100 | 101 |   ...   | 121 |

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

-- [ Page 99 ] --

(2) [LL] two sessions weekly of traditional summary lecture with teacher-presented examples on the topics to be covered in computer-assisted instruction, and (3) [GL] a blend of treatments (1) and (2), with one weekly meeting traditional lecture, and one weekly meeting inquiry-based group work.

Students registered for one of four time periods in the Fall 2009 semester schedule for one 50minute class meeting and one 50-minute required lab meeting. Students in each time slot were randomly assigned to one of the two treatments for the semester, similar to (1) designated [G] and (2) designated [L], above, with just one class meeting per week. Each instructor involved taught all treatments, and all instructors had previous experience in both didactic and inquirybased teaching. Each instructor also met with his/her class in the mathematics computer lab.

Data gathered during the experiments in Fall 2009 and Fall 2010, and reported by Mayer (2010, 2011) on the two cohorts of elementary algebra students, included (1) course grades and test scores, (2) pre-test and post-test of content knowledge based upon a test which incorporated three open-ended problems, (3) for the 2010 cohort only, pre-test and post-test of content knowledge based upon a test consisting of 25 objective questions, (4) student course evaluations using the online IDEA system (IDEA 2010), and (5) RTOP observations of the instructors (RTOP 2010, Sawada 2002).

For this study, in Summer 2011, (6) data on performance of students in the next mathematics course taken after the elementary algebra course was collected from the university data base. At the time of submission of this paper, student performance in subsequent courses was available for Spring 2010, Summer 2010, Fall 2010, and Spring 2011. Thus, we have more data on performance in subsequent courses for the Fall 2009 experimental cohort than for the Fall 2010 cohort. By the time of the RUME 2012 meeting, we expect to have data for Summer 2011 analyzed, and possibly also for Fall 2011.

Results of the Research. Analysis of student success in subsequent courses, as measured by students’ final grade in the next course, was analyzed by using the comparisons of means independent t-test with an alpha of 0.05. Students’ grades in subsequent courses were coded as follows: A-5, B-4, C-3, D-2, and F-1. Figure 4 depicts statistics on students’ grades for the Fall 2009 cohort in their subsequent math course making no distinction between subsequent courses.

There was no significant difference between student grades in the next course based on the MA098 treatment (G or L) they received. Figure 5 breaks down the Fall 2009 cohort based on the specific subsequent course taken: MA110 is finite mathematics and is taught only in an inquiry-based/computer-assisted format and MA102 is Intermediate Algebra, taught only in a lecture/computer-assisted format. There was no significant difference between MA098 treatment groups for either MA110 or MA102 as the next course, though the MA098(L)MA102 trajectory narrowly missed significance. There were three treatments in the Fall 2010 cohort: GG, LL, and GL. Figure 6 shows data on how these treatment groups compared pair-wise based on student success in subsequent courses, making no distinction 492 15TH Annual Conference on Research in Undergraduate Mathematics Education between the next two possible courses. There were no significant differences between any of the three MA098 treatments as measured by final grades in subsequent courses. In summary, we found no differences in success in subsequent courses ascribable to treatment in MA098.

Questions for Further Research/Analysis. We will be analyzing data about subsequent courses for the 2010 cohort to include in our final report. We would like the audience’s input on

the following:

1. What additional data on students would be useful if we want to try to understand the differences between students going on to MA110 (a terminal mathematics course) versus students going on to MA102 (a pre-requisite for pre-calculus algebra)?

2. What would be a reliable and rigorous way to determine what impact the treatment has on a student’s course trajectory?

Implications for Practice. We now teach all regular sections of elementary algebra following the blended treatment of the Fall 2010 experimental cohort: three class meetings weekly, one inquiry-based, one lecture, and one in the lab. We made our decision to change MA098 instruction prior to analyzing student success in subsequence courses based upon gains on openended problems and student satisfaction. In view of the inherent coherence of algebra-related topics cutting across courses (Oehtrman, 2008), we expect to extend this study in subsequent years to credit courses such as intermediate algebra, pre-calculus algebra, and pre-calculus trigonometry, all of which presently incorporate computer-assisted instruction together with one weekly lecture meeting, and all in the course trajectory leading to calculus.

–  –  –

494 15TH Annual Conference on Research in Undergraduate Mathematics Education

References

Alrø, H., & Skovsmose, O. (2002). Dialogue and learning in mathematics education: Intention, reflection, critique. Boston: Kluwer Academic Publishers.

Cohen, E. (1994). Restructuring the Classroom: Conditions for Productive Small Groups.





Educational Research 64(1): 1-35.

Doorn, D. and O'Brien, M. (2007). Assessing the Gains from Concept Mapping in Introductory Statistics. International Journal for the Scholarship of Teaching and Learning 1(2); online at \url{http://academics.georgiasouthern.edu/ijsotl/v1n2/articles/doorn/index.htm}.

Duch, B. J., Groh, S. E., & Allen, D. E. (2001). The power of problem-based learning. Sterling, VA: Stylus.

Gautreau, R. and Novemsky, L. (1997). Concepts First – a Small Group Approach to Physics Learning. Am. J. Phys. 65(5): 418-429.

Gillies, R. M. (2007). Cooperative learning: Integrating theory and practice. Thousand Oaks, CA: Sage Publications.

Goodsell, A., Mahler, M., Tinto, V., Smith, B. L., & MacGregor, J. (Eds.) (1992). Collaborative learning: A sourcebook for higher education. University Park, PA: National Center on Postsecondary Teaching, Learning and Assessment.

Hoellwarth, C., Moelter, M. J., and Knight, R.D. (2005). A direct comparison of conceptual learning and problem solving ability in traditional and studio style classrooms. Am. J. Phys.

73(5): 459-463.

Hough, S. (2010a). The effects of the use of inquiry-based learning in undergraduate mathematics on student outcomes: A review of the literature. [Report prepared for Ethnography & Evaluation Research, University of Colorado at Boulder.] Hough, S. (2010b). The effects of the use of inquiry-based learning in undergraduate mathematics on prospective teacher outcomes: A review of the literature. [Report prepared for Ethnography & Evaluation Research, University of Colorado at Boulder.] IDEA (2010). The IDEA Center. \url{http://www.theideacenter.org/our-services/student-ratingsinstruction/0030-idea-online}.

Johnson, D., Johnson, R., & Smith, K. (1998). Active learning: Cooperation in the college classroom, 2nd ed. Edina, MN: Interaction Book Co.

Lerman, S. (2000). The social turn in mathematics education research. In J. Boaler (Ed.),

Multiple perspectives on mathematics teaching and learning (pp. 19-44). Palo Alto, CA:

Greenwood.

Laursen, S., Hasai, M-L., Kogan, M., and Hunter, A-B., Evaluation of the IBL Mathematics Project: Student and Instructor Outcomes of Inquiry-Based Learning in College Mathematics.

\url{http://www.colorado.edu/eer/research/steminquiry.html}.

Marrongelle, K. and Rasmussen, C. (2008). Meeting New Teaching Challenges: Teaching Strategies that Mediate Between All Lecture and All Student Discovery. In M. Carlson and C.

Rasmussen (Eds.), Making the Connection: Research to Practice in Undergraduate Mathematics, pp. 167-178. Mathematical Association of America, Washington, DC.

15TH Annual Conference on Research in Undergraduate Mathematics Education 495 Mayer, J.C., et al. (2009). Incorporating Inquiry-Based Class Sessions with Computer Assisted Instruction. Electronic Proceedings of 2009 SIGMAA Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, February, 2009.

Mayer, J.C., et al. (2010). Blending Inquiry-Based and Computer Assisted Instruction in a Basic Algebra Course: a Quasi-Experimental Study, Electronic Proceedings of Conference on Research in Undergraduate Mathematics Education, Raleigh, NC, February, 2010.

Mayer, J.C., Cochran, R., Fulmore, J., Ingram, T., Stansell, L., and Bond, W. (2011), InquiryBased and Didactic Instruction in a Computer-Assisted Context. Electronic Proceedings of Conference on Research in Undergraduate Mathematics Education, Portland, OR. February, 2011.

Oerhtman, M., Carlson, M., and Thompson, P. (2008). Foundational Reasoning Abilities that Promote Coherence in Students' Function Understanding. In M. Carlson and C. Rasmussen (Eds.), Making the Connection: Research to Practice in Undergraduate Mathematics, pp. 65-80.

Mathematical Association of America, Washington, DC.

Perkins, D. N., & Tishman, S. (2001). Dispositional aspects of intelligence. In Collis, J. M., & Messick, S. (Eds.), Intelligence and personality: Bridging the gap in theory and measurement (pp. 233-257). Mahwah, NJ: Lawrence Erlbaum.

Prince, M. (2004). Does active learning work? A review of the research. Journal of Engineering Education, 93(3), 223-231.

Prince, M, & Felder, R. (2007). The many facets of inductive teaching and learning. Journal of College Science Teaching, 36(5), 14-20.

RTOP (2010), Reformed Teaching Observation Protocol. Developed by ACEPT Project (Arizona State University). \url{http://physicsed.buffalostate.edu/AZTEC/RTOP/RTOP_full/} Savin-Baden, M., & Major, C. H. (2004). Foundations of problem-based learning. Maidenhead, UK: Open University Press.

Sawada, D., Piburn, M., Judson, E., Turley, J., Falconer, K., Benford, R. & Bloom, I. (2002).

Measuring reform practices in science and mathematics classrooms: The Reformed Teaching Observation Protocol. School Science and Mathematics, 102(6), 245-253.

496 15TH Annual Conference on Research in Undergraduate Mathematics Education Factors influencing students’ propensity for semantic and syntactic reasoning in proof writing: A case study Juan Pablo Mejia-Ramos1, Keith Weber1, Evan Fuller2, Aron Samkoff1, Kevin Calkins1 1- Rutgers University 2- Montclair State University Abstract. We present a case study of an individual student who consistently uses semantic reasoning to write proofs in calculus but infrequently uses semantic reasoning to write proofs in linear algebra. The differences in these reasoning styles can be partially attributed to his familiarity with the content, the teaching styles of the professors who taught him, and the time he was given to complete the tasks. These results suggest that there are factors, including domain, instruction, and methodological constraints, that researchers should consider when ascribing to students a proving style that have been ignored in previous research.

Keywords: Proof; Proving styles; Semantic proof productions; Syntactic proof productions Introduction and research questions In recent years, mathematics educators have noted that there are two qualitatively distinct ways to produce formal mathematical proofs (e.g., Raman, 2003; Vinner, 1991; Weber & Alcock, 2004). A prover can concentrate on the formal and logical aspect of proving, starting with appropriate definitions and hypotheses, carefully formulating what needs to be proven, and applying theorems and other valid rules of inference to these starting points until the desired conclusion is reached. This is sometimes referred to as a syntactic proof production and reasoning in this way is referred to as syntactic reasoning.

Alternatively, a prover can try to represent relevant mathematical objects, explore their properties, and see why the theorem is true using informal representations of mathematical concepts, such as exploring prototypical examples, diagrams, or graphs, and using this insight as the basis for constructing a formal proof. This is referred to as a semantic proof production and reasoning in this way is referred to as semantic reasoning.

Researchers have recently advanced a number of intriguing hypotheses about these constructs (and related constructs). First, based primarily on case studies, some researchers have hypothesized that some students rely predominantly on one form of reasoning in most of their proof production tasks—that is, we can reasonably refer to some students as syntactic provers or semantic provers (e.g., Alcock & Inglis, 2008;

Alcock & Simpson, 2004, 2005; Alcock & Weber, 2010a, 2010b; Burton, 2004;

Moutsios-Rentzos, 2009; Pinto & Tall, 1999, 2002; Weber, 2009). From hereon, we refer to students’ propensity to use semantic or syntactic reasoning as their proving style.

Second, again based on case studies, some researchers have speculated that there is not a strong correlation between proving styles and success in proof writing in advanced mathematics (e.g., Alcock & Simpson, 2004, 2005; Pinto & Tall, 1999; Weber, Alcock, & Radu, 2005). We have recently begun a NSF-funded large-scale study on examining 15TH Annual Conference on Research in Undergraduate Mathematics Education 497 the proving processes of 100 mathematics majors to assess the viability of these hypotheses.

A primary purpose of this preliminary report is to gain feedback on research goals and methodologies of our project from the undergraduate mathematics education research community. However, we also want to present a research finding. While numerous case studies have illuminated a consistency in individual students’ propensity to use syntactic or semantic reasoning in proof writing (e.g., Alcock & Inglis, 2008; Alcock & Simpson, 2004, 2005; Alcock & Weber, 2010a, 2010b; Burton, 2004; Pinto & Tall, 1999, 2002;



Pages:     | 1 |   ...   | 97 | 98 || 100 | 101 |   ...   | 121 |


Similar works:

«CONTENTS PAGE Colours of the Union 2 Company, Secretary & Office Details 3 Directors of NLD 4 Member Clubs 5-7 Subscriptions 8 Officers of NLD 9 Management Committee 10 Committee Personnel 11 14 Playing Management 15 NLD Representatives 16 NLD Schools of Rugby 17 Community Coaches 17 R D O’s 18 Domestic Union Officials 19 21 NLD Referees Society 22 23 Personnel Directory 25 34 Past Presidents Directory 35 38 Principal Fixtures 2011-12 39 46 NLD Cup-Plate-Shield-Vase Draws 47 50 NLD Knockout...»

«Persistent Posturo-Perceptual Dizziness (PPPD) (Functional Dizziness) Information sheet from www.neurosymptoms.org Dizziness is a common symptom in neurology and has lots of different causes FACTSHEET There are lots of different causes of dizziness migraine, middle ear problems (vestibular disorders like BPPV or labyrinthitis)and drug side effects are all common ones. Dizziness occuring as part of a functional disorder is also relatively common accounting for up to 20% of patients seen in a...»

«THE SOCIOLOGY OF FASHION AND REBELLION: 1900-PRESENT An Undergraduate Research Scholars Thesis By REBECCA BACSIK Submitted to Honors and Undergraduate Research Texas A&M University in partial fulfillment of the requirements for the designation as an UNDERGRADUATE RESEARCH SCHOLAR Approved by Research Advisor: Dr. Edward Murguia May 2015 Major: Sociology TABLE OF CONTENTS Page Abstract DEDICATION ACKNOWLEDGEMENT CHAPTER (or SECTION) I INTRODUCTION II METHODS AND OBJECTIVES III RESULTS Defining...»

«Cover Page The handle http://hdl.handle.net/1887/32972 holds various files of this Leiden University dissertation. Author: Bondéelle, Olivier Title: Polysémie et structuration du lexique : le cas du wolof Issue Date: 2015-05-13 ANNEXE 1 : les représentants du wolof des primitifs sémantiques de NSM Anglais Fonctions et (d’après Français (d’après Wolof Domaines Wierzbicka Peeters 2010) 1996) MA, NGA I, YOU JE, TU / LI ~ ~ ~ LU SOMETHING QUELQUE CHOSE DARA THING CHOSE Substantifs (K),...»

«The Impact of Financial Bootstrap Strategies on Value Added in New Ventures: A Longitudinal Study Tom Vanacker Ghent University, Kuiperskaai 55E, 9000 Gent, Belgium; TomR.Vanacker@UGent.be Sophie Manigart Ghent University, Kuiperskaai 55E, 9000 Gent, Belgium & Vlerick Leuven Gent Management School, Reep 1, 9000 Gent, Belgium; Sophie.Manigart@Vlerick.be Miguel Meuleman Vlerick Leuven Gent Management School, Reep 1, 9000 Gent, Belgium & Nottingham University, Jubilee Campus, Nottingham NG8 1BB,...»

«Chapter 9 Community-Driven Development Philippe Dongier, Julie Van Domelen, Elinor Ostrom, Andrea Ryan, Wendy Wakeman, Anthony Bebbington, Sabina Alkire, Talib Esmail, and Margaret Polski 9.1 Introduction 9.2 What Is Community-Driven Development? 9.3 Why Community-Driven Development? 9.3.1 Complements market and public sector activities 9.3.2 Enhances sustainability 9.3.3 Improves efficiency and effectiveness 9.3.4 Allows poverty reduction efforts to be taken to scale 9.3.5 Makes development...»

«Read e-Book Eaten By A Giant Clam at Online Library. Get file Eaten By A Giant Clam PDF to free download EATEN BY A GIANT CLAM PDF Update method of help documentation is really a hard copy manual that's printed, nicely bound, and functional. Itoperates as a reference manual skim the TOC or index, get the page, and stick to the directions detail by detail. The challenge using these sorts of documents is the fact that user manuals can often become jumbled and hard tounderstand. And in order to...»

«RIGO Research en Advies Woonwerken leefomgeving www.rigo.nl 10-06-2015 Wonen met zorg in IJmond en Zuid-Kennemerland Een onderzoeksmatige basis voor beleidsvorming De verantwoordelijkheid voor de inhoud berust bij RIGO. Het gebruik van cijfers en/of teksten als toelichting of ondersteuning in artikelen, scripties en boeken is toegestaan mits de bron duidelijk wordt vermeld. RIGO aanvaardt geen aansprakelijkheid voor drukfouten en/of andere onvolkomenheden. RIGO Research en Advies Woonwerken...»

«UNITED STATES NUCLEAR REGULATORY COMMISSION ADVISORY COMMITTEE ON REACTOR SAFEGUARDS WASHINGTON, DC 20555 0001 March 23, 2011 The Honorable Gregory B. Jaczko Chairman U.S. Nuclear Regulatory Commission Washington, DC 20555-0001 SUBJECT: POINT BEACH NUCLEAR PLANT, UNITS 1 AND 2, EXTENDED POWER UPRATE APPLICATION Dear Chairman Jaczko: During the 581st meeting of the Advisory Committee on Reactor Safeguards, March 10-12, 2011, we reviewed the Extended Power Uprate (EPU) application for Point Beach...»

«PROFESSIONAL DEVELOPMENT AP® English Literature and Composition Writing About Literature Special Focus The College Board: Connecting Students to College Success The College Board is a not-for-profit membership association whose mission is to connect students to college success and opportunity. Founded in 1900, the association is composed of more than 5,400 schools, colleges, universities, and other educational organizations. Each year, the College Board serves seven million students and their...»

«European Centre for the Development of Vocational Training RESEARCH PAPER No 39 Attractiveness of initial vocational education and training: identifying what matters Attractiveness of initial vocational education and training: identifying what matters Luxembourg: Publications Office of the European Union, 2014 A great deal of additional information on the European Union is available on the Internet. It can be accessed through the Europa server (http://europa.eu). Cataloguing data can be found...»

«Archimer http://www.ifremer.fr/docelec/ The ISME Journal Archive Institutionnelle de l’Ifremer JUN 2007; 1 (2) 111-120 http://dx.doi.org/10.1038/ismej.2007.1 Copyright © 2007 Nature Publishing Group The original publication is available at http://www.nature.com Recovery in culture of viable but nonculturable Vibrio parahaemolyticus: regrowth or resuscitation? François Coutard, Philippe Crassous, Mickaël Droguet, Eric Gobin, Rita R. Colwell, Monique Pommepuy and Dominique Hervio-Heath...»





 
<<  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.