Preparing to Teach Algebra (PTA). Jill Newton Purdue University. Today’s Talk. Description of algebra projects PTA journey/project team Rationale for the PTA study Research questions/Methodology/Timeline What have we learned so far? What challenges have we faced? Framework development - PowerPoint PPT Presentation
Preparing to Teach Algebra (PTA)
Jill NewtonPurdue UniversityPreparing to Teach Algebra (PTA)Todays TalkDescription of algebra projectsPTA journey/project teamRationale for the PTA studyResearch questions/Methodology/TimelineWhat have we learned so far? What challenges have we faced?Framework developmentProtocol developmentSurvey developmentPreliminary findingsQuestions/Comments
Algebra as a Research FocusJustification and Argumentation: Growing Understanding of Algebraic Reasoning (JAGUAR)Megan Staples (University of Connecticut)Sean Larsen (Portland State University)Pre-service Secondary Teachers Mathematical Knowledge for Teaching Equations & InequalitiesRick Hudson (University of Southern Indiana)Aladar Horvath, Sarah Kasten, & Lorraine MalesPreparing to Teach Algebra (PTA)Yukiko Maeda (Purdue University)Sharon SenkPTA JourneyEXCITE Conference (MSU, 2008)Two algebra groups (K-12, TE)K-12 Mary Kay Stein, Ed Silver, Glenda, Beth, etc.TE Raven, Kristen, Mike, Sandra, Sharon, Jill, Betty, etc.NSF REESE, 2009Important conceptImplementation challenges - participationScale downRevised, NSF REESE, 2010 (Funded)Sharon Senk, Jill Newton, Yukiko MaedaScale down morePTA TeamMSUPI - Sharon Senk GAs Jia He & Eryn Stehr Purdue PIs Yukiko Maeda, Jill NewtonGAs Vivian Alexander, Hyunyi Jung, Alexia Mintos, & Kari Wortinger/Tuyin AnUndergraduates Adam Hakes, Jules McGee/Ali BrownProject Team MeetingsMSU, Purdue, Advisory Board Meeting (MSU), South Haven
PTA TeamAdvisory BoardTom Hoffer, Joint Center for Education Research at NORCEric Hsu, San Francisco State UniversityKaren King, NCTMVilma Mesa, University of MichiganMSU Internal Advisory BoardDorinda Carter Andrews Robert Floden Glenda Lappan Jean Wald Suzanne Wilson Rationale for the StudyAlgebra as foundation for advanced mathematics and gatekeeper for post-secondary opportunities (e.g., Kilpatrick & Izsk, 2008; Moses & Cobb, 2001)Algebra course and/or end-of course exam requirement in most states and increasing diversity of population of students taking algebra (e.g., Perie, Moran & Lutkus, 2005)Failure rates in algebra are high (e.g., Loveless, 2008)Debates about how algebra should be taught (e.g., Chazan, 2008; Kieran, 2007) Rationale for the StudyCommon Core State Standards for School Mathematics (CCSSM) includes both old and new visions of algebra in three strands: (1) Algebra, (2) Functions, (3) Modeling(CCSSM, 2010)Research base about teaching algebra is thin, and lacks strong connection to the research on students learning algebra.(Kieran, 2007)Most extant mathematics teacher education literature was written by researchers studying aspects of programs offered by their own institutions.(Adler et al., 2005)
Rationale for the StudyBoth strong content knowledge (a body of conceptual and factual knowledge) and pedagogical content knowledge (understanding of how learners acquire knowledge in a given subject) are important(NRC, 2010, p. 4)Prospective high school teachers of mathematics should be required to complete the equivalent of an undergraduate major in mathematics, [including] a 6-hour capstone course connecting their college mathematics courses with high school mathematics.(CBMS, 2001, p. 7)RationaleGreat variation exists across mathematics teacher education in the US (less variation in other countries); less mathematics than A+ countries, also more general pedagogy than math pedagogy.(Schmidt, Cogan, & Houang, 2011)More students taking algebra earlier; underprepared students admitted to algebra do not fare well (without additional supports); different versions of algebra are being created.(Stein, Kaufman, Sherman, & Hillen, 2011)Research QuestionWhat opportunities do secondary mathematics teacher preparation programs provide to learn about: AlgebraAlgebra teachingIssues in achieving equity in algebra learning The algebra, functions, and modeling standards and mathematical practices described in the Common Core State Standards for Mathematics (CCSSM)?
MethodsNational survey of a stratified random sample of at least 200 secondary teacher preparation programsCarnegie classification for stratification, oversampled 2xCase studies of learning opportunities in four purposefully chosen secondary teacher preparation programsDoctoral-granting university with very high research activityLarge masters level universities (rural/suburban, urban)Focus groups with student teachers at each of the case study programs TimelineYear 1Develop, pilot, and revise instrumentsSurveyFrameworksInterview protocols (Instructor, Focus group)Select sampleLocate contact people at institutions in survey sampleCollect and analyze pilot case study dataThree institutionsSurvey think-aloudFive instructor interviews & one focus group interviewTimelineYear 2Administer revised surveyAnalyze, Summarize, & DisseminateIdentify courses at three case study institutionsCollect course materials (with site coordinator)Interview instructorsConduct focus groupsAdminister surveyTranscribe, Analyze, Summarize, & DisseminateIdentify fourth case study institutionCollect course materials (with site coordinator)
TimelineYear 3Identify courses at fourth case study institutionCollect course materials (with site coordinator)Interview instructorsConduct focus groupsAdminister surveyTranscribe, Analyze, Summarize, & DisseminateSurveyContinue analysis, summarizing, & disseminationThree case study sitesContinue analysis, summarizing, & dissemination
What have we learned so far?Framework developmentStay focused on AlgebraSelect a set of big ideas in AlgebraNature of Algebra (CBMS, 2001; InTASC, 1995)Reasoning & Proof (InTASC, 1995; NCTM, 2009; TNE)Contexts & Modeling (CCSSM, 2010; NCATE, 2003)Algebra Connections (CBMS, 2001; NCTM, 2000) Tools & Technology (CBMS, 2001; CCSSM, 2010) Equity in Algebra Learning (NBMS, 2010; NCTM, 2000) Functions (InTASC, 1995; NBMS, 2010; NMP, 2008)History of Algebra (NBMS, 2010; NCATE, 2003)ConnectionsWithin algebra Between algebra & other mathematical fields Example: symmetry groups of polygons geometry of transformationsBetween algebra & other non-mathematical fieldsExample: quadratic functions used to model motion of projectile in physicsBetween college level algebra & school algebra Example: Rings, integral domains, and fields related to the number systems used in high school algebra
What have we learned so far?Protocol developmentInvestigated semi-structured and focus group protocolsDeveloped series of parallel questions for interviewsInstructor interviewWhat are the big ideas that you would like students to take away from this course?To what extent does your course emphasize functions?Focus group interviewWill you please give us some examples of experiences from this list in which you had opportunities to either learn algebra or learn how to teach algebra?What experiences have you had to learn about functions or to learn to teach functions?
What have we learned so far?Protocol developmentChallengesTypical interviewing challengesProbingAvoiding evaluative languageConsistency across interviewers Parallel structures of instructor and focus group interviewsMaintaining focus on algebraSharing big ideas (When? How?)
What have we learned so far?Survey developmentReviewed items from related surveysThe Mathematics Teaching in the 21st Century (MT21) Study (Schmidt, et al., 2007)TEDS-M Institutional Program Survey (Tatto, et al., 2008)Secondary Mathematics Teacher Education Programs in Iowa Survey (Murdock, 1999) 2000 National Survey of Science and Mathematics Education School Mathematics Program Questionnaire (Horizon, Inc., 2000). Developed items to collect information to answer our research questions
What have we learned so far?Survey developmentChallengesLocating program information and contact personDiversity and complexity of programs across diverse institutions4 year/5 year?Degree?Online?Licensure by exam?Variable knowledge of program contact personDepartment?Instructor/Coordinator?Limited previous studies on mathematics teacher education
Survey Item (Program characteristics)What is the most common degree that pre-service secondary mathematics teachers obtain upon completion of the secondary mathematics teacher education program at your institution? 4-year Bachelor's degree5-year Bachelor's degreePost-baccalaureate(i.e., for licensure only, not for Master's degree)Master's degree and initial certification (e.g., M.A.T. not for previously certified individuals)No degreeOther: Please specify___________________
Survey Item (Research questions)To what extent does the secondary mathematics teacher education program provide opportunities to learn in the following areas? Opportunity to Learn Great extentSome extentLittle extentNo extentDo not knowAlgebra Algebra teaching Issues in achieving equity in algebra learningAlgebra as described in the Common Core State Standards in Mathematics (CCSSM)Survey Item (CCSSM)How has the recent release of Common Core State Standards for Mathematics (CCSSM) influenced your secondary mathematics teacher education program? (Check the one answer that best describes the situation at your institution.)Discussions about CCSSM have not begun in our program.Discussions about CCSSM are ongoing, but no programmatic changes have been made.Minor changes have been made to the program as a result of CCSSM.Major changes have been made to the program as a result of CCSSM. I am not familiar with CCSSM.Briefly describe the changes that have occurred in your program based on CCSSM.
Preliminary FindingsContexts & ModelingInstructors seemed to hold a similar conception of the purpose of modeling; that is, one which connects the use of mathematics to solve real world problems (e.g., loan repayment schedules, population growth, and security problems). For example, the Str