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Building for Success in Calculus David Bressoud St. Paul, MN The First Two Years of College Math: Building Student Success Reston, VA October 5–7, 2014 A pdf file of this PowerPoint is available at For more information see A pdf file of this PowerPoint is available at For more information see NSF #

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Characteristics of Successful Programs in College Calculus Three parts: 1.National survey of students in mainstream Calculus I and their instructors (Fall, 2010) 2.Statistical model of factors influencing changes in student attitudes and intention to persist from start to end of Calculus I 3.Case studies of 17 institutions with “successful” Calculus I programs (Fall, 2012)

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Characteristics of Successful Programs in College Calculus PI: David Bressoud co-PI’s: Vilma Mesa U Michigan Marilyn Carlson ASU Michael Pearson MAA Chris Rasmussen SDSU Linda Braddy MAA Statistical Consultants: Phil Sadler & Gerhard Sonnert DRL REESE #

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Progress through Calculus PI: David Bressoud co-PI’s: Sean Larsen Portland State Linda Braddy MAA Jess Ellise Colorado State DUE IUSE # Chris Rasmussen SDSU

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Fall 2010 Phase I: Survey Responses from 213 colleges and universities 502 instructors representing 663 Calculus I classes and 26,257 students 14,184 students

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researchmaster s undergrad2 year Average high school math GPA Took calculus in high school 70%43%53%24% ≥ 3 on AP Calc 26%9%14%5% Took Precalculus in college 13%31%17%60% Agree that to succeed in Calculus I, must have taken it before. 49%36%40%37%

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PhDBAMA2Y CollAVG Mean age (SD) 18.3 (2.4)18.8 (2.9)20.5 (5.3)22.0 (7.4)19.7 (3.5) Freshman 83%73%50%25%63% Soph- omore 10%16%27%40%21% Junior/Se nior 6%10%17%18%11% Enrolled full time 99%98%91%76%92% Age, year in college, enrollment status

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PhDBAMA2Y CollAVG Father completed college 65%58%49%44%56% Mother completed college 62%56%47%40%53% Some concern about paying for college 54%40%57%55%51% Major concern about paying for college 13%10%13%23%14% Socio-economic status From The American Freshman, 55% of all incoming full-time students at 4-year institutions have some concern, 11% have major concern, about paying for college.

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PhDBAMATYC Comfortable with graphing calculator Somewhat 14% 18% Yes 81%82%77%74% Graphing calc allowed on exams Sometimes 60%55%53%48% Always 31%39%32%29% TI-89 or -92 allowed on exams Sometimes 25%22%25% Always 31%37%30%28% Prepared for calculation without calc Somewhat 28%29%30%27% Yes c 59%58%57% Graphing calculator usage in high school

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Gender differences of career goals of students in Mainstream Calculus I

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Source: HERI

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3-Level HLM Model Structure Main Effects Student Course Institutional Selectivity# of students Initial Career Goal PedagogyHS Pedagogy Professor Characteristics HS Math grades

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Dependent Variables Attitudes – Change, pre to post – Confidence I am confident in my mathematics abilities – Enjoyment I enjoy doing mathematics – If I had a choice If I had a choice: I would never take another mathematics course to I would continue to take mathematics” – Change in Interest, post only This course has increased my interest in taking more mathematics Intention to take Calc II – Change, pre to post Do you intend to take Calculus II?

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Statistically significant drops in confidence, enjoyment, and desire to continue Variable All InstitutionsResearch Universities Mean (SD) Effect SizeMean (SD) Effect Size I am confident in my mathematical abilities (1–6) 4.89 (1.01) – (1.01) – (1.18) 4.40 (1.19) I enjoy doing mathematics (1–6) 4.63 (1.27) – (1.24) – (1.37) 4.28 (1.35) If I had a choice, I would continue to take mathematics (1–4) 2.93 (1.02) – (1.00) – (1.08) 2.83 (1.07) lowest = strongly disagree, highest = strongly agree

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Instructor Pedagogy Factor Analysis 61 student ratings of what teachers do – 53 used 3 factors arose from analysis – Variables loading on the same factor – 49% of the variance average classroom ratings Factors – Good teaching, 22 variables – Technology, 17 – Ambitious pedagogy, 14 – 8 did not load onto factors

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“Good Teaching” My Calculus Instructor: listened carefully to my questions and comments allowed time for me to understand difficult ideas presented more than one method for solving problems asked questions to determine if I understood what was being discussed discussed applications of calculus encouraged students to seek help during office hours frequently prepared extra material Assignments were challenging but doable My exams were graded fairly My calculus exams were a good assessment of what I learned

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“Ambitious Pedagogy” My Calculus Instructor: Required me to explain my thinking on homework and exams Required students to work together Had students give presentations Held class discussions Put word problems in the homework and on the exams Put questions on the exams unlike those done in class Returned assignments with helpful feedback and comments

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Main effects and Interactions InstructorGood teaching0.246*** Pedagogy Technology use0.041* Ambitious pedagogy *** InteractionsClass size × ambitious pedagogy 0.002***larger classes benefit from ambitious pedagogy Initial state × good teaching **students with poorer initial attitudes benefit more from good teaching Initial state × ambitious pedagogy 0.037**students with higher initial attitudes benefit more from ambitious pedagogy Graduate instructor × technology use **Graduate student instructors who use technology impact attitude negatively

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Interaction on student confidence

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Low Ambitious Pedagogy High Ambitious Pedagogy Switching percentages. p < Low good teachingHigh good teaching Low ambitious teaching16.2%10.4% High ambitious teaching11.9%7.0%

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Conclusions: 1.Calculus I is very effective at lowering student confidence and is a significant factor in discouraging students from continuing in STEM. 2.“Good teaching,” characterized as interacting with students in class and establishing the belief that you are there to support them, is essential. 3.Benefits of ambitious pedagogies are highly dependent on how they interact with other factors, but active learning strategies are generally beneficial. A pdf file of this PowerPoint is available at For more information see A pdf file of this PowerPoint is available at For more information see

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