Mary Nelson, Micah Mysiuk George Mason University Department of Mathematics Accelerator Math Lead  Noyce Conference, May 2013 Funded by NSF Grant: Robert Noyce Scholarship Program

 Only four undergraduate STEM majors were licensed through GMU since 2004  All four pre-service teachers were Earth Science majors  President Obama has challenged us to educate 100,000 new teachers  In the current financial crisis in the US, we need to help promising new STEM teachers

 Twice a year we accept applications from faculty for learning assistants  Advertise student learning assistant positions through posters and College of Science broadcast s  Spring semester we had more than twice as many requests for LAs as we could fund  Spring semester we had 90 student applications for 28 positions.

 New LAs must attend the Teaching and Learning seminar once a week  All LAs meet weekly with their supervisor  All LAs are provided time for preparation, which may include the following:  Attend the class for which they are LAs  Work through homework assignments that students in the course are doing  Ask mentors questions about any topic that they do not understand

Participate in weekly LA Seminar in their first semester as an LA Meet weekly with their course mentor Facilitate math oral reviews for Business Calculus, Calculus with Algebra, Calculus I, Calculus II, Quantitative Reasoning Facilitate Biology oral reviews for Cell Structure and Function Conduct on-line peer tutoring Create on-line modules to assist in student learning Provide review sessions prior to tests Provide peer to peer instruction in help sessions Work with small groups during classes Assist students in labs Teach mini-lessons

 Sexual Harassment Prevention Training  Learning Styles  Constructivism  Importance of Discourse  Student Centered learning  Wait time  How to write and use rubrics  How to facilitate oral reviews

 LAs have genuine teaching experiences  LAs work with faculty who are excited about teaching and learning  Students learn some basic educational principles at the Teaching and Learning Seminar  LAs become an integral part of their department’s teaching effort

 Grant pays for 10 LAs/year  Accelerator funds additional  Community college has LAs  Year 1:  Began with 1 math Noyce – looking for a job now  Second semester – added Chemistry Noyce  Next fall – 7 confirmed Noyce, possibly 3 more – all former LAs

 When asked “what would you tell a student who was thinking about being an LA?” One LA answered,:  “Go for it! If you believe you have any future in education this is a must have collegiate experience!”  Another claimed: “I would tell them to definitely try it. The experience was great and taught me a lot; I really think it educated me an equal amount that I educated others. Being an LA gives you experience, patience, knowledge, and public speaking skills.”  Another explained that as a K-12 student, he wanted to be tennis pro and “anything but math.” He still has visions of being a tennis pro, but now his aspirations include being a mathematician and a teacher.

 The result of having Taylor in the lab was an increase in the number of A grades compared to Fall In Fall % of the enrolled students earned A’s. In Spring 2013, when Taylor was assisting, the percentage of students earning A’s increased to 42%. Similarly, in Fall 2012, 27% of enrolled students failed to pass the course. In Spring 2013, this number dropped significantly to 15%.”  “Stephen was phenomenal. He arranged weekly oral reviews to help the Business Calculus students, and his attendance was amazing. Students really appreciated the help in understanding the material.”

 Ungraded, voluntary  Often cited by students as most important aid to learning  Small groups of 3-5 students for an hour  Emphasis on conceptual questions ◦ Why would you use linearization? ◦ What does it look like on a graph? ◦ From the graph, what kind of functions will give the best results? ◦ Does it matter where you center the linearization?

1. Vehicle for getting students to discuss mathematics and other sciences - typically pattern match without understanding -need to put understanding in their own words -need others to correct and clarify misconceptions -then they need to “say it again!” to convince themselves that they understand -teachers often have ah-ha moments - excellent training for LAs in student-centered teaching

 questions:

 Students learn the importance of understanding the basic concepts in order to be able to apply those concepts to novel situations  Students learn better ways of studying  Students work harder because they believe their instructors are invested in their success.  All of the above improvements increase with the number of orals in which students participate

Students agreement increased significantly on:  Item 8 – I am not satisfied until I understand why something works the way it does. (p=.042)  Item 11 – I study math to learn things that will be useful in my life outside of school. (p=.012)  Item 16 – To understand math I talk about it with friends and other students. (p=.002)  Item 23 – Mathematical formulas express meaningful relationships among measurable things or amounts. (p=.001)  Item 36 – When studying something new in math, I compare it to what I already know rather than just memorizing the way it was presented. (p=.028)

 Item 7 – There is usually only one correct way to solve a math problem. (p=.037)  Item 18 – If I don't remember a mathematical method needed to solve a problem on a test, there's nothing else I can do. (p=.007) *Students answers to all other questions were not significantly different pre/post

 University of Colorado, Boulder  Penn State University  Seattle University  Shippensberg University  Santa Clara University  George Mason University

 Calculus I, II and III  Matrix Methods  Complex Analysis  PDEs  Statics  Component Design  Dynamics  High school algebra

 More time/slower pace ◦ Comprehensive exam after two semesters ◦ Workshops add 2 hours/week Motivation ◦ 1. Workshops ◦ 2. Review sessions

 Helps me understand the hard concepts  Helps me determine what I know and don’t know for the upcoming test  It clarifies things I was unclear about  It gives me confidence before the written test  It helps to hear how other students think about some of these things

 QUESTIONS?

 Developing better motivation measures  Examining the “caring” effect  Using orals in other venues ◦ Mechanical Engineering: Component Design ◦ Aerospace: Statics ◦ High school algebra  Teaching students to run their own orals in Calculus III

 Regular students  Treatment students

 74/150 was the average grade of the students in the one- semester class  97/150 was the average grade of students in two-semester class (treatment group) on the identical exam.

GROUPSMean Exam Score Standard Deviation Mean Difference Effect Size Treatment At-risk Control At-risk Treatment Not At-risk Control Not At-risk Treatment At-risk Control Not At-risk

GROUPAt-risk students taking final Mean course grade Standard deviation % at-risk who took Calculus II Of the at-risk who took Calculus II, % who passed Treatment at-risk (C+) %89% Regular at-risk (D-) %80%

GROUPSPercent of Students At-risk Percent of at-risk No longer at CU Treatment N = 34 62%30% Control N = %45%

 Randomly selected 1 of my 2 large classes – coin flip before semester began  Trained all Calculus I TAs and 2 Noyce to do orals  Provided orals questions each time  Each TA did 1 and each Noyce fellow did 2  I facilitated the rest  About 50% of the class participated

GROUPSControlTreatment Test Test Test 36572

GROUPSControlTreatment Percent taking Quiz

As reported by a student from control class  “It’s like a different class…I want to be in that class next semester. Which class will get those things next semester? I want to be in there.”  When asked why, “They are really into it. Everyone is answering your questions. They’re really excited about it. It’s not like our class.”

 Offered orals to all APPM 1350 students  My class had over 50% attendance  Some classes as low as 20%  Analyzed results using Answer Tree  Complications due to 30 students took final- because of snow storm  Major question is effect of motivation – compare to Workshop and Review sessions

Typical Failure Rate30-33% Failure Rate for Fall %

YearFailure Rate % % %

 We have been given CCLI Phase II grant  Implementation in all Calculus I and II classes  Implementation in UCCS Calculus classes  Implementation in high school algebra classes  Implementation in Mech E Component Design class  Implementation in Aerospace E classes Fall 09  Broader participation by TAs and LAs in facilitating orals  Observations of TAs and LAs to ensure fidelity of treatment

 For years, failure rate for Calculus I has wavered between 30-33%  Last semester, fail rate was below 20%

 Is control group same as all previous  Covariance due to placement scores  Counterfactuals ◦ Class size: vs  Compared to 48 person class ◦ Time on task  Workshop students had same time-on-task  Treatment had entire year’s material on final  Common final exam  Enrollment and success in Calculus II  Retention at the University

◦ At-risk determined by 30 question placement test ◦ Students scoring below 18 are considered at-risk ◦ All but two treatment students who were not designated “at- risk” by the placement test were in the class because they failed the first test in the regular class (20-30%) and dropped back to the treatment class

 We hope to f’ll scale up to all Calculus I classes  Orals will take place in recitations and workshops AND before each midterm  On-line homework will free TAs to contribute more time to orals  Analyses will examine effect on ◦ Overall class ◦ Women and minorities ◦ Students whose placement scores designate them at-risk

 Is the conceptual framework basically there?  What needs to be eliminated?  What needs to be reworked?  Suggestions PLEASE!

◦ At-risk determined by 30 question placement test ◦ Students scoring below 18 are considered at-risk ◦ All but two treatment students who were not designated “at-risk” by the placement test were in the class because they failed the first test in the regular class (20-30%) and dropped back to the treatment class Treatment Students Control Students 34 person class person class Two - semester One – semester 62% at-risk16% at-risk Mean Place 16.5Mean Place 21.4

 Study based on constructivist view of learning  Mathematics reform movement is an embodiment of constructivism ◦ Emphasis on: *Vygotsky’s notion of ZPD *Scaffolding *Discourse *Formative Assessment / misconception theory

TESTWorkshopNon-workshop 147%25% 252%26% 343%26.9%

TESTORALS Failure Rate NO ORALS Failure Rate 110%12.5% 29%13% 38.5%13.1%