Building a Learning Community:

Michael A LundinCentral Washington University

Pre-Service Mathematics Teachers as Embedded Tutors

OverviewThe Oz-like Journey

Demand for more authentic training of secondary mathematics teachers

Introductory mathematics education seminar for prospective secondary mathematics students to ease them into the teaching process via tutoring

Two versions tutoring › Phase 1: Tutoring in the CWU Learning Commons (two quarters over two

years)› Phase 2: Tutoring in survey-level mathematics courses with mentor

instructors (one quarter) Evaluation Results

› Mathematics Education Seminar› Tutoring in the Learning Commons (Phase 1)› Embedded Tutoring with mentor instructors in mathematics survey

courses (Phase 2)

Motivation “Better get under cover, Sylvester. There's a storm blowin' up - a whopper, to speak in the vernacular of the peasantry.”

NCATE and Washington State began requiring more “authentic” learning for pre-service teachers who must now practice teaching more often in realistic environments.

Our university is isolated, lacking nearby schools in which teachers can practice their craft.

College costs continue to rise as state and federal support decline, forcing creative efforts to find authentic learning venues for prospective teachers.

Challenges “Bring me the broomstick of the Witch of the West.”

Meet the new Washington State “authentic contact” certification requirements for secondary mathematics teachers.

Provide a mutually beneficial learning experience for › Beginning secondary mathematics students;› Students in entry level mathematics courses; and› Entry level mathematics course instructors.

Solution: Tougher than we imagined!“How about a little fire Scarecrow?”

Create a learning community among

› Entry level secondary mathematics students (Freshmen and Sophomores);

› Students needing help in lower level mathematics courses (Pre-calculus, Mathematics for Liberal Arts, Mathematics for Elementary Teachers, Calculus);

› Instructors teaching lower level mathematics courses.

Plan”It's how to do it. These things must be done delicately...or you hurt the spell.”

Prospective secondary mathematics education students enroll in an entry level seminar (2 quarter credits, meeting twice per week) in which they learned to tutor via the INSPIRE method; and

Students tutor two hours per week in the CWU Developmental Mathematics and Writing Center, which delivered developmental courses and tutoring services in writing and mathematics.

Course Prerequisites (Very Basic!) Two quarters of calculus One quarter of linear algebra English and mathematics basic skills

requirements (or AA degree) Acceptance into Professional Education

Program Co-requisites: more mathematics courses

Introductory Math Education Seminar” Follow the yellow brick road.”

Seminar students (Tutors) were assessed on their tutees’ demonstrations of the National Council of Teachers of Mathematics Process Standards: › Reasoning and Proof› Problem Solving› Communicating Mathematical Ideas› Making Connections Among Mathematical Ideas› Multiply Representing Mathematical Ideas

Note that getting the right answer is NOT in the above list, although important, but how to get the right answer is strongly implied.

Assessment: Tutors documented their tutees’ demonstrations of the NCTM Standards in electronic portfolios. Portfolio assessments › constituted most of the credit for the seminar course; and› provided data to evaluate the tutoring program.

Introductory Math Education Seminar“How do you talk if you don't have a brain?”

In Class ActivitiesThe INSPIRE Model of Tutoring (Wood & Tanner, 2012)

Introductory Math Education Seminar“Well, some people without brains do an awful lot of talking don't they?

Intelligent: Superior content as well as pedagogical content knowledge Difficulty of questions optimally matched to

students’ levels of understandingNurturant: Establish and maintain personal

rapport and empathy with students Feeling accepted, supported, and free to explain their thinking

Socratic: Provide almost no facts, solutions, or explanations, but elicit these from tutees by questioning

Constantly thinking, doing, and responding

Progressive: Move from easier to progressively more challenging cycles of diagnosis, prompting toward a solution, and posing of a new problem

Moving in small steps to higher competency through deliberate practice

Indirect: Provide both negative and positive feedback by implication; praise solutions, not the student

Working in a nonjudgmental atmosphere

Reflective: Ask students to articulate their thinking, explain their reasoning, and generalize to other contexts

Gaining insight into their own thinking throughmetacognitive reflection

Encouraging: Use strategies to motivate students and bolster their confidence (self-efficacy)

Experiencing productive learning and gaining confidence intheir abilities

Other In-Class Activities› Decompression: Lessen anxiety about

inexperience and lack of content knowledge.

› Highlight learning by doing (repeated often).

› Discuss readings: major papers on mathematics education themes.

› Problem “stumper” of the week: problems or issues with which tutors struggled.

› Technical writing (for portfolio entries).

Introductory Math Education SeminarSome students are Lollipop Kids.

Issues: Phase 1 “Nobody can see the Great Oz! Not nobody, not no how!

After one year of planning, the Developmental Mathematics and Writing Center was dubbed a “Learning Commons.” Our on-board management was suddenly replaced with inexperienced administrators.

Quality problems developed in the Learning Commons, leading to territoriality issues between it and the Department of Mathematics.

Our Pre-service teachers (tutors) were not getting the required two hours per week tutoring time. They competed against professional (paid) tutors there.

After two years, we had to develop another plan, Phase 2.

Phase 1 Evaluation“…and so what the Munchkins want to know is…are you a good witch or a bad witch?”

Data Sources› Tutors in Developmental Mathematics (2012),

masters degree project by Danielle Jacobson, Director, Developmental Mathematics Center

› Middle and End of Course Assessments from Introductory Mathematics Education Seminars

› Electronic Portfolios from Seminar Students (Tutors)

Seminar EvaluationMid- and End-of-Course surveys, evaluated free-form around emerging themes

Generally Positive Themes

Learning Process Standards Tutoring Practice in class Hands-on Experience Tutoring Improvement of attitude/patience

toward teaching/tutoring

Seminar EvaluationMid- and End-of-Course surveys, evaluated free-form around emerging themes

Exemplary Comments “The experience I’m getting in the university math center is helping me learn about teaching by exposing me to a variety of questions in a number of different subjects. People may be working on the same problems but have totally different areas of concern. This is making me understand [students] better, which will allow me to help them with their own understanding.”

“Class activities like problem-solving and [using] representations are helping greatly. I use everything I learn and incorporate it into my tutoring.”

“I’ve gotten more comfortable with not knowing answers right away. Now I don’t get exasperated when students have no idea what I am trying to explain to them. I’ve also gotten a lot more patient with students in the tutor center.”

“By working with tutees to problem solve we are improving our own problem solving skills.”

“Now I understand the values of knowing the material enough to represent topics in different ways.”

“This class was one of the better education courses, because it allowed us to actually get a glimpse and a feel for the career we are actually going into. If this had only been a class seminar and there was no real tutoring, I don’t think the class would’ve benefited as much from it.”

Seminar EvaluationMid- and End-of-Course surveys, evaluated free-form around emerging themes

Negative Themes

Feeling unwelcome within the Learning Commons Math Center

Discomfort with the higher level of mathematical content covered in the Learning Commons Math Center

Too little time spent with individual tutees

Seminar EvaluationMid- and End-of-Course surveys, evaluated free-form around emerging themes

Exemplary Comments

“It would be easier if we were assigned one class to tutor, that way we could prepare and be knowledgeable about the subject we are helping with”

“It would be nice to work with students on lower content levels.”

“I would have been more comfortable if we were to pair up with a math center tutor and observe more to see their strategies.”

“I’m not good enough to help students with calculus one and two and this is what most students needed help with.”

“Something that may have helped me learn better would be if I had any idea of possible material that the student I would be tutoring would be covering.”

Lessons Learned from Phase 1 “…Courage! What makes the Hottentot so hot? What puts the ‘ape’ in apricot?”

Novice tutors outperformed the Learning Commons professional (paid) tutors in their processes as indicated by tutee assessments (Jacobson, 2012).

A culture clash developed between professional tutors and novice tutors, which seemed to subside near the end or the trial period.

The new Learning Commons administration made no distinction between tutoring assignments for content advanced tutors and novices.

The new Learning Commons administration never bought into our effort.

Lesson for Mathematics Departments: Universities, now more than ever, are experiencing pressure to push students through programs. Developmental programs must articulate well with the programs they feed. Never give away your real estate, or you may get hit by a house.

Phase II“You, my friend, are a victim of disorganized thinking. You are under the unfortunate impression that just because you run away you have no courage; you're confusing courage with wisdom.”

Keep the format of Introductory Mathematics Education Seminar, because evaluations regarding its effectiveness were largely positive.

Change the tutoring practicum venue from the Learning Commons to survey courses taught by experienced mentor instructors.

Phase 2: “Open” Embedding of Tutors in Survey Courses. “You should have thought of that?”

14 seminar students (tutors) were paired with 11 survey course instructors.

Tutors logged on average approximately two hours of tutoring per week.

Tutoring in class, during activities, or outside of class Once in process, tutoring replaced one seminar

meeting per week. Other aspects of the Seminar remained the same:

Tutors “INSPIRE” their tutees to demonstrate NCTM process standards.

Phase 2 Evaluation

Positive Themes emerging from course evaluations› More than enough tutor-tutee contact› Positive feelings about course instructor

mentorship› Problem-solving trumped knowing it all› Appreciation of good process leading to good

teaching› Embedded tutoring means constancy of care.› Manageable difficulty of mathematical content

Positive Themes

Phase 2 EvaluationExemplary Comments

“Something I developed from tutoring this quarter is strong dispositional values that helped me be encouraging and consistently hold high expectations for all students. Instead of just providing students with the answers, I posed questions that prompted the tutees to come up with answers on their own.”

“This experience helped me become more confident in myself to teach and guide students to solve mathematical problems. I learned how to work in big groups, adapt to situations when I did not know how to solve a problem, and I learned that students always expect the tutors to know everything about the problems at hand. Through this experience, I have learned no one truly knows everything [or has]answers to everything.”

“The best part about taking this course was my mentor. She was absolutely enthusiastic, knowledgeable, and was very respected by her students. It became easier for me to adapt to her classroom because she provided a comfortable, open atmosphere for students to learn, ask questions, and work with each other. This is the type of atmosphere that I want in my future classroom.”

“I do feel confident about my ability to do math. But there is a difference between knowing how to do the problems and being able to explain them to others. With this tutoring experience I have learned a little more about the math I already knew. I have learned different ways of explaining the processes and different ways to explain it for different people. I have learned to cope with the abilities of others and how to work with it.  I have learned how to condense my thoughts and get to the point as clearly as possible.”

“I met with one student twice a week to assist in different work he was doing for the class.  Working one-on-one really helped him because I was able to focus all of my attention on his needs. I mainly let him run the tutoring session because it was for his benefit and I wanted to be a resource there for any of his questions. ”

Course Instructor and Mentor: “Having the tutors in class helps keep instructors in check, more organized.” Course Instructor and Mentor: “Students began asking for tutors.” Course Instructor and Mentor: “Grades improved after working with tutors.”

Phase 2 EvaluationNegative Themes

Course Instructors and Mentors asked for more prescriptive instructions on how to manage tutors.

Tutors (still) concerned about lack of knowledge in content areas.

Tutors must learn to pace themselves in terms of the amount of contact with tutees.

Karmic EpilogI received the following e-mail from a former tutee while completing the last slides for this talk Monday.

Hello Mike,

Your name popped into my head for some unknown reason and I found you with a google search.  You may not remember me, but I hired you as a tutor (first semester Calculus) at the University of Montana in the fall of 1989.  I was preparing to enter engineering as a second career with next to zero math skills (not the best plan).  I refused to take the math entrance/placement exam and entered straight into calculus. Then, I asked the main mathematics department secretary who a good tutor was and she gave me your name.  Long story short, I took math and physics at U of MT, and then received a B.S. in Civil Engineering from CSU.  Passed the PE exam on my first attempt and have worked in the engineering field since 1993.  I wanted to thank you, and recognize your efforts, for being patient with me and inspiring me to persevere in a field that scared the %$#@ out of me.  

Take care and hope all is well, Jon Melhus