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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
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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
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Mathematics Education Seminar
Tutoring in the Learning Commons (Phase 1)
Embedded Tutoring with mentor instructors in mathematics survey courses (Phase 2)

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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.

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Meet the new Washington State “authentic contact” certification requirements for secondary mathematics teachers.
Provide a mutually beneficial learning experience for
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Beginning secondary mathematics students;
Students in entry level mathematics courses; and
Entry level mathematics course instructors.

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Create a learning community among
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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.

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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.

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 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

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Seminar students (Tutors) were assessed on their tutees’ demonstrations of the National Council of Teachers of
Mathematics Process Standards:
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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
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The INSPIRE Model of Tutoring (Wood & Tanner, 2012)
Intelligent: Superior content as well as pedagogical content knowledge
Nurturant: Establish and maintain personal rapport and empathy with students
Socratic: Provide almost no facts, solutions, or explanations, but elicit these from tutees by questioning
Progressive: Move from easier to progressively more challenging cycles of diagnosis, prompting toward a solution, and posing of a new problem
Indirect: Provide both negative and positive feedback by implication; praise solutions, not the student
Reflective: Ask students to articulate their thinking, explain their reasoning, and generalize to other contexts
Encouraging: Use strategies to motivate students and bolster their confidence (selfefficacy)
Difficulty of questions optimally matched to s tudents’ levels of understanding
Feeling accepted, supported, and free to explain their thinking
Constantly thinking, doing, and responding
Moving in small steps to higher competency through deliberate practice
Working in a nonjudgmental atmosphere
Gaining insight into their own thinking through metacognitive reflection
Experiencing productive learning and gaining confidence in their abilities

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› Decompression: Lessen anxiety about inexperience and lack of content knowledge.
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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).

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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.

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Data Sources
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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)

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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.”

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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

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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.”

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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.

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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.

Positive Themes
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Positive Themes emerging from course evaluations
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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

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Exemplary 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.”

Negative Themes
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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.
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Take care and hope all is well,
Jon Melhus