Math 158T: Tutor Training in Math
Math 158FT: Field Teaching for Math & Science

Susan Tappero, Ph.D.

Office: 832C STEM/MESA Study Center

Phone: 479-5785

E-mail: sue.tappero AT



158FT Course # 89778.....158T Course # 89782.....Fall 2015

Class Meets: Tuesdays, 4:30-5:20, Rm 806
Room 716

This seminar course will provide an overview of mathematics and science instruction at the middle school, high school and college levels. It will provide an initial exploration of some theories and practices of designing and delivering excellent science and math instruction at these levels. The course has a component of student field work consisting of 2-3 hours per week in the MESA Study Center at Cabrillo, or 5 hours per weekin a placement in a math or science classroom of a local middle or high school.

  • Student Expectations:
    attend every class meeting,
    keep up with the required readings,
    participate fully in class discussions,
    keep a course journal to be turned in periodically

Course Schedule              

Reading and Reference List

What to Include in the Journal

Critical observations of your daily experiences in teaching or tutoring, reflections in what went well, what did not go as well, critical reflections of others' techniques you observe for teaching mathematics in a one-on-one, small group or large group setting and your developing philosophy and individual approach to teaching. Reading notes from the classroom materials that are assigned.

Santa Cruz City Schools

Pajaro Valley Schools

Scotts Valley Schools

Students in the Aurora Teaching Initiative are placed with math and science classroom teachers iin middle schools, junior high schools or high schools in one of these local districts.

California Content Standards

Content standards were designed to encourage the highest achievement of every student, by defining the knowledge, concepts, and skills that students should acquire at each grade level. The content standards were designed by professionals from the appropriate fields of study and then they were adopted by the California State Board of Education. To help students achieve at high levels, local school officials and teachers are encouraged to take these standards and design the specific curricular and instructional strategies that best deliver the content to their students. The content is attainable by all students, given sufficient time, except for those few who have severe disabilities.


California Math Framework


California State Board of Education commissioned mathematics professionals to describe the rigorous content that students need to acquire at each grade level so that California schools can be on a par with those in the best educational systems in other states and nations. This was done in response to the report, A Nation at Risk, by the National Commission on Excellence in Education (1983), described the"rising tide of mediocrity" in our schools.

California Science Standards

Academic content standards for science education at kindergarten through grade twelve, adopted by the California State Board of Education. Grade 7 focuses on life science and Grade 8 focuses on physical science


Rising Above the Gathering Storm Read through Ch 5.

Rising Above the Gathering Storm Revisited

This 2007 report by the National Academies of Sciences and Engineering and the National Institute of Medicine lays out the urgent need to increase America's talent pool by major improvements in math and science education at all levels. It is behind many of the federally- and state- funded initiatives, such as the Aurora Initiative, to increase dramatically the production of math and science teachers. The "Revisited" version came out in 2010.

Contemporary Educational Psychology:Wikibook



This "Wikibook" book deals with topics, themes, and examples that represent one way of understanding educational psychology. It is organized to parallel closely the content of the commonly used PRAXIS II test called Principles of Learning and Teaching , published by the Educational Testing Service. The PLT test is required in 25-30 American states for persons seeking permanent certification as public school teachers. Developed at the University of Manitoba.

Developing Your Own Educational Philosophy

Here are some links to samples of personal philosophies of education for you to explore and some discussion of the answer to the question:. Why should I develop a personal philosophy of education?

Brain-based Learning and Related Research

Brain Rules



classroom applications

some surprises

resource list
(some of these links are no longer live, it is a page maintained by another entity)

Current research results about the brain and learning is providing insights for teachers and for learners alike, in many ways providing new understandings, in other ways giving suggestion for classroom practices. These are just a few links to many references you can find about this subject online and in journals and books.

Middle school math lesson resources

High school math lesson resources

Middle and High school lesson plans

Computing technology for math excellence

Classroom resources for science teachers

Professional organizations such as the National Council of Mathematics Teachers, NCTM, or National Science Teachers Organization, NSTO, are a good source of ideas about ways of teaching specific topics. These websites have some materials that are available even if you are not a member of the organization.

Learning Styles & Preferences

Your Cognitive Profile

Index of Learning Styles

Learning Style Inventory

It is a popular educational belief that most people favor some particular method of interacting with, taking in, and processing stimuli or information. Based on this concept is the idea of individualized "learning styles." A learning style is the method of learning particular to an individual that is presumed to allow that individual to learn best. Teachers have developed some techniques to allow teachers adapt their classroom methods to address the varied learning styles of their students.

Art of Questioning

Asking Good Questions in the Mathematics Classroom

Questioning in Class (videos)

Questioning Strategies

Questioning Techniques

Class ideas to stimulate student discourse

Do we teach students to think? The answer to this may depend on whether a teacher has the skill and practice to build a climate of inquiry and shared discovery in the classroom. Skilled teachers can raise questions that ignite student curiosity and discussion, or offer a question that can simmer over several days, or pursue a line of questioning that leads to understanding. It takes lots of practice, but the result is worth it.
Class responses to specific situations

Professional Organizations

National Council of Teachers of Mathematics: NCTM

National Science Teachers Association: NSTA

Phi Delta Kappa

What are professionals in the field talking about? What is the state of the teaching profession and the issues at different grade levels that matter in teaching for the U.S? What can be learned from other educational systems found in the world? The professional associations are an excellent resource for anybody interested in these questions.

To Review

Teaching Tips Index

Tips for Teachers


Lesson Plan Ex 1

Lesson Plan Ex 2

Lesson Plan Ex 3

Lesson Plan Template Ex. 4

There are many different formats in use for a lesson plan. One of the most helpful tips in writing your first lesson plans would be to look at lesson plans that are already fully developed to get a better idea of what needs to be in the lesson plan. Some key ingredients are: develop clear objectives, determine what students need to know beforehand, decide how you will know if they are learning the material, create an opening and a closing, and estimate the time involved for each part of the lesson.

Additional Reading List

these texts are available for check-out in my office

Brain-Based Learning by Jensen

Positive Discipline in the Classroom by Nelsen, Lott, Glenn

How To Solve It by Polya


Dates . ..Class Discussion Topics........ Homework Assignments for next week

Sept 1

Overview of course; support for students in local classrooms, training for MESA tutors and workshop facilitators.

Past experiences in teaching or tutoring. Importance of communication skills. Classroom culture and your place in the classroom. Background to current teacher initiatives.

Take care of fingerprinting, TB tests, if needed

Read excerpts from the original study Rising Above the Gathering Storm

and the updated version:

Rising Above the Gathering Storm: Revisited

Sept 8

Classroom Tips for Creating a Learning Environment for Math:
Issues of teaching English language learners math and science

Read about educational psychology from the linked sites given. Choose chapters that pertain to your assignments or seem interesting.
Sept 15


Guest Lecturer

Assessing learning

Read the applicable California Math Standards & Science Content Standards to your placement. Use the Word version
of the Science Content Standards, the pdf is corrupted.

In journals, assess students in your class according to the math standards for that grade level.

Sept 22


Discussion: where do the students in your classroom stand with respect to the state standards?

Prompts for journal entries this week:

What is the role of the student voice in your classroom?

What techniques for managing class discussion are being used in your classroom?

Sept 29


Role of student voice in the classroom. How brain research relates to education.
Reference: Positive Discipline in the Classroom, Brain Rules, Brain-Based Learning


Read materials on brain research in the area of learning. See links above.
Oct 6

Nano tech Classroom Kits Demonstration & Practice

including Powers of Ten Video

Read about educational philosophies from the linked site given. How is your personal educational philosophy developing?


Oct 13 Introduction to Manipulatives: Chips, Algebra Tiles Follow the links under Learning Styles to see some discussion about learning preferences and take the surveys to see what it predicts for you. How accurate is it?

Oct 20

Manipulatives continued:
Cuisenaire Rods and Geoboards



Oct 27


Introduction to Lesson Plans

Decide on the topic you will use for the lesson plan that is the class final assignment. Do some research on lesson plans on the web and decide on the format you will use.

Nov 3


Discussion: Art of Questioning

Read through the links for the Art of Questioning
Journals: How does your placement teacher use questioning? Jot down some questions you like.


Nov 10


Student misconceptions in math Watch these youtube videos: Fixed versus Growth Mindsets, Changing mindsets, Intellectual struggle    
Nov 17


Multiple Learning Styles & Multiple Approaches in Math and Science Subjects


Journals: Note evidence of learning styles in students and in teaching approaches
Nov 24 Classifying some difficult student behaviors in tutoring or teaching situations, strategies for dealing with them. Read through the ideas for dealing with difficult teaching/tutoring situation in Part I and Part II

Dec 1



Discussion: Characteristics of a Good Tutor and a Good Teacher




Final Assignment:
this 1-1.5 page assignment is due by the end of finals week

Teacher trainees:

Select one of the standards relevant to the teaching/tutoring assignment you are in to develop a short lesson on that topic, using at least one of the following:

  • learning styles,
  • brain-based research,
  • educational psychology,
  • manipulatives,
  • art of questioning

Tutor trainees:

Write a self-evaluation of your own tutoring. Include strengths, weaknesses and ideas for improvement. Incorporate at least one of the aspects from the bulleted list above.



Dec 8




Student Presentations of Lesson Plans

Finals Week All materials must be turned in to me sometime during the week: Timesheets, journals, and projects.