How I make assessment of students’
knowledge to be a integral part of learning
How I incorporate recent research
findings into my teaching practice
Conclusions and potential for growth
in teaching
Introduction
Mathematics and teaching
mathematics are my passions; I find both stimulating and
intriguing. The focus of my teaching is to share my passions with my
students. When I am successful in pursuing my passion, teaching
is rewarding and more importantly, I know that I have made a difference in
the lives of students and in the lives of the children they will care for and
teach.
Teaching at Wheelock
College is simultaneously comfortable and challenging. It is
comfortable because I teach small classes, where I know my students and I can
address their individual needs. I also have time to use a variety of
assessment tools and I have the freedom to experiment with, and reflect upon,
my teaching. On the other hand, I am challenged because many
students arrive with poor preparation in mathematics. Some even
actively dislike mathematics, an attitude which unfortunately appears to be
socially acceptable in the general society. Sometimes those of us
who teach mathematics have to overcome twelve years of unfortune
school mathematics experiences which focus on rote learning and memorization
without understanding. I also have to counter students’ dissapointment and frustration at their inability to learn
mathematics and make sense out of it. Teaching mathematics to those
who compare learning mathematics to “going to a dentist” or “swimming with
sharks” can be difficult. However, when students write at the end of
the course that they finally understand mathematics and enjoy attending math
classes for the first time in their lives, I realize how fullfilling
my profession can be.
My teaching
statement will be organized around answering the following questions: How
can I communicate the importance and the beauty of mathematics? How
can I stimulate students’ active participation in learning mathematics and
their intellectual curiosity about and interest in mathematics? How
can I address students’ different learning styles and incorporate students’
feedback in my teaching? How can I learn about students’ background
experiences in mathematics and their attitudes towards it? How can I
make my assessment of students’ knowledge an integral part of
learning? How can I incorporate recent research findings into my
teaching practice? I keep asking these questions every time I
prepare for teaching a course, a topic, or a lesson. I repeatedly
ask and try to answer these questions as I teach. Obviously, this is
a significant reason why teaching is never dull for me. Moreover, I
refuse to seek a less challenging and more profitable position.
Teaching Goals
I view the teaching and
learning of mathematics as challenging and exciting adventures for students and
for myself. I begin the adventure with multifaceted goals for
students. I want my students to understand mathematics concepts and
processes, share ways of doing mathematics, challenge each other to formulate
and test hypothesies and to prove opinions and
conclusions, reflect upon the victories and pitfalls of the learning process,
and enjoy mathematics. I also want my students to develop intellectual
power and raise their self-esteem, so they can be empowered to become life-long
learners of mathematics.
To achieve these
ambitious goals, a community of learners must be born. The birth of a such community requires the long term commitment of all
participants. Although I plan the course syllabus carefully, pick appropriate
books and readings, state and require high learning standards, prepare and
facilitate interesting mathematics activities, I realize that the course will
only succeed if my students are willing to share a learning adventure and
overcome the obstacles along the way.
What I teach and how I
communicate the importance of mathematics to stimulate students’ active
participation in learning mathematics
The process of teaching
mathematics includes stages of planning and replanning
before and after each class, each topic, and each semester based on assessing
and reflecting on what has happened at each level. From the very first
class my students and I start constructing a body of mathematical knowledge and
positive attitudes towards leaning and doing mathematics. With patience and
time, we convince each other that everyone can be successful in learning
mathematics.
In my classes, the
process of learning mathematics incorporates several vital interwoven
components: content knowledge, positive attitudes and beliefs towards
mathematics, and reflection on what has been learned in order to formulate new
goals and continue the learning process. When planning a class, an
activity, or a homework assignment, I always consider my goals both in terms of
the mathematical content and in terms of influencing students’ attitudes and
beliefs. It is much easier to identify and prepare content materials to
be learned, than it is to involve students in an active learning process that
is both intriguing and supportive of their self-esteem. To
accommodate students’ differences, I employ a range of teaching strategies and
course assignments and ways students can demonstrate their knowledge of
mathematics in all my classes.
To ensure students’
active participation in learning, I often teach mathematics content through
problem-solving. The most vivid examples where mathematics content
is learned trough problem-solving are courses: Concepts
and Processes I and II (MAT 130-131), Concepts and
Processes I and II (Intensive) (MAT 140-141), Developing
Problem-Solving Skills (MAT 150) and Problem-Solving
Seminar (MAT 151). Problem solving, and inquiry allow me
not only to teach serious mathematical content to students but also to
stimulate students’ curiosity and refine their discovery techniques. When
preparing the course syllabi, I keep in mind that most of my students will not
become mathematicians. However, all of them need to know how to analyze
problem situations, how to organize data in a useful way, how to reason and
justify their actions, and how to check their results. Thus, the courses
are aimed at achieving these skills.
Problem-solving skills
can be mastered only by solving problems and reflecting on the process (Schoenfeld, 1992). It is a craft to be learned
patiently by doing mathematics and thinking about what one is doing.
Students cannot read about problem solutions in the book and learn to solve
problems, they have to face a problem and with support from a teacher and
peers, if necessary, solve it. It is almost impossible to find a
textbook that really teaches these problem-solving skills. Therefore,
such courses are challenging to design and teach. They require intensive
work on the part of the instructor to prepare problem sets and guiding
questions and hints that assist students to approach problem solutions.
I prepare many
discussion questions and handouts with problems to solve. I expect
students to take detailed notes, write problem solutions and reflect on solved
problems in problem-solving classes. After solving a problem or a set of
problems individually or in small groups, students write problem solutions and
list strategies they used. Then we have a whole class discussion about
the solved problems. We compare and contrast successful and unsuccessful strategies
and approaches to problem solutions. In addition, I ask students to
compare and contrast problems and write summary reflections.
I periodically collect
students’ reflections on solved problems and comment on them. This
exchange of thinking helps me to keep track of students’ learning and it helps
students to assess their progress and prepare for future learning and for
tests. For example, MAT 130 and MAT 140 students
write letters to themselves about mathematics they learned during the first semester
of the year-long course and these letters serve as a final assessment which
also helps us start the second semester.
Another vital component
of the problem solving courses is lab activities. For
example,
I give students in MAT 140 the following written instructions for lab
explorations:
For this exploration you
will work in a group of 3 or 4 people. Each group will do one of the
following activities: Tower Puzzle, Toothed Squares, Figurate Numbers, and
Diagonals of Polygons.
After collecting and analyzing
problem data, formulating the general conclusion, finding recursive and
explicit formulas, and comparing the problem with those solved before, you will
prepare the problem/activity to be presented for your class peers.
The presentation will
take place next class. It should be interactive. Your group will have
20-25 minutes to teach your activity. Make sure that all your peers
understand the problem you present.
Students carry out these
hands-on, minds-on activities and then present them to their peers. Each
group performs a different activity. When presenting, the group is
responsible for the mathematical understanding of the rest of the class.
I encourage each group to reflect on what happened when they did the activity,
what difficulties they encountered and how they overcame them. These
presentations put students in charge of their learning and therefore increase
their self-confidence. They motivate students to learn more mathematics.
Finally, these presentations allow us to strengthen a community of
learners in class. Students love mathematical labs and quickly overcome
their fear of presentations. For the students who need extra support, we
use the workshops in oral presentations offered by the faculty in the Wheelock
Theater.
Problem-solving courses
teach mathematical content, but even more important, they teach that there is
more than one way to think mathematically. To challenge students’
mathematical critical thinking, I often use problems with multiple solutions
and no solutions. When students encounter these types of problems for the
first time, they are resistant. Students view a mathematical problem as
one that has a unique solution. As soon as students overcome the initial
resistance, they begin to have fun. Students are excited about playing
with problems, changing them to have multiple solutions or no solutions.
To promote students’
thinking and their ability to communicate mathematically, I combine individual
and small group work with whole class discussions. Students are
encouraged to present their thinking in front of their groups or the whole
class. I support and value all students’ thinking and ask my students to
be respectful of each other. After a while students are not afraid to
raise tough questions and challenge me and each other. I assign a lot of
homework and often start my classes with checking it. I ask students to
volunteer to explain homework problems at the board. Students have
commentated on the usefulness of my assignments and home-work evaluations as
follows:
She was fair with
homework and tests. And every assignment had something to do with work we
did in class.
Nobody likes homework,
but all the assignments given were related to material and helpful.
The assignments were
appropriate. The group project needs some improvements. It needs to
be more defined and expectations made clearer.
Many of the problems
assigned were very appropriate although I did not care for the book.
In addition to lab
activities, in class and home-work assignments, I use projects and poster
activities in almost all my classes. For example, in History of
Mathematics course, students have to choose and investigate historical
topics. The assignment is the following:
Find a partner and start working on a project in
January. You have to sign for your project before January 29.
For your project you have to use several books in addition to the text required
for this class. You can borrow books from me. The written project
is due on March 4. See possible project topics and a
corresponding timeline below. You can suggest a topic of your interest to
be included.
Topics
Presentation
Date
Presenters
1. Roman
numerals
February 5
2. The Hindu-Arabic
numerals
February 15
3. The Mayan numeration
system
February 23
4. The Chinese numeration
system February
26
5. Al-Khowarismi’s
algebra
March 7
6. Pythagorean music and
astronomy
April 5
7. Plato and the Platonic
solids
April 15
8. Aristotle’s
statements
April 22
Doing projects and/or
preparing poster presentations allow students to demonstrate their mathematical
maturity and independence. Some students have never experienced
mathematical power before taking my classes. To motivate my students, I
try to select project topics and other educational materials that are
interesting and challenging for them. By solving problems, doing lab
activities and projects, and presenting them to peers, my students increase
their knowledge of mathematics and develop their self-confidence to become
life-long learners of mathematics.
Communication with
students: How I address students’ different learning styles and
incorporate students’ feedback in my teaching
I have already described
a variety of course materials I use to accommodate students’ differences.
Yet, communication with students is more vital to address students’ differences
than the choice of materials. Mathematical communication is one of the
explicit goals of the National Council of Teachers of Mathematics (NCTM,
2000). I consider this goal to be essential for learning of mathematics
because oral and written communication is a vehicle for my students and me to
realize whether they reach mathematical understanding of the content, whether
they are ready to present a convincing argument about their solutions,
strategies, or findings, or whether we need to work more on tasks.
Communication during
mathematics activities is a complicated responsibility for a teacher. It
involves monitoring and orchestrating individual students’ work and work in
small groups as well as discussions among students. Mathematical
communication in my classes goes in all directions. The flow of
information looks like on a diagram below.
Student
Student
Teacher
Group of students
I organize a variety of
opportunities for students to share opinions and questions in front of the
class or a small group. After a problem or a question is raised and
clarified, I arrange students to work in pairs or small groups. I
facilitate and scaffold group work by observing students’ work, listening
carefully to them, and questioning their thinking. One of my teaching
goals is to emphasize and be explicit with my students about the importance of
taking time and listening to each other. I always try to model listening
and questioning skills during my teaching.
I constantly encourage
students to evaluations and critique my teaching and use both to
change and advance my teaching. However, I do not reduce the high
expectations and standards I have for my students. I do not want to lose
the integrity of the mathematics, nor to compromise the teaching and learning
process to make students “happy.” I communicate high expectations and
demands to students through syllabi, and on a day by day basis. I believe
that all students can learn mathematics if they are provided with right
opportunities.
In my classes, students
have to demonstrate their knowledge of the mathematical content but they have
opportunities to demonstrate it differently. For example,
in MAT 130-131 and MAT 140-141, I use a list of
proficiencies all students need to pass to pass the course. Yet, to
accommodate students’ different learning styles, I allow students many attempts
and many ways to pass the proficiencies. Students can complete the task
of passing proficiencies through quizzes, tests, make-up tests, and individual
interviews with me.
I use
students’ feedback and reflections to improve my teaching
craft. For example, teaching calculus (MAT 280) assumes deep
knowledge of algebraic ideas. I started the course with a pretest that
demonstrated to students and me the level of students’ algebra knowledge.
Students and I agreed that the pretest did not impact their grades and served
as their self-assessment, to help them to realize whether they needed extra
review time and help. The results of the pretest provided feedback for me
to replan, and choose a comfortable pace for
students, to ensure that they understood important calculus ideas, rather than
being concerned about the coverage of topics.
My teaching practices
continuously change under the influence of learners' outcomes. According
to a constructivist paradigm, teachers should provide a sequence of experiences
allowing students to construct their knowledge actively. In following this
paradigm, I view my role as a facilitator, a coach, a coworker, and a monitor
of student progress. Here are a few quotes from student evaluations to
support my claim:
Galina is able to explain math in different
ways, because she understands
all individuals learn differently.
Galina understood that
some students learn faster than others, and that different teaching methods may
be used for some. She was always willing to help.
Galina was always
available for extra help.
Everything was very
organized but Galina was able to roll with punches if something unexpected came
up in class.
How I learn about
students background experiences in mathematics and change students’
attitudes towards mathematics
I usually start the
first class of a course by asking students to share their past mathematics
experiences and their feelings about learning mathematics. I use a
written survey or ask students to write anonymously. I then mix students’
responses in a box, and have each student randomly pick and read someone else’s
response. As the first home-work, I have students
students write their math autobiographies.
These activities give me opportunities to learn about students’ individual
mathematical backgrounds.
While teaching at
Wheelock, I have come across many students who experienced poor mathematics
teaching and have lost the faith in their mathematics abilities. Starting
from the first class and the first problem, my students and I work on their
self-esteem. We agree upfront that there is no such thing as a “stupid
question” and everyone can make a mistake. From time to time I
purposefully make mistakes during my explanations to find out whether students
listen and understand. Other times I make mistakes because I am
human. Students love catching my mistakes. Once caught, I make sure
to be explicit about what kind of mistake students have caught and how we can
learn from our mistakes. Through these activities, I encourage students’
attention and critical thinking.
Many of my students come to class with a view that
mathematics is an artificial, complicated body of facts and algorithms they
have to memorize and perform. I find that providing students with examples of alternative
algorithms for multipling numbers or historical facts
about the birth and development of algebraic ideas, helps to establish
mathematics as a human activity through creative thinking.
I consider the
course History of Mathematics to be a major influence in
changing students’ understanding of mathematics and improving students’
attitudes and beliefs about mathematics and themselves as learners of
mathematics. The course gives students an opportunity to explore how
mathematics ideas were born and developed through time by people in different
countries. For example, I stress that it took centuries for the emergence
of algebraic symbols, concepts, and methods. I view History of
Mathematics as an interdisciplinary course because it incorporates
aspects of history and geography, as well as mathematics. I discuss with
my students geographical facts and historical needs for the birth of
mathematical ideas. For example, we connect agricultural needs
of Babylonia or Egyptian peasants to restore land marks after river
floods and the development of geometrical and measurement ideas.
How I make assessment of students’ knowledge to be a integral part of learning
Because I consider
assessment an integral part of my teaching and students’ learning, I use a
variety of assessment tools in all classes. The following table
summarizes the types of assessment I use in my mathematics classes. The
table also links them to the corresponding educational goals developed by the
General Education Task Force and which I have adapted to mathematics.
|
Educational Goals |
|
|
In class assessment on day by day
basis:
|
Gaining ongoing feedback from
students. Communicating ideas and concerns
among learners and teacher. Strengthening skills in
mathematics and oral presentations. |
|
Weekly or monthly assessments:
|
Gaining feedback from students. Strengthening skills in
mathematics, writing, and oral presentations. Developing understanding of modes
of thinking. |
|
Topic assessments:
|
Gaining summative feedback from
students. Strengthening skills in
mathematics, writing, and oral presentations. Developing understanding of modes
of thinking and inquiry in mathematics. |
|
Course assessment
|
Gaining comparative feedback from
students. Achieving the ability to engage in
analysis and interpretation of complex materials. |
I described above how I organize communication with students and how I conduct
in-class assessment on a day by day basis. I use many other types of assessment
in classes. Written assignments are aimed at checking students’
thinking. I employ challenging problems that take a week or two weeks for
students to solve. Students can solve these problems with others in study
groups, but they must individually write how they came to their
solutions. To learn from experiences, students need to reflect on their
work. That is why I often ask students to look back at solved problems
and summarize what they learned. It is hard to assess these summaries;
yet, students and I find them extremely valuable for further learning and
preparation for tests.
I try to make tests an integral part of students’ learning and to reduce
students’ test anxiety by applying several techniques. First, we always
have a review class before the test. For the review, I ask students to
look at their notes and summaries and tell me what they think will be on the
test. I write students’ ideas on the board and we discuss what will be
assessed. Students pose mathematics examples corresponding to their ideas
and we design a mock class test to be solved as homework. Second, I may
ask students to design mock tests individually as homework to review materials
and solve their own tests. Sometimes I ask students to exchange their designed
mock tests and assess each other’s knowledge and readiness for the real
test. Third, I always divide the real test into two parts: the take-home
test and the class test. The take-home test includes complex
problems. Students can discuss take-home problems with each other, but
they must do their own solution and reasoning in writing. For the class
test students are allowed to bring one page of summary notes because I do not
assess students’ abilities to memorize; I assess students’ abilities to apply
their knowledge, to think in new situations, and to explain their
thinking. Fourth, after I grade students’ tests, I arrange a whole class
discussion of the test results and connect them to future goals. Fifth, I
ask students to analyze my comments about mistakes they made and to fix
them. If the class part of the test includes proficiencies that students
must pass, they have to work on test mistakes and then I interview students
individually to give them another opportunity to pass their proficiencies.
In addition to tests, I
employ portfolios as an alternative assessment method in several of my
classes. For example, students in MAT 131 and MAT 141
are asked to prepare portfolios as a final assessment of the sequence. The
portfolio assignment for MAT 141 is as follows:
Goal: You will reflect
upon your experiences in MAT 140-141 and use a portfolio format to
demonstrate the most important things you have learned in this class.
Your portfolio will consist of four parts. Please typed the needed descriptions
and put your portfolio in a folder.
Part 1: Select good four
examples of your work for different topics. Make sure that you include
work from both semesters. You can use photocopies of your old work.
With each example, include a short-typed description of why you
selected the work and what it shows about your learning. Descriptions can
be a paragraph or two on a separate page. Examples of your work can be
papers, solved problems, or tests/quizzes.
Part 2: You must also
include two examples that show your growth and improvement on a particular
topic along with a description of how the examples show the improvement (i. e. a “before” work, an “intermediate” work, and a
“final” work.) The description can be a paragraph or two on a separate
page.
Part 3: Select two
activities you would use with students of a certain grade. Identify the
grade level(s) the activity is appropriate for. State learning goals of
each activity. Speculate about learner’s difficulties and discuss how to overcome
them.
Part 4: Write a new
reflection (2-3 pages) about your attitude towards mathematics and towards
yourself as a learner of mathematics as the result of
taking MAT 140-141 courses. You might also wish to include your
math autobiography and the reflective letter you wrote in December 2004 in the
part.
Teacher reflections and
reevaluations of courses are ways to improve teaching methods. I reflect
on courses during winter and summer vacations and make summary notes for future
use. I am always in search of better mathematics problems appropriate for
different courses and levels of abilities. I also keep everyday class
notes for every mathematics course I teach. I read my notes before
planning each class. Student course evaluations also help me to improve teaching
and assessment methods.
How I incorporate recent research findings into my teaching
practice
I keep current with
research findings in the areas of mathematics and mathematics education.
As a member of the Mathematical Association of America (MAA), the National
Council of Teachers of Mathematics (NCTM), the National Council of Supervisors
of Mathematics (NCSM), the American Educational Research Association (AERA),
and the International Group for the Psychology of Mathematics Education, North
American Chapter (PME-NA), I receive and read recent research publications in
both fields. I incorporate new recearch
findings into my teaching. For example, I found “Principals and Standards
for School Mathematics” published by NCTM in 2000, useful in my revision of
syllabi for MAT 130-131 and MAT 140-141.
I actively participate
in local, national and international conferences devoted to mathematics
education. I learn what is new in the field and apply new ideas as
appropriate to my teaching. I share what I learned at the conferences
with my students in classes. For example, I co-presented at the annual
National Council of Supervisors of Mathematics (NCSM) conference about
Bulgarian and Russian elementary schools in April 2005. At the conference,
we had a motivating discussion with mathematics supervisors and teachers about comonalities and differences in teaching mathematics in
different countries. Since I had discussed using alternative algorithms
from different countries in MAT 140-141 class, and students had
expressed deep interest in how mathematics is done in other countries, I
decided to share with my students the results of my conference
presentation. The students and I had a passionate discussion in class and
it was clear that much learning occurred during this discussion. We
compared elementary school textbooks used in
the US and Russia and students were amazed to see the
levels of mathematics problems required for K-3 students in Russia.
I told my students about the reform mathematical movement in
the US and the expectations the National Council of Teachers of
Mathematics (NCTM) would have for them when they start working with
children. We talked about the NCTM school standards for elementary
schools and students realized that they would teach algebraic and geometric
thinking starting in kindergarten. That was a revelation for them.
Trying new ideas and
taking risks in classes causes difficulties or students’ resistance from time
to time. For example, at the beginning of a semester students are not
happy that I refuse to give away answers to problems, that I ask them questions
to clarify their approaches to problem solutions, or that I always ask them
“why” questions. After a while students get used to my teaching style,
and even learn to appreciate the opportunity to express their thinking and
reasoning.
I have learned that it
is important to be extremely explicit with students when I use teaching methods
that are unfamiliar to them. For example, in MAT 140, before
using videos of elementary school students performing addition and subtraction
of whole numbers, I told my students that the goal of the activity is to
understand new algorithms suggested by kids, to compare these algorithms with
ones they know and used, and to evaluate algorithms effectiveness. Later,
my students wrote in their reflections that watching videos was really helpful
for them to realize that children think differently than adults.
Furthermore, several of my students experimented with their young siblings,
asked them to perform operations with whole numbers in alternative ways, and
reported about their findings in class.
I conducted my
dissertation research on the topic of algebraic thinking. Algebraic
thinking is a complicated higher-order process that cannot be mastered
instantly. For this reason, the National Council of Teachers of
Mathematics (NCTM, 2000) has called for an algebra strand in pre-kindergarten
through grade 12. Educational researchers claim that if grades K through
8 students are introduced to algebraic concepts gradually, they will be able to
build meaning of such abstract concepts as variable, equation, and
function. It is crucial that Wheelock students, especially prospective
teachers, learn algebraic thinking and how it evolves to formal algebra.
To ensure Wheelock students’ transition from arithmetical to algebraic
thinking, I carefully design and teach algebraic problems
in MAT 130-131 and MAT 140-141.
I realize that
understanding the nature of algebraic thinking is also vital for in-service
teachers. In collaboration with Pat Willott and
Debra Borkovitz, I participated in designing and
teaching two summer institutes at Wheelock College in 2002 and
2003. The most recent content institute, “Algebraic Thinking for
Teachers” (Wheelock College and Boston Public Schools,
2003), was funded by the Massachusetts Department of Education. Based on
experiences I drew from teaching summer institutes, I revised and improved the
course College Algebra (MAT 210) and taught it in the Fall
of 2003 more successfully than before. For instance, I added project
presentations to the course, coaching students to research topics in pairs and
make presentations to their peers.
The 2003 summer
institute applied the NCTM idea that algebra is a content strand for grades
Pre-K to 12. The ultimate goal of the institute was to deepen teachers’
knowledge and understanding of algebra so that they can more effectively
increase students’ mathematical abilities and achievement in algebraic
thinking. The institute was designed for elementary and middle schools
teachers and aimed to promote and improve teachers’ knowledge of key algebraic
ideas (patterns, variable, equality and inequality, equation and system of
equations, and functions). Through problem-solving and hands-on activities,
readings and discussions of readings and classroom experiences, participants
increased their own knowledge of algebra. They learned how to use
symbolic and concrete representations for unknowns or quantities that vary in
expressions; how to use and explain the commutative, associative, and identity
properties of operations; how to solve problems involving proportional
relationships, including unit pricing and map interpretation; and how to
create, describe, and extend symbolic and numeric patterns.
The general format of
the institute included three parts. Each morning participants engaged in
an activity or activities designed to use, extend and deepen their knowledge of
a specific algebraic concept. The activities were followed by time to write
a reflective journal entry, and to discuss the concept and the learning that
took place during the activities. The afternoon was devoted to small and
large group discussion of how the morning activities link to appropriate
learning standards from the curriculum frameworks, and how participants might
alter classroom practices to be more effective.
A three-day break in the
two-week institute allowed participants time to work on their projects.
During these days, the participants completed one of the following projects: a
curriculum design project (design a curriculum unit that focuses mainly on
activities to help students develop algebraic thinking and will take at least
one week to implement in the classroom); an action research project (ask a
question concerning some aspect of students’ thinking or understanding of
algebraic thinking, or some aspect of teaching or curriculum design, and carry
out classroom research designed to answer the question); or an in-depth
mathematical study of an algebra concept (identify a key algebraic concept,
research the concept and write a paper to explain the major components of the
concept).
This institute offered
participants an opportunity to deepen their knowledge of key algebraic concepts
and processes as well as to apply their learning to develop instructional
materials appropriate for using in classrooms. Participants took a pre-
and post tests assessing knowledge of key algebraic
concepts. The institute was partially evaluated by the results of pre-
and post-tests that I designed and graded. The assessment demonstrated that
Class Average Content Gain was 30-40 %.
Managing summer
institutes with in-service teachers gave me an opportunity to advance my
understanding of fundamental issues in mathematics teaching and teacher
preparation. Dr. Willott and I are going to
share our experiences and results of teaching the 2003 content institute at the
regional NCTM conference in October 2005 and at the AMTE annual conference in
January 2006.
Conclusions and potential for growth in teaching
I try to provide an
exciting and challenging appropriate learning environment and to show high
expectations for my student achievement. I love working at Wheelock
because I love making a difference in students’ mathematics knowledge and in
their lives and in the lives of the children they teach and care for.
I want my classroom to
be a place of active leaning for every student. Teaching is a never
ending adventure: students have diverse backgrounds and different learning
styles, educational researchers reveal new trends and opportunities to teach
mathematics more effectively, and I keep learning how to improve my teaching
craft. I constantly work on advancing and enriching my teaching
techniques. I listen to opinions of students and colleagues to make
changes. I dream of more collaboration among colleagues that will
include visiting each other’s classes on a regular basis and analyzing
mathematics content taught and pedagogy employed. I also hope that we
will continue the math/science department collaboration with the education
division.
I continue to learn and
understand more about students, teaching, and myself. I plan to improve
in the following areas:
· Ways I plan my classes. For instance, if I
teach a course for the first time the pace of the course is uncertain and I
have to watch whether I try to cover too much material.
· Ways I explain mathematics. For
example, I have to watch how fast I speak when I teach. I have
to deal with a cultural language habit: I speak too quickly when I am
enthusiastic about the material. I ask my students’ help to overcome this
habit.
· Ways I communicate the mathematics demands to
all students. For example, based on students’ feedback in class and
their course evaluation comments, I need to make my demands even more
explicit.
References
National Council of
Teachers of Mathematics. (2000). Principles and standards for school
mathematics. Reston, VA: National Council of Teachers of
Mathematics.
Schoenfeld, A. H. (1992). Learning to think
mathematically: Problem solving,
metacognition, and sense making in mathematics. In D. A. Grouws
(Ed.),
Handbook of research on
mathematics teaching and learning. (pp. 334-370). New
York: Macmillan
Publishing Company.