Action Research Project
Jessie
Houghton
Problem
Statement
As an Advanced Placement
Calculus teacher one of my problems is isolation within my school. When my students have questions, concerns, or
need assistance with an assignment, I am the only person they are able to come
to. Most teachers at the high school
level, including other mathematics teachers, have difficulty helping the A.P.
Calculus students because they too are isolated into their own subject area. Often times the calculus material is more
in-depth and complicated than other mathematics teachers are accustomed to
working with (for many it has been a long time since they have seen the
topics).
I have found that students
at this level of learning need constant reinforcement for correct solutions and
methods as well as guidance throughout many problems. Most of the mathematics in calculus is very
new to the students and they are unsure of their techniques until feedback is
provided. This creates a problem for me. When I am not able to be around or when
multiple students need lots of individual attention, I have problems helping
each of my students.
I want to increase my
students understanding and development of calculus by enhancing the student
collaboration within my classes. Collaboration
within mathematics can be a strong tool used to help deep thinking
development. By using collaboration,
instead of students sitting ‘stuck’ on a problem (usually becoming very
frustrated) they are able to work together to reach a solution, while expanding
their individual understanding. My goal
is for my students to not simply supply each other with numerical answers but
be able to discuss major concepts and topics that are woven throughout calculus
and mathematics.
My hope is that some type
of technology could help to provide my students with more (and better) calculus
help to foster student collaboration and answer questions when I am not able to
be available. This technology should provide feedback or input about certain
problems that the students are struggling with, while informing me the areas
that may need to be re-taught with entire classes. I am looking to find online support, which
all students can access, to evaluate their work and supply them with more
practice problems that will promote collaboration.
Project
Goals
I want to create an
atmosphere of mathematical collaboration with my calculus students. This collaborative environment will promote
mathematical discussions, debates, and reasoning. I will see and hear my
students building and connecting knowledge with one another. Students will begin to ask each other for
support and share their finding when tackling new complex problems. Students will help to foster each other’s
knowledge of calculus, leading to enhance understanding. I will see this increased understanding in
the students’ ability to be flexible with their knowledge. They will be able to justify and support
their conclusions verbally, numerically, symbolically, and graphically. Students will feel comfortable working
together to build and link new concepts together.
Technology will serve as
the base board when creating each collaborative group. The
program WeBWork will provide my students with proper material that will drive
student collaboration about advanced mathematical concepts. WeBWork will provide each student with an
individualized problem and feedback, which will push student learning and
knowledge of calculus concepts.
Collaborative groups will form around topics that WeBWork presents to
each student.
Before constructing
mathematical collaborative groups, I need to carefully separate between the
idea of cooperation and collaboration. Cooperation in mathematics is defined as the
process when students work individually on separate components of a problem.
After each student completes their own component they compile the
findings. This is unlike the definition
of collaboration. Collaboration in
mathematics is defined as the process when students work together on the same
problem simultaneously. Peer collaboration
creates situations where students have to explain and justify their decisions
to each other and describe their choices.
Supportive
Research
Collaboration can be an
effective tool to use to develop student understanding in mathematics. Collaboration is an important tool to be used
to see student growth and development within specific topics (Connell, 2004). With collaboration students are able to dig
deeper into topics and build connects between new and old ideas when working
together. When students are working
together they are focused to verbally explain and justify their work to each
member of the group (
Technology can be used to
support and enhance collaboration (Gadanidis, 2001). Teachers need to define the specific role of
technology in learning to help students to understanding their use of technology.
By using appropriate educational software, there is a potential to take a
positive step towards engaging students more actively in the process of
mathematical thinking and mathematics learning (Manoucherhri, 1999). The appropriate technology can create
collaborative environments. Technology
that pushes students to explore concepts and major topic understanding will
drive mathematical collaboration.
Further research related to my Action Research Project is located
in the annotated bibliography.
Connections
to Educational Standards
AP Calculus Standards:
Course Goals
·
Students should understand the meaning of a derivative in terms of rate
of change and should be able to use derivatives to solve a variety of problems.
·
Students should understand the meaning of a definite integral as the
accumulation of sums and should be able to use integrals to solve a variety of
problems.
·
Students used understand the relationship between the derivative and
definite integral.
---------------------------------------------------------
Using WeBWork to support and enhance collaboration
within my Advanced Placement Calculus course perfectly fits with the College
Board standards. The College Board
standards state that students must learn the relationships and evaluation
techniques of limits, derivatives, and integrals. These connections can be developed through
mathematical collaboration and WeBWork provides teachers with access to
thousands of problems that practice all of the methods described and required
by the College Board. Teachers are able
in WeBWork to structure their lessons so that students can see connections and
layering of new problems onto old problems, therefore enhancing the connections
and understanding of each topic.
Technology Standards:
Technology productivity tools
---------------------------------------------------------The use of WeBWork in
Advanced Placement Calculus also fits within the ISTE technology standards
given above. The first standard promotes
a requirement of technology as a tool to enhance learning and collaboration
between students. WeBWork allows
students to do all of this. It enhances
learning by providing student with instant feedback and individualized problems. The program enhances collaboration by pushing
students discuss concepts, instead of individual problems. By providing each student with individualized
problems, instances of cheating or copying between students is eliminated,
therefore allowing students to openly work together to answer each others’
questions and concerns.
Instructional
Plan
Overview of Project:
The goal of my Action
Research Project is to create effective mathematical collaboration within my
Advanced Placement Calculus courses. In
forming a collaborative environment for mathematical thinking, I will need to
tackle three issues with my students.
These issues are: the definition
of what a collaborative environment is, facilitating students work within a proper
collaborative environment, and providing students with materials that foster advanced
mathematical collaboration. These three
issues will be continuously revisited and explored. Each issue will be addressed and examined at
the beginning of the year, however as students become more comfortable with
collaborative environments the issues will be redefined and restructured to
include new findings. My general plan is
to apply a constructivist method of using collaboration. This constructivist approach allows for
student knowledge to develop and build through each step. I hope that students will explore and further
their understandings as they work through collaborative environments.
A fully operational
environment will contain students that properly use collaboration to foster
their own and others’ understanding. The
students will use a program WeBWork to receive questions to work on in small
groups. WeBWork will act as a tool to
providing the students with mathematical material, assessing students solutions
and giving the students a base to build collaboration. WeBWork will provide each student with a link
to one another, by presenting each student with similar (not identical)
problems. Students will then be
encouraged to discuss and explore one concept that is represented using
multiple methods.
Resources:
Element 1: Defining Collaboration
I plan to carefully outline
the definition of collaboration with my students. While I am defining and explaining collaboration
to my students, I will also state my expectations for group
collaborations. One expectation is that
students are working on each part of their problems simultaneously. Student may
look toward their classmates for assistance in completing parts, but the
student, themselves, will complete each part.
Another expectation is that after the student has completed the task,
he/she should be able to share how each part of the part is evaluated. Lastly, students are expected to share their
findings and evaluation techniques with an open mind. Group members who reach different conclusions
or use different methods to evaluate problems should be given time to explain
and justify their findings. Mathematical
collaboration is formed when the group members compile their findings, not
simply supply each other with solutions.
Students will develop a
list of how they define collaboration. This list will be hung in the classroom,
to be reviewed throughout the year. As
the students work through their collaborative environment, they will have the
ability to go back and add descriptions to the class definitions of
collaboration. I want the students to
continuously revisit the concept of collaboration and allow their understanding
to grow and mold as they work in groups.
Element 2: Facilitating Collaboration
The second part of my
Action Research Project is facilitating my students as to how collaborative
learning takes shape. I will do this by
having my students practice, in class, how to work in a collaborative group. I plan to assign each group a set of problems
that they are to complete by working together.
My first expectation to the analysis process will help the students
develop collaborative techniques by assuring that all students must be working
on the same parts of a problem at the same time. This will force students to complete each
problem together. Therefore, they will be
facing challenges and obstacles together, driving them to discuss and justify
work to one another. This will create a proper collaborative environment. During this initial phase of mathematical
collaboration, I will be present to monitor developments and interactions. After the activity, I can address problems
and assesses the ability of my students to work together correctly. In class activities, like these, I can help
to support my students in becoming more successful in using collaboration to
enhance their mathematical understanding.
We will finish the first task with an entire class discussion, were I
will reinforce strategies used and discussion I heard that promoted
mathematical collaboration within each group.
Again, I will continue to revisit this element as students develop
stronger collaborative skills. Continue
growth and development will occur as students and I learn how to better
collaborate.
After I have worked, in
class with my students, I will transfer the collaboration activities to study
groups that meet outside of school. I
meet with a large study group twice a month to work on reviewing and practicing
mathematics. The focus of this study
group will shift into a collaborative mode as students begin explore
mathematical collaboration. I will
encourage students to work together to understand and build concepts. I will continue to attend the large study
groups; however I will take on the role of a facilitator by supporting the
students work in collaborative groups. I
will then encourage students to bring the collaborative tools, into their
smaller study groups. The smaller groups
meet to discuss daily assignments and projects.
Within my Action Research Project these smaller collaborative groups
will form around topics presented by WeBWork.
The technology will provide a foundation for the student collaboration.
Part 3:
Providing Mathematical Material
After my students have
begun to understand the meaning of collaboration and have begun to correctly
build collaborative mathematical groups, I will supply my students with more
mathematical material that will push them into using collaborative techniques
to discuss complex concepts. Technology
will deliver material to my students, which will advance group collaboration. The program that I have chosen to deliver
mathematical materials that will provide my students with a foundation for
collaboration is WeBWork. I have chosen to use this program because it provides
students with problems that I have picked out but each student receives a
different problem. This technology
ensures that, no two students will reach the same answer, however all students
will be using the same techniques to solve and evaluate their problems. This program will then promote student
collaboration about concepts.
Technology Program:
The program WeBWork will
provide my students with problem sets to evaluate. WeBWork will act as an interactive,
individualized textbook for each student.
Each student will login to their personal WeBWork account, which I have
set up for them. Their accounts will
contain a list of various assignments that coincide with topics that are
currently being covered in class. Within
each assignment, students will have an individualized problem set containing
eight to fifteen problems, which I have chosen for them. Students will be required to complete the
entire problem set by a date selected by me. Students will need to work through
problem sets by transferring and applying their in-class knowledge to each
problem. WeBWork allows students to
check their work throughout a problem, by entering their work into the program.
The instructor can select whether students
are required to enter work as a problem develops or simply require a solution
to each problem. After the solution is entered, a box will appear on the screen
telling the student whether the solution is correct or incorrect; no other
information is given to the student, unless the instructor has set the program
to do so. Therefore, WeBWork provides
students immediate feedback which allows them to assess their understanding and
isolate specific questions and concerns they have within a unit. However, WeBWork will not provide students
with tutorials or assist when they do not understand a problem. Students will need to use each other to ask
and answer questions about their specific concerns.
WeBWork is a very advanced
software program that not only allows me to tailor each assignment around a
specific topic, but it also provides each student with a different problem set. As the instructor, I will choose the content
for each problem and WeBWork will write an individually unique problem for each
student. Since each student is required
to complete different problems within the same content, students will be forced
to discuss and justify concepts to each other.
This practice of using concepts to explain and expand ideas with one
another will develop mathematical collaboration within groups that is far more
advanced then simply the discussion of one single problem. Students will view multiple problems (other
member’s problems) which relate to a single concept. As they are explaining evaluation techniques to
each other, they will not have the ability to use their specific problem, since
no one else is solving it. This will
drive the discussions to be about mathematical concepts, instead of specific
number issues. By viewing, assisting,
and answering questions, mathematical ideas will be deeply explored and
discussed within each group. These
mathematical discussions will direct the group into collaborative thinking,
where each member of the group is explaining and justify ideas. WeBWork will
help to broaden and adapt my students’ knowledge of calculus.
WeBWork will also help to
direct entire class discussions on mathematical concepts. With the click of a button I will have the ability
to view the number of times students attempted problems and the accuracy of
solutions. WeBWork will provide me with
an overall pattern of student knowledge, therefore informing me of how to
better spend classroom time; leading to deeper student understanding. I can use weak areas (seen through WeBWork)
as the focus of a large group discussion, leading to collaborations on how
ideas and concepts are connected. This
collaboration in smaller groups and larger groups will develop and challenge
student understanding. Students will
learn how to more deeply connect concepts and build ideas, using other
student’s examples.
Technology Setup:
I will set each of my
students up with a login and password, so that they are able to get into
WeBWork at the beginning of the year (fall 2005). I plan to write at least one assignment in
WeBWork for each unit that we cover. Within
each assignment, students will need to login and complete each assignment
before the due date. Each assignment
will be open for about two weeks, and then problem sets with solutions will be
posted a few days before a traditional assessment. I will continue to assign students with some
bookwork; however most of the bookwork will not be graded. These grades will be replaced with the
problem sets on WeBWork. I will
encourage students to download a hard copy of their problems when they are
working with their collaborative groups.
Students will be given some time in class to work with each other in
their groups, during the beginning of the year.
As the students feel more comfortable with WeBWork and effectively
collaborating together, they will receive less time in class to work in
groups. I will then, strongly encourage
groups to meet outside of school. Questions
and concerns will be answered and discussed within their mathematical
groups. I will not provide direct
assists to students; instead I will encourage them to work collaboratively
within their groups.
Time Frame:
I am planning to implement
my Action Research Project with my three Advanced Placement Calculus courses. I plan to have about 75 calculus students
enrolled in these courses. All of these
students are very bright and driven.
These students have chosen to take the most difficult math courses
possible, throughout their high school career.
Most of these students will have internet access in their homes but
others will need to use school computers to enroll into WeBWork. All of these students are planning to attend
college next year and will be taking the Advanced Placement Calculus Exam in
May 2006. A lot of these students will
be technologically gifted and talented; therefore I think that they will not
have any hesitations to using WeBWork. I
am accessing WeBWork through
Evaluation
Plan
Evaluation Questions:
My Action Research Project
explores the use of collaboration to increase and expand student understanding
of calculus. Through my Action Research
Project my students will use WeBWork to enhance mathematical collaboration and
interaction. The following questions will be explored while I am evaluating the
effectiveness of my Action Research Project.
o How will my students collaborate outside of class?
Will my students
collaborative weekly, daily, or monthly?
Does WeBWork assist the collaborative process? Does this program drive collaboration toward
concepts, instead of individual solutions?
How will collaborative interactions develop with my students? What type of conversions will be heard?
o What will my students collaborate with?
What type of materials will
foster mathematical collaboration? Will
the WeBWork program provide them with materials to collaborate with? What types of other materials will students
use in collaborative groups? Will they collaborate when studying and preparing
for tests?
o How will collaboration help their understanding?
Will the students more
deeply understand topics as a result of collaboration? Will students develop the ability to transfer
knowledge to new topics? Will WeBWork
promote the transferring of knowledge between students and within new
concepts? Will students bring more
questions to class? Will test scores
increase?
o How will collaboration affect my teaching?
How will my lesson plans
change with collaboration? Will I be
able to better address student concerns and questions? Will I see my students pushing topics and
digging for more information? Will
students continue to need me for assistance and concerns?
Data Collection:
I plan to use the following
tools to collect data on my Action Research Project. These tools with be used to measure and
document the findings of my research.
o Journal
This will be kept and
updated by me through the year. It will
serve as a record of in and out of class collaboration that I witness. It will also reflective about how to better
collaborative activities.
o Students Surveys
This will be given out the
students after collaborative activities and after major unit tests.
o Student Reflections
I will provide students
with time to write about how their group collaboration formed shape and what
their role in the collaboration process was.
I plan to use student reflections after every few collaboration
activities.
o Records of Online Activities
These will be kept within
WeBWork. They will provide me with
quanititative and qualitative data about student process with mathematics and
collaboration. WeBWork has the ability
to organize and systematically keep the data for me, until it is needed.
o Classroom Observations
This will be an on-going
data collection tool. I will use my own
observations during collaborative activities and during small group study
sessions by using an audio recorder or sitting off to the side during
collaborative activities. An audio
recorder will allow me to review discussions multiple times, to break down
types of conversions that pushed student understanding. My own classroom observations will allow me
to document immediate student reactions.
I will also attempt to setup observations preformed by other
teachers. All observations will be
recorded into my journal.
o Calculus Assessments
The typical calculus
assessments will be exams, tests, and quizzes.
I can also use the student scores on WeBWork material. Within the use of all of these tools I can
explore the amount of student collaboration that occurred before the
assessment. The major assessment tool
will be the Advanced Placement Exam in May.
I will be able to compare my student scores with national scores and
previous
Data Analysis:
I am using each evaluation
tool to explain the effects of mathematical collaboration. I am also interested in the role that WeBWork
will play in the collaboration process.
Below is a description of how I plan to use each tool.
o Journal
I plan to keep a journal
about the collaboration activities that I use with my students. In each entry I will write a detailed
description of the activity and a reflection about the activity. I hope that by using a journal, I will be
able to record the collaboration process as it happens and document the growth
of my students’ knowledge; therefore providing a link between mathematical
collaboration and student learning.
These entries should show me how the collaboration process develops and
what signs will I discover that show good mathematical collaboration (leading
to further, deeper understanding). The
time that I will spend after each lesson reflecting will help to guide me as to
what I need to do to future the improvement of student collaboration. This reflection time will help to mold and
shape each next collaborative activity by showing me what I can do to help
promote good mathematical collaboration.
o Students Surveys
I will give my students
surveys after each unit throughout the year, to evaluate how and when they used
collaboration when they were outside the classroom. I hope to see a growth in their collaborative
skills by the end of the year. This
growth would be shown by increased time and commitment to a collaborative
group. I will also give the students a
chance to evaluate the effects of collaboration on their understanding. Students will have to reflect upon their own
learning process to see if collaboration was a positive tool for them to
use. Lastly, I will ask students to
evaluate the effect of WeBWork on their understanding. I will use statistical tools such as: mean, standard deviation, and significance
tests to compare and analyze the findings.
Examples of sample surveys are available in the student
survey section.
o Student
Reflections
Student reflections will
give me the opportunity to get into my students’ heads to further understand
how the collaborative processes with take form, when I am not around. These reflections will allow students to
voice their opinions and ideas of collaboration. I also hope to see who the students
collaborate with, when, and with what materials. These student reflections will help me to not
only see how mathematical collaborative groups are working, but also the role
of WeBWork in the process.
o Records of Online Activities
WeBWork will allow me to
examine how many times students attempted problems and which problems students
struggled with. These records will help
me to reshape classroom lectures and activities. WeBWork will also allow me to watch for
improvement with my students throughout the year. I can check to see if improvements in online
problems correlate with collaborative activities done in class. I also plan on entering survey questions into
a few assignments on WeBWork. Example
survey questions will ask students: (a) how many people they worked with to
complete an assignment, (b) how many times they needed assistance, and (c) how
they used the assistance they received.
These occasional surveys will provide me with immediate feedback as to
my students’ collaboration process outside of school. They will also help me to redirect any
individuals or groups, if needed.
o Classroom Observations
As I implement
collaborative mathematical activities with my students I will record the type
of student interactions in my journal. I
will be examining how the conversion between my students drives their
understanding of new ideas, while continuing to make connections to previous
knowledge. I will specially be exploring
the role of WeBWork in group discussions.
Does WeBWork provide my students with material for proper collaboration?
I will be looking for examination of ideas and concepts to show that WeBWork
did develop a collaborative environment.
Problems discussions, questions and disagreements, will all be signs
that mathematical collaboration is taking place. Again, all of these signs will be documented
in my journal.
o Calculus Assessments
The exams, tests, and
quizzes that I used in class test for understanding and transfer of
knowledge. They do not simply ask
students to restated material talked about; instead I try to push students to
apply and adapt their knowledge to new situations. These traditional classroom assessments will
provide me with quantitative data about the improvement and development of my
students understanding within each unit.
Each assessment can be compared with three different groups: last year’s test scores, students that did
not choose to finish WeBWork, or units that did not involve WeBWork. Significance tests will be use to look for
the differences in these three groups.
Data that records a p-value
less than 0.05 will clearly indicate a difference between the groups. This difference will show that groups that
used or completed WeBWork had a deeper understanding of the materials. Along with significant tests, a correlation
coefficient will be used to explore any relationship between WeBWork and
collaboration. I am hoping to find that
as students use the problems in WeBWork their collaboration will be stretched
and expanded.
Summary
My Action Research Project
is attempting to explore how to enhance mathematical collaboration through the
use of WeBWork. Within this mathematical
collaboration my students will develop a deeper and richer understanding of
advanced mathematics and this understanding will be shown in class discussions,
student work, and traditional assessments.
Students will work together to build and connect ideas that are
presented in WeBWork. Throughout the
implementation of my Action Research Project, I will be looking for the effects
of collaboration with students’ learning.
I am hoping to track how and when my students use collaboration and the
effects of collaboration on the learning process. I will also be exploring whether WeBWork
helps to promote student collaboration.
This collaborative environment will provide students with mathematical
support to dig deeper into topics, to ask questions, and to receive answers and
guidance, when an instructor is not available.
1. How
often do you collaborative?
Never Sometime Always
2. Do you always collaborative with the same people?
Never Sometimes Always
3. What do you collaborative with the most:
WeBWork Other Homework AP Problems
4. What else do you collaborative with (circle all that
apply):
WeBWork Other Homework AP Problems
5. Has collaboration help your understanding of
calculus:
No A little A lot
6. Do feel that collaborative groups are helpful? Explain.
Reference
List
Connell, Susan L. (2004).
Comparing Blogs, Wikis, and
Discussion Boards as Collaborative Learning Tools.
Edwards, Julie-Ann &
Jones, Keith. (2002). Exploratory Talk
Within Collaborative Small Groups in Mathematics.
Gadanidis, George, Graham,
Lynda, McDougall,
Manoucherhri, Azita.
(1999). Computers and School Mathematics Reform: Implications for Mathematics Teacher
Education. Jl. of Computers in Mathematics and Science Teaching, 18, 31-48.
Taylor, Janet. (2002). The
Evolution of Online Learning in Bridging Mathematics at a Distance. In Statham, M. (Ed.) Crossing the Bridge. (p
67-74) Proceedings of the 10th Australasian Bridging Mathematics
Network,
Connell, Susan L. (2004).
Comparing Blogs, Wikis, and
Discussion Boards as Collaborative Learning Tools.
This article outlines a
research project that explores how to use technology as a collaborative
learning tool. The author includes the
comparison of blogs, wikis, and discussion boards in enhancing learning and
fostering collaboration when exploring the use of technology. This article was written to introduce the
study. The research findings are not
documented in this paper.
The author stated how the
assessment of technology in classrooms will occur after the trial period. The assessment will be based on how to best
use each piece of technology to offer the most interaction to students. The researcher included pre and post surveys
that are to be given out to students. A
student’s participation level will be the main measurement used by the author
to explore the effectiveness of each tool.
This article also outlines
the importance of using collaborative learning tools. Connell states that the requirement to
collaborate is being more commonplace in both the academia and industry
fields. Identifying technologies and
techniques that can facilitate various types of collaboration and promote active
participation can contribute greatly to the exchange of knowledge within a
department, a corporation, an entire academic discipline, or even to the world
at large. The article states that one
tool to be explored, weblogs, can be used to enhance students’ critical
thinking, literacy skills, and ability to use the Internet for research
purposes. Another tool to be explored,
wiki format, is based on constructivist foundation that aids in the development
of collaborative website posting, student assignments with peer reviews,
problem solving, focused discussions, interdisciplinary projects, and community
building among students. Using these
technologies as collaborative tools can build professional development
communities for both teachers and students.
This article is relates to
my Action Research Project because it outlines several options that can be used
to create an online collaboration group.
All three of the tools explored in this article, are possible tools that
I could used with my Action Research Project.
The author provided me with information on each tool and how each tool
can be used to enhance collaboration with my students. This article also provided me with example
surveys for me to use or modify for my project assessment.
Edwards, Julie-Ann &
Jones, Keith. (2002). Exploratory Talk
Within Collaborative Small Groups in Mathematics.
This article begins by
defining cooperating and collaborating in mathematics. Edwards and Jones define cooperating in
mathematics as the process when students work individually on separate
components of a problem. Then, after each student completes their own component
they compile the findings. This is
unlike the definition of collaboration.
Collaboration in mathematics is defined as the process when students
work together on the same problem simultaneously. Peer collaboration simulates situations where
students are having to explain and justify their decisions to each other and
describe their choices, according to Edwards and Jones.
This article goes on to
research the use of collaborative activities to learn mathematical topics. The authors examine three different sets of
students: 15-16 year olds, 14-15 year
olds, and 12-13 year olds. Each group
used a type of collaborative activities within a mathematical unit. Then students were asked to answer questions
about the activities under the following subjects: putting work together, knowledge of
collaborators, teacher insights, enjoyment, and developing mathematical
understanding.
The authors’ conclusions
favor the use of collaboration in teaching mathematics. They state that “knowledge of peers improved
confidence to offer solutions and express opinions”. This improved confidence leads to a deeper
insight into what the students are learning.
Students involved in the study found that collaboration allowed them to
pile individual ideas on top of each other therefore building and linking to
new concepts to old ones.
I choose to use this
article in my project because it explored the benefits of forming collaboration
groups within a math course. It also
clearly defined what is considered collaboration. While defining collaboration, the article
also pointed out the results that are seen when collaboration is applied
correctly. I think this is important to
my research project. I want my students
to form a collaboration of support using technology, where they are able to
share opinions and provide each other with feedback.
Ernest, Paul. (1991). What
is the Philosophy of Mathematics Education?.
In this article, Ernest
explores the philosophy of mathematics by posing five questions: what is mathematics, how does mathematics
relate to society, what is learning mathematics, what is teaching mathematics,
and what is the status of mathematical education as knowledge field. Under each category he asks more in-depth
questions such as: (under what is
learning mathematics) what elements of learning mathematics are valuable, what
is the role of the learner, and what assumptions, possibly implicit, underpin
views of learning mathematics.
Throughout the sixteen page article Paul asks more questions with the
attempt of exploring the basic philosophy of mathematics. He approaches each question philosophically
raises concerns within each question.
Paul also attempts to
explore the link between the philosophy of mathematics education and the
practice of mathematical education. He
shows the possible implication of mathematical theories in a classroom. However, the article does not discuss how the
theories are put into a classroom.
I chose to read this
article because it asked some very basic questions that I need to continuously
revisit as I create my Action Research Project.
How do mathematicians (or students) create new knowledge? What are the aims of mathematical
education? What is the role of the
learner (or teacher)? What methods are
used when teaching mathematics? How can
the teaching and learning of mathematics be evaluated and assessed? When does understanding occur? How can tools (technology) be used to enhance
student involvement and understanding?
Through exploring these questions, I will have the ability to better
assess the effectiveness of my project.
Gadanidis, George, Graham,
Lynda, McDougall,
This article explores the
use of online educational tools; both on the small-scale, individual teachers
using the web to provide their classes with current information and experiences
that are outside their classrooms and on a larger-scale, an entire course
taught online.
The article first defines
what teachers expect of their students:
to be immersed in a mathematical culture that gives them an opportunity
to: (a) refine inquiry, investigation,
experimentation, and problem solving processes, (b) develop the habits of a
life-long learner and (c) learn significant concepts and procedures (with
understanding).
The article continues with
exploring the focus, advantages, disadvantages, roles of teachers and students,
and the implementation of learning mathematics online. The focus of online learning should be to
allow for exploration of concepts and relationships. Through the exploration of concepts and
relationships the intent is for students to develop a broader understanding of
mathematics. Online learning has the
potential of providing interactive exploration based mathematics experiences
where multiple representations are linked and explored dynamically, according
to this article. The role of the
teacher, student, and implementation of the technology should be carefully
developed and considered so that the use of technology benefits the
mathematical education.
Online learning allows
students the opportunities they need to experience thinking and attitudes
associated with mathematical activities.
It can provide students with opportunities to solve and express their
mathematical thinking and ideas. The
article also states that online learning gives students situations to receive
immediate feedback to check for their understanding of mathematics. Presented, in the article, are some issues
and challenges students face with online learning. Online learning is dependent on student
skills in technology. Students must have
the ability to understand graphical software, spreadsheets, or mathematical
programs used to pose mathematical problems.
Another limitation is student access to the Internet.
This article outlines how a
successful online learning environment is created. Through clear learning goals and
collaboration between students, teacher planning and preparation, and proper
use of mathematics a positive online environment is formed. A successful learning environment is also
defined in this article as, a place where students feel safe and secure to
express opinions and questions. Online
activities should allow for exploration of concepts and relationships. Technology should not become an obstacle when
engaging in online learning, the environment should have a simple focus of
design.
This article has given me a
great insight as to the advantages of online learning. It has also helped me to avoid likely
pit-falls when creating my environment.
The central theme throughout this article is that online tools should be
used in combination with proper mathematics.
The use of mathematics is very important for me to keep coming back to
and examining with my online community.
After reading this article, I believe that a well-designed online
mathematical learning will be educational for me and my students.
Herrington, Jan, Oliver,
Ron, & Reeves, Thomas C. (2002). Patterns of Engagement in Authentic Online
Learning Environments. ASCILITE
conference proceedings.
This article explores the
use of authentic activities within online learning environments. The authors define authentic activities with
ten characteristics: real-world
relevance, ill-defined, complex tasks that need to be investigated over time,
opportunities for exploration through different perspectives, opportunities for
collaboration, reflection, integration across different subjects, integrated
assessments, competing solutions, and creation of polished products. This paper discusses the patterns of
engagement that have emerged from research on authentic learning tasks. The authors explore the impact of
constructivist philosophy and advances in technology on educational design and
practice.
The article states that
there are two patterns of engagement with authentic learning. The first is willing acceptance and
relief. Students in this engagement
pattern give themselves over to the action with comfort and ease. In this pattern students are willingly and
instantly engaged in the activity.
Students can readily become so immersed in the learning context that has
been created for them that they begin to see the characters as real. The second pattern of engagement is delayed
engagement. In the second pattern,
students experience problems with learning environments that use authentic
tools. They have difficulty in changing
dependent learning habits; this occurs when students have low self-motivation
or are not familiar with authentic learning tools. However, the research within this article
showed that in all the environments using authentic tasks, even reluctant
students (delayed engagement) were reported to have engaged within a few weeks
of the semester.
The authors’ findings
provide support for the use of online learning settings. Their research
suggests that the use of the authentic setting encourages and supports learners
in their development of skills in self-regulation and self-learning.
This article has shown me
the importance of using authentic teaching tools. Authentic settings have the capability to
motivate and encourage learner participation.
With technology as an aid, using authentic mathematical tools will be
easier. Authentic online learning should
be involved within the online support system that I create for my
students. I want to use authentic
learning to help humanize the online experience for my students.
Manoucherhri, Azita.
(1999). Computers and School Mathematics Reform: Implications for Mathematics Teacher
Education. Jl. of Computers in Mathematics and Science Teaching, 18, 31-48.
Current mathematical reform
has encouraged the use of technology in mathematical classrooms. This article researches about what teachers
are using technology and how they are using the technology. The author went on to perform an exploratory
study investigate the extent in which computers were being used by middle and
high school mathematics teachers by asking the following two questions: how
frequently teachers’ used computers and what factors influence teachers’
decisions about the use of computers.
The results of the study, found that teachers did not use computers for
purposes other than drill and practice.
The lack of use was due to poor training with the teachers.
The article goes on to
state that with the availability of computer technologies and appropriate
educational software, there is a potential to take a positive step towards
engaging students more actively in the process of mathematical thinking and
mathematics learning. The article’s
findings provide strong evidence that the use of computers as a thinking aid
and an intellectual tool enrich learners’ mathematical explorations, facilitate
students’ growth of mathematical understanding, and improve their problem
solving skills and concept development.
However, according to the article, computers and technology not widely
used in mathematical classrooms.
The article states that
when technology is used correctly teachers as able to construct explicit
knowledge, develop understanding, and composition for new concepts. Mathematics instruction currently advocated
focuses on developing students’ mathematical thinking and nurturing their
conceptual understanding of mathematical ideas and interrelationships. This article states that mathematical
instruction can be enhance and deep-in by the proper use of technology.
I choose this article
because it researched how and why teachers use technology in their
classroom. This article supports the
fact that most mathematics teachers are either not using technology or not
correctly using technology in their classrooms.
As I begin to develop my Action Research Project, I need to learn how to
correctly infuse technology into my classroom and help other math instructors
to do the same.
Martindale, Trey &
Wiley, David. (2004). An Introduction to Teaching with Weblogs. <http://teachable.org/papers/2004_techtrends_bloglinks.html>
This article provides a brief
history and explanation of weblogs. The
authors describe weblogs as they have used them to facilitate learning, share
information, interact as part of a learning community, and build an open base
of knowledge. The authors write about
the uses of weblogs in teaching courses and other enterprises.
Weblogs are described as
‘holdings’ of knowledge. They can
significantly reduce the technical barriers to effective Web publishing. A weblog can be easily and widely distributed
via a subscription model. Educational
blogs are a unique and convenient way to write about ones work and also direct
others to interesting research, resources and viewpoints in complex
concepts.
The authors also found that
webogs are a key tool to be used in improving the quality of student work. Students can use blogs to post their ideas,
view new resources, and comment on other ideas.
For the authors’ students blogs offered a clear advantage over discussion
forums, because the blogs had greater sense of permanence. Students appreciated being able to write,
without the extra step of needing to notify professors that writing assignments
had been completed, according to the article.
One the authors found that by recommending students to read other’s
blog, students’ weekly writings became lengthier and much more thoughtful.
This article helps me as I
develop towards my Action Research Project because it explores and explains a
solution that I could use, weblogs.
According to this article, weblogs can be used to create online learning
communities. These communities can be
easily accessed by my students and can aid them in developing their calculus
understanding.
Owston, Ronald D. (1997).
The World Web: A Technology to
Enhance Teaching and Learning? Educational Researcher, Vol. 26. No 2.
March. P 27-33.
This article discusses the
impact of the World Wide Web on educational systems. The author explores three questions that
educators must consider when using the web:
does it make learning more accessible, does it promote improved
learning, and does it increase the cost of education. This article answers each of the big
questions with examples from all areas of education: k-12, home schooling, and college level
students.
This article is relevant to
my research because it asks some very important questions that I need to be
aware of as I create my online learning community. Will my students all have easy access to my
community? How will my community promote
better understanding and support for students?
What will be the cost (time) for developing and managing the
community? Will the increase in
knowledge offset the time cost to developing the community?
Taylor, Janet. (2002). The
Evolution of Online Learning in Bridging Mathematics at a Distance. In Statham, M. (Ed.) Crossing the Bridge. (p
67-74) Proceedings of the 10th Australasian Bridging Mathematics
Network,
This article was written to
explore the methods that the University of Southern Queensland (USQ) uses to
help support their mathematics students.
USQ is faced with two challenges: student diversity and new
technologies. USQ has developed many
methods to help assist with the continuing struggle to mange student diversity
and the pressures and challenges imposed by the introduction of the new
technologies in teaching and learning.
The article explores the
instances used by USQ within the bridging mathematics community such programs
are designed within a constructivist philosophy of learning aiming to shift
learners from passive to active roles and from de-contextualised tasks to
authentic experiences. The university
provides students with the following online materials to help bridge the
gap: a set of review materials, a
mechanism to assess their mathematical readiness, a clear pathway to receive
advice, personal support, and structures to work with fellow students in group
situations.
USQ was very concerned with
providing their distance learners the opportunities to interact with other
students. The article stressed the
process of intellectually interacting in the content that results in changes in
the learner’s understanding, perspective or the cognitive structures of the
learner’s mind. USQ states that the
collaborative component is achieved only in the asynchronous online discussion
groups in which groups of students are allocated to a tutor whose role is to
facilitate discussion and answer mathematical questions as needed.
I chose to include this
article in my research because it provided me with real examples that have been
used to enhance distance support. It
also supported my idea that collaboration within subject area is important to
the growth and development of new ideas.
This article, however, did not provide me with any results or student
opinions as to what type of technology was the largest support. Data in that form could help me, to focus my
project into a certain tool.
Williams, Jeremy &
Jacobs, Joanne. (2004). Exploring the use of blogs as learning spaces
in the higher education secor. Australasian Journal of Educational
Technology. Vol. 20. p 232-247.
This article explored the
use of blogs as learning communities for students in higher level educational
settings. It defined blogs as clusters
having formed which link learners together with common interests. The authors claim that blogs are easy to use
as a communication tool with others.
Blogs can post new ideas, individual responses, and contain hyperlinks
which lead to more information. The
paper compares blogs to wiki software and concludes that blogs boast a level of
participation not experienced by wiki and a great sense of community.
The researchers examined
data from a
One mistake they, possibly,
found was the requirements of contributions.
They found that some students grew intellectually by simply reading other
student comments and felt that they viewed the reading as participation to the
group. The results found that some
students clearly submitted solely for the sake of getting the marks and this
detracted from the overall quality of the experience for some students.
The article concluded by
stating that their results show that students are broadly in favor of the
continued use of blogs as an effective aid to teaching and learning. The authors found blogs to be a truly
transformational technology in that they provide students with a high level of
autonomy while simultaneously providing opportunity for great interaction with
peers.
I chose to use this article
because it provided me with an overview of how blogs functions with
applications and examinations of actual blogs.
It was great to read about what other students thought about the use of
blogs to enhance understanding. I found
the conclusions that the authors found about how students view their
participation within a blog very helpful.
Their results have shown me that students (higher level) may not need
requirements placed on the quantity of the interactions. One assumption that needs to be considered
when using a weblog is the level of student that will be involved. I think that one reason why the research in
this article found that requirements may not be needed is because the students
were all high achieving and motivated.
Requirements, as to number of interactions, may play a larger role when
dealing with lower level, less motivated students.