Gateway to Mathematics

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Gateway to Mathematics
David A. Thomas Professor of Mathematics Education Department of Mathematics University of Idaho Moscow, ID 83844-1103 dthomas1_at_uidaho.edu Zhongxiao Li Graduate Research Assistant Department of Mathematics University of Idaho Moscow, ID 83844-1103 li0418 _at_uidaho.edu
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Purpose

• A shortage of well-qualified workers in many
  science, mathematics, and engineering/ technology
  (SMET) fields limits Idaho corporate
  competitiveness, just as a shortage of
  well-qualified K-12 mathematics and science
  teachers limits our childrens educational
  opportunities. Gateway to Mathematics and the
  University of Idaho are creating a statewide
  partnership of Idaho educational stakeholders,
  including state agencies, corporations,
  communities, and K-12 schools, focused on making
  high quality university level courses and
  professional development activities and services
  available statewide.

Funded by grants from the US Department of
Education and the Idaho State Board of Education
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Guiding Principles

• Academically --- Courses should reflect the
  values and standards of mathematics and
  mathematics education faculty throughout the
  Idaho university system and related educational,
  governmental, and industrial associations
• Pedagogically --- Courses should implement best
  practices identified by mathematics education
  researchers, rather than imitate traditional,
  face-to-face instruction

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Goals

• Practically --- Courses should be easily
  transferable between university campuses and
  readily recognized by accrediting agencies (e.g.,
  the Idaho Department of Education) and
• Theoretically --- Courses should be
  systematically studied by researchers focused on
  the evaluation and improvement of web-based
  teaching and learning.

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Partnership

• Partners
• University of Idaho
• K-12 Schools Corporations
• Idaho Department of Education
• Collaboration Principles
• Courses are only available via K-12 and corporate
  partners and
• Policies procedures are developed
  collaboratively by project partners.

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Community of Inquiry Model
Community of Inquiry Model (Garrison et al, 2000)
http//cade.athabascau.ca/vol14.2/rourke_et_al.ht
ml
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Learning Model
Representations Algebraic Expressions Geometric Models Numerical Models Reasoning Examples Counter Examples Informal Arguments

• Data Analysis
• SNA (NetMiner II)
• Statistics

Communication Synchronous Asynchronous Small Group Technologies Scientific Notebook Bernoulli WebCT
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Future Courses

• Fall 2006
• Math 170 Calculus and Analytic Geometry I
• Spring 2007
• Math 170 175 Calculus and Analytic Geometry I
  II
• Geometry Measurement for Middle School Teachers
  
• Number Operations for Middle School Teachers
• Fall 2007
• Repeat Spring 2007 Courses
• Probability Statistics for Middle School
  Teachers
• Spring 2008
• Repeat Fall 2007 Courses
• Algebra for Middle School Teachers

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Math 170 --- WebCT Home Page
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Math 170 --- Assumptions

• Students are mathematically ready
  SAT/ACT/Compass.
• Students are technologically ready Technology
  Readiness Test.
• Students are independent learners, patient,
  confident, and collegial Recommendation of local
  principal.
• Students have a daily 50 minute opening in
  their schedule for study and synchronous chats
  Coordinated by local Administrative Liaison.
• Partner high schools coordinate recruitment,
  registration, and other administrative aspects of
  the course, including daily attendance and
  examination proctoring. Coordinated by local
  Administrative Liaison.
• Partner high schools will provide and maintain a
  networked student workstation Coordinated by
  local Technical Liaison.

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Math 170 --- Overview

• Calculus Analytic Geometry I Traditional topics
  delivered using non-traditional pedagogies
  technologies.

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Collaborative Groups

• Research on web-based university courses has
  shown that individual student satisfaction and
  achievement are strongly related to the sense of
  community and cohesiveness engendered by the
  course. In Gateway to Mathematics courses,
  students participate in two types of communities
  Whole class and small collaborative groups.

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Beta-test Spring 2006

• Enrollment
• 14 students from 4 Idaho high schools
• 12 seniors and 2 juniors
• 10 males and 4 females

Small Group Chat Times 2 chats/week
Group 1 (840-900) 3 students from 2 schools
Group 2 (940-1000) 3 students from 2 schools
Group 3 (1140-1200) 2 students from 2 schools
Group 4 (140-200) 3 students from 2 schools
Group 5 (300-320) 3 students from 2 schools
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Math 170 --- Content

• Spring 2006
• Partial Table of Contents
• Links to lessons
• Links to videos

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Math 170 --- Scientific Notebook
Traditional expository mathematics
MacKichan (2005). Scientific Notebook.
Available on-line at http//www.mackichan.com/
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Math 170 --- Scientific Notebook
Interactive practice Answers and occasional
hints
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Math 170 --- Videos
Video presentations of key concepts and procedures
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Math 170 --- WorldWideWhiteboard
Synchronous mathematical demonstration dialogue
www.link-systems.com
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Math 170 --- Bernoulli Menu
Algorithmically generated scored practice
quizzes Partial list of homework sets
www.link-systems.com
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Math 170 --- Bernoulli Item
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Math 170 --- Bernoulli Item
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Math 170 --- Bernoulli Item
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Math 170 --- Bernoulli Item
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Math 170 --- Bernoulli Item
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Exam 1
Exam 1 First WebCT Quiz Score vs. Examination
Score
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Exam 1
Exam 1 Average WebCT Quiz Score vs. Examination
Score
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Exam 4
Exam 4 First WebCT Quiz Score vs. Examination
Score
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Exam 4
Exam 4 Average WebCT Quiz Score vs. Examination
Score
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Overall Achievement
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Sample Student Survey Items
Q Are you satisfied with the course? A Yes,
14-0. Q  Would you recommend this course to a
friend? A  Yes, provided they are self-motivated
and responsible. Q What have you learned so far
that has interested you the most? A Application
of calculus in real life, science, etc. Q What
is the most beneficial/enjoyable aspect of the
course? A Bernoulli, WorldWideWhiteboard,
getting a start on college mathematics. Q  On
average, how many hours do you speed each week on
this course? A  6 - 8 hours
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Instructor Observations

• Students need about a month to become proficient
  in the use of course technologies.
• Students adapt somewhat reluctantly to printed
  readings and video lectures. They would prefer
  to receive daily direct instruction in
  WorldWideWhiteboard.
• Differences in local school calendars, field
  trips, and so on require flexibility on the part
  of both project partners and students.

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Complex Networks

• Telephone networks
• Computer networks
• Military command control
• Corporate communications
• Social networks
• Biological networks
• Neurons
• Animal behavior
• Learning networks

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Network Matrix
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Network Graphics
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Learning Networks

• Students (Actors)
• Leaders
• Followers
• Lurkers
• Emergent structures, roles attributes
• Cohesiveness
• Cliques
• Brokers
• Status

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Research Questions

• How is cohesiveness associated with achievement?
• How does cohesiveness originate and evolve?
• Is there an optimal level of cohesiveness?
• Is cohesiveness associated with student
  satisfaction?
• What other factors are associated with individual
  achievement and student satisfaction?
• Readiness mathematics, technology, learning
  style
• Synchronous asynchronous dialogues
• Automated practice quizzes Bernoulli

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Professional Opportunities

• The Gateway to Mathematics Project invites
  interested mathematics faculty and educational
  researchers to contact project leadership to
  discuss RD opportunities related to the design,
  development, delivery, and investigation of
  web-based mathematics, statistics, and
  mathematics education courses.

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Contact Information
Principal Investigator Dr. David Thomas 208-885-6740 dthomas1_at_uidaho.edu
Partnership Director Dr. Cynthia Thomas 208-885-2046 cthomas_at_uidaho.edu
Content Director Dr. Monte Boisen 208-885-6742 boisen_at_uidaho.edu
Research Assistant Zhongxio Li 208-885-6719 li0418 _at_uidaho.edu
Research Assistant Angela Windley 208-885-6719 will7385_at_uidaho.edu
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• Thank you for your attention and interest in the
  Gateway to Mathematics Project