Gateway to Mathematics

Gateway to Mathematics

David A. Thomas

Professor of Mathematics Education

Department of Mathematics

University of Idaho

Moscow, ID 83844-1103

dthomas1@uidaho.edu

Zhongxiao Li

Graduate Research Assistant

Department of Mathematics

University of Idaho

Moscow, ID 83844-1103

li0418 @uidaho.edu

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 children’s 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 theUS Department of Education and theIdaho State Board of Education

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;

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.

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.

Community of Inquiry Model

Community of Inquiry Model (Garrison et al, 2000) http://cade.athabascau.ca/vol14.2/rourke_et_al.html

Representations•Algebraic Expressions•Geometric Models•Numerical Models

Reasoning•Examples•Counter Examples•Informal Arguments

Communication•Synchronous•Asynchronous•Small Group

Technologies•Scientific Notebook•Bernoulli•WebCT

Data Analysis•SNA (NetMiner II)•Statistics

Learning Model

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

Math 170 --- WebCT Home Page

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].

Math 170 --- Overview

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

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.

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: (8:40-9:00) 3 students from 2 schools

Group 2: (9:40-10:00) 3 students from 2 schools

Group 3: (11:40-12:00) 2 students from 2 schools

Group 4: (1:40-2:00) 3 students from 2 schools

Group 5: (3:00-3:20) 3 students from 2 schools

Math 170 --- Content

Spring 2006

Partial Table of Contents

• Links to lessons

• Links to videos

Math 170 --- Scientific Notebook

Traditional expository mathematics

MacKichan (2005). Scientific Notebook. Available on-line at http://www.mackichan.com/

Math 170 --- Scientific Notebook

Interactive practice [Answers and occasional hints]

Math 170 --- Videos

Video presentations of key concepts and procedures

Math 170 --- WorldWideWhiteboard

Synchronous mathematical demonstration & dialogue

www.link-systems.com

Math 170 --- Bernoulli Menu

www.link-systems.com

Algorithmically generated & scored practice & quizzes[Partial list of homework sets]

Math 170 --- Bernoulli Item

Math 170 --- Bernoulli Item

Math 170 --- Bernoulli Item

Math 170 --- Bernoulli Item

Math 170 --- Bernoulli Item

Exam #1

Exam #1: First WebCT Quiz Score vs. Examination Score

Exam #1

Exam #1: Average WebCT Quiz Score vs. Examination Score

Exam #4

Exam #4: First WebCT Quiz Score vs. Examination Score

Exam #4

Exam #4: Average WebCT Quiz Score vs. Examination Score

Overall Achievement

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

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.

Complex Networks

• Telephone networks• Computer networks• Military command &

control• Corporate

communications• Social networks• Biological networks

– Neurons– Animal behavior

• Learning networks

Network Matrix

Network Graphics

Learning Networks

• Students (Actors)– Leaders– Followers– Lurkers

• Emergent structures, roles & attributes– Cohesiveness– Cliques– Brokers– Status

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]

Professional Opportunities

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

Contact Information

Principal Investigator Dr. David Thomas208-885-6740dthomas1@uidaho.edu

Partnership Director Dr. Cynthia Thomas208-885-2046cthomas@uidaho.edu

Content Director Dr. Monte Boisen208-885-6742boisen@uidaho.edu

Research Assistant Zhongxio Li208-885-6719li0418 @uidaho.edu

Research Assistant Angela Windley208-885-6719will7385@uidaho.edu

Thank you for your attention and interest in the Gateway to Mathematics Project