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TitleTeaching Mathematics Online: Emergent Technologies and Methodologies
Author
TagsMathematics
LanguageEnglish
File Size14.4 MB
Total Pages415
Table of Contents
                            Title Page
Copyright Page
Editorial Advisory Board
Table of Contents
Forward
Preface
Acknowledgement
Section 1
	A Model for Asynchronous Discussions in a Mathematics Content Course
	A Blended Learning Approach in Mathematics
	Screencasting for Mathematics Online Learning
	Mathematics Education
	Best Practices for Hybrid Mathematics Courses
	Implementation of Learning Outcomes in Mathematics for Non-Mathematics Major by Using E-Learning
Section 2
	Online Communities of Practice as Vehicles for Teacher Professional Development
	Mathematics Bridging Education Using an Online, Adaptive E-Tutorial
	Teaching Mathematics Teachers Online
	Developing Teachers’ Mathematical Knowledge for Teaching through Online Collaboration
	Self-Regulated Learning and Self Assessment in Online Mathematics Bridging Courses
	Long-Term Experiences in Mathematics E-Learning in Europe and the USA
Section 3
	My Equations Are the Same as Yours!
	Interactive Web-Based Tools for Learning Mathematics
	NAUK.si
	Software Tools Used in Math Refresher Courses at the University of Alcalá, Spain
	Formula Editors
and Handwriting in
Mathematical E-Learning
	The Role of Technology in Mathematics Support
About the Contributors
Index
                        
Document Text Contents
Page 2

Angel A. Juan
Open University of Catalonia, Spain

Maria A. Huertas
Open University of Catalonia, Spain

Sven Trenholm
Loughborough University, UK

Cristina Steegmann
Open University of Catalonia, Spain

Teaching Mathematics
Online:
Emergent Technologies and
Methodologies

Page 207

190

Teaching Mathematics Teachers Online

Based Ranger), handheld/mobile technologies
(e.g., iPod, laptop, cell phone), and, increasingly
popular at the elementary level, interactive white-
boards (e.g., SmartNotebook).

INSTRUCTIONAL STRATEGIES FOR
EFFECTIVE ONLINE MATH
LEARNING

Having taught many online mathematics courses
within three different online Content Manage-
ment Systems (WebCT, Blackboard, ICZ) at two
Canadian universities during the past decade,
I have attempted to develop several strategies
that I believe, based on candidate feedback and
my own repeated observations and reflections
as facilitator, enhance the overall professional
learning experience for mathematics educators
enrolled in such teacher development courses. In
this chapter, I will highlight five such strategies
which have been implemented with hundreds of
online participants and which may offer some
insight into effective instructional practice.

Building Community
with Class Profiles

Like in any regular classroom, the first few
instructions given and interactions experienced
within the online forum are of extreme impor-
tance in terms of setting the tone or “creating the
ambience” for learning (Kimball, 1995, p. 55).

Adult learners enrolled in my Honours Special-
ist Mathematics courses are first asked to “sign
in” online within the “Aftermath Café” folder,
sharing various details about their professional
experiences and personal interests. After several
days, I have found it very useful, for both myself
and the candidates, for me to take the time to
collate this data in two forms: a simple table or
chart (see Table 1) with columns highlighting
their location, school, courses taught, years teach-
ing, and other miscellaneous information; and a
geographical map upon which each individual is
situated according to location and name. These
files are shared with candidates online, and I ask
them to provide me with feedback regarding any
possible errors or omissions. As the second and
often third drafts are posted, I am already model-
ing positive collaboration, personal interest, and
direct involvement within the course (Childers &
Berner, 2000; Slagter & Bishop, 2009).

The Class Profile chart provides the instructor
with instant access to important facts which often
become helpful throughout the course in terms of
mentally “locating” an individual, asking good
questions, and mindfully drawing upon candidate
expertise as one extends or redirects online inter-
action. The map (see Figure 2) serves to actually
situate learners within a visual context, allowing
them to obtain a general “feel” for what the course
looks like in terms of geographical representation,
and rendering a sense of “place” in an otherwise
distant or disconnected context. One obvious
benefit of online learning is that it allows the

Table 1. Class Profile chart of professional and personal information

AQ Candidate Location School Courses Taught
Years

Teaching
Interests/Other Information

Toronto,
Ontario

AASS Mathematics/Business 2a
Worked in Business; MBA; likes

new technologies

Montreal,
Quebec

BBSS Mathematics/Computers 18a
Physics/Science background; enjoys

cycling and climbing

Ottawa,
Canada

CCSS Mathematics/Visual Arts 7a
Black belt in karate; loves to sketch,

paint, and integrate

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191

Teaching Mathematics Teachers Online

learner to not only participate at her/his leisure,
but also permits she/he from studying at great
distances or while on the move. I’ve had candidates
take my mathematics education courses while
teaching in China, working in western Canada,
and touring Europe with a backpack and laptop.

Because the instructor and course participants
are often denied the visual element (i.e., as in
onsite settings or video-conferencing situations)
in much of distance education, this chart/map
Class Profile is very much a part of building com-
munity and constructing individual “portraits” of
each learner. Mounted near my monitor for the
duration of the course, the Class Profile provides
for quick identification regarding who is who, and
who is where.

Engaging Minds with Rich
Mathematical Problems or Tasks

The importance of both teachers’ mathematics
content knowledge (i.e., the curriculum expecta-
tions) and Mathematics Knowledge for Teaching
(Ball, 2000)(D. L. Ball, 2000) (i.e., deeper under-
standing of mathematical connections, and, how
children learn, err, and represent/communicate
their mathematical thinking) cannot be under-
stated. Within the online learning environment,
it is often difficult to engage in the types of rich
tasks/problems and rich assessment activities that
speak to these required skills and competencies,
insofar as face-to-face engagement is arguably

Figure 2. Class Profile map of candidate names and locations

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397

Index

Online education 44, 56, 86, 118, 144-145, 164,
245, 248, 256-257, 301, 353

Online Graphing Calculator 284, 303
online learning 20, 23, 25, 41-44, 46, 55, 93, 117,

161, 163-164, 166, 187-195, 197-199, 202-203,
213-214, 229, 236, 241, 257, 285, 300, 302-
303, 306, 352, 360, 369, 377, 381-382

Online Teaching 18, 26, 93, 165, 187, 193, 328,
353, 367, 369, 382

OpenCourseWare (OCW) 248-250, 252
Open University of Catalonia (UOC) 41, 57, 86,

139, 162, 198, 235, 238-239, 242-243, 256, 364
Organisation for Economic Co-operation and Devel-

opment (OECD) 137, 240, 257, 324, 351, 365,
369, 382

P-course 219, 228-232
pedagogy 62, 75, 117, 121, 126, 136, 143, 161-162,

188, 193, 197, 204, 246, 272, 325, 351, 363,
371, 380

phenomenographic research 3
Phenomenography 3, 19-21
physical manipulatives 300
pilot program 5
PISA mathematics tests 310
Plotting & Graphics 344
podcasting 57, 367, 374, 376-377, 380
podcasts 46, 53, 58, 324, 367, 369, 374, 376-377,

379-381
polyline 321
polynomials 221, 264-269, 273, 328, 344
Portable Document Format (PDF) 40-41, 47-48,

56-58, 86-88, 94-95, 117-118, 138, 161-162,
164-165, 184-185, 194, 223, 225-227, 235-236,
251, 257, 301, 321, 323-325, 353, 357, 359,
361, 364, 375, 382

Preservice Teacher 21, 214, 274, 301
problem solving 9, 19, 24, 63, 71-72, 79, 87-88, 91,

121, 124-125, 127-128, 130-132, 136, 139-140,
192, 203-205, 207, 242, 244, 260, 272, 305,
329

professional development 2, 21, 55, 122, 137, 142-
147, 151, 153, 157-163, 166, 187-188, 196-
199, 213

propensity score 168, 176, 179-184, 186
Purplemath 277, 304

quality assessment 122, 138

Quantcast 276-278, 303
quasi-experiment 169

rational form 268
reflective portfolio 133
reform-oriented mathematics 187-188, 193, 199
regression discontinuity 169, 184
remedial education 168, 178, 183-184, 186
Research in Higher Mathematics Education 237
Resuable Learning Objects (RLOs) 371
retention in mathematics 120, 127
Riemann sums–function integration 283-284, 302
rubric 15-16, 99, 112-115

SAGE 19-20, 131, 193, 327, 329, 345-348, 364
SCORM 226-227, 316, 320
SCORM-environment 225, 227
Screen Capture 44, 48, 59, 118, 195
screencasting 43-44, 48-49, 51-52, 54-56, 109, 116,

118, 367, 374, 377, 379
screencasts 43-46, 48-57, 59, 94, 97, 109, 111, 118,

367, 374, 377-380, 382
Screen Dump 118
Screenshot 48-49, 111, 113, 118, 222, 224, 245,

249-250
Secondary-Tertiary Transition 235, 237
selection effects 168, 177-178, 181, 183, 186
Self-Assessment 82, 84, 133, 162, 223, 235, 237,

242, 272
Self-Diagnostic Tests 223, 237
self learning 23-25, 36
Self Learning Method (SLM) 23, 25-27, 35-36,

38-40
self-monitoring 135
Self-Regulated Learning 216-218, 220, 228, 231-

232, 234, 236-237
self-selection 85, 169, 175, 186
semiminor axes 280
short pdf script 223, 226
sliders 281, 292, 340-342
Slovenian Education Network (SIO) 318, 321
smartphones 345
snippet 59
social bookmarking 132, 136, 194-195, 197, 199
social software 119, 121, 125, 131-132, 136, 149,

153
Socratic Method 10
spatial reasoning 5

Page 415

398

Index

State University of New York (SUNY) 197, 239,
246-247

Static Web-Based Resources 306
statistics education 142-143, 146-147, 149, 152-

153, 161, 165-166, 382
stopwatch 321
strategy for e-learning 126
student-cantered approach 137
Student Engagement 367-368, 379
student workload (ECTS) 126, 353
subject attitudes 176
Sympodium 370, 374-376
system for teaching and assessment with a computer

algebra kernel (STACK) 222-223, 260, 262-
263, 268-273

System of Equations 259-262, 264-266, 268-270,
273

systems of linear equations 265-266

tablet technology 45, 56
talking textbooks 309
taught knowledge 63
taxonomy 41, 87, 123, 125, 127-129, 137-138, 246,

256, 305, 383
technology enhanced learning 43, 58, 119, 135, 163
Tertiary Education 58, 235, 240-241, 257, 351, 365,

382
TeX code 361, 366
TeX filter 360-361, 366
The Math Forum 144, 163, 202, 213, 277, 279
The National Library of Virtual Manipulatives

(NLVM) 277, 287-288, 290, 292, 294, 304-
305

Theoretical Foundation 3
The Universidade Aberta (UAb) 244-246
The Wire Problem 281-282, 304
threads 1-3, 5-6, 8-12, 14-17, 51, 77, 99, 143, 154-

155, 159, 161
touchscreen 367, 374, 376
transformational geometry 5

trigonometric functions 221
Two Points Determine a Line 281-282, 304
typical-mistakes 222, 225, 228

univariate polynomials 264-267, 269
University of Alcala (UAH) 328
upper sums 340

Variation Theory 1-4, 7-9, 21
vertex angles 10, 12
video-based demonstration 111
Virtual learning 128, 132, 139, 164, 239, 244, 255,

319-320, 369
Virtual Learning Environment (VLE) 128, 132,

139, 239, 241, 244, 246-248, 253-255, 319-
320, 369-370

virtual manipulatives 193, 277, 287, 300, 304-305
virtual technologies 15
Virtuelles Eingangstutorium Mathematik (VEMA)

217-218, 220, 223, 228, 233-234
visualization 64, 222, 227, 274, 276, 281, 283, 300
Voice-Thread 118

walking encyclopedias 309
Web 2.0 61, 65, 100, 118, 165, 202
Web-based education 214
Web-Based Resources 196, 274-277, 300-301, 306
Webcam 104-105, 110, 118
Wiki 61, 65, 74-76, 78-80, 94, 101, 103, 105-106,

116, 118, 121, 131-132, 136, 153, 162, 164,
305, 320, 325, 332-333

WIRIS 244, 327, 329, 333-338, 343, 347-348, 360
WIRIS CAS 327, 334-338, 343, 347-348
Wolfram Alpha 285-286, 327, 329, 344-348
Word Exercise 273
Wordle 101, 104-107, 116
word problems 260, 273, 281

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