**THE UNIVERSITY OF TEXAS AT EL PASO
COLLEGE OF SCIENCE**

DEPARTMENT OF MATHEMATICAL SCIENCES

*¡BIENVENIDOS
(WELCOME)!*

*note*:
From the top of **http://www.math.utep.edu/Faculty/lesser/schedule.html**,
you can access this syllabus if you misplace yours, want to __explore its
links__, or see any updates to it. Syllabus
is subject to modification by instructor to meet course needs, especially if
there are disruptions such as an H1N1 epidemic or
unexpected changes in class size, resources, student backgrounds, etc.

**Course Number**:
MATH 5360-001 (CRN#26033)** **

**Course Title**: Introduction to Research in Mathematics
Education

**Credit Hours**:
3

**Term**:** **Spring 2011

**Prerequisite**: Departmental
Approval

**Course Fee**: none

**Course Meetings & Location**: Bell 130A MW 5-6:20pm, except March 14 &
16

The
instructor will announce which meetings may be held in a lab or library area
for hands-on explorations of research tools.
In the event of a major disruption (e.g., H1N1 epidemic), be prepared to
maintain course progress via alternative means (e.g., phone, Elluminate, Internet, a Blackboard course shell, etc.).
Also, check your email (especially your UTEP address) regularly. * *

**Instructor**: **Dr.
Larry Lesser** (rhymes with “professor”, spelled like “<”). I’ve been a
UTEP Assoc. Prof. since 2004 and began teaching university classes in 1988. I
am Editor of *Teaching for Excellence and
Equity in Mathematics* and I’ve served on other national journal editorial
and research advisory boards. I have
published in selective research journals such as *Statistics Education Research Journal* and more background at **www.math.utep.edu/Faculty/lesser/**.

**Office Location**: Bell Hall 213

**Contact Info**: Phone: (915) 747-6845

Email **Lesser**** (at) utep.edu**
(include “5 pm class” in the subject line)

Homepage: **http://www.math.utep.edu/Faculty/lesser/**

Fax: (915) 747-6502 (note: this is a math department fax, so be sure to

have my name clearly on it; be aware that staff are not available to relay faxes to me outside the math dept’s hours of M-F 8-12, 1-5

Emergency Contact: (915) 747-5761 (during math dept office hours)

**Office hours**: initial office hours are MW 12:45-1:20, M
6:30-7, and by appointment;

changes and additions will be announced or posted later; students are also welcome to try stopping by anytime for short questions; for longer questions, students should email me several possible appointment times that would work and I will reply with which option works in my schedule

**Textbook(s),
Materials**:

ú **Required textbook: **Hendricks, Cher C. (2008). *Improving Schools through Action Research: A
Comprehensive Guide for Educators*
(2^{nd} ed.). Allyn
& Bacon.

Because no single book completely
covers all of the goals of the course, we will supplement this book with
handouts, individual articles, online resources and demonstrations, taking into
account class backgrounds, interests, and time available. Some materials and announcements may be sent
via email or posted on Blackboard.** **Other resources will be accessible on the
Internet (e.g., certain journal articles and websites like **http://www.math.utep.edu/Faculty/lesser/ResearchResources.html**).

or UTEP library reserve -- either hardcopy reserve at the Circulation
Desk or electronic reserve via UTEP library homepage (Services for studentsàcourse reserves).

**Read/do each assignment before the class meeting we discuss it. **

**Course Objectives (Learning
Outcomes)**: Students will….

- Learn how to appropriately formulate a research question of
interest in mathematics education (which in this syllabus is assumed to
include statistics education)
- Increase their ability to navigate and synthesize the research
literature in mathematics education
- Increase their ability to critique a mathematics education
research paper and make connections between theory and practice
- Gain further insight into methodology and choosing methodology to
support the research question
- Understand pitfalls and ethical principles of research and how to
fulfill compliance requirements with your school district and the UTEP
Institutional Review Board
- Write a mathematics education research paper that uses APA style, includes a solid review of the literature for the research question of interest, and describes methodology in appropriate detail
- Learn how to contribute to and benefit from being part of a community of (emerging) scholars
- Write a research proposal (to satisfy the standards of an IRB, a grant, an article, a professional presentation, etc.) to collect data to investigate a research question of interest in mathematics education (so that you would be prepared to conduct a study that culminates in a Math 5396 paper with these sections: introduction, literature review, design/methodology, results, conclusions, bibliography).
- Learn how to contribute to and benefit from being part of an inquiry community, including peer debriefing and feedback on oral and written communication

**Course Activities/Assignments**: Students will participate in in-class activities,
read assigned articles and chapters, facilitate/participate in discussions,
take exam/quizzes, write reflections, do homework exercises, and submit a
written research paper (and give a short oral presentation of it). The instructor will make clear which
assignments or assessments may be done in pairs (or small groups) and which
must be done individually.

**Assessment of Course
Objectives**: Assessments include
written reflections, exam, quizzes, class discussions, written research paper,
oral presentation of research paper.

**Course Schedule**: Census
Day: Feb. 2

Deadline to Drop with a “W”: April 1

Last Regular Class Meeting: May 4 (research paper is due)

Final Exam Week Meeting: as scheduled by UTEP registrar; if you have a

pre-approved reason not to be able
to present during this time, you need to arrange with me as soon as possible
how to meet your obligations *before*
the exam week meeting date

**Grading Policy**:** **after any rescaling needed for all
components to be on the 0-100 scale, the grade is determined by the usual
cutoffs of 90-80-70-60 based on these parts:

Quizzes, Short Reflection Papers, Homework Assignments, Discussion Facilitation: 30%

Written Research Paper and Proposal: 50% (details are found later in this syllabus)

Oral Presentation of Research Paper: 20% (details are found later in this syllabus)

Attendance: Subject to change if required by UTEP policy, your final course

average will have 2 – 3U – E points added to it, where U = number of unexcused absences and E = number of excused absences. This reflects how crucial participation is for a course with “beyond-the-book” discussion, but without penalizing someone with ≤ 2 (excused) absences.

**Makeup Policy**: Much of this course involves beyond-the-book group
activities, experiences or discussions that are virtually impossible to
recreate or “make up”. Successful
completion of this course is intended not only to imply you have demonstrated
sufficient knowledge acquisition, but also that you have been exposed to key
processes, modeling, and experiences. Therefore, if you are now in a situation
where you expect to have frequent absences, you might consider taking this
class another semester. In general (out
of fairness and logistics), **late work
will not be accepted**, and may be subject to a penalty in the rare
borderline cases that it is accepted at the instructor’s discretion. A makeup __exam__ is possible if: (1) it
is taken at the earliest opportunity, and (2) missing the exam was unavoidable
for a serious reason that is relayed to me (preferably by email) within 24
hours (or the earliest possible opportunity), followed up if necessary by
documentation like a doctor’s note.

**Attendance Policy**: Attendance
is __required__. The instructor may count late arrival, early departure, or
blatant nonparticipation as a half-absence or even a full absence, depending on
what is missed.

It’s
** your responsibility** to….

(1) Sign any attendance sheet each day you attend *before* I pack up my materials.

(2) Let me know by email (**Lesser (at) utep.edu**) or
voicemail (747-6845) or daytime math dept. fax (747-6502) in advance at the
earliest opportunity if you have a situation which may affect a test, major
assessment deadline, or multiple regular class meetings.

(3) Give me a written note or email by the 15^{th}
day of the semester [Feb. 7]

if you will have absence for religious holy days (which are excused, of course).

(4) Give me an email or written documentation as soon as possible if you anticipate the possibility of missing large parts of class due to exceptional circumstances such as military service/training, childbirth, or competing on official UTEP athletic teams.

(5) Have a classmate give you copies of notes, handouts and
announcements if you miss a class; write down *right now* three classmates’ contact information *right
here* for this purpose:

classmate
#1 name_____________________ phone_____________ email____________

classmate
#2 name_____________________ phone_____________ email____________

classmate
#3 name_____________________ phone_____________ email____________

As the UTEP *Catalog* says, “When in the judgment of
the instructor, a student has been absent to such a degree as to impair his or
her status relative to credit for the course, the instructor may drop the
student from the class with a grade of “W” before the course drop deadline [April
1] and with a grade of “F” after the course drop deadline.” In practical terms, this means a student
could be dropped for more than 4 absences (unless there has been a reason I
have approved). If you choose to withdraw, I ask you to submit the formal
paperwork and send me an email to let me know rather than just stop attending
class and assume you will be withdrawn automatically. On a positive note, __a strong record of
attendance will be taken into account if your final average is a point below a
letter grade cutoff__.

**Academic Integrity Policy**:** **It’s
UTEP’s policy (and mine) for all suspected violations to be referred to the
Dean of Students for investigation and disposition (See __Section 1.3.1__ of the __Handbook for Operating Procedures__;
**http://academics.utep.edu/Default.aspx?tabid=23785**)
Cheating, plagiarism and collusion in dishonest activities are serious acts
which erode the university’s purpose and integrity and cheapen the learning
experience for us all. Don’t resubmit work completed for other classes
without specific acknowledgment and permission from me. It is expected that work you submit
represents your own effort (or your own group’s effort, if it is a group
project), will not involve copying from or accessing unauthorized resources or
people (e.g., from a previous year’s class).
Cite references that you do consult, using **APA style**
(an older edition of the guide is on 2-hour reserve in the UTEP Library) with
complete citations even for websites and people you consult. __For Group Work__: Within a group, members are allowed to divide
up subsets of the project for which individuals will take the initial
responsibility for coordinating efforts, but it is assumed that by the time a
group turns in a writeup that all members have read,
discussed, contributed to, and understand what is being turned in. Group members may even discuss general ideas
and strategies with members of other groups, but NOT share parts of actual
written work. At a minimum, to be safe,
put away all written notes and writing materials and recording devices before
having any intergroup conversations. And
if you still see a “gray area,” play it safe and ask the instructor!

**Civility Statement**:
You are expected to follow basic standards of courtesy (e.g., **“Student Conduct”
and “Disruptive Acts Policy” in the UTEP Catalog**) and may be
dismissed from class for blatant or sustained disruptive behavior. Your
comments during classroom discussions need to focus constructively and
respectfully on the intellectual merit of a position,

**Disability Statement**:
If you have or believe you have a disability requiring accommodations, you may wish to self-identify by
contacting the Disabled Student Services Office (DSSO; 747-5148; East Union Building 106; **dss@utep.edu**; **www.utep.edu/dsso/**)
to show documentation or register for testing and services. DSSO
will ask you to discuss needed accommodations with me within the first 2 weeks
of the semester or as soon as disability is known, and
at least 5 working days before an exam.
You are responsible to make sure I receive any DSSO instructions and
accommodation letters. DSSO
provides note taking, sign language, interpreter, reader and/or scribe
services, priority registration, adaptive technology, diagnostic testing for
learning disabilities, assistance with learning strategies/tutoring,
alternative testing location and format, and advocacy.

**Military Statement**:
Give me an email or written documentation as soon as possible if you anticipate
the possibility of missing large parts of class due to military service.

ADDITIONAL INFORMATION

**“Part One/Part Two”
Distinction: **As we discussed, there
is a “Part One” and “Part Two” version of this course, Math 5360a and Math
5360b, respectively.** **Basically, Math
5360a introduces you to the mathematics education literature and how to
navigate it, choose a research topic, and write the introduction and literature
review sections of a research paper, with just a general outline of a
methodology approach. Math 5360b
strengthens these sections, especially methodology, and involves an
IRB-approved data collection so that the final paper includes a full
methodology chapter and the beginnings of a results section (which may have to
be finished and fully discussed as a Math 5396 course).** This semester’s course is being
delivered (as originally scheduled, and consistent with what most students
need) as Math 5360b. If, for example, a
student who has not had 5360a chooses to enroll in this class instead of
waiting for the fall 2011 Math 5360a course, he/she will need to take most of
the responsibility for learning the 5360a material more quickly or
independently. Depending on the
backgrounds of the final enrollment for this class, the instructor reserves the
right to restructure or tailor assignments, expectations and meeting times
accordingly to best serve student needs within programmatic and resource
constraints. **

**Professionalism
Statement**: Beyond the previously mentioned Civility Statement, students in
this course are required to exhibit professionalism that goes beyond avoiding
negative behaviors. This includes making
a good faith effort in preparation for and participation in individual and
collaborative class activities. A
classroom culture must be actively supported that understands that “wrong
answers” are usually correct answers to a different question or valuable
learning opportunities to address a common misconception. Finally, be open to
local opportunities for professional growth or service, and consider planning
to present your work (even if still “in progress”) at conferences. Local options include the UTEP student
research expo (April), the **SUN**
conference (March 10-11), and the COE **CIRCLE conference**
(June 10-11). You may even look for ways that the profession can support your
classroom research with a grant: **http://www.nctm.org/resources/content.aspx?id=198**.

**Confidentiality**:
UTEP policy requires that inquiries about confidential information such as
grades cannot be done over the phone, but must be from your miners.utep.edu
account and accompanied by your 800 number.
If you want your course grade during the few days before UTEP puts grades
online, you will have a chance in the last week of class to give me a “secret
code word” that I will post your course grade by at the bottom of **my homepage** if time
permits.

**Details on the Research
Paper**:

__Due date__: papers are due by our May 4 class
meeting. This deadline gives you several
days to focus only on the oral presentation and gives me time to read and
assess your paper in a timely manner (and hopefully in time to give you feedback
that can inform your oral presentation). Many research conferences work this
way -- you submit your paper well before you present it so that a proceedings
volume of everyone’s papers can be released in a timely manner.

__Teams__: in
recognition that most 5360b students took a 5360a course in which they were
allowed to work in pairs and may wish to continue building on this
collaborative work they have invested in, I will give students the choice to do
either a “solo” paper or a paper as a team of two (but not more than 2).

__Empirical Data__:
this paper cannot merely be a theoretical or philosophical piece – it
must include the collection of data, whether it is from an entire class or
perhaps some type of case study involving just a few purposively-selected
students. The participants in your study
may come from a student population that you teach or that someone else teaches,
but IRB approval must be in place BEFORE data collection can begin, and you
need to **submit IRB forms as soon as
possible **so that you will get approval in time to have a reasonable data
collection window.

(Goal: submit IRB forms as early in February as possible, hopefully get approval by early March, and then you have March and April for data collection). If you have another idea for research (e.g., where participants might be teachers instead of students), feel free to let me know.

__Oral presentation__:
Time constraints will be announced in advance and depend on how many
paper presentations there are and how much time is available. The presentation will occur on the final exam
week meeting day scheduled by UTEP (if someone has a conflict with attending
that date, they will need to do their presentation during one of our last
regular class meeting days). The presentation (including visual aids, spoken
content, and responses to questions) is assessed on clarity and appropriateness
for the audience. See **tips for oral
presentations**. This
presentation is an important experience for your career and professional
development. On the day of the
presentation, you will give me a printout of your PowerPoint slides (it’s okay to save trees by putting 4 or 6 slides per
page).

__Topic__: must be approved in advance by the instructor,
and generally should involve empirical research on a topic involving the
teaching and/or learning of math or statistics. General education topics such
as ‘technology’, ‘group work’ or ‘gender issues’ are acceptable only if
explored in the specific context of teaching and learning
mathematics/statistics. If you’re
unsure, ask me!

Typically, this would
involve a plan to analyze data you collect from your (or, perhaps someone
else’s) classroom, with all needed IRB materials (e.g., assent/consent forms, research
protocols and instruments, etc.) and approvals in place before data collection
begins. During this course, you will go
through the first few steps of the IRB process but not necessarily get to
collecting data (see SECTION THREE of **http://www.math.utep.edu/Faculty/lesser/ResearchResources.html**).

__Formatting__: This paper and all other written
assignments should be word processed with double-spacing and a standard
12-point font (e.g., Times New Roman), checked for spelling/grammar (you are
allowed to get feedback on writing mechanics from the UTEP Writing Center in Library 227, **http://academics.utep.edu/Default.aspx?tabid=47508**,
747-5112), and have any appropriate output/graphics electronically
pasted into the document. Sections
should be clearly marked, assembled in order, and stapled (not put into a
folder or sleeve) with a meaningfully-titled (i.e., not just “5360 research
paper”) identification coversheet on top. Use APA style (**http://www.math.utep.edu/Faculty/lesser/APA.html**)
for references, etc.

__Sections__: This paper will mirror the first three
chapters of a the “five-chapter format” of a thesis in a scaled-down manner
that is closer to what a journal article has (and I’m happy to help you later
submit your paper to an appropriate journal if you’re interested!). Be sure to check the appropriate parts of
Table 8.1 in your book. There is no specific minimum or maximum page limit for
this paper, but I expect that to address all the requirements, it will probably
end up being around 15-30 pages long, not counting appendices. Math 5360a (“part one”) focused mainly on the
introduction and literature review, but this course will expect you not only to
strengthen those sections, but also to go much deeper in the methodology
section so that your proposal will be fully fleshed out and ready to go. The paper must be broken down by the
following section headings that must appear in this order:

**Abstract**of 100-200 words that summarizes paper, including the purpose, type of research strategy, main results, and main implication

**Introduction**– this section is a “statement of the problem”, including the purpose and need for your study (think about what made you decide this was an important or interesting thing to explore for your own curiosity and for the benefit of the education community) and its guiding research questions and theoretical/conceptual framework/model/theory; include delimitations that you impose at the beginning to narrow the scope (these are different from ‘limitations’ -- conditions you would not have chosen but were beyond your control); define any complex terms; also include any prior pilot study work you did) [this kind of material goes into*chapter 1*of a thesis]

**Literature review**this is a detailed expansion of the relevant references from the introduction section, appropriately taking into account relevant literature within and beyond mathematics education (see literature search tools at**http://www.math.utep.edu/Faculty/lesser/ResearchResources.html**); be sure to point out positive and negative sides, gaps, etc., and be sure to not just give a chronology of results from other studies, but synthesize, organize and critique them [this kind of material goes into*chapter 2*of a thesis]

**Methodology –**the rationale for the design of the study needs to be given, hopefully in a way that naturally “follows” from the information in the preceding two sections (e.g., does the research design “support” the research question?); it is often nice to see a visual diagram that maps out the flow of the steps of the study; the procedures or protocol for carrying out the study (including any intervention or treatment) and collecting data needs to be given in at least enough detail to allow for replication; describe the population and sample (and how they were selected) in a way that provides the appropriate level of anonymity, but still gives the reader a useful idea of relevant characteristics; describe the data collection instruments used (e.g., written questionnaire, interview questions, tests, observation forms, etc.) and how they were chosen or constructed (the actual instruments can be included in the appendix), and how you have addressed issues such as reliability and validity (e.g., see Table 6.2 in your book); if you haven’t already, be sure all hypotheses have been stated in terms of variables with concrete operational definitions; describe the data analysis techniques and tools that are used; note any triangulation (of method, of subject, of researcher, of data source) used [this kind of material goes into*chapter 3*of a thesis]

**References**section with appropriate and complete APA referencing style (**http://www.math.utep.edu/Faculty/lesser/APA.html**), even for websites and people you consult. At least 3/4 of your references should consist of refereed journal articles and book chapters rather than webpages and ED documents that have not been peer reviewed. Most of the journals should have a research focus rather than being aimed only at practitioners or general audiences.

**Appendix**– Here is where you would put a copy of data collection instruments (e.g., surveys, list of interview questions) as well as any data or charts that would have broken up the flow to insert them in one of the main sections of the paper (but in those sections, you would be sure to tell the reader that they can find the additional material in the Appendix)

*The following 2
sections (Results and Discussion) of the paper would come between the
“Methodology” and “References” sections, but a thorough detailed job is not
necessary to meet the basic expectations of this course, due to the amount of
time you may have once data collection is complete. For this course, you can have a very brief
version of these two sections, and perhaps do a comprehensive complete job in a
later course (e.g., Math 5396).*

**Results –**this is reporting what the data actually say and should be organized by research questions; don’t just give us a very long sequence of narrative here – find ways to summarize analysis/output with tables/graphs/charts or move certain details to an appendix to maintain the flow for the readers [this is like*chapter 4*of a thesis]**Discussion**-- summarizes actual findings and interprets what the data mean and what they imply (i.e., practical implications for researchers and teachers), and gives conclusions that are specifically supported by your results and connect back to the literature; discuss possible impacts of limitations, threats to validity, etc., and offer suggestions for future research [this is like*chapter 5*of a thesis]

MANY PAPERS ASSIGNED FOR READING AND
DISCUSSION WILL COME FROM THIS LIST

Articles without direct URLs should be accessible via UTEP library, using one of these methods:

- Go
to the UTEP library home page (
**http://libraryweb.utep.edu**), click “Services”, then click “Course reserves”, then type in “Math 5360”, then click on “Readings” - Go to the UTEP library home page, and type the exact name of the journal’s title into the “search Encore” window at the top left of the page. This usually results in your being able to access the journal from one or more sources.

1.) Wentzel, K. R. (2005). Developing and
nurturing interesting and researchable ideas. In Clifton F. Conrad and Ronald
C. Serlin (Eds.), *Sage handbook for
research in education: Engaging ideas and enriching inquiry* (pp. 315-330). Thousand Oaks, CA: Sage.

2.) Garfield, J., & Ahlgren, A. (1988).
Difficulties in learning basic concepts in probability and statistics:
Implications for research. *Journal for Research
in Mathematics Education*, *19*(1), 44-63.

3.) Wills, D.(2004). Teaching
the unteachable: Helping students make sense of the
web. *College Teaching,52*(1), 2-5

4.) National Council of Teachers of Mathematics (2010). How can
teachers and schools use data effectively?
**http://www.nctm.org/news/content.aspx?id=27192**

5.) Mettetal, G. (2001). The
what, why, and how of classroom action research. *Journal of Scholarship of Teaching and Learning, 2 *(1), 6-13. **https://www.iupui.edu/~josotl/archive/vol_2/no_1/v2n1mettetal.pdf**

6.) Schoenfeld, A. H. (2000). Purposes and methods of research in mathematics education. *Notices of the American Mathematical Society, 47*(6), 641-649.
**http://www.ams.org/notices/200006/fea-schoenfeld.pdf**

7.) Tinto, P.P., Shelly, B.A., & Zarach,
N. J. (1994). Classroom research and classroom practice: Blurring the
boundaries. *Mathematics Teacher, 87*(8), 644-648.

8.) Nolen, A. L., and Vander Putten, J. (2007).
Action research in education: Addressing gaps in ethical principles and
practices. *Educational Researcher*, *36*(7),
401-407.

9.) Holcomb, J. (2002). The ethics of comparison: A statistician
wrestles with the orthodoxy of a control group, with response by Corrada, R., Garfield, J., and Persell,
C., in Pat Hutchings (Ed.), *Ethics of Inquiry: Issues in the Scholarship of
Teaching and Learning* (pp. 19-26). Menlo Park, CA: Carnegie Foundation for the Advancement of
Teaching.

10.) Green, J. L. (2010). Highs and lows: Exploring
university teaching assistants’ experiences. *Statistics Education
Research Journal, 9*(2), 108-122.

**http://www.nctm.org/news/content.aspx?id=27192**

11.) Shaughnessy, J. M. (2007). Research on
statistics learning and reasoning. In Frank K. Lester, Jr. (Ed.), *Second handbook of research on mathematics teaching and learning* (pp. 957-1009). Reston, VA: National Council
of Teachers of Mathematics.

12.) Shaughnessy, J. M. (1977). Misconceptions of probability: An experiment
with a small-group, activity-based, model building approach to introductory
probability at the college level. *Educational Studies in Mathematics*, *8*(3), 295-316.

13.) delMas, R. C.,
Garfield, J., & Chance, B. (1999). A model of classroom research in action:
Developing simulation activities to improve students’ statistical reasoning. *Journal of Statistics Education*, *7*(3), **http://www.amstat.org/publications/jse/secure/v7n3/delmas.cfm**

**http://www.springerlink.com/content/?Author=J.+Michael+Shaughnessy**

14.) Lesser, L. (1998). Countering indifference using counterintuitive examples. *Teaching Statistics*, *20*(1), 10-12.
**http://www.rsscse.org.uk/ts/gtb/lesser.pdf**

15.) Lesser, L., & Melgoza,
L. (2007). Simple
numbers: ANOVA example of facilitating student learning in statistics. *Teaching Statistics*, *29*(3), 102-105.

16.) Lesser, L. (1998). Technology-rich
standards-based statistics: Improving introductory statistics at the college
level. *Technological Horizons in Education Journal*,* 25*(7),
54-57. **http://thejournal.com/Articles/1998/02/01/TechnologyRich-StandardsBased-Statistics-Improving-Introductory-Statistics-at-the-College-Level.aspx**

17.) Garner, R. L. (2006). Humor in pedagogy: How ha-ha can lead to aha!, *College Teaching*, *54*(1), 177-180.

18.)
Lesser, L., & Winsor, M. (2009). English language learners in introductory
statistics: Lessons learned from an exploratory case study of two pre-service
teachers. *Statistics Education
Research Journal*, *8*(2), 5-32. **http://www.stat.auckland.ac.nz/~iase/serj/SERJ8(2)_Lesser_Winsor.pdf**

19.) Brase, G. L. (2008). Pictorial
representations in statistical reasoning. *Applied*
*Cognitive Psychology*, *23*(3), 369-381.

20.)
Lesser, L. (2001). Representations of
Reversal: An exploration of Simpson's paradox. In Albert A. Cuoco and Frances R. Curcio (Eds.), *The roles of representation in school mathematics* (pp. 129-145). Reston, VA: National Council of Teachers of
Mathematics. **http://www.statlit.org/pdf/2001LesserNCTM.pdf**

21.) Lesser, L., & Tchoshanov, M. (2006). Selecting representations. *Texas Mathematics Teacher*, *53*(2), 20-26. The issue is at **http://www.utdanacenter.org/tctm/downloads/TMT_Fall_06.pdf**.

22.)
Lesser, L., & Tchoshanov, M. (2005). The
effect of representation and representational sequence on students’
understanding. In G. M. Lloyd, M.R. Wilson, J.L.M.
Wilkins, & S.L. Behm (Eds.), *Proceedings of
the **27th annual meeting** of the **North American Chapter of the International
Group for the Psychology of Mathematics Education*. **http://www.math.utep.edu/Faculty/lesser/pmena05.pdf**

23.) Ozmantar, M. F., Akkoc, H., Bingolbali, E., Demir, S., & Ergene, B. (2010). Pre-service
mathematics teachers’ use of multiple representations in technology-rich
environments. *Eurasia Journal of Mathematics, Science and Technology Education*, *6*(1), 19-36. **http://www.ejmste.com/v6n1/EURASIA_v6n1_Ozmantar.pdf**

24.)
Tchoshanov, M., Lesser, L., & Salazar, J. (2008). Teacher knowledge and
student achievement: Revealing patterns. *Journal of
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