Abstracts of Selected Publications
*
Lesser, L. & Winsor, M. (in press; expected in the Nov. 2009 issue), English
Language Learners in Introductory Statistics: Lessons Learned from an
Exploratory Case Study of Two Pre-Service Teachers. Statistics
Education Research Journal, 8(2). Abstract: Despite
the rapidly growing population of English language learners in US colleges and
schools, very little research has focused on understanding the challenges of English
language learners specifically in statistics education. At a university near
the United States-México border, the authors conducted an exploratory
qualitative case study of issues of language in learning statistics for
pre-service teachers whose first (and stronger) language is Spanish. The two
strongest findings that emerged from cross-case analysis of the interviews were
the importance of the role of context (the setting in which information is
communicated) and the confusion between registers (subsets of language). This paper overviews and synthesizes
relevant literature and offers resources and recommendations for teaching and
future research.
* Lesser, L. M. & Glickman, M. E. (in press; expected
in Dec. 2009 issue). Using Magic in the Teaching of
Probability and Statistics. Model Assisted Statistics and
Applications, 4(4), pp. _____ This paper explores
the role magic tricks can play in the teaching of probability and statistics,
especially for lectures in college courses.
Demonstrations are described that illustrate a variety of probabilistic
and statistical topics, including basic probability and combinatorics,
probability and sampling distributions, hypothesis testing, and advanced topics
such as Markov chains and Bayes' Theorem. In addition to magic tricks providing visual
demonstrations to supplement traditional blackboard-based lectures and the
opportunity to engage students in class-participatory activities, possible
benefits include a focus on conceptual understanding, development of critical
thinking, and an opportunity to reflect upon the role of assumptions and
estimates of probabilities.
* Lesser, L. (accepted; expected around late 2010). Simple Datasets for Distinct Basic Summary Statistics.
Teaching Statistics
Datasets with simple numbers that lead to distinct
basic summary statistics and preserve certain types of generality are provided,
accompanied by criteria and rationale.
Connections to the education literature are made and suggestions are
made for classroom use.
* (in press; expected in October 2009 issue; Matthew
Winsor & Larry Lesser). Hot Wheels: A Vehicle for Proportional Reasoning.
Mathematics Teaching in the Middle School, 15(3),
pp. ____ This article describes an activity that uses Hot Wheels cars to
examine concepts of scale and proportionality. Student thinking and extensions
to other real world applications are also addressed.
Lesser, Lawrence (in press;
expected Dec. 2009/Jan. 2010). Sizing
Up Class Size: A Deeper Classroom Investigation of
Central Tendency [a featured “Delving Deeper” paper]. Mathematics Teacher. Abstract:
A common real-world question about
“average class size” yields a surprisingly rich exploration of
conceptual and procedural knowledge about measures of location. Pedagogical connections are made to the role
of simple numbers (Lesser and Melgoza 2007), the role of assumptions,
algebra-based deductive reasoning, real-world context, and the inspection
paradox. [note: The exploration was
classroom tested as a survey of (N= 50) pre-service elementary and
middle school teachers in two sections of a required introductory statistics
course at a mid-sized doctoral research intensive university in the
Southwestern United States. The
pre-service teachers uniformly focused on the simplest interpretation of mean
and were generally surprised to see how many other interpretations were
possible.]
* Sorto, M.
Alejandra & Lesser,
Lesser, L. & Groth, R. (2009).
Technological Pedagogical
Content Knowledge in Statistics. In Joanne Foster (Ed.), CD-ROM Proceedings of the Twentieth
Annual International Conference on Technology in Collegiate Mathematics,
pp. 148-152.
Lesser,
Abstract: Equity, service learning, and social justice are
powerful vehicles for motivating students to take statistics seriously and also
for empowering citizens with the statistical literacy needed to be able to speak
out more intelligently against injustices they may uncover. This paper begins
by outlining key references from the recent, rapidly emerging literature on
these topics in statistics education. A
major grant on the author’s campus dealing with gender equity in the
context of STEM (science, technology, engineering, and mathematics) fields
yielded a natural vehicle to implement many aspects of these themes in a
redesigned introductory statistics course for pre-service elementary and middle
school teachers. After describing the
grant, the student population, and features of the course, this paper presents
the results of a quantitative pretest-posttest survey as well as representative
narrative data such as artifacts (e.g., student reflection papers) and a peer
observation. Further connections and
reflections are made and situated in the literature.
Garfunkel,
Solomon; Malkevitch, Joseph; Lesser, Lawrence M.; Moore, David S.; Taylor, Alan
D.; Conrad, Bruce P.; Brams, Steven J.; Gallian, Joseph; Campbell, Paul J.;
(2009). For All
Practical Purposes (8th
edition of
critically-acclaimed, top-selling math-for-liberal-arts textbook).
Abstract: The four
statistics chapters cover distributions (including graphical and numerical
summaries of quantitative data), correlation, regression, sampling,
experiments, observational studies, confidence intervals, and probability. I made extensive refinements throughout all
four of these chapters, and roughly 30% of the examples, exercises,
spotlights, etc. have been changed or replaced.
I added new technology spotlights (covering graphing, scientific, and
nonscientific calculators) to aid in calculating standard deviation, five
number summary, correlation, line of best fit, and combinatorics. Standard deviation and correlation formulas
are now provided in both computational as well as conceptual forms. Coverage of sample space, probability rules,
combinatorics, and descriptive statistics was
expanded. Connections to history,
multiple representations, etymology, culture, and the classroom have been added
to make these chapters more engaging for readers and more friendly for English
language learners.
Lesser,
Abstract: This paper presents an overview of modalities that can
be used to make learning statistics fun. Representative examples or
points of departure in the literature are provided for no less than 20
modalities. Empirical evidence of effectiveness specific to statistics
education is starting to emerge for some of these modalities – namely,
humor, song, and cartoons. To reinforce their effectiveness as an
intentional teaching tool, the authors offer practical implementation tips.
Kosheleva, Olga; Lesser, Lawrence; Munter,
Judith; Trillo, Sylvia. (2008) Parent Power Nights: A Vehicle for
Engaging Adults/Families in Learning Mathematics. Adults Learning Mathematics
International Journal, 3(2b), 36-52.
http://www.alm-online.net/images/ALM/journals/almij-volume3_2_b_nov2008.pdf
Abstract: Located on the U.S./México border, The University of
Texas at
Abstract: University researchers and teacher facilitators
implemented a state-funded professional development project during the 2005-06
academic year to help county middle school teachers
improve student achievement in mathematics. In this paper, we discuss lessons
and results from this innovative model, whose iterative cycle includes teacher
content knowledge, item analysis from a high-stakes test, pedagogical content
knowledge, big mathematical ideas behind test items, and designing/
implementing/ reflecting on lessons to address critical problem areas in
student learning and understanding.
Lesser,
Abstract: While social justice may be perceived as a more
“radical” or marginal realm than equity, these realms are shown to
be intertwined with each other and with the mission of TODOS. Furthermore, the author’s exploratory
pilot survey of a class of (N = 8) inservice
secondary teachers reinforces evidence from the K-12 research literature (e.g.,
Shaughnessy 2007) that people’s (prior) concepts of fairness may impact
how they encounter standard mathematics concepts, thus providing another reason
to take concepts of social justice seriously.
Resources are provided for those interested in beginning to learn about
social justice teaching in mathematics/statistics education.
Lesser, Lawrence
and
Abstract:
An improved pedagogical sequence of datasets was created to increase
secondary school inservice teachers’ conceptual
intuition for one-way analysis of variance(ANOVA). During one 80-minute meeting of a course on
statistical methods in mathematics education research, the teachers (n =
12) were given a pre-survey to assess their intuition about concepts of ANOVA
(e.g., “between group variation” versus “within group
variation”), then the intervention (individually answering questions
about the structured sequence of datasets), then a post-survey. The intuition gain was about one point (on a
7-point Likert scale), but because of the small class
size, the one-tailed paired t-test value (t = 1.363, df = 10) did not reach statistical
significance (p = .101). There
was, however, a statistically significant result (p = .0012) that
teachers felt it was helpful that the numbers in the datasets were
‘simple’ (e.g., integer means and standard deviations).
Lesser,
Abstract: An activity tested
and easily tailored for multiple grade levels uses the
vehicle of classifying a variety of functions (or even numbers) by a variety of
traits as a way to deepen understanding about both mathematics and tolerance.
Lesser,
21, 26-28.
Lesser,
Abstract: Definitive comprehensive overview of modalities that can
be use to making learning statistics fun, including humor, song, books, games,
game shows, literature, word games,
movies, videos, food, and celebrations.
Most of the strategies are research-based and/or classroom tested and
the paper includes a lengthy annotated bibliography.
Lesser,
Abstract: Despite the dearth of literature specifically on
teaching statistics for social justice, there is precedent in the more general
realm of teaching for social justice, or even teaching mathematics for social
justice. This article offers an overview of content examples, resources, and
references that can be used in the specific area of statistics education. Philosophical and pedagogical background
resources are given, definitional issues are discussed, and potential
implementation challenges are addressed.
A substantial bibliography of print and electronic resources is
provided.
Lesser,
Abstract: We explore
and discuss pedagogical opportunities presented by two subtle graphing
calculator pitfalls that can be readily encountered in the secondary school
classroom when doing statistics on common (TI) calculators: (1) confusion about
bounds when computing cumulative probabilities for the normal distribution, and
(2) confusion about the order of variables when computing regression lines of
best fit to a dataset.
Lesser, Lawrence and
Abstract: Trigonometry classes can explore interactive sketches
which allow them to connect the secant
and tangent trigonometry functions to those words in a geometry context, and
connect all six basic trigonometry functions (sin, cos,
tan, cot, sec, csc) to specific segment lengths in a
single simple diagram. The interactive
nature of the diagram will also allow students to make connections to major
inequalities and identities. The paper
concludes with discussion and another applet using the applied context of the
Ferris Wheel Problem.
Lesser, Lawrence
and
Abstract:
This paper is an accessible overview of key research (by the authors and
others) and pedagogical considerations related to choosing representations and
representational sequences in school mathematics. Examples are explored from a variety of
content areas.
Lesser, Lawrence
and Blake, Sally (2006). Mathematical Power: Exploring Critical
Pedagogy in Mathematics and Statistics.
In C. Rossatto, R.L. Allen, M. Pruyn (Eds.), Re-inventing
Critical Pedagogy: Widening the Circle of Anti-Oppression Education,
pp. 159-173.
Abstract: We
discuss how negative attitudes are perpetuated that many students have about mathematics
and their mathematical abilities.
Informed by concrete classroom experiences, we then discuss how the
tools of mathematics and mathematical reasoning can be applied towards
culturally-relevant pedagogy and teaching for social justice to confront this
and help students utilize the opportunities for empowerment and success they
deserve in mathematics class and in life.
Lesser,
Abstract: At a pluralistic Jewish community high
school in the southern US, the author sought, adapted, and integrated into his
teaching examples of culturally relevant mathematics (in ways adaptable for
other grades or cultures). Topics/techniques explored included: quotations about
mathematics from traditional Jewish sources and sages, mathematical
“firsts” (first statistical graphic, first fair division problem,
etc.), counting (permutations, marking time, etc.), connecting mathematical and
Jewish ideas about the infinite and about pi, mathematical modeling (e.g., Mikva’os 7:2), use of geometry in Judaism,
connections between structures of logic used in mathematics and Judaism, and connections to Jewish text, customs or games (e.g., dreidl). In addition to their intrinsic interest
and value, these enhancements connected to school culture/activities and
appeared to help motivate additional students towards a broader view of and
deeper engagement with mathematics, and possibly with Judaism as well. This
article offers both scholarly background as well as a collection of diverse
classroom-tested examples.
Lesser,
Abstract: An overview of how to motivate and
bring intuition to concepts that are initially nonintuitive
or even counterintuitive to students.
Examples are provided that use a variety of means, including using
multiple representations, intuitive analogies, and using(and
resolving) counterintuitive examples. A
thorough bibliography of additional resources and references is included.
Lesser,
Abstract: The author explored pitfalls of
technologies common in the secondary classroom with his “technology in
the math classroom” class for preservice and inservice secondary teachers. Examples
involving the TI 83/84 graphing calculator include regression syntax, nonzero
value for sin(4*pi), a defined
derivative at an absolute value function’s corner, graphical display of
discontinuous functions, and order of operations. Other technologies for which pitfalls were
identified include Excel, Mathematica, and even
presentation/projection technology.
Discussion is augmented with contributions by inservice
high school teachers.
Lesser, Lawrence and
Abstract: This study investigates the effect of
representational sequence on students’ understanding of mathematical
concepts. Pilot studies were conducted with 129 high school students on solving
inverse trigonometric identities and with 10 pre-service secondary teachers on
representing Simpson’s Paradox.
Structured activities with a variety of representations and
representational sequences were used to examine the impact on students’
learning. This study also includes outcomes of surveys of 8 middle school
teachers on different aspects of using representations in mathematics
classroom. Our ongoing work finds this impact significant and claims that
particular representational sequences need to be sensitive to specific content,
learning outcomes, student prior knowledge and learning style.
Lesser,
Abstract: The author
discusses several specific ways in which he has attempted to bridge theory and
practice in teaching courses for preservice
elementary teachers and courses for preservice
secondary teachers. The column also
references pitfalls and suggestions from the literature on this topic.
Lesser,
Abstract: the
example of Simpson’s Paradox is used as a vehicle to discuss the many levels
and facets of specialized mathematical/statistical knowledge needed for
teaching, beyond just general mathematical/statistical maturity.
Lesser,
Abstract: To support the newest process standard of NCTM
(National Council of Teachers of Mathematics), the potential of multiple
representations for teaching repertoire is explored through a real-world
phenomenon for which full understanding is elusive using only the most common
representation (a table of numbers). The phenomenon of "reversal of
a comparison when data are grouped" can be explored in many ways, each
with their own insights, including: table, platform scale, trapezoidal
representation, unit square model, probability (balls in urns), and verbal
form. Lesser also commented on this topic in a letter published in The American Statistician (November 2004, p.
362).
Lesser,
Abstract: This
article gives intuition for the magnitude of the MegaMillions
jackpot probability and then goes on to show how a lottery can be used to
explore all the major topics of an introductory statistics course.
Lesser,
Abstract: Describes an innovative
curriculum module the first author created on the two-way exchange between statistics and applied ethics. The module, having
no particular mathematical prerequisites beyond high school algebra, is part of
an undergraduate interdisciplinary ethics course which begins with a
3-week introduction to basic applied ethics taught by a philosophy
professor (the second author), and continues with 3-week modules from various
other professors. The first author’s module’s emphasis
on conceptual and critical thinking makes it easily adaptable to
service-level courses as well as readily expandable for
more mathematically sophisticated audiences. Through in-class explorations
and discussions, the module made connections to contemporary topics such as the
death penalty, equal pay for equal work, and profiling. This article shares resources, strategies and lessons
learned for instructors wishing to develop their own specific modules of
various lengths, but also contains valuable, provocative material and framework
ideas for all teachers and practitioners of statistics.
Lesser,
Lesser,
Lesser,
Lesser,
Abstract: Students’
ready understanding of and interest in the context of songs and music can be
utilized to motivate all grade levels to learn probability and
statistics. Content areas include generating descriptive statistics,
conducting hypothesis tests, analyzing song lyrics for specific terms as well
as “big picture” themes, exploring music as a data analysis tool,
and exploring probability as a compositional tool. Musical examples
span several genres, time periods, countries and cultures. [note:
this appears to be the first refereed
comprehensive article on using song in the statistics classroom]
Lesser,
Abstract: Mathematics
students and teachers with even minimal musicianship can enjoy mathematical
connections and motivations involving existing popular songs, raps or new words
for existing songs. This article provides strategies, activities and
examples as well as resources to "do it yourself." The
article offers song-based problem solving, critical thinking and enrichment
activities, and includes several highly original math lyrics (such as
"American Pi", which can be sung to the tune of the song
"American Pie" -- a #1 hit for Don McLean in 1972 and a Top-30 hit
for Madonna in 2000) to support the multiple intelligences-based learning of
mathematics procedures, content, process, and history. [note: this appears
to be the first refereed
comprehensive article on using song in the mathematics classroom]
Lesser,
Abstract: Algebra
offers opportunities for all students to engage the richness of diversity
without needing extra class time. Examples are illustrated from
multiculturalism/history (e.g., solving linear equations using Egyptian method
of "false position"), multiple representations (e.g., geometric
representation of completing the square), and the object concept of functions
(e.g., classifying a function by a given property).
Lesser,
Abstract: Line
of best fit, interpolating polynomials, and complete graphs provide fresh
opportunities for viewing technology and mathematical theory as partners rather
than as competitors. In particular, when the computer outputs a
line of best fit, a student may engage the formulas involved using algebra
instead of calculus (which nicely complements the Summer
1999 Teaching Statistics article). When the computer crunches an
interpolating polynomial, a student may do the same using the intuitive
Lagrange pattern of factored form. And finally, a student can more
effectively utilize a graphing calculator to graph functions such as
polynomials by applying a theoretical result (accessibly provable using
the Factor Theorem and the triangle inequality) to ensure the entire function
is within the rectangular viewing area.
Abstract: This
article presents a sequence of explorations and responses to student questions
(Why not use perpendicular deviations? Why not minimize the sum
of the vertical deviations? Why not minimize the sum of the absolute deviations?
Why minimize the sum of the squared deviations?) about
the rationale for the commonly used tool of line of best fit. A noncalculus-based motivation is more feasible than is often
assumed for each aspect of the least-squares criterion “minimize the sum
of the squares of the vertical deviations between the fitted line and the
observed data points.”
Lesser,
Abstract: The
Birthday Problem is “How many people must be in a room before the
probability that some share a birthday (ignoring the year and ignoring leap
days) becomes at least 50%?” Multiple approaches to the
problem are explored and compared, addressing probability concepts, problem
solving, modelling assumptions, approximations
(supported by
Lesser,
Mayes, Robert L. and Lesser,
Abstract: This
article explains and synthesizes two theoretical perspectives on the use of
counterintuitive examples in statistics courses, using Simpson’s Paradox
as an example. While more research is encouraged, there is some reason to
believe that selective use of such examples supports the constructivist
pedagogy being called for in educational reform. A survey of college
students beginning an introductory (non-calculus based) statistics course
showed a highly significant positive correlation (r = .666, n =
97, p < .001) between interest in and surprise from a 5-point Likert scale survey of twenty true statistical statements
in lay language, a result which suggests that such scenarios may motivate more
than they demoralize, and an empirical extension of the model from the
author’s developmental dissertation research. [this paper was
subsequently selected by the editors for inclusion in Getting the Best from Teaching Statistics, a collection of the best
articles from volumes 15-21] available
at: http://www.rsscse.org.uk/ts/gtb/lesser.pdf
Lesser,
Abstract: A
university’s introductory statistics course was redesigned to incorporate
technology (including a website) and to implement a standards-based approach
that would parallel the recent standards-based education mandate for the
state’s K-12 schools. The author collected some attitude (pre
and post) and performance (post only) data from the “treatment”
section and two “comparison (i.e., more traditional)”
sections. There was a pattern of positive attitude towards the
redesigned aspects of the course, including group work, lab and project
emphasis, criterion-referenced assessment and examples from real-life. On
the three problems given to the three sections at the end of the course, the
only significant ANOVA (F2, 101 = 4.2, p = .0168)
involved the treatment section scoring higher than the other sections.
This occurred on a problem involving critical thinking (with a graphic from USA
Today), an emphasis supported by the particular standards of the redesigned
course.
Lesser,
Abstract: Spreadsheets
are used to explore the lottery, addressing common misconceptions about various
lottery "strategies" and probabilities and providing real-world
applications of topics such as discrete probability distributions, combinatorics, sampling, simulation and expected
value. Additional pedagogical issues are also discussed. Examples
discussed include the probability that an integer appearing in consecutive
drawings, the probability that a single 6-ball drawing includes at least two
consecutive integers, the probability that exactly one person wins the jackpot,
and the probability that a frequent player eventually wins the jackpot.