Abstracts of Selected Publications
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 this major revision of the 23-chapter book, I had sole responsibility for
the 4 statistics chapters). For All
Practical Purposes (8th
edition of top-selling
math-for-liberal-arts textbook). New
York: W. H. Freeman and
Company (with COMAP: Consortium for Mathematics and its Applications). One of those chapters (Ch. 5) was selected
as the featured FAPP chapter for the company’s webportal
(expected to launch Jan. 2009 at http://courses.bfwpub.com
or http://www.whfreeman.com/portals).
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 to be more
engaging for readers and more friendly for English language learners.
Lesser, Lawrence
(in press; expected 2009). Sizing Up Class Size: A Deeper Classroom
Investigation of Central Tendency. [a featured “Delving Deeper”
paper] Mathematics Teacher. Abstract: A simple, common
question about average class size yields a surprisingly rich exploration of
conceptual and procedural knowledge about measures of location. 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.
Pedagogical connections are made to the role of simple numbers (Lesser
and Melgoza 2007), the role of assumptions, algebra-based deductive reasoning,
real-world scenarios, and the inspection paradox.
Lesser, Lawrence & Pearl,
Dennis (2008). Functional Fun
in Statistics Teaching: Resources, Research, and Recommendations. Journal of Statistics Education, 16(3),
http://www.amstat.org/publications/jse/v16n3/lesser.pdf
(or http://www.amstat.org/publications/jse/v16n3/lesser.html). 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 El Paso offers academic programs in K-12
school teacher preparation. Many of the
courses integrate parents and families into teacher preparation courses. One
example of effective adult/community learning is the “Parent Power
Night” (PPN) component. This model builds a learning community, engaging
university faculty members with pre-service teachers and family members in
effective teaching/learning activities. Pre-service teachers are concurrently
enrolled in mathematics content and pedagogy courses, taught together in a
“block” on the campus of a public school. PPN activities aim to engage parents and
community members together with the university students in meaningful
investigations of mathematical concepts. Preliminary evidence suggests that PPN
activities have impacted knowledge and attitudes towards mathematics of
participating parents, children and pre-service teachers from this
predominantly Hispanic, high-poverty area.
An unanticipated outcome has been the impact on adults with limited
previous formal education; many acquired the knowledge necessary to understand
rather sophisticated mathematics concepts their children were learning in
school. The paper will discuss instructional methods used and implications for
effective adult/family learning of mathematics content in Hispanic communities.
Tchoshanov,
Mourat; Lesser,
Lawrence; Salazar, James (2008). Teacher Knowledge and Student Achievement:
Revealing Patterns. Journal of Mathematics Education Leadership, 10(2),
39-49. 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, Lawrence (fall 2008). Equity,
Social Justice, and the Mission
of TODOS. Noticias de TODOS: News from TODOS Mathematics for All,
4(2), 7-9.
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, exploratory pilot survey of (N=
8) inservice secondary teachers reinforces evidence
from the K-12 research literature (Shaughnessy 2007) that people’s
concepts of fairness may impact how they encounter standard mathematics
concepts. Resources are provided for
those interested in beginning to learn about social justice teaching in
mathematics/statistics education.
Lesser, Lawrence
and Melgoza,
Lorraine
(2007). Simple Numbers: ANOVA Example of
Facilitating Student Learning in Statistics. Teaching
Statistics, 29(3), 102-105.
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, Lawrence (fall 2007). Using
‘Objects’ to Object to Objectification. Teaching Tolerance. No. 32, p.15.
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, Lawrence (2007). Learning
Stats is Fun … with the Right Mode.
Stats, 48, pp.7-11, 21, 26-28.
Lesser, Lawrence (2008). Even More Fun Learning
Stats. STATS
, 49, pp. 5-8, 19, 27.
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, Lawrence (2007). Critical Values and
Transforming Data: Teaching Statistics with Social Justice. Journal of Statistics Education, 15(1),
1-21. www.amstat.org/publications/jse/v15n1/lesser.pdf.
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, Lawrence (2007). Using
Graphing Calculators to do Statistics: A Pair of Problematic Pitfalls. Mathematics
Teacher, 100(5), 375-378. 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 Winsor, Matthew (2006). Interactive Representations of the Big Six Trigonometry Functions:
Connections to Geometry and Language. ON-Math:
Online Journal of School Mathematics, 5(1). 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 Tchoshanov, Mourat (2006). Selecting Representations. Texas Mathematics Teacher, 53(2),
20-26. A teacher-friendly 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. Lanham, MD: Rowman &
Littlefield. 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, Lawrence (2006). Book of Numbers: Exploring Jewish
Mathematics and Culture at a Jewish High School. Journal of Mathematics
and Culture, 1(1), 8-31. www.ccd.rpi.edu/Eglash/nasgem/jmc/jmc.htm.
http://www.ccd.rpi.edu/Eglash/nasgem/jmc/issue_1_1.html
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, mathematical “firsts,” gematria,
counting, infinity, pi, and connections to Jewish
text/customs/holidays/games. 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, Lawrence (2006). Engaging the Intuition in Statistics to Motivate. Juried paper (also
presented at 50th national AP Conference) published on AP Statistics Course Home Page
at College Board AP Central. 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, Lawrence (with Liz Rayas, Gabriel Trujillo,
Aracely Vargas, Yogesh Velankar)
(2006), Teachers’
Technology Class Continues Discussion of Pitfalls. Mathematics
Teacher, 99(5), 340-342. 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 Tchoshanov, Mourat (2005). The Effect of Representation and Representational Sequence on
Students’ Understanding, 7-page
research report. 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. [proceedings
at http://convention2.allacademic.com/index.php?cmd=pmena_guest
and on CD-ROM]. 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, Lawrence (fall 2005). Bridging the Potential Divide Between Theory and Practice. “Theory and Practice” column in [Association of Mathematics Teacher Educators] Connections, 15(1), pp.10-11. 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,
Lawrence (March
2005), Mathematical Knowledge for Teaching, Theory and Practice” column in [Association of Mathematics Teacher Educators] Connections, 14(2), pp. 8-9. Also at: http://amte.sdsu.edu/resources/Mar05.pdf. 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, Lawrence (Spring 2005), Illumination
Through Representation: An Exploration Across the Grades, Statistics
Teacher Network, 66, pp. 3-5.
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, Lawrence (Winter 2004), Take
a Chance by Exploring the Statistics in Lotteries, Statistics Teacher
Network, 65, pp. 6-7. 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, Lawrence M. and Nordenhaug, Erik. (November
2004). Ethical Statistics and
Statistical Ethics: Making an Interdisciplinary Module. Journal of Statistics Education. (14,000+ word article published by the American
Statistical Association on the world-wide web at: http://www.amstat.org/publications/jse/v12n3/lesser.html) 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, Larry. (Fall 2004). Slices of Pi: Rounding Up Ideas for
Celebrating Pi Day. Texas Mathematics Teacher, 51(2), 6-11. (the
issue is also available at http://www.tenet.edu/tctm/downloads/TMT_Fall_04.pdf
) Abstract: A creative, comprehensive user-friendly overview of ideas,
activities and resources for educators (particularly secondary school teachers)
to implement “Pi Day” (3/14) celebrations at their
schools. Connections are made to many realms, including: literature,
music, art, food, humor, contests, mnemonics, mathematics history, media,
hands-on activities, etc.
Lesser, Larry. (Fall 2003). A Whole
Lotto Education! Texas Mathematics Teacher, 50 (2), pp. 12-15). (the issue is also available at http://www.tenet.edu/tctm/downloads/journal_fall03.pdf
) Abstract:
Describes classroom explorations of the interpretation and calculation of
probabilities involved in a representative state lottery. TI-83 calculator
commands are given for simulating drawings as well as for calculating relevant
probabilities using the binomial, geometric, Poisson, and other distributions.
Lesser, Lawrence
M. (2002). Letter to the Editor. [critique/response
to Sowey (2001) "Striking
Demonstrations in Teaching Statistics", JSE, 9(1)].
Journal of Statistics Education, 10 (1).
Abstract:
Frameworks for "striking examples" and "counterintuitive
examples" are further articulated in light of recent work of E.R. Sowey, and additional examples are contributed. The importance
of classifications by Lesser (1994) is reinforced, and there is a review of
effort that has been made to identify and use such demonstrations in teaching.
Lesser, Lawrence
M. (Winter 2002). Stat Song Sing-Along! STATS, #33, pp.
16-17. Abstract: Examples of highly creative lyrics (e.g.,
educating “The Gambler” about playing the lottery) are given that
are rich in statistical content and/or related to current events.
Lesser, Lawrence
M. (2001). Representations of Reversal: An Exploration of Simpson's
Paradox. In A. A. Cuoco and F. R. Curcio (Eds.), The Roles of Representation in School
Mathematics, pp. 129-145 [chapter of the NCTM's
juried annual yearbook]. Abstract: To support NCTM's newest
process standard, 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" is explored in surprisingly many ways, each with their own
insights: table, circle graph, slope & correlation coefficients,
platform scale, trapezoidal representation, unit square model, probability
(balls in urns), matrix determinants, linear transformations, vector addition,
and verbal form. For such a mathematically-rich phenomenon, the number of
distinct representations may be too large to expect a teacher to have time to
use all of them. Therefore, it is
necessary to learn which representations might be more effective than others,
and then form a sequence from those selected.
Pilot studies were done with pre-service secondary teachers (n1
= 7 at a public research university and n2 = 3 at a public
comprehensive university) on exploring a sequence of 7 different
representations of Simpson’s Paradox.
Students tended to want to stay with the most concrete and visual
representations (note: a concrete-visual-analytic progression may not be
expected to apply in the usual manner in the particular case of Simpson’s
Paradox).
Lesser, Lawrence
M. (Autumn 2001). Musical Means: Using Songs in Teaching Statistics. Teaching
Statistics, 23 (3), 81-85.
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, Lawrence
M. (May 2000). Sum of Songs: Making Mathematics Less Monotone! Mathematics
Teacher, 93(5), 372-377.
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, Lawrence
M. (January 2000). Reunion of
Broken Parts: Experiencing Diversity in Algebra. Mathematics
Teacher, 93(1), 62-67.
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, Lawrence
M. (December 1999). Making the Black Box Transparent. Mathematics
Teacher, 92(9), 780-784.
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.
Lesser, Larry (Summer 1999). The
Y’s and Why Not’s of Line of Best Fit. Teaching
Statistics, 21(2), 54-55.
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, Lawrence
M. (May 1999). Exploring the Birthday Problem with Spreadsheets. Mathematics
Teacher, 92(5), 407-411.
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 Taylor series),
recursion, (Excel) spreadsheets, simulation, and student
preconceptions. The traditional product representation that yields
the exact answer is not only tedious with a regular calculator, but did not
provide insight on why the answer
(23) is so much smaller than most students' predictions (typically, half of
365). A more intuitive (but slightly inexact) approach synthesized
by the author focuses on the total number of "opportunities" for
matched birthdays (e.g., the new "opportunities" for a match added by
the kth person who enters are those that the kth person has with each of the k-1 people already
there). The author followed the model
of Shaughnessy (1977) in having students give predictions in advance of the
exploration and these written data (as well as interview data) collected from
students indicated representative multiplier or representative quotient
effects, consistent with the literature on misconceptions and heuristics. Data
collected from students after the traditional and “opportunities”
explorations indicate that a majority of students preferred the opportunities
approach, favoring the large gain in intuition over the slight loss in
precision.
Lesser, Lawrence
(1999). Investigating the Role of Standards-Based Education in a Pre-Service
Secondary Math Methods Course. In Myra L. Powers and Nancy K.
Hartley (Eds.), Promoting Excellence in Teacher Preparation:
Undergraduate Reforms in Mathematics and Science [juried monograph for NSF-funded Rocky
Mountain Teacher Education Collaborative, also ERIC ED439089],
pp. 53-64. Ft. Collins, CO:
Colorado State University. Abstract: A case study was conducted
on a math methods class for preservice secondary
teachers that were exploring ideas and implementation of standards-based
education. A variety of qualitative data
was collected and analyzed about students’ experiences with
performance-based assessment scoring rubrics as well as with state and national
mathematics content standards, in a context of evolving professional identity
and commitment.
Mayes, Robert L. and Lesser, Lawrence M. (1998). ACT in Algebra: Applications, Concepts, and
Technology in Learning Algebra. McGraw-Hill.Abstract:
Progressive college algebra textbook progressive in its incorporation of
technology, having mathematics introduced by applications rather than by
definitions, conceptual connections, etymology, math history,
etc. The book has a realistic treatment of the place of factoring,
having a chapter on factoring-dependent mathematics for those students who need
that material for later mathematics courses, but a chapter that can be omitted
without loss of continuity for more applied or terminal versions of this
course.
Lesser, Larry (Spring 1998). Countering
Indifference Using Counterintuitive Examples. Teaching Statistics,
20(1), 10-12.
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, Lawrence
M. (February 1998). Technology-Rich Standards-Based Statistics:
Improving Introductory Statistics at the College Level. Technological
Horizons in Education Journal, 25(7), 54-57.
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, Lawrence
(Nov. 1997). Exploring Lotteries with Excel. Spreadsheet User, 4(2),
4-7.
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.