Abstracts of Selected Publications
Lesser,
L. (2014; in press). Mathematical lyrics:
Noteworthy endeavors in education. Journal of Mathematics
and the Arts
Abstract: Mathematical
lyrics are song lyrics connected to, or inspired by, mathematics or statistics.
This paper explores various types of mathematical lyrics and their roles in
mathematics education. In particular, the paper contains many examples of my
own lyrics as well as an extensive bibliography of lyrics composed by others.
It also provides resources and strategies for creating such lyrics and for using
them in an educational setting.
* Lesser, L., Wagler, A. & Abormegah, P. (2014). Finding a happy median: Another balance
representation for measures of center, Journal of Statistics
Education, 22(3), 1-27. http://www.amstat.org/publications/jse/v22n3/lesser.pdf
Abstract: This paper
explores the use of a lesser-known dynamic model for the median, a foundational
topic that starts in
the middle school curriculum and is associated with student misconceptions
and knowledge gaps. This model
appears to offer a rich vehicle to explore the median
interactively in greater
conceptual depth that includes some of its more subtle associated ideas.
An
exploratory study to assess performance of this model in a class for pre-service
middle school
teachers yielded evidence
that students who completed the dataset sequence associated with the
model gained further
insight about the median, especially concerning how the mean and median
are affected differently by outliers.
Analyses of open ended questions as well as empirical
results
of multiple-choice questions are
used to assess the overall learning outcomes gained by students.
* Harrell-Williams, L.; Sorto, M. A.;
Pierce, R. L.; Lesser, L. M.; Murphy, T. J. (2014). Validation of scores from a
new measure of pre-service teachers’ self-efficacy to teach statistics in the
middle grades. Journal of Psychoeducational Assessment, 32(1), 40-50.
Abstract: The influential Common Core State Standards for Mathematics (CCSSM) expect students
to start statistics learning during middle grades. Thus, teacher education and
professional development programs are advised to help pre-service and inservice teachers increase their knowledge and confidence
to teach statistics. Although existing
self-efficacy instruments used in statistics education focus on students, the
Self-Efficacy to Teach Statistics (SETS) instrument measures a teacher’s
efficacy to teach key CCSSM statistical topics. Using the results from a sample
of n = 309 participants enrolled in a
mathematics education or introductory statistics course, SETS scores were
validated for use with middle grades pre-service teachers to differentiate
levels of self-efficacy to teach statistics. Confirmatory factor analysis using
the Multidimensional Random Coefficient Multinomial Logit
Model supports the use of two dimensions, which exhibit adequate reliabilities
and correspond to the first two levels of The
Guidelines for Assessment and Instruction
in Statistics Education adopted by the American Statistical Association.
Item and rating scale analyses indicate that the items and the six-category
scale perform as intended. These indicators suggest that the SETS instrument
may be appropriate for measuring pre-service teacher levels of self-efficacy to
teach statistics.
* Lesser,
L., Wagler, A., Esquinca, A., & Valenzuela, M. G. (2013). Survey of native English
speakers and Spanish-speaking English language learners in tertiary
introductory statistics. Statistics Education Research Journal, 12(2), 6-31. Abstract:
The
framework of linguistic register and case study research on Spanish-speaking
English language learners (ELLs) learning statistics informed the construction
of a quantitative instrument, the Communication, Language And Statistics Survey
(CLASS). CLASS
aims to assess whether ELLs and non-ELLs approach the learning of statistics
differently with respect to the distinctive linguistic features of the field of
statistics and with respect to language resources they bring to the class. The CLASS was administered to all (n = 137)
students in an introductory statistics literacy course at a university with a
majority Mexican-American student body. Findings suggest ELLs often have
distinctive patterns in how they experience aspects of statistics instruction
(e.g., wait time) as well as movement between mathematics/statistics and
everyday registers.
* Lesser, L.
(2013). Types of average and sampling:
‘Household words’ to dwell on. Statistics
Education Web: Online Journal of K-12 Statistics Lesson Plans (pp. 1-12).
[Bronze medal prize-winner in contest sponsored by ASA] http://www.amstat.org/education/stew/pdfs/TypesofAverageandSamplingHouseholdWordstoDwellOn.pdf
Abstract: This lesson is designed to give students more insight into both mathematical and real-world assumptions that can be involved even in what appears to be a simple task: to find the “average household size” for students at their school. The context of this lesson has real-world relevance: it is not only part of the Census at School questionnaire, but is also part of what the Census Bureau regularly estimates. The lesson can efficiently set the tone for better habits of mind and questioning and more precise usage of vocabulary and more explicit awareness of assumptions and possible biases in a broad range of future student work in statistics.
*
Lesser, L.M.; Wall, A.; Carver, R.; Pearl, D.K.; Martin, N.; Kuiper, S.;
Posner, M. A.; Erickson, P.; Liao, S.-M.; Albert, J.; Weber, J.J. (2013). Using fun in the statistics
classroom: An exploratory study of college instructors’ hesitations and
motivations. Journal of
Statistics Education, 21(1),
1-33. http://www.amstat.org/publications/jse/v21n1/lesser.pdf
Abstract: This study examines statistics instructors’ use of
fun as well as their motivations, hesitations, and awareness of resources. In 2011, a survey was administered to
attendees at a national statistics education conference, and follow-up
qualitative interviews were conducted with 16 of those (N = 249) surveyed to provide further context for interpreting the
quantitative results. Motivations were
similar for men and women, but female instructors admitted more hesitations in
many areas. While many instructors are
using or are open to using fun in the statistics classroom, the findings
suggest that not having available resources at hand and not being aware of
resources such as the CAUSEweb collection are major
hesitations. Methods of alleviating
hesitations are discussed.
*Lesser,
L. (2013). Using
context to classify variables. Teaching Statistics, 35(1), 29-31. http://onlinelibrary.wiley.com/doi/10.1111/j.1467-9639.2012.00527.x/pdf
Asking
clarifying questions and utilizing context can help students with several
aspects of introductory statistics, such as appropriately classifying
variables.
*Lesser, L. & Guthrie, J. (2012). Uncommon Connections with
Common Numerators. PRIMUS:
Problems, Resources, and Issues in Mathematics Undergraduate Studies, 22(8), 634-642. Abstract: Undergraduate students who are pre-service teachers
need to make connections between the college mathematics they are learning and
the precollege mathematics they will be teaching. Spanning a broad range of
undergraduate curricula, this article describes useful lesser-known
connections, explorations and original new proofs involving fractions. In
particular, we use standard tools of number theory to investigate when an
integer results from bc/(b+c), an expression that arises
from the not necessarily uncommon situation of adding fractions with a common
numerator.
* Rubel, L., Driskill, M., and Lesser, L. (October 2012). Decennial Redistricting: Rich Mathematics in Context. Mathematics Teacher, 106(3), 206-211. http://www.nctm.org/publications/article.aspx?id=34455
Abstract: Decennial redistricting is a real-world context rich
in mathematics accessible to high school students. This article provides
teachers an overview about redistricting with resources and examples of its
diverse mathematical connections.
* Lesser, L. (2012). High-Speed Hypotheses! Teaching Statistics,
34(1), 10-12.
Abstract:
This article presents engaging interactive hypothesis tests which can be
conducted with students very efficiently.
*Lesser,
L. (2011). Low-Tech,
Low-Cost, High-Gain, Real-Time Assessment? It’s all in the cards, easy as ABCD! Texas
Mathematics Teacher, 58(2),
18-22. http://www.math.utep.edu/Faculty/lesser/LesserABCDcardsTMTpaper.pdf or at http://tctmonline.org/TMT_archive.html. Abstract: An accessible overview of
method, rationale,
and references for using classroom voting cards in the college statistics
classroom, including concrete examples and
data collected to assess the innovation.
*Lesser, L. M., & Kephart, K. (Nov. 2011). Setting the tone: A discursive case study of problem-based inquiry learning to start a graduate statistics course for in-service teachers. J. of Statistics Education, 19(3), 1-29. http://www.amstat.org/publications/jse/v19n3/lesser.pdf [This paper won the Scholarship of Teaching and Learning Award at the 2012 International Sun Conference on Teaching and Learning]
Abstract: The first day
of a course has great potential to set the tone for the entire course, planting
the seeds for habits of mind and questioning and setting in motion expectations
for classroom discourse. Rather than let the first meeting contain little
besides going over the syllabus, the instructor (Lesser) decided to use two
sustained open-ended scenarios to put in place from the start the problem-based
inquiry learning approach he wanted to use throughout most of the course. After
reviewing the literatures involved, this paper shares a description of the
lesson‘s design and instructional cycle and a discourse analysis of that
lesson‘s implementation. Strategies identified by the case study analysis
include varying participation structures, well-crafted problems, and the
instructor‘s role as facilitator and co-learner.
*Wagler, A. E., and Lesser, L. M. (2011). Teaching statistics to
culturally and linguistically diverse students.
Proceedings of the 2011 Joint Statistical
Meetings, Section on Statistical Education (pp. 821-830). http://www.statlit.org/pdf/2011Wagler-Lesser-JSM.pdf
or https://www.amstat.org/membersonly/proceedings/2011/papers/300678_65313.pdf Abstract: Resources, strategies, and lessons learned are shared based
on the authors’ research and
experience in teaching statistics (especially introductory statistics)
to diverse student populations in varied settings.
*Lesser, L. (2011). On the use of mnemonics for teaching
statistics. Model Assisted
Statistics and Applications, 6(2),
151-160.
*Lesser, L. M. (2011) Making statistics memorable: New mnemonics and motivations. Proceedings of the 2011 Joint Statistical
Meetings, Section on Statistical Education (pp. 1118-1124). https://www.amstat.org/membersonly/proceedings/2011/papers/300805_65461.pdf
or http://www.statlit.org/pdf/2011Lesser-JSM.pdf
Abstract:
This paper is a comprehensive attempt to compile and classify mnemonics (memory
aids) that can be used in statistics education.
*Sorto, M.A., White, A., and Lesser, L. (2011) Understanding Student Attempts to Find a
Line of Fit. Teaching Statistics, 33(2), 49-52.
Abstract:
The least squares method of fitting a line is not one that naturally occurs to
students. We present three tasks to understand student views on how lines may
be fit.
*Lesser, L. (2011). Supporting Learners of Varying Levels of
English Proficiency. Statistics
Teacher Network, 77, 2-5.
Abstract: Ten concrete research-informed
recommendations are given for those who teach statistics to K-12 students with
varying levels of English proficiency.
* Lesser, L. (2011). Simple
Datasets for Distinct Basic Summary Statistics. Teaching
Statistics, 33(1), 9-11.
Abstract:
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.
*Lesser,
L. (2010). The
Necessity of Equity in Teaching Statistics. Philosophy of Mathematics Education Journal, no. 25, http://people.exeter.ac.uk/PErnest/pome25/index.html,
8 pp.
Abstract: Students have prior conceptions about fairness, and
these must be acknowledged by teachers of statistics because these prior
conceptions may interact or interfere with learning or embracing statistics
concepts such as expected value, random sampling, random assignment, bias, and
discrimination. To the extent equity
includes not just fairness, but also matters of culture, it may also be worth
considering how culture can interfere with the interpretation of a common
metaphor for hypothesis testing.
*
Lesser, L. (2010). Equity and the
increasingly diverse tertiary student population: challenges and opportunities
in statistics education. Proceedings
of the 8th
International Conference on Teaching Statistics (6 pp.).
Abstract: Professional
organizations and educators are increasing their focus on equity issues for the
diverse (sub)populations they serve, such as second
language learners. This focus is
especially important in statistics because of the importance of context in both
diversity and statistics, and because of the ways in which diversity issues
interact with the actual practice and teaching of statistics. Also, there are many ways in which diversity
and equity can be natural vehicles for motivating or exploring particular
statistical concepts and content. Recently emerging evidence suggests that
students in diverse classrooms can be motivated by such examples and there have
been a variety of courses that have recently been developed to do this with
varying emphases and degrees of integration. The totality of efforts in this
area suggests that the challenges of teaching diverse populations ultimately
yield opportunities, resources, and vehicles for student learning.
* Lesser, L. (2010). An Ethnomathematics
Spin on Statistics Class. Notices
of the North American Study Group in Ethnomathematics
(NASGEm News), 3(2), 5-6. http://nasgem.rpi.edu/files/2055/
Abstract: Ethnomathematics can
also be applied to probability and statistics, and one concrete example that
was explored by the author with a predominantly Mexican-American college
student population is the Mexican game of Toma Todo. Connections
are made to ethnomathematics/research literature,
pedagogical issues, and related multicultural games.
* Sorto, M.
Alejandra & Lesser,
* Lesser, L. (Dec. 2009/Jan. 2010). Sizing Up
Class Size: A Deeper Classroom Investigation of Central Tendency. Mathematics
Teacher, 103(5), 376-380. 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.]
* Lesser, L. M. & Glickman, M. E. (Dec. 2009). Using Magic in the Teaching
of Probability and Statistics. Model Assisted Statistics and
Applications, 4(4), 265-274. Abstract:
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. & Winsor, M. (Nov. 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. 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.
* Matthew Winsor & Larry Lesser (November 2009) Hot
Wheels: A Vehicle for Proportional Reasoning. Mathematics
Teaching in the Middle School, 15(4), 239-243. Abstract:
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, 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. Boston: Pearson. ISBN
0-321-64488-3 [Reprint available in the Electronic Proceedings of the
20th Annual ICTCM: http://archives.math.utk.edu/ICTCM/i/20/S118.html]
Abstract: This paper is
a conceptual articulation and exploration of what technological pedagogical
content knowledge (TPCK) would look like in statistics education. Connections to the GAISE College Report
(ASA, 2005) and other literature are synthesized and various concrete examples
are provided and discussed.
Lesser, L.
(2009). Equity,
Social Justice, and the Mission of TODOS: Connections and Motivations. Teaching for Excellence and Equity in Mathematics, 1(1), 22-27. Abstract:
Equity and social justice are shown to be intertwined with each other and with
the TODOS mission. Also, Shaughnessy
(2007) and the author’s pilot survey of in-service secondary teachers suggest
interaction (or even interference) between students’ prior concepts of fairness
and certain mathematics/statistics topics.
Recommendations for exploration are provided (as well as pre-reading and
post-reading discussion questions).
Lesser, L. (2009). Social Justice, Gender Equity, and Service Learning in
Statistics Education: Lessons Learned from the DOE-Funded Project ACE (ACtion for Equity). Proceedings of the 2008 Joint Statistical Meetings,
Section on Statistical Education,
pp. 424-431. Alexandria, VA: American
Statistical Association. [ISBN: 978-0-9791747-5-9]
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). New
York: W. H. Freeman and
Company (with COMAP: Consortium for Mathematics and its Applications). [For
this major revision of the 23-chapter book, I had sole responsibility for the 4
statistics chapters, pp. 147-282, SC-1, A8-A11.
One of those chapters (Ch. 5) was selected as the featured FAPP
chapter for the company’s webportal (expected to launch
spring 2009 at http://www.whfreeman.com/newcatalog.aspx?technology=Portal.]
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, 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 (e.g.,
from forming categories out of the responses from semi-structured interviews
and surveys of individuals and small groups at different times) 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, 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 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.
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, 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.
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. 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. [the first juried comprehensive article on Jewish culturally
relevant mathematics]
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, 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.