Download Department of Curriculum and Instruction Course Syllabus

Towson University
MATH 235 (4 credits)
Statistics and Probability for Middle School Teachers
Spring 2012
W 10:00 am – 11:50 am, YR127
F 10:00 am – 11:50 am, YR104
Professor
Office Hours
TEXTS AND CALCULATOR
Required Texts:
Rossman, Chance & von Oeshen (2008). Workshop Statistics: Discovery with Data and
the Graphing Calculator, 3rd ed., Hoboken, NJ: John Wiley Publishing.
Shaughnessy and Chance (2005). Statistical Questions from the Classroom. Reston, VA:
National Council of Teachers of Mathematics.
Common Core State Standards Initiative (Math)
http://www.corestandards.org/the-standards/mathematics
Calculator - TI-84 with linking cable
COURSE DESCRIPTION
Objectives: This course is designed to help students discover and explore basic statistical
principles and concepts and apply them to real-life data sets and research study scenarios. This
course also seeks to expose future middle school mathematics teachers to current resources
and technology specifically designed to improve the teaching and learning of topics in data
analysis. It will accomplish the aforementioned by having students actively engaged in
discussions and reflections of global threads that permeate statistics pedagogy; investigation
into specific questions frequently asked about statistics, problem solving using recent and
interesting data sets, conducting data exploration activities using java applets, graphing
calculator, and Tinkerplots demonstrations. Course activities have been designed keeping in
mind relevant content and process standards of the National Council of Teachers of
Mathematics, as well as the recommendations of the Guidelines for Assessment and Instruction
in Statistics Education (GAISE) K-12 and College Reports funded by the American Statistical
Association.
Specific expectations include:
 Gain an appreciation for the proper use of technology in teaching data analysis;
 Apply critical thinking skills and understanding of basic experimental design to identify
and distinguish key features of data analyses (observational units, variables, types of
data, sample, population, statistics, parameters, and appropriate inferential statements)
and critique summaries of statistical studies;
Towson University
1 of 3
















Demonstrate understanding of and distinction between quantitative and categorical
variables; sampling bias and confounding; observational and experimental designs;
random sampling methods and non-random sampling methods; random sampling and
random assignment;
Construct, interpret, and describe visual displays (stemplots, histograms, bar graphs, dot
plots, boxplots, value bar charts).
Demonstrate understanding of how shape, center, and variation are three important
aspects of data analysis in general and apply these ideas summarizing data sets;
Use correct language to identify and discuss distributions that are uniform, bell-shaped,
skewed, as well as symmetric or not;
Calculate and interpret mean and median as measures of center, as well as
demonstrate appreciation of properties of those measures;
Measure the variability of a distribution using range, mean absolute deviation (MAD),
interquartile range (IQR), and standard deviation, as well as the empirical rule;
Develop understanding of the meaning of z-scores and compare relative positions of
data through z-scores;
Demonstrate flexible understanding of the mean of a data set through problem solving
and concrete modeling;
Use normal curves as mathematical models, using both a table of standard normal
probabilities and the graphing calculator to perform calculations on normal distributions.
Understand the sampling distribution of a proportion and a mean and the effect of
sample size on those sampling distributions.
Use simulations to examine the sampling distributions of sample means, and understand
the implications of the Central Limit Theorem;
Perform calculations related to the Central Limit Theorem;
Understand concept and structure of parameter estimation and apply this to constructing
and interpreting confidence intervals for a single mean and/or proportion;
Understand the concept and structure of significance tests and apply this to problems
about means and/or proportions;
Identify bivariate data, and use correct language to discuss certain patterns of
correlation (positive, negative, or none; linear vs. non-linear or none);
Perform correlation/regression analysis; interpret findings (r-value, slope, y-intercept).
Topics Covered and Tentative Distribution of Topics by Number of Days
Throughout the topics covered student explorations will be supported by the TI-84 graphing
calculator and other statistical software (Minitab and Tinkerplots). Pedagogical content
knowledge will be embedded throughout investigations into statistics and probability concepts.
Outside readings from Statistical Questions from the Classroom and other sources will
complement unit topics.
Unit 1 Collecting Data and Drawing Conclusions (Topics 1-5)
approx. 5 days
 qualitative (nominal and ordinal) versus quantitative (interval and ratio) data
 experimental design
o explanatory, response, confounding and lurking variables
 sampling techniques and issues
o population vs sample; parameter vs statistics
o random sample and sample bias
o sample size and variability
Towson University
2 of 5
Unit 2 Summarizing Data (Topics 6-10)
approx. 5 days
 two-way contingency tables
 graphical representations (value bar chart, bar graph, pie chart, dot plot, stem-and-leaf
plot, boxplot, histogram, time plot, scatterplot)
o similarities and differences of different graphical representations
 by data type (quantitative versus qualitative)
 distribution of a variable
 preservation of raw data versus grouped data
o effect of scale
o interpretations of general trends and outliers
 shapes of distributions (skewed versus symmetric; uniform, bell-shaped)
 measures of central tendency (mean, median, mode)
o developing concepts of the mean as fair share, balancing point, and “average”
 measures of variability (range, MAD, IQR, variance, and standard deviation)
 integrating concepts: data type and effect on choice of graph type, shape of distribution
for quantitative data, appropriateness of measures of central tendency and variability,
graphical interpretations of central tendency and variability for qualitative and
quantitative graphs, effect of outliers on measures of central tendency and variability
 misconceptions of graphical representations
Unit 3 Randomness and Probability (Topics 11-15 and additional material)
approx. 7 days
 experimental versus theoretical probability
 Law of Large Numbers
 fundamentals of probability
o classical rule of probability
o addition and multiplication rules
o conditional probability and independent events
o Bayes’ Theorem
 connections across multiple representations of conditional probability
o trees, Venn diagrams, charts, notation
 normal distribution
o empirical rules
o standardized scores and related probabilities
 sampling distributions of the sample mean and sample proportion
o confidence and significance
o Central Limit Theorem
o effect of sampling size
Unit 4 Inferences from Data: Principles (Topics 16, 19, and 20)
approx. 4 days
 confidence interval (proportion and mean)
 basics of hypothesis testing
o probabilities conditioned on null hypothesis
o Type I and II errors
o p-value
 hypothesis testing about the mean
Unit 5 Inference from Data: Comparisons
approx. 2 days
 two-sample versus matched pairs
Unit 7 Relationships in Data (Topics 26-29)
approx. 3 days
 correlation coefficient
 least squares regression
o fit, outliers, influential observations, inferences, and prediction
Towson University
3 of 5
NOTES
General
 You are responsible for course requirements announced during class. I will be using
blackboard http://www.towson.edu/blackboard for additional announcements and posting of
course documents.
 You are responsible for checking your Towson University email account for course
communications.
 This course will make use of the TI-84 graphing calculator and linking cable.
 Homework is an integral part of the course. It will be announced in class or via Blackboard.
Be prepared to discuss your homework in class. Homework will be collected at the end of
each unit. Grading will be based upon completion, accuracy, and presentation (no rough
edges, problems clearly labeled, detailed easy to follow answers).
 Reading Reflection assignments will be posted as Blackboard documents. Your
submission should include a copy of the original questions and your typed answers, doublespaced.
 Late assignments will not be accepted.
 Quizzes will be announced one class period in advance. No make-up quizzes will be given.
 No allowance for missed exams will be given without prior consent from the instructor or
a physician’s note.
Expectations of Professionalism
 The student is present for class, arriving on time.
 The student completes and participates in discussion of the homework assignments.
 The student demonstrates flexibility in changes to the schedule or syllabus.
 The student communicates with the instructor and peers in a constructive manner.
 The student demonstrates a commitment to learning.
 The student refrains from using cell phones during class.
Important Dates
 3/18– 3/25 – spring break
 4/13 – last day to withdraw with a “W”
 5/14 – last day of class
 5/17 (Thursday) 10:15-12:15 in YR127 - final exam
EVALUATION
exam 1
exam 2
cumulative final exam
quiz / homework average
reading reflections
total
25%
25%
20%
15%
15%
100%
Final Grade Cut-Offs
(minimal percentage needed)
A
AB+
B
B-
93%
90%
87%
83%
80%
C+
C
CD
77%
73%
70%
60%
ACADEMIC INTEGRITY AND ACCOMMODATION
All students are expected to adhere to the Towson University Student Academic Integrity Policy, which can be
accessed at http://www.towson.edu/provost/resources/studentacademic.asp. Cheating or plagiarism in any form is
unacceptable and failure to abide by the Student Academic Integrity Policy may result in the grade of F for the course.
If you have a documented disability and wish to discuss academic accommodations, please contact me as soon as
possible.
Towson University
4 of 5
2011 Interstate Teacher Assessment and Support Consortium (InTASC) Model Core Teaching
Standards /
COE Assessed INTASC Professional Practice Standards
1
Learner Development
The teacher understands how learners grow and develop, recognizing that patterns of learning and
development vary individually within and across the cognitive, linguistic, social, emotional, and
physical areas, and designs and implements developmentally appropriate and challenging learning
experiences.
2
Learning Differences
The teacher uses understanding of individual differences and diverse cultures and communities to
ensure inclusive learning environments that enable each learner to meet high standards.
3
Learning Environments
The teacher works with others (learners, families, colleagues) to create effective learning
environments that support individual and collaborative learning, and that encourage positive social
interaction, active engagement in learning, and self motivation.
4
Content Knowledge
The teacher understands the central concepts, tools of inquiry, and structures of the discipline(s) he
or she teaches and creates learning experiences that make these aspects of the discipline accessible
and meaningful for learners to assure mastery of the content. .
5
Application of Content
The teacher understands how to connect concepts and use differing perspectives to engage learners
in critical thinking, creativity, and collaborative problem solving related to authentic local and global
issues.
6
Assessment to Prove and Improve Student Learning*
The teacher understands and uses multiple methods of formative and summative assessment to
engage learners in their own growth, to monitor learner progress, and to guide the teacher’s and
learner’s decision making.
7
Planning for Instruction
The teacher plans instruction that supports every student in meeting rigorous learning goals by
drawing upon knowledge of content, curriculum, cross-disciplinary skills, and pedagogy, as well as
knowledge of learners and the community context.
8
Instructional Strategies
The teacher understands and uses a variety of instructional strategies to encourage learners to
develop deep understanding of content areas and their connections, and to build skills to apply
knowledge in meaningful ways.
9
Professional Learning and Ethical Practice
The teacher engages in ongoing professional learning and uses evidence to continually evaluate
his/her practice, particularly the effects of his/her choices and actions on others (learners, families,
other professionals, and the community), and adapts practice to meet the needs of each learner.
10
Leadership and Collaboration
The teacher seeks appropriate leadership roles and opportunities to take responsibility for student
learning, to collaborate with learners, families, colleagues, other school professionals (including
resource personnel), and community members to ensure learner growth, and to advance the
profession.
11
Use of Technology
The teacher views technology not as an end in itself, but as a tool for learning and communication,
integrating its use in all facets of professional practice, and for adapting instruction to meet the needs
of each learner.
Towson University
5 of 5