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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. 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