SOCR Events LAUSD Oct2013
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SOCR News & Events: SOCR blended approach for teaching Probability and statistics for the California Common Core State Standards
Overview
This one-day seminar on statistics and probability will discuss the main subjects incorporated in the mathematics courses for 6th, 7th, and 8th grade based on the California Common Core State Standards for Mathematics. The following topics will be discussed: Data analysis, measures of central and non-central tendency, variation, graphical methods. Inference on population parameters from sample data using simulations to assess variability of the distribution. Axioms of probability, sample space, events, conditional probability, independent events, addition rule, multiplication rule, law of total probability, De Morgan's law. Probability trees and tables to aid the computation of probabilities. Simulations to approximate probabilities. Probability models (binomial, geometric, hypergeometric). Regression analysis. Explore relations between variables through scatterplots. Fit a straight line to data, compute intercept and slope of the line, interpretation of the slope. Measure of the strength of the association using the sample correlation coefficient.
Background
The Statistics Online Computational Resource (SOCR) designs, validates and freely disseminates knowledge. Specifically, SOCR provides portable online aids for probability, statistics and mathematics education, technology based instruction and statistical computing. SOCR tools and resources include a repository of interactive applets, computational and graphing tools, instructional and course materials.
The California Common Core State Standards (CCSS) describe the K-12 knowledge of California pupils by subject and grade. In California, the State Board of Education decides on the standards for all students, from kindergarten through high school.
The LAUSD Mathematics Instructional Guide (MIG) promotes a balanced and designed mathematics curriculum for students as part of a coherent educational system. The Los Angeles Unified School District's (LAUSD) vision is to provide its students with:
- A designed curriculum based on the Mathematics Content Standards for California Public Schools and the Mathematics Framework for California Public Schools.
- A balanced curriculum that teaches computational and procedural skills; conceptual understanding of mathematics; and problem solving.
Presenters
- Nicolas Christou, UCLA Statistics
- Albert Wong, UCLA Statistics
- Ivo Dinov, UCLA and University of Michigan
Advantages of the SOCR IT-Enhanced Blended Instruction Resources
The SOCR technology-enhanced blended instruction model to K-12 science-education has the following advantages:
- Multi-lingual support: All materials are auto-translated into 24 different languages;
- CCSS support: The SOCR learning materials, tools and activities are community-built and cover most of the mathematics and statistics components of the CCSS standard;
- Open-access: All SOCR resources are always freely and openly accessible to all (students, teachers and the community) and can be customized for specific curricular needs (e.g., K12HSN Calaxy network);
- Blended Instructional Model: the SOCR learning resources blend information technology, open-datasets, scientific techniques and modern pedagogical concepts.
California Common Core State Standards (CCSS)
- General California Common Core State Standards
- Mathematics CCSS Standards
- Probability and Statistics (Grades 6-8)
- Summarize and describe distributions: Relating the choice of measures of center and variability to the shape of the data distribution and the context in which the data were gathered (e.g., Coin-Sample Experiment (Java and JavaScript).
- Use random sampling to draw inferences about a population (e.g., Discrete Uniform Simulation).
- Draw informal comparative inferences about two populations (e.g., Binomial Coin with varying p=P(Head)).
- Investigate chance processes and develop, use, and evaluate probability models.
- Investigate patterns of association in bivariate data (e.g., Interactive Scatter plot).
- Probability and Statistics (Grades 9-12)
- Interpreting Categorical & Quantitative Data (e.g., Mendel's Pea Experiment)
- Making Inferences & Justifying Conclusions (e.g., Gender of Siblings Example)
- Conditional Probability & the Rules of Probability (e.g., Type and location of cancer example)
- Using Probability to Make Decisions (e.g., Monte Hall Problem/Demo)
- Probability and Statistics (Grades 6-8)
- Mathematics CCSS Standards
SOCR Professional Development Activities
SOCR faculty, students and fellows regularly conduct onsite and remote continuing education training sessions and participate in local and National educational workshops. The future, current and past training activities are listed on the SOCR News website.
SOCR Demonstrations
- Java Applets (analyses, distributions, games, experiments, charts/plots, data-modeler)
- HTML5/JavaScript webapps (mobile devices)
- Interactive Learning Activities
- Datasets
Additional Resources
Exemplary SOCR Resources
- The complete SOCR Teaching Statistics with Technology EBook is freely available in PDF format from the following digital libraries:
- SOCR AP Statistics Resources
- SOCR Online Probability and Statistics EBook
Probability and Statistics CCSS
- Grades 8-12: Mathematics Content Standards: This discipline is an introduction to the study of probability, interpretation of data, and fundamental statistical problem solving. Mastery of this academic content will provide students with a solid foundation in probability and facility in processing statistical information.
- 1.0 Students know the definition of the notion of independent events and can use the rules for addition, multiplication, and complementation to solve for probabilities of particular events in finite sample spaces.
- 2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
- 3.0 Students demonstrate an understanding of the notion of discrete random variables by using them to solve for the probabilities of outcomes, such as the probability of the occurrence of five heads in 14 coin tosses.
- 4.0 Students are familiar with the standard distributions (normal, binomial, and exponential) and can use them to solve for events in problems in which the distribution belongs to those families.
- 5.0 Students determine the mean and the standard deviation of a normally distributed random variable.
- 6.0 Students know the definitions of the mean, median, and mode of a distribution of data and can compute each in particular situations.
- 7.0 Students compute the variance and the standard deviation of a distribution of data.
- 8.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
Advanced Placement (AP) Probability and Statistics
- Grades 8-12: Mathematics Content Standards: This discipline is a technical and in-depth extension of probability and statistics. In particular, mastery of academic content for advanced placement gives students the background to succeed in the Advanced Placement examination in the subject.
- 1.0 Students solve probability problems with finite sample spaces by using the rules for addition, multiplication, and complementation for probability distributions and understand the simplifications that arise with independent events.
- 2.0 Students know the definition of conditional probability and use it to solve for probabilities in finite sample spaces.
- 3.0 Students demonstrate an understanding of the notion of discrete random variables by using this concept to solve for the probabilities of outcomes, such as the probability of the occurrence of five or fewer heads in 14 coin tosses.
- 4.0 Students understand the notion of a continuous random variable and can interpret the probability of an outcome as the area of a region under the graph of the probability density function associated with the random variable.
- 5.0 Students know the definition of the mean of a discrete random variable and can determine the mean for a particular discrete random variable.
- 6.0 Students know the definition of the variance of a discrete random variable and can determine the variance for a particular discrete random variable.
- 7.0 Students demonstrate an understanding of the standard distributions (normal, binomial, and exponential) and can use the distributions to solve for events in problems in which the distribution belongs to those families.
- 8.0 Students determine the mean and the standard deviation of a normally distributed random variable.
- 9.0 Students know the central limit theorem and can use it to obtain approximations for probabilities in problems of finite sample spaces in which the probabilities are binomially distributed .
- 10.0 Students know the definitions of the mean, median, and mode of distribution of data and can compute each of them in particular situations.
- 11.0 Students compute the variance and the standard deviation of a distribution of data.
- 12.0 Students find the line of best fit to a given distribution of data by using least squares regression.
- 13.0 Students know what the correlation coefficient of two variables means and are familiar with the coefficient's properties.
- 14.0 Students organize and describe distributions of data by using a number of different methods, including frequency tables, histograms, standard line graphs and bar graphs, stem-and-leaf displays, scatterplots, and box-and-whisker plots.
- 15.0 Students are familiar with the notions of a statistic of a distribution of values, of the sampling distribution of a statistic, and of the variability of a statistic.
- 16.0 Students know basic facts concerning the relation between the mean and the standard deviation of a sampling distribution and the mean and the standard deviation of the population distribution.
- 17.0 Students determine confidence intervals for a simple random sample from a normal distribution of data and determine the sample size required for a desired margin of error.
- 18.0 Students determine the P- value for a statistic for a simple random sample from a normal distribution.
- 19.0 Students are familiar with the chi- square distribution and chi- square test and understand their uses.
Supporting materials
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