# Algebra level symbolic math

• ### General Central Limit Theorem (CLT) Activity

This activity represents a very general demonstration of the effects of the Central Limit Theorem (CLT). The activity is based on the SOCR Sampling Distribution CLT Experiment. This experiment builds upon a RVLS CLT applet (http://www.ruf.rice.edu/~lane/stat_sim/sampling_dist/) by extending the applet functionality and providing the capability of sampling from any SOCR Distribution. Goals of this activity: provide intuitive notion of sampling from any process with a well-defined distribution; motivate and facilitate learning of the central limit theorem; empirically validate that sample-averages of random observations (most processes) follow approximately normal distribution; empirically demonstrate that the sample-average is special and other sample statistics (e.g., median, variance, range, etc.) generally do not have distributions that are normal; illustrate that the expectation of the sample-average equals the population mean (and the sample-average is typically a good measure of centrality for a population/process); show that the variation of the sample average rapidly decreases as the sample size increases.
• ### Instructors Notes for the t-distribution activity

The t-distribution activity is a student-based in-class activity to illustrate the conceptual reason for the t-distribution. Students use TI-83/84 calculators to conduct a simulation of random samples. The students calculate standard scores with both the population standard deviation and the sample standard deviation. The resulting values are pooled over the entire class to give the simulation a reasonable number of iterations. This document provides the instructor with learning objectives, context, mechanics, follow-up, and evidence from use associated with the in-class activity.
• ### Categorical Data Activity

This activity will allow students to familiarize themselves with technology and its use in calculating marginal, conditional, and joint distributions, as well as making conclusions from these tabular and graphical displays. The corresponding data set 'Pizza Data' is located at the following web address: http://www.causeweb.org/repository/ACT/PIZZA.TXT
• ### Introduction to Experiments Activity

This activity will allow students to learn the difference between observational studies and experiments, with emphasis on the importance of cause-and-effect relationships. The activity will also familiarize students with key terms such as factors, treatments, retrospective and prospective studies, etc.
• ### Inference for Proportions Activity

This activity provides practice for constructing confidence intervals and performing hypothesis tests. In addition, it stresses interpretation of confidence intervals and comparison and application of results in context.
• ### Regression Activity

This activity focuses on basic ideas of linear regression. It covers creating scatterplots from data, describing the association between two variables, and correlation as a measure of linear association. After this activity students will have the knowledge to create output that yields R-square, the slope and intercept, as well as their interpretations. This activity also covers some of the basics about residual analysis and the fit of the linear regression model in certain settings. The corresponding data set for this activity, 'BAC data', can be found at the following web address: http://www.causeweb.org/repository/ACT/BAC.txt

• ### Sample Survey Activity

This activity stresses the importance of writing clear, unbiased survey questions. It explore the types of bias present in surveys and ways to reduce these biases. In addition, the activity covers some basics of surveys: population, sample, sampling frame, and sampling method.
• ### Statistics Before Your Eyes

This site presents several photographs from real life that demonstrate natural statistical concepts. Each picture shows a statistical distribution made by some pattern occuring in everyday life. An explanation of each picture tells what distribution is being represented and how.
• ### Using Statistics Effectively in Mathematics Education Research

Funded by the National Science Foundation, workshops were held over a three-year period, each with about twenty participants nearly equally divided between mathematics educators and statisticians. In these exchanges the mathematics educators presented honest assessments of the status of mathematics education research (both its strengths and its weaknesses), and the statisticians provided insights into modern statistical methods that could be more widely used in such research. The discussions led to an outline of guidelines for evaluating and reporting mathematics education research, which were molded into the current report. The purpose of the reporting guidelines is to foster the development of a stronger foundation of research in mathematics education, one that will be scientific, cumulative, interconnected, and intertwined with teaching practice. The guidelines are built around a model involving five key components of a high-quality research program: generating ideas, framing those ideas in a research setting, examining the research questions in small studies, generalizing the results in larger and more refined studies, and extending the results over time and location. Any single research project may have only one or two of these components, but such projects should link to others so that a viable research program that will be interconnected and cumulative can be identified and used to effect improvements in both teaching practice and future research. The guidelines provide details that are essential for these linkages to occur. Three appendices provide background material dealing with (a) a model for research in mathematics education in light of a medical model for clinical trials; (b) technical issues of measurement, unit of randomization, experiments vs. observations, and gain scores as they relate to scientifically based research; and (c) critical areas for cooperation between statistics and mathematics education research, including qualitative vs. quantitative research, educating graduate students and keeping mathematics education faculty current in education research, statistics practices and methodologies, and building partnerships and collaboratives.

• ### Data Collection: Quantitative Environmental Learning Project Data Set #50

This dataset contains information on temperature, precipitation, and weather stations for 48 states. The data is available in Excel and rich text formats.