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Math 1: Statistics**
 
Course Description
    

This on-line course is designed to help teachers with the descriptive statistics content required in the WV Math I curriculum. After completion of this course, teachers should have activities and additional resources needed to properly teach the statistics unit. Participants will review mathematical content, practice instructional strategies and use some lessons from the Teach 21 unit available for this course.

** Participants must hold certification through Algebra I and be seeking Math I Authorization or participants must be working toward an alternative route to certification in Mathematics as a certified special education teacher seeking to become highly qualified.
 
Course Syllabus
    

 

Overview

This on-line course is designed to help teachers with the descriptive statistics content required in the WV Math I curriculum. After completion of this course, teachers should have activities and additional resources needed to properly teach the statistics unit. Participants will review mathematical content, practice instructional strategies and use some lessons from the Teach 21 unit available for this course.

By the end of this course, participants will:
  • represent data with plots on the real number line.
  • use statistics appropriate to the shape of the data distribution to compare center.
  • interpret differences in shape, center and spread in the context of the data sets, accounting for possible effects of extreme data points.
  • investigate the learning progression for statistics.
  • view and create histograms.
  • calculate standard deviation.
  • examine the normal distribution and its properties.
  • explore limits of sequences by using graphs of discrete functions.
  • summarize categorical data for two categories in two-way frequency tables.
  • interpret relative frequencies in the content of the data (including joint, marginal, and conditional relative frequencies).
  • recognize possible associations and trends in the data.
  • represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • fit a linear function to given data.
  • use functions fitted to data to solve problems in the context of the data.
  • interpret the slope (rate of change) and y-intercept (constant term) of a linear model in the context of the data.
  • compute (using technology) and interpret the correlation coefficient of a linear fit.
  • represent data on two quantitative variables on a scatter plot and describe how the variables are related.
  • fit an exponential function to the data.
  • use exponential functions fitted to data to solve problems in the context of the data.
  • showcase and discuss student work from selected course activities.
  • create a student assessment for Math I Statistics.
Course Organization
This course includes several different activity components, all of which are described below. During each session, you will participate in a unique collection of these activity components, depending on the particular focus of that session.

Read
When you see this icon you will be reading relevant articles, resources, and instructional materials that will help inform your online course development process.

Activities
When you see this icon you will be completing activity-based curriculum and inputting various components of your course content into course project.

Discuss
When you see this icon you will be using the online discussion board to share ideas, resources, and thoughtful conversation with your fellow course participants and facilitator.
Prerequisites

This course is designed for High School Math 1 teachers.

High School Mathematics I Course Description (graphic)
The fundamental purpose of Mathematics I is to formalize and extend the mathematics that students learned in the middle grades. The critical areas, organized into units, deepen and extend understanding of linear relationships, in part by contrasting them with exponential phenomena, and in part by applying linear models to data that exhibit a linear trend. Mathematics 1 uses properties and theorems involving congruent figures to deepen and extend understanding of geometric knowledge from prior grades. The final unit in the course ties together the algebraic and geometric ideas studied. The Mathematical Practice Standards apply throughout each course and, together with the content standards, prescribe that students experience mathematics as a coherent, useful, and logical subject that makes use of their ability to make sense of problem situations.

Although not a requirement, high speed Internet access definitely enhances the online experience. Participants should be proficient with using email, browsing the Internet and navigating through computer files. Access to Microsoft Office is recommended. Participants who do not have Microsoft Office should click here for some available options.
Prior to Session One course participants at to secure:
1. a WVDE WebTop account.
2. a SAS Curriculum Pathways teacher account.
3. the SAS Curriculum Pathways school account for students.
4. graphing calculators, TI-84 or TI-Inspire, for student and teacher use. Online graphing calculator information is provided within the Session One readings/resource section.
5. a scanner for scanning course assignments to be uploaded to the course drop box.

Format and Requirements
This workshop is divided into six one-week sessions which each include readings, activities, and an online discussion among workshop participants. The time necessary to complete each session is estimated to be seven to eight hours.

The outline for the workshop is as follows:
Session One Measures of Central Tendency and Graphic Representations
Session Two Histograms, Standard Deviation and the Normal Distribution
Session Three Categorical Data
Session Four Fitting Data with Linear Functions
Session Five Fitting Data with Exponential Functions
Session Six Connect, Reflect and Assess
Session One: Measures of Central Tendency and Graphic Representations
Students will have studied measures of center and graphic representations in middle school. This session reviews the content that is included in the middle school, as well as extends the material by using these measures and graphic representations to further describe and understand the data in real-life applications. Course participants will investigate the statistics standards and explore their importance.

Session Two: Histograms, Standard Deviation and the Normal Distribution
Participants will use and create histograms based on real world data. Participants will apply sequences and series in an activity with standard deviation. Participants will also examine normally distributed data, calculate standard deviation, and answer questions about the data based on their calculations.

Session Three: Categorical Data
Participants will summarize, represent, and interpret data for two categorical variables. They will read about quantitative versus numerical data and two-way tables before completing activities organizing and analyzing categorical data. Participants will use the proper vocabulary related to two-way tables.

Session Four: Fitting Data with Linear Functions
High school Math I students should be very comfortable with linear functions and will extend this knowledge to use of scatterplots to find relationships between quantities. Participants will use linear regression to fit a function to given data, and interpret attributes of a graph based on the context of the situation. They will become familiar with the usefulness of the correlation coefficient and residuals to analyze the goodness of fit for a regression equation.

Session Five: Fitting Data with Exponential Functions

Students in Math I will focus on functions that are both linear and exponential. Participants will examine multiple representations of exponential functions and fit exponential functions to real world data. The readings and activities highlight various applications that can be modeled with exponential functions.

Session Six: Connect, Reflect and Assess
Participants will make connections among the different Math I credential courses and sessions within those courses with the development of a Math 1 portfolio and comprehensive student assessment/solution key with work.

Assessment

Workshop participants will complete an orientation and then six weekly workshop sessions that include readings, activities, and online discussions. There will be a pre-workshop survey and a post-workshop survey. In addition, participants will incrementally develop a Math I portfolio components throughout the duration of the course. The time for completing each session is estimated to be six to seven hours weekly.

Math 1 Portfolio:
Course participants will choose three activities to use in their classroom from those suggested throughout this Math I Functions course. The activities must be from three different sessions throughout Math I Functions. Portfolio items are to be selected from the following course activities:

Session One-Activity 3:
Teach 21 Math 1 Unit 4 Lesson 2 Graphic Representations (complete the entire lesson)

Session Two-Activity 3:
Teach 21 Math 1 Unit 4 Lesson 3 Normal Distribution (complete the entire lesson)

Session Three-Activity 3:
Teach 21 Math 1 Unit 4 Lesson 4 Two-Way Street Activity

Session Four-Activity 1:
Teach 21 Math 1 Unit 4 Lesson 6 Does That Data Fit, Regression Worksheet #1

Session Five-Activity 2:
SAS Curriculum Pathways Pathways Quick Launch #294 The AIDS Epidemic

Session Five-Activity 3:
National Debt and War Activity

Complete the following for each activity to be submitted to your portfolio:

  • Submit two samples of your students’ work that show different levels of understanding.
  • Explain why you selected each sample of student work and describe the level of understanding demonstrated by each student.
  • Discuss how this particular lesson or activity has helped develop your students’ understanding of the mathematics involved.

A total of six student samples are to be included your portfolio for Math I Functions.
 

Culminating Assessment:
Course participants will create a Math 1 Functions culminating assessment for students along with a solution key, complete with all work. This assessment may be used with Math I students to evaluate their conceptual understanding of the Next Generation CSO’s that were targeted in this course. Categories and indicators from the Student Assessment Rubric are to be used to guide the development of the Math 1 Functions culminating assessment for students.

Self-Assessment of the Culminating Assessment for Students:
Course participants will complete a self-assessment of their Math 1 Functions student assessment using the Student Assessment Rubric.

Discussion Participation
Participants will be evaluated on the frequency and quality of their participation in the discussion forum. Participants are required to post a minimum of one substantial original posting each session reflecting on the question for that session. They are to read all original postings made by the other workshop participants and reply thoughtfully to at least two of them per session. Participants’ original postings will be evaluated on their relevance, demonstrated understanding of workshop concepts, examples cited, and overall quality. Postings that respond to other participants will be evaluated on relevance, degree to which they extend the discussion, and tone.

Certificate of Completion
Upon successful completion of this course, Math 1 Functions, and the successful panel portfolio review participants will receive a Certificate of Completion documenting successful completion of the course requirements.
Non-Degree Graduate Credit Information

Participants in this course are eligible to receive non-degree graduate credits from either West Virginia University, Marshall University or Concord University. Credits will be awarded at the end of the semester in which the course occurs. Additional information is available on the course News/Welcome Page.

Content and Technology Standards

This workshop, Math 1 Functions, will help participants meet the ISTE Educational Technology Standards and Performance Indicators for All Teachers (http://edtechleaders.org/documents/NETSAdminTeachers.pdf), especially Standards II, III, IV, and V. For more information about Technology Integration visit: http://www.iste.org

In addition, participants will identify specific WV Content Standards and Objectives (http://wvde.state.wv.us/csos/) as they engage in course content.

About this Course

This workshop was developed for the West Virginia Department of Education (http://wvde.state.wv.us). Original design (before format modifications) by EdTech Leaders Online (http://www.edtechleaders.org), a project of Education Development Center, Inc, © 2007. All rights reserved.