Math 102 "Pathway to Statistics"  selected elements from official Course Outline of Record
College of the Redwoods
College of the Redwoods

Math 102 Pathway to Statistics – from Course Outline 09.26.14
Catalog Description
A course designed to be a nontraditional, accelerated pathway to transferlevel statistics. Topics in algebra, data analysis and critical thinking skills relevant for success in statistics are the focus. The learning experience for this course emphasizes active learning via collaborative work. This course is designed for students who plan to major in fields such as biology, social sciences, nursing, art, and English, and not for students pursuing degrees in math, enginering (sic), computer science, business or economics.
Course Learning Outcomes
Course Objectives
Method of Instruction
The primary method of instruction for this course will be group activities. Generally, each activity will be introduced via a brief lecture to set the stage, then students will work in groups to achieve course learning objectives #1 and #3. This method of instruction is based on the idea that deep understanding comes through productive struggle and that students learn efficently (sic) by working together in groups. To facilitate acquisition of course learning objectives #2 and #3, the instruction will follow the model of "just in time remediation" through mini lectures, group activities and individualized instruction via oneonone tutoring in class. To further achieve all three course learning outcomes active learning methods will be utilized such as instructorled demonstrations, class discussion, guideddiscovery, use of manipulatives, and interactive computerbased instruction.
Course Content
Concepts
Issues
THEMES
1. Groupbased inquiry through lowstakes collaborative learning.
2. Conceptual understanding as opposed to rote memorization and procedure.
3. Developing statistical intuition.
Math 102 Course Outline SKILLS
1. Graphing/exploratory data analysis:
2. Numerical reasoning:
3. Algebraic reasoning:
4. Basic principles of study design:
5. Mathematical models:
6. Probability
REPRESENTATIVE LEARNING ACTIVITIES
1. Engaging in classroom discussion will facilitate student learning with regard to course learning outcomes #1 and #3 since these outcomes involve interpretation and communication.
2. Participating in group activities will facilitate student learning with regard to all three course learning outcomes based on the idea that active learning is an effective way to keep students engaged.
3. Participating in inclass assignments will help students achieve all three leaning outcomes through practice and evaluation of each other's work.
4. Making meaningful inquiries will aid students in aquiring all three learning outcomes by surfacing confusion giving the instructor information that can then be used to redirect and deepen the students' understanding.
Representative Assessment Tasks
1. Assignments that offer an opportunity to express mathematical concepts in writing.
2. Quizzes.
3. Group projects or other inclass activities.
4. Portfolios.
5. Individual projects.
Required Assessments
1. Homework assignments.
2. At least 8 cooperative learning acitivities.
3. At least 2 major cooperative projects.
Catalog Description
A course designed to be a nontraditional, accelerated pathway to transferlevel statistics. Topics in algebra, data analysis and critical thinking skills relevant for success in statistics are the focus. The learning experience for this course emphasizes active learning via collaborative work. This course is designed for students who plan to major in fields such as biology, social sciences, nursing, art, and English, and not for students pursuing degrees in math, enginering (sic), computer science, business or economics.
Course Learning Outcomes
 Formulate questions that can be addressed with data, then organize, display, and analyze relevant data to answer these questions and communicate results.
 Use the properties of algebra to simplify expressions, solve equations and answer questions in context.
 Construct, use, and interpret mathematical models, specifically linear and exponential functions, to represent relationships in quantitative data.
Course Objectives
 Prepare students for success in transferlevel statistics.
 Teach students effective learning strategies for success in college.
Method of Instruction
The primary method of instruction for this course will be group activities. Generally, each activity will be introduced via a brief lecture to set the stage, then students will work in groups to achieve course learning objectives #1 and #3. This method of instruction is based on the idea that deep understanding comes through productive struggle and that students learn efficently (sic) by working together in groups. To facilitate acquisition of course learning objectives #2 and #3, the instruction will follow the model of "just in time remediation" through mini lectures, group activities and individualized instruction via oneonone tutoring in class. To further achieve all three course learning outcomes active learning methods will be utilized such as instructorled demonstrations, class discussion, guideddiscovery, use of manipulatives, and interactive computerbased instruction.
Course Content
Concepts
 Graphs of distributions of categorical data: bar charts and pie charts. Graphs of univariate distributions of quantitative data: histograms, stemandleaf plots, boxplots; graphs of linear, exponential, and logarithmic functions.
 Contingency tables: marginal and conditional distributions.
 Measures of center and associated measures of spread and position: mean, variance, standard deviation; median, quartiles, percentiles.
 Computing with and interpreting fractions, decimals, percents, signed numbers as they relate to statistical formulas and concepts.
 Graphing fractions, decimals, and signed numbers on a number line.
 Evaluating expressions using the order of operations.
 Graphs and models for bivariate distributions of quantitative variables, including leastsquares regression using linear and exponential models, transforming exponential into linear models using logarithms and logarithmic scales, along with using the correlation coefficient (r) as a measures of strength and spread in linear regression.
 Data production.
 Developing effective learning skills.
Issues
 The connection between statistics, science, and the real world.
 The necessity of productive struggle to develop understanding.
 A student's adaptation from passive to active learning.
 The development of writing skills necessary to communicate statistical meanings.
THEMES
1. Groupbased inquiry through lowstakes collaborative learning.
2. Conceptual understanding as opposed to rote memorization and procedure.
3. Developing statistical intuition.
Math 102 Course Outline SKILLS
1. Graphing/exploratory data analysis:
 graphically represent the distribution of categorical and quantitative data;
 use graphical representations to investigate patterns and trends in data;
 compare different graphical representations of the same data and evaluate how well each representation shows important aspects of the data;
 compare related data sets using numerical measures and appropriate graphical representations and communicate findings in the context of the data;
 Investigate relationships in bivariate quantitative data, display a scatterplot, describe its shape, and determine regression coefficients, regression equations, and correlation coefficients using technological tools and communicate findings in the context of the data;
 set up twoway tables for bivariate categorical data and use appropriate marginal and conditional percents to investigate relationships and answer questions;
 interpret graphs and tables in the context of a publication.
2. Numerical reasoning:
 understand the placevalue structure of the baseten number system and be able to represent and compare rational numbers (including negative rationals) in decimal form and find their approximate location on a number line;
 recognize, generate, and fluently use equivalent forms of fractions, decimals, and percents;
 identify, compare, and explain the contextual meaning of fractions that represent the marginal distribution of a single categorical variable;
 identify, compare, and explain the contextual meaning of fractions that represent the relationship of two categorical variables in a conditional distribution.
3. Algebraic reasoning:
 understand the concept of a variable and the concept of a function, and interpret functions as communicating relationships between variables;
 recognize the difference between variables and parameters in general forms of linear and exponential models (e.g. in y = mx + b, x and y are variables, but m and b are parameters that define a specific line);
 identify relationships that are proportional, define the constant of proportionality in the context of the problem, and use proportional reasoning to solve problems;
 relate proportionality to linearity (y=kx) and also to the concept of slope ;
 identify functions as linear or exponential and contrast their properties by relating their symbolic form to verbal descriptions, tables of values, and graphs;
 use the order of operations to evaluate statistical formulas by hand and with technology;
 describe a statistical measure (e.g. mean, variance, standard deviation, correlation coefficient) and its characteristics by referencing its symbolic form.
4. Basic principles of study design:
 the purpose of randomization in the design of experiments;
 explanatory, response, and confounding variables;
 simple random sampling;
 statistical bias;
 bias due to undercoverage, nonresponse, interviewer behavior or characteristics, question wording, or aspects of the survey that influence responders;
 difference between correlation and causation and the connection of these concepts to observational studies and random, controlled experiments.
5. Mathematical models:
 identify trends in bivariate quantitative data and determine the class or classes of functions (linear, exponential, or none of these) that could reasonably model the data;
 define variables in a context using appropriate units;
 use linear regression on x, y or x, log(y) to find an appropriate linear and exponential models;
 analyze model assumptions about how one variable changes with respect to the other;
 draw reasonable conclusions about a situation being modeled;
 interpret the correlation coefficient as a measure of spread of data about the least squares regression line;
 interpret the square of the correlation as the percent of variation in y (or log(y)) that can be explained by x;
 explain the difference between causation and correlation and identify the confusion of these concepts as a fallacy.
6. Probability
 Relative frequency interpretation;
 Simulation;
 Probability Distributions (Binomial, Normal).
REPRESENTATIVE LEARNING ACTIVITIES
1. Engaging in classroom discussion will facilitate student learning with regard to course learning outcomes #1 and #3 since these outcomes involve interpretation and communication.
2. Participating in group activities will facilitate student learning with regard to all three course learning outcomes based on the idea that active learning is an effective way to keep students engaged.
3. Participating in inclass assignments will help students achieve all three leaning outcomes through practice and evaluation of each other's work.
4. Making meaningful inquiries will aid students in aquiring all three learning outcomes by surfacing confusion giving the instructor information that can then be used to redirect and deepen the students' understanding.
Representative Assessment Tasks
1. Assignments that offer an opportunity to express mathematical concepts in writing.
2. Quizzes.
3. Group projects or other inclass activities.
4. Portfolios.
5. Individual projects.
Required Assessments
1. Homework assignments.
2. At least 8 cooperative learning acitivities.
3. At least 2 major cooperative projects.