Welcome to the First Year Seminar in Numeracy! The goal of this course is to help you succeed in the math courses you take at SLU. Over the next three weeks, you will gain the skills you need to draw inferences from data and critically evaluate numerical information you encounter in your everyday life, such as in the media, college-level math courses, and in your future careers.

Contact

Michael Rymer

Associate Director of the SLU Learning Hub

michael.rymer@slu.cuny.edu

Course Overview

This course is three weeks long. Each week will have a subset of objectives, activities, and readings for you to work through. We recommend you start by going over the checklist for the week, reading through the introduction, and working your way through the activities at your own pace. As you go through the readings, take notes of what you think is important.

Additional Support

SLU has a dedicated Quantitative Reasoning Fellow (Grace Flores-Robles) available for tutoring support throughout the semester.

Week One – Algebraic and Numerical Methods

Statistics (like any math courses you will take in college) build off mathematical concepts you encountered in high school. That means, in order to be successful in college math courses, you should have a working knowledge of these concepts. And, you should know how to perform basic mathematical operations in the appropriate order (using “PEMDAS” or “the order of operations”).

The goal of this week is to make sure you meet the requirements for introductory math courses at SLU. First, you will review the order of operations. Then, you will apply these concepts in algebraic problems. Finally, you will learn how to read word problems and represent the information numerically. These concepts set the foundation for statistics, as well as higher-level math courses so it is important that you feel confident in these materials.

After going through the content this week, we recommend that you complete the self-assessment to test your working knowledge of algebra and determine whether you are ready for more advanced math courses. If your self-assessment score is lower than 90%, it is recommended you review the concepts until you feel confident (as algebra is foundational for many college math courses). Note that this is a general review, and there is much more to learn in algebra.

Learning Objectives

By the end of this week, you should be able to…

- Use algebraic and numerical methods to draw accurate conclusions and solve mathematical problems.
- Represent quantitative problems expressed in natural language in a suitable mathematical format.

Order of Operations

Introduction

Sometimes, math problems involve multiple operations (multiplication, addition, etc.). In this lecture, you will learn how to solve math problems with multiple operations in it, and you will learn how to do this in the correct order.

Checklist

- Read the introduction to Order of Operations
- Go through the Order of Operations Lecture Slides
- Complete the Order of Operations practice problems

Learning Objectives

By the end of this lecture, you should be able to:

- Understand the order of operations

Applying the Order of Operations to Algebra and Statistics

Introduction

Now that you’ve reviewed the order of operations, we can begin to apply PEMDAS into more complex problems. Within statistics, the order of operations is most often used in solving summations (for means, standard deviations) and factorials (which you will encounter when you learn about probability). In this lecture, you will practice applying the order of operations within summations and factorials.

Checklist

- Read the introduction to Applying the Order of Operations
- Go through the Applying the Order of Operations Lecture Slides
- Complete the Summations and Factorials practice problems

Learning Objectives

By the end of this lecture, you should be able to:

- Calculate summations
- Compute factorials

Taking Word Problems and Making them Numerical

Introduction

Number-based word problems can be very confusing, and it takes practice to convert them into mathematical equations. In this lecture, you will learn how to convert word problems into numbers. Knowing how to pull quantitative information from word problems is important because you will have to know how to represent hypotheses and research questions in mathematical notation as you move into higher level classes, like statistics.

Checklist

- Read the chapter on Numeric Word Problems
- Complete the “Writing Numeric Word Problems” Worksheet

Learning Objectives

By the end of this lecture, you should be able to:

- Identify your comfortability with sharing personal data on Facebook
- Describe three ethical concerns in data collection

Review

It’s time to review what you’ve learned this week!

Complete the self-assessment and review the answers before moving on to Week 2.

Week Two – Interpret and draw inferences from quantitative representations

Last week, you completed a review of the basic concepts you need for introductory math courses at SLU. This week, you will focus on interpreting real-world data. First, you will learn about best practices in visualizing data – including how to create bar graphs and tables. Then, you will practice interpreting data and drawing inferences from existing graphs. Finally, you will learn how to identify misleading graphs, particularly in the media.

Learning Objectives

By the end of this week, you should be able to…

- Make decisions about the most appropriate ways to visualize a set of data
- Draw appropriate inferences from quantitative representations, such as tables or graphs
- Critically evaluate statistics and data in the media

Visualization of Data

Introduction

Last week, we learned all about mathematical notation. Now, we will begin to plot our data. The types of graphs we use will depend on the kind of information that is available to us. If we are plotting X values, for example, we can use frequency distribution tables (like stem-and-leaf plots). If we are plotting means, bar graphs might be more useful. The goal of this lecture is to help you decide how to best plot your data.

Checklist

- Read introduction to Data Visualization
- Go through the Graphing Data Lecture Slides
- Complete the “Graphing It!” Activity

Learning Objectives

By the end of this lecture, you should be able to:

- Identify methods of graphing qualitative and quantitative data
- Make decisions about the most appropriate ways to visualize a set of data

Drawing Inferences from Graphs

Introduction

Now that you know how to create graphs, you can begin to interpret real-world data. In this activity, you will practice inferring research questions and results from existing graphs.

Checklist

- Read Introduction to Drawing Inferences from Graphs
- Watch the video on reading graphs
- Complete the worksheet on “Reading and Drawing Inferences from Graphs”

Learning Objectives

By the end of this lecture, you should be able to:

- Draw appropriate inferences from quantitative representations, such as tables or graphs

Evaluating Data in the Media

Introduction

Data can help you make informed decisions. However, sometimes data can be manipulated so that what is shown on graphs isn’t the best decision or the “real story”. In this lecture, you will learn how to identify (and improve) misleading graphs so that you can be a critical consumer of data in the media.

Checklist

- Read Introduction to Data in the Media
- Read the article on “Making Sense of Data in the Media”
- Watch the video on “How to Spot a Misleading Graph”
- Complete the Identifying Misleading Graphs Activity

Optional / Supplemental Material

- Read the article on “Misleading Graphs…and How to Fix Them”
- Watch the video on “How Statistics can be Misleading”

Learning Objectives

By the end of this lecture, you should be able to:

- Critically evaluate statistics and data in the media
- Describe the factors that make graphs misleading

Week Three – Basic Statistical Concepts

Welcome to the final week of our course! This week, we will apply the concepts you’ve learned into one course you may take at SLU – Statistics for Social Change. In our discussion of statistics, we will primarily focus on how our samples influence the data we collect. First, you will learn the difference between populations and samples, as well as the types of parameters you can collect for one vs. the other. Then, you will learn about how your sampling methods can bias your results. Finally, you will learn how your data changes as your sample size increases.

Learning Objectives

By the end of this week, you should be able to…

- Identify the basic language and fundamental ideas of statistics
- Apply the fundamental concepts of sampling and probability
- Utilize technology to understand simulation-based distributions

Populations and Samples

Introduction

Now that you have reviewed some basic concepts in algebra, you are ready to begin your introduction to statistics!

The goal of this lecture is to introduce you to basic statistical concepts. You will learn the definition of variables, learn to differentiate between populations and samples, and review mathematical notation. There will be learning checks throughout the lecture and another self-assessment to help you test your knowledge before moving forward with more advanced statistical concepts.

Checklist

- Read the introduction to Statistical Concepts
- Go through the Populations and Samples Lecture Slides
- Complete the Identifying Populations and Samples Worksheet

Learning Objectives

By the end of this lecture, you should be able to:

- Distinguish between a population and a sample
- Distinguish between a parameter and a statistic
- Read scientific notation

Sampling and Probability

Introduction

This week, we are taking a step back to look at how data are actually collected. You will learn about several sampling techniques and will apply these techniques in context. For example, you’ll learn why polls are beneficial and why sometimes polling results are wrong (think back to the 2016 Presidential Election for one case in point). In short, the goal of this lecture is to help you think critically about how your data are being collected and what we can infer from them.

Checklist

- Read introduction to Sampling and Probability
- Go through Sampling Methods Lecture Slides
- Watch Polling Video

Learning Objectives

By the end of this lecture, you should be able to:

- Identify probability and non-probability sampling methods

Work

- Lecture Slides – Sampling Methods
- Video – Public Opinion Polls After watching this video, you should be able to answer the following questions:
- What are three ways a sample can be bad (which in turn can make your polls wrong)?
- How can interviewers affect the outcome of polls?

Simulation-based distributions

Introduction

If you were to repeatedly take multiple samples from your population, they wouldn’t all look the same. In this activity, you will create sampling distributions (i.e., plots of your sample means) to see how different samples compare to one another. You will also learn how sample size and standard error influence the distribution of sample means.

Checklist

- Read introduction to Simulation-based Distributions
- Go through Sampling Distribution Slides
- Complete the “Sampling Distribution” Lab

Learning Objectives

By the end of this lecture, you should be able to:

- Define distribution of sampling means
- Describe distribution by shape, expected value, and standard error
- Describe location of sample mean
*M*by*z*-score - Determine probabilities corresponding to sample means using
*z*-scores, unit normal table

Course Conclusion

You made it through the First Year Seminar in Numeracy! Our goal in this course was to help you succeed in the math courses you take at SLU. Over the last three weeks, you reviewed the basics of algebra, you learned how to interpret data in graphs and in the media, and you built a foundational knowledge of statistics. We hope that this course has helped increase your confidence in mathematics and has prepared you for your upcoming math courses at SLU.