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.

Michael Rymer
Associate Director of the SLU Learning Hub

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…

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

Order of Operations


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.

Applying the Order of Operations to Algebra and Statistics


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.

Taking Word Problems and Making them Numerical


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.

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…

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

Visualization of Data


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.

Drawing Inferences from Graphs


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.

Evaluating Data in the Media


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.

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…

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

Populations and Samples


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.

Sampling and Probability


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.

Simulation-based distributions


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.