MATH 121: Mathematical Ideas

The Course

The major purpose of this course is to explore mathematics and its uses. This means the actual topics covered vary from professor to professor, but the goals are always the same: let the student see the beauty and utility of mathematics.

Course Catalog Description

This course offers an introduction to the history and concepts of elementary mathematics. Topics may include properties of number systems, geometry, analytic geometry, mathematical modeling, and probability and statistics.

Course Objectives

By the end of this course, you should

1. use Polya’s methods for problem solving;
2. perform operations on sets;
3. illustrate ease with linear, quadratic, exponential, and logarithmic functions;
4. calculate elementary probabilities;
5. model real-world phenomena using mathematics; and
6. use a spreadsheet program (like Microsoft Excel and Google Sheets) to automate calculations.

Required Materials

Textbook:

Kimberly Denley. Viewing Life Mathematically: A Pathway to Quantitative Literacy, second edition. Mount Pleasant, SC: Hawkes Learning System, 2023.
⟨ISBN: 978-1-64277-496-27⟩

Hawkes (HLS):

This course also utilizes the online homework system provided by Hawkes Learning System (HLS). Once at the Hawkes website, you will need to either “Purchase Access” or “Create an Account.” Directions are given there. Make sure you access this soon; it will make your first week much easier. Also, note that there is an option for a couple of weeks of free usage. By the way, I am Ole J. Forsberg, and this is MATH 121-1 at Knox College.

The cost of the online homework is $88.99 (as of 25 February 2022). This may seem expensive, but note that education is an investment in your future… and in the future of the world. If you consider it as such, how does that affect your education and how you view it? When you invest this money, what does that mean about your dedication to your education and learning? It is important that you consider these questions because you are in charge of your education, with the realization that your professor is an expert in the subject matter.

Be Aware:

When you buy access to the online homework, you also receive access to the Denley book. The text also available as a physical entity, if you would like that. Unfortunately, it costs additional money.

Current research suggests that physical books help with learning more than do eBooks. Thus, while the physical textbook costs money, you need to determine if you will gain sufficiently more education from its purchase.

Hawkes Support:

Here is the support page offered by Hawkes. Use this if you are having problems with Hawkes.

Behavioral Expectations

If your question is “What will it take to succeed in this course?” then the answer is “Being a good student.” In my experience, your ability as a student is the greatest predictor of success in courses such as this. Being a good student means that you

1. read and outline the readings before class;
2. make sure your notes make sense to you;
3. summarize your notes using diagrams and figures;
4. ask questions about the readings during class;
5. are an active participant;
6. begin homework as soon as it is assigned;
7. are aware of course deadlines;
8. spend enough time on the material to learn it;
9. study for mastery;
10. are observant;
11. use learning techniques you developed in previous courses; and
12. recognize your limitations and work to strengthen them.

You are responsible for all material covered during the class period and all material in the readings and activities. Feel pressured to ask questions during the class regarding the material, since the material covered during the classes may or may not cover everything that is in the text.

As with most courses at this college, you should be prepared to spend 10 hours per week on the coursework for this class. That includes time in class and time outside class. Since you spend 3 hours and 30 minutes in class, you should be willing to spend 6 hours and 30 minutes outside class in preparing for class, working on homework, reviewing notes, and anything else associated with the course.

Being an A-student is tough. It requires you to be a success as a student. Just because you have received A grades in the past does not mean you are an A student. Being a good student requires a specific set of skills that you may not have. Working on those skills will help will help you in life, since learning is a life-long endeavor.

Key to Success: While this course focuses on mathematics, it actually exists to emphasize your learning. This requires you to realize that college is not about the final grade; it is about preparing you for the future. This means you will be frustrated at times… learn from it. This means you will be struggling at times… figure out how to achieve your goals. This means you will be failing at times… accept that life is tough and that the goal of success requires overcoming barriers.

Academic Integrity ( honor )

Knox College is committed to the maintenance of the highest standards of academic integrity, including ethical conduct, of its citizens. Personally, I strive to maintain this level of ethical behavior and integrity in this course, because it encourages you to understand how to advance humanity at the local level. Should I discover that you participated in a behavior that violates academic integrity (e.g., unauthorized collaboration, plagiarism, cheating on examinations, fabricating information (lying), helping another person cheat, unauthorized advance access to examinations, altering or destroying the work of others, and fraudulently altering academic records), I will sanction you because your actions undercut the value of Knox College and what it offers to its students (you), its alumni (you), and the world (you).

Please read through the Knox College Honor System to familiarize yourself with what constitutes a violation. Ultimately, this has little to do with cheating. It has everything to do with understanding what it actually means to learn. Your personal value has not increased because of your grades. It increased because of your learning. To cheat is to claim two things about yourself and your skills: I am not able to do this; and I am only focused on today and not the future.

Specifically for this class:

• For the Hawkes assignments, I thoroughly encourage (expect) to fully work with others. This allows you to do the assignments together. This does not allow you to just copy what another did.
• For the Chapter Assignments, these must be done entirely by you. I am here to help with these, however.
• In-class activities should be done with others in the class.
• Quizzes must entirely be done by you with absolutely no help beyond your notes (if allowed).
• Examinations must entirely be done by you with absolutely no help (no calculator, notes, people, etc.).

Office of Disability Support Services ( odss )

Knox College abides by Section 504 of the Rehabilitation Act of 1973 which stipulates that no student shall be denied the benefits of an education “solely by reason of a handicap.” Disabilities covered by law include, but are not limited to, learning disabilities, psychological disabilities, health impairments, hearing, and sight or mobility impairments.

If you have a disability that may have some impact on your work in class and for which you may require accommodations, please contact the awesome Stephanie Grimes in the Office of Disability Support Services (ODSS information; office: SMC E-115; email: sgrimes@knox.edu) so that such accommodations may be arranged. Note that the accommodations are not retroactive; I do not make adjustments until ODSS contacts me to let me know what I can do. Furthermore, accommodations need to be reinstated at the start of each term.

Red Room Tutoring ( CTL )

Needing help in college is a positive sign that you are engaging your learning and coursework. And the Center for Teaching and Learning (CTL) wants to help you! The CTL is responsible for the academic support needs of ALL Knox students. Here is some information provided about the CTL tutors this term:

Writing Tutors. If you want help on a paper, no matter the course, you can find writing tutors in the CTL office (466 S. West St.), Monday through Friday, from 10:30 to 4:00pm, and again on Tuesday, Wednesday, and Thursday nights, from 7:00 to 9:00pm. You can also schedule appointments to meet with a writing tutor either online or in person (should you both so desire) by visiting the Center for Teaching and Learning website.

Subject Tutors. Got a kink in your coding or want to test out a solution to that vexing homework problem? You are ready for the Red Room study tables! The Red Room study tables are great resources for students wanting help with virtually any subject, including MATH 121.

There are two Red Room Study Tables: “Red Room” and “Red Room SMC.” Red Room SMC is intended to support classes taught in SMC and is located in the SMC Learning Commons (under the whale), while Red Room is for most other courses and is located in the Red Room on the second floor of Seymour Library. Both study areas are free and open on a walk-in basis from 7:00pm to 9:00pm, on Tuesday, Wednesday, and Thursday nights.

You can also get help from a subject tutor by scheduling an appointment to meet one-on-one with a tutor. These tutors can be reached by visiting the Center for Teaching and Learning website. When scheduling appointments, please be sure to sign up for them no later than 10:00pm the night before you want to get help. In this way, our tutors will have time to adjust their work and schedules and can plan to meet with you.

Specifically, for this class:

• MATH 121 tutoring is held in Red Room SMC.

There are two tutors attached to this class. They are

• Ridham Dholaria
• Nea Schramm

I have had the pleasure of teaching both of these students, and I trust them implicitly. You may want to just go and chat with them about their majors and their research. They are awesome people!

Grading Information

Your grade for this course depends on how well you meet the requirements set forth in the syllabus. The following section provides information about the various grade inputs. All times are Galesburg, IL, time (CT).

Attendance

I expect you to be there for each and every class period. I do not grade attendance. You are responsible for what you miss. If you want a really good way to fail this course, then stop coming.

Key to Success: If you want to succeed, you will be in class “early.” Spend the time before class looking over your notes from the readings you did. This will help you understand what the professor will be talking about in class on that day. Since the slides are available online, you will want to have those downloaded and looked over before class.

Hawkes Learning Assignments ( HLS )

These are assigned for every section we cover in the course. These are found on the Hawkes Learning Systems website. Expect an online assignment for each section we cover in class. These will be due shortly after we finish the chapter in class. These are 10 points for mastering each section.

Because you can work on these until you achieve mastery, there is no legitimate reason for not obtaining 100% on this category. These will tend to be due on the Wednesday following the end of the chapter. However, note that I will accept these with just a 50% penalty until the last day of class, November 14, 2023.

Key to Success: Practice helps one better learn the material. Practice is very important. These online assignments offer that practice. Think of the Hawkes online assignments as being the “entrance requirement” to understanding what we are covering in class. It should not be the goal, only the first step towards the goal.

Hawkes is just the start. Think of it as a key, allowing you to open the door to the discussion. It should not be the goal for you. It should be the first step on your journey to understanding the material… the first step, not the last.

By the way, the sections are assigned. The review at the end of the chapters are worth five points of extra credit each.

Chapter Assignments ( ChA )

The online assignments are awesome for learning/testing small parts of the course. They offer everyone an opportunity to be successful. To encourage a greater cohesion among the many topics we will cover, I include these chapter assignments. These will tend to be due on the Friday following the end of the chapter.

For these, make sure you show and explain your work. Make them look neat. Type these. Un-typed submissions automatically receive a grade of (at most) 50%. If you do not like the grade you received, you may revise and resubmit your original submission. The due date for the revision is one week after the due date for the original. The exception is the last Chapter Assignment. There is no opportunity to revise and resubmit it.

These are 50 points each.

In-Class Quizzes and Other Things

I will infrequently give quizzes in class covering the assigned readings. These will take the first few minutes of the class and be worth some points towards your final grade. These cannot be made up. If you are late, you earn a zero on any quiz that day.

In addition to the quizzes, we will have in-class activities. These are designed to give you practice in applying the mathematics we have covered in this course. If you have continued to study the math, these should be easy. If they are not, then you know you need to study more effectively. Check out the tips and tricks to learning how to study more effectively. It is not always just about studying longer.

Examinations

There will be three examinations in this course. The first, which covers the first two chapters, is worth 50 points. The second, which covers Chapters 5 and 7, is worth 100 points. Finally, the final examination covers the entire course and is worth 100 points.

The dates for the examinations will not change.

Key to Success: You are prepared for an examination when you can do any problem without having to think through the process. An analogy is that you are ready to go to kindergarten when you can tie your shoes without thinking about it. Reflex indicates mastery.

To encourage you to properly study, I will have no review sessions (feel free to drop by my office hours and discuss mathematics, however). When you show up for the examination, you should have already determined what will be on it.

Key to Success: Key to success: Start studying for the final on the first day of classes. Review the current day’s every evening. Review the current week’s each weekend. Keep working with the material. If you are cramming, you are losing. Remember, you should be willing to spend 10 hours a week on this course. That is what it means to be a “full time” student.

Late Assignments

The last day to turn in any assignment is the last day of our class, November 14, 2023. Except for the Hawkes Learning System assignments, I accept no late assignments without an excuse that I find acceptable. Such excuses include varsity sports, deaths, dismemberments, and zombie apocalypses.

Key to Success: To be early is to be on time. Plan ahead. As emergencies can (and do) come up, you should aim to have all assignments completed at least 24 hours before they are due. Such a safety margin allows you to focus on the emergency when it happens, thus reducing the stress in your life.

To help you plan your time, especially the times when the assignments (and examinations) are due, there is this document.

Planned Assignment Calendar

Overall Course Grade

I calculate your percent in the course by adding all of the points you earned during the semester and dividing by the total number of points that you could have earned. This percentage is then used to determine your final letter grade for the course. I do not round.

Should you ask me what your grade is, or what you need on the final to get a _________ (whichever the grade), I will suggest you calculate it for yourself. You should have the skills to do so.

By the way: If you earn at least a 97% in the course and have earned the highest number of points, then you will receive an A+.

Grade Expectations

I fully expect the average for the class to be in the 73 – 77% range. Because of this, the grade of C implies “average” in terms of my experience with student achievement in courses like this throughout the years. As STEM courses require mathematical skills, you should be in the 85 – 100% range in this course if you have life goals of science, medicine, engineering, statistics, mathematics, etc. If you are not in this range, drop by and we can see what needs to be done to get you there!

What it Means to Learn in College

Remember that college is not high school. Strive for a deeper understanding. Bloom’s Taxonomy is helpful here. You may not appreciate it until you do poorly on an examination, but you should be very familiar with it.

Look through it to check the level you were expected to achieve in high school. In college, you need to hit all levels. The higher you get, the better you have mastered the material. For many of you, this is your only chance to master the elementary levels of statistics. Take advantage of me for your edification.

Humankind cannot gain anything without first giving something in return. To obtain, something of equal value must be lost. That is […] the first law of Equivalent Exchange.

Here is a list of the verbs associated with each level. Use them to ensure that you are operating at the college level.

Source: Fractus Learning

Finally, there is an old adage that one never knows more than when teaching. That means you will never understand the material better than when you can teach it to others. You will want to achieve that level. It takes a lot of time, but the activities and labs push you to achieve the higher levels of mastery. Take advantage of them; you are paying for them.

Life tests you first, then gives you the lesson.

Suggestions on Learning in College

Here are three videos that will help you better understand what it means to be a successful adult (college student). They encourage you to think about thinking. “Blowing these off” shows either that you do not care about mastery or that you think I do not know what I am doing.

• Scientifically Proven Best Ways to Study. What is it makes learning more effective? This video looks at some scientifically-proven methods. Some methods are obvious (exercise and avoiding cramming) others may be surprising (testing and sleeping).
  
  Link: Scientifically Proven Best Ways to Study
  [5:38]
• Marty Lobdell. If you spend hours and hours of studying, without improving your grades, or information retention, then learn how to study smart by Marty Lobdell. Lobdell taught Psychology at Pierce College in Washington State for 40 years. During Lobdell’s career, he has taught tens of thousands of students and he wants students to succeed. After watching students cram for eight hours or more for a test without any improvement, Lobdell has developed a studying technique that helps the brain retain the information that you are studying in this video.
  
  Link: Study Less, Study Smart
  [59:56]
• Matt Walker. Sleep is your life-support system and Mother Nature’s best effort yet at immortality, says sleep scientist Matt Walker. In this deep dive into the science of slumber, Walker shares the wonderfully good things that happen when you get sleep — and the alarmingly bad things that happen when you don’t, for both your brain and body. Learn more about sleep’s impact on your learning, memory, immune system and even your genetic code — as well as some helpful tips for getting some shut-eye.
  
  Link: Sleep is Your Superpower
  [19:09]
• Lera Boroditsky. There are about 7,000 languages spoken around the world — and they all have different sounds, vocabularies and structures. But do they shape the way we think? Cognitive scientist Lera Boroditsky shares examples of language — from an Aboriginal community in Australia that uses cardinal directions instead of left and right to the multiple words for blue in Russian — that suggest the answer is a resounding yes. “The beauty of linguistic diversity is that it reveals to us just how ingenious and how flexible the human mind is,” Boroditsky says. “Human minds have invented not one cognitive universe, but 7,000.”
  
  Link: How Language Shapes the Way We Think
  [14:03]

By the way… One of the most important things you can do to ensure your success in a course is to read — and understand — the entire syllabus. To help encourage you to gain proper habits in college, I will give five points of extra credit for those who email me a meme that makes me smile. Since I am easily amused, this should be an easy five points for you. I like cats and dogs and beavers and clever wordplay. This must be done by the end of the first Sunday of class (September 17, 2023).

Topic Schedule

The actual schedule can be downloaded from the calendar page.

You should make sure the assignments are moved to your personal calendar or planner. Remember that one of the goals of this class is to teach you have to be a better student. Your grade at the end of the course will reflect how well you were a student. Don’t believe otherwise. Each of you has the ability to earn an A in this course. Please do so.

Topics to be Covered in the Course

Chapter One: Critical Thinking and Problem Solving

Topics: Thinking Mathematically; Estimating and Evaluating; Problem Solving: Processes and Techniques

Chapter Two: Set Theory

Topics: Set Notation; Subsets and Venn Diagrams; Operations with Sets; Applications and Survey Analysis

Chapter Five: Equations, Inequalities, and Functions

Topics: Linear Equations and Functions; Linear Modeling; Solving Linear Systems of Equations in Two Variables; Linear Inequalities in Two Variables; Linear Programming; Modeling with Quadratics; Exponential and Logarithmic Functions

Chapter Ten: Probability

Topics: Introduction to Probability; Counting Outcomes; Probability of Single Events; Addition and Multiplication Rules of Probability; Binomial Probability; Expected Value