Readings
Overview
Although success in mathematics relies on many of the same universal study habits used for courses generally, there are aspects of mathematics courses that require different skills to be successful. In this chapter, we will explore those differences and strategies to maximize your success.
Introduction
Why Mathematics is Important
Most college degrees require completion of courses known as the general education core curriculum. These courses include curriculum in English, mathematics, science, social studies, and humanities and can comprise up to 1/2 of the total required coursework in your degree plan (Fleming, 2020). Completion of the general education core curriculum is usually required before you can progress into courses within your academic major.
Mathematics courses included in the core curriculum are often perceived as barriers to student success. Pass rates in first-year mathematics courses are frequently lower than other general education core curriculum courses (Gupta, et al., 2006). Students who are unsuccessful in mathematics courses may be required to take the course again, adding both time and cost to the degree. Poor academic performance can also impact your overall GPA, which can result in academic probation or suspension.
It is also important to recognize that mathematics has value beyond simply serving as a gateway course in your degree plan. Mathematics courses help students to develop analytical thinking skills which are needed in real-world problem-solving situations that may be encountered once in the workforce. The content learned in mathematics courses enables individuals to make good purchasing decisions and it is the basis of all financial activities. It is also a critical component of numerical and statistical literacy, particularly given the increased use of data in our lives. It is important that students be aware of how data are used to promote or discourage ideas and activities.
Although success in mathematics relies on many of the same universal study habits used for courses generally, there are aspects of mathematics courses that require different skills to be successful. In this chapter, we will explore those differences and strategies to maximize your success.
Learning Objectives
Upon completion of this lesson, students will:
- Understand how college mathematics courses differ from high school mathematics courses and other college-level courses;
- Develop strategies to decrease math anxiety;
- Identify time-management practices needed to be successful in college-level courses
- Set mathematics goals and develop a plan to meet them;
- Understand the need to develop processes that allow for problem analysis;
- Develop note-taking skills that emphasize critical components of the problem-solving process;
- Understand best practices for test preparation;
- Understand the need for persistence and options for getting timely help on course material.
References
Fleming, G. (2020, August 25). What Are Core Academic Classes? Retrieved from https://www.thoughtco.com/what-are-core-academic-classes-1857192
Gupta, S., Harris, D. E., Carrier, N. M., & Caron, P. (2006). Predictors of student success in entry-level undergraduate mathematics courses. College Student Journal, 40(1), 97-109.
How Studying Mathematics is Different
Think back on the mathematics classes you took in junior high and in high school. You can probably recognize differences between courses at each level. Those differences might include:
- Complexity of the material;
- The amount of time spent studying outside of class;
- The number of assigned homework problems;
- The increased need to work with other students on course material.
A similar comparison can be made between mathematics classes in high school and those at the college level. One difference is the amount of information that is memorized versus the amount of information that is analyzed and applied. In high school, you probably found that many courses required you to memorize information, while fewer courses focused on the application of material and content. These differences are explored further below.
Memorizing vs. Problem-Solving
Attributions: "Pork Chop Dinner" by Alex Munsell on Unsplash is shared CC0
An example of memorizing information might include a cooking competition where competitors learn how to prepare a meal and then create it in a short amount of time. Individuals are not required to create new recipes or deviate from prescribed cooking methods. Instead, they rely on their knowledge of past recipes to successfully complete the competition. College-level mathematics problems are rarely completed in this way. Instead, formulas such as those used to find simple, compound, and continuous interest rates are discussed in the classroom. Students are then given assessments (often word problems) requiring them to analyze the problem, identify appropriate strategies (formulas), and gather the information (numbers) needed to answer the problem.
The Note Taking Process
Attributions: "Notetaking" by David Travis on Unsplash is shared CCO
Note-taking in mathematics also differs from other courses. Notes tend to contain two primary components. These components include definitions and worked examples. Definitions clarify new concepts using words and/or graphics. It is important to include both of them when presented. Worked Examples contain illustrations along with the steps required to reach the answer. Using the earlier example of interest rates (e.g., simple, compound, and continuous), your notes would likely contain the following information:
- Definitions – A list of each formula and the words used to identify each component (symbol) of the interest rate formula.
- Worked Examples – Examples and highlighted words that identify which interest formula is needed and when. You may want to note the letters each number represents in the formula, write out the formula, and then use a calculator (if appropriate) to find the answer.
Applying Your Knowledge
Attributions: "Driving" by Stephan Mahlke on Unsplash is shared CCO
Success in mathematics requires that you are actively engaged and apply what is learned in class. It is not enough to simply memorize terms and formulas. One example of an activity that requires application of knowledge is learning to drive a vehicle. You first need to memorize the signs and driving rules for your state. You then take a written test and get a permit to begin applying your knowledge in driving situations. However, it is not enough to just observe others as they drive. You must take the wheel and engage with the vehicle and your surroundings to become a proficient driver.
In the case of a mathematics course, the information learned provides a foundation for how it will be used in practice. To build on this foundation, you must practice solving a variety of problems in order to become proficient with the material. Watching the instructor is usually not enough. You must engage with the material by doing homework and other practice problems.
Strengthening Your Skills
Attributions: "Olympic Rings at Centennial Olympic Park in Atlanta, Georgia" by Bryan Turner on Unsplash is shared CCO
Like learning a sport, you must actively apply new information in mathematics. Watching others play might help you become familiar with the rules, but you will not be successful unless you learn the required skills and put in the necessary practice time. As you progress, more skills are added but you must continue to improve on the skills already learned. The same is true in your mathematics course. You will learn new skills each time your class meets, but these will usually be tied to information discussed in previous classes. Homework and studying with peers will allow you to practice what you have learned. Practice pays off on quizzes and tests.
Mastery takes time
Attributions: "Violin and Piano" by David Lusvardi on Unsplash is shared CCO
As in the performing arts, mastery also takes time. It can take years of lessons and practice to become proficient at an instrument or other area of artistry. Similarly, mathematics requires using what you have learned in the past to be successful in your current course. You cannot forget everything and expect to do well. Each lesson builds on those of the past and regular practice is essential to understanding new material as well as helping you to remember new processes or notations. It is important to review past material at least weekly to ensure you retain information. Cramming prior to a test or quiz rarely results in a high level of performance.
Learning Activity
Click on the link below to engage in an activity comparing mathematics in high school vesus college.
Math Anxiety
Mathematics can be challenging because of differences at each level of instruction, but also because of psychological factors associated with learning. One of those psychological factors is math anxiety, which has been the subject of a great deal of research in recent years. Joseph (2017) defined math anxiety as the feeling “that one cannot perform efficiently in situations that involve the use of mathematics.” Others have defined math anxiety as the “state of fear, tension, and apprehension when individuals engage with math” (Zhang et al., 2019, p. 1). This anxiety can result in poorer academic performance in mathematics courses. It can also result in avoiding mathematics, which provides fewer opportunities to practice math skills (Zhang et al., 2019). Avoiding mathematics or delaying enrollment in these courses can increase the likelihood that a student will not persist to degree completion (Lane et. al, 2020; Zientek, 2020).
It is believed that math anxiety results from past embarrassment in mathematics classes or other situations where an individual perceives failure (Joseph, 2017). These feelings of anxiety can also become amplified as the difficulty of curriculum increases (Zhang et al., 2019). Higher level mathematics courses typically involve more complex problem-solving skills and cognitive engagement. As a result, the relationship between math anxiety and math performance becomes stronger at higher grade levels (e.g., Zhang et al., 2019). This makes math anxiety an important factor to explore as you begin your college career.
Figure 1. Math Anxiety Cycle
Because many students experience some level of math anxiety during their time in college, you should assess and reflect on how your math anxiety may be affecting your academic performance. One tool to help evaluate your math anxiety is the math anxiety test, available online at http://www.mathpower.com/anxtest.htm. Learning activities at the end of this unit provide an opportunity to reflect on your test results and explore opportunities for help and support.
Learning Activity
Click on the link below to engage in an activity to test your mathematics anxiety and reflect on your prior experiences.
References
Joseph, A. (2017, April 24). Definition of Math Anxiety. https://sciencing.com/definition-math-anxiety-5666297.html
Lane, F. C., Zientek, L. R., Sechelski, A., & Schupp, S. (2020). Effects of timely enrollment in college-level mathematics on degree completion. Journal of College Student Retention: Research, Theory & Practice. https://doi.org/10.1177/1521025120973949
Zhang, J., Zhao, N., & Ping Kong, Q. (2019). The relationship between math anxiety and math performance: A meta-analytic investigation. Frontiers in Psychology. https://doi.org/10.3389/fpsyg.2019.01613
Zientek, L. R., Lane, F. C., Sechelski, A., & Shupp, S. (2020). Effects of delaying college-level mathematics course enrollment for underprepared students. Journal of College Student Retention: Research, Theory & Practice. https://doi.org/10.1177%2F1521025120923113
Procrastination in Mathematics Classes
It was discussed earlier how mathematics classes are different and that procrastination rarely leads to skill mastery. Procrastination is an issue that most college students will experience while in college. One definition of procrastination is to intentionally and regularly put off something, or to intentionally put off doing something that needs to be done (Waqar, 2020). This might include hanging out with friends rather than studying, working extra hours, or waiting to start a project until just before its due. The implications of procrastination often include failure to complete assignments, lower grades, an increased level of frustration, and failure to progress in your degree program. Realizing that the tendency to procrastinate is common, Waqar (2020) offers several strategies for dealing with procrastination.
- Focus on how you will set aside time to complete the task. Focusing on what you haven’t done can creating feelings of failure. Instead, focus on strategies you can take to make progress toward your goal.
- “Choose” to do it instead of “telling” yourself to do it. This puts you in control and allows you to decide what actions you will take.
- Focus on starting the task rather than finishing it. The act of starting a task allows you make progress that will eventually lead to a finished product.
- Break larger tasks into smaller ones. Creating more manageable steps will improve your chances of making meaningful progress.
- Set realistic goals and expectations. Setting standards too high can increase anxiety. It is more important to complete the project than do it perfectly. You can go back and work to improve what you have completed, if there is extra time.
- Disconnect from distractions/devices such as phones and social media. Turn off technology that you may be tempted to use while working.
- Balance studying and non-academic activities. Organize your study time so that you can accomplish what is needed while still taking time to be with friends and family. Finding school-work-life balance is important to maintaining a healthy lifestyle and positive mental attitude.
- Meditate/Self-Reflect. If you find that you are procrastinating, consider the reasons why and how you might address those issues.
- Use a to-do list and limit yourself to 3-5 goals. Make sure to refer to your list often and remove items as you complete them. Also, work to make sure that the items on the list are the most important goals, rather than adding every possible task.
- Celebrate your accomplishments. You might enlist the support of a friend if you are struggling with a task. Decided ahead how you will celebrate the completion of tasks.
Learning Activity
Click on the link below to engage in an activity to help you identify strategies to avoid procrastination and reflect on how you might use them.
References
Waqar. (2020, June 19). How to overcome Procrastination & Actually Study https://www.intellecquity.com/how-to-overcome-procrastination-actually-study/
Steps to Succeed in Mathematics
It is important to avoid procrastination, but there are other steps that can also improve your chances of success in mathematics.
- Do homework early and often. Even though you might not think homework is important, most instructors use it as a starting point for quiz and test questions. Begin homework no more than a day after the material is first covered. Once you complete an assignment, do not just set it aside. Retry practice problems after a few days and without looking at your initial attempts. After a week, go back and re-work questions from all previous assignments. This allows you to spread out a test review so that you do not have to re-learn the material the day before a test.
- Identify confusing questions and those you get wrong. As material is presented in class, identify confusing material so that you can go back to it or schedule a time with the instructor to revisit material. Do the same with homework questions that are confusing and take time to contact the instructor or a peer for help.
- Don’t be discouraged by mistakes. We discussed earlier in this chapter how stress can hinder progress. Be aware that mistakes will happen and use them as a learning experience. Take time to re-work problems that you miss and re-work them again after a few days to re-enforce the correction. It can also be helpful to check with a peer or your instructor on ways to avoid the mistakes you may be making.
- Change your mindset from “I can’t” to one of “I can”. A positive attitude is important when you are working on a subject that you might find difficult. Avoid starting out defeated. Even if you had difficulties with mathematics in the past, you are in a new class and with a new instructor. Give yourself a chance by starting out with a positive outlook.
- Organize your notes. Keep track of definitions, examples, and any formulas or properties that are given to you. There are many formats that might be used to take notes, including a separate section for definitions, one for formulas/properties, and worked examples. When taking notes in class, it is frequently faster to follow the process used by the instructor. You can transfer the material into a format that works for you after class. This has the added benefit of going back over the material a second time.
- Explore what resources are available and use them early in the semester. Resources exist on campus, including the ability to request additional testing time through the Services for Students with Disabilities office. Other math-specific resources include:
- Tutoring sessions offered by your instructor or math department;
- Individual and group tutoring sessions through the Math Center.
- Group study sessions with other students in your class;
- Study sessions in your residence hall.
- Use a calculator if one is allowed. Calculators can be useful tools if you are familiar with how to use them. Find out what calculator the instructor will allow and use in on a regular basis so that you know how and when to use it. While a phone can act as a calculator, some instructors do not allow phones to be used in class and they are rarely as easy to use as a standard calculator.
- Use an organized notebook that is specific for your mathematics class. Mathematics classes require a lot of paper and keeping all your work in one notebook can help you be better prepared. Keeping homework close to your notes will also make searching for information easier should you forget steps when reworking problems. Realize that the format that you select is not as important as finding a workable format and using it consistently.
- Review problems to fully understand your mistakes. Re-work missed problems to make sure you understand the process and how to get the correct answer. Doing this regularly will help ensure you retain important information. Make sure to know what information will be required on future tests and assessments (e.g., comprehensive final exam). It is especially important to correct mistakes while the information is fresh in your mind. Make sure to review material from past assessments several times during the semester. Even if material will not be included on a final exam, understanding content and correcting mistakes may be important for future classes.
- Focus on understanding rather than memorizing. Many students believe that college-level mathematics information is to be memorized like the multiplication tables. While there may be times when you will need to memorize specific information, college-level mathematics courses focus more on concepts and applications. You will be building on past information and applying it in new ways you may not have seen before.
How to Take Notes in Mathematics
Taking good notes is an important skill for success. We also discussed previously that note-taking in mathematics classes is different. At a minimum, your notes should contain:
- A date and the topic to be covered. The date can be used to track if the material is new and will be on an upcoming quiz or test. This can be helpful when you cannot remember where a particular example is in your notes.
- Definitions. After class, transfer any new definitions to a single location in your notes. This will help you learn them. It also gives you a place to quickly look them up rather than having to go through pages of notes searching for a particular term. As a part of each definition, include a short example or graphic to demonstrate the definition. This will help you remember how it is used.
- Worked Examples. Copy the examples given in class with enough detail so that you can follow your notes later, but don’t spend so much time copying every step that you get behind. Go back after class and fill in any missing information that might be helpful when reviewing your notes at a later point in time. You can also write in explanations of steps to clarify the process being used to solve the problem.
In addition to the items covered above, some students have also suggested these strategies as ways to enhance their notes.
- Use different colors of highlighters for different parts of the notes. Definitions might be one color and the start of an example another color.
- Consider putting a symbol like a question mark or asterisk (*) in the margin if you do not understand something. After class, get with the instructor, tutor, or a group of peers to go over the areas that have the mark.
3-Column Note Taking Method
The 3-column method is one way to organize notes in your mathematics class. An example of the formatting used for this method and how it can be used in practice are illustrated in the figure below.
Figure 1. Formatting for the 3-Column Note-Taking Method
Figure 2. Illustrative Example of the 3-Column Note-Taking Method
Boxed Notetaking
Another approach for taking notes in mathematics is the boxed notetaking method. Important information, such as definitions or process steps, are included in boxes so that they stand out and are easy to find when you are looking back over what was covered in class. Below is an example of how this method might be used with the example of factoring.
Figure 3. Illustrative Example of the Boxed Note-Taking Method
Mathematics Test Taking Tips
There are many websites with suggestions on ways to approach test-taking in a mathematics class. Being well prepared prior to taking a test is one of the best things that you can do. Several strategies are provided below to help you better prepare before the test.
Prior to Taking a Test
- Follow the suggestions in the “Steps to Succeed in Math” section is an excellent starting point.
- Review homework and quizzes on a regular basis prior to a test allows you to space out your study time so you do not feel pressured at the last minute.
- Practice making a test review from a mix of homework and quiz questions. When you work test reviews, set a timer so that you are under some of the same time constraints you might experience on the test.
- As the test approaches, make sure to review any material that the instructor specifically mentions.
- Make a list of any formulas or definitions that you need to know and review them both several days before the test as well as in the classroom just before you take the test.
- The night before the test, go to bed early enough so that you are rested in the morning. Taking a test when you are tired will make it more difficult to concentrate and students who are tired generally do not test as well.
During the Exam
Once it is time to take the test, consider the following strategies so that you can complete the test and get as many problems correct as possible.
- Come to class early and be ready to start when the test is passed out. This will give you the maximum amount to time to take the test.
- When you get your test paper, write all the formulas that you memorized in the margin of the test. This gets them on the paper while they are still fresh in your mind and it gives you a reference point to come back to when you need them.
- Read the directions carefully and make sure that you follow them. It is frustrating to lose points on a test because you think you did the questions correctly only to find that the directions specified an answer that was different than you gave. Items like the number of decimals required or if you need to include units are important to check.
- Once you begin working, go through the entire test and answer all the questions that you recognize and can complete quickly. This will give you an idea of all the test questions as well as making sure that you have answered the easier questions.
- Wear a watch or know where there is a clock in the room so that you can keep track of how much time is left. At the start of the test, decide about how much time you can spend on each problem and try not to spend too much time on any one problem. If you find you are spending over 2-minutes on a problem, make a note of the problem number and come back to it. Accept that you will miss a few problems and concentrate on the ones that you can do successfully.
- If there is time at the end, go back to any problems you might have skipped and try them again. You may remember something you forgot during your initial attempt after working other problems.
- Do not leave any questions blank. Many instructors will give partial credit for work that you show. Take advantage of partial credit opportunities. Also, make sure to give an answer. There is a chance you might get the problem correct!
- Use a highlighter or circle important words or information. This can help you focus on the critical parts of each problem which can help you remember how the words were used in homework and quiz problems.