28 Studying Math

Introduction

This chapter provides strategies to empower you to study math in whatever form you encounter it here at the university. It begins by describing how math and mathematical thinking are vital to many professions. It then discusses math anxiety and presents six strategies for overcoming this common problem. Next, the chapter addresses how to approach studying math in general, and how to approach a single module of work in math, followed by a discussion of problem-solving and hints for success. It concludes with some tips for how to approach math assessments. Altogether, the chapter will put you on the path to a successful encounter with math at the University of Arizona.

Who Needs Math?

Many professions are highly dependent on math. Student scientists, engineers, and accountants may work with math in every subject. Students in other disciplines may encounter one or more math courses or assessments. Nursing and paramedics students will encounter medication calculations, for example. Similarly, many students who wish to work in people-helping professions will need to be able to interpret statistics to ensure their approaches to problems and interventions are sound. This will include students of psychology, human services, and education. No matter your discipline, this chapter will help you approach the math content in your courses with successful strategies and a positive attitude.

Math Anxiety and Its Impact on Studying Math

When studying math, students often become anxious and start to overanalyze the math content. Overanalyzing can further elevate their anxiety and create difficulty in understanding the underlying math concepts.

The Australian Council of Educational Research (ACER) defines math anxiety as “feelings of unease and worry experienced when thinking about mathematics or completing mathematical tasks.”^[1] Math anxiety causes people to have significant self-doubt in their ability to do math, causing them great distress.

When a person has math anxiety, their brain continually thinks about the anxiety rather than the actual math problem. The brain allocates the working memory and other resources that it would normally use for computations of the math problem to the anxiety itself, making it very difficult to learn or retain the relevant skills or information.^[2] Math anxiety is highly prevalent. Sadly, between 25% to 80% of the college population in the United States of America has some form of math anxiety.^[3]

Symptoms and Causes of Math Anxiety

Math anxiety can easily be identified. The symptoms of math anxiety range from simple low-confidence problems to more complex physical symptoms. If you experience the following, you may have math anxiety:

• low confidence and negative thoughts such as “I am no good at math”, “I won’t be able to do this”, “I am never going to understand this math concept” (Department of Education, 2020).
• physical symptoms ranging from increased heart rate, increased breathing, to a panic attack when thinking about or doing math.^[4]

The symptoms of math anxiety are triggered when doing math or from the thought (anticipation) of doing math. The level of anxiety will vary from person to person.^[5] While math anxiety is common, it can be managed or resolved, allowing you to succeed in your math learning journey.

Strategies to Reduce Math Anxiety

You will be able to recognize when you are starting to feel stressed or anxious and having difficulty trying to complete math problems. This could include avoiding math classes, revision, and assessment.  At this point, you could develop some methods to help you to relax and unwind. Some different strategies you may be able to use distraction techniques including reflecting on how you feel; leaving the room to do another activity for short periods; mindful breathing techniques (such as breathing in for a count of 5, and breathing out for a count of 7); or any other techniques you may already use for reducing anxiety.

It is also helpful to remind yourself of what you can do by returning to a problem that you can do before attempting the problem that caused the stress. More information about mental health resources (including sections on stress and anxiety) can be found in the chapter Mental Health and Well-Being.

Math anxiety can be managed in a positive way using six strategies. The strategies will need to be employed over time to see the results. Addressing your math anxiety using these six strategies also allows you to study math effectively.

The use of the six strategies will increase your confidence and help you to form good mental maps within your working memory. Over time, this will reduce your math anxiety and break down the associated barriers that make studying math more difficult than it needs to be.

Focus on Understanding the Process

The strategies presented to help reduce math anxiety are good practices for any student learning math. To be successful in math, you will also need to understand the process used for solving math problems. That means you need to understand why the process works. Understanding the process will help you remember how to do the math.

To develop understanding, revise and rewrite the calculations that you are shown in lectures or tutorials. Things always look easier when someone else is showing you how to do it, compared to when you try at home on your own! Rewriting the steps will make it easier to complete different questions, and you will have good notes for revision.

Understanding the process also gives you some flexibility when approaching math problems. Sometimes there may be more than one method for coming to the right answer. If you understand the processes, you will be able to identify the most effective method to complete the question and then apply it. If a question doesn’t specify a particular method to use to solve the problem, you can also choose a method that suits you best.

Approaches for Studying Each Module

Now that you have some strategies for combating math anxiety and studying math effectively, you can begin your math journey at the university with a positive mindset. We will now discuss how to study the math module by module. But what are modules? Some degrees will have entire courses that focus on math, such as Fundamental Statistics, Foundation Mathematics, or Algebra and Calculus. Within these courses, the math concepts are broken up into smaller segments for you to study, often known as modules. Modules allow you to look at one new concept at a time and gradually build your knowledge, experience, and confidence. When beginning a new module, try these approaches to make your math study more manageable:

• Work out what the module is about and what you are expected to learn. Before you start any exercises, scan the entire module and check the learning objectives for a summary of what to expect.
• Start at the beginning of the module, reading through the text and examples. When you come to an activity, attempt the questions yourself. This will help you to learn the formulae and when and how to apply them, thus developing your problem-solving techniques. It will also give you an idea of what you know and where you need to focus.
• Do not skip over any of the study materials. Math is an iterative process; you will need to develop strong foundations and repeatedly revisit and build upon these foundations.
• Summarize the module as you work through it. List any new formulae and problem-solving techniques, and take note of anything that you do not understand so you can seek assistance.
• Talk about your math. It is amazing how problems can be clarified by talking with somebody. You can do this with friends, work colleagues, at tutoring (in person or online), or through course discussion forums or groups.
• Ensure that you have a complete understanding of the topic that you are studying. If you cannot understand a topic, look for alternative resources that may explain it in a different way, contact the teaching team, or the university math support team.
• Contact your teaching team or university math support team for help if you get stuck. Do this as soon as you have a problem so that you can move on with your studies and not fall behind. Tutoring is available at the University of Arizona in-person or online. Give it a try earlier rather than later.

Strategies for Problem Solving

In many ways, math is like solving a puzzle, where a question is posed, and you must find the answer. At the heart of this process is what we call problem-solving skills. Problem-solving questions are typically worded questions you find in the application sections of your materials or your assignments. Problem-solving skills are something that can be practiced and developed to make you more confident and capable with your math. Most people find problem-solving difficult, and as such, it is an area they need to spend time developing. Here are some tips to help develop your skills:

• Read the question or problem carefully and identify what you are expected to find.
• Determine whether any of the information is not needed for solving the problem.
• Express the relevant information in mathematical terms, defining any variables that you are given and noting any special conditions.
• Break down the problem into smaller parts.
• Estimate the answer to the part of the problem that you cannot solve yet and proceed from there.
• Decide which of the skills or techniques you have learned in the course could be applied to solve the problem.
• Apply the technique that you think will solve this problem. Try a different technique if the first did not work.
• Check that your answer makes sense to the problem.

Even if things haven’t gone quite right, there are problem-solving strategies you can use to help put yourself back on the right path. You can:

• Check that you copied down everything correctly.
• Scan for errors in your calculations.
• Look back at your work and answers to similar questions.
• Start with a fresh page where you cannot see what you have done previously.
• Read the question aloud and slowly.
• Leave the problem for tomorrow (but don’t leave it too long).
• Ask for help from your teaching team, university math support team, study group, or whatever other math support might be available to you.

Making the Most of Help

Often, students need assistance with math. As discussed, getting help is both a successful strategy for managing math anxiety and a problem-solving strategy. Here are some suggestions to maximize the benefits of the help you have available:

• Be specific as to what you don’t understand — you do not want the tutor to cover areas where you do not need help. Being specific about what you need will likely save you some time.
• Attempt to solve the problem(s) yourself first and have your work available so that the tutor can discuss it with you. This will develop your problem-solving skills because you will have thought through the problem. It will also show where your understanding is lacking and where you become stuck. This is why it’s so important to write out all the steps when you work on your problems.
• Attempt similar problems from the study materials or other textbooks/websites that have answers provided, so that you can discuss your problems with the tutor rather than requiring tutoring in the basic concepts. This can help tailor the support to your specific needs.
• Be organized and specific. Make a written list of problems that need clarifying, including page numbers in the text or the title of the section in your ALEKS program, along with your work.

Tips for Math Assessment

After you have studied the modules, you will need to complete an assessment. This section provides hints and tips for your assignments and exams.

Math Assignments

When studying math, it is essential to develop regular study patterns. Often, your tutoring questions will help you to develop the skills needed in your assignments, so do not leave your math study until just before an assignment is due.

When undertaking a math assignment, you must express yourself clearly both in English and mathematics. Many students think that doing math just involves “doing the sums.” However, “doing the sums” is only one part of doing and being involved in math. It doesn’t matter how good you are at doing these sums if you cannot communicate your answers or solutions with others. Remember — in your career, you must be able to convince your colleagues or clients that your answer is the appropriate one. Therefore, communicating is just as important in math as it is in all other subject areas.

Finally, you need to allow adequate time to complete your assignment. Just like your other assignments, you need to complete a rough draft and then prepare a final “good” copy. Your instructors are looking for assignments that are neat, tidy, with the math formatted correctly, and with logical, well-documented communication (mathematical and English). This could be as simple as following the guides for best practice for math notation, such as aligning equal signs, centering equations on the page, and defining any variables you have used, including their units. Your textbooks and study modules are a good guide to how your instructors are expecting you to format your assignments.

Math Exams

The best preparation for exams is to work consistently through the semester and keep up to date with the recommended study schedules provided to you in your courses. This includes working through suggested questions and practice quizzes/tests.

In the weeks and days before the exam, you might like to use these preparation techniques for math exams:

• Review the information about spaced practice to maximize your exam preparation.
• As you have been practicing your math throughout the course, you won’t need to cram the night before the exam.
• Review your notes (and worked examples) and make a concise list of key concepts and formulae. Make sure you know these formulae and, more importantly, how to use them.
• Work through your practice problems again (without looking at the solutions). Don’t just read over them. Working through problems will help you remember how to do them.
• Work through any practice or past exams that have been provided to you. You can also make your practice exam by finding problems from your course materials.
• When working through practice exams, give yourself a time limit. Don’t use your notes or books. Treat it like the real exam.
• For those who suffer from math anxiety, practice any breathing or other techniques that help you to reduce or manage the anxiety.
• Finally, try to get a good night’s sleep before the exam so you are well rested and can concentrate when you take the exam.

Further details about preparing for a math exam can be found in the general chapter on test taking.

During your exams, remember to write out and communicate your math in a way that the person grading can follow. Normally, the grader is not looking for perfection, but rather that you have used the correct methods (processes). Once again, communicating what you are doing is just as important as completing the actual calculations.

If you experience math anxiety, be aware that it may be heightened during timed exams, so you will need to remember your strategies for managing it.

Conclusion

Math is an integral part of university study, regardless of which discipline you are studying. This chapter identified the value of studying math and provided strategies to help students manage math anxiety. It also presented methods for approaching studying math in general, how to study single modules, hints for success in problem solving, and concluded with tips for how to approach math assessments. Equipped with these tips and strategies, you are ready to learn and work successfully with math in your university studies.

License & Attribution

Adapted from Academic Success © 2021 by University of Southern Queensland, which is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted. Any changes to the original chapter can be found in the Appendix.