Flashcards: Understanding Z-Scores

What is the \(\displaystyle z\)-score for a value of 115 when the mean of the population is 103 and the standard deviation is 8?

\(\displaystyle 1.7\)

\(\displaystyle 14.37\)

\(\displaystyle 1.5\)

\(\displaystyle 12\)

\(\displaystyle 2.3\)

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For many students in high school, memorization is their shortcut to making it through the most challenging classes. Instead of understanding difficult and abstract concepts, students memorize the steps to solve problems and simply reproduce their memorized content on exams.

This approach can be especially tempting in high school mathematics courses, which can be consistently frustrating for many students as they find the dizzying array of variables, numbers, and mathematical expressions with which they are expected to familiarize themselves to be overwhelming. It’s easy to allow that frustration to reduce motivation, and fall behind as a result.

Once you fall behind in a high school math course, it can be nearly impossible to get caught up. High school mathematics courses are usually dense, introducing new content at a fast page; furthermore, much of that new content often relies on content the class has previously covered, so any confusion or misunderstandings can create a ripple effect and cause consternation when facing more advanced related topics.

Precisely because of this structure, high school math courses reward consistent effort from an early point. You can stay motivated, reduce your frustration, and maximize your potential in your high school math course by keeping your perspective well grounded throughout. Maintain context, and constantly ask yourself why you are learning the content you study.  Instead of trying to memorize your way out of your coursework, define your perspective by focusing on the concepts.

In fact, a great way to help ensure long-term retention and promote understanding in your current course is to minimize rote memorization. If you understand the conceptual reasons for why you must solve a problem a certain way, or precisely what a mathematical expression is trying to communicate, you are far better situated for success. While this approach to learning enhances your experience in the long-term, true conceptual understanding of fundamental principles takes work. Memorization may seem like a shortcut, but it is a shortcut that can incur major costs later.

These costs are magnified because the concepts introduced in early high school math coursework permeate almost everything you will study in later math courses. All of your subsequent math classes, as well as science and logic courses, depend extensively on the concepts presented in earlier classes. When you are asked to solve equations regarding projectile motion in physics, or geometric expressions in trigonometry, you will tap directly into the skills you built in previous classes.

While putting in the needed effort for true conceptual understanding, many students feel that high school teachers are unable to provide the attention that they need. This is an understandable struggle, considering the widely different skill levels of students. It’s nearly impossible for a single teacher to adequately meet the needs of the highest achieving students as well as those of students who are struggling. Whether you’re struggling or succeeding, taking ownership of your own mathematics education is critical.

You may find that collaborative learning with other students, tutors, or online can help make your high school math classes more manageable. You may be posting the highest scores on exams, but find yourself bored or at risk of losing interest. Alternatively, you may be struggling to meet the minimum passing score. Either way, you can use interactive learning to help keep you interested, understand the conceptual basis for problem solving, and benefit from the strengths of others.

Varsity Tutors offers great free high school mathematics resources on its Learning Tools website. Our high school math flashcards can help you review particular topics or general areas of mathematics whenever and wherever you find the time to do so, either online or through Varsity Tutors’ free apps. Each high school math flashcard features a multiple-choice problem; as soon as you select an answer, the correct one is revealed, along with a complete explanation of how the problem can be solved correctly. Whether you answer them correctly or not, our high school math flashcards can help benefit your mathematics knowledge: if you get a question right, it reinforces your understanding, and if you get it wrong, it presents an even more valuable opportunity: the chance to identify any misunderstandings or points of confusion well before you get to an exam situation only to realize that you don’t a concept quite as well as you thought.

Reviewing your mathematics understanding frequently and making use of Varsity Tutors’ free high school math resources can help you enhance your understanding of fundamental mathematics concepts and position yourself for long-term success in a variety of classes.

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