You may think of yourself as a “math person” or perhaps “not a math person.” But regardless of your perception, would you like to feel more at ease when working with quantitative material? Learn about strategies for taking notes and organizing your notes, keeping homework journals, and doing homework.
Gain new stills in studying, taking math exams, and learning from any test-taking errors.
Many students work hard in math classes – studying long hours, nights and weekends – yet many of them do so using ineffective strategies. Others simply withdraw effort soon after the course begins, or they make mistakes. To help you successfully complete
your academic goals, we want you to both persist in your studying and attendance (tenacity) and to do so efficiently and effectively (good strategies). This is called productive persistence. The next few pages of this course will
help you develop a plan for how you can implement the idea of productive persistence as an effective way of passing a math course.
In grade school, you may have had a teacher who praised students for having neat, tidy papers. Learning can be messy, and if we restrict ourselves to neat, tidy papers, that is all we will have. Sometimes we need to try a homework problem over and over before we understand how to find a solution. In our hectic lives, it is important for us to allow ourselves time to reflect on the messy parts so we can tidy them up in our minds.
Prepare for your classes as you would practice for an upcoming athletic event. Know the topics you are going to cover, and make a goal of being current with your assignments. Learning is not passive, so if you want to learn from your class time, you must prepare yourself to learn.
Consider these two scenarios:
Scenario One: Greta is busy. She has a job and works at night after spending hours at school every day. The last thing she wants to do is prepare for class when she gets home from work at night. Despite her exhaustion, she takes 15-20 minutes before bed to check the syllabus from her math class to see what topic will be covered in lecture the next day. She then finds the text material related to the lecture topic and quickly skims it, reading over the headings.
Scenario Two: Greta is busy. She has a job and works at night after spending hours at school every day. The last thing she wants to do is prepare for class when she gets home from work at night. She decides to watch an episode of her favorite TV show before she goes to sleep at night.
How much value do you think Greta is gaining from her math lectures in each of these scenarios? Do you think 15–20 minutes really makes a difference? If you haven’t before, try spending 15–20 minutes skimming the material related to your lecture before you go – even if you just read the headings in your text. Maybe you take public transportation to campus. If so, you could skim your text or lecture notes on the bus. If you drive, maybe you can get to campus a few minutes early to do the same thing.
Preparing for class does not necessarily mean having read all the material related to that day’s lecture. Some people gain more from reading after lecture. In general, most people do retain more from lectures if they focus their mind on the topic of the class before entering the class. Ask yourself these questions before your lecture: what did we talk about last time? What are we going to talk about this time? Am I current with my assignments?
Math concepts build on each other. Because of this, keeping up with homework and assignments will help you be prepared for the next session. If you are behind, you will lose a valuable opportunity to make important connections between last week’s content and this week’s.
It is impossible to write down everything your teacher says during a lecture. As you become a more skilled learner, you will learn how to glean what is important from a lecture. Here are some things that can help you organize your notes and your understanding of the content in them.
Consider these things before you start writing:
As with any kind of class, you may need some time to figure out how to best organize the information you want to record. There are many popular styles of note-taking and if you have one you prefer, there is no reason to change. If you want to explore more ideas that have worked well for other students in math courses, consider these:
There is a good chance you are going to be assigned online homework in at least one of your math or science classes while you are in college. Often, students fall into the habit of working through online homework without keeping track of their work.
If there is one thing you take from this page, it should be this: Keep an online homework journal!
Here are some important things to include in your homework journal:
Allowing yourself to make mistakes in your homework journal gives you freedom to learn and not be worrying about a perfect paper.
Summarizing and reviewing what you have done will help to solidify the ideas that are now swirling around in your head. You go to lecture, take a bunch of notes, do a ton of homework problems, and then what? Your brain needs time to make connections between practice, what you have in your notes, and what you may have read in the text.
What is the point of taking notes or doing homework if you never look at them again?
Recall from the Active Learning section that effective reading requires more engagement than just reading the words on the page. Reading a quantitative math text effectively uses the same skills as reading any academic text effectively. It is still a good idea to do things like circle key words, write notes, and reflect. You can still employ the same steps that were presented previously:
Math texts may be organized in a way that is new to you. They are full of symbols and notation, and not as much text as other subjects. A few important features make up a math text. These include:
You may be tempted to skip over examples or boxes with definitions in them when you are reading a math text and just get to the “regular” text part. BEWARE! Most of the important information in a math text is in the definitions, examples, and notation. Notation is very important to most college math instructors, so take the time to pay attention to how mathematical ideas and processes are written.
If you do not understand a definition or how it is applied, make note of your confusion. You can circle an example or the definition, or write it in your notes. Ask for help to clarify your confusion. Try rewriting mathematical expressions or equations as words if you are confused by them. Remember that being confused is probably the most important part of learning: it means that you know where to focus your learning strategies!
Rather than presenting ideas with a thesis statement, then supporting them with examples and discussion, a math text will present a mathematical definition or classification, and support it with examples. As a college student, you are not expected to understand every single word or idea presented in a reading, especially if you have not discussed it in class yet. However, you will get more out of class or homework practice if you can identify the main concepts in a reading.
Math texts present a numerous graphs, tables, charts, and images. These items contain valuable information to help you more deeply grasp a topic. Graphs can show a visual representation of a mathematical rule or equation. Tables can help you see trends or describe relationships.
Data-rich graphics can take longer to “read” than the text around them because they present a lot of information in a condensed form. Give yourself plenty of time to study these items, as they often provide new and lasting insights that are easy to recall later (like in the middle of an exam on that topic!).
Recall the four sensory modalities in Fleming’s Learning Styles model:
You can use the understanding you have of your own learning style to your advantage as you prepare for a math exam.
Visual learners make sense of the world through pictures and images. They learn well when lesson plans incorporate photos, videos, or visual maps. A visual learner may describe their understanding as images or pictures rather than with words, and are drawn to design and spatially focused.
Aural learners are best equipped to understand and store information absorbed via sound and music. Their ears are particularly adept at deconstructing and parsing heavy mixes of tones. They will often do better with books on tape versus printed versions.
Many aural learners enjoy listening to music. Playing pleasant music in the background while learning mathematics can evoke positive emotions and stir up a bit of energy while you are working. Just make sure that the music is not overly distracting or played too loud. In addition, musical minded people can try to organize formulas and operations into musical patterns or rhymes. Coming up with a rhyme or melody to remember the quadratic equation may be more effective than simply attempting to remember the visual image of the formula. It may also help to find someone who will listen to you explain what you are learning or studying.
Read and write learners may prefer learning with words – with speech and writing. If you are a read and write learner you may soak up knowledge through various mediums centered around language. If you prefer learning this way, try sitting down after class to rewrite your notes. Translating a mathematical expression, graph, or equation into words may also help. If you learn from reading and writing, keeping a homework journal may be very beneficial to you.
Physical learners learn best by touch and movement. A lot of superb athletes tend to fall into this category as physical processes and activities seem to sync well with their learning and memorizing capabilities.
For physical learners, studying may seem like torture, but if you are committed to it, there are ways. If you tend to learn best when active, it is important for you to stay in motion while studying. This could involve squeezing a stress ball while working, or simply taking a break every 20 or 30 minutes to walk around the room. Hands on models are terrific as well when applicable. If there is a tangible learning device that you can actually touch and interact with, all the better.
As you work through problems to study for your exam, use this decision tree to help you optimize your time.
Some learners prefer to learn in groups surrounded by other people. If you thrive in social environments, you may benefit from working in teams to complete homework assignments and prep for exams. This kind of activity can can often charge your energy levels and can create a supportive network of caring classmates. It is imperative that at least one person in the group be willing and able to keep the group on track and focused; otherwise your study session will turn into social hour.
If you plan to study in a group, try preparing an agenda before you get together. Your agenda could include a summary of the topics you will review, and a few problems for each topic that you want to try to work out together. Beware of the “attention seeker” when you are part of a study group. Try to share the work of solving problems or answering each other’s questions. All of you will get much more our of the experience.
Just as it is important to think about how you spend your study time (in addition to actually doing the studying), it is important to think about what strategies you will use when you take a test (in addition to actually doing the problems on the test). Good test-taking strategy can make a big difference in your grade.
Your instructor passed back your first math exam and you are devastated. You thought you did so well preparing, you kept up with assignments, and came to every class. Why did you get a C−? You may feel like you have failed, but this is an opportunity take charge of your education! You have been given several opportunities by getting a C− on your exam.
Do not throw away any tests, even if you are upset about your grade. It is very important to take an inventory of the errors you made on each question. Use the following inventory to assess your mistakes.
Identifying what kinds of error you made will help you focus your strategy for study and preparation for the next exam. You can develop a plan for how to prevent similar types of errors, once you know where to concentrate your efforts.
Answer the question(s) below to see how well you understand the topics covered in the section. This short quiz does not count toward your grade, and you can retake it an unlimited number of times.
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