The purpose of this presentation is to offer you tips on how to read effectively mathematics textbooks. Learning is a personal experience and it starts when learners open the course textbook. Active math learners do not wait for the instructor to start learning and doing mathematics; instead, they start their learning by reading the course textbook. They read ahead to expose themselves to the course content and internalize such content better. However, “reading a math textbook requires unique knowledge and skills not taught in other content areas” (as cited in Rust, 2008). We hope that watching this presentation, you get ideas of acquiring such required knowledge and skills. Reference: Rust, A. (2008). What does reading have to do with math (Everything!)? . Retrieved June 14, 2009, from www.amatyc.org/Events/conferences/2008DC/proceedings2008/rust2.ppt . Image source - http://www.flickr.com/photos/32397140@N00/21203171
“ Math is dense” (Myers, 2009). “The flow of a math book is not like the flow of a novel” (Arem, 2002, para. 1). You should take your time reading the pages of a math textbook. Do not just skim the pages of the textbook, as it is often done with other types of books. Reading a math textbook requires time, concentration and an inquiring mind. Take the habit to constantly ask the what’s, why’s and how’s of what you are reading on a page of a math textbook. The goal is to actively seek understanding of what you are reading! Reference: Arem, C. (2002). Reading a math textbook . Retrieved June 14, 2009, from http://wc.pima.edu/~carem/Mathtext.html. Myers, P. (2009). Reading a mathematics text . Retrieved June 14, 2009, http://home.sandiego.edu/~pmyers/textbook.html. Image source - http://www.flickr.com/photos/67038539@N00/2694774543
“ Mathematics is about ideas” (Lee, n.d., para. 2 ). The chapter openers give you the big picture of the concepts and skills contained in the chapters. Typically, you will find in the chapter openers an outline of the sections contained in the chapter or the expectations of what you should have learned by the end of the chapter. In some instances, the chapter openers make connections of the chapters’ content with historical events or real-life applications, personalizing and giving purpose or relevance to your reading. This section of the math textbook provides a glimpse of why is important to read the chapter, a question that you probably often ask when learning mathematics. Reference: Lee, K. (n.d.). Tips for reading mathematics . Retrieved June 15, 2009, from http://ems.calumet.purdue.edu/mcss/kevinlee/mathwriting/readingtips.pdf. Images sources: Bello, I. (2006). Introductory Algebra: A real-world approach . Second Edition. McGraw-Hill: New York. Bluman, A.G. (2005). Mathematics in our world . McGraw-Hill: New York.
The headings throughout the chapters also provide a broad idea of what to expect and focus when reading and doing mathematics. The headings are clues, so don’t skip them! Images source - Lial, M., Greenwell, R., & Ritchey, N. (2005). Finite mathematics (8th ed). New York: Addison Wesley.
“ Math textbooks contain more concepts per word, per sentence, and per paragraph than any other text type or content area textbook” (as cited in Rust, 2008). Learning mathematics is a cumulative process, meaning that new concepts and skills are built from previous ones. For such reason, math textbooks avoid repeating information. Watch for the bold and/or italic words contained in a paragraph since these are terms particular to mathematics. You should pay careful attention to the meaning of words to fully grasp the math concepts and skills presented in a page. Look up the meaning of unfamiliar words or terms using the textbook’s index pages or glossary section, math dictionary or Internet. Another alternative is asking a classmate or instructor to explain in plain English what the math words or terms mean. There is a good chance you will have to read several times a sentence, paragraph, or page to comprehend what you read. Remember, the goal is to seek understanding of what you are reading! Reference: Rust, A. (2008). What does reading have to do with math (Everything!)? . Retrieved June 14, 2009, from www.amatyc.org/Events/conferences/2008DC/proceedings2008/rust2.ppt . Image source - Hutchison, D., Bergman, B., Hoelzle, L., & Baratto, S. (2005). Beginning algebra (6th ed.). New York: McGraw-Hill.
Mathematics is like learning a foreign language. This language consist mostly on using symbols to describe whole ideas that would take too many words, sentences, or even paragraphs to describe. Math symbols perform the same function as the abbreviations or acronyms that people use when texting with their phones, instant messages or in chat sessions. Understanding text messages requires the ability to decode the abbreviated text or acronyms. Similarly, understanding mathematics involves knowing how to decode math symbols into our language. Become proficient reading in the language of mathematics!
Many textbooks contain additional notes on the margin of the textbook pages to clarify concepts that may be complex and confusing. Margin notes are also used to emphasize important points contained in a paragraph or page. These notes also caution students of typical misconceptions or mistakes that they are known to do. In other instances, these notes offer tips or study aids to improve retention of concepts and skills covered in the textbook page. Therefore, do not skip reading the margin notes since it contains valuable information to help you comprehend and retain what you are reading. Image source - Hutchison, D., Bergman, B., Hoelzle, L., & Baratto, S. (2005). Beginning algebra (6th ed.). New York: McGraw-Hill.
An illustration is worth a thousand words, in particular in mathematics. “Like the words, pictures need slow and careful study” (OSU Math Center, 2004, para. 12). You should observe carefully every detail in the illustrations and make interpretations and connections based on what you read from the text near the illustrations. Reference: OSU Math Center. (2004). How to read a math textbook… (…and get the most out of it) . Retrieved June 15, 2009, from http://www.newark.osu.edu/osunmathlab/pdf/handouts/howto/pdf/readmath.pdf. Image source: Bello, I. (2006). Introductory Algebra: A real-world approach . Second Edition. McGraw-Hill: New York.
“ We learn mathematics by participating, so &quot;participate&quot; while you read” (Myers, 2009, para. 2). You should take notes while you are reading by rephrasing what you read in your own words. Write these notes on the margin of the textbook page, notebook, or index cards. Highlight, mark or underline points that you might consider important in the reading. Re-work the examples or work similar problems as the examples. Re-work also the proofs of theorems or derivations of formulas. Write down questions that may arise while you are reading for future clarification. Create cheat sheets for future reference. In summary, do not be a passive reader when reading a mathematics textbook. Reference: Arem, C. (2002). Reading a math textbook . Retrieved June 14, 2009, from http://wc.pima.edu/~carem/Mathtext.html. Myers, P. (2009). Reading a mathematics text . Retrieved June 14, 2009, http://home.sandiego.edu/~pmyers/textbook.html.
As it was mentioned previously, learning mathematics is a cumulative process. Therefore, authors of mathematics textbooks assume you have mastered pre-requisite skills involved in a new concept or skill. It is common to find examples in which several steps were omitted. For such reason, you should re-do the examples by filling up any missing steps, which will help you grasp the new concepts or skills. If you do not understand how a step was done or calculated, you should just refer back to the previous chapters where the pre-requisite skill was explained or ask for help from a classmate, tutor or instructor. Remember, reading a mathematics textbooks require having an inquiring mind. In addition, most textbooks include an additional and similar problem (often called self-practice or check yourself ) in every example as a way to check your understanding of the concepts and skills involved in the example. You should not skip these problems since it is an opportunity to practice immediately what you just read about the examples. Reinforce your reading by doing mathematics!
Once you have read actively the chapter pages, you should check your reading comprehension by doing the practice problem sets at the end of the chapter. Typically, the focus of the first group of problems (5-10 in total) in this section is to check understanding of definitions and concepts. It is okay for you to go back into the chapter pages and find the answer of these questions. Remember, the goal is to seek understanding, not memorization! The next set of problems (15-25 in total) focus on mastering algorithms or procedures to simplify or solve expressions or equations. You should go back to the chapter examples to find similar problems to the ones you are practicing. Try at first mimicking the steps used in the example to start understanding the process involved. Practice, practice and practice, so using the algorithms or procedures become second nature. However, you should always reflect why these steps were used. Seek understanding! The last set of problems (5-15 in total) focus on applying concepts and skills in real-life scenarios or in new situations. It is here when understanding the chapter content pays off since your critical thinking skills will be challenged. Use the section ‘ Answer to Selected Exercises’, located at the end of the math textbook, to check the answers of the odd exercises you practiced. If you have access to the solutions manual, use it to check any exercises you practice. Otherwise, find a study partner or group to work together the even exercises and compare answers. If you cannot find a study partner or group, use symbolic manipulation tools or discussion groups available in the Internet to check your answers. In case of discrepancies with your answers, always refer to the chapter and find out the reason for having the incorrect answer. Image source http://www.flickr.com/photos/51035609331@N01/3992381
In summary, use the following strategy to read effectively a math textbook. Reference: Brown, S. (2003). How to read a math book . Retrieved June 16, 2009, from http://www.tc3.edu/instruct/sbrown/math/read.htm.
Use these strategies to start becoming an active math reader and learner! Reference: Brown, S. (2003). How to read a math book. Retrieved June 16, 2009, from http://www.tc3.edu/instruct/sbrown/math/read.htm.
Reading A Math Textbook
Reading a Math Textbook Steven Diaz Math Instructor Academic Enhancement Center St. Thomas University
So, what is the strategy ? <ul><li>Look at the chapter openers and page headings to get the big picture of the content. </li></ul><ul><li>Skim through the pages to get a sense of the content. </li></ul><ul><li>Reread but this time thoroughly. Write as you read. </li></ul><ul><li>Practice the examples. </li></ul>
So, what is the strategy ? <ul><li>Fill in any gaps you still have about the chapter content by asking for help or referring to other sources. </li></ul><ul><li>Reflect on what you have read to make connections and internalize the content. </li></ul><ul><li>Take ownership of what you read by explaining the content in your own words. </li></ul><ul><li>Practice what you have learned. </li></ul>