Story: Working with emergent readers.

I began my Master’s program in January of this year. As I sat through the orientation I became more and more apprehensive: my desire is to work with adult learners, especially those at community college level, and the emphasis seemed to be on child-learners. One of my other classmates asked “if my goal is to work with adults, is this program really for me?” I’m glad she asked because that is exactly what I was thinking.

One of the instructors explained it this way: we have you start at the earliest readers because if you can work with the most basic, emergent readers then you can take what you know of those readers and understand better what is going on in the minds of your struggling adult learners. It will help you get perspective.”

I was not sure what to think but I have tried to keep an open mind.

One of my projects this semester is that I have to work with an emergent learner (age 4-9) who is “different” from myself, meaning they have a different educational back ground, are growing up in a different area, or are of a different culture. I asked one of my students if I could work with her daughter and she asked if I would work with both of her daughters: I agreed; after all, the more experience I have the better.

This is a good place to note that I have very little experience with children. I did no baby sitting as a teen, not even cousins or neighbor kids. My husband and I do not want children–we are happy with our furbaby

Our furbaby, Hephaestus.
Our furbaby, Hephaestus.

(though we are considering adopting another). My brother has no children, yet, and neither does my best friend. I do not have any close friends with children and I do not have any extended family with small children or, those who do I do not have opportunities to spend time with them outside of holiday functions. I did not realize until I started looking around my life for this project how little experience I have with children.

For this project, I must work with an emergent reader a total of 5 hours minimum. I ended up working with three different children at three very different ages: 4, 9, and 11. These girls are just delightful! The nine year-old loves to read; she brought a book that the wanted to read with me, and has shown an enthusiasm about sharing her reading with me that has completely surprised me. The four year-old has a great deal of manual dexterity; she has the best handwriting I have seen in a child. She is also quite patient for only being four. I worked with both children for almost an hour before the four year-old quietly asked, “¿Podemos hacer algo más ahora?” (Can we do something else now?)

The ten year-old claims she does not like to read. Her mom looked surprised when she admitted it. I asked her why she felt that way and her response was “well, I like to read stuff I like, but I hate the stuff my teacher makes us read. It’s so boring!” When I asked her what her favorite book is, she replied that she loved A Child Called It, a book with many complex ideas. She wants to one day be a veterinarian and her favorite subject in school is math.

The nine year-old says she loves to read. When I asked her what she liked best, she giggled and said “lots of stuff.” I asked if she had a favorite author and it took her a minute but she finally settled on Barbara Park and the series of books Junie B. Jones. Her favorite subject in school is Language Arts, and when I asked her why she replied “because in Language Arts we learn about everything!” In her class currently, she is reading about volcanoes. She says she good at making bracelets to sell and someday wants to be a teacher, maybe.

The four year-old speaks little English and mostly Spanish. She loves to copy her nine year-old cousin, and will whisper questions to her in Spanish as we would talk. She has a surprisingly long attention span and excellent manual dexterity. Though she often did not “know” what she was writing, she could copy clearly what her cousin would write in clear handwriting. The first time I met her she watched me work with her cousin, patiently, for almost an hour, neatly copying what her cousin wrote on her own paper, and asking questions quietly in Spanish (her cousin translating). At one point, when I told them I had a kitty at home and showed them pictures, she exclaimed in Spanish, “¿Podemos ir a tu casa?” as her eyes lit up in excitement.

Basically, I learned so much from these kids.

All the children in this family are bright, articulate, and curious, with a thirst for learning and reading. These children love to read, are excited by the prospect of being good readers, and they understand that reading is important for their goals; the nine-year-old knows that, if she wants to be a teacher, she must read and the ten-year-old, who wants to be a veterinarian, said several times that the only thing she “needs to know how to read” are science materials—again, acknowledgement of the importance of reading to being a professional.

What I learned is that children have a great deal of fearlessness and curiosity that adult learners do not have toward reading. Adult learners who struggle with reading are often victims of the system from which they came and, in slipping through the cracks, have been instilled with a deep phobia of learning to read or, more so, of failing, again, to learn. Children, refreshingly, come with very little, if any, of these bad experiences, hesitations, or phobias and often have an open mind and an eager willingness. It is refreshing to work with students who love learning, who are unafraid to learn, and who are willing and eager to learn and try new things. If anything, this project has refreshed my own reading spirit as I remember all I love about reading, seeing it in the eyes of these young readers.

While I have definitely not changed my mind about working with adults, working with children in this way has taught me something valuable about my adult learners that I have never experienced. Since I have never worked in a child’s classroom, I never realized that much of the fear that my adult learners have is not something inherent in their personality: they were taught to be afraid; they were taught they were not smart enough; they were taught that they were failures. In order to really understand my struggling, fearful, hesitant, seemingly incurious adult learners, I must first know what experiences in education they have had to bring them to their current state. It’s not enough for me to assume that what “worked for everyone else” just “didn’t work for them.” Just like other children, they were once excited, optimistic, curious young learners and, as their teacher, I I hope to help to lead them back to that state.

The Reading Social Science Workshop

Slide 1: The Reading Social Science WorkshopSlide1

“It was books that taught me that the things that tormented me most were the very thing that connected me with all the people who were alive, or who had ever been alive.” – James Baldwin (author, playwright)

The social sciences (including anthropology, history, ethnic studies, psychology, sociology, economics, and some philosophy) study the very essence of what it is to be human. Part of what many students enjoy about the social sciences is that it gives them a feeling of connection with themselves and others; it allows one to begin to understand some of the most mysterious and universal things in existence: love, hate, violence, money, politics, culture, social status, religion, familial connections, and much more. These are topics that mankind has been trying to understand–and master–for a very long time.


Slide 2: Previewing

Slide2

Previewing Before reading, get an understanding of what the material has to offer you. Spend 10-15 minutes looking over the material, prior to reading it, so you can be prepared to make the most of your reading time. While you preview, come up with questions you have, note unfamiliar words, make connections between topics, and spend a few minutes looking at pictures, charts and graphs in the material. Make mental notes of whether the material is completely new, entirely review, or a combination of new material and old material. To preview:

  • Read the title, author information, key terms, introduction, and/or the abstract or summary.
  • Reading the headings and subheadings throughout the article or chapter.
  • Read the first and/or the last sentences in each paragraph.
  • Look at the bolded, italicized, or any other emphasized terms; also look for any words you do not recognize. You may want to take a moment to look up what any words mean before you begin reading, too.
  • Examine any picture, charts, tables, and any other graphics.
  • Read the chapter summary, end-of-chapter questions, reviews, and any other information at the end of the chapter or article.

Slide 3: While Previewing Look For…

Slide3

Each section of a text provides the reader with important information that you must pay attention to in order to make the most of your reading. For instance, if you’re writing a research paper that requires that you use statistics or quantitative information, you will want to locate that information within the paper and spend extra time interpreting it for you own research. If, on the other hand, you must read to gain background information for a class discussion, you may want to spend more time on the background, results, and author motivation areas. In any case, you should always look carefully at who funds the study, why the study is being done, and what kind of conclusions are being drawn as a result of the study.

Social Science readings, especially peer reviewed journals and articles, have specific features that can help you navigate the text more efficiently if you know what they are and the information the provide.

  • Title: Specific, usually jargon-heavy. Be prepared to look up any unknown words in the title as you know they’ll be important to the rest of the text.
  • Abstract: Short, usually one paragraph summary/overview of the study and information collected with the outcome of the study. Use this to familiarize yourself with the material.
  • Key Words: Jargon/terms used for search purposes but also terms you should know before reading. Make sure you look them up if they are unfamiliar.

Subheadings/Subtitles: these split up the article to help the reader navigate the material. Each section supplies different information and, though they can be different from article to article, there are some consistencies. Some important subheadings/subtitles include:

  • Background: gives background on the study.
    Important because: explains related studies, background information about the study, and/or the researcher(s), and the motivations of the author(s).
  • Theories & Evidence: presents the question the author hopes to answer, along with evidence they may be using as support.
    Important because: this section will usually present the hypothesis of the study as well as the preliminary evidence that may or may not support the initial hypothesis.
  • Methods or Data & Methods: describes how the study was done, how data was collected, and what was recorded and why.
    Important because: it explains the way the author(s)/researcher(s) set up the study, who was involved (patients, volunteers, etc.), the size of the study, what data was kept, and why.
  • Results: the results of the study, usually recorded quantitatively (with numbers or statistics) along with the author’s interpretations of how the support or do not support the hypothesis.
    Important because: goes into detail of the results; it’s heavy on numbers but important if you need information to support a hypothesis of your own.
  • Discussion and/or Conclusion: an in-depth look at the data, usually to eliminate any misinterpretations of the data or explain any inconsistencies that may have arisen in the course of the study.
    Important because: it talks about why the results of the study support or deny the hypothesis, including details about statistical analysis, etc.
  • Notes: Any extra information the author feels important but does not directly fall into any of the other sub-headings.
    Important because: there may be other information about the study, including extra data, related arguments, or subsequent additions or thoughts on the study or other studies that are similar.
  • References: Any outside sources, studies, data, or information the author uses to support or argue the hypothesis.
    Important because: allows the reader to check sources; evaluate the author’s previous research, and connections between ideas.
  • Acknowledgements: Usually thanking the people who took part in the study, supported the author/researcher, or assisted in some way in the course of the study.
    Important because: may give the reader more information about the motivations behind the study, the author’s background, or other research that has been conducted on the topic.
  • Funding: some studies get grants or other financial support from outside sources (such as governments, private companies, or non-profit agencies); the author may want to disclose those to the reader.
    Important because: gives insight into who is behind the study, more motivations for the study, and any outside influence that may or may not skew the the results or the interpretations of the research.

Slide 4: Preview to Plan Your Reading

Slide4

Purpose could be any, all or any combination of the following things:

  • to identify arguments;
  • to weigh evidence;
  • to evaluate sources and resources;
  • to look for conflicts of interest and opinions disguised as facts;
  • to question assumptions;
  • to understand the “big picture;”
  • to add additional details to other source (such as lecture).

Once you determine your purpose for reading you can decide how you want to read your text. If your purpose involves a more comprehensive understanding of the text, such as to do well on an exam or essay, you will want to read slowly and deliberately, annotating while you read, asking questions, and critically thinking about the material. If you are reading for a class discussion, you may want to read slightly faster, focusing on only some of the most important details so you can participate and understand the discussion; you should still annotate, but you will not need to be as thorough. Use purpose to guide your style of reading and your reading speed.


Slide 5: Annotation

Slide5

Annotation Once you finish previewing, you can go back and carefully read the chapter or article and annotate it as you go. Your annotation style should reflect your purpose for reading, the style you’ve decide to read, how much time you’ve decided to invest, and how familiar (or unfamiliar) you are with the subject.

There are many ways to annotate and your method of annotation should depend on your purpose for reading. Consider the following purposes and methods, and keep in mind this is not an exhaustive list:

  • Are you reading to gain a basic understanding of the subject for a quiz or an exam? 
    Consider marking main ideas, key terms, and important ideas.
  • Are you planning to write a paper or essay using the article or book as a source?
    Mark facts, figures, statistics, and other factual information relevant to your essay topic.
  • Are you reading to participate in a class discussion?
    Mark points of personal interest, ideas you agree or disagree with, questions you have, and points you want to raise to your classmates.

Slide 6: While Annotating – Ask Questions!

Slide6

As you read you want to ask questions. Questioning as you go encourages you to stay involved with the text and helps to prevent boredom. More importantly, it helps you to identify main ideas, key topics, important themes, and makes your reading far more meaningful and productive. Questions you want to keep in mind include:

  • What is the structure of the text?
  • What questions is this text trying to answer?
  • What are the author’s sources?
  • Is this information opinion or fact? How do you know?
  • What evidence does the author use?
  • Is this a primary or secondary source?
  • Whose perspective(s) are we learning?
  • What information can one learn from the graphics?
  • How does this information fit into the class?

Slide 7: Two Note Taking Strategies

Slide7

Mapping is a visual note taking style that emphasizes relationships between ideas and the “big picture.” Mapping lends itself to the social sciences as it allows you to see all the details, especially those emphasized in lecture, as well as how those details fit into the larger subject. Mapping has many different ways it can be done depending on the material itself. Mapping can be used as either a lecture note taking strategy or a book note taking strategy.

When students think of “maps” they often think of bubbles and arrows that can go all over a page in a (sometimes) very disorganized way. Though this is one kind of mapping, there are many different kinds of maps, and you should make a point to be familiar with the different kinds so you can utilize them when you need them.

Timeline Map
This map is from an American history text; note that it is both a timeline (chronology) as well as cause & effect (see the arrow going from May 1773 to December 1773) (Rooney, 2010).
Stages of Adulthood Map
Done from a human services text, maps can help clear up differences (however subtle) between theories, people, or ideas.
Econ Map
This is a map of supply & demand done from an economics text. While I’m not an Econ major, I learned a great deal from just making this map to help me make sense of the material.
Bullying Map
Maps can also show processes, as this one shows the process (stages) of bullying, clearly, with use of color.

Some examples include:

  • Economics: graphs, flow charts, process graphs.
  • History: timelines, Venn diagrams, “comic strip” style pictures, cause/effect charts.
  • Behavioral Sciences: flow charts, Venn diagrams, process maps, cause/effects charts.

Slide 8: Two Note Taking Strategies

Slide8Grid Notes is another visual style of organizing information but has a structure that is “built-in” so you will find it more organized than traditional mapping. Grid Notes can be done during a lecture, while reading, or used as a way of studying information as preparation for an exam. One great thing about Grid Notes is that it makes it clear if there is any missing information.

You begin by drawing a grid on your paper (in your notebook or on a plain sheet of whit paper), or you can create a worksheet for yourself in Excel or Word. Standard Grid Notes use the “5W+H” method: Who, What, Where, When, Why, + How: write those in the very top of your grid. It should look something like this:

5WH

As you find information, white it in the corresponding box. For example, if your teacher mentions a name, write that name in one of the boxes under the “who” column; when your teacher gives you dates (like when that person was born, when they were active, etc.) write that in the “when” column. If, at the end of the lecture, you have an empty box, you may want to ask your teacher if that’s important information, or double check that you did not miss anything.

This can also be used while reading or reviewing your text. You can add to your Grid Notes from lecture, or create a grid specifically for your textbook. Either way, Grid Notes is an excellent way to organize your information!


Tips, Hints, & Strategies: Two Kinds of Math Errors

When it comes to any subject, there is nothing more frustrating than the feeling that you “just don’t get it.” I know because I felt that way many times in my math courses.

As I learned more about reading and metacognition, however, I learned that there are really two kinds of errors that are problematic in math and that the first step to success in math is figuring out what kind of errors you are most prone to making, then correcting those errors. Here are two types of errors in math that can be especially frustrating.

  1. Simple Math Errors.
    Simple Math Errors are exactly what you think they are: simple, straightforward reasons you missed an answer. It could be something like adding numbers up wrong, forgetting to carry a one, or adding an extra digit to a long number. Simple Math Errors usually mean you understand the concept of the problem (you know what formula/equation to use and how to use the equation, formula, etc.) but that you have trouble actually implementing the steps without making errors in simple addition, subtraction, multiplication, division, etc.If you have a tendency to make Simple Math Errors here are a few things you can try. Try a few and see what work best for you:
    * Slow down when writing down problems, and when solving them.
    * Double-check your numbers before you solve your equation.
    * Count the number of digits before you solve your equation.
    * Review each step before committing to your answer.
    * Use graph paper and put one digit in each box to help you line your number columns up when doing formulas/equations.
    * Use clear, neat, deliberate handwriting during tests so you can clearly see what you write; this also makes it easier to review before you submit your exam.
  2. Concept Errors.
    Concept Errors are far more problematic. If you do now know what formula to use or if your teacher writes on your paper “check your steps,” “using the wrong formula,” or “review this chapter” then you are probably making Concept Errors. Concept Errors mean you do not understand the concept of the problem; it means you do not know how to do the problem, where to start, what formula to use, or how to complete the steps.

    If you’re making Concept Errors, there are a few things you might want to try; try a few and see what works best for you:
    * Review the material in your textbook more frequently, especially spending time with the end-of-chapter and example questions.

    On the left side is the step-by-step breakdown of how to do the problem. On the right is the "translation" of the problem into English. This is one way to make sure you understand how to do a problem: Translate it into a language more familiar to you.
    On the left side is the step-by-step breakdown of how to do the problem. On the right is the “translation” of the problem into English. This is one way to make sure you understand how to do a problem: Translate it into a language more familiar to you.

    * Create Maps of problems and translate them into your “own” language so you better understand the steps (see picture).
    * Spend time with a peer tutor and work through problems together.
    * Organize a study group with other students in your class; explain problems to one another.
    * Go to your instructor’s office hours to get a more in-depth explanation of problems and how to solve them.


Math can be challenging but it is not impossible. When you get a disappointing grade on a math exam, use it as a learning experience. Spend some time with that exam, look at where you went wrong, and try not to make those same mistakes again. Learning from your mistakes is one the best things you can do to improve your scores in any class, especially math.

The Reading Math Workshop

Slide 1: The Reading Math Workshop Slide1

“What distinguishes a mathematical model from a poem, a song, a portrait or any other kind of ‘model,’ is that the mathematical model is an image of…reality pained with logical symbols instead of with words, sounds, or watercolors.” – John Casti, Mathematician, Author

Math is beautiful. Any person dedicated to the study of math will tell you that there is beauty in how numbers, formulas, and proofs work together. However, for those of us who have had negative experiences with math, it can seem overwhelming. Once you see that math is a kind of art form–albeit an exact one–it becomes much easier to appreciate the beauty of it. Do not be afraid of math: try to find the beauty in it.


Slide 2: Myths of Math Textbooks Slide2

Myth 1: “A math book isn’t for reading! I only use it to get my homework sets!”

False: Math is a written language; if you’re not reading it then you’re not learning it.

All the pages before your homework sets–the chapters–contain valuable explanations, examples, detailed processes and instruction beyond what your teacher can provide in class. Learning math is really about learning a new and very detailed written language; it has its own symbols and grammar that is often unfamiliar. A student would never expect to learn a different language, like German or Japanese, without taking the time to at least look over and familiarize himself with the writing of that language.

Math, like other languages, as definitions, sentences, paragraphs, syntax, and grammar. Unlike most other languages, math is almost exclusively a written language so if you are not reading it then you are not learning it.

Myth 2: “Everything I have to learn for my class will be explained in detail during my teacher’s class lectures.”

False: The textbook is there to both complement and supplement your class lectures.

While in class, your teacher has 20, or oftentimes many more, students who all must understand the material being presented. Each student has a different background with math, different education levels, different comfort levels, and different learning styles. The teacher simply does not have the time to teach the class specifically to each student to assure that each one understands it. It is your responsibility to learn those things that you personally did not understand, or the material that was not covered at the depth you needed, by reading the textbook. The textbook is there to both complement and supplement the lectures.


Slide 3: Myths of Math Textbooks (continued) Slide3

Myth 3: “When reading a math book, you start at the first page and you end at the last page, and there’s no deviation from this.”

False: You must read in all directions and the author intends for you to make connections between many parts of the text.

Math is a subject that is learned cumulatively–that is, it is a subject that demands that you understand older, already taught information before you can completely understand new information. For this reason, you must read in all directions and, more importantly, the author intends for you to skip around and make connections between paragraphs and chapters. By skipping around, you are making mental notes of the connections between the ideas, and the significance of the relationships between the new information you’re learning and the old information you are already familiar with. Examples of skipping might be skipping back a chapter to review how exponents work when you begin a new chapter on multiplying exponents. Or, the author may prompt you to flip to an appendix in the back of your book to look at a chart or table to help you understand a problem better. Do not skip the temptation to review previous chapters or the author’s prompting: you may miss an important tool that will make your homework easier.

Myth 4: “Even if I do read, take notes, and study I’m not naturally talented at math and I know I’ll fail anyway!”

False: Anyone can learn math!

Think about a skill or talent you have, like driving, reading, fixing cars, writing, or playing an instrument. Were you born with this ability? Of course not; with years of training, education, and practice you have learned to drive, read, fix cards, write, or play an instrument. There are, however, people out there who may possess and ability that allows them to go far beyond the average ability, like race car drivers, famous novelists, or virtuoso pianists but, by and large, they are not the majority. Math is the same: anyone can learn math. There are people who can solve complicated mathematical formulas and study well beyond calculus, but these people are not the majority. Instead of focusing on how terrible you are at math, be positive and assert yourself into the subject like you would any class in which you feel confident. By staying positive, you will be more likely to succeed and you will not suffer the mental pressure of predicting your own failure.


Slide 4: Surveying – Pre-Read for Maximum Readiness!Slide4 Surveying, or previewing, is a way of getting to know your textbook. Math texts are like toolboxes: they contain a number of important tools to help you understand the material more fully. You should know what materials you have in your Math textbook. Survey your textbook at the beginning of each semester from front to back. Look at:

  • the cover (front and back) – note any websites, or inserts that might be important.
  • the preface – this will often tell you, the student, how the book should be used.
  • the letter from the author(s)/editor(s) – this will usually give tips on how to study from the book, how to effectively use the text, and what outside resources are available to you (like websites, study guides, etc.)
  • all the materials in the back including appendices, glossary, homework solutions, practice problems, and the index(es) – knowing what materials are available to you will make it easier should you need to find them again.

As you find useful materials in your text, put a sticky note so you can find them quickly and easily when you need to.


Slide 5: Surveying – Pre-Read for Maximum Readiness! (continued)Slide5 Before you begin a new chapter, take a few minutes to preview. Knowing what to expect as you read through a chapter will make it easier to plan your time and will often ease anxiety because you will know what to expect. To survey a chapter:

  • Read the title carefully.
    • Based on the title, what is the chapter going to be about?
    • Do I know anything about this topic/subject already?
    • What kinds of things might the author tell me or explain to me in this chapter?
  • Read the first paragraph.
    • How does the author start out the chapter? Is it an example, a formula, or something else?
    • What might the rest of the chapter say to support this introduction?
  • Read the headings, subheadings, and bulleted lists.
    • Are there words you do not know? Look up the definitions in your glossary.
  • Examining pictures, charts, graphs, and other visual aids; read the captions, too.
    • Do you recognize any of them? Can you make sense of any of them?
  • Read the chapter summary, problems, solutions, and chapter questions at the end of the chapter.
    • Can you answer any of the questions already?
    • Is there anything in the chapter that is particularly challenging? Or anything that is mostly review?
  • Write down any questions you have before you read.
    • Once you finish reading, use these questions to check what you’ve learned. If you can answer the questions you’ve asked after you’ve read, then you can be more certain that you understand the material.

Slide 6: Annotation

Slide6

Annotating your math books is just as important as any of your other books. Typical math texts have short chapters, lots of example problems, and not a lot of explanation, so it is sometimes easy to justify skipping them.

Annotating math books is not hard, but it is different from other kinds of annotation.

“Students [can] annotate mathematics [by]…annotating lecture notes with comments, questions, additional steps or reflections on learning. Solutions to problems and important theorems can be annotated. You can add ntoes to a mathematical model about the assumptions that underpin the modeling or annotate a definition with a range of examples that satisfy it. The range of material that can be annotated is clearly vast, as are the types of annotations.”

– Dr. Peter Kahn, Annotating mathematical material: a route to developing holistic understanding and learner autonomy.

Annotation is a way of carrying on a “conversation” with the text. While you read your math text, make a point to ask questions, look for answers, add steps, or write down your schema. All of these things, and more, can help you connect with the materials.

Keep in mind as you read that math is a cumulative subject: this means that what you learned in previous classes is very relevant to your current class. As you annotate, it is important to make connections between “old material”–those things you already know and have learned–and the “new material”–the information in your current class. One way to annotate is to simply remind yourself how this new material connects to old material.

Another important annotation method is to add steps to the examples in your text. Oftentimes, the text will present you with a series of steps to follow to complete a problem but, since there is limited space on a page/in a text, they may skip steps deemed “simple,” or “unnecessary.” If, however, you find these steps (no matter how small) to be important to your understanding, make a point to add those steps in to help your understanding of the problem.

This is an example of annotation in a statistics text:

Math Annotation


Slide 7: Annotation – Don’t Skip the Examples!Slide7

Examples are a very important part of your math text. While it is tempting to see an entire page dedicated to an example problem as one less page you must read, you need to read those examples carefully to make sure you understand how to complete the problem. One method of “reading” the examples is to treat them as problems you must work through on your own, then compare your answer and steps with that of the book to see if you are understanding what you must do.

Follow these steps when your reach an example problem in your text:

  1. Take a sheet of paper and cover up all but the first line of the problem.
  2. Using what you have learned so far in the chapter (or what you should have learned) work through the problem on your own.
  3. When finished with the problem, uncover the answer and steps and compare your answer and steps with those of the book.
  4. Ask yourself: is my answer correct?
    1. If yes: did your steps match those in the text? What was different? Why?
    2. If no: What did you do wrong? What kind of error did you make? A simple math error or a concept error?
  5. Use the explanations/summaries in the chapter to decide how best to do the problems: sometimes the way that works for you is the best way but other times it is best to practice the way your book (or teacher) recommends.

Slide 8: Outlining Slide8

Outlining is an excellent method to help organize chapter information into short, manageable notes. Once you have surveyed and annotated your chapter, go through and pull out the most important main ideas, formulas, processes, and information to put into an organized outline.

  • After reading, go through the chapter and focus on only the most important ideas, formulas, processes, and questions.
  • Summarize and paraphrase those things into manageable parts.
  • Break problems down with explanations and steps.
  • Add “definitions” of symbols, formulas, and functions in language you understand (translate from “math” to English [or a more familiar language]).

When you are done with your outline, you can put it in your notebook and use it to study from or refer back to it to keep the chapter fresh in your mind as the semester goes on.

Here are two examples of outlines. These are from a Geometry textbook:

Math Outline1 Math Outline2


Slide 9: Mapping

Slide9

Mapping is a visual form of outlining that can be particularly helpful for students who have trouble “translating” from math to their own language. In the example on the slide, the student uses an example problem of the quadratic formula to move through each step while using color to show where the work in the formula is occurring. On the right side of the map is the “English translation” of each step. Remember, if you can explain how and why each step works then you can feel confident you will remember those same steps on an exam.

Steps to mapping are:

  • After reading, go through the sample problems (or homework problems) that give you trouble.
  • Creating a map to find each solution.
  • With each step in the problem, write exactly what you are doing to solve the problem.
  • Be specific and do not skip steps!

References

Kahn, Peter. (2010). Annotating mathematical material: a route to developing holistic understanding and learner autonomy. MSOR Connections 10(1). Liverpool, UK: University of Liverpool, Center for Lifelong Learning.

Tips, Hint, & Strategies: My beef with “flashcards.”

I have always hated flash cards.

I remember the first time a teacher had the class make flash cards and the directions were something like:

Write the word on the front of the cards and then put a simple definition of the word on the back.

Following these directions, I made twenty or thirty cards, then lost half of them in my room a few days later. The ones I managed to find I ended up not studying because well, I was bored reading the same things over and over and the definitions were hard to remember anyway.

No matter how many times I tried to make flashcards the result was the same. Tons of cards, some lost, other avoided. Then, once I got to college, “memorized” definitions were never on exams anyway. Honestly, when is the last time you saw a question on an exam that asked you to provide the textbook’s definition of anything? I had an anthropology teacher once who had us memorize the definition of culture but that was the one and only time in all of college when I was required to memorize a definition verbatim. All other times I was required to know context of words or examples, and the definition of a word was of little use.

This is why I like vocab cards.

Vocab cards encourage critical thinking and creativity. This is why vocab cards are hard to make but also what makes them so effective. Look at my cards below:

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There are lots of different ways to make effective vocab cards but, no matter how you make them, you should do some thinking while you make them. Simply copying information out of your textbook is not enough to help you learn the material.

The best part of vocab cards–at least for me–is how fun they can be. If you put questions on your cards you can pretend to play jeopardy. If you put pictures, you can spend time with crayons and color. I can brainstorm questions I think my teacher might ask, or those posed by my classmates in class, then put my answers on the back. When I make vocab cards I feel like I care.

I still, however, had problems keeping track of my cards. While I consider myself pretty organized, it always happened that I would lose one or two cards in my bag, in my car, or somewhere in a drawer at my desk.

So annoying.

A few years ago I worked with a student who was very disorganized and refused to make vocab cards because she would “always lose them anyway” and she hated to “waste time making something I’ll lose!” I challenged her to be creative and find a way to make vocab cards and find a way to not lose them. She came up with Flippers.

Flippers are amazing. Basically, take a sheet of paper; white, lined, three-hole-punched paper works just fine. Then, get a pack of Super Sticky Post-It Notes. The regular work, too, but the Super-Sticky kind really stay stuck long-term. Then, voila! Flippers:

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Call them whatever you want: flash or vocab cards can and do work, if you know how to make them effectively. Basically:

  • Be creative.
  • Be smart.
  • Think hard.
  • Ask questions.

For more tips about improving your vocabulary and making vocab cards see my Vocabulary Improvement Workshop.

The Vocabulary Improvement Workshop

Slide 1: Introduction Slide Slide1

The limits of my language means the limits of my world – Ludwig Wittgenstein (philosopher, mathematician, logician)

Language is powerful. It is powerful enough that, if a person finds himself in a place where he cannot use language he will often feel limited and helpless. This is true in every facet of life. That is why knowing how to communicate effectively is key to success in college. For this reason, it is important you learn the language of your courses, called jargon. Jargon is discipline-specific vocabularies you must master to do well in your courses. Some jargon can sound familiar and some can sound very foreign. To maximize your success in college, and later in the workforce, find ways to learn and integrate new jargon into your vocabulary.


Slide 2: Previewing – Identify Important Words Before You Read Slide2

Previewing is a powerful way to begin to introduce new words into your vocabulary. Previewing is also very simple to do. You simply look over material before you read it and make a point to identify and look up new or unknown words.

There are places you can look to help you identify the most important terms. The most obvious places are:

  • Titles, Headings, and Subtitles – As you look at each heading, note any unknown words and look them up in the glossary, if necessary. Also make a note of any words that appear multiple times; repetition usually is a sign of importance when it comes to terminology.
  • Objectives and Key TermsObjectives usually appear before the chapter begins; Key Terms usually appear at the end of each chapter. Focus on these areas  because terms that appear in these sections are those that the author feels are most important within the chapter.

Another important strategy is to say new words out loud when you encounter them for the first time. There are many words that sound different from how they are spelled. Take for example the word genre. This is word you might encounter in an art, music, history, humanities, or literature textbook. Do you know how this word is pronounced? If you do not know, you may go to class and wonder what your teacher is saying when she says a word that sounds like “jon-ra.” Believe it or not, the word genre sounds like “jon-ra.” If you had not connected the word with the sound, it might lead you to be very confused because you cannot connect the word you see on the page (genre) with the word you hear (“jon-ra”).

Example Dictionary
To hear how to pronounce a word, click on the speaker symbol next to the word on the Merriam-Webster site. If you have headphones on, or your speakers turned up, you will hear the word being “spoken” by a voice on the computer.

If you’re not sure how to pronounce word, there are many sites online to help you. Merriam-Webster’s Online Dictionary offers a link you can click that allows you to “hear” the word through your computer speakers or headphones.

You can also ask your peers, friends, and family to help you pronounce the word. They might know how to say it and you can practice saying it, too. Making this connection between the way a word looks and the the way it sounds can make learning new vocabulary in your class much easier to do.


No Slide: Knowing Vocabulary Resources

An important part of expanding your vocabulary is  knowing what resources are available and when to best use those resources. The following section is going to introduce three of the most commonly used vocabulary resources, how to use them, and when to use them. These resources are:

  1. The Glossary – For discipline-specific definitions.
  2. The Dictionary – For general definitions.
  3. The Thesaurus – To find words with a similar definition.

Slide 3: The Glossary

Slide3

A glossary should be your first stop to finding the definition of a word. You also want to be sure to use a glossary that is specific to your class, if possible. As you will see in the next slide, if you try to use a glossary from a different course, you run the risk of using a wrong definition if you rely on glossaries from other texts or disciplines.

The glossary is a resource the gives a single, very specific definition of a word. The definition of the word is dependent on the discipline or field in which the word is being used; the dictionary contains jargon. Jargon are words and expressions that have a specific meaning within a specialized context. Jargon can make understanding especially difficult if you are unfamiliar with the specialized terms.

If you find yourself with a text or class that does not provide a glossary to define terms, ask your professor for a recommendation. Your professor might recommend a handout, book, or website to help you get specialized definitions. If that is not possible, you can often find specialized glossaries online like the American Psychological Association’s Glossary of Psychological Terms, the Oxford Reference Dictionary of Sociology, or the Oxford Reference Dictionary of Literary Terms. When using an outside glossary, use caution that the definitions provided match the context of your class. If you are not sure, be sure to ask your professor.

To use a glossary follow these simple steps:

  1. Locate a glossary.
    Glossaries are usually found in the back of your textbooks. If you cannot find one that suits your purpose, you may consider making one of your own in your notebook.
  2. Look up the term.
    Glossaries are almost always organized alphabetically, like a dictionary.
  3. Paraphrase the definition.
    To be sure you understand what the word means, put the definition in words that are simple and clear. If you cannot do this, make a note of some questions that might help you figure it out.
  4. Apply the definition to your text.
    Once you know what the definition is, take your paraphrase and apply it to the term in the book.

Slide 4: The Glossary – Example Slide4

Let’s look at an example of why it is important to use a glossary instead of a dictionary in many college courses. Compare the two definitions:

  • Gender is “the social and culture differences a society assigns to people based on their biological sex. It is a social concept. It refers to the social and cultural differences a society assigns to people based on their biological sex.”
  • Gender is “recognizing that biology and culture interact, gender is defined as the state of being male or female. When we use the term sex we are referring to sexual behavior.”

These definitions are of the word gender; and this word appears in both sociology, which is where the first definition appears, and in psychology, which is the second definition. If you use one definition you learned in sociology in your psych class, then you will be confused and you will most likely lose points on exams and quizzes. Be sure that you always refer to a specialized glossary first, even if you believe you may know the answer already.


Slide 5: The Dictionary

Slide5The dictionary should be your second choice for finding the meaning of unknown words. While a glossary provides only one definition, a dictionary will provide several, if not dozens. When using the dictionary, it is the responsibility of the reader to decide what definition is most relevant based on the context of the word in the sentence.

To use a dictionary:

  1. Find a dictionary.
    Paper dictionaries are fine but if one is not available use an online dictionary.
  2. Look up the term.
    Dictionaries, like glossaries, are organized alphabetically; if using an online dictionary, then just find the search box and type your word in and click search.
  3. Locate the most relevant definition, based on context.
    This is the hard part of using the dictionary: you have to examine each definition given to determine which one works best for your purpose. I will cover this more in the next few slides.
  4. Paraphrase the definition.
    To be sure you understand what the word means, put the definition in words that are simple and clear. If you cannot do this, make a note of some questions that might help you figure it out.
  5. Apply the definition to the text.
    Once you know what the definition is, take your paraphrase and apply it to the term in the book.

Slide 6: The Dictionary – Example Slide6

Take the word mole. If you look at a dictionary for the definition of the word mole you will find that there are six different definitions of the word, and each definition is completely different. On the slide above, you will see I pulled out the four that are most related to education: zoology, chemistry, anatomy, and political science.

Now consider the following sentence:

“Each mole of sodium hydroxide dissolves to give a mole of  hydroxide ions in solution.”

How could you determine which definition to use?

Slide 6: The Dictionary – Example (continued) Slide7

Here is the sentence again:

“Each mole of sodium hydroxide dissolves to give a mole of hydroxide ions in solution.”

Take each definition given by the dictionary and paraphrase it in the most basic terms, then insert those definitions into the original sentence. You will probably find that any definition that does not fit the context will become clear.

So, for mole, the definitions are:

  • Zoological: “Each animal that burrows underground of sodium hydroxide dissolves to give an animal that burrows underground of hydroxide ions in solution.
  • Chemical: “Each single atom of sodium hydroxide dissolves to give a single atom of hydroxide ions in solution.”
  • Anatomical: “Each mark or blemish on human skin of hydroxide dissolves to give a mark or blemish on human skin of hydroxide ions in solution.”
  • Political: “Each long-term spy who infiltrates a country of hydroxide dissolves to give a long-term spy who infiltrates a country of hydroxide ions in solution.”

Clearly, the chemical definition is the one that is intended by the context of this sentence. However, you can also see that, had you chosen the first definition the dictionary presented, using the wrong definition can make understanding near impossible.

Slide 7: The Thesaurus Slide8

2011-05-31-advice
From the genius(es) at Buttersafe.com.

Many students misuse the thesaurus. Before I explain how to use a thesaurus, let me explain how not to use it:

Do not use the thesaurus to make your writing “sound” smarter.

If you try to rephrase your writing using words that you do not understand, then all you are doing is creating a paper full of nonsense. Teachers would much rather you say what you mean simply and clearly than to read a paper full of what is best described as “word salad.”

A thesaurus is a great tool to learn new words but not in the way you suspect. Use it to search for unknown words and find words that you understand already. A thesaurus is a tool best used to paraphrase.

The steps to using a thesaurus are:

  1. Find a thesaurus.
    Of course you can get a paper one, or you can use sites like Thesaurus.com.
  2. Look up the unknown or confusing term.
    A thesaurus is organized alphabetically or you can type the word into the search box if using a website.
  3. Identify alternate, more familiar word(s) that help you understand the original word.
    Select a few words from the list of given terms that you know or are very familiar with.
  4. Paraphrase the definition of the unknown words using the more familiar words.
    Using the known words, create a new sentence (paraphrase) so you can understand what the original sentence is saying.

Slide 7: The Thesaurus – Example

Slide9

Take, for example, the sentence:

“In literature, the unpleasantness of cacophony is utilized by the writers to present dreadful or distasteful situations.”

In that sentence, the word cacophony is particularly hard to understand. On Thesaurus.com, I typed in the word cacophony and looked at other words that have a similar meaning. I chose the words dissonance, harshness, and jarring
because those are the words most familiar to me. You might select other words from the list you are more familiar with.


Slide 8: The Thesaurus – Example (continued) Slide10

Now I can return to my original sentence and paraphrase it with new words–the ones I understand better–to better understand what the sentence says:

“In literature, words that sound harsh, jarring, or not pleasant to hear are used by writers to present bad or unwelcome situations.”

This sentence is much easier to understand!


Slide 9: Word Parts – Understand a Word Without a Resource
Slide11

Another way to improve your vocabulary is to learn affixes and roots. Affixes include prefixes and suffixes and are added to root words to change their meanings or parts of speech. Prefixes in particular can be useful in understanding words. In fact, there are nine major prefixes that cover 76% of all prefixed words (Roe & Smith, 2012, p. 175) so learning these nine prefixes can unlock a great deal of meaning.

The prefixes most useful to college students are:

Prefixes
Word prefixes that are most useful to college students.

Prefixes can be especially useful in unlocking unknown words. If you do not have access to a dictionary or other resource, knowing even basic prefixes can allow you to at least make somewhat educated guesses about the meaning of a word. Since many root words are generally more familiar, chances are you know the definition of the root and just need to know how the prefix is working to change the definition. (For example, in the table above, the root words in the far right column are, in order from top to bottom: freeze, frost, agree, justice, possible, act, way, view, turn, port, and friend.)

Prefixes and roots are especially useful to students who are interested in studying sciences–especially nursing students or aspiring doctors. A great deal of biology, anatomy, and chemistry consists of prefixes that identify quantity (mono-, di-, pan-, etc.), location in the body (cervico-, chole-, boncho-, etc.), or position (circum-, co-, para-, etc.). Learning common prefixes is essential to success in studying medicine or nursing.


Slide 10: Word Parts – Example

Slide12For this example, I pulled some terms from a nutrition book:

  • Monosaccharides
  • Disaccharides
  • Polysaccharides
  • Oligosaccharides

If unfamiliar with nutrition, these words can seem intimidating. Broken into parts, however, they are a little less scary:

  • Monosaccharides
  • Disaccharides
  • Polysaccharides
  • Oligosaccharides

It turns out that these four words are really one root (saccharides) with four different prefixes (mono-, di-, poly-, oligo-). These prefixes tell you quantity and the root tells you what:

  • saccharides means sugars
  • mono- means one
  • di- means two
  • poly- means many
  • oligo- means few

With this knowledge, these once intimidating words now seem accessible and much easier to learn. Also, once you learn these four prefixes, you also learn a number of other words that include these prefixes. Words like monotheism, dilemma, polyglot, and oligospermia all seem much more accessible even if you do not yet know what the root word means.

Slide 11: Vocab Cards – Memorizing is not understanding!

Slide13

When it comes to making flash cards, I must admit, I am biased: I have always disliked making them. This is why I call my cards vocab cards instead of flashcards because these cards I have found especially helpful, unlike flashcards which I have found to be a waste.

My beef with flashcards is that they are often to taught one way (term on the front & definition on the back), and the definition is almost always copied out of a textbook with very little thought. Furthermore, students (like me) would make dozens, if not hundreds, of these cards and everything about them from making them to studying them, became completely impractical.

Vocab cards, on the other hand, encourage critical thinking, originality, and prioritizing your materials. Here are the keys to good vocab cards:

  • Include examples.
    Examples can go a long way to help give context to material. You can add the example as an extra feature to your card, like dividing the card and putting the definition on one side and an example on the other, with the term on the opposite side.
  • Draw pictures.
    Especially useful for foreign languages or sciences, drawing a picture of a word is especially helpful. For example, you might put a word from the foreign language on one side, and draw a picture on the other. Or, you might recreate a picture from your biology book on one side, then put the term on the other.
  • Use color.
    Adding a touch of color to your cards can give them personality! If you are a person who enjoys pictures and visuals, drawing and then coloring your pictures can help you make connections and help long-term memory. Even just color coding your cards (green for one subject, pink for another; or green for one chapter, pink for another chapter) can help improve memory.
  • Write questions instead of statements or definitions.
    Instead of just writing statements or paraphrasing definitions, think up questions that might show up on an exam and put those on your cards instead. Then you can use your cards for a jeopardy-style game and quiz yourself or have someone else quiz you. This is much more fun and useful than simply trying to memorize.
  • Be creative! 
    There is no one right way to make vocab cards! Try new ways to make them and make a variety of cards. Most importantly, make cards that work for YOU.
  • Only make cards for things you do not know; do not make cards for words you already know.
    Basically, do not make a vocab card for something you already know. It wastes your time and the paper. Before you make your vocab cards, sit down and quiz yourself from you key term list. If you can do the following three things, then do not make a vocab card:

    • paraphrase the definition of a word;
    • give an example of a word;
    • explain why the word is important in the context of your course.

Final Thoughts:

Improving vocabulary is a lifelong process. Even when you finish school, you will need to find ways to help you learn new words on the job. Learning strategies now to help you do that will only help you in the job market.

The thing to remember about vocab or flash cards is that they only work if you study them. Do not make so many cards that you do not have time to back and review them often. If you find yourself in a class with many new words, you might consider making vocab cards as you go through the class–perhaps even daily–so you can continue to review them long-term.


Examples of Vocab Cards

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Psychology Vocab Cards (Front Side). Note: I put the chapter number on the top right corner so I can go back to the chapter if necessary. There are fill-in-the-blank style questions and open-ended questions.
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Psychology Vocab Cards (Back Side). The backs of the cards have questions, too. See that the answers for one side are found in the questions on the opposite side. These cards are very challenging to make but encourage critical thinking about the material and trying to think of ways your instructor might ask about material on an exam.

Flippers

I had a student a few semesters ago who refused to make vocab cards because she would always lose them. I encouraged her to be creative: she did not have to use “cards” if she did not want to but she had to come up with another way to learn the vocab. This was her solution: flippers.

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Flippers are best when made with Super Sticky Post-It Notes because the regular ones fall off pretty fast. The regular-sized notes work great for half-sheet of paper and you can fold the notes up once you stick them to the page. Label your page so you can remember what class/chapter you made them for.

Story: “10 minutes a day makes an A!”: A Story of Review

I love skeptics.

A few semesters ago I was giving my Lecture Note Taking Workshop to a group of students. Part of that workshop explains the importance of reviewing and that many students, who complain about “memory problems,” really just have a “lack-of-reviewing problem.” At the end of the workshop a student I did not recognize approached me and asked “Does reviewing really work?”

I told him, yes, for most students reviewing is the best way to improve memory. He scoffed, explaining he’s had memory problems in school his whole life. No matter how much he studied, he just could not remember anything for more than day or two. He said that he did not believe me but would try it anyway–just to prove me wrong. I just smiled and told him I’d love to hear his results if he tries my review tips for himself.

Over a month later I was in my center working when a student walked in. I did not recognize him at first, and asked if he needed any help. He said he did not need help, but that he did want to talk with me. He went on to explain that, after my workshop, he did start reviewing every night. He would simply open up his note book and spend 10 minutes each day looking over all his notes, beginning with the most recent and working his way back to his oldest. He did this for 2 weeks then had to take a quiz.

He was shocked when he got 10/10 on the quiz; he usually got a 7.

Then he thought that maybe his score was a fluke; maybe the material was easier than normal, or maybe he guessed better than usual. But he kept reviewing, 10 minutes each day, until his next quiz 2 weeks later.

Another 10/10.

This was no fluke; he was remembering more, and for longer. And what the teacher said made more sense with each lecture. Things were coming together.

After his second perfect score, he sat down and tried to remember what he used to do to “study.” Often he would just reread his book (or, he said, read a few paragraphs, then quit because he was bored), or review his notes in the week before his exam (going months without looking at some of the material) and try to cram the old material he had forgotten.

He had a “lack-of-reviewing problem” not a “memory problem.”

Before he came to see me that day he had received another perfect quiz score, and a stellar mid-term exam score. “10 minutes a day makes an A!” he laughingly admitted. He felt he should probably come by and tell me that I was right: Reviewing really does work.