Guest Appearance on Vermont Reads Institute Blog

Check out a recent post I did for Vermont Reads Institute.

Updating the Book Review

Prior to getting married, buying a house, and having kids, one of my favorite things to do on a Sunday was to buy the New York Times and spend the morning drinking cup after cup of coffee and reading it cover to cover.  Once my husband and I realized that we were trying to read the paper while using it to start our wood stove, we understood this form of entertainment was gone.  Although I should admit to missing knowing the news of the week, what I miss most is the Book Review.  

As someone who is always trying to find out about the next new book, I used to read the hard copy of the paper, as well as talk to people about what they were reading and what they might recommend.  However, as my life has become more busy, the ability to take five minutes to have a face-to-face conversation or read a review in a newspaper has disappeared.

Luckily, book reviews and conversations have grown with the times and become digitized.

In trying to engage my students in learning more about books (as well as letting others know about their choices), I have to say I am a fan of all the new ways to stay up on your books.

Here are a few that I recommend:


Shelfari -- One of my best friends from high school introduced me to this site.  This site allows for you to keep track of all your books on a bookshelf.  As I type this entry, I have 821 books listed on the site and I am guessing there are more out there that I haven't included yet.  In addition to keeping track of books you have read, you can also note books you are reading or want to read.  Beyond your own personal shelf, you can see other people's shelves, as well as join online book groups with different topics.  Some groups I belong to are: YA Books That Adults Should Read, Moms Who Read to Escape Their Weary Lives, and 1001 Books You Must Read Before You Die.  Although I have yet to use Shelfari in my classroom, I know plenty of teachers who use this with students and have found it to be very successful in getting students excited about reading, as well as discussing what they read.


GoodReads -- Like Shelfari, GoodReads allows you to keep track of books, join groups, etc.  Different from Shelfari (which is probably why I belong to both) is the ability to read blogs of different authors, as well as use its app on your mobile device.  This is really cool because rather than write down that book you see at the bookstore you can just scan its bar code and upload it to your list of books to read.  Lastly, many authors or professionals have accounts on GoodReads so you have the opportunity to look at their shelves/blogs as well.  A couple of note are:

• Donalyn Miller
• Penny Kittle

Blogs -- Many people have blogs that include "book talks" of sorts on a regular basis so you can keep up on the latest and greatest that is out there.  Since Young Adult Fiction (YAF) is what I tend to read, I find myself drawn to these blogs, but there are plenty of them out there for picture books and chapter books as well.  In addition, I also tend to read both professional blogs and blogs by authors.  Some of my favorite blogs are:

• Laurie Halse Anderson
• Teri Lesesne
• Anita Silvey
• Dana Huff

Twitter -- Many authors and professionals have found a venue for letting us know about books and other literacy related ideas through their "tweets."  As Donalyn Miller noted at a conference that I attend recently that Twitter is a great way to find out about things and you don't have to follow it all the time, but whenever you get a chance there is usually something you can find on it.  Many authors and professionals "tweet" under the following:

• Donalyn Miller -- @donalynbooks
• Laurie Halse Anderson -- @halseanderson
• Kate Messner -- @KateMessner
• Teri Lesesne -- @ProfessorNana
• Penny Kittle -- @writer
• Jim Burke -- @englishcomp
• New York Times Books -- @nytimesbooks
• Neil Gaiman -- @neilhimself 

Facebook -- Like Twitter, many authors and professional organizations have taken to the social network to get their word out.

Overall, I still prefer the smell of the newspaper or cup of coffee (if I am chatting with friends), but until I can slow my life down to appreciate those smaller details, as well as learn about books, I am excited to know that I can keep up books and what is going on in the world of literacy with my computer or smartphone.  In addition, I hope it is a way to get students engaged in the conversation about books!

 

Getting the Conversation Started

According to Wosley and Lapp (2009), "conversation and discussion promote independent and deep thinking, and are at the same time social activities.  In the past, literacy has been traditionally associated with reading and writing; however, Kevin Lander, a professor at Vanderbilt University, "see[s] literacy as a set of social practices—where people make and use all manner of texts to act and interpret the world in meaningful ways" (2007).  

According to Buehl (2001), "the interactions between four conditions (reader, text, context, and strategies) determine what meaning a reader will construct from a text."  The one most important when thinking about conversation or discussion in your classroom is "the learning context that defines the task and purpose of the reader (Buehl, 2001)."  For many of our students, the opportunity to participate in a social setting with the text can allow for more motivation from the learner.  In addition, according to Wosley and Lapp (2009), "discussion is also a means to shape thinking."  Many student benefit from the ability to take an idea and reshape it through a conversation with peers.  


In addition, according to Nystrand and Gamoran (1990), we want students to participate in culture of learning based on substantive engagement, "a sustained commitment and involvement with academic work" that involves having students being willing, and hopefully eager, participants in the process.  Rather than, having students participate in procedural engagement which involves having students respond on demand when called on in the traditioanl IRE (Initiate-Response-Evalution) manner.  


There are a range of discussion ideas out there that can help students get the conversation started in the classroom. 


Socratic Circles (or Seminar)

Socratic Circles come from the ideas used by Socrates.  He believed that "students could improve their reasoning skills and ultimately move toward more rational thinking and ideas more easily supported with logic" (Copeland, 2007). 


Although there are different variations of Socratic Circles or Seminars,
it all starts with Socratic questioning which is "a systematic process for examining the ideas, questions, and answers that form the basis of human belief" (Copeland, 2007).  According to Mortimer Adler, we must teach "by asking questions, by leading discussions, by helping students to raise their minds up from a state of understanding or appreciating less to a state of understanding or appreciating more" (Copeland, 2007). 


Questioning


Developmentally, adolescents want to question everything, as well as directly connected it all to themselves; however, we have many adolescents who seek teachers out for the "right" answer solely because they don't want to be wrong, but more importantly so they don't get a bad grade.  Questioning allows students to develop some critical thinking skills to go beyond the one right answer dilemma.  Question-Answer Relationships (QAR) or Questioning the Author  (QtA) might be ways to get student thinking about ways to question.

Annotating the Text

In order to help develop good critical question, it is also important that the students annotate the text .  Being able to critically interact with the text, in order to construct your own meaning, is necessary if you are going to be able to share and contribute to a discussion.  Although many great discussions happen on the fly, for many of our students they need to learn how to come prepared to a discussion.  Some folks have students use bookmarks to write down their thinking, write in margins, or use sticky notes.


Modeling/Providing Prompts

It is important to help students learn the discourse or language of discussion by both modeling and providing examples of prompts that help extend the conversation.  For example, students familiar with Question-Answer Relation (QAR)  might benefit from a list of prompts which when modeled can show them how to expand their interactions in a discussion.  Other more general prompts like "I saw it a different way" or "Can you explain more about why you thought that?" get students to think critically about what other members of the discussion are saying.


Discussion Webs


These graphic organizers allow for students to take a "look at an issue from both sides before drawing conclusions" (Alvermann, 1991).  Having a student do some work where they have to critically look at an issue before deciding where they fall allows for them to challenge what they believe, and maybe even come to a new conclusion.

Planning

The other piece to think about when thinking about including discussions/conversations in your classroom -- whether it be in pairs, small groups, or whole class -- is your plan.  Guiding conversations for students at all grade levels requires an art of planning so that the students have the knowledge and vocabulary necessary to participate, as well as a clear purpose as to why they are doing it.  Spiegel (2005) mentions using a planning chart for whole-class discussion that focuses on essential background knowledge, essential vocabulary, and goals and purposes.  These same elements can be consider in any instruction related to using discussions and conversations in class.

In addition, it is important to think about a gradual release of responsibility model for any work with discussion to help teach students the discourse or language required for participating in an active conversation, as well as for showing students how we act within a conversation.  For example, it is okay to challenge an idea, but not a person.  Creating clear guidelines is important for all grades, as well as modeling what they look like.  Adler and Rougle (2005) use the following as an example:

• Everyone comes having read the text.
• Everyone needs to talk.
• Listen actively to others.
• Wait for quiet before you speak.
• Raise your hand after someone has finished.
• No one has a bad idea.
• Build on other's ideas.
• Maintain eye contact.

These are just an example of ones you might agree on for your classroom.

Technology

In a world filled with technology, there are many ways to have this conversation through a social networking site.  Some examples are Moodle, PBWiki, Ning, Google Groups, etc.  Schools recently have created their own social networking sites through their websites or other places like Global Classroom and others.  It is probably best to check if your school already has a forum for discussion so you don't reinvent the wheel.

Overall, these are only a snapshot of things to think about regarding discussion and conversation in your classroom.  Listed below are some resources that hopefully can extend your knowledge if you are interested in pursuing this idea more in your classroom.

Resources:

Adler, M., & Rougle, E. (2005). Building literacy through classroom discussion: research-based strategies for developing critical readers and thoughtful writer in middle school. New York, NY: Scholastic.

Buehl, D. (2001). Classroom strategies for interactive iearning. Newark, DE: IRA.


Copeland, M. (2005). Socratic circles: Fostering critical and creative thinking. Portland, NH: Stenhouse Publishers.

Crownover, A. (2007), "A new frontier: Kevin Leander finds new definitions of literacy." Peabody Reflector. url: http://peabody.vanderbilt.edu/x8084.xml.

Harvey, S. & Daniels, H. (2009). Comprehension & collaboration: Inquiry circles in action. Portsmouth, NH: Heinemann.

Nystrand, M., & Gamoran, A. (1990). "Student engagement: When recitation becomes conversation." Madison, WI: National Center for Effective Secondary Schools
 

Spiegel, D.L. (2005). Classroom discussion: Strategies for engaging all students, building 
higher-level thinking skills, and strengthening reading and writing across the curriculum. New York, NY: Scholastic.


Wilhelm, J.D., Baker, T.N., & Hackett, J.D. (2001). Strategic reading: Guiding students to lifelong literacy 6-12. Portsmouth, NH: Heinemann

Beyond Memorization: Using Critical Thinking Strategies for Learning Vocabulary

After getting the chance to observe in an English classroom during a vocabulary review session, I began thinking about how often we look for vocabulary strategies to help struggling learners who have a variety of literacy or executive functioning issues.  Yet, as I watched the students engaging in an activity that had them using visual associations to guess the definitions of words, I began to see how often we forget about using strategies as instruction to get our higher end learners to think beyond the dictionary definition.  So often, based on the type of test we give or their ability to memorize information easily, it appears as if non-struggling learners grasp the nuances of vocabulary.  In reality, many of these students don't truly understand the associations or connotations that go with many vocabulary words.  I am reminded of a Word Girl episode where the Butcher creates all of his own words, but seems to think that he is using the correct word.  In turn, I see this happening when students try to use certain words outside of the classroom where they have "learned" them.

While brainstorming some "strategies" for struggling learners to use as they embarked on a new list of words for the play The Crucible, I decided I would share strategies that not only would help the struggling learners understand the words, but challenge the other students in the class to go beyond memorizing the words for a quiz, test, or final exam.  In an ideal world, the students would be so familiar with the words that when they received the list for the final exam they would leap for joy knowing that they had very few words to "study," as well as be able to use them correctly outside the classroom.


The first thing I thought of when I looked at the list of words from The Crucible was how many of them can be connected directly to a particular character or event from the story -- most noticeably to the character of Abigail Williams.  [NOTE: If it has been a while since you read the play, she is the niece of Reverend Parris.  Until recently in the story, she was a servant at the Proctor house until she was caught having an affair with the husband.]  

To help the students connect the words to a particular character I created an organization chart that connected the following words with Abigail [callous, calumny, perjury, malign, potent, taunting].  [NOTE:  The links to these words come from two different web-based dictionary sources Merriam-Webster and Heinle Newbury House Dictionary of American English.]  The goal of the chart is that students will be able to find examples within the story where the vocabulary word can be associated with Abigail Williams.  Due to her character in the story, it is likely that students will be able to find multiple examples of the various words.  [NOTE: I would recommend that the teacher model a few of the words prior to having the students work on it individually.]  

Here is an example of how one can connect the word callous to Abigail Williams.  The word callous means "not caring about others." (Heinle)  In The Crucible, there are many places where we can see different people not caring about the well-being of others and only looking out for themselves.  One example of Abigail having a callous regard for someone is in her treatment of Elizabeth Proctor.  Since Abigail is looking to get rid of her in order to be with her husband (or get revenge on her husband for choosing Elizabeth over her), we can say that she shows a callous regard for Elizabeth when she accuses her of being a witch.  If this example is the one you choose to provide to the class as a model then students can look for other examples of Abigail acting in a callous manner to others.  In some ways,  I think often we use synonyms of words to help students understand the meaning of a words; However, sometimes, this use of scaffolding often ends up with the student using the synonym instead of the vocabulary word in conversation or application because of their familiarity with it.

Another approach to use with students comes from the book Words, Word, Words: Teaching Vocabulary in Grades 4-12 by Janet Allen (1999).  The approach "Words in Context" allows the student to break apart the word into its parts (prefix, suffix, etc.) and other words they know.  Two examples to model from the list of words from The Crucible are defamation and demonic.  Due to technical difficulties, I can't attach the organizer I created, but the idea is that the vocabulary word is at the top of your organizer with branches that break off with the headings "Word Parts" and "I recognize..."  With defamation, you break it down into de- (from, down) and -tion (act of, state of) as the two word parts and list their meanings underneath the prefix or suffix.  On the other side of the organizer, you have the word fame and underneath it a definition.  I also like to include with the word parts what part of speech the word usually becomes when that particular word part is added.  For example, -tion usually is a noun.  Once the students have broken down the word, they need to put it all back together by guessing at a definition.  The good thing about this approach is you can use it across content areas.  However, I would be carefully about overusing this strategy.  I think that using for a couple of your vocabulary words is fine, but using it for all of your vocabulary words makes it more formulaic than thoughtful.   An extension of this activity might be to include other words that come from the word parts or recognized word to help increase vocabulary (i.e. famous, defame, familiarity, etc.)


The following ideas are from a workshop run by Nancy Wood (Vermont Reads Institute Literacy Consultant) titled "Vocabulary 12-40 Exposure: A Collection of Approaches You Can Sprinkle Throughout Your Day."  However, I have noted the resource that you can find these approaches in at the end of this post.

Connect Two (Blachowicz, 1986)

•  Words are listed in random order in two columns (5 or 10 apiece)
• Students are challenged to find similiarities between the two words

Example of directions:

Find a word in column one that has something in common with column two. (Students need to find similarities in meaning or construction of the two words.)

An example from the vocabulary from The Crucible could be the words predilection and abomination.  A student might notice that both end in -tion signaling that these two words are both nouns.  Using this strategy while introducing the words might allow students to become familiar with parts of speech or allow you to get a sense of whether students have a familiarity with the words.  However, you could also use this near the end with the expectation that students are thinking more closely about the ways in which words can be connected both in and out of the content area.  For example, perjury and defamation could be linked together because of the role they play in The Crucible, but they can also be connected in a legal sense.

Words Associations (Beck, McKeown, & Kucan, 2002)

"After having presented explanations for words, ask students to associate one of their new words with a presented word or phrase, such as the following examples:

• Which word goes with crook? (accomplice)
• Which word goes with "gift to a new hospital?" (philanthropist)
• Which word goes with piano? (virtuoso)
• Which word goes with kindergartner? (novice)

Ask why they decided on the connection they have made.  Associating a known word with a newly learned word reinforces even further the meaning of the word.  The associations are not synonyms: rather the student must develop a relationship.  Having students explain their reasoning is an essential component of the kind of instruction that requires learners to process information" (44-45).

Idea Completions (Beck, McKeown, & Kucan, 2002)

"Provide students with sentence stems that require them to integrate a word's meaning into a context in order to explain a situation.  

Examples:

The audience asked the virtuoso to play another piece of music because...

The skiing teacher said Maria was a novice on the ski slopes because...

Other variations include:

When might you...?
How might you...?
Why might you...?

The key to effective activities is that they require students to attend to a word's meaning in order to apply it meaningfully to an example situation" (45-46). 

These are just a couple different activities connected to vocabulary instruction and strategies.  Although these are great ideas in vocabulary, they may not be right for your students or the words you choose all of the time.  I think one of the most important things about vocabulary instruction is to remember that due to the different types of words (whether you call them tiered words, academic words, etc.) there are a plethora of ways to approach them so that students can get the most out of them.  I think about the idea of using the game show Jeopardy as a review before a big test and including a category about vocabulary -- if it is out of context to the big ideas or understandings you want the students to learn, they may be able to pick out the word on that day or the day of the test; however, the odds of them remembering it for life or connected to that big idea or unit may not be that great.  Jeopardy might be good some, but not every time you do a review just like these strategies might be good some of the time.  It is important to think about how vocabulary ideas like the ones above can be embedded in the instruction of your curriculum so that they don't become an add-on.

Do you have a favorite vocabulary activity, lesson, or idea that others might benefit from?  Please attach these ideas (and links if you have them) to the comment section.

 
Resources

Allen, J. (1999). Words, words, words: Teaching vocabulary in grades 4-12. Portland, ME: 
     Stenhouse.

Beck, I.L, McKeown, M.G., & Kucan, L. (2002) Bringing words to life: Robust 
     vocabulary instruction. New York, NY: Guilford.

Blachowicz, C. (1986) "Making connections: Alternatives to the vocabulary notebook."
     Journal of Reading, 29, 642-649.
Blachowicz, C. & Fisher, P.J. (2006) Teaching vocabulary in all classrooms. Upper      
     Saddle River, NJ: Pearson.

Beyond the Style: The Importance of Determining Information in Note Taking

"Determining important ideas and information in text is central to making sense of reading and moving towards insight...Simply put, readers of nonfiction have to decide and remember what is important in texts they read if they are going to learn anything from them." (Harvey & Goudvis, 2000)

[Bold is mine]

In the work I do as a literacy coach, I get called in at certain times of the year to do lessons on the skills of note taking.  Usually, teachers want me to review the different types (Cornell, Concept Map, Outline, etc.).  Not very often, do I get teachers who want me to talk to students about the true skill of note taking -- determining what is important in the text. 

Surprisingly, many students who I work with in varying grade levels say that the most important "stuff" in a text is in bold, italics, or underline.  In their mind, the rest of the chapter can be left behind.  My response is what about all those maps, charts, graphs, formulas, pictures, and the context in which those words are found?

In the last couple classes I have been in, I've asked students how they take notes.  These are the two most common responses: I copy only the bold/italics/underline words and the definitions that follow OR I start from the beginning of the chapter/article/web page and write pretty much everything down.  Neither of these is a good strategy for truly understanding the material. 

For those who only write down the bold words, they are having a hard time understanding the context or concept attached to that word when it comes time for an assessment.  Those who write everything down say that they don't even bother to go back and look at their notes when it comes time for a test.  In both cases, students are taking down notes, but they aren't learning anything from them.  Many say they do the notes to get a homework grade, but not to learn what is in the reading. 

As I was about to start a series of mini-lessons on note taking in a Biology class, I came to a big realization.  How could the students take good notes IF they had no idea what they SHOULD be taking notes on?  I started trying to take notes from the beginning of a section on Photosynthesis and I became completely overwhelmed.  It became so much that I got up and left my office.  Upon returning, I decided I needed a different strategy.  If I (an adult who cared about taking decent notes) had no idea what was important in the chapter, how could the student figure it out without some form of modeling or scaffolding? 

Rather than give up, I opened up the textbook and looked at the Objectives for the section:

These were my way in.  If I could understand these objectives then in my mind I knew the important pieces of the section.  In fact, I would be a true Biology goddess because I would understand the material beyond just rote memorization.

•  Explain why almost all organisms depend on photosynthesis.
• Describe the role of chlorophylls and other pigments in photosynthesis.
• Summarize the main events of light reactions
• Explain how ATP is made during light reactions.
  

However, I needed a way to break down these objectives because they were still pretty dense.  I decided that I would look at the academic language first.  Another thing I found in my work recently with students is that they think all academic language means the same thing.  For example, one student told me that define is the same as discuss, but according to Christenbury, Gere, and Sassi define means "give an explanation of the term and supply enough detail to demonstrate understanding"; whereas, discuss means "consider important characteristics and include examples" (2005).  After I explained the difference, one student said, "No wonder I keep getting those questions wrong."

In class, the teacher and I modeled for students what academic language is and how to know what it is asking for in the question.  We asked students to box in the words so they could easily determine what the question was asking.

Next, I looked at the science words (or content language/vocabulary).  In class, we had students underline the science words.

Lastly, we asked the students for what we called focus words.  These were words that clarified what the objective (or question) might be asking -- how, why, depend, all, etc.  These words allows for us to clearly understand what we are supposed to learn from the objective. 

Once we broke down the language in the objective, we asked students to think about things they would need to know in order to answer the objective.  By writing up questions, the students were breaking down the objective into manageable pieces of information they would need to know.  Once they broke down the objective and understood the smaller pieces, they would then be able to put it all back together and explain in a thorough manner.

At this point, you may wonder what the students are taking notes on.  The answer is the questions.  We explained that the students would only take notes by answering the questions and then modeled how the process would look.  Below are a couple examples of the types of questions we asked using the objectives and how we looked at the language of the objective.

Example #1:

Bold = Academic Language

Underline = Science Language

Italics = Focus Words

Objective 1:  Explain why almost all organisms depend on photosynthesis.

Q(uestion)1:  What is photosynthesis?

• Process of taking light energy and turning it into other forms of energy
• Two Stages -- Light Reactions & Calvin Cycle

Q2:  How/Why do organisms (animals/plants) use photosynthesis?

• Autotrophs (create their own food/energy) -- light energy becomes chemical energy (carbohydrates)
• Heterotrophs (get their energy from other sources) -- need autotrophs to get energy/food.  (e.g., tree (autotroph) <-- caterpillar (heterotroph) <-- bird (heterotroph)

Q3:  Why is photosynthesis necessary?

This question prompted a lot of conversation because students agreed that they needed to know what photosynthesis is in order to answer this question, but they had already wrote the definition in Q1.  We explained that they could do one of two things -- write the definition again (if they are the type of learner who needs to write things down more than once to learn it) or make a note to look at Q1 (if they are someone who just needs to know where to look to get information. 

Modeling in class allowed for students to process how they learn. In addition, they also had to figure out what information they needed to take away from the text to learn the material.  We had some great conversations about whether or not we actually needed certain types of information or if we were just writing it down because it was interesting, but not necessarily important.

The other good thing about taking notes this way was that the teacher could tell the students which objectives she wanted them to take notes on to learn the information and which objectives she wanted to introduce to them in class first because of the complex nature of the material.  Having the teacher name which objectives they needed to take notes on took away students taking blanketed notes on the entire section or chapter.


Here is another example using Objective #2.

Objective #2: Describe the role of chlorophylls and other pigments in photosynthesis.

Q1:  What is chlorophyll(s)?

• Pigment located in the membrane of thylakid (students had done a pre-lesson on some vocabulary words using morphology so they were familiar with this term before reading chapter).  [NOTE: I have underlined many of the science words so you can see how heavy the language can be in both objectives and textbooks, but students did not need to do this in their notes (although, we did mention it might help them find information more easily).]
• Several types -- most common chlorophyll a and chlorophyll b

Q2:  What is a pigment?

• compound that absorbs light

Q3:  What are the other pigments?

• yellow, orange, brown carotenoids (accessory pigments) [Note: again, this vocabulary word was introduced in the pre-lesson using morphology.]

Q4:  What are their roles in photosynthesis?

• a and b -- both allow green light to be transmitted
• a -- directly involved in light reactions
• b -- help capture light energy (accessory pigment)
• carotenoids -- absorb colors that a cannot absorb to capture more energy in light.

We asked students to take notes on these two objectives using the questions created [NOTE: I filled in information from my experience taking notes.  Students may have had different variations of how they put information in their notes.]  The next day in class we asked students to share their impressions of taking notes this way versus their old way.  Many said that they took less notes AND that they had a better understanding of the material.

The last piece of information we shared with students around taking notes in ANY subject area is that if a teacher asks you to read something for their class without giving a clear purpose (or objective) that it is more than likely going to be impossible for them to know what their teacher (or the student) thinks is important from the text.  If this is the case, we suggested they look to see if the section has objectives or a statement of purpose.  If the reading doesn't have either of these, we suggested the student ask in a respectful manner the purpose (or objective) for reading the text.  Although we acknowledge that students will need to do this skill independently as they continue in their high school career and in any post-secondary work, we know that they are just learning how to do the strategy/skill and it would be unfair to do both at this time.  Students will likely work on deciphering purpose (or objectives) independently in the Biology class mentioned above as the year continues.

Resources

Writing on Demand: Best Practices and Strategies for Success by A.R. Gere, L. Christenbury, & K. Sassi (2005)

Modern Biology (Holt, Rinehart, and Winston)

Quantitative Literacy

“If we are going to have a successful democratic society, we have to have a well-educated and healthy citizenry.”
Thomas Jefferson

According to an article from The Mathematics Association of America (MAA), "a quantitatively literate person is a person who, with understanding can both read and represent quantitative information arising in his or her everyday life" (Richardson & McCallum, 2003).

Some elements that may factor in to a person being quantitatively literate are:

• confidence with mathematics
• cultural appreciation
• interpreting data
• logical thinking
• making decisions
• mathematics in context
• number sense
• practical skills
• prerequisite knowledge
• symbol sense (Richardson & McCallum, 2003).

The tricky thing about talking about quantitative literacy is the belief that it should be taught solely in the vacuum of a mathematics classroom. However, according to Richardson & McCallum (2003), "quantitative literacy is not simply a matter of knowing how to do the mathematics but also requires the ability to wed mathematics to content." In many ways, it can be likened to the belief that writing should be taught across curriculum in order for students to become better writers. Quantitative literacy taught across the different content areas will allows students to become more critical in their thinking.

Teaching quantitative literacy across the curriculum allows for teachers to incorporate matheracy, "the capability of inferring, proposing hypotheses, and drawing conclusions from data" into their lessons (D'Ambrosio, 2003). In addition, it allows students to have a conceptual understanding of mathematics in a variety of settings. Becoming someone who is quantitatively literate means he or she can understand how to stock market works, balance a checkbook, or understand the concept of risk (Colwell, 2003). All of these things are important in making a well-educated citizen who has the ability to think critically for themselves.

The definition of literacy from the Adult Education Admendments of 1988 reminds us that literacy "is an individual's ability to read, write, and speak English and compute and solve problems at levels of proficiency necessary to function on the job and in society to achieve one's goals and to develop one's knowledge and potential" (Colwell, 2003). In some ways, Congress was ahead of their time because what their definition of literacy looks a lot like what people are calling 21st Century Skills.

Recently, in a professional learning community, I shared a mini-lesson on inferences using a scientific procedure of sorts for inferring what was happening in a literature passage to show that quantitative literacy can happen anywhere. The worksheet that accompanied the min-lesson/conversation is below:

Passage

From: The English Patient by Michael Ondaajte

She moves backwards a few feet and with a piece of white chalk draws a rectangle onto the wood floor. Then continues backwards, drawing more rectangles, so there is a pyramid of them, single then double then single, her left hand braced flat on the floor, her head down, serious…
She drops the chalk into the pocket of her dress. She stands and pulls up the looseness from her skirt and ties it around her waist. She pulls from another pocket a piece of metal and flings it out in front of her so it falls just beyond the farthest square.
She leaps forward, her legs smashing down, her shadow behind her curling into the depth of the hall. She is very quick, her tennis shoes skidding on the numbers she has drawn into each rectangle, one foot landing, then two feet, then one again until she reaches the last square.

Step 1: Form a hypothesis (inference) about what is happening in this passage.

Step 2: List all information that supports your hypothesis.

Step 3: Explain what is happening in the passage above. (Information from passage + Your knowledge = Inference or explanation)

Step 4: What steps did you take to figure out what was happening in this passage?

This mini-lesson was a great way to talk about inference, critical thinking skills, metacognition, and active reading strategies all in one -- plus it connects to another content area if you really think about it. The formula used to come up with a solid inference or explanation looks a lot like a basic math problem. Plus, the way in which different people determined was happening showed how each of us thinks critically when faced with different types of information. The teachers who read this passage noted that they made connections, visualized, determined important details, used prior knowledge, etc.

In fact, I look forward to watching this lesson in action in a math class. The teacher plans to use this passage, as well as a few others, to show how logical thinking skills/steps are essential in all areas of life not just in explaining a geometry proof. This use of the lesson is just one way of showing how literacy spiderwebs across all content areas in a variety of different and creative ways.

Using quantitative literacy in a variety of content areas is a great way to bridge the divide between literacy and content areas because it gets at an area of literacy (critical thinking, inferring, etc.) that isn't always address in a conscious way. In addition, it can help have the conversation with teachers that literacy is much bigger than just reading and writing or rather the idea that reading and writing encompass a lot more than we give them credit for in all we do.

Some other ideas for working on quantitative literacy in the classroom are:

• Using Data -- graphs, charts, statistics, etc. to get students to analyze what it is really telling us. In addition, looking at how certain media or other places use data incorrectly OR to get their point across. Getting our students to be critical consumers of information is extremely important in them becoming good citizens.
• Using Writing -- focus on having students write to learn versus learn to write. Ask them to explore their ideas through writing prior to sharing in discussions or discourses in the classroom. Allowing this think time might produce students who rely on their own thoughts rather than wait for his or her peers to suggest the answer. Let students get messy with their thinking on paper so they have something to go back to at the end to see if what they thought initially still holds true. Also, maybe even have them use "Silent Discussions" or "Written Conversations" to get the conversation going with peers in the classroom as well. This writing can happen by hand or through a technology resource like moodle, blog, wiki, etc.
• Modeling how to make Inferences -- using material you might encounter in your life -- share with students how you make inferences, hypotheses, and analyze data in your life. Share how it connects with skills both at school and in the world outside of school.

Question-Answer Relationships and Three-Level Study Guides

With two weeks before April break and what seems like forever since I have had a good night's sleep, I am beginning to reflect on what works and what doesn't. Over the course of the last couple weeks, I have been working with different students on a range of different literacy tasks. As I walk them through the task and guide them along, I feel good that they are getting something out of it. When they forget to do the tasks I assign outside of my office or even to show up, I wonder who is working harder -- the student or me?


As many know, I am more than willing to give my all to any student or colleague who needs me, but in an ideal world I guess part of my job is to help provide guidance and resources so eventually I won't be needed. In working towards that theory, I have found two great strategies that focus on using a gradual release of responsibility model to help students learn higher level critical thinking and comprehension skills. In addition to the resources on this blog, there is a bulletin board with information, examples, and handouts outside my office.


Question-Answer Relationship (QAR)and Three-Level Study Guides are two strategies that focus on asking the student to know the difference between the literal, interpretative, and applied levels in the area of comprehension.

Question-Answer Relationships (QAR)


QAR is "a language for use in the classroom" for "thinking about and talking about sources of information for answering questions" (Raphael, Highfield, & Au, 2006). The two overarching categories are In the Book and In My Head. Questions that focus on information from In the Book ask for author information to develop an answer. Ones that focus on In My Head have answers that are based on a reader's experience, ideas, or background knowledge. Within these two categories, there are subcategories.


In the Book is broken down into Right There and Think and Search. Right There questions focus on answers that can be found in one sentence within a text; whereas, Think and Search require using different parts of a text to develop an answer.


In My Head is broken down into Author and Me and On My Own. Author and Me involves using information from the text and the reader's experience, ideas, and background knowledge to answer it; whereas, On My Own involves only the thoughts and ideas of the reader.


Example of Different Types of Categories:
Math Example --
Right There --
Q: "State the slide model for addition."
A: "The slide model for addition is..."


Think and Search --
The text shows an example of how to simplify
-3 + -x + 7
Q: "Simplify -2 + y + -9


Author and You --
After learning how to simplify (as in Think and Search example above), the author shows students how to solve simple equations like x + 6 = 10, and 17 - y = 12
Q: "Solve -3 + t - 4 = 0"


On My Own --
Negative numbers appear on television in many situations.
Q: "What real situation might each negative number represent? a.) -1.32 in stock market averages, b.) -9 in rocket launches, c.) -3 in golf."


Music Example --
Right There --
Q: What kind of music is this -- band, orchestra, piano?


Think and Search --
Q: What instruments do you hear throughout this piece?


Author and You --
Q: What feelings do you think the composer was trying to convey? How did the composer create feeling?


On Your Own --
Q: If you could play any instrument, what would it be and why?


Art Example --
Right There --
Q: What is the subject of the painting?


Think and Search --
Q: What colors did the artist use?


Author and You --
Q: How did the painter show perspective in this piece? What feelings do you think the artist was trying to convey?


On My Own --
Q: If you made a living as a painter, what medium would you use? Why?


From Project CRISS: Creating Independence through Student-owned Strategies by C.M. Santa, L.T. Havens, & B.J. Valdes (2004).


Social Studies Example
Science Example
English Example

Three-Level Study Guides
According to Janet Allen, Three-Level Study Guides are "instructional tools that guide students into higher levels of comprehension. The first part asks you to consider questions at the literal level. The second asks you to consider questions at the interpretative level. The third asks you to consider questions at the applied level. As a teacher, you can construct a guide that allows you to direct students' attention to the most important aspects of the text." (2008)

In creating the types of questions, it is important to use sentence starters that guide the reader to think either at the literal, interpretative, or applied level. For example, when creating a question at the interpretative level you may consider using summarize, predict, or determine; whereas at the literal level, you may consider using name, select, or define. In addition to using questions to guide the reading, you may also make statements that ask students to think at the literal, interpretative, or applied level. Check out the link at the top of the page for Three-Level Study Guides to see examples from math and science.

These strategies are just two ways to get students thinking about higher level critical thinking and comprehension skills by having them practice these strategies with you and on their own. Having students understand the language involved in this type of thinking might allow for them to move beyond the facts of a topic and really be able to apply the concepts they have learned. Guiding students through the process of learning this type of language and thinking will help them become independent in it as they move along. As always, contact me if you have questions or thoughts.