An Engaging Mathematical Environment

My mathematics methods class this quarter has prompted my thinking about the many ways in which math is taught and the importance of creating an environment that promotes learning among students.   I now realize that the teacher in my dyad placement last quarter, a fifth grade classroom at Einstein Elementary, was extremely successful at creating just such an environment.  Every student seemed to be engaged in the lessons he taught.  As an “observer” I wasn’t able to guess which students seemed more challenged by this subject than others.  They all actively participated.    Now that I’ve begun reflecting more on his teaching methods, however,   I  realize that he incorporated  many important  strategies into his classroom that  helped create this amazing “mathematical environment” (that I, of course, hope to replicate in my own classroom some day).  This blog is devoted to sharing some of these strategies.

One of the first things I noticed about his classroom was the level of attentiveness of his students.  Everyone was facing forward and quiet while he was speaking during his lesson.  They were also quiet and respectful when other classmates were speaking.  When I asked him about this he told me that he had established the rule early on that no one should talk over anyone else.  I later realized that this behavior didn’t happen by chance.  He would abruptly stop, mid-sentence, and look directly at an offending student if they were talking out of turn and would not begin speaking again until they were quiet.  This method was extremely effective.  It reinforced the message that each member of the classroom had something valuable to contribute and, therefore, should be listened to.   

Another effective strategy he used was his warm-up activity.  He always had the students play a math game that related to the lesson he would be teaching.  He usually asked for a student volunteer to come up to the document camera to play the first round with him, as he explained the rules, before handing out the game pieces and “boards” (papers) to play.  This seemed to generate excitement among his students.  The class would then be broken up into partner groups to play on their own.  During this center activity part of his lesson, when the students were in these table groups playing the math game, the teacher often called out a group that was on task.   This reinforced the expectation that all students were to stay focused on the game and not get sidetracked in conversions about anything other than math.  He also did this during student independent work time.  These “gentle” reminders seemed to keep his students on the right track.    

This teacher also taught very engaging lessons by using just the right mix of direct instruction and student involvement by asking students to volunteer to solve problems on the active board that reinforced the concepts he was teaching.   He was also adept at keeping the lesson moving at a comfortable pace by often checking in verbally with his students by asking them if they understood how he got a particular answer to an equation.  He’d ask for a “thumbs up,” close to their heart (so only he could see) if they understood.  If he didn’t see many thumbs he’d review the problem again.  This enabled him to “slow down” if necessary, but also to “skip forward” if the concept was understood by all.

He also had great strategies for involving all of his students.  When he asked questions about a solution to a problem he’d often wait until most hands were up before continuing on, and then he’d ask them to form partner groups to discuss the answer (instead of just asking one person to give it).  This method of student involvement was discussed in the Questioning Your Way article, by Mewborn (that was assigned reading in my class).  Per the article, “By sharing their solutions in pairs first, students can try out their ideas on someone else and practice what they are going to say to the class.  Students receive feedback on their solutions in a non-threatening setting, and their self-confidence is boosted.”  This seemed to be true as I witnessed this practice in my dyad placement classroom.  I noticed the “hands” of students that didn’t typically participate to offer a solution when the teacher brought the class back to attention.

This teacher was also very respectful of his students when handling “wrong” answers by calling on others to assist the student having trouble, so they could eventually be successful.  (A student that made a mistake on the active board was never permitted to return to his or her seat until they had successfully completed the problem.).  Another part of his lessons that I especially liked was when the teacher purposely made a mistake when solving a problem, and then asked for volunteers to find his “oops”.  (By doing this he kept the lesson light hearted.) He would also, on occasion, take on the entire class as his opponent during a math game to spur competition among his students.   They seemed to be especially involved and engaged during a lesson when they had the opportunity to “beat” their teacher.

I truly enjoyed observing these math lessons during my dyad placement.  This teacher modeled many of the strategies we’d been discussing in my mathematics classes.  I was able to watch as he put many of these effective strategies to practice in his classroom.

Writing Analysis

Project 1:  Analysis of Thien’s writing and Lesson Plan

Analysis

T (pronounced “T”) is a 6^th grader at Juanita Elementary.  My analysis of his writing is based on only one sample, a “Where I’m from….” poem that he wrote in response to a prompt he was given by his teacher.  This prompt gave very specific instructions as to what he should include in this poem.  I additionally had Thien complete a spelling inventory test to determine the spelling stage that summarizes his development in this area. 

Ownership and Meaning of the Piece

I learned a lot about T form reading his poem.  I knew he loved computers and enjoyed playing video games (I am from a laptop screen and a TV screen that plays video games.)  I also knew he loved to spend time in his backyard and enjoyed living in his neighborhood (His poem referred to his neighborhood four times and he mentioned several items in his backyard; the grass, a storage shed, gardening tools, a broken rake, etc.)  When I asked him about writing he told me that he didn’t mind doing this assignment but it wasn’t his favorite subject.  (He told me  his favorite academic subject is math.)

Six Traits Assessment

IDEAS

T has good ideas and knows a lot about his topic because he chose to write a poem about himself (and, of course, no one is better qualified to do this, then T).  His “Where I’m from” poem is an attempt to create a piece of writing that is representative of specific moments in his life that has contributed to who he is today.   The writing prompt he was given helped him do this.  It prompted him to think about; items found in and around his home, yard and neighborhood, individuals in his life that may have influenced him, family sayings, food served at family gatherings and special places around his home or room where he may keep special items.  He has done an excellent job of reflecting on these things and mentioning them in his poem.  He talks about laptop and computer screens, his backyard and neighborhood, his grandpa and uncle, frequent sayings he hears in his home, foods he likes and some of the toys/things enjoyed when he was much younger.  All these ideas helped me get to know T as a person. (Incidentally, Thien mentioned many of these same ideas during our first meeting.) 

The details he includes about the subjects he writes about, however, are very general.  It would help the reader if he included more information in these details.  He writes, for example, about a couch his family sits on.  What do the family members do while sitting on this couch?  Do they watch TV?  Do they play games, visit?    T leaves these important details out of his poem and keeps the reader wondering.

ORGANIZATION

T’s poem is very well organized.  He exactly follows the writing format he is given.  His poem has eight stanzas and each one includes the specific details he was prompted to write about, according to the assignment instructions.  The first prompt, for example, tells him to list items found around his home.  Thien lists a laptop screen, a TV, a couch and a desk.  The second instruction tells him to list items found in his yard.  He lists grass, bugs, thorns, leaves and a broken rake.  He carefully read each line of instruction to be included and then wrote about something in his life that related to it.  The very last instruction was to end his poem with a line or two that connected his present to his past.  Thien does this quite nicely when he makes the observation that his life now really isn’t that much different from his life as a child.  (He just has different clothes and different toys.)  He makes the statement that he’s just, “growing up” – a natural progression in his life.  

VOICE

Thien’s writing seems sincere, but it doesn’t seem fully engaged or involved.  His writing has a discernable purpose (writing about himself), but it’s not compelling.  He seems to keep his readers at a comfortable distance.   There is one section of his poem, however, where he does take a risk, by including more personal details about his home life.  When he’s asked to include family sayings he writes, “I told you so,” “Stop bugging your brother” and “TV smaller”.  These “sayings” are quite telling about his family and of a more personal nature.  They provided a window into T’s relationship with his family members, although it is not clear which family members he is referring. 

WORD CHOICE

The words T uses are adequate and correct in a general sense but they don’t paint a vivid picture in the reader’s mind.  He includes very few adjectives in his poem and the ones he does use are somewhat ordinary.   For example, he writes about the big couch his family sits on.  This term is somewhat relative.  Does T say the couch is big because all members of his family can sit on it comfortably together? Or is it big because it takes up so much space in the room it occupies?  This description of the couch in his home fails to give a clear picture of this piece of furniture or the meaning it has for him.  (Is the couch a focal point in his family? Does his family spend a lot of time together on it?)  T could give additional details such as its color, its style or whether it’s covered in fabric or leather to help his readers picture it in their minds.  Thien writes about many different items in his poem, such as a desk, rocks and grass, but fails to go into any detail about them.  

SENTENCE FLUENCY

T’s poem is easy to read but, at times, doesn’t flow smoothly when read aloud.   For example, he writes, “I am from leaves and broken rake.”  This line seems to read much smoother when merely adding an “a” before the word broken.   He also uses the line, “I am from” in twenty-four out of the twenty-eight lines in his poem.  Although this is clearly a style used in this type of poem Thien may have provided more “interest” if he hadn’t repeated these three words quite as often as he does.  In fact, of the few times he didn’t write “I am from” it almost appears to be a mistake because it varies from his format.  For example, in the fourth stanza of T’s poem, he writes, “I have an uncle who is in medical school and might go to Afghanistan” doesn’t seem to “flow” because he writes, “I am from an uncle…..in his first line, “I am from a grandpa…..” in his second line and “I am from a grandpa…..” in his third line.  Instead of adding interest, it makes me wonder if he did this deliberately or if it’s an oversight on his part.  Thien may also want to try varying the length of his sentences to add interest because most of them are fairly short

CONVENTIONS

Thien demonstrates a good grasp of writing conventions.  He has very few errors in his final draft so his poem is readable and easy to understand.   I believe the few errors that do appear in his paper, however, could have been caught if he had consulted a list of  previously set up editing expectations, such as the ones listed in Routman’s book, Writing Essentials, as he read his paper one final time.  (It was evident that he had proofread his paper earlier because quite a few corrections/changes had already been made.)  For example, if T had referred to a pre-established list instructing him to look for repeated words, I am sure he would have caught the repetition in his first line of verse.  The first line of T’s poem reads, “I am from am from a laptop screen…..”  I believe he inadvertently repeated the fourth and fifth words, “am” and “from” because they are listed twice.  T also omitted the article “a” before the adjective “broken” in the fourth line of his second stanza.  His poem seems to read much better when the “a” precedes the adjective describing the noun he uses, rake.  T, for the most part, has used capitals correctly.  He correctly capitalized the first line of every line of his poem as well as all the proper nouns listed, for example, “Afghanistan”.    In one line, however, he fails to capitalize the first letter of the first word in a line of dialogue.  It’s hard to know if he’s aware of this rule because in the other two lines of dialogue the first words are “I” and “TV”( both of which are capitalized, regardless of where they appear in a piece of writing).  A final error I noticed was T's representation of the letter six, which should be spelled out rather than being written as a number. 

Spelling

T is an excellent speller.  There was only one misspelled word in his original draft and that was corrected after he proofread and typed his final paper.  (He had spelled neighborhood as “neighboorbood” in his original draft.)  The only word Thien misspelled, when I gave him the spelling inventory test, was cellar.  According to this inventory, his spelling level would likely be assessed to be in the middle syllables & affixes stage (Bear et al, 2004) where he needs to focus on syllable junctures, consonant doubling, inflected endings, and prefixes and suffixes.     

PRESENTATION

T typed the final version of his poem so his presentation is excellent.  He used an easy to read font and alternately indented the stanzas of his poem.  He also used two different colors for the words and then another color for his title, in a much larger font, for added interest.  The font, size, and spacing are very eye-catching.

 Lesson Plan

Using Word Webs to Teach Synonyms for Commonly Used Words

Objectives: 

The students will increase their knowledge of synonyms for common words such as good and nice.

The students will expand their written and oral vocabularies.

The students will increase their use of vivid description words.

  

Standards:

EALR 3:  The student writes clearly and effectively.

 Component 3.2:  Uses appropriate style.

GLE:  3.2.2:   Analyzes and selects language appropriate for specific audiences and purposes

-Searches for alternatives to commonly used words, particularly in persuasive writing and poetry.      

Materials:

-Print-outs of partially completed word webs

-Pencil and lined paper

-A dictionary, thesaurus and/or online resources to find synonyms

Instructional strategies:

This lesson would start with the whole class.  Later, it would be divided up into groups of three to four students.

The lesson would begin by reading a description of something prepared in advance, containing the words good, and nice several times.  A second description would then be read, about the same thing, but this time many descriptive synonyms would be used in place of these two overused words.  The students would be asked to choose which description was more interesting and why.  The students would be informed that effective writers use specific, descriptive language to appeal to their readers because they want them to be able to “visualize” the person, place or thing they’re describing. A classroom discussion about the importance of using specific adjectives in certain situations, such as in the case of a travel brochure or a car advertisement, would then follow.

Partially completed word webs would then be distributed with the frequently used words, good and nice in the center of the web.  It would be explained that these adjectives are very commonly used in student writing and speaking, noting that more specific, descriptive words could often be used more appropriately instead.

These word webs would then be reviewed with the class.  The students would brainstorm other synonyms that they already knew and then discuss the various categories to which they would belong.  The students would then be asked to use these synonyms in sentences.

At this point the class would be divided into groups of three or four students.  Each group would be assigned two categories from the word web.  For example, one group would be asked to find good and nice words that describe the weather (such as pleasant and sunny) and food (delicious, healthy, and tasty).  Each group would be give a thesaurus, a dictionary, and/or access to the internet to search for words on Dictionary.com and Thesaurus.com.   

After the students finished their group work they would be asked to present the words they found in their search to the entire class.  As students discussed the words they found during their research, they will be asked to add the ones they don’t already have to their individual webs.  This addition of items will be modeled for the students under the document camera.

The students will then be asked to individually write a short description of something (a movie, a book, an article of clothing, etc.) using at least five adjectives other than good and/or nice that they found during their research.

-This lesson was adapted from the ReadWriteThink website

Assessment

The teacher will assess whether the students have increased their knowledge of synonyms for common words, such as good and nice, by reviewing the descriptions the students were asked to write during this assignment, as well as in future written work.

The teacher will also assess whether students have expanded their written and oral vocabularies by observing students’ use of synonyms during classroom conversations and discussions and through future written assignments.

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Tagxedo

Last weekend I explored the possible uses for the tech tool, Tagxedo.    This tool is much like the Wordle. It visually displays texts by creating word clouds that show the most commonly used words in a document by their relative size, but additionally, it displays them in a particular shape.   There are many shapes to choose from; a heart, football, clover, foot, hand, flower, fish, dinosaur, etc.  The possibilities are endless.    If, for example, I wanted to use Tagxedo to introduce myself to my future students at the beginning of the school year, I could load the words of various things I enjoy doing, such as volleyball, biking, reading, etc. and then choose a shape of something that would provide additional information about me.   For example, I might choose a coffee mug because I am an avid coffee drinker.   (I created one but had difficulty embedding it on my blogJ)

Another great application for this tool would be to use it for an assigned project in the classroom.  Students could be asked to write about a famous figure in U.S. history.  After researching their assigned subject and writing an essay that highlighted their accomplishments, they would be asked to create a Tagxedo cloud.  This cloud would be created by loading various words in a particular shape that would be “telling”of this person’s life.  These Tagxedo clouds would then be displayed around the room and the remaining students in the class would be asked to guess the person being described by looking at its shape and the various word clues. 

I created an example above for Amelia Earhart.  I chose the shape of an airplane because she was a famous aviator.  The words I chose to load were; aviator, missing, mystery, fly solo, Atlantic ocean, set records, American, pioneer, author, Ninety-Nines, Purdue University, Lockheed, Electra, Pacific, Howland Island, disappearance, Kansas, and Canary. 

The Tagxedo I created was truly amazing.  Unfortunately, the embedded image on my blog (above) doesn’t do it justice.  The shading in blue, that formed the shape of the plane behind the words, did not transfer over, so only the words are visible.  (You can tell they’re in the shape of a  plane if you use your imagination!)   The program works great.  I just had difficulty putting it on my blog.  These Tagxedo clouds can easily be printed for classroom use.

Giving the Wordle a whirl

The word cloud below, generated in Wordle, was created from the I AM poem I received yesterday from my 6th grade buddy, Thein, at Juanta Elementary.  This tech tool (Wordle) can be used to visualize texts.  It gives a snapshot of the most commonly used words in a document shown by the relative size of them in the cloud.   So for example, in Thein's poem, the words he used most frequently; neighborhood, big, grass, screen and tree are written in a larger font than the others.  This is very telling because when I asked him to introduce himself to me he mentioned that he loves to play video games as well as play in his backyard with kids around his neighborhood.  I'm planning to give him a copy of his "cloud" when I meet with him again next week. 

This is a very fun program.  I can think of many uses for it in my main placement, 1st grade classroom.  Currently,  we're studying families in social studies.  One of the main ideas being taught is that all families are unique but they also share many things in common.  To show the class what they share in common with one another I could load the responses from their worksheets about their families (what they like to do together, the holidays they celebrate, the number of siblings they have, whether they live in a house or apt., etc.).    

Math Autobiography

My experiences with math, for the most part, have all been very positive.  I enjoyed doing math problems in elementary school and it was something I thought I was very good at.  I was initially attracted to this subject because of its relative objectivity in comparison to my other subjects.  I liked that there was usually just one correct answer to every problem.  In grade school, I distinctly remember participating in an SSR math program where students could work ahead in various math subjects by completing math problems at their own pace.  I was an extremely motivated student and I enjoyed working through this program independently. 

In high school, I took four years of math and considered it to be one of my favorite subjects.  I seemed to have a knack for memorizing formulas and if I followed a series of methodical steps I was usually rewarded with a “correct” answer.  I truly thought I had a mathematical mind and eagerly signed up for calculus (Math 124) as a freshman at the University of Washington in Seattle.  This is when I learned that my mathematical ability wasn’t quite as strong as I had originally thought.  This was truly a crossroads for me in my mathematical career.  After struggling in my calculus class (and eventually dropping it) I realized that it made more sense for me to take business math because I had aspirations of becoming an accountant.   I then enrolled in a beginning algebra class (in which I did well) before moving on to business calculus (math 157), since I was planning to get a Bachelor of Arts in business (as opposed to an engineering degree).  I did well following my “new path” but realized that I didn’t necessarily have the “mind for math” that I originally thought I had.

 Eventually, after getting married and having a family, I began volunteering in the classrooms where my children attended school.  It was during this time that I became involved in a program called Math Adventures.   This program offered math enrichment activities to students in grades K- 6 and was originally set up to help students expand their mathematical thinking and to promote the idea that Math is fun. While volunteering, I lead many math enrichment activities.  Resource materials were available to plan lessons but I often searched the internet for new ideas and/or developed my own.  I also spent a great deal of time planning activities to ensure that all of the students in my classes fully engaged in them. This experience, as a Math Adventures leader, was one of the critical incidents that lead me to make the decision to return to school to get my teaching certification.  I so enjoyed teaching, and math (at least at the younger grade levels) was one of my favorite subjects to teach.

The above is an except from the math autobiography I wrote for my Mathematics Methods class.  After turning in this assignment I started to reflect on the reasons why my experiences in math were all so positive throughout school.  One of the reasons, I believe, were the teachers I had.  Their enthusiaum for math seemed to rub off on me.  As a future teacher, I hope to continue to pass along this enthusiasm

to my students.  One of the things I'd like to take into my classroom is the use of games to reinforce mathematical concepts.  For the most part, all kids love to play them so this seems like a logical approach to take. My experince volunteering as a Math Advertures leader has convenced me that this is an effective method of teaching when trying to reinforce math concepts.  These "games" can also sevrve as a reward for good behavior in a classroom, which is an added bonus for any teacher. 

It will be my job to ensure success among my students.  I've found, in my main placement, that when students figure out or solve a math problem on their own they gain confidence and thus have a positive experience.  I believe students formulate their opinions about math at a very early age so it will be important that I quickly identify all my "struggling" math students so I can work with them in an attempt to avoid this "negativity" surrounding math.