Informal Geometry

Today's activities provided another opportunity for people to be "smart at math" in different ways.  The visual and tactile nature of folding paper into boxes and squares made geometry very concrete.  As I am starting to get used to, it may have been informal, but I felt less smart in math as than usual.  I am more familiar with drawing a geometric shape and learning all the rules about how angles and sides are related.  My stretching is continuing.

I was hoping we would discuss the use of creative writing in math class that was the subject of the Halpern article.  I thought that was a different type of example of how to make geometry (or any math) more accessible for students who have strong written expression skills.  As students get into Middle School, I often hear that students start being divided into those that are more humanities focus and those that are more math/science focused.  I read The Phantom Tollbooth last quarter and I felt it was a fiction book that would appeal to students who love words and/or numbers.  A bored boy travels in a toy car through a tollbooth to a place filled with adventures based on letters and numbers.  The Mathemagician rules the Kingdom of Digitopolis and a character called the Dodecahedron has 12 faces with different expressions.  It is another possibility for giving our strong writers an informal entry point into geometry.

Group Worthy Tasks

I loved the readings this week.  I got inspired while reading the article on Orchestrating Discussions, so I went online to join NCTM to be able to start reading the middle school journal regularly.  The bag of marbles problems is a marvelous and simple example of a group worthy task and gives me something to contemplate for the lesson assignment.  The article makes so much sense to me that I pulled out the five practices planning worksheets from last quarter so that I actually start using them in my main placement.  I like the idea of trying to anticipate all the possible ways that my students will solve the problem- especially the ways that they may solve incorrectly due to common misconceptions.  Monitoring, selecting and sequencing becomes a whole lot easier when I know what I am looking for.  As a new teacher, I am not as good "on the fly" as I would like to be so I want to plan as much as I can until my comfort level increases.  Making connections to the lessons goals and then extending and making generalizations are all things to strive for.  But it gives me a template and something to try and I like that.

The Lotan article on GroupWorthy Tasks is exciting and a bit daunting.  I know it is a lot of work up front, but the group work in the article really did help even the playing field for students from different racial, ethnic and social groups.  I loved the multiple entry points and opportunities for students to display "smarts" in different ways in response to complicated problems.  The frightening truth is the quote from the article that "one dimensional tasks require the same skills and the result is uniform success for some students and uniform failure for others."  We need to carefully craft group work to enhance participation and learning for all our students - it is worth the effort.  Our lesson plan will be an authentic opportunity to consider this goal.

Finally, I continue to struggle with manipulatives.  The Mira symmetry manipulative was a challenge to me.  I was slowly getting the hang of it, but I need remedial work.  I think I will need to make my way to Math and Things store sometime soon.  My experience with virtual manipulatives is even more challenging.  Just give me the algorithm!

Writing Analysis and Lesson Outline

Analysis of Student Writing

S. is an outgoing and talkative 4^th grader and clearly proud of her writing ability.  We briefly looked at several pieces in her writing folder before she selected one for us to review.  My analysis is based on S.’s response to a writing prompt about a talking animal.  S. wrote about her own kitten “Fuzzball” and she described what a day might be like if he could talk.  Her story described a series of events including eating breakfast, reading the comics, and washing dishes with the cat.  She engages the reader with her vivid descriptions and choice of language. 

Six Traits

S. has terrific ideas but instead of focusing on one, she has written about several vignettes – some more developed than others.  She is always on the general theme of a day with her talking kitten, but the ideas are not always connected and do not flow logically.  We are left with gaps and questions about the story.  (NREL .p. 2)  Reading the comics leads to a pillow fight with no explanation.  S. suddenly calls a friend and a fashion show is introduced.  These events have some detail, but are confusing because they seem a bit random.  Regarding organization, the story is a bit uneven.  S. starts with a very inviting introduction and I was eager to continue reading.  Subsequently, there are several ideas competing for focus and therefore the middle feels disorganized and somewhat fuzzy.  The story ends with a conclusion that is recognizable, but not completely satisfying for a piece that started so strong. (NREL p. 3)

S.’s strong voice and word choice are “powerful and engaging” and give her writing sparkle. (NREL p.5). Her words and phrases are thoughtful and specific; examples include “muted knock” by the kitten’s paw and “under the whistling voice of the tea pot”.  Vivid verbs include blurted, bounded and pranced.  Descriptions like “happy as a lark,” “thin, high heeled black shoes”, and “purple polka dot dress” all add color and drama to the story.

S.’s sentences always get the job done and in some cases are varied and energetic.  She does use dialogue in her story, although sometimes it is a bit choppy.  Her conversations succeed in introducing varied structure and length of sentences and helps move her story along. (NREL p. 6) Her fluency shows and conveys the excitement that she feels about her new found ability to communicate with her kitten.

S. has a very good grasp of standard writing conventions.  Evidence of S.’s ability to revise and edit for conventions were apparent in the marked up Fuzzball final draft.  There are a couple of small spelling errors (meant and licking) but I am not sure that they accurately reflect S.’s stage of development.  I suspect that with an additional review, the spelling would be corrected and the piece would be ready for publication. (NREL p. 7))    This is consistent with S.'s “Message in a Bottle” writing prompt that was published on the class bulletin board.  Spelling, grammar, paragraphs, punctuation, and capitalization were once again excellent.

Ownership

S. enjoys writing and she is confident and highly motivated to create stories at home and school.  In the Fuzzball piece, her delight in having her kitten talk makes the story silly but fun.  S. sees herself as a capable writer and she proudly showed us several writing pieces in addition to the Fuzzball story.  She was working earnestly on a pre-write about what one thing she would change at school.  Another completed piece was an “All About Me” story and she read us the clever conclusion “if you need more information, call 1-800- SAMI”.  S. enjoys acting in plays and I believe that adds to her love of language and dialogue. 

Spelling

In addition to spelling in context in her writing, S. did well on the spelling inventory.  She spelled all the words correctly except “celler”, “civiliazed” and “oppisition”. This would place her beyond vowel patterns on the developmental continuum.  Derivational relations (opposition) and suffixes (cellar and civilized) would be her stage of development in spelling.  In identifying words from a list, S. was very strong and tested at the independent level through the 6^th grade.  She insisted on continuing through all the word lists and she successfully identified many middle school and some high school level words.  She was eager and proud to know what words she had gotten correct.

In conclusion, S. is a strong writer whose voice and word choice shine.  Her writing is supported by her sentence fluency and correct use of conventions.  Two areas for improvement are ideas and organization.  S. has so many ideas that she would benefit by narrowing the focus of her writing.  Focus would enable her to elaborate on her main theme without getting sidetracked by random and distracting information.  The improved focus would help with her organization as transitions and clarity would improve.  For that reason, I would start a writing lesson on idea development and focus. 

Lesson Outline

Objectives

To brainstorm how to identify the main idea and narrow the focus for the tetherball story.

To identify overlapping and/or unrelated ideas in the tetherball pre-write.

Standards

EALR 1 Student understands and uses a writing process

1.1. Pre-write to generate ideas and plan writing.

EALR 3 Student writes clearly and effectively

3.1   Develops ideas and organizes writing

Materials

Pencil, post-it notes, new prewrite graphic organizer

Instructional Strategies

This lesson is designed as an individual writing conference and a follow-up .  Alternatively, it could be given as a small group lesson to students all working on narrowing the focus for their ideas.

I would ask S. to bring a copy of her tetherball pre-write.  I would have a copy of her Fuzzball story and start the conference by praising her terrific voice, word choice and conventions she demonstrated in the piece.  I would then gently point out that after an engaging introduction, the middle became a bit fuzzy with several competing and unconnected ideas (I would be specific).  I would then focus on the new project and explain how a pre-write helps to narrow a main idea before she starts her draft.  The goal being that the tetherball piece have a clear, well defined and narrow focus before starting the draft.

I would show S. a sample pre-write using the same prompt.  This could be from a previous year or one that I created for illustrating how to narrow topic focus.  I would demonstrate how after I finish a pre-write, I review with the goal to identify and narrow the main idea.  I would use a series of questions.  Are my ideas all different and distinct or do they overlap? Are they all equally important to the story I am trying to tell?  Are they related or connected in some way?  As I ask the questions, I would show how I could eliminate or combine repetitive ideas.  I would show how I could connect related ideas with so there is logical flow.  I would show how to identify the one idea that seems to be the most important in the story I am trying to tell – that is her main idea..

Next, we would turn to S.’s pre-write and together we would ask the first “review” question.  Are all my ideas different or do they overlap?  As S. identifies similar ideas, I would ask how she might combine or eliminate some of the information to help narrow the focus.  Although we did not spend a lot of time on this piece, my recollection is that S. had “listed” three reasons why she wanted to have more tetherball courts.  Yet all of the reasons were related to the main idea that students in different grades need to play on different courts.

When I was confident that S. could revise her pre-write on her own, I would have her go back to her seat to complete the revisions using the questions we used on the sample to combine, eliminate and revise her pre-write.  I would have S. come back when she felt that her revision focused on a narrow topic with all the other ideas connected to one main theme.

During the follow-up conference, I would have S. read her revised pre-write.  If the pre-write was focused on a main idea with related supporting information, I would have S. proceed to begin her draft.

Assessment

I will document how well S. can narrow the focus of the tetherball paper by comparing the revised pre-write to the original pre-write and checking for a main idea with a narrow focus and connected ideas.  As the assignment progresses, I will use the ideas section of the six traits rubric to assess the clarity and focus of her story. 

Differentiated instruction using ipod touch

R. is a student in my 5^th grade class who moved here from Japan at the beginning of the school year.  He arrived knowing very little English but goes to ELL each day – but not during reading time.  As I am returning to my 5^th grade, this is a subject area where R. continues to struggle.  The class uses a Houghton text and often has a “packet” of activities about the reading to complete.  The teacher works with a small group while the rest of the class works independently on the packet.  R. sometimes works on something from ELL or Rosetta Stone and I am wondering if there is an opportunity to help R. using the ipod touch and Google translate as demonstrated by Jane in our first class.  At this time, I do not have wireless access at school, but I am working on that.  As a first step, I would like to be able to get the homework assignment (usually modified) translated into Japanese and sent home by email to R.’s mom, who reads and writes English pretty well.  Right now R. usually brings home the same homework as everyone else and my master teacher tries to remember to write a note home about the modifications and what to focus on, but it is difficult with 31 students in our class.

H. is a bright boy who has significant difficulty with writing.  He attends special ed to get help with writing skills as he gets so frustrated during writing, he completely melts down.  I am wondering if letting him use the ipod and the Dictation app could be helpful as it gets his ideas down by speaking and then the written version could be sent to an email or Google doc for him to continue.  Getting started seems to be the biggest hurdle.

C. is a quiet and bright girl in my class who has is looking for opportunities to have her thinking extended in science.  C is asking for more difficult science experiments or opportunities to learn something beyond the Foss kits.  Is there an opportunity for me to use the ipod to help her get there?  Even using Google to research erosion and deposition from our lab last week might help extend the lesson for her.

Getting Kids to Do the Talking

I really enjoyed the practical article that was full of strategies and tactics to try in math class.  I think the teacher had a terrific personal goal of trying to change his own practice by 10% every year.  I think that is a manageable goal that ensures teachers are continually improving their own practice.  As a new teacher, I liked many of the ideas and plan to incorporate them into my initial classroom plan.  One of ideas that was brand new to me was how to handle students who say " I do not get this" when responding to a problem.  I think that "I don't get it" should be banned from classrooms.  I loved trying to get the student to ask a question when they are stuck so that others (peers, teacher) can help them get unstuck.

I am wondering how to implement some of the ideas in my class where math is very scripted.  We have direct instruction, guided practice and independent practice every day.  I know that there are opportunities for pair/share, group work and asking questions.  I just need to get comfortable with the curriculum so I can add to it in a way to help more students learn math well.

In my main placement (5th grade), we are just starting algebra.  I will be looking for manipulatives tomorrow!  I loved the tiles and think that they will be very helpful in my class.  The students were very confused last week with the introduction of variables.  Statements like n=3 were confusing and I think it is a big shift for students.  If we do not have manipulatives, I plan to take a look at the virtual manipulatives to see what I can find to supplement the book.

Math Thinking

In math class today, I learned that I am much better seeing patterns in numbers than I am seeing patterns in pictures.  It felt natural for me to write the numbers in a chart and figure out the general equation for the nth number.  However, it took a while for me to figure out how to manipulate the tiles to show the associated geometry picture for the garden equation.  It took me even longer to figure out how to show the picture for the snake equation.

I am trying to figure out how to be more flexible in my own math thinking so that I can understand and help all my students.  Heather had a great (and very fast way) to do the garden problem and it took me several times before I was on the same page and understanding her thinking.  I need to figure out several ways how to solve problems so that I become more flexible and get out of long held patterns.  Next time, I should start with the picture and not the numbers!

 Last quarter, Prof. Allison Hintz gave us some tools –including worksheets to help us plan how we might want to use students’ math thinking to show different problem solving strategies to our class.  Sometimes a particular sequence can help guide our students to move to a more efficient strategy.   As a new teacher, I would benefit from using the planning sheets or trying to solve problems in a number of ways to help me preview what I might expect to hear/see in class. It is powerful to share students’ math thinking, but I think it needs to be facilitated well by a flexible thinker. 

Teacher as Reader and Writer

I have enjoyed and learned from our literacy readings this quarter.  The Routmann book and the Elbow article have given me a lot to think about and they will help me teach writing to my students.  Both emphasize the need for students to write frequently and for sustained periods of time so that our students write fluently and effortlessly.  They also emphasize that writing need not always be graded.  And when it is graded, you need to be careful to look at the whole as well as the parts and focus only on what the writer (or class) is working on to move forward and improve. I love Routman’s continued modeling in class of “this is what good writers do”.

I am thinking that if your teachers do not employ the writing techniques recommended by Routman and Elbow, you will likely need Lamott to help you write when you are an adult.  In my writing group this week, I learned that not everyone loves Lamott as much as I do.  I understand that she can be depressing, irreverent and somewhat repetitive.  I also know that as pre-service teachers we are not exactly her target audience, but despite all of that, for me she has been magical and what I needed to help me write.  I have laughed at her black humor when she described some of her bad days when she sometimes had the urge to “drink gin out of a cat dish” and “grab her infant by the ankles and swing him around her head like a bolo”.  Only on hearing the perspective of others did I realize that this might be viewed as “whackadoo” by those saner than me.

Lamott says that she wants her students to “see the bleak unspeakable stuff” to turn the “unspeakable into words- not just any words but if we can into rhythm and blues”.  The writers who can do this are the writers we want to read and compare notes with.  They take us deeper into ourselves by letting us see deeper into them.  So  perhaps it says a whole lot about me that I find myself “comparing notes” with Lamott and empathizing that we all have bad days, but we pick ourselves up and move on.  The book gave me insight into her struggles with writing and allowed me to look at my own writing in a new light.