Math Reflection

Wowie Zowie, do I have a lot of questions.  I just looked over my blog posts from the last quarter, and I have far more questions about mathematics teaching methods now than I did at the beginning of the quarter.  I must be really good at math.

Another exciting result of my blog review's metacognitive process is that I now feel much more empowered in my ability to provide more equitable educative experiences for all students.  I see how group-worthy tasks in which students have designated roles and are assigned randomly creates access to opportunities for understanding for everyone.  I even know how to make a mathematical group-worthy task.

Technology's rising role in equitable education and the complete change of my conception of mathematics teaching technology has catalyzed, makes me really excited to be involved with technology and math education.  I am so looking forward to having all students bring in some data of something from their outside-of-school lives and understand it better mathematically.  I am equally excited to help guide every student in understanding math better to take back to use throughout their outside-of-school lives.

Finally, I am going to use manipulatives in my main placement.  They aren't used right now, but I have seen and personally experienced far too much in terms of manipulatives to ever convince me that they aren't invaluable tools for every single student to use at least sometimes.

I know the new mathematical teaching understandings I came to this quarter will not only help me be a better teacher, but they have definitely, definitely helped me become a better mathematics learner, a skill I want to pass on to everyone I meet.

Today's Math I.D.s for Tomorrow

What struck me most about the math reading and class this week was the connection to that and my experiences in 7th grade math classes in the fall, and the deeper understanding I have now about how much of math teaching is not actually specifically teaching math facts.  On top of that, how much not only isn't math facts, but is actually life skills.  Additionally, all of it, the math facts, deeper mathematical reasoning skills, and life skills all are learned through every individual's self-identity and emotional relationships with the subject.  Through this "healthier" (Leatham & Hill, p. 228) math class consciousness I myself even felt more comfortable and empowered to do the geometry puzzles and measurement algebra work with my group. 

As a result of this, I will make self-reflection and discussions of what mathematics really is about, how it really is relevant in students' daily lives, and even personal emotions, a major part of any math instruction I will do.  

In thinking about what mathematics students actually need to know and how my mind has pretty much been blown away in class this quarter thinking about all the potential of the math tools that could easily be in everyone's hand soon,  like motion and temperature probes for smart phones, measuring devices, the WolframAlpha site that seems to have every-everything, I have some questions.  Mostly my questions have to do with, what really are students going to need to be taught in class, what do they need guided experiences with in class, what are they being taught that is a waste of their 21st Century time?  And not only what are they going to need to be taught that I don't even know I don't know, but what of the same stuff did I learn  that they should learn even better than me.  I guess this last question is, if I had grown up with the technology that exists today, would I be using the mathematical knowledge I did gain in school much more regularly or effectively?  What in my life would be different if I was using mathematical thinking more regularly or effectively?  I think there is a solid chance I would really understand my world at a deeper level than I do already.  As an educator, I will do my best through professional development and any other means I can find, keep my own learning progressing with an awareness of what is possible in the present looking towards the future.

Differentiated iTouch Learning - Updated March Thinking

After this past quarter of utilizing the iTouch, I have greatly benefited from and seen its potential as an effective, yet basic tool.  Not that it isn't fully capable of being used for incredibly complex teaching and learning, it just took me a while to realize it's more basic yet useful potentials.  For example, it has been immensely helpful as a recording device during lessons, guided reading, and informal reading conferences, freeing my attention to other more important events to be able to return to the recording for analysis later.  Although this use of the iTouch does not directly apply to the students I was working with, I can clearly see how a student could use it in the same way.  Especially a student whose attention is more hindered than others in the act of writing notes, for example.  They could potentially benefit like me in having the ability to focus attention on other immediate matters and have the iTouch audio recording to return to at a later time. 

During the quarter I have developed a deeper understanding for the power of a small, hand-held skill builder, such as an iTouch with educational game apps.  From my peers I have heard examples of how an iTouch meant the difference between a struggling student having the opportunity to positively work on basic skills to catch-up to their peers, and a struggling student silently slipping more permenantly behind during in-class inaction. 

Through the mathematical methods course this quarter I have seen exciting learning experience potentials that can be realized through the use of iTouches, and how empowering it will be for every student to have this potential in their own hands.  I am really excited to see how it is going to integrate classroom learning with students' outside, real, lives, especially because they will be able to take this learning tool with them into the outside world, and of course, bring the outside world through hand-held learning tools.  The potential to make all learning authentic, relevant and meaningful to all students is fantastic.  I am very curious what parents and community members will have to say about the use of iTouches as learning tools as well as any learning ideas they have for students.

At the beginning of this quarter I think I was in search of much more earth-shattering ideas in using an iTouch and I underestimated the power of an iTouch as a basic, yet effective tool when used thoughtfully to enhance and encourage critical, equitable, pedagogy.  The future with them as learning tools is sure exciting.

Dynamic Mathematical Thinkers and Technology

After today's class I am really thinking about how I can't know what mathematics students are actually going to need to know in their lives.  But I do know I can help them practice mathematical thinking, that I can help this thinking be transferable across the great technologies that are constantly coming about, and help give them the self-confidence that they are mathematical thinkers that can and should use these new technologies for the betterment of their own lives and others'.  For example, if they can use a variety of programs to make a histogram, understand and analyze a histogram in meaningful ways, then making a perfect histogram by hand won't be of the utmost importance.

If in the not-so-distant future everyone has cell-phone probes to understand the world around them, will we be assessing if their understandings are logical?  With more technology, will mathematics assessments and materials be less hands-on with the real world or just more integrated?  For example, we worked with the shapes on a screen this afternoon, this is hands-on, right?  Collecting our own data and analyzing it with technology, that makes it all very "real-world" for students, right?   

As for implications for classroom practice, my thoughts from class today will help me keep my own reality-check for what students really could find useful in knowing and being able to do in their lives.  How will I keep perceived mathematical limitations off and away from every individual - probably by guiding them through mathematical practices with dynamic technology that keeps them as mathematically dynamic as the technology that will hopefully always be viewed as individuals' personal tools.

Mathematics with the Right, Slight Struggle

From class this past Monday, I learned that by doing something like posting a review sheet online for everyone to do two problems and comment on one another's answers, students are challenged in a way that makes them more responsible to one another and especially responsible for their own learning.  It also adds a slight element of struggle, which I've noticed the right amount of "slight" struggle can really help learning.  I learned there are great viable options for math journaling; there are super fun ways to incorporate learning about measurement, mean, and range; and, there can be quite high-order mathematical thinking involved when working with those elements and tanagrams.

A question I have right now is if the group task we did on Monday, making our tanagram giraffes twice as big, was a group-worthy task, right?  Because it helped a whole lot to have more than one of us working on it and because mathematical tasks involving changing size like that do come up in the real world? 

Implications for my classroom would be that I see the direct relevance of using math journaling, tanagrams, and fun activities, all in every grade, all advancing learning to deeper levels.  I think this seems so plausible because they all help me with my mathematical thinking as an adult and can see how they all help in the 1st/2nd grade classroom I'm in right now.  Even in this class of young students they have something called Math Notebooks where they respond reflectively to written mathematical prompts like journals where they explain their thinking.

Differentiated iTouch Learning - February Updated Thoughts

 

My thinking now is that iTouches are a fantastic opportunity for students to take responsibility for their own learning and construct it in their own ways to make it most meaningful to them.  I made a few more realizations and thought connections over the last few weeks.  One is that some students in my main placement (especially the ones I described in my last Tech post that could possibly benefit from iTouch differentiation) are disturbingly low on classroom learning motivation right now.  Another observation has been that when they get the opportunity to unleash their imaginations for a moment they are as engaged in the classroom learning environment as the others. 

If an iTouch was in every students’ hands for even a little time every day in connection with some classroom learning subject matter, they could be guided and encouraged to use a little freedom and creativity to make a digital story or interactive poster or timeline, anything, as partners, small groups, or the class.  There wouldn’t be a power struggle between the students and the teacher because the teacher would be putting concrete power in their hands. 

I got pretty excited over this BBC news article: Genes ‘play key role in classroom performance.  It explains that learning environment really only counts for about half of student achievement, the rest is due to our individual genes.  This strengthens the potential value of personalizing education with tools like interactive information technology.

New questions I have are what are the potential pitfalls that I am still unaware of?  I understand there are safety issues and the technology must be supported by effective teaching, that it must be used to support a cohesive community not separate everyone, but what else? 

What if not every student can hold an iTouch in his or her hands?

 Would it be a detriment to the students if they have one year with a teacher that incorporates tons of personalized learning with interactive technology, followed by years without any (could the experience discourage them in later more traditional-technology-lacking-unpersonalized education)?

Moving from Assessment to Instruction

What I have learned about my buddies needs, abilities, and interests:

 

Word identification in Isolation and in Context (Accuracy and Strategies)

Based on the Spelling Inventory done on 1/11/11, D.  was strong in using consonants, short vowels, and diagraphs and blends.  He could use some more support in his long and other vowel patters as well as with his affixes. 

Based on the oral reading of Amelia Earhart on 2/1/11,  D.’s miscue analysis shows that most of his errors have to do with word endings and vowel letter patterns, and although he is still able to self-correct about half of the time, his reading comprehension is probably limited because of these miscues considering that they change the meaning of the words about 80% of the time.

Fluency (Rate and Phrasing)

Based on the oral reading of Amelia Earhart on 2/1/11, D.’s fluency rate (as correct words/minute) was about 45 wpm, a very low percentile for a fourth grader according to the 2006 Hasbrouck & Tindal Oral Reading Fluency Data. Based on the NAEP Oral Reading Fluency Scale, D. would be somewhere between a Level 1 and a Level 2, because although much of his reading is word-by-word there are frequent three-and four-word groupings, but these are mostly awkward and unrelated to larger context of the sentence.  His reading does seem labored and difficult.  His reading pattern seems like a roller coaster in that when he first hits a word he is unsure about he slowly sounds it out and moves ahead very slowly, careful of each word, and then will suddenly zoom easily, as if on the downhill part of a roller coaster through the end of a long sentence and ahead into the next until he hits the bottom of another word that catches him and slows him almost to a stop, like the bottom of a roller coaster hill.  He is not yet fluent enough to read with expression.

Vocabulary (addressed in Comprehension below)

Comprehension (Content and Strategies)

After the oral reading of Amelia Earhart on 2/1/11, when asked to retell the story D. gave little information, but what he did say were big ideas in the story, that Earhart wanted to fly across the ocean in a time period around WWI when it was dangerous and that she had been a passenger on a plane which made her want to fly a plane.  He also retold how she was flying across the Pacific Ocean when she disappeared. 

During the cued recall of the story, D. was at the frustration level, only answering 4 questions correctly, though he answered more Implicit right (3) than Explicit (1), making me wonder if as he was slowly reading he was keeping up his comprehension to transfer to meaning that wasn’t verbal-English based.

D.’s comprehension is quite impressive considering his rating is at a frustration level.  I think that maybe because stories are so much of a positive part of his life, that he enjoys writing stories on his own in English at home and reads stories on his own in his first language at home, he is well practiced in linking text and meaning, he just gets slowed down in recognizing English text.  I think that because English and culture is relatively new for him it brings down his fluency and accuracy drastically.  He is often unfamiliar with vocabulary, not that he doesn’t understand the ideas he just doesn’t recognize the English names for them.  So when he does slowly but correctly identifies an idea he is able to translate or visualize it for himself so quickly that he has trouble going backwards in his knowledge to answer explicit retelling questions, but has made the meaning so strong for himself, does much better at implicit retelling.

Ownership including enjoyment

After the oral reading of “Amelia Earhart” on 2/1/11, and after the retelling and questioning, I asked D. if he thought reading this text was easy, hard, or just right.  He said, “Just right, I can read almost all the words.”  We had also read the “Early Railroads” text without time for the retelling, and he read it with about the same fluency.  For the Amelia Earhart text he was completely unfamiliar with the American history of women’s rights which I believe caused a little of his difficulty in understanding the full meaning of the story, and although he was more familiar with railroads he was completely unfamiliar with much of the vocabulary, such as “carts”, “engine”, “Thumb” as a name, and “locomotives”, making this story very difficult to comprehend.  I think if someone had translated or explained so he could translate for himself what much of the vocabulary was he would have had a much easier time comprehending this text.

When he was predicting about the text of Amelia Earhart he included that he had knowledge about the dangers of flying small planes from a video game he has, that based on the clues of the text he knew it had to do with someone using a plane to go on an adventure, and added that if he were to write a story about this he would have them go into a jungle, get lost, and when they make it back to the airport they wouldn’t be able to find their plane because some other people came to the airport and took it on an adventure of their own.  This leads me to believe that D. is immediately ready to make personal connections to the text and enjoys thinking about stories.  During the retelling, when he was describing what might have happened to Amelia Earhart he showed me with his hands what a crashing plane does. 

Between reading this story, his interest in thinking of his own story, his enjoyment of reading and writing stories on his own at home, I believe that D. really enjoys stories in general, especially when they include a main human character and then a surrounding out-of the ordinary story, such as animals or monsters interacting with the main character in unusual ways, or adventures. 

Context:  The informal interviews happened at D.’s desk in the classroom.  While there were others working and talking around us D. usually seemed to focus well on what just we were doing, although at the end of his oral reading he did stop to look at and listen to a student reading quite fluently behind us.  D. has started out every session seeming reserved and quiet, so I’ll start by chatting a moment about how much I enjoyed his written story I saw or about how I was thinking the past week about the interesting things he was telling me last time.  After a little bit of this I usually have asked an easy, open-ended question to him to hopefully help him get started talking with me more easily.  He is hesitant but positively tries very hard and doesn’t seem to let difficulty bring him down at all.  Even though the oral reading ratings had him at the frustration levels he always wanted to continue and never at least let on to me that he was frustrated.

AS A RESULT OF THIS KNOWLEDGE: 

Objectives I am considering for a lesson would be to focus on the vocabulary comprehension skill of using context and structural cues to gain new word meanings.  I wonder if this could be considered a “monitoring & fix-up strategy” and if it could be taught in a similar way.  For example, possibly I could find a text that has to do with an animal or adventure like he would enjoy, and we could go through a targeted small group instruction lesson.  For this I would explicitly explain we would be practicing understanding the text better by focusing on figuring out new vocabulary from our knowledge and the rest of the text, then I could model, he could read a little and then try with me there helping as guided practice, and then he could try on his own. 

If I were to do a lesson like this I would need a text he would be interested in at his instructional level, in which there would be unfamiliar vocabulary but that could be understood from previous knowledge and surrounding text.  I would need to be prepared with the vocabulary I thought he would have trouble with and ways to help scaffold this practice.

I am very open to other ideas of lessons though, and am just feeling like it is a little hard to decide on exactly what specific objectives would be most helpful for D. at this time because on page 51 of Reading Essentials Routman explains that for language acquisition students “need to hear, speak, practice, and interact with the rich language of stories and literacy”.  The broadness of this statement leaves me somewhat unsure on choosing specifics for my specific buddy when it seems that just about everything would be helpful for him.

Understanding Geometry Understanding

After our class this week focused on thinking about geometry, and then the reading, "The Rationale for Using Manipulatives in the Middle Grades", by Dana M. Freer Weiss, my understanding of geometry understanding has definitely increased. 

In class I learned about the Ban Hiele Levels of understanding geometry, and that visualization is the first.  This makes sense to me because anytime I am doing any kind of mathematical thinking I am visualizing.  I really start running into trouble when my visualizations start becoming just memorized number rules because then I've lost the meaning, I don't have those mathematical ideas connected to anything else, so when I try to build some new information in I don't have anything to connect that to either, it has to have its own isolated little spot and isn't very useful then. 

In the 1st/2nd grade class today the students were struggling to find the differences between 2-digit numbers and were getting frustrated because their fingers weren't getting them very far and drawings were taking forever.  As I moved through the students trying to help and wondering how to best suggest manipulative to my master teacher, I remembered the 7th grade math classes I was I was in this past fall and how the teacher always encouraged them to use manipulatives, even on tests, and the students at that school were some of the highest achieving math students in the district.  Probably not just because of the manipulatives, but I bet there were part of it.  I am fully convinced, whatever time I spend finding and learning to effectively use manipulatives with students will be worth it.

Finally, I am just wondering about geometry.  How can it make sense all the time?  Is it because it is all repeated patterns?  Is it because of the physical properties of the universe, like a plant growing straight up from flat ground makes a right angle and if another is close by and a leaf lays across the two you have a rectangle and it's properties just because that's how it is?  Is there any geometry that hasn't been explained yet or has it all made sense to somebody sometime?

Project 1 Final Response

Since my first analysis and lesson plan development for my 4^th Grade buddy after one meeting, I have been able to meet with D. for a second time and learn much more about him as a reader and writer.  In regards to ownership, D. not only enjoyed writing the story about the talking cat but he also often writes funny animal stories for his own pleasure at home on the computer.  He writes them in English rather than in Ukrainian because there are not enough letters on the computer keyboard for him to write in Ukrainian (he would need 36 letters to type in that language).  Additionally, he shared with me that he also enjoys reading animal stories, and that he has a gigantic book full of them at home written in Ukrainian that his dad gave him and encourages him to read. 

The idea for this lesson came from Fox (2008) where there are many suggestions for teaching English language learners including the helpful hint that “older children enjoy creating and publishing their own versions of books”, and also to “not hesitate to share predictable books with older children who are crossing the threshold of English literacy” (232).  Goldilocks and the Three Bears has some predictable, repeated lines, and would give my student a structure to that might actually help free him in using his creativity in English as well as fluency and word choice as tnashty pointed out.

The aspect of the lesson that includes the kindergarten buddies is critical because it makes the project relevant by giving it an authentic purpose and audience (Routman, 2003, 50).  Additionally, Routman encourages a focus on language acquisition “not just letters and sounds” (51).  Routman emphasizes the importance of promoting oral language development through productive talk about stories, and through hearing, speaking, practicing and interacting through language as a whole (51-52).  In Routman’s Writing Essentials (2005) she sates “writing for a real audience (not just the teacher) is one of the best ways to get quality writing” (145).

Cambourne explained the necessity of recognizing the similarity and strong connection between oral and written language learning.  This lesson provides repeated opportunities for D. to hear more advanced English language users vocalize the same story, provides him with opportunities to vocalize the story, and provides opportunities for students to discuss stories with one another. 

I would really like to incorporate tnashty’s suggestion of planning specific questions for students to use with each other about their stories, such as his example, “Why did you feel x was the best word to use here?” to engage D. in conversation about his writing.  This again would help his oral English language development which would in turn support his written English language development, as well as support all students in guided deeper thinking into their writing.

An additional detail about D.’s English spelling skills I would like to add following Leah’s Litmus suggestion, is that from what I have seen of his writing and experienced through hearing him read aloud I would describe him as being in the Middle to Late Letter Name-Alphabetic Stage.  This is because he spells primarily phonetically, with correct initial and final consonants and some blends, omits some silent letters, and reads slowly in a word-by-word manner (Bear, Invernizzi, Templeton, Johnston).  Based on this there are also some ideas for furthering reading and writing development such as holding students accountable for words and features they have studied, and doing simple editing such as punctuation and high frequency words, and even doing some work with vowel sounds and their families.

Myjourneyasateacher helpfully suggested to state why I think the rewriting of Goldilocks and the Three Bears would be engaging for my 4^th Grade Buddy D.  What I first thought of was that it included talking animals and a human main character, which this student said most of even his own stories at home have.  I think D. would also quickly spot places to incorporate his own creative silliness to enhance his own enjoyment of the story.  He described time he spends playing with and even helping his five year-old little brother and I think that the kindergarten buddy sharing aspect of the lesson would be a challenge that still held a comforting familiarity in the experience.  Myjourneyasateacher also suggested allowing plenty of read aloud practice for him, maybe this would be something he could practice with his own little brother at home for some time first, as well as with his table group in class, to aid in the feeling of a safe fun challenge throughout the lesson.

References

Cambourne, B. (1988). An alternate view of learning. In The whole story: Natural learning and the acquisition of literacy in the classroom (pp. 28-42). New York, NY: Ashton Scholastic.

Fox, B. (2007). Word identification strategies: Phonics from a new perspective (4^th Ed.). Upper Saddle River, NJ: Merrill.

Invernizzi, M., Johnston, F., & Bear, D. (2004). Words their way. Upper Saddle River, NJ: Prentice Hall.

Routman, R. (2003). Reading essentials. Portsmouth, NH: Heinemann.

Routman, R. (2005). Writing essentials. Portsmouth, NH: Heinemann.

Group Tasks

I had a super-great learning experience in class this week.  My group and I had felt our data story poster was near completion two weeks ago, but upon seeing it again yesterday with only a data table and no graphs, we decided graphing would help others understand the data and our story better.  It took some hard thinking and discussion to decide how we wanted to show phone subscriptions over time to GDP of different countries over time, but finally decided for a reason we couldn’t really put a finger on, that two graphs would work well: one showing phone subscriptions to time and the other showing GDP of the three countries we chose over time. 

Our brains warmed-up nicely as we traveled the room of posters, discussing our questions and thoughts of the data stories as we went.  At one point we reached a poster that was challenging to understand at first, comparing U.S. military and education expenditures to each other.  After looking and discussing further we did understand, and again, didn’t really put our finger on exactly why the graph had been tricky to understand.  Finally, back at our own poster, we saw a post-it question from another group asking why didn’t we put our two graphs together as one.  That’s when I really got it, that we didn’t put them together because if that meant comparing phone subscriptions to GDP, it might imply that one determined the other.  We didn’t necessarily conclude that GDP determined phone subscriptions, we just wanted to show the trends of each GDP and phone subscriptions over time.  We wanted both to be compared to time (as our x-axis) and would have had trouble combining GDP and phones for the y-axis in a meaningful way. 

This group task of the entire process of creating the data story, representing it in a poster, discussing other posters for understanding, and finally considering where others thought our poster could share understanding better, made me really understand an aspect of graphing quite consciously.  It was more meaningful for me to experience why my group and I felt more comfortable sharing our data in a certain way, considering other ways other groups shared theirs, and then thinking about ours again together that my understanding deepened. 

Now, not only do I have a deeper understanding of graphing, but I also have a deeper, more meaningful understanding of the value of group tasks in the learning process.  I will definitely take this awareness of the value of group tasks for understanding with me into classrooms.  I guess I am just left wondering when does the teacher need to step in if understanding is not coming through the group tasks?  How patient with the process should the teacher be?

Analysis of Student Writing and Lesson Plan - Project 1

Analysis

This analysis is based on one meeting with D., in which he shared with me a short story draft, his own personal stories primarily about his pets back in the Ukraine where he has spent a large part of his childhood so far, and also the spelling inventory.

Meaning of the Piece

In the short story D. wrote about his pet cat that suddenly begins to talk, demanding coffee one morning.  The main character seems taken aback by his cat’s actions, including singing, crying, and insults, even calling the main character “dumbo”.  Almost as suddenly as he begins to speak, the cat dies ending in the relief the cat is gone.   Through the main characters’ actions and dialogue the reader gets a clear impression that the boy is quite logical while the cat is not and the interaction between the two is amusing throughout the story. 

Six Traits Assessment

Ideas:  D.’s topic is manageable because it takes place within a relatively small amount of time, from the sudden realization the cat can speak to within a couple days, the cat dies which also gives closure but leaves questions.   Support is attempted to flesh out the story line, which does go beyond the obvious and predictable, such as the cat ordering macaroni and cheese before it dies.  Ideas are reasonably clear although they could show a stronger sense of purpose, such as why does the cat start to talk and what does the main character think and feel about it? The writer’s insight is experienced when the reader’s attention is immediately caught with a somewhat familiar idea (talking cat) but with intriguingly quirky dialogue and events.

Organization:  The introduction of this story captures attention, “When I was sleeping somebody said, “Give me some coffee,” though a few more details to supplement this introduction as well as the story’s conclusion of the cat’s sudden death, would support the story better.  Transitions could be improved, such as “An hour later I came to school but before that I said to my cat to stay in the house”, where the student could restructure this transition and sequence to be easier to follow.  Pacing is fairly well controlled in that the reader can keep-up, but it is still somewhat abrupt, with the sudden death at the end, for instance.  There are effective paragraph breaks, such as an indent and then transition, “An hour later”.

Voice:  The writer does connect strongly with the audience through the intriguing use of engaging language, “After that my cat said, ‘Didn’t you hear me, I said give me some coffee,” and screamed at me.  I said, ‘ok, ok, fine!”  The writer seems aware of a purpose to write this piece but could be more clear with a more detailed and directed story.  The writer does take risk with the inclusion of personal details that reveal himself, such as, “I told the doctor to give me one hundred thousand million thousand five hundred seventy three dollars,’ and Dr. said, ‘Poopy pants, give me that money,’ and I left.”  This narrative writing is personal and engaging.

Word Choice: Improved word choice could help portray accurate meanings and a smoother flow throughout the story.  Familiar words and phrases communicate but don’t capture the reader’s imagination, such as “I can still remember that day like it was yesterday.”  Language and phrasing are somewhat natural and effective in that the reader is able to follow the story, such as, “my cat was saying, ‘sorry crazy boy.’  I said, ‘Stop it.’ ‘ok’, and my cat went to the treehouse.”  This sentence also shows that there is a limited vocabulary and misused parts of speech that do affect understanding,

Sentence Fluency:  Sentences are awkward in a way that naturally reflects awkward speech, “I cam to my cat and said what wrong?  My cat say’s that’s all your felt stuped!!!”  Sentences vary in length and with different beginnings such as, “Then after school”; “My cat says”; and “I came to”.  Sometimes the reader needed to look for connecting words and phrases to show how sentences interrelate.

Conventions (spelling below): Punctuation is often missing or incorrect, “I came to my cat and said what wrong?”  Most words are capitalized correctly, especially at the beginning of sentences.  Errors in grammar are somewhat noticeable but meaning is still clear.

Ownership

While I will need to ask D. more about his writing ownership, during our meeting he shared with me all about his pet cat and dog he misses a lot because they are both staying with his grandparents back in the Ukraine.  While D. was at first shy to talk with me, he opened-up a lot with enthusiasm during this discussion and was somewhat slowed down with his own struggle to translate his thoughts into English. This leads me to believe that between the stories of his pets he loved telling me and the lively story about a cat he wrote, D. enjoys pet stories.

Spelling Development

In D.’s written piece and the spelling inventory, D. has very strong phonemic awareness; he is able to write words how they sound.  His spelling needs some improvement such as “dishis” for dishes, and “averything” for everything.  Between speaking with D. and reading his writing, it looks like he is writing with the accent he speaks English in.

Lesson Plan

Objectives

• ·      Students will extend and refine their ability to write.
• ·      Students will communicate with English-speaking readers.
• ·      Students will write for a variety of purposes, here, to share a creatively rewritten story with a familiar theme.

Standards

GLEs for fourth grade writing standards:

1.   Student understands and uses a writing process.

1.6 Adjusts writing process as necessary.

2.   The student writes in a variety of forms for different audiences and purposes.

            2.1 Adapts writing for a variety of audiences.

Materials

Photocopied booklets of a simple, illustrated version of Goldilocks and the Three Bears – enough for every student and teacher to provide the model to follow for story structure, as well as proper word structures and patterns.

Identical booklets in size and page number, as well as space for text, but with no text or illustrations – enough for every student and teacher, plus a few extra.  These provide the physical structure of the booklet to ease following the story structure of the model. 

Sharpened pencils to begin immediately, with confidence that any modifications can be made at any time.

Colored pencils or crayons for those students who wish to add color to their finished illustrations, allowing students to express their writing and stories with personally (and enjoyably) illustrated contextual clues for their readers.

Instructional Strategies

This is a lesson that could be for a small group or the whole class.  First, the teacher will explain that students are going to rewrite and illustrate the story of Goldilocks and the Three Bears for sharing with kindergarten buddies; that this will not only help improve our own writing skills but will also inspire and excite our younger buddies in reading and writing.  This will give an authentic purpose and audience for the fourth graders’ work.  To provide the structure of the writing, the teacher will supply each student with their own small paper booklet of the illustrated story of Goldilocks and the Three Bears.

To demonstrate the project, the teacher will read the story aloud and then explain her thinking aloud as she models rewriting her own version with illustrations, most likely for only the first couple pages.  The written story provides the story structure and even sentence structure while the writer is encouraged to unleash their creativity to change the characters and descriptors.  During this time students are listening and observing.

Next, a shared demonstration will have the class collaborating in shared writing with the teacher to rewrite a class version of the story, again, probably only the first few pages.

Students are then each given their own blank booklets and go through a guided practice in which they write and illustrate the first couple of pages of the story while the teacher actively circulates and assists.  The teacher will encourage students to talk together and help one another, while simultaneously noting work that would benefit the whole class to see, such as particularly creative writing as well as writing that is clear and has correct spelling and grammar.

Closure will happen as students get through their first couple of pages. After an appropriate amount of time students will share their story beginnings with one another in partners or small groups.  The examples the teacher noticed earlier will be shared in front of the entire class with the writers’ permission.  Students will have the opportunity to ask any questions as a group and the teacher will ensure all students are clear that their finished version of the story will be due with the entire story completed with illustrations, along with clear writing, as correctly written as they can, ready to share with their kindergarten buddies.  There may be additional class time or the opportunity to work on the project at home as well.  Teacher will continue to assist as needed, respond to questions, and acknowledge efforts.

The final event of this lesson will be reading aloud the finished stories to kindergarten buddies.

Assessment

Teacher will assess students’ progressing abilities to communicate with English-speaking readers.  Teacher will assess word formation such as appropriate suffixes on singular and plural nouns, as well as different verb tenses. 

Teacher will assess spelling with particular attention to long-vowel patterns, which this story was chosen specifically for (“three”, “too cold”, “just right”, etc).  

Mathematics and Creative Writing

I just read the article about using creative writing and literature in mathematics classes, and what stood out most to me was the point that not only do students enjoy it while utilizing math concepts and vocabulary in personally authentic and meaningful ways, but it is also a really good way for the teacher to assess student knowledge.  The examples given made it clear that between the written story plots, descriptions, and graphics, students' mathematical misconceptions can be spotted to be addressed in instruction in ways just as effective as well-designed tests meant to identify misconceptions.

While thinking about mathematics and literature I was reminded of the mathematizing literature assignment from last quarter.  I worked with a small group of 7th and 8th grade girls, and I read a children's storybook to them while we stopped periodically to discuss what math ideas stood out to them and what math they thought younger kids might pay attention to in these stories.  It was quite an exciting endeavor as they considered so much of their own mathematical knowledge and fed off of one another's ideas.

I wonder how the 1st and 2nd graders I am working with in my main placement now might use creative writing in their mathematics studies.

Differentiating with iPods

The prompt for this blog is to write about three different students in my 1st/2nd grade main placement classroom, and how an iPod Touch could support differentiated instruction for them.  I am immediately made aware of how difficult it is to select only three students, especially after reading and seeing how many different ways iPods are already being used in schools for all students.  The first student that comes to mind, though, is very quiet, shy girl whose first language is Spanish.  She specializes in staying under the radar and only seems to do the amount and quality of school work that allows her to stay there.  An idea I have is to encourage her to use the iPod application StoryKit, in which she can write her own versions of digital stories on the iPod.  I would encourage her to do something I had heard suggested, re-create the text for one page and then have a family member do another in any language.  If a language besides English is used it will be valued and can be translated by the student or another app so that any family members and I could read what is being written.  I see this as potentially getting her more excited about literacy, giving her space to unleash her creativity in ways that are hopefully comfortable and allow multiple entry points for family to support her advances in literacy as well.

Another student I can see potentially benefiting from an iPod in the classroom likes to "check-out" from most things academic and even social in the classroom.  To help support him in both areas I would hope offering him opportunities to use a math game app.  My idea here is that he loves games, especially computer games, and he does like playing with other students at recess, so maybe he would like playing a math game to increase his own skills and comfort in math, and then, he could teach other students how to play.  For example, one game I found includes lots of basic arithmetic to practice, and another game involves counting money coins, just like we often do in class.  Usually in class other students are trying to help him complete the math he is uninterested in and I think that it would be empowering and joyful for him to reciprocate and help others with a fun game that encouraged learning at the same time.

Finally, I think of a student who is academically much more advanced than many of her classroom peers, has difficulty maintaining positive social connections, and is desperate for more attention, always.  Maybe, when she finishes her reading and writing work early, she could use an iPod app like Dictionary.com to go to students who need to know a definition or spelling and look it up to share with them.  She could become more of a helper to other students instead of someone who often disrupts community learning.

After thinking of these ideas plus so many more for all of the students, the biggest limitation I saw was when I brought the iPod to school and discovered that the school did not have WiFi.  I could not use any of the iPod applications I had been spending so much time researching, downloading, and experimenting with for this class of students.  In today's world, however, I cannot imagine the school will stay WiFi-less forever.  Then the potential limitations shift, and it seems that most limitations would then come from instruction that wasn't effective in using the technology.  If iPods were used to supplement instruction they must be used equitably and I would want to ensure that they were never a substitute for what the entire class community was doing, that they in no way would ever allow one student to be more separate than the others, but that the technology would aid in community learning inclusion. 

Equity and Algebra Tiles

Using the grid frame with algebra tiles to work through multiplication in algebra blew-my-mind.  It made algebra so much more clear to my head, and I don't remember ever particularly struggling with it, I guess I just never understood there was a bigger concept to understand.  After that activity during our last class, where we experienced many different ways algebra can be thought about, the readings, Group Worthy Tasks (Lotan, 2003) and Orchestrating Discussions (Smith, Hughes, Engle, Stein, 2009), really hit home.  Just as described, I needed time to think about an algebraic equation myself, discuss with others, and work through with manipulatives a variety of thought processes to get to the point where the algebra tiles on the grid made sense to me.  And it was the connection I made myself, just as we talked about in class and was discussed in both readings, that x2 is an area and on the grid I could see an actual area.  If only I knew I was such a mathematical wizard when I was younger, well, I'd probably actually be in the same place, but I would have gotten a lot more of a thrill out of math classes.

I must admit, I am still working through the beans as negative and positive numbers.  Is it that you don't subtract because you can't really subtract in real life anyway, you can just move it or change it?  Money doesn't actually go away, it just leaves one pocket for another; apples that get eaten don't disappear, they go through the digestive tract.  Is all this why we don't subtract, we just add the opposite?

Some points in the readings remind me of the Culture of Power Delpit described, and that when we were talking in class and the readings explained having multiple entry points to the learning, it is about equity, so that complex instruction with group-worthy tasks and effectively organized discussions in mathematics isn't just a good suggestion, it is necessary for equity.

Math Questions

Allowing the time and space for students to work through contextualized math problems is what stood out most to me in our class this week as well as in the readings (Reinhart, 2000; Herbert & Brown, 2000).  Space is the multiple entry points good math problems can provide, and I think that by encouraging small groups to work together with a variety of materials even more space and entry points are provided.  One of the readings (Reinhart) emphasized the importance of allowing some time in the beginning for students to work independently and then work together.  I appreciated this point because I think it is an important part of providing multiple opportunities for students to participate.  The independent work at the beginning is more time to think about the math and provide the space for independent ideas to be generated that can be shared and tried out in the group discussion that follows, even encouraging some metacognition as the student thinks about what they know and what they want to know.

As I engage in a mental wrestling match with the iPod Touch, I wonder more about how it can be used to aid learning and I wonder if it can be used as a tool for this larger question I have had over this week's math class and readings: How do we document progress in learning using these mathematics techniques of group work, questioning and communication?  Maybe digital technology can help.  Because when a student is working as a small group discussing and working with manipulatives together, questioning their classmate's ideas as they deepen their own understandings, how do I document this?  Maybe I could record their communication of ideas to the group?  Take pictures of how they show their thinking?  Should I just go ahead and do written summative assessments along with this complex style of teaching?

I definitely appreciate how what we have been studying this week, especially the importance of student questions in their own learning has brought up many of my own questions, and I will absolutely utilize questions as a learning resource and tool in classrooms.