Learning to be prepared...is it possible?

Today I learned, to be much more specific with my objectives. I had it drilled into my head again, that they HAVE TO BE MEASURABLE! Indeed...this is why I love math; I can learn how to measure things, even objectives!! Okay seriously, ensuring that the concepts and ideas that are taught, are done so in a measurable way. I'm thinking more concretely...which is good, because I like having my feet on the ground...preferably grass but I'll settle with concrete.
Anyway, I also learned the more math I can immerse myself in the better prepared I will be for my students. I have to have the experience that will enable me to be able to teach math better to students. It is my responsibility to be prepared to offer students different ways solving and understanding problems.
My favorite take away message, is to start with the end in mind! Plan our lessons backwards.

I'm still wondering, about the idea of modeling. Well, when we model we have to be sure to model how to handle failure, struggle, and humility. More on this to come after some heavy percolation...
Confidence is the most intrinsic motivation for math. How do I use this as  a tool and/or power to help them learn, enjoy, and do well in math?

To use these ideas in the classroom...in order to establish confidence and interest in math.... (and this is another favorite quote and thought from today)...use "Open ended work that can be assessed in different ways and taken in different directions...." I'm learning more about this every week. Heck! Every day!

Good timing on the "pep talk"  we have all been being burnt out and beat up with the massive lesson plans and observations....You give us a realistic balance to be "prepared" for teaching. 

Gap Find the Mira

In math I learned and found fun ways to do lessons and activities with the ultimate graphing resource Gapminder. As I've said before, this tool has endless possibilities with students of various ages! And it's pretty fun to just play with for kicks. I really enjoyed the gallery walk...specifically I thought it was unique that we got to leave questions and comments on the graphs and posters. Thinking about how others organized their data forced us all out of our comfort zones. When I came back to my own graph and poster, I loved seeing the comments that everyone left for us. I had to think of alternative ways to represent my data, findings, and conclusion. This can be hard as a teacher..presenting students with alternative explanations of material...

I'm still pondering the Mira that we got to experiment with during class. It was such a simple device...with manipulatives like that it makes me wonder if we really need the virtual manipulatives on my ITouch...Then I play with the fancy apps and ponder the seemingly endless opportunities it brings.
How can we use the Mira in other ways than just for Congruence?
In my school we have a very specific math curriculum, how can I fit these creative math activities into the curriculum? Am I allowed to venture into my own ideas?

I can picture classrooms using the Mira to work with patterns, especially when the patterns are geometric. Patterns are accessible for all ages...I can still remember working with patterns in the second grade. If I'd have a Mira to work with I would have been able to make and understand complex geometric patterns even at such a young age.

Project 1: Analysis of Student Writing and Lesson Plan

Project 1: Analysis of Student Writing and Lesson Plan

Analysis

This analysis is inferred after reading two short writing samples of E’s (Pseudo-name) work in his class. He gave us a final draft of a writing that was assumingly from a prompt in class. He wrote about his feelings for various subjects in class. His rough draft writing piece that he supplied for use was about an adventure story where he searches for gold. The spelling analysis is based on the spelling in the writing then also the spelling inventory that we took from our student.

Meaning

E was happy to share his writing with us. He first gave us a final draft piece that is about his school work and shows his interest and skills from a personal, first hand view. In this, he explains clearly his struggles in writing are in brainstorming. His final draft shows he is a strong writer in all of the six traits, regardless of these struggles. E shared with us that his mother wants him to be a writer when he grows up because of his advanced skills so far. However, it was clear in conversation and in his writing that he does not favor it. Instead he favors math; he told us this right away in conversation and again in his writing, “I think math is really important even when you have a job!” He then showed us his rough draft pieces of writing. Some were about finding gold, animals, and other fantasy style stories. He was excited to show us his story about gold. This gave us a good look at his personal interest in fantasy and adventure. He repeatedly told us this was his favorite style of writing. He uses his personal creativity to shine in this story; you can tell he was really having fun with “The Adventure of Gold!”

Ownership

 E’s ownership is strong. He is proud of his adventure stories and enjoys showing off his creative work. His preferences are in fantasy and fiction writing. This is where he uses his creativity to grab his audience’s attention. While reading the first draft of his story “The Adventure of the Gold”, the reader can sense and feel that he is having fun trying out new possibilities with his writing.  E knows he writes well and experiments with this skill. In his final draft piece, he mentions that he gets frustrated with coming up with ideas for writing. The topics of the pieces I collected and looked through were exciting and attention grabbing. I’m wondering if he is focusing too much on picking the “perfect topic” which holds him up during brainstorming. He writes at home in journals too; there is a sense of enjoyment that he gets from doing well in his writing, even though he says it’s not his favorite.

6 Traits

                Ideas: In his final draft and rough draft work, the ideas are understandable and focused. As a reader, I am interested and able to comprehend his thoughts and ideas clearly and effortlessly. In the final draft piece, he writes of his personal strengths and struggles in school. The ideas keep me reading with anticipation and excitement. His sentence phrases are unique, and attention-grabbing, “My most serious gripe of all is when I discourage myself.” The rough draft piece was a detailed story of finding “Mt. Gold and Silver”; a treasure hunt.

                Organization: The organization of his final draft is concise and orderly. Transitions are present between paragraphs, but he could use more work with it. He writes in a controlled manner. In his rough draft, he could use work on his transitions and connections: Ex. “It made no sense to me. Then, I found myself packing for the trip there.” This part of the story was unclear to the reader, as he was switching the focus of his story. Also, pacing and sequencing make it a little more difficult to read. His creativity sometimes gets him into too much detail that can detract from the focus of the story.

                Voice: In both pieces, his writing is original and inviting. His ideas are detailed and stay focused on the writing topic. He is not afraid to take risks with what he reveals in his writing.  In the final draft he writes personally, for example, “I always take a really long time: just to make one juicy page like this.” He tries to connect with the audience with his use of voice.  In his rough draft piece, he writes with a more story telling sense, very step-by-step basis, “Then, I found myself packing for the trip there.”

                Word Choice: He uses word choice in a natural and effective way. The words are colorful and put in precise places to bring power in the piece. In both the rough draft and final, I was intrigued by his word choices: “gripe, discourage, mysterious, parchment”. They add personality, character, and interest.

                Sentence Fluency: In his final draft the sentence fluency flows well and is usually easy to follow. The sentence structure varies and is creative. Thought is put into the purpose of each sentence; for example, “All that preparing goes to waste when I get 4’s or 3’s on my not-to-good.” The effort is there, but it still comes out a bit choppy. In his rough drafts, the sentences are much more choppy and don’t always transition. There isn’t much variation in the structure, often they start with the standard, “then there was… It was… Then we…” etc. Simply telling “what happens next in the story”.

                Conventions:  Conventions in E’s final draft are used well and consistently. In the rough draft, punctuation varies. It is always correct at the end of sentences, and there is thought put into it to make it unique. There is need for more attention to punctuation within the sentence, i.e. commas and semicolons. He does attempt to manipulate conventions to use for style; however, his use is often confusing to the reader. I assume from this that he is confused about the proper places for them. Capitalizations skills need work. In the final draft it is appropriate, but in the rough draft, he struggles with capitalization of nouns; for example, “Juanita Beach and Pirate.”

Spelling

E’s Spelling is generally correct in both the final and rough drafts.  He is very advanced for a fourth grade student. The rough draft has more mistakes than the final, and it’s fair to assume he will put more effort into this during revision/editing. Spelling overall is very good. His mistakes are on complex words that show he is willing to take risks. During our spelling inventory he spelled all words correct until we got to the last four upper level words, confindnt, forutanate, civlize, oppopssion.  These spelling errors put him in the middle-late syllables and affixes spelling stage. These mistakes were close to the correct spelling, and he used knowledge of his previous experiences with prefixes and suffixes to help his spelling. He would benefit from practice with syllable junctures, consonant doubling, inflected endings, prefixes and suffixes (Bear & Barone 1989). E was on the independent level on the Examiner spelling lists for our spelling inventory up to the sixth grade word list. This shows his spelling strengths well. Even on the upper middle school and high school word lists he scored in the instructional level.

In his writing work that we collected he misspelled “unfourtulay” and “mysteryous”. These spelling mistakes are on higher level words and again show his placement in the syllable stage of the spelling development (Templeton & Morris 1999).  They also show that he is willing to take risks in order to improve his writing.

                During our conversations E had mentioned how uses the meaning of words to figure out the spelling. In the middle of our spelling inventory, he stopped to tell us how he had used the meaning of the word in our example sentences to know what spelling to use. The word was “celler” and he said at first when he heard the word he started to write “seller”, but after hearing it in the sentence he knew the meaning changed the word. This was striking to hear that he was so aware of his knowledge that spelling represents both sound and meaning (Templeton & Morris 1999).

Lesson Plan

Objectives

Students will be able to use their timeline of events as a tool for brainstorming ideas in their pre-writing of non-fiction, realistic-fiction, or fiction stories.

Standards

GLE: 1.1: Prewrites to generate ideas and plan writing.

GLE: 2.3: Writes in a variety of forms/genres.

GLE: 3.1: Develops ideas and organizes writing.

Materials

Ruler (to make straight lines)

Large paper (Construction or legal size document)

Pencil and pen or marker

Instructional Strategies

Teacher will explain to students that she is providing them with another pre-writing  tool to use while brainstorming for stories.

Teacher will model for the students how to create a timeline of events and moments in his/her life that can be plotted in order. Then transferred and modified to make into a story.

Teacher will draw a horizontal line across the paper, starting with your birth year, to present (using the pen or marker as the line for different colors).

Teacher will use short fragments to label the moments. These will be just enough information to remind him/her of the event or moment, including the year. Talk through how one could use this idea for a potential story. Be sure to expand on how they could use it for different genres of writing. The main focus is to take an event and find ways to transfer it into a story/writing.

Model at least five events.

Have students get their papers out and draw their lines. Guide the class through the first few. Give the students time to work on ideas. Ask a few to share how they remembered that and how they would use it in a story. Have them give examples of different genres.

Give students 15-20 minutes to create as many ideas as possible on their brainstorming timeline. At least ten.

To wrap up ask a handful of students to share what helped them come up with more ideas when they were stuck and what strategies they used to keep finding more ideas.

Explain your thought process when you try to get out of the moments when you feel stuck and can’t think of other ideas.

Assessment

Teacher will assess by listening to students ideas to use their memories to create plots for new stories, during whole group share and conversations with other students. Teacher will also assess by looking for at least ten events on the brainstorming timeline that could possibly be used for a fiction, non-fiction, and/or realistic-fiction story.

IPods for Differentiated Instruction

Three students who come to mind that benefit from differentiated instruction in my class are "Bruno", "Cornelius", and "Maximus" (Pseudonyms for all). These students vary in a multitude of ways, but I'll explore possible ways the IPod Touch can benefit them in the class and limitations it might also have with each of them.

Bruno is a very intelligent boy. He is the first to finish most assignments and enjoys challenges. He prides himself with his organization and preparedness. I am continually impressed with Bruno; however, I struggle to find the time to give him the challenging work he deserves and would benefit from. Using the Touch with him could potentially do great things. He would be comfortable using the technology if promptly shown how. He could use applications to strengthen and push his skills when I am unable to give him other work to do after finishing the normal class work. Having various math applications that are beyond what the rest of the class is doing, would be beneficial and fun for him after he finishes his normal class work. I worry that this might deepen the gap between him and his classmates thus making it harder to help him in whole class work. This student also speaks two languages fluently and is learning a third. If I could find an application that would help his speech, that would be another way to utilize the extra time he has after completing his assignments.

Cornelius is a whole other story. I struggle being able to give him the time he needs to comprehend my instruction and direction. I feel guilty when I move on, because I am unsure he had grasped my entire lesson. Using a Touch for support in his differentiated instruction would be helpful if I had an app that recorded my instruction as I said it. This way he could reference it when needed if he had missed something. His family could also use this recorded instruction to help him at home with his school work. If the recording was in script or in audio, they both would be helpful. I worry that using this in class would slow him down more. He already has a hard time finishing his work in the allotted time. Wouldn't this slow him down more? But if he is gathering the information better, then isn't it worth that time? At least the time at home, would be very helpful. I could even email the written recorded script of my lessons to his parents, for easy access while doing homework and maybe even daily reviews.

Maximus is challenge and a delight. His learning disabilities cause his mind to be all over the map throughout the day. Keeping his attention for more than one minute is a feat! Having the application that records my lessons into script would be helpful for him in similar ways as Cornelius. Having it to take home, or send home etc. I wish there would be an option to take that text and re-size it. Maximus has a hard time taking information from up on the doc cam and transferring it to his paper. It is most beneficial when he has the information right on his desk. If I could have a personal Touch for him at his desk, that I could re-size my recorded scribes for him, I believe would benefit him greatly. His attention span requires information to be directly in front of him; not up on the board. If I can't find a way to re-size the text, the Touch would be far too small of font to keep his attention.

Man-Manip-Manipulate!

Today we spent our day working through math problems using different manipulates. At first, I, like many, was reluctant to see how they could possibly strength my understanding of math facts and rules, on problems that I have long since "mastered"...or so I thought.

By using the various beans and algebraic blocks I was able to represent my thinking in a way that thoroughly strengthened my understanding AND my ability to teach or explain the idea to others. However, I will not try to explain these mathematical concepts in the same way I learned them long ago...No no no, what purely simple strategy to keep with math... to start with concrete examples and explanations THEN move to the abstract ideas, concepts, theories, and rules that math is so full of. The over used expression, "But where will I ever use this rule?" does not hold the same power as before...Still yes, I'll give it to us all...I'm not sure where the heck you'd be forced to use a quadratic equation...but now I can at least show you with real objects what exactly it is and/or what it at least represents. Awwww it feels good to have a picture for it...not just a rule.


I used to accept that math was full of rules, facts, and theories that you simply follow, just because...they are what they are...you are either right or wrong. In fact I used to like it for that reason... I loved that it was like a book of rules that I could follow...but I found myself at dead ends when I couldn't grasp concepts fully in calculus. Instead, I just plugged and chugged along...jumping through the hoops, thinking it would eventually make sense. With the understanding of math that I'm growing now, I look back shocked that I used to like thinking math were that way. My growing understandings of math are now seemingly endless, and I look forward to the knew ways of thinking that I will learn from other teachers, students, and people! Seeing different solutions as equals and learning from them all to strengthen my own tools to solve.


...So in all...
I learned to use manipulatives for quadratic and algebraic expressions!
This a great tool to use in class when teaching students math in a concrete to abstract method.
I'm wondering how to dig concrete examples deeper with higher level math. I won't be teaching higher level math but just out of wonder....how do manipulatives connect to calculus?
How do uphold our expectations of participation in class, but move onto another student if one student is struggling with an answer??

Inquiry

Today in math I learned that it can take a lot of warm up to get back into the groove of things... this does not just for running, but for math thought processes and inquiry.
Of course I always "knew" this, but today I truly felt this. It was the first day back from winter break and my first time trying to complex and layered solve quadratic problems and sequences in ... longer than I can remember.

I am still looking forward to finding out other ways that people think and how some people are so much quicker at recognizing math problems than others. Practice? Maybe.
Using the complex problems like we did today with the Gardens and Snakes, we covered a lot of standards...all seemingly in "one" problem. This was exciting. The many steps of the problem were rewarding at the end. What other ways can we use overlapping problems like this in our younger classrooms? How much stamina will the students have to do this and how far do I push them? Indeed that will be different for each class, but these thoughts are floating around in my mind.

I think it's exciting to use such an overlapping problem or scenario to get all standards connected and used. It makes me and the students see that the requirements we have to learn in math are not random and separate but useful and connected to each other.

It was fun to reflect on my own thinking processes through these math snakes and gardens!

Resolving to find something Shinning!

Ok, I have recovered since the last week. All my assignments that are due online or in some tech form are done. Signed, sealed, and delivered. PHEW! (except for those final word documents--but I will leave those out of the "Tech" category ;)

Anyway, I have to keep in mind the assingments will soon start up again. This time, I'm going to be ready. I've learned many lessons through my explorations this quarter, mouse in hand, keys flicking and clicking away. I will use the time saving and efficiency skills I've learned using Google to help the hours of assignments and head aches of organizing be lessened. I will continue to use our Wiki web page to help us organize, share, and find resources. I will modify my Weebly to create a fun and organized web page to keep my portfolio useful and functional. I MIGHT even continue to blog....Well maybe, if they make me! Overall, I am now more able to use technology in a way that allows me to be the creater not just the user. I know that I have the tools, resources, and power to take this upcoming quarter into my own hands. One more down, two to go! June will be coming quickly, I hope.

As much as I do hope for June, I am so excited it's Christmas time!  December is such a festive month! The Festival of Lights (Hanukkah), blues and whites all around me! Then the greens and reds of Christmas! Oh and the music! I've been whistling "Silver Bells" loudly for years and years. It doesn't stop after December like 'normal' people. Oh no, I've been notoriously known for whistling and singing Christmas songs of all types well past July and straight into the next December. So man, am I thankful that I can sing it as loud as possible right now without receiving strange looks....Although the looks are pretty entertaining. I am glad to be able to experience another December full of cheer and love in every way possible, no matter what obstacles stand in the way of showing the love and light to the world! Let it Shine!