Final ITouch

I have enjoyed exploring the Ipod touch this last quarter. I had never looked at it as a means of education. The endless educational applications are intriguing. I wasn't really able to use my ITouch in my main placement, but I was able to use it in my experiences through literature class. I also got the chance to use it with my math assignments and explore the opportunities it brought me through this. Mostly I've been given a stepping stone to find resources to expanding my teaching and education through technology. This was major part of the steps I'm taking to keep technology present in my teaching and in my own learning.

The most efficient way I've been able to consistently use my ITouch is through the option of voice memo.During all my one on one meetings with my literacy buddy, I was able to use the recordings to further my learning from my buddy. It wasn't too difficult to keep track of my conferences with E during these visits because I only was dealing with one student. However, when I have twenty one on one conferences these recordings will be extremely helpful. I can keep track of growth and progress in a more detailed and exact way! I can use it to show the students their personal growth. Conveniently it can all be stored in my pocket! I hope I am able to bring the many other applications and uses that I've been learning about through both other technology blogs and my cohort member. Even if the voice memo is the only thing I get to apply for now, that is still a tremendous help. I look forward to expanding my use with the ITouch for differential learning and sharing technology skills. 

Final Math Blog

Throughout this quarter I’ve been given a very unique and inspiring view on teaching and mathematics. The inspiration is continually growing. The tools you’ve given us are things and ideas we can apply in any subject while teaching. You’ve shown us ways to continue growth in ourselves and our students. These are incredibly valuable skills. I aspire to always be learning and as a teacher, I believe that’s something we must always be willing and seeking to do. Throughout the quarter I’ve been learning tools for myself and my future students.

Ideas and thoughts that I’m taking away are:

I’m thankful for the more emphasis and ideas about creating opportunities for integrated learning, specifically creating opportunities for connecting abstract concepts with practical application. I love the idea of having multistep problems that benefit the cohesive understanding of math concepts.

 

The missing and lack of use of manipulatives in the classroom has definitely stayed on my mind. I’m brainstorming how I can bring manipulatives into the class to strengthen the concrete understandings my students will have of mathematics. They deepen and strengthen my own understanding; I know they will help my students too. 

The need for alternative explanations is great! We as teachers need to be searching for ways to help students understand things in any way that we can. It is our responsibility to learn to teach other ways. It is a goal of mine to immerse myself in as much math as possible and in all different ways, even the forgotten ways such as the Mira!

I am experimenting planning my lessons backwards in creative ways. I’m still thinking about what I want them to learn and how I am going to get them there. How can we do this and use confidence as a motivator in math? We need to have “open ended work that can be assessed in different ways and taken in different directions.” We can do this in multiple ways, one way is by embracing and utilizing integrated lessons to build up students’ strengths and let it transfer over to math.  This even lets us get a whole different way to assess our students. It can be more cohesive for us and our students if we bring writing into math, or any other way of bringing other subjects to show students strengths.

Technology lets us access both math and education in a totally new and dynamic ways. I’m looking forward to finding electronic manipulatives with both the computer, applications and any other ways I can find for my students.  This is another tool to help create interest for our students.

Overall creating interest and confidence in our students is at the upmost importance and should be what governs our decisions so we are always making the best decisions for our students.

Oh, The Places You'll Go!

This week was the birthday of our dear old Dr. Seuss! As I took a moment to reflect on him, I remembered something lovely I once read by him...still I wonder if it wasn't really from a hymn!? Well anyway, I could even read it in the gym.

Okay but seriously, my most favorite book by this clever crook, is Oh, the Places You'll Go! Why do I say you need to go buy it? It is full of the most inspiration quotes that you'll ever give a child...or yourself for that matter. A simply wonderful book to push you farther and make you strive for more.
The inspiration can be found for almost anything...
I was thinking about the importance of reading and I remembered this quote from the most wonderful book of them all....“The more that you read, the more things you will know. The more that you learn, the more places you'll go.”


I know it's a simple quote, but that is what draws me in deeper... 
Well if you haven't read it yet, please do. You know... in all our spare time. 
Tah-Tah for now! “And will you succeed? Yes indeed, yes indeed! Ninety-eight and three-quarters percent guaranteed!”

“Adults are just obsolete children and the hell with them.” ~Dr. Seuss (not from this book)

It doesn't hurt to ask...

Today, in math we learned...so many things...but what's sticking in my mind is how important it is to know what you need and want for your classroom. Just as important, know how you might use it in the classroom, and why it would make you a better teacher/ help students learn. If you don't ask for the things that will help your career and help students, then how on earth are you going to get them?? You have to ask! And if they say no...No big deal! At least you can reroute and know how to ask again later if needed or if you get the opportunity.


I need to apply this element of preparedness into my life, into my career, into my classroom, because I want to be prepared to help my students and colleagues. Really, it's just a part of being prepared...prepared with ways to grow, learn, and teach. I need to apply this by quite literally having a list of the things I could use and need. So I will be making my list...both in  my mind and physically on a handy piece of paper...My need list!

I'm still wondering how to do we create interest in math? Some students find relevance in school or subjects very easily compared to others. How can we help students find interest to do the work and to do it well?
 For that matter, how do we encourage a passion for education that will continue throughout their lives so they can use it to create opportunities in life?
Yeah..lots of questions..that's just how I think.

Acorns take a long time to grow...

Thank you for the acorns today. I do love those trees...but man do they grow slowly!

I'm thinking about the many ways we learned to be active and interactive while teaching math. Today was full of wonderful tips, ideas, inspiration! I'm letting it all setting in and looking forward to how these ideas will grow with me and become a rooted part of my teaching.

The manipulatives that we worked with today were helpful in numerous ways. The geometric shapes we were interacting with helped me in numerous ways. Being able to understand which shapes and rules apply to each other and can or cannot change in various ways, deepened my understanding of geometry. It helped my technology skills working! That's interdisciplinary (at least for me ;)!

Using the program and interaction with shapes on the "Can you make it" program helps build technology skills AND mathematics; it could be use with students of various ages. I work with second graders and I could see them benefiting from the interaction of these virtual manipulatives. It not only will sharpen their understanding of the quadrilaterals, or other shapes, but it helped them use their motor skills and technology skills at the same time. Sounds like a great way to keep kids of all ages (even in college) interacting with technology and math of all shapes, sizes, and styles....

I'm still wondering about...  How on earth did you get that "Buzz Light Year" to show you exactly the motion and   bounce that you wanted to demonstrate!! That is some serious corduroy, jumper, teacher skill!!

Literacy

I've been having a wonderful time getting to know my buddy, E. He has welcomed my partner and I with smiles and loads of information each time we've been able to visit with him. He shares his interests, skills, and strengths willingly. In school, he likes math the best, although he excels in all subjects that we've seen. His communication is entertaining and exciting; I'm always looking forward to what things I will learn of him next! Amongst his many talents, his reading and writing are exceptional! Although he doesn't claim it's his favorite, he does spend a lot of time immersing himself in both. His favorites are fantasy, fiction, and futuristic style of reading and writing.We were able to get through both the 4th grade reading passages and he scored solidly in the 75th percentile! Only making one or two miscues in each passage! His comprehension is good, and his retell is impressive. Details of the text stay in his memory seemingly effortless.

This last session with E finally revealed something we can work on with him. His comprehension was excellent with explicit questions; however, the implicit questions strained him. He was able to get about half of them right without looking back into the text. When able to look back he found implicit answers quickly and used good strategies to look through the text quickly to help him find the place of interest to the question.
I would like to work with E on his implicit comprehension. Inference skills are always in need for improvement with readers of all levels. I would like to work with E in a book that is favorable to him; a fantasy or futuristic style book would probably be the best. I would like to take the time to slow his reading down and prompt his thinking of the text. E's reading is fast and he is usally eager to hear the story, so he might be missing key parts of the text that allow inference to be embedded. Using prompting questions, predictions, and slowing him down would help him grasp the hidden, deeper meanings that texts can hold.
What have you learned about your buddy’s needs, abilities and interests?
As a result of this knowledge, what learning objectives and materials are you considering using for your lesson?

Tangram! Just make a square...how hard can it be?

Today I learned a new way of using writing in math as a method of interdisciplinary instruction and as a tool to better understand mathematics. In our discussion about creative writing in mathematics, my mind was opened to endless opportunities of mathematical writing. (This discussion  was based off the fun and enlightening article we read, Using Creative Writing and Literature in Mathematics Classes). This interdisciplinary idea is using math as a tool in so many different ways: creativity, assessment in their understanding of mathematical concepts, expression, etc. This isn't a way to assess grammar and fluency, this is a way to understand the mathematical ideas and concepts that they are grasping and/or struggling with.

This would be so great to use in the classroom. It opens the door for students who struggle in math. They are able to use their writing, drawing, and/or story telling skills to express themselves in math in a better way. They no longer have to feel as if they are not "good at anything" in math. Their "strengths" in other  subjects will let them do well in math too. It could help them feel more confident and secure with their work in math. Because after all, math is connected to everything else right? Well lets show the students how, and maybe ourselves! This is useful to both the teacher and the students! Beautiful!

I am still wondering if this lesson can be used often in our "scheduled curriculum" that I'm being more immersed in? I'm picturing teachers struggling with implementing this, because it is a little more time consuming than just asking a student questions via worksheet to find out what they know about concepts and ideas etc. But it is such a valuable resource, isn't it worth the time for both us and our students? If we (as teachers) only resort to the worksheet questions for evaluating how are students understand the material, then we will miss so much that they have to offer. They have much more to offer us in their understanding if we expect them to express it, and if creative writing is the way to get them there, then let's do it! Plus it's fun, refreshing, and supportive of their varying strengths! So how can we get more teachers to take the time to use this lovely interdisciplinary lesson?

Also, I'm still wondering if I'll EVER solve a Tangram puzzle on my own!!!??? It's been slowly eating at my ego my whole life! 

ITouch Differentiated Learning 2

In my thinking about how to use the ITouch in the classroom, I am really stuck. I love the ideas my cohort members have and are sharing via our Wiki site. Using the ITouch for the entire classroom's use and/or for my use with students, sounds like an interactive and exciting way to keep the students involved. Most ideas really utilize time and efficiency. It's beneficial to both me as a teacher and my students. I truly do look forward to using these ideas in my classroom instruction.

 In our literacy class, we get to use it a little with our buddies. So far, my buddy gets really excited that we are using the technology with him. It even seems to let him know that he is so important to us, that we are willing to use this tool to enhance our experience/learning together.  

However, I'm struggling with using the ITouch for differentiated instruction....Other than the ideas  I was able to pull out that could possibly help Cornelius, Bruno, and Maximus. I struggle to find ways in which students who are struggling can find support from the ITouch, especially if they are on their own. If they are struggling to keep up, how will they be able to handle the ITouch? So I guess, I'm wondering how to let struggling students use this tool individually?  

I'm going to need to stretch my mind in the next few weeks. How else can I use this to help my struggling students do better and without my complete support? (other than using apps that scribe the lesson for them etc....)?

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!