Best Practice in Mathmatics

Article: Best Practice in Mathematics
Author: Zemelman, S., Daniels, H., & Hyde, A. (2005)

This article had wonderful ideas pertaining to my new action research topic which will focus primarily on the effects of journaling on mathematical understanding. As with the Best Practices in Reading article that I read last week, there were some consistent themes found within the reading.

One re-curring theme that is found in successful math classrooms, is the presence of real, authentic mathematical experiences for the students. The authors state that math needs to be "meaningful"(pg. 3), which is similar to the essential understanding of other subject matters as well. One of the most important ways to help assist with a student's understanding is also to relate math to patterns and relationships. The authors state, "teachers should show students how to use the concepts taught in math powerfully, and with full understanding."

How do you accomplish this? By promoting coherence and emphasizing BIG ideas, and connections over and over again. The authors describe 5 intertwined processes to help build mathematical understanding which are:

1) connections: relating math to the "real-world" and using authentic experiences. "Making connections requires reasoning."   p.11
2)problem solving: working in small and large groups, using specific strategies to work through problems
3) representations: Using manipulatives, journaling, drawing a pictures, make a list or table, acting math out
4) communicating ideas: Working in small groups
5) reasoning and proofs: Talking to others, sharing invented strategies

Another re-accuring theme was the use of math language. As teachers, it is important for us to develop a classroom environment that promotes math thinking and math talk. Allowing students to share ideas with the whole group and with small groups gives the opportunity to collaborate with others and make connections. We also need to be aware of the questions we ask to ensure we are intentionally guiding our students to the understandings we need them to obtain.

I am intrigued with the concept of math journals and am anxious to implement these tools in my classroom next year. I have incorporated an abundance of "math-talk" sessions over the last year, where students share their thinking with fellow classmates. I would like to see how journaling, communicating and representing ideas through words and drawings will help me to see conceptual understandings for formative assessments and guidance.

Chapter 8-Seven Strategies

Main Points: 2 Important Points
-best practice is a philosophy
-organization is key

Connections and Ideas Want to Incorporate...

*Small Groups: In my classroom, at the first grade level, small groupings have been beneficial for modeling and role-playing various concepts, such as proficient reading and writing. Creative writing centers with iPads has also been something that gives the students an opportunity to bounce creative ideas off of each other as they make a story.

*Text coding with Mind Maps has been a wonderful tool for me, and also for my students. It is has been beneficial for them to visualize how the different parts of a concept or story work together. I can see how text coding will be beneficial for them to use in communicating their understandings to me or to themselves.


*RTL: Have my students keep a math and reading journal's or "learning logs" and the to enrich the learning process and allow students the to write and draw with their ideas to become active learners.

* Classroom WKSP: I love schedule and the ideas of classroom workshops, because of the ability to model various ideas and concepts for your students, and the time it gives students to work on their own needs. This would definitely be a bit of work to get started, to ensure you could effectively have resources available for each student to have their choice of materials, whether it be with a reading book at the appropriate level, a writing topic available for each student, or setting up conference schedules. Once again, it comes back to organization.


*The concept of making learning authentic has been something I continue to strive for. I have a ways to go, but I have given more accountability to my students and have given them a "say" on how we've done certain groups, classroom design and small group activities. Like I've stated in past blogs, although I do work with first graders, their abilities for self-regulation and independence are well beyond what some might think. I continue to work on how to incorporate this at home and would like to involve other classrooms during our math, reading and science times to team-teach and learn together.

*Integrative units is something that I am working on throughout the summer. As a team, we've looked at home we can combine different subjects together under a BIG umbrella to ensure connectivity and fluidity.

*I believe in the idea of getting away from a one-size-fits-all way of teaching. The author states, "Teaching doesn't mean "talking" compared to what we've thought in the past." We can demonstrate techniques and strategies, but we need to determine where our efforts should be placed. Instead of re-teaching a concept to the whole class, when only 1/3 of the students need re-explaining, we need to channel our energy to setting up worth-while experiences that can engage the other 2/3's of students while we reteach.

Attention

This article was so reassuring to read. I have so many great pieces to discuss and use, it would take a while to get it all down! I've decided to choose the most influential to me for discussion.

1. Prioritize your life, get to the core of what’s important to you, and simplify things.(p.33)

It sounds easy to do, but I struggle to put it into practice. As Houston and Sokolow state, the there are so many distractions in the world that it is hard to sift through what is important and what isn't. I continue to work towards simplification and minimalism.

2. There’s a call for urgency and a call for what’s important. (p.23)

Another great reminder. I feel this most in my classroom as I find myself making what seems like a hundred decisions a second some days! With my students, anything can seem like it needs attention right now, but in all reality, I think it’s important to sit back, address the situation and allow the students to do some problem solving on their own. In regards to new ideas and projects that come forth throughout the year, I need to analyze how the idea should be use, why it’s important and how it will benefit my kids before I use it.

3. Pay more attention to your thoughts and how they shape you. (p.21) Your thoughts set up an energy field, and that field tends to attract like-minded energy.

You are what you think!

4. Attention , in part is an effort to be attentive to what’s happening around you, by being grounded to what’s happening around you, and by being grounded in who you are.

I believe it’s important to be a part of your surroundings. I can lack effort or attention at times with things that I don’t find important, but what others might enjoy. I find myself stuck in my own thoughts and need to continue to find a way to focus on the foreground and the background more effectively.

AGAPE: IDEA

The Lasaillian Concepts of Association, Generativity and Adaptation have truly been trans-formative to the way I approach my classroom now. Whether it be the way I'm thinking about my classroom, students, learning plans, spiritual approach or intention, I am continually thinking of my classroom as a "living" organism (which I've mentioned earlier in posts.)  This living organism concept has worked for me, because living organisms are constantly changing and growing, as is a classroom.

In the area of instruction, I have continued to be mindful of our early readings and discussions regarding play and community. We start each morning off with a Morning Meeting routine, to allow for sharing and greetings. The UbD is another concept has been a new concept that I continue to grow with in terms of instruction. It's benefits are very clear and it has allowed me and my classroom to be more creative, engaging, effective and efficient. During the school year, I've incorporated the idea of Mind Mapping which has added another aspect on creative thinking. I've also enjoyed using many new instructional strategies during my instruction.

In the area of discipline, the most significant change has revolved around my action research project based off of oral reading fluency. This research process has opened a new lens on the possibilities in the area of early childhood literacy that is very enticing. I am anxious to continue to implement and incorporate new best practice methods in my future classroom. Through Kidblog entries, I've also noted a few other instructional areas that I would like to think more deeply about and research possible interventions.

My classroom environment has been an area that I have enjoyed playing around with over the course of the year. The possibilities seem endless when thinking about engaging classrooms. The article "Look Before You Leap," had many strategies to keep in the forefront as I become a more constructive teacher. I plan on applying the "less is more" concept to the environment I create and want to make the classroom ownership my students rather than thinking it needs to be mine.

The area of assessment continues to be guided by formative and summative assessments that drive my UbD unit planning. As with my instruction, thinking of the assessments and essential understandings first, allows the educational environment and learning plans to become more meaningful, focused, effective, efficient, and engaging.

UbD Unit Relfection

UbD Unit Reflection

By planning the unit with the standards in the forefront, the unit objectives were much more focused and centered around a “theme.” They can be seen leading in each lesson, and also show adhesiveness towards lessons in the future. I found it more effective to lay out the standards and was also able to determine whether or not an objective/standard was met.

It was extremely manageable to incorporate the EU’s and EQ’s during the teaching phase. I found that I was able to use the EQ’s in many different scenarios such as a morning meeting question, or just a note on the board.  The EU’s gave my students and myself several opportunities to come together and reflect on what we had learned, what we wanted to continue learning, and where we were going as a group. The EQ’s allowed us many different avenues to travel while investigating our topic.

I felt and still feel that the EU’s and EQ’s were road signs and maps for us. Both entities of the BD philosophy allow many opportunities to see where the unit is going and also gives the students meaning and relativity to what is being discussed.

With my BD development, the formative and summative assessments were already developed with our curriculum series. I can tell you though, that it has made a difference in how I've prioritized and focused each part of each lesson.  In my experience with the assessments, it has helped to guide my lessons and allowed me to look at where I am putting my energy as well as my students'. The students' performance has improved, because everything we work towards and practice during our daily lessons, is something that will need to mastered by the assessments, but can also be applied to a greater understanding to be used in the future.

The biggest benefit to this style of planning, has been the constant funnel effect back to the “main” EU’s. During any lesson, you can ask any student, any time, to tell you how this related to what we are discussing and 9/10 times, they can give you an appropriate answer. I believe with this style of planning and teaching, it also allows students to have more control over what they are discussing and what they find important. It seems to give more ownership to the learner, and challenges to become a leader, instead of being reliable on you for each new piece they learn.

Praxis

Continuing along with the theme of my own growth, guidance, and intention, along with what really makes a difference in the fluency improvement among students, I can highlight and cite some pivotal changes I've incorporated into my classroom this year and plan to use next year.
Here is what the research says, according the BIG WIGS...and a small bit on what I've done because of it...

1. Types of materials to choose could be Reader's Theaters, poems, leveled books, audio books, songs, plays or song lyrics, which all lend themselves most fittingly to fluency instruction (Rasinski, 2005). 

Towards the final portion of my school year, I have incorporated numerous poems, listening activities, and plays which have been intended to give my students an opportunity to delve into effective, enjoyable and relative reading materials that are fun to read! 

2. Regardless of a student’s age, fluent oral reading to the students, coupled with discussion of a response to the reading, should be a regular part of any instructional package for children who are struggling with reading (Opitz and Rasinski, 1998). Modeling various readings can give teachers a chance to reflect before, during and after a story, giving insight to emergent readers on how they use various reading skills and how to process the information read.

Even I get excited about reading aloud to my students. Partly, because I love getting into character and performing, but also because nothing compares to the engagement and excitement in each students eyes when you have a read aloud that comes to life. When the students see, hear, and watch you model an effective, fluent, expressive read aloud, they want to be like you! That is what they take with them. 

3. Listening centers also provide additional, effective fluency practice. At listening centers, students can listen to an audio story, poem or play read through a reading curriculum CD, read by a teacher or even a student. Listening centers and assisted reading have a positive impact on fluency (Rasinski, 2005). 

One of the biggest questions among the teachers I worked with this year was, "What do we do with all of our new iPads?" A listening center gave me a wonderful opportunity to showcase how this technology can be used. With an idea from a fellow master's colleague, and the app "WavePad" for the iPhone, I set out a few iPads and our monthly poems at a listening center, and had student's record themselves reading the poems. Students were in groups of 2-4. When I first discussed the center, you would have thought it was Christmas morning! They were so excited. Soon after the centers began, you could hear the voice inflection, and variation; the students became different characters, and soon I began to hear character parts evolve...remember, all I asked them to do was record themselves! They took this center to a whole new level and they had FUN with it!

4. For independent reading routines to succeed, students need support, excellent materials to read, ample and consistent amounts of time, and opportunities to share their responses while reading with others (Padak and Potenza-Radis 2010). As students are surrounded by caring, knowledgeable, enthusiastic teachers, their chance of succeeding with fluency will be greatly enhanced. 

One last area that was truly a "game" changer in my classroom was the implementation of STAR time (Stop, Take a Book, and Read). We began this experiment by challenging ourselves to 10 minutes of silent reading. Students chose appropriate leveled books from our Guided Reading selection, and I had to sit down and read as well. Nothing is worse than having to be a student watch their teacher cruise around the room trying to get something besides reading done. A big piece of fluency success is modeling. After our first bout with 10 minutes, the students asked for 2 more minutes! Soon after the first, second, and third day of this procedure, I found that after they had read, most students wanted to share something about their books, so we added another "quick" time period to share 1 interesting item about their books with a neighbor. I felt as if we truly fostered a "love" of reading. I plan on using this time as soon as possible next year, and might include a day to read with a buddy (fellow student) or two.

Change and Growth

For the reflection on my growth and change over the school year, please follow the link provided.

Change and Growth: 2012-2013 School Year

5 Best Practices in Reading-Best Practices in Reading-Zemelman and Hyde-Chapter 2

While reading this chapter, I realized soon that it hit very close to home.  There were many great ideas pertaining to my first grade classroom. As I read, I was happy to hear that many of the strategies and practices mentioned, I consciously and unconsciously implelenent.The list of ideas consumed 2 pages, so I will choose 5 of the ones I am most anxious to embed into my literacy program.

1. Spiral Bound Notebooks for Small Groups: I would like each student to have a spiral bound notebook to jot down ideas and notes pertaining specifically to them in regards to reading. They could put down spelling words, vocab, or other information.

2. Prioritize my phonetic time and recognize which students need it most. If students are still struggling during the second half of the school year, continue to meet and intervene during small groups. I want to try to use a more meaningful and rich method that will give students an opportunity to continue to build their phonetic skills through literature.

3. Focus more on Heterogeneous and Homogeneous groupings. I would like to develop when and where to split my kids up.

4. Incorporate more Reflective opportunities for my students.

5. Work towards literacy circles.

The Peer Partner Learning Strategy

What is Peer Partner Learning? Peer partner learning is a collaborative experience in which students learn from and with each other for individual purposes. Currently, I have been able to implement this strategy in few different areas, but I've use it primarily for reading fluency and vocabulary development.  Each week, every student in my class has a fluency passage at their level that they work on to read as fluently as possible. Time is given for them to practice on their own, and on 1 day per week, the students get together with a partner and read their passage to each other.  One student becomes the "teacher," who listens and the other becomes the "student" who reads. They are timed for 1 minute. The "teacher" provides feedback and prompts the other to work on any errors that were heard during the reading. After 1 minute of discussion time, the roles reverse and the "teacher" becomes the "student." The reading continues for 1 minute. We complete this series of events 2 times.  Each week we usually have a focus to work toward during our readings, such as pausing for punctuation, using inflection, and so forth.  It has been beneficial, because the students collaborate well with each other and most strive for their best in the eyes of their peers.  One reminder I always give them is...fluency is not speed, it is decoding accuracy and comprehension. Read like you would want to be read to!

The Search for Understanding-The Case For the Constructivist Classroom

After reading this article, the key concepts made most sense to me in a before, during and after teaching format. There were many strong points that I would like to ensure I look at in those three different development and implementation stages of my teaching. First and foremost, I'd like to look at the "before" teaching stage. While utilizing the UbD approach to developing units, it's important to incorporate:

1. Problems of Relevance (meaningful and relative to students understanding)
2. Primary Concepts: Less is More, the idea that students take control of their own learning, the teacher uses "Big Ideas" to run the learning plan
3. Learning plans that seek and value student's point of view
4. Curriculum that can be adapted and adjusted to fit each students needs
5. Learning Plans and Unit development should include time for questioning, experimenting and facilitation. 
6. Cognitive Language: classify, analyze, predict, create

While implementing the learning plan it is important that students continue to be guided by the 1) primary concepts relative to their understanding. 2) Learning plans should be guided by "student" conversation rather that teacher directed talking. Cognitive language should be used to develop understand . One way to think of this concept is to ask what students know, instead of telling them what to know. 3) As discussed earlier, in the UbD  development, time for experimenting with materials such as manipulatives are beneficial, because it is interactive and physical. 4) Another piece to be carried out during the learning plan is the use of formative and summative assessment to guided the learning plan and give the teacher an idea of each students understanding on the topic. 

And finally, after the learning plan, the assessments given can be looked at and curriculum can be adapted to meet each students needs as the teacher continues through the unit. More time might need to be given  for students to meet the benchmarks for any given primary concept, but through the reading, I've found it to be important to continually think of creating an leaning environment that is focused the constructivist concepts. 

To read the book for yourself:

Title: In Search For Understanding: The Case for the Constructivist Classroom by Jacqueline Greenon- Brooks and Martin Brooks

The 5 to 2 Instructional Strategy

I've been using a new instructional strategy in my classroom over the past couple of weeks that is labeled " The 5 to 2." With this strategy, the is idea revolves around lessening the amount of your talking time as a teacher and  open up the door for more conversation amongst your students. I know that I, at times, can tend to use my role as a teacher to talk too much at times in front of my class, and with this strategy, I've been able to keep my verbal lessons down to 5 minute chucks at a time. After the 5 minutes are up, the students then have 2 minutes to share or teach the new information to a classmate or group.  It is very comparable to a " think, pair, share" set up. 

Overall, it has been best I'm implemented during our reading or math blocks. The students have used whiteboards, actions, or small presentations to review the 5 minute discussion by me.   The strategy is effective, because it allows the student not only to be a listener, but also a facilitator and teacher. Their retention rate for information has shown an increase, and it allows them time to move and collaborate with their peers. I am sure there are many other benefits that will come out of this learning strategy and I am encouraged to continue to try it out in new settings.

Pulling away from the traditional and Moving into the Constructive!

This past week, I was encouraged through my masters program to change a few minor things in my classroom routine. These minor adjustments were the product of an article we just read out of the book "Creating and Sustaining a Constructivist Classroom," by B. A. Marlowe  &  M. L. Page. One area I wanted to work on was my student/teacher role. To often, I feel like I am a knowledge dispenser. If my students ask me a question about a topic, I tend to tell them the answer. But, in the correct setting, that pattern needs to change. I want my students to be responsible for finding their own knowledge on topics they have questions on. 

So, this past week, I had the opportunity to put my plans into action. We were studying space with our reading series and one student had a question about whether or not the sun was a planet. The old "me" would have said, "No, it is a star." The new me, took a moment and asked, "where could we find an answer to this question?" We decided that the plethora of space books on our reading table must have some answers for us! So, we set off on a knowledge hunt. 

About 5 minutes later, another student shouted out that the sun was indeed a STAR! We found this statement in about 5 more books before we stopped searching. In the end, this turned into a great lesson on proving facts, searching out your questions, and topics regarding various space questions. The students felt responsible for their work and I fel like a facilitator instead of a knowledge dispenser. These are the lessons that we strive for as teachers. 

I hope to continue giving my students the opportunity to search out their own answers and conclusions, instead of relying on me for mine. 

Teaching Strategies Used

Mike

1. Cooperative Learning-Writer’s Workshop https://docs.google.com/document/d/19Ksnmo QelhdzEWDqhcuA88bQCMOf_7PGV9zHDN4NQX0/edit) http://olc.spsd.sk.ca/de/pd/instr/alpha.html 2. 5 + 1 (Five Plus One) http://www.beesburg.com/edtools/glossary.html 3. Illustrated Talks http://www.beesburg.com/edtools/glossary.html 4. Story Telling and Retelling (STaR) http://www.beesburg.com/edtools/glossary.html 5. Scavenger Hunt. http://www.isbe.net/common_core/pdf/ela-teach-strat-read- text-k-5.pdf 1.We are currently working on an opinion paper in my classroom. I am going to have students get into groups of 2 and edit their papers. They will need to be aware of our classroom guidelines for group work and will grade themselves with smiley faces based on how many goals they met while working together. This would be a useful strategy, because of students using each other’s feedback to improve their individual writing. 2. This would work best when introducing vocab and spelling patterns. I would have the students use their whiteboards and markers to work with each other towards correct spelling and usage after I had discussed the new concepts. 3. I would use this strategy while completing and art project for mother’s day. The students would only be shown (with pictures) the individual steps for each section of our project while I explained the process. 4. Each week, we use “oral” reading cards with stories that fit our theme. I would read our story, and have students retell it with a group, act it out, and draw the beginning, middle and end of the story by themselves. 5. Students work in small groups collaboratively.I can provide groups with books on the same topic which would be “Space and Planets.” Assign each group a topic and have the team look for words and pictures in the multiple sources that are connected to that topic. Invite groups to share discoveries. Facilitate a discussion around their “I didn’t know that!” discoveries highlighting the similarities and difference in the texts. 1. This worked alright. Self correction and editing is a big topic for students at this age group to swallow and completely understand. Some students are ready for it and some aren't. I would make the process a bit shorter next time. 2. This strategy works well. My kids are used to it because we do a lot of think, pair share in my classroom to get the students moving. I will continue to insert this into my class. 3. As we made our mother’s day cards, I used this strategy. We took baby steps and I only showed my kids what the end project would look like. Most of them were able to make a similar end product based off of pictures and verbal instruction. 4. The students loved this activity. Any chance that they get to act or engage in something in front of the class is special to them. Most are fantastic storytellers. 5. The students spent about 15 minutes, literally, engaged in finding facts about planets and space. All I heard were the murmurs of "ohhs" and "ahhs" from kids finding new information and collaborating on it with another student. I asked them to write down 2 of their most interesting facts at the end.

Reflection Quotes

“It’s hard to look at modern life and see our capacities for reflection or meaning-making.  We don’t use our gifts to be more aware or thoughtful.  We’re driven in the opposite direction.  Things move too fast for us to reflect, demanding tasks give us no time to think, and we barely notice the lack of meaning until forced to stand still by illness, tragedy, or job loss.  But in spite of our hurry, we cannot stop life’s dynamic of self-reference or the human need for meaning. If we want to influence any change, anywhere, we need to work with this powerful process rather than deny its existence.”

Margaret J. Wheatley, Leadership and the New Science (San Francisco: Berrett-Koehler 

Publishers Inc., 2006) at 147.

This quote reaches me because of the fact that life does get busy and we make a plethora of reasons not to reflect and ponder why things happened the way they did. We too often make the same mistakes again, because we weren't thinking about the steps we could've changed to change our outcomes. It reminds me to take time and make reflecting a priority. 

“The capacity to reflect on one's own strength and weaknesses, to learn from constructive criticism, and to practice critical reflection by monitoring one's own work performance and interpersonal interactions is essential to the ability to learn from experience and is the cornerstone of the journey to becoming a lifelong learner.”

Judith McNamara & Rachel Field, “Designing Reflective Assessment for Workplace Learning in Legal Education” (Paper presented at the ATN Evaluation and Assessment Conference, 29-30 November 2007) online: <http://www.eac2007.qut.edu.au/proceedings/proceedings_ebook.pdf> 87.

This quote makes me think about building character and integrity. It reminds me to slow down a digest what is going in my life both personally and professionally. We can learn so much from other individuals, but we can also learn a lot from ourselves. 

“The word “professional” originally meant someone who makes a “profession of faith” in the midst of a disheartening world. That root meaning became diminished as the centuries rolled by, and today it has all but disappeared. “Professional” now means someone who possesses knowledge and techniques too esoteric for the laity to understand, whose education is proudly proclaimed to be “value free.”

The notion of a “new professional” revives the root meaning of the word. This person can say, “In the midst of the powerful force-field of institutional life, where so much conspires to compromise the core values of my work, I have found firm ground on which to stand—the ground of personal and professional identity and integrity—and from which I can call myself, my colleagues, and my profession back to our true mission.”

Higher education needs to educate people in every field who have ethical autonomy and the courage to act upon it—who possess knowledge, skill, and the highest values of their vocations. Can such an education become a reality? Yes, if we who educate can think and act like the new professionals we need to raise up.”

From Parker Palmer’s The New Professional: The Aims of Education Revisited retrieved 2 February 2010 http://www.changemag.org/Archives/Back%20Issues/November-December%202007/full-new-professional.html

This quote reminds me that reflecting leads to change and change is growth. By reflecting, I can see the differences I make in the lives of others, and I can also see my values and beliefs integrated into my daily routines. 

212 Degrees Video:

Wow! What a powerful message in a short amount of time. I think the first thing that comes to mind after watching this video, is that you can always be better than you are right now. Of course, we all need to stop and smell the roses and enjoy our accomplishments, but there is always something more we can improve on. It should be a goal of everyone to strive towards their best at all times. It my classroom, it could be tackling an opportunity to implement a new strategy, listen more, talk less and taking a moment to reflect each day. At home, it means enjoying everything that much more and cherishing the things that are important to me and my family. Instead of making excuses I can make time and relax and enjoy the moment.

http://www.youtube.com/watch?v=NPEeEqkEjAQ