Thinking Mathematically

Our Classroom Poster of the 8 Mathematical Practices!

Last spring I had the chance to gain a different perspective of our classroom, seeing it in action, not as the teacher who needs to make sure that engagement is high and problems are appropriately challenging, but as an outside observer. What I noticed amazed me and had me thinking and reflecting on what THINKING MATHEMATICALLY means in the new day and age of the CCSS.

Common Core Connections -- Breaking the Mold

Last night I had a deep discussion with my husband, who does not work in education, about the Common Core State Standards. He was asking about my take on them, given the frequent bad press that he has heard: that the Common Core will stick all kids in the same box, increase conformity, etc. I kind of laughed, because hasn’t that what traditional education has done all along, stuck kids in a grade level and expected them to process through whether ready or not?

This whole conversation had me reflecting on what the Common Core means to me and really what I expect of myself and my students to achieve. 

1.       I connect Common Core to the needs of the Whole Child through the focus Students-Standards-Curriculum

Celina and I have always approached our work within the classroom through the lens of students first, their social-emotional needs as well as their academic needs. The 8Mathematical Practices and the 7 Capacities of a Literate Individual also speak to students first. They are pushing for the development of habits of mind that ensure all students are prepared for a world that is ever changing and are able to think critically about their experiences. For myself and my students I see the practices and capacities as the ways in which I can help all students succeed. Students who persevere in math, become students who persevere in all areas of life, those who demonstrate independent use of the skills of literacy become students who can think and act for themselves.

 The Whole Child blog recently had a podcast that truly spoke to this idea: "Educators need to prepare kids to be career and college ready, but they also need to prepare them for their present world. The Common Core State Standards set out to do that. They're not perfect, but they are a starting point" (Peter DeWitt).

The blog continues with: The standards are not a curriculum. Standards are targets for what students should know and be able to do. Curricula are the instructional plans and strategies that educators use to help their students reach those expectations. Central to a supportive school are teachers, administrators, and other caring adults who take a personal interest in each student and in the success of each student. A whole child approach to education is essential to realizing the promise of the standards. Only when students are healthy, safe, engaged, supported, and challenged will they be able to meet our highest expectations and realize their fullest potential.” http://www.wholechildeducation.org/blog/

For me that means connecting with kids, recognizing that their needs are not purely academic and making choices for the classroom that support a wide variety.  Working from the needs of the students, and then developing their understanding of the continuum of standards helps them to see learning as building up their foundation, something that is not solely achieved in school!

2.       Common Core Standards are broad in nature and deep in focus, pushing for authentic learning experiences, as opposed to discrete skills.

In order to meet the depth and breadth of the standards, Celina and I have had to rethink the purely skill focus of the past.  Our classroom activities of Passion Projects and inquiry based learning have helped us to infuse the standards into learning experiences that incorporate a multitude of goals. Students no longer read non-fiction text as an isolated skill, but rather to build up their knowledge and understanding for expository writing, presentations, multi-media projects and finding evidence to support their thinking. Students authentically connect the once separate skills into a cohesive whole that helps them to express and share what they know! Our day is no longer a segmented container but a set of links and blocks that boost engagement and relevance.

3.       Common Core has increased the level of rigor, not just for students but for teachers too.

Achieving the goals of the Common Core means raising our level of expectations! We can no longer just accept a curriculum as the end-all-be-all, or dumb down the work for students or teachers. Building our professional capacities as educators means doing the work that the Common Core requires of our students: reading for meaning, finding evidence, thinking across the grades, boosting conceptual understanding, as well as regularly interacting with complex text and academic vocabulary.  It makes me grateful that my work with Celina in  creating a child centered classroom has pushed me to learn more and grow. Truly understanding that message makes me more aware of the expectations I place on my students, the growth mindset that is necessary and the goals that can be achieved through this work.

So while the talk shows and pundits can banter back and forth about what they think Common Core means, I am left to marvel at the improvements implementing the standards has meant for myself, my students and our classroom as a whole. Conforming? I think not, more like connecting meaningfully and breaking the mold!  ~Ann

 

Our Self Assessment Rubric

With ROBOTS as our theme this year, we decided to name our standards-based grading scale in alignment with our theme!

Moving beyond the standard is a Level 4; NEEDS AN UPGRADE
Meeting standard is a Level 3; OPERATIONAL
Working towards standard is a Level 2; NEEDS A REBOOT
Introduction to the standard is a Level 1;  ANALYSIS NEEDED

Our students have really enjoyed this metaphor.  Recently our students created the rubric (in the photo above) to describe what it would look like and sound like to be OPERATIONAL as independent learners during our math block.  Since our students are fluidly moving between project-based learning activities, independent goal work, partner math, and small groups, it was crucial to have our students develop a deep understanding of their expectations as learners.  This rubric has provided us a platform for self-assessment, reflection, and goal-setting --- truly empowering our students as learners.

 A new favorite slogan of ours?  "Be OPERATIONAL."

~Celina

Building Blocks to Success

Our building blocks to success have replaced our traditional "rules."  Our focus is now directed to acting responsible as a learner, making personal choices to be courageous and engaged, and taking the time to focus on and celebrate the growth that is being made in our community (and selves).  We begin the conversation with our students by stacking building blocks as a visual model, also relating this concept to SYSTEMS.  What happens if one of these 3 is not present?  The blocks will not be stable; the system will fall a part.  

So why is WORK HARD on the bottom?  Because it is the foundation of our system.  We must choose to make responsible choices on a daily basis to be a focused learner.  A learner who comes to the learning community with a purpose.  A learner who has the mindset of participating and choosing to be engaged each and every moment. 

BE COURAGEOUS is our middle block because it is what truly makes the difference for us as successful learners.  It holds the hard work and celebration together, as without having a growth mindset to endure challenges it is easy to give up.  

CELEBRATE GROWTH is the top block, as it represents the goals we are trying to reach.  It reminds us that moments of celebration are necessary and should be a part of our community.  We must take the time to recognize the success of each other through the learning process.  And as one of our students mentioned, "By taking the time to celebrate the goals we accomplish we just want to learn more and more and more!"

This year our students recognized PERSEVERANCE as the overall theme of these building blocks, as well.  As we focus directly on the 8 Mathematical Practices, Capacities of a Learner, and Habits of the Mind, we are currently making genuine connections to where perseverance applies in our daily life.  Our students instantly noticed that perseverance was a key ingredient deep within each of the blocks.

Our shift in thinking from such an intent focus on "following the rules" to "being an engaged/dedicated learner" has truly made all the difference.  We have had a higher rate of focus, participation, and excitement.  Through this perspective we are able to build a community within our classroom more quickly, establish a solid foundation for our learning environment, and offer challenges more readily.  But more than anything, these blocks provide our students with a clear purpose when they walk into their learning space.  They know the expectations are high, but we offer them an environment for individuality to shine, and a safe space for risks and challenges to exist because we will celebrate each other every step of the way together.

~Celina

Starting the School Year with a Student-Centered Perspective

Poster found here.

Ann and I start the school year now from a completely different perspective:  We are facilitators in a student-centered classroom.  

Sure we can choose our color scheme (blue, black, and silver!), our concept of focus (SYSTEMS), our theme (Robots), and even a slogan ("Gearing up to learn...Sparks will fly!").  But those are just things we choose in the hopes that we will inspire our students from the moment they walk into their learning space.  Preparing anything beyond that is nearly impossible.  

Something wasn't feeling right as we approached the first day this school year, and we finally we realized what is was:  our kids were missing!

Then I was reading some of my favorite blogs the day before school started and came across a post by Pernille Ripp.  She too was feeling the same way me and Ann were.  In a student-centered classroom, you can only prepare so much for the first day of school; and the second day, and the third, and the fourth... for that matter.  The students drive our decision making on a daily basis.  In order to know the direction we will go, to make our lesson plans definite, to decide on specific materials and strategies, our kids must be present.  We must have countless opportunities to get to know their personalities, their strengths, their challenges, their interests and their ambitions.  

And as if it was meant to be, I came across the poster above created by Krissy Venosdale.  It put everything I have expressed and felt into very simple terms.  As educators with a student-centered mindset, we focus on one day at a time.  And everything we do is built on the premise of truly making dreams come true.

Here's to all the classrooms that whisper "you complete me" to students as they enter each day.

~Celina

  

More Great Reading Moments

Celina, as usual, inspired me to jump on the blog and reflect on what I have read so far this summer. So far my Kindle has been my go to resource for reading, as I can stay up and read as late as I like without complaints!

My first read was the book Well Spoken by Erik Palmer about teaching speaking to all students.

This book caught my eye when I was researching the CCSS in speaking and listening anticipating where we will be going in the fall with our next shift in instruction. Our kids have done a lot of speaking this year, as we chose to work with what they are really good at: TALKING!  We consciously focused on teaching our students how to turn & talk effectively. I quickly noticed a transformation in the way kids communicated with each other. Conversations were more purposeful and students began to add on to their partner's thinking as opposed to simply telling their one-sided point of view. We used more debate in our classroom, as well as building on our work with Arts Impact to help students more effectively express themselves in character.

Well Spoken is about teaching speaking skills and so much more, making it highly relevant for the 21st century classroom. Several things that stuck with me: Effective communication requires building and performing, not unlike reading, writing and skills in math. Speaking requires being mindful of audience, content, organization, using visuals effectively and the way in which you present yourself.  We work on many of these same skills in writing, building effective beginnings and endings, organizing our writing to explain or entertain and viewing our work through the lens of what makes writing interesting to read. When we presented our Passion Projects throughout the year, students also had the opportunity to use visuals and presentation skills, yet from reading Well Spoken I can see some areas where we can help our students to more effectively share their message. Palmer also suggests 6 Traits of effective speaking, otherwise knows as PVLEGS or Poise, Voice, Life, Eye Contact, Gestures and Speed. I saw many connections between these performance needs and building fluency in oral reading, such as expression (Life) and pacing related to what you are reading for effect (Speed).

I can't wait to use these ideas to effectively draw our students into effective communication, not only with speaking but also listening actively for these traits, writing clearly in building essays and speeches, as well as reading with expression and fluency.  When the work connects across more areas, I see my students finding greater relevance in the learning and more meaning in the strategies and ideas. Plus I love finding ways to prepare my students for the uncertain future, as Palmer says, "Now, let me make a radical statement: the mission of education should not be to make students better at school but rather to prepare them for life."

My second read was Who Owns the Learning? Preparing Students for Success in the Digital Age by Alan November, a recommendation I found via Twitter.

 This book pulled me in with thinking about the digital age and how students can be helped to take their learning on a larger scale. It speaks to a Digital Learning Farm model of instruction where students are doing authentic work with purpose, working as tutorial designers, scribes, researchers, and global communicators and collaborators. The model reframes the educational structure by increasing autonomy for students, publishing student work to a global audience, and creating a community of contribution within the classroom. November sees technology as a "transformational tool to change the culture of teaching and learning" not just pushing in lots of technology where it just becomes the "thousand dollar pencil". The significant take away was the shift in control, as November states, "Much of what used to be teacher directed in the traditional model is powered by students in the Digital Learning Farm model." This so fits my thinking about education, the more that students have the opportunity to direct their learning, the more they are engaged with the learning itself. ~Ann

Summer Reading Recommendation #1

Can be purchased here

Summer brings about many things for me, one in particular being a summer reading list.  I have been an avid reader since I was a kid, which is probably when the expansive book lists began.  One thing I have learned in my lifetime is that when you love books, reading lists are forever growing and never shrinking!  I am a balanced reader between fiction and non-fiction, and plan to blog about books that inspire me as I reflect on the past year of teaching, learning, and growing and establish goals for the upcoming school year.

Brain-Based Teaching in the Digital Age, by Marilee Sprenger, was a great first PD book for me this summer.  It confirmed so many professional beliefs I have developed over the past 3 years teaching within multiage classrooms.  These years have truly pushed me to let go and expand my understanding of a student-centered classroom.  This book brought forth 5 important points for educators to consider: 

1. The Net-Generation, more than any other, will be coteachers in the classroom. (pg.31)  Ann and I have dynamically shifted our practice to involve our students in every aspect of the teaching and learning process.  Students increase their memory by being a part of the discovery process and are courageous when researching information that meets their individual goals.  Providing opportunities for them to teach others enhances their learning and makes information relevant.  I really appreciated the term "coteachers" being used in this statement!
2. Students can both learn and teach in this world.  Education is available everywhere. (pg.43) ...well isn't that the truth!  Adapting this mindset is the first step in providing opportunities for our students to learn and teach globally.  Education no longer has to be confined to the walls of the classroom, or the building.  Rather there are a plethora of tools, resources, sites, etc. that spark communication among students around the world.  Imagine the possibilites! 
3. Brains learn best when working with other brains. (pg.50)  Ann and I both had professional goals in the area of speaking & listening this year.  Pushing ourselves in this realm of literacy enabled our students to authentically communicate with each other.  Their dialogue, silent signals, debating skills, and sharing of creative ideas added another dimension to learning within our classroom.
4. Your job as knowledge keeper is obsolete. (pg. 69)  In the beginning years of my teaching career this was a hard concept for me to grasp.  My college experience prepared me as the keeper of knowledge and how to share this knowledge with my students.  Technology has advanced at such an immense rate, it was difficult to shift my thinking and become comfortable with how accessible information is these days.  However, it has relieved the pressures of having to feel as though I had to play that role.  Instead I bask in the glory of teaching my students how to be learners in the world we live in and navigate the infinite information at our finger tips.  How cool is that?!?
5. Memories make us smarter and give us the tools to be creative, to synthesize, and to build relationships.  These are 21st century skills that our students need to succeed. (pg.125)  Everyday as a learner should be full of enriching experiences.  These experiences allow us to view the world from different angles, sparking creativity.  These experiences help us to be able to make genuine connections and deeply synthesize concepts.  These experiences provide opportunities to engage in conversations with other and problem solve together, building natural relationships.  Enriching experiences should be a part of our learning environment to build these skills that our students so desperately need.

At heart, I am a brain-based educator.  It is important to me to teach students about their brain and how we gather information through experiences and novelty, sparking creative juices along the way.  It is important to me to provide ample opportunity for my students to reflect during their learning journey and solidify the information they have encountered and establish goals to continue mapping their learning path.  I want my students to be a part of the learning process, every step of the way;  a navigator, rather than a tourist.  Sprenger's book helped me confirm my teaching philosophy and provided me with more strategies to strengthen my teaching skills, as a facilitator of the learning process.

 ~Celina

A New Summer Brings New Adventures

Image found here.

The summer break has brought rain in abundance.  The smell in the air is wonderful and very much welcomed.  It brings on the encouragement of something new.  It suggests change.  It makes you want to get outside and enjoy life.  It is the spring weather I usually miss out on inside the walls of a classroom... so I truly am enjoying the cool, fresh, clean air as I breathe in and embark on summer adventures:

1.  Adventure #1- Extreme Sports: My husband has been encouraging me to participate in some of his favorite hobbies, which have allowed me to experience feeling like a kid again.  Driving a Toyota through a MUD BOG or riding in the back of a monster truck are thrilling moments everyone should experience at least once in their life.  The mud, dust, and minor bruises are completely worth it.  But there is nothing more exhilarating than riding a Drift Trike (oversized customized tricycle with PVC on the back tires) down a long hill at 30 MPH.  Definitely brought me back to my days, as a kid, riding my motorcycle though the mountain air... These adventures are surely just the start of an exciting summer!

2.  Adventure #2- Feet to the Pavement:  My daughter is now old enough and has the stamina to run with me.  Running/walking, listening to music and chatting is the perfect adventure to experience alongside her as we both mentally and emotionally prepare for her journey as a middle schooler. ;)

3.  Adventure #3- Grant Award:  Ann and I spent time recently planning for the expenditure of our technology grant, awarded to us at the end of May.  We wrote the grant over a year and a half ago, so the celebratory assembly was truly a surprise.  Planning for the "Multiage Minutes University" has been an inspiring process.  This will definitely be an adventure that helps us to enhance, and in some ways recreate, our learning environment.  

4.  Adventure #4- New MAC BOOK!!: Tonight has brought forth a big adventure... digging my way through a new device.  One that has been well worth the wait.  First came the iPhones, next an iPod for my daughter.  I was hooked.  An iFanatic!  Then my iPad followed (along with iPads in use in the classroom).  Now I am the proud owner of a Mac Book.  A perfect addition to the iFamily :)

5.  Adventure #5- GLAD Training:  I have wanted to experience GLAD Training for several years, and recently Ann and I were able to jump at the opportunity to commit to training this summer.  Many visitors/observers to our classroom have made comments assuming we are, so we definitely feel as though the GLAD strategies will fit our brain-based philosophy and style as teachers.  This adventure is sure to provide new inspiration as we move into the new school year, much like Arts Impact did for us this past year.

Adventures are not moments that are necessarily planned out, but should be welcomed with arms wide open.  You can never pinpoint what to expect exactly, but what fun would unfold if you could?  Embracing the change, chance and risk within each new adventure sparks growth to an exponential power.  The benefits may appear immediately or have a longterm affect; irregardless they are each worthy in their own way. Allow yourself a moment to be free and seek out the adventures that await you.

~Celina

Wow, April?

It is shocking and amazing to realize that we are well into April. The longer days, warmer weather and upcoming testing remind us that we are well into Spring! Our students are a bit more chatty and restless, yet we are also seeing the work we have done over the year expand the capabilities and processes within our classroom. 

We've been working on debating issues about the environment for this month's Passion Project. We've discussed endangered biomes, water use and even the #1 most endangered river the Colorado River. Students are backing up their opinions and assertions with evidence, seeking reliable websites for resources, and even discussing point of view and bias. What I love is they just get more thoughtful, excited and engaged. One student, who is traveling to Colorado this summer, told her dad all about the endangered Colorado river, which had him checking out the websites too.

At the same time, Celina's work with CCSS ELA has our kids doing close readings of songs, poems and informational excerpts on math concepts. Students are making connections back to culture, discrimination and personal acceptance. They are marking their texts with their thinking and wonderings. I love that when I come back to school after a meeting I am greeted by a student who is gleefully telling me about the Text Talk song they listened to! So much delight over connecting words, feelings, thoughts and ideas.

Today was our first day of the "testing season" with a measure of reading skills. Our students were so focused and on target, it was inspiring to me to see their determination and perseverance with this assessment. It reminds me of all the hard work they are capable of, renewing in me that sense of pushing through in my own goals and matching their drive!

Our theme this year is "Learning is Growing" and our students are certainly coming into their own as we wind down. It makes for an exciting time of year, there is much to celebrate!

Welcome Spring!  ~Ann
 

 

(The photo above is of a card my dad picked up for me this week at Trader Joe's (by Angela Duncan) to tell me that he and my mom are super proud of me! It was fitting that a line came up in the book I am reading called Point of No Retreat by Colleen Hoover that fits this card to a T --"Sometimes it feels good to have your biggest fears discounted with a simple compliment.")

Top 3 Issues Impacting Students of Today

Yesterday I came across a challenge by Marty Stevens (@martylstevens) encouraging educators to personally identify the issues they believe to be impacting students the most. For me, the following 3 issues quickly came to mind:

1. An Increased Need for Social/Emotional Development

The students in our classrooms today need us in different ways than the generations of the past. The times have changed dramatically, and our current world requires an increase in skills that support effective relations and acceptance of diverse perspectives. Our students need us to not only strengthen and support their minds, but their hearts as well. Unless we are reaching our learners through relationships we will not reach them academically. We must first work to establish safe learning environments for our students, ones in which they feel supported to take risks. This begins with positive interactions among the entire classroom community, as well as the school culture as a whole. A safe environment, through, is not created through a laborious list of rules and expectations, but rather through the development of social skills that support the affective domain of our learners. Intentional lessons and activities must be infused into our classrooms daily to support social and emotional growth. Listening intently to student voice will also prove to be valuable as community expectations are discussed. When this foundation is in place our learners will then, and only then, thrive academically.

2. Insufficient Resources within Education Today

Educational funding is very limited these days. We have experienced an insane amount of cuts especially over the past 5 years. These cuts have not just affected teachers' salaries and benefits, but also the supplies and tools we can put in the hands of students. And I am not necessarily even referring to large scale curriculum adoptions, but rather genuine resources our students need access to regularly (updated technology, a variety of literature, field trips, supplies to support the Arts, manipulatives that enhance science and math explorations, etc.). These are the resources that provide our students more opportunities for genuine learning experiences and direct connections to the real-world. These are also the resources that allow the basic skills or reading, writing, and math to be authenticated and solidified. And most importantly these resources support teachers in helping students achieve true retention and master relevant skills.

Stripping the educational budget of professional development monies allotted to school districts has also dynamically impacted students. The advancement of technology and the skills required in this era have outpaced teacher development. A large gap now exists between what students need in a learning environment and what teachers are able to naturally provide. Teachers need time to collaborate in order to learn and grow and meet the students' needs in the classrooms of today. Frequent (inexpensive) professional development opportunities must exist in order for teachers to advance with the rate the changes of today are requiring, otherwise the gap will just continue to widen.

3. Learning Environments that Meet the Needs of this Generation

Our students are facing an unknown future; that much we know. However, some of the materials, skills/strategies, and curriculum existing within the classrooms of today are equipped for the generations of the past. Traditional practices were not developed to meet the needs of the learners of today. They were developed during different times to prepare students for a different future. Our students struggle with engagement within environments that is so extremely different than the world they know. They are acquainted with the technological advances, the momentum of the world, the desire to connect and collaborate with people frequently, the need to question in order to learn, and the aspirations that are building inside them as they recognize the possibilities the world has to offer. It is our current responsibility to teach students, in this innovative generation, to think critically, create, communicate, and collaborate with the people of the world. We must recognize these as essentials and find a way to ensure that our learning environments foster these skills so students are prepared for success as they approach their future.


These are 3 issues that constantly weigh on my mind as an educator. What about the issues that weigh on the minds of our students? As Marty also mentioned, maybe we should be asking students to identify 3 issues that impact them. I think the answers to this question would prove to be of value. Ann and I will definitely be infusing this question into a Brain Breakfast this upcoming week. I am very curious to find out if their perspectives will overlap at all with mine... I absolutely look forward to listening to their collective voice.

~Celina
- Posted using BlogPress from my iPad