Differentiating in Math

After reading two articles regarding the importance of differentiation and "how-to" better differentiate I decided to dive in and try some of these strategies out in my math classroom.

I began my double-digit addition unit by providing students with a pre-test containing various problems which assessed their ability to add two and three-digit problems with and without regrouping. This pre-test, along with some observation, gave me great insight as to where my students were...and there were ALL over the board!

Seeing that I had about 3 students who had no clue how to add two-digit numbers (without any regrouping), 7 students who could confidently and consistently add two and three digit numbers with regrouping, and everywhere in between, I knew I had to create groups to address where they were at.

I decided to begin my first two classes with a whole-group mini-lesson on the steps to add two-digit numbers with no regrouping. I figured getting us all on the same page as to how I wanted them to solve these problems (and a little review for some) wouldn't hurt anyone! After these mini-lessons we then split up into three groups (based on the pre-test). (I think) I used the differentiation strategy called Tiering By Resources. 
-The students who had very little understanding worked with a title para (whom I have for 30 minutes each day) using manipulatives to build and add provided numbers. They recorded their answers on a piece of paper which contained boxes to signify the top number (ones and tens) and bottom number (ones and tens).

-The group of students who showed strong understanding with solving two and three-digit problems without regrouping worked with a partner and a deck of cards (using only cards A-4..no possibility of a sum of more than 10) to create a double-digit problem and solve. They recorded these answers on a piece of grid paper and a modeled problem so they could see how to line up the numbers and separate the 10's and 1's column. After some practice time, I then signified that they may "challenge themselves" by creating 3 (OR 4!) digit problems if they felt ready for it (still no regrouping).
-Finally, for my students who fully grasped adding with and without regrouping-they were given a deck of cards (A-9) and worked to create problems on a piece of paper, provided only with the steps to solve as a reminder. While they worked I pulled two students at a time and modeled the "partial sums" strategy to help them see how to use mental math to solve these problems.

Overall, I was very pleased with how this went. Mind you, this occurred after having set the tone for "building math stamina" last week. We practiced how to work independently and in a group in a way that was productive for all and this definitely played a role in the success of this activity.    

Children's Principles of Learning...1 year later!

After having had a year of learning and experience within the MED Teaching and Learning program I was reaffirmed in many of my Children's Principles of Learning that I set for myself last year. I, of course, have been able to add to those principles as well.

Principle 1: A Safe Environment

Students must feel that they are physically and emotionally safe in an environment in order to blossom in it. They first must physically safe before you can ever expect them to worry about their learning. Constructivist research also supports that students playing a role in the physical layout of the classroom is very beneficial as well. While physical safety is important, as is knowing that they can freely share ideas without being judged or having the fear of failure restrain them from trying. My summer research on best practices of writing has provided many examples of how providing this safety can increase self-esteem and abilities as a writer.  

Principle 2: Sounds Relationships

No matter the student’s background, they must feel a connection to their teacher in order to have a passion to learn. If they don’t trust the instructor, they will find it very difficult to trust that what is being presented has a purpose. Students need not to just know that we care for them and their learning, but to feel that we do. It is these sound relationships that stick with them through their schooling “careers.” As I researched best practices in writing, as well as the Lasillian Concepts, I was reaffirmed that relationships are key between teacher and students, as well as amongst the students themselves.

Principle 3: Sequencing of content

In order for a student to feel successful within a lesson, unit, or school year, content must be scaffolded in a way that they can succeed. The philosophy of explicit instruction is formatted as such: “I do, we do, you do.” Knowing your students and being able to gauge when they need more “I do” or “we do” before being able to get to the “you do” is crucial. Setting students up for success by sequencing content and processes will help them see that they can succeed. Having learned more about designing units in a “backwards format,” that is, starting with the big picture in mind…the “what do I want all students to know” and then using what they already know to guide your lessons has proven to be very beneficial when sequencing content and helping students to grasp the big ideas.

Principle 4: Reflection

No matter their age, students should be given multiple opportunities to reflect on their actions and learning. They grow more when they are able to “score” themselves in a situation. Reflection causes the students to take a moment to truly think about their learning and how they were successful, or not, and how to continue or improve the next time. The writing process is a key example of a time in which students have multiple opportunities to reflect on different aspects of their writing as they’re constantly revising after having been presented with examples and mini-lessons on what good writing looks like.

Principle 5: Ideas, feelings, actions

Students need to be able to connect some schema, feeling or action to their learning in order for it to stick. Lessons that are remembered are often tied to some sort of auditory or kinesthetic cue that help trigger a certain muscle memory or emotion. Backwards Design also helps to students to make connections to bigger, umbrella concepts, as well as seeing connections amongst “separate” curricular activities throughout the idea.  

Principle 6: Immediacy

But WHY?? Students must know why what they’re learning is important and how they’ll be able to use it in their own lives. By starting a lesson with a goal, stating why or how we’ll use it, and allowing students to make connections to their own lives, they are more motivated to learn and use the content again. Again, this is supported when using a Backwards Design model.

Principle 7: Teamwork

Two minds are better than one. This is a very simple, but true statement. Most students are very social learners and like to be able to discuss what they’re learning about or what they already know. By allowing students to work in small groups we are opening up the possibility of creative thinking, coming to conclusions more efficiently, and developing problem solving skills. I was privileged to attend a very beneficial class on cooperative groups this summer that provided me with a multitude of examples that encourage cooperative learning. One example given is called “Numbered Heads Together” in which students work in small groups to collect information, solve problems, check work, etc. The teacher then calls on a random student within each group to provide an answer. Having had that team support prior to being asked to speak for themselves helps all students to be successful.

Principle 8: Engagement

Students must be engaged in the content in order for it to stick. It is important to “tap into” the various learning styles of your students in order to best address their learning needs. When a student is engaged in the lesson and content they are more likely to tie an emotion and connection to it making it more likely for them to remember and utilize what they’ve learned.

Principle 9: Have fun!

With the many stresses that nationwide testing and standards can put on classrooms and the teachers and students within them, it’s important that the learning environment still be fun! After much reflection of my own schooling, it’s the experiences I had and relationships I made that I remember most…not the algorithms I “learned” in algebra.   This has been reaffirmed through my experiences with community building activities in class. I see the strong benefits of having fun to build community amongst a group of learners.

ENVoY Non-Verbal Teaching Strategies

Yesterday I attended another training on ENVoY (Educational Non Verbal Yardsticks). There are so many beneficial techniques that any information I can share may be useful! Use this link to get some basic information on this management technique!

If at first you don't succeed...

What a powerful post! After reading this veteran teacher's post reflecting on her experience with persistence in her classroom, both with her students and how it's affected her, there are many things I can relate to and agree with.

I'm inspired by the idea of persistence because, quite frankly, without it, I may not show up to work each day. What we do as teachers is one of the hardest jobs there is and you have to have grit, passion and persistence to do what we do. I also easily relate to having students like "Kara" in my class who seem nearly impossible to figure out. However, I learned very early on in my first year that if I gave up on these types of students...I'd be no different than all the other adults in their lives. Most often, these students are behaving the way they are because they WANT you to give up on them...why not, when everyone else does?

I too discovered that keeping the consistently positive relationship is key to making any progress.

However, it is this that I struggle most with. Sticking to it is EXHAUSTING!! Both emotionally and physically draining in every sense of the word. You love them, yet you can only be knocked down, rejected and faced with failure so many times. What I have learned is that these truly are the students you learn the most from and these students inspire me to teach all students the importance of persistence.

I feel that teaching my students what persistence means, looks like, FEELS like is key to success in my room. All students can benefit from knowing how to persist in times of struggle and why persisting is worth the effort. As Lily Jones quotes: "The road to success is filled with failure." Many of my students know what failure feels like, so to help them understand that persistence leads us to overcome these failures is a a life lesson I'd love to leave with them.

My Virtues

My top virtues were empathy and enthusiasm. I wasn’t at all surprised to see these as either of my top virtues because I feel that my empathy is what makes me an effective teacher. I strive to teach my students how to empathize for another and see our class as a team that succeeds only when we work as one and help each other when we "fall." I strongly connected to this quote regarding the virtue of empathy in our classrooms: "If parents, teachers, and administrators can’t teach their children to empathize with another child’s suffering, then all the other academic and social things we do for them are for naught...we should educate all our children not only for competence but also for caring. Our aim should be to encourage the growth of competent, caring, loving and lovable people."

I also feel this virtue plays out in my role as a spouse and colleague as I frequently find that I try and place myself in someone else's shoes in order to better understand and support any situation they're in.

While my virtue of enthusiasm can play to the benefit of others, sometimes I feel that the high level of enthusiasm I have for my job tends to take away from the enthusiasm I have left for my home life. I put so much thought and effort into making my classroom an engaging and successful place that I have little left to give at home. However, with our first son coming in just a few months I'm certain that the source of my enthusiasm will drastically change :)

Both empathy and enthusiasm play a strong role in many aspects of AGAPE (Association, Generativity, Adaptation, Presence).

Association: Because of my virtue of empathy, I feel that I'm able to better encourage teamwork amongst a group of people. First, helping them to see the to unique qualities and goodness in each other, and empathize with any weaknesses, allows them to more easily collaborate towards a common goal.

Generativity: Empathy plays an essential role in the area of generativity as I can model to my students, and colleagues, how to respect and empathize with others in order to create and caring, safe and welcoming environment for all involved.

Adaptation:I feel that my virtue of enthusiasm is most beneficial here, in the adaptation aspect of AGAPE. Because I have a high level of enthusiasm I frequently find myself looking for ways to keep our learning interesting, authentic, and meaningful.

Presence: I think in order for your students, colleagues and family to benefit from your virtues you have to first be aware of them. Presence allows us to self-reflect and become more aware of our strengths and just how we can apply them in many facets of our lives.

Best Practices in Writing-The Highlights!

After spending the summer immersing myself in articles and books regarding best practices in writing there are ideas and concepts that have reshaped how I will teach writing and I feel, could benefit any "writing teacher."

The most important concept that stuck with me is the importance of teaching writing in both an explicit, mini-lesson format, as well as workshop method that allows for students to write...a lot! Without the opportunity to see themselves as writers and practice actually being a writer, no amount of teaching will help to improve their skills. However, without guidance through explicit, focused mini-lessons, students can feel overwhelmed with the task. It was this knowledge that led me to my action research topic of implementing daily, 10-15 minute explicit mini-lessons focused on the Six Traits of writing. The mini-lessons will be determined based on what I see my class of writers needs to work on (with various conventions and grammar mixed within the lessons). 

Another "epiphany" I had was the concept that every student, regardless of age, academic level, or language abilities is a writer and they have to know that! It's okay if the student can only draw a picture to express their story. It's a starting place. It's important that students are given some way to take a story they want to tell and put it on paper, whether that be via words or pictures. 

Being that there is so much research out there and, so little time to read it, I'd highly suggest looking into using the book Daily 6-Trait Writing. It provides explicit mini-lessons focused around one trait at a time. I plan to use these, along with a few other supplemental activities to take my students through the writing process. I'd also refer you to Steve Peha's Website: Teaching That Makes Sense. The left side provides many tabs that link you to PDF's full of mini-lessons and information if you're hoping to establish a writer's workshop model in your classroom!

Roadblocks and Successes

Another first week of school is in the books and I'm feeling better about this year than any before! There are many factors that contribute to that feeling of success and I know having a year of grad school learning and reflecting is a huge factor. Because I was "forced" to really focus on the truly important  components, both socially and academically, in my classroom, each activity I taught had a purpose! No more coloring pictures just to pass the first few days! Each lesson was thought out and I really believe helped to reaffirm our class routines and expectations. The activities were also centered around continuing to build the relationships we worked so hard to form last year! 

I face two roadblocks when I continue to look forward into the year. The first is also my biggest question...the unknown. This is a new grade level for me and, while having the same class certainly helps, it's hard to think ahead and plan in a Backwards Design kind of way when I've not taught some of these standards or this curriculum before. Luckily, I have a wonderful team of experienced teachers who have already stepped in to help in any way possible. I'm trying to even out the deal by sharing what I've learned about community building and Backwards Design with them :) My second roadblock is by far and above the most common for teachers...TIME. Not necessarily time within a day because I feel as though cutting out the "fluff' and teaching my lessons as big ideas and concepts and not isolated learning experiences will help. I struggle with balancing my desire to want to spend HOURS researching best practices or supplemental interventions (which is not hard to do) and remembering to leave time to PLAY and enjoy these last few months with my husband before our little guy joins us :) I have to keep reminding myself that every lesson doesn't have to be this overly planned, complicated 45 minute time frame and that, sometimes, the students' questions and experiences guide me to something bigger than what an internet search could've provided. 

In the meantime...I'm going to take my own advice...play today..plan tomorrow :)