Pictures of a Mice do not Mean Pictures of a Mice

My professor asked my to check out this NPR link, <>

And then added, “Again and again we hear that mathematics is universal and language-free, but is this really true?”

Here is my response:

I teach the language of math. Within my lessons I also teach number sense. Last week I taught 3rd-5th graders the basics of the Trivium through poetry, which means that our logic, our words for the logic, and the way we put those word together are all separate events. The classic reference words for the three are logic, grammar, and rhetoric and they are distinct. That is an important notion because students need to realize that a number is as different from a digit as a mouse is from a picture of a mouse, and as different, again, as the mouse scampering across the floor (but not my floor). While E.A. Poe and A. Einstein may have processed their thoughts differently, being able to separate symbols from the objects they represent is profoundly important.

Matthew Peterson explains to us in a Ted video how he has been able to teach mathematics while circumventing words. I think that is great. Working with adult ESOL students, I recognize how I do not need to teach the students how to think. They have the notions organized in their heads. We are focusing on connecting English language.  The language we teach must be about the concepts and relationships between concepts beyond their definition. Of course students must be able to demonstrate their understanding via language, but we do not want them to be talking about a picture of a mouse when they display a picture of a mouse. We want them to be referencing the actual scampering mouse.

I believe there is a trans-cultural language of math that we cannot do without, but meaningful language must be based on a logic that is real with or without the words, and I see no reason  mathematical reasoning cannot come without words.

Here is the Ted link: <>

New School Mission Statement Ties Purpose to Expected Outcomes

The elementary school where I work has a new Mission Statement. It reads:

“At [CBES] we will be a positive, supportive community focused on helping all children become responsible learners who are well versed in 21st Century Skills, and who are able to express a purposeful attitude of life-long learning by demonstrating consistent improvement of North Carolina Standards.”

The new mission statement makes a connection between the learning community the school wants to be and the accountability it must be responsible to fulfill without making those two efforts synonymous. CBES teaches students to be curious, to pay attention to detail, and to discover new ideas that will stay and serve them with them as they grow.

To some, it may seem as though the school is making a pledge to force students to go to infinity and then beyond, as if solid school-wide standardized testing scores are unattainable, and then to ask for more. Instead, the school’s intent is the other way around. If CBES helps students become thoughtful problem solvers with a useful vocabulary, the students will be able to navigate benchmark probes and End of Grade Tests as one more of life’s problems to solve. This way life-long learning comes first.

Accountability is necessary. The school’s new mission statement reminds the school community to stay on the track of ensuring that each student achieves his/her highest potential. It is a track that passes through successful End of Grade Testing.

Giving Students the Vocabulary They Need to Describe Their Levels of Understanding

While teaching students new information, I recognize their need for a cognitive strategy to help them identify their own level of understanding.  I think this is certainly true when the they are learning verbal information such as lists, and I think similar strategies would benefit the students when they are learning intellectual skills such as concepts  and even motor skills.

I came up the vocabulary to describe four levels of understanding based on degrees of prompting and  fluency. Cleverly, I decided to call the levels, Level One, Two, Three, and Four. Greater understanding is the higher level, but the levels are not directly associated to letter grades or the four-point grading scale. Let me explain.

Level One Understanding means that the student can achieve 100% accuracy of a knowledge set WITH assistance and WITH hesitation. Level Two Understanding means the student can achieve 100% accuracy of a knowledge set WITH assistance but WITHOUT hesitation. Level Three Understanding means the student can achieve 100% accuracy of a knowledge set WITHOUT assistance, but WITH hesitation. Level Four Understanding means the student can achieve 100% accuracy of a knowledge set WITHOUT assistance and WITHOUT hesitation.

After introducing and working with these levels in class, students and I  have come up with a description at each end of the scale for learners above and those below the four basic levels. When students know a poem so well that they can recite it with emotion and meaning, we call that “Level Four-Ahhhh!.” When a student cannot muster correct answers to a reasonable list with a reference aid and with plenty of time, we call that, “Level One- Yeech!”

It is important for each student to know that Level One Understanding of a new list is a normal part of the learning process and not an embarrassment. From my experience, students who are comfortable with the beginning stages of their own learning tend not to advertise their ignorance as they progress. On the other hand, students who are not comfortable with their own learning process tend to make loud, demeaning jokes about the material and/ or themselves which halts their learning process. When my students learn to be comfortable with themselves at Level One, they move to two and three and four more readily.

My students reach Level Two Understanding when they become more familiar with the material. They still need help, but level two offers the students a license to receive help while taking on increasing responsibility.

Students achieve Level Three Understanding when they know material without any help or prompting, but when they still hesitate. Level Three can get a student an A on a test, but in conversation and in practical terms, level three understanding is not really effective because the opportunity to apply the knowledge usually comes and goes quickly which leaves the students with the notion that they knew what they should have said because they staggered to recall information. One of the key elements of this strategy is to get students to recognize the value of their effort to achieve Level Four Understanding.

Therefore, Level Four Understanding is the goal of learning materials for application, and the goal of the students study efforts. Fluent recall of some knowledge sets are used for life. Multiplication facts are one such example. In a future blog I will share the method I use teach math facts that incorporates the Four Levels of Understanding. I created a notebook on it to keep me organized as work with students who progress at different rates and everything. Stay tuned.

5′ by 6′ Salt Marsh Serves as Classroom Focal Point

Mini Salt Marsh of Room 412

Mini Salt Marsh of Room 412

When the students return from spring break, this mini salt marsh is what they will find in the classroom. The materials were collected, with permission, locally. The mini salt marsh  is a fantastic jump-off point for the class’s study of both ecosystems and land & water. From my past experience with pond-like water features in the classroom, this will last up to eleven school days.

The topic of my last post on “Academic Respect” gives me reason to believe that the students will be able to focus together on the science of the mini marsh, and not simply play around.

As I was collecting material, I know there are a variety of life working together in this small 5 foot by six foot space. Watch for future posts on how to put this feature together in the classroom.

Academic Respect in the Classroom

As I work in the  classroom, I seek a vocabulary that will help my students become better learners. One recent word-convention I now share with my class is the phrase, “academic respect.” The practice of shared academic respect gives my students permission from their peers to ignore social pressures and pecking orders that are normally negotiated on the playground and in the lunchroom.

The difference between socializing and academic respect is a shift in focus. When we socialize, our focus is on the people, the players, the human interaction. With academic respect the focus is the concept at hand. With that shift in focus to the concept, the rules change. For instance, when two students discuss a problem together, there is no stipulation that the students are close friends, or that their peers will talk about how the two like each other. They can discuss the topic without the fear and distraction of what others think because the focus is the topic not the people.

Academic respect means social-game-off. During the time of shared study in a room that accepts academic respect, the learning is respected. The social games are simply put on hold. Academic respect is a zone.

During academic times I ask students to be sociable without being social. The students are expected to speak to each other kindly. The skill of listening as a way to hear and learn new ideas from other students replaces the ineffective social habit students have of impatiently waiting for the opportunity to talk. Harry S. Truman said, “It is amazing what you can accomplish if you do not care who gets the credit.

Teaching students to have academic respect in the classroom is a way to develop a culture of learning that does not disregard individual and group differences. Academic respect is a coming together. It is a meeting place over ideas that affords the  possibility of closer ties between unlike individuals once they return to the rules and regulation of the roving pack.

A Recent Reflection: My Educational Philosophy

Education Philosophy, October 3, 2009

Three points stand out to me as, once again, I reflect on my educational philosophy. First, education is served best by hook and least by crook. Next, educators must know-now the details of the population of learners they serve, and finally, pedantry is not mastery. Teach students a new rule as soon and as well as possible: Use General Thinking Skills All Day Long!

Our American society, the civilized world community, and any careful, broad examination of the way to go all promote the necessity and benefit for individuals to pursue and receive a post-high school degree. This argument can be formed soundly. In practice, though, at the on-set, day-by-day, and year-by-year, the logical argument to pursue education requires a boost to be effective and motivating within the context of learning. Learners and communities need to see some recognizable substance to hook into in order to participate. As Keller’s ARCS Model promotes, each specific educational settings must gain the attention of the learner. It must establish and maintain relevance in the learner’s point-of-view. It must offer the learner reasons for confidence, and it must, in the end, be satisfying. The specific path to fulfill these requirements varies with the diversity of learners each educational setting serves. So some learners come willingly, initially spurred by a prevailing logic or an inner wonder while other learners need to be gathered and re-gathered by crook, and offered worthwhile hooks to connect delicately and with dignity.

In order to meet the specific needs of all specific learners, the importance of a front-end learner analysis cannot be ignored. Within an ever-increasing variety of instructional delivery systems of technologies, ideologies, educational theories and best practices, institutions, to the point of teachers, must exhort the effort to broaden its scope within the confines of its mission and goals to meet the specific needs of any student within its scope. The call is to find ways to include students who, at one time, were not included, and to continually improve instruction for students who are presently being served. As Thomas Edison once announced, “There must be a better way. Fine it!”

Learners need the opportunity to make decisions despite a lack of experience. To fill-in a lack of decision-making prowess, learners commonly memorize short lists of examples to cover their understanding of concepts and they often act on rules whether the procedures apply or not. This expression of knowledge does not count as mastery because, “Mastery is not Pedantry.” Students must be able to determine when new examples of concepts and when rules and procedures apply beyond simply knowing that the concepts and rules exist. The Seventh Perspective is a method of instruction I have crafted to offer students the opportunity to develop skills to make decisions within the continuum of teacher-directed to student-lead times of learning. The way to teaching habitual decision-making is an essential and difficult path. To the learner, it often includes the decision to defer leading thoughts and accept directions from others. To the instructor, it includes a detailed effort to incorporate instruction that gives learners the opportunity to listen, model, negotiate, problem solve, and present all within the normal course of instruction. As A. E. Housman once quoted, “Three minutes’ thought would suffice to find this out; but thought is irksome and three minutes is a long time.”

Scott J. Dodd

Wilmington, NC

The Creativity of Following Directions

In class last week the fifth graders completed an activity that  addresses the relationship between following directions and being critical and creative. The lesson was not complicated, but the implications of it were profound in developing a student-centered learning environment.

I asked the students to make a detailed technical drawing of a K’NEX vehicle we had built earlier. The directions were to draw the vehicle as accurately as they could. It was a straight-forward assignment, and to start, I was rather explicit about modeling  a technique for drawing the wheel and tire onto quarter-inch graph paper for the students. Then, beyond the tire, I expected the students to apply similar techniques to complete the graphic representation of the vehicle.

To illustrate my expectation of independence to the students I shared a couple of stories. First, I told them about the time I was on a flight out of Hartford, CT next to a Yale medical school professor who was grading papers on the plane. I asked him if he would rather work with students who were good at following directions or students who were creative and better at figuring out  problems. He said, without hesitation, “If medical school students cannot follow directions they will never make it through medical school.” I told my students that his response confirms the importance of following directions, but what about creativity? Is it separate? How does it relate to directions?

The educational process is not all rote. During our scale drawing lesson I drew a smiley face and started to write a message inside the circumference of the face. As the sentence arched around the curving line I realized I was demonstrating my point, and I explained it to the class. By beginning to write around the the curve I had set up a rule. As the sentence continued, I had to figure out how I was going to follow that rule by writing upside down and way. Figuring out how to follow rules and directions is a necessary skill.

The skill of writing an effective persuasive letter is a key element of the fifth grade NC standard course of study (NC SCOS), and my next example to my students. To write a persuasive letter well requires rule following and creative problem solving within one assignment that includes a strict adherence to accepted form and a convincing argument in the body of the letter that needs to stand out to the recipient. We need to follow directions and be creative.

Fifth graders confront the need for creative problem solving when they process directions. Student-centered classrooms need to identify and promote this built-in relationship  between decision-making and following instructions. I was pleased to participate with the classes as they looked to themselves and to discuss with each other about how to complete their task.

Discussing Our Mission Statement- part I

As a grade-level, we now have a mission statement. It is the common purpose Mrs. Proetsch, Mr. Smith and I developed, share, and hope to extend to our whole fifth grade community. It goes,

“We are the Carolina Beach Elementary School Fifth Grade: A learning community set in the love of learning, built on strong character and academics, seeking to understand our roles in the world outside ourselves.”

Mr. Smith sees this statement as the sum of four elements; the love of learning, strong character, strong academics, and a yearning to connect with the world that is getting both larger and smaller at the same time. Mrs. Proetsch and I see the mission statement as only three elements. We combine in our minds character and academics as either a curricular convention or an inherent blend. Regardless, we all share a solid mission that offers us good reason to meet the week-day morning with meaning and a smile.

During our flex period today the classes saw the mission statement written out for the first time. Each of the three classes worked to identify the concepts of the love of learning, strong character and academics in community, and what it is to look outside ourselves. It was a tall order for a short period. For instance, my class discussed the subtle difference between the student who rushes to the turtle terrarium to be the first to tell what will happened next between the fern and the tank glass, and the student who watched and learned a new box turtle behavior over time. One student missed the love of learning, and the other student nailed it solidly. To a casual eye the two student behaviors look very much the same, but at CBES Fifth Grade, we encourage students to consider the value of what they experience, and that is an example of how we are striving to be, “A learning community set in the love of learning.”

The Incurred Costs of Elementary Education

As a fifth grade teacher at Carolina Beach Elementary School (CBES), I would like to respond to Steve Rosen’s column of the Wilmington Star News, Sunday, August 30, 2009. Mr. Rosen’s focused on the legitimate concern of the rising cost of K-12 public education. From my six year experience at CBES, we pay very close attention on what it costs to get our kids through kindergarten and the balance of elementary school. Much is at stake.

Several factors went unmentioned in the column. First, the return on investment (ROI) of whatever a family pays during the formative K-12 years is profound. Our community places a high value on education, and the inevitable economic bite becomes more tolerable. Second, the cost can be shared. At CBES, we strive to gain the respect and support of our community on the conduct of our school operation by organizing curriculum-related field trips with no out-of-pocket cost to families. Our PTO is superlatively supportive of our cost-ridden activities. We also seek and receive grant funds $1000 at a clip. Further, we have families in our community who quietly extend their purse strings knowing there are other families in need.

Finally, the importance of establishing a personal responsibility for one’s own education includes paying for part of it. When pencils are provided ad nauseum in order to keep lessons moving, student responsibility for the lesson at hand becomes lost. Some cost for a free education is justified as part of the education. Mr. Rosen is correct to say we need to pay attention to costs because the return on that investment is so grand, and our small school community does everything it can to support it.

Open House: An Important Night at an Important Place

Hello everybody. To get this blog going I would like to share about open house. Most of the seventy-plus fifth grade students, parents, and extended family members stopped by Carolina Beach Elementary School Thursday afternoon to see their new school rooms and teachers. Smiles and pleasant greetings were shared throughout the two-hour event. In my classroom, I asked the families to participate in the bulletin board activity in place. I handed each a slip of paper and asked then to complete the sentence:

“This classroom/ This school is an important place because… ”

Below are the responses I received. We will use these ideas beginning the first week of school as we build a community together. Here they are. What do you think? Add a comment at the bottom of the page.

This classroom/ This school is an important place because:

>school is fun and fundamental. (Parent)

>it is the start of many things. You will need the things you learn here to be successful in middle school/ high school. Plus it is great fun!! (Supporter)

>we love Carolina Beach School. (Parent)

>I get to help students learn to be good mathematicians and I hope they learn to be better citizens in my class. (Teacher)

>It has a cool design and good teachers. (Student)

>all these children come for an education and this is where it starts. One step closer to the job/ career of you dreams.(Big Sister)

>education- quality education – is important for my children as well as social adaptation.(Parent)

>the classroom allows a child to grow and learn. (Parent)

>it builds a base for future work and 5th grade is important because they are starting to look outside their own scope to begin choosing their future. (Parent)

>it gives us the background for future education. (Parent)

>beautiful children that will one day shape the future of this amazing island come here hungry to learn each day. (Teacher)

>I have an opportunity to learn about healthy choices and be physically active enhancing the quality of my life. (Teacher)

>it offers people the opportunity to explore the world in the company of their peers and friends and with the guidance of their teachers as well as the whole community. I hope all enjoy the adventure. (Parent)

>true opportunity begins with learning new things. (Parent)

>you learn and study. (Sibling)

>it teaches my child to become a responsible citizen of the world! (Parent)

>(it) allows for children to be themselves with a bit of “free-spirit” in the unconventional and beautiful environment- All outdoors/ indoors should be utilized in the learning / growing process. (Parent/ participant)

>it offers a safe and fun way to learn. (Parent)

>(it) is here to learn everything he can to prepare him for the future. (Parent)

>I think this classroom important because it helps knowledge. (student)

>it is where I learn how to become a more useful and productive part of my world. (Teacher)

>it prepares us for the future. (Teacher)

>it will provide a nurturing environment for my child to learn and grow through the year. (Parent)

>the teachers are AWESOME! and this school has been here a very long time. (Student)

>I can learn a lot of things in this classroom. (Student)