Montessori 101 - Freedom and the Environment

True to Montessori form, two fundamental principles of Montessori education follow an overarching idea from the concrete to the abstract: the first is freedom and the second is the environment. How are these principles defined in relation to my personal belief system is the purpose of this essay. My reason for choosing to follow the Montessori path is that it follows natural laws that are in tune with who I am. It gives me great joy to work alongside the boundless energy of children, and to wrap myself in the meaningful endeavor of service to humanity. I am a natural, kinesthetic and visual learner. Montessori philosophy and methods endorse a natural environment, integrate freedom of motion, and harness sensorial means, including visual, into purposeful learning. I respect the free will of all people. I value creativity, self-discovery, and guide toward collaborative and independent, critical thinking. When paired with an open, respectful and socially responsible environment that recognizes and supports where students are developmentally, I see self-confidence grow, inner discipline flourish, and proud choices being made in preparing them to enter the world.

FREEDOM

There is no more powerful, intrinsic, motivating force than the fulfillment of one’s free will. A Montessori classroom provides the opportunity to unfold the child’s true self, by enabling their freedom of choice. Activity may be sustained for minutes, days or even a week at a time, as the child learns through repetition and self-motivated interest.

“The children in the Montessori class are given the freedom that is the liberty of the human being, and this freedom allows the children to grow in social grace, inner discipline, and joy.”¹

A result of this freedom is serious concentration that leaves an imprint of satisfaction, accomplishment and peace. After all that effort and hard work a child may feel remarkably rested.  I wonder, is inner-discipline simply an awareness to follow free will?  All people are free to regulate their behavior and to choose conscious control over their lifestyle. This is an empowering and liberating idea!

Promoting brain development, freedom of movement is intimately connected with learning. Montessori forewarns, “Man who does not move is injured in his very being and is an outcast from life.” ²
How can we participate with others if we fail to interact and move?  I enjoy seeing freedom of kinesthetic motion routinely integrated into Montessori practice. Golden beads, red rods, and sand paper letters are a few such examples. Effective teaching welcomes the child’s free will a uses all of our senses.

ENVIRONMENT

A Montessori classroom environment holds several key concepts for creative young minds to flourish. These include freedom, order, reality, beauty, materials and community. Freedom of choice provides the opportunity to lift a child’s independence. It is the child’s free will to choose which material to work with and for how long. It is not the adult’s role to interfere and perform acts that the child may learn to do for himself. A Montessori teacher protects the child’s choice and creates an environment for constructive work to surface. Montessori children are not forced to join group activities or compete with other students if they are not developmentally ready to show interest for that particular task. As a result,
this non-competitive environment gives rise to a natural human desire to help others.

                  Sequentially ordered across all content areas from easiest to most challenging, a Montessori environment is arranged from top to bottom and left to right. While appearing quite linear at first, this structure is extremely fluid as children move their bodies in and out, repeating the same works until fulfilled. Consequently, the child learns to trust the environment and interact positively with the materials. Importantly, the child is an integral part of this classroom structure. Students work diligently to maintain order when completing a cycle of activity by returning a work to its’ proper location.

                  Understanding the limits of reality and nature help students assign meaning to their new world and to separate the illusions and imaginative fantasy of role-play. Through contact with nature, inside and outside the classroom, children grow to appreciate order, harmony and beauty. Activities that are rich in natural content help the child to feel secure, maintain a sense of place, and feel free to observe life with exceptional detail. The benefit, according to Lillard is that children become an “acute and appreciative observer of life.” In addition, caring for living plants or animals helps children to coexist and live in awe of the natural world.

                  Beautiful Montessori environments typically include ample light, warm colors, glass walls, open space, and an inviting, relaxing atmosphere exhibiting high quality materials. Quality, in fact, permeates many aspects of this space. Well-designed activities of wood, metal, and natural elements encourage the child to treat the environment with care and to recognize that learning can be a sacred experience. Harmoniously arranged in ordered shelves, these activities invite participation.

                  Because many tasks in a Montessori environment are independent, the materials are designed to capture attention, promote self-construction and concentration. Through observation, a teacher may realize the child’s level of intensity and interest. Is this work meaningful? Is it at an appropriate level? Is it consistent with the child’s internal needs?

Lillard explains further (1972), “The teacher watches for a quality of concentration in the child and for a spontaneous repetition of his actions with a material. These responses will indicate the meaningfulness of the material to him at that particular moment in his growth and whether the intensity of the stimulus which that material represents for him is also matched to his internal needs.”³ (p. 60).

                  Clearly, when there is a quality of concentration, learning is most meaningful. Learning is suited to a particular stage of mental growth and matched to internal needs. Moreover, the child feels pleased with his/her accomplishment, peaceful and rested. In addition, the teacher should be flexible to alter the sequence or omit activities that the child shows no need for. At times, it is possible for a child to learn simply by observing another child, and to leapfrog activities.

A Montessori environment is a true community. Modeling respectful social behavior, people come to care for each other, solve problems together and consider the greater good of the group. Sitting beside a student and not only listening, but also hearing what they have to say, is a vital life skill for individuals. In this community, children learn to make choices that everyone can agree with.

Can You Prove It?

The process of learning is the polar opposite of a passive experience. Actively constructing knowledge, Constructivism, is rooted in Piagetian theory. Children construct meaning, building upon what they already know. Students are not empty vessels to be filled with our magic. They are their own shining stars that perform at center stage. As Kloosterman and Gainey suggest, students are “thinking individuals who try to make sense of new information.” (ch1, p.5). The cumulative effect of building upon prior knowledge has implications in all content areas, especially mathematics. According to the NCTM, Notional Council of Teachers in Mathematics,

    “The mathematics curriculum should include the investigation of mathematical connections…describe results using mathematical models…and use a mathematical idea to further their understanding of other mathematical ideas.”

Stated simply, this boils down to two simple words, explain and justify. Exploring problems together as a whole class and in small groups, a student’s job is to investigate and make connections, (to real life, to other mathematical models through a spiraling curriculum, and to a multiplicity of solutions). When we shape an environment that encourages sharing solutions and explaining what students believe and why they think the way they do, we help them recognize relationships and add meaning to their conceptual knowledge. 

Approaching mathematical problem solving in this way mimics the method of scientific inquiry. This process of discovery, followed by elaboration, discussion, and articulating a cohesive conclusion, provides structure for students to prove their thinking with evidence. It is hard for me to imagine students blindly following rules without reasons, yet, in some classrooms, I know it happens every day. I expect more from my students than the ability to get something correct and memorize a formula. They must be able to justify, explain, and prove, how they know what they know. I expect my students to engage in active learning, to process then apply their content knowledge, to question, share and reflect as they learn. When students reach this level of understanding in mathematics, they validate their own beliefs as they construct relationships to past and future conceptual meaning. Ah… but, can they prove it?

iTouch apps … to be continued …

Today, I am teaching myself to do more with iTouch applications by exploring literacy tools in the palm of my hand. For instance, imagine accessing the complete works of (insert your favorite author here). Recently, I discovered two apps worth mentioning. The first, Story Book Reading, offers the titles, “Three Little Pigs, “Waldo at the Zoo,” and “Black Ear Blonde Ear”. Each has beautiful illustrations to share and text that may be zoomed in for reading clearly. While the fables are ethnically diverse and maintain strong values, I have a hard time imagining sharing a 2-inch by 2-inch window with a class of 26 students. Where is the visual impact? How can this display be synched with projection on the ActiveBoard? I imagine this is only a matter of time.

A second app that I find useful for small group learning, is World Wiki. How demonstrative this would be for the World Geography unit I conducted last October. Differentiating instruction with a group of four students in a split 2/3-grade classroom, this app can quickly convey a myriad of statistics on any country from around the world. Students can learn that Vietnam, for instance, earned independence from France on September 2, 1945. In addition, the capitol city is Hanoi and the currency is the Dong. Advanced grade level students may chart, compare and contrast mathematical data between different countries, such as the G.D.P. of Vietnam in 2008 reaching 290 billion dollars. Today, information is literally at our fingertips. The mobility of these devices keeps us joined with knowledge. Is there really any excuse for ignorance? When we integrate these devices into the classroom, a key remaining question I have is: How do we design the experience to be equitable for all students? Does the “i”  in iTouch stand for independent, interactive, or irresistible? Certainly, I believe that it is far more than an iToy. I imagine the iTouch will evolve as an integrated educational tool, strategically shared with all students.

Forming a Healthy Self-Concept of Math

This week I learned to think about math in a healthier way. Before students can develop a healthy self-concept of Math, they must be given the opportunity to share their thoughts, beliefs, ideas, and perceptions on what math is and how they use math in their daily life. It is easy to take for granted how much mathematical reasoning goes into everyday activities.

Through open discussion and social context, the below mini-lesson from Leatham, K. (2010), helps students to recognize different patterns and to re-examine their definition of math. Simple everyday language is mathematically categorized and discussed. Examples: driving a car, quilting, playing the drums, hanging  a picture on the wall. In a second group lesson today, I was introduced a similar theme when I was asked to use a variety of atypical measuring tools (paper clip, post-it, poker chip), to measure a specific rectangular shape.

After plotting the length and width data points on an x, y graph, I came to realize that the slope was constant, forming a linear line. y = mx + b.  I found this to be surprising, as all data points were in different units of measurement. The implications for classroom practice in this 2nd exercise revealed a new way of seeing the x, y data when applying the concept of slope. Connecting the relationship to the content through experience, is a healthier way to see mathematics than memorizing and plugging in a formula without context.

I am reminded to continue asking what do the students know? What do I want them to know? How do I get them there? Did they get there and where do we go next?

The Largest Container

A vod presentation by Annenberg Media, Learner.org, by Suzanne Duncan a 7th and 8th grade class discusses length, width, and height of volume of a rectangular prism and area in a container.  shows a lesson “The Largest Container.”

Moving her arms in the air, Ms. Duncan defines the volume as a cylinder as a circle moving through space (height). Maximizing the idea of surface area and volume she asked the students to design the largest area possible out of a sheet of paper. What elements come to mind? Volume. Surface area. Once students had a possible solution they were encouraged to flatten out their shape, and write out the dimensions, and their computation of surface area and volume (so their thinking doesn’t get lost).

Causes for intervention in helping students correct for computational errors: 1) running out of time in the lesson, (stop where you are and move to the next phase), 2) adjusting to individual needs and learning dispositions. 3) redirect after students have had the opportunity to explore and discover on their own, preferably through small group engagement and whole class sharing.

As the topic of volume and formulas is too advanced for a 2/3 split classroom, I can restructure this lesson for my students by modeling and constructing a cube and a rectangle from a blank sheet of paper. An essential question may offer, “How many sides are in a cube?” Can you prove it? Can you build a cube? Sharing the many different possibilities in a class poster can encourage discussion and knowledge transfer. I can introduce vocabulary of length, width and height and touch upon concept of surface area.

Ms. Duncan holds a strong belief that mathematics is for all students. Moving from teaching a select few, who either understood the concepts or didn’t, to reaching and teaching all students, gave Ms. Duncan a sense of pride and accomplishment. Re-charging her batteries at the end of a 15 year career, she believes today that all students are naturally gifted learners. According to Gardner (1993), student intelligences can be categorized as follows: Verbal-linguistic (word smart), Visual-spatial (picture smart), Musical-rhythmic (music smart), Body-kinesthetic (body smart),  Interpersonal (people smart), Intrapersonal (self smart), Naturalist (nature smart). Considering the multiplicities of how all people learn, an important goal of education is to apply knowledge outside of school in the social and cultural settings of our greater life.

How can we make math exciting?

Ted Talk - Adora Svitak

Thinking in 3-D

A vod presentation by Annenberg Media, Learner.org,  shows a lesson called “Building Viewpoints.” Seventh-graders learn about spatial sense and geometry from a blueprint of 
ancient buildings. They then create their own three-dimensional models and draw them from different viewpoints.

One questioning strategy Ms. Hardaway uses is to follow the students’ lead and ask a probing questioning to build on the story being shared. “Can anyone tell me what this is a picture of?” After one student commented that they are blueprints, she continued along the same path of questioning, “What are blueprints used for?” This formed a natural segue to the objective to build and draw a 3-D model from the left, right, front and back. A second questioning strategy helped students to consider how their views were alike or different from each other. A comparative-based question such as comparing all four views falls within the analysis stage of Bloom’s Taxonomy of learning.

The content of this activity is important in middle grade because it builds on a visual and special sense of geometric problem solving. Students were actively engaged in sculpting 3-D figures and translating this information into 2-D drawings. Leading up to an activity that will involve analyzing a 3-D model and transferring their new knowledge into 3-D drawings. This newly acquired prior knowledge will be useful to apply to future projects.


When constructing 3-D buildings from manipulatives, tactile learners are engaged as they move it, feel it, turn it around and flip it upside down. Through small group sharing, I would enrich this activity with writing a conclusion paragraph to restate the main idea, include supporting details, and build on higher-order questioning. Bloom’s Taxonomy continues to open minds by moving into a stage of synthesis. At this stage, students may contrast, categorize and discriminate the various views observed. Evaluation can encourage students to reconstruct, reorganize, summarize and validate their ideas as they explore their understanding along an investigative path.

Cluless about Tactile Clues?

This week I learned that alternate interior angles (from a bisected parallel line) are equal to each other. I was lead to draw this conclusion by the use of a simple paper manipulative. Folding the points of a square in on themselves to form another square, and then folding in half to create parallel lines and perpendicular bisectors. I was asked to prove what I know through open class conversation. According to Marshall (2000), “Saying out loud what one has just learned is an excellent reflective strategy to improve learning.” Whole class discussion solidified this Math manipulative experience.

There is no substitute for direct experience. Yet, when might a mathematical manipulative not be appropriate as a teaching tool?

According to Freerweiss, when we use manipulatives we can reach up to 10% more students who naturally gravitate toward kinesthetic and tactile learning. Indeed, anytime I incorporate a wider range of teaching with the senses I routinely see greater engagement. In addition, manipulatives lower anxiety in a historically anxiety rich content area that is frequently plagued with memorizing facts and formulas.

Learning through experience first, and teaching for conceptual understanding can help students to solve problems they have never seen before. To successfully take a mathematical formula out of a text book, requires a teaching strategy that incorporates real world context. If I introduce a tactile experience along the way, and connect this to prior learning, I can help students’ understanding take hold with permanence.

Lasting Impressions with iTouch apps

My impressions of using iTouch applications in the classroom as a learning tool are evolving with hit or miss results. I continue to experiment with hope and optimism – this week with the free ap Story Builder. Of note, this is not to be confused with the Mobile Education store ap by the same name. This week, after completing a reading conference with a 4th grade student, I gave him the opportunity to build his literacy in a different manner. One example: “A drunken jewel thief with OCD Must save a city from a swarm of killer bees.”

A word of CAUTION: Sincere discretion should be used with respect to grade level vocabulary. Word choice such as: cross-dresser, and gigolo may be contrasted with options to stop global warming and gain the respect of his/her peers.

On a positive note, changing the genre feature in this micro-ap. to an uplifting documentary can deliver, “A superhero werewolf stranded on an island must go back to grade school to save a secret world.” Toggling between genres can offer surprising results. I would prefer to see a more extensive G-rated vocabulary list. Given the sophistication of the genres and word choice options, this ap is better suited for a young adult audience. My point…be mindful of the audience and resources when connecting the student to literacy at his/her just right level.

From Assessment to Instruction

What have you learned about your buddy’s needs, abilities and interests?

Alan is interested in tetherball, soccer and ping-pong. His scientific mind embraces future potential writing topics of liquid, solid and gas, water vapor, salinity, and the life cycle of insects. He willingly embraced new reading content of electricty and magnetism while showing joyful expression and a sense of humor in his writing.

Alan is a curious, self-motivated reader and a pleasure to collaborate with. Scoring at a 65-70 percentile with his oral reading fluency, Alan is on target for where he should be during the beginning of the winter trimester. Alan performed with 97% accuracy on the fluency scale at 4th grade level for words correct per minute. Strong suits: reading motivation, fluency and decoding for meaning.

Occasionally, Alan misses critical details of the story. While Alan reads at a steady pace with efficiency and three-four word phrase groups, there is room for improvement in comprehension. Alan should continue to read 4th level material while focusing on gaining strategies for comprehension. He can benefit from reading more carefully and asking questions along the way to more fully capture details of the main idea. 


As a result of this knowledge, what learning objectives and materials are you considering using for your lesson?

A reading lesson for Alan will focus on teaching a strategy for recognizing main ideas with the purpose of summarizing a challenging work of non-fiction. In addition, scoring well into a 5th grade frustration level, shows that Alan can move beyond common word use to work with new vocabulary and more challenging text.  Importantly, laying the groundwork of prior knowledge within the context of interdisciplinary instruction (his intrinsic motivation is Science) can guide toward greater engagement, ownership and comprehension.

The process for this lesson includes creating an “I wonder” poem to preload for conceptual understanding of doing what good readers do — asking questions. Modeling, I will read a short passage, and think aloud as I ask predictive questions. Following this exercise, together we will read a grade level text while placing sticky notes and writing Alan’s questions in the margins. Materials: journal notebook for poem, pencil, grade level text (2 copies), question prompts on cards, sticky notes.

Prove Your Mathematical Thinking

Good mathematicians explain their solutions and can prove their reasoning.
It’s not enough for a student to get the correct answer. We learn through discussion, through sharing our ideas with others. When teachers ask, “How do you know?” How can you prove what you know?” It compels students to think more deeply and to justify mathematical concepts through informal deduction. Stage three along Van Hiele’s scale of Geometric thinking encourages us to look at the properties of things. Stage one: visualize. Stage two: analyze. Stage three: informal deduction. Stage 4: deduction. Stage five: Rigor. This final stage address non-Euclidian (Spherical) Geometry where all lines meet at the poles.

What do I have questions about?
Questions I have are how can we encourage quiet students to engage in dialog in sharing their solutions? In a classroom where proving solutions is the expected norm, what does a forum for ongoing dialogue look like? How can we record, track, post, and reflect on student work in a more public manner. Is there a Math wall dedicated to the days thinking and the “whole class” ideation? How can we elevate the status of low performing students and give them an opportunity to succeed in a more dynamic conversational environment?

What are the implications for classroom practice?
Asking higher-level questions and not settling for correct answers, by asking kids to prove their ideas, is a way to invite discussion and reflection into a lesson. We can ask why? How did you solve that? What does another student think of what you said? Can you Prove it? A second implication for classroom practice is collaborative work – SOLVING PROBLEMS IN TEAMS -  I believe this is an essential strategy for teaching math to kids in the classroom. It’s easy to over think group work. A way to simplify this in my mind, is to imagine playing games in teams. 2-on-2. For instance, to extend a manipulative lesson, ask kids to solve their problem in pairs. The first one with a justifiable solution earns 2 points and moves 2 places around a board game, a bonus round could include proving how they know this is true (deconstructing the problem), before moving to the next shape. And so on.

Scientists at Play!

Today, I observed a group worthy task in action while exploring the force of water on a wheel. Students were given an array of materials (manipulatives) with little instruction and asked to solve a problem. The objective was clear: lift a weight from the floor to the desk by using the force of water. Communicating explicit criteria increases the classroom interaction. Repeating the objective several time, posting on the active board, and asking the class for a choral response to demonstrate understanding, are a few ways to reinforce the message and to keep kids on task. Building on prior knowledge of mathematics vocabulary, the concept of surface area was given a practical hands-on application. During this highly engaged activity, students were lead to discover surface area as a powerful factor in helping the wheel to turn. Not only did this Science lesson incorporate mathematics, but also the structure of the group effort taught communication skills and team collaboration. A concern with group work however, is ensuring that all students are engaged through having clearly defined roles. I noticed that one person withing a group was called the “getter” (those who gather the materials). Other potential roles in the group dynamic are: facilitator, resource manager (getter), recorder/reporter, and a team captain.

Another benefit of group work is the sharing that takes place after all groups have an opportunity to problem solve. First, is the jigsaw strategy of requesting an individual to leave their own group and to observe another group’s progress. After an individual is chosen, he/she comes back to report the findings to their original group.  Second, a class may be prompted with numerous questions before, during and post lesson. How do we build a water wheel? What did you notice? What force drives this action? Is there another way to manipulate these interlocking wheels to have more surface area? While a class that is engaged in high quality discussion may be an early predictor of the average level of writing performance, Lotan (2003), excited voices, captured in the moment of learning are often eager to share. I look forward to seeing the results of the follow up writing and water wheel re-design lesson. Using the prompt, “What did you find the most challenging?” a host of hurdles were offered. Discussions of the different results between experiments, water pressure vs. water weight were mentioned. (two different types of force) Higher order thinking compare/contrast statements can happen in real time. Students begin to question why some solutions perform differently than others. Importantly, they begin to infer and to see what to try next. How can we make this process easier next time? How can we improve our designs? “We poured the water instead of spraying it and that made it spin really fast.” Perhaps the greatest benefit of group work is the sharing of group ideas. It may be a difficult task to reflect and substantiate ones thinking, yet, having a willingness to critique and participate in this part of the process can lead to improved individual and group learning, Lotan (2003).  Shaping an environment for quality discussion, presenting clear criteria and encouraging a willingness to critique and substantiate ideas leaves only one question in my scientific notebook. Are group worthy tasks worthy of teaching? I have seen students theorize, explain, and become immersed in continuous investigation who would probably answer, “Yes!” The funny thing is, I don’t think they would call it learning. On this day, they are simply scientists at play.

The day all animals could talk.

“The day all animals could talk,” is an engaging topic for 4th grade writers to explore. One student, I will use the pseudonym Allan, explored this fictional, narrative prompt with vigor...a scarlet macaw parrot hides away in a blanket, surviving a snowy trip to school. This story is playful, imaginative and fairly well organized.

Beginning with classification of Ideas, in the six traits of writing, Allan’s demonstrates relevant and telling quality details that move beyond the obvious and the predictable (NWREL, 1992). Allan admitted that his weakness is having too many ideas and wanting to write about everything. He goes back and crosses out or his teacher will delete a whole block of copy. I paraphrased by saying, “So, it sounds like you need help focusing your story?” Adding lots of detail is good, but only if it supports the one thing the story is about— the topic. Allan’s story builds to enrich the central theme. The parrot in his story,  played games such as: “Pin the tail on me!” and “trampoline.” He tells the story with humor, “Imagine having 24 parrots jump on you. It’s humiliating.” His organization sounds inviting when snow is falling like “meteors.” A satisfying close ties back to the beginning of the story in the parrot’s own words, “It’s freezing out there!” Compelling information carries the reader throughout. Allan’s writing style is entertaining and dynamic offering solid word choice such as, “making a ruckus.” His fluency has an easy flow, rhythm and cadence, “In the morning, all was quiet. I have to admit…” Sentence structure varies in length form 5-15 words, with about 66% close to the 15 range. Voice is captured with sensitivity in the subtle details of how the parrot spoke about his life in being separated from his family. Conventions are overall very reasonable, with infrequent miss-spellings, idol to (idle), and with numerous examples of self-correction during the editing and publishing phase.

When I asked where his ideas come from, Allan responded, “I write and write and write, and then I go back and cross out what I don’t want.” Clearly, he has ownership of the writing process and sees himself as a writer. Allan exhibits an eager attitude and a firm understanding of the process of using graphic organizers. Regularly using a 1st , 2nd and 3rd writing draft he takes out and adds on content. Allan is also interested in tetherball, soccer and ping-pong. His scientific mind embraces future potential writing topics of liquid, solid and gas, water vapor and salinity, and the life cycle of insects.
Spelling development for this student reveals a need for working with doubling, rippen (ripen); suffixes, sivilies (civilize); and the initial consonant sound of a hard “c” in kattle (cattle); and oppisition (opposition). A discussion of the base root (civil) welcomed, “Oh, like civil with a ‘c’.” After sharing a host of base words beginning with (oppose), and surrounding the topic of  table tennis (opponent), Allan quickly understood the meaning of this new word (opposition).

Concluding thoughts for this student are: While topic sentences are clear and concise, I suggest improving his organization by developing an original title.  I suggest teaching with greater emphasis on thoughtful transitions and guiding towards the expression of personal voice. Finally, to improve vocabulary, spelling lessons may surround the areas of suffixes and base roots.


Lesson Plan:
"SUPER SUFFIX COMIC BOOK" 

Objective(s)/Learning Target(s):
Students will learn to improve their writing through creating a based word suffix chart.
Students will apply their learning of suffixes by creating an eight-panel comic book.

Standard(s):
GLE 1.3.1:  Revises text, including changing words, sentences, paragraphs, and ideas
GLE 3.1.1: Analyzes ideas, selects a narrow topic, and elaborates using specific details and/or examples

Instructional Strategies / Teacher Instruction:
This small group lesson will occur in two stages.

STAGE 1  :20
I will discuss how suffixes affect word meaning.
I will distribute directions with 20 base-root words and 8 suffixes.
I will model creating a chart with 21 rows and 9 columns. Suffixes will be listed horizontally across the top (-ed, -er, -est, -ful, -ing, -ive, -ly, and -s/es).
Base words will be written and fall vertically down the page in the left column.
I will ask students to consider and cross check the dictionary to be sure they are recording REAL words.
Color in the empty boxes with marker.
Share your chart with the class. Compare/contrast results.

STAGE 2  :20
Students will create their own cartoons using dramatic illustrations, dialogue bubbles and words with suffixes from the previous lesson.
I will ask the students to divide their oak tag into 8 sections. (one section per scene).
I will encourage students to create a new story line on a personal topic of interest.     (perhaps giving super-powers to an inanimate object)
I will remind students to use a smattering of base words with suffixes from their chart.
I will look for discussion points on word and passage meaning as affected by suffix choice.

Materials/Preparation needed: 
A large piece of oak tag, a ruler, a pencil, a dictionary, a set of directions, colorful markers, 11 X17 paper. Chart answer key.

Suffixes: -ed, -er, -est, -ful, -ing, -ive, -ly, -s/es
Base Words: act, blame , bold, bubble, burn, clam , cheer, color, create, drive, elect, happy, help, jump, last, like , pass, play, sick

Assessment of Learning:
I will note to the degree students are able to accurately complete their suffix chart.
I will project an answer key on the active board and ask students to self assess.
I will look for learning opportunities by comparing inconsistent class chart results.
I will request a gallery walk, giving writers the opportunity to share their cartoons.
I will request that each student present or speak to at least one base word and one suffix in their final product.

ScienceHouse

iTouch mini apps are infiltrating the airwaves. Science can be brought into the classroom with short videos that are designed to inspire and excite kids of all ages. With topics such as: Chemistry, Convection and Fire, the ScienceHouse app is free and definitely hot! Science Class Experiments are brought to you by Science House and feature Science Teacher Dan Menelly, winner of the NSF Einstein Fellowship in Cyberinfrastructure!

The limitless applications that are available today, usher in a new era in teaching that can motivate and inspire while instruction is differentiated in the classroom. Whether fast finishers have the opportunity to watch an extended science lesson, or those who are more visual learners have an immediate means of seeing and hearing the instruction for a 2nd and even for a 3rd time, video is certainly a compelling way to teach. While choices seem endless, however, limitations do exist. First, not all students can afford the technology. If the school supplies the equipment, it will need to be managed with firewalls and instruction. In fact, apps have a new rating system all their own. As a word of caution, this rating system should be closely reviewed and ranges from 4+, 9+, 12+ and 17+.

While high energy students and short attention spans may be engaged by the always on, fast-paced appeal of video game-like iTouch apps, I wonder if teaching more moments of silence and controlled breathing can help students to regain a better sense of focus and concentration. The upside, is that relevant content can now be delivered immediately, repeatedly, and in a way that is accessible at all times. The downside, is that iTouch apps have an enormous power to engage and at the same time are at risk of being addictive. My hope is for educators to have the foresight to teach students to be responsible with this technology. For more... educational apps click here.

Algebraic Reasoning: Concrete to Abstract

Today, while practicing teaching best practices of negative integers, I learned (1) the importance of teaching numerous strategies for solving math problems, and (2) the effectiveness of moving from concrete to the abstract when teaching algebraic reasoning.  What is subtracting, after all, but adding the opposite.  To quote a colleague, “Negative numbers doesn’t mean it doesn’t exist. It forces the value in an opposite direction.” An abstract thought indeed. In the real world, we may relate this to the debt side of an accounting spreadsheet, or a host of engineering and science career paths. Yet, how do we teach? We begin with the concrete method of manipulating black and white beans. We point to and count aloud along a number line, or walk facing forward and then walk backward along a masking tape line on the floor. We can list the pattern in a series of related numeric equations, so kids can “see” the answer in a new way. We can manipulate poker chips; base ten blocks, rods, cubes and sticks. We can flip over algebraic tiles from positive to negative as we move from concrete demonstration and practice, to the lattice method, and finally to the abstract “Foil” method (first, outer, inner, last). Using multiple strategies can help students of different learning dispositions to solve, factor and determine the product of two binomials.

Getting kids to open up and explain their thinking is one way to welcome a host of solutions into the classroom. “What do you think about __________’s idea?” or “Next?” This encourages reflection and conversation which is student-centered. Reinhart, S. (2000) shares, “I concluded that if my students were to ever really learn…they would have to do the explaining, and I the listening.” The implications are that kids not only get it, but also thrive to become teachers themselves. The result is more guided teaching in the class, less direct instruction and more demonstration of student knowledge.

The uncomfortable struggle all students face, is showing confidence in the face of the unknown. Will the teacher call on me? Will I open my mouth and stick my foot squarely in it? Can we set the environment for a safe caring classroom making it okay to say, “I’m stuck.” I plan to offer excessive wait time in my classroom to gather more thoughtful response. Seeming like an eternity, I will move on and offer, “(student) I know you have valuable ideas to contribute, will you promise me that you will raise your hand on another question when you have something to share?” It is important to validate the effort. Struggle makes our brains grow!

Numeric and Geometric Patterns

Today, I learned that group worthy tasks have multiple entry points for every problem. When students solve math problems together, share their ideas, and when multiple solutions from the group are valued, learning takes place at an accelerated rate. Math is no longer obsessed with finding only the right answer but by finding a host of solutions. Indeed, as human beings we naturally see patterns in the world. In the “Sneaky Snake” math problem below, I stumbled upon a realization. First, I saw a geometric pattern where a central block increased by one tall and by one wide. I wrote a numeric equation for each consecutive group. When comparing this new group, I saw yet another pattern emerge. 5 = (6 x 4) + 2,   6 = (7 x 5) + 2,   7 = (8 x 6) + 2.  I could see that the next number in line would be one greater and one less than the number “n”, where 2 is constant. This lead to the algebraic equation of n = (n - 1)(n + 1) + 2.  The remaining question I have is how many ways can the formula be solved?  I welcome pattern recognition in a linear numeric manner and in a geometric visual approach, and I can see the benefits of encouraging both in the classroom. While there is always a definitive right or wrong answer, there is never a single solution. How we get there is up for grabs. It all depends on how we look at it.