How Do I Love Thee? Synthesizing

Ignite Creativity

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Creativity is one of the most powerful learning tools that students all possess, yet it is rarely utilized in schools today.  Students may be told to “be creative” on an assignment, however they are not given instruction on how to nor time to do so.  With the focus on test scores and performance of content knowledge teachers and administrators may argue that there is no longer time to be creative.  As more art programs are cut from schools it is crucial for educators to bring this focus into their classrooms.  Creativity is not something that a person has or doesn’t have, it is something that can be developed and improved over time.

As a high school special education teacher in a Geometry classroom I have struggled with finding ways to tap into my students’ creativity.  The curriculum moves quickly and notes can become routine and boring.  Making changes to develop more engaging lessons is a challenge.  Robert and Michele Root-Bernstein have outlined cognitive tools that may be used to spark creativity in people of all ages.  These seven tools include perceiving, patterning, abstracting, embodied thinking, modeling, playing, and synthesizing.  Educators may use these tools in their instruction allowing students to express themselves creatively and build a deeper understanding of the content.  I have discovered a new side of my own creativity and developed lessons that I can implement in my classroom.

Perceiving

Perceiving requires a combination of both observing and imaging.  Observing entails more than just visual perception.  We must use all five senses to observe and then translate the sensory information into an image.  Right triangles are a crucial part of Geometry and connect many different topics and ideas together.  Learning about right triangles dates back to elementary school math class, however they still tend to be a tricky concept for students to grasp.  There is so much to learn with their properties including their angles, names of sides, and how to apply various theorems and postulates to them.  As I observed my topic I found it easy to list characteristics and examples, but hard to describe the triangle with “non-mathematical terms”.  As I continued observing, I tried to use all of my senses and although this sounds crazy, imagine what it would be like to be a right triangle.

At first I really struggled with re-imagining a right triangle.  It was difficult to “see” the image in another way other than what was in front of me.  As a former college athlete and huge sports fan, I started to imagine myself becoming the right triangle in sport.  I chose to write a basketball poem where I was the right triangle and detailed my multi-sensory experience.  It describes the last few plays of an exciting basketball game where I end up completing a right triangle as the hypotenuse to win the game.

By presenting the material this way, I may reach more students and bridge some gaps in understanding.  The most common question I am asked is, “when will I use this in real life?”  By using re-imaged right triangles for problems in math students will discover that they use this content without even realizing it.  I could have students go to the gym/field and act problems out, or create their own word problems.  By perceiving and re-imagining we can make math real and bring it back to life for our students.  Perceiving is a powerful cognitive tool that we need to bring into the classroom more often.  By using all of our senses we can discover new meanings, experiences, and a deeper understanding beyond what is there on paper.

Patterning

It is important that students see patterns in figures in order to solve problems and proofs in Geometry.  When I thought of existing patterns with right triangles I immediately thought of special right triangles.  We usually cover this idea after learning the Pythagorean Theorem with some direct instruction on the shortcuts: x – x – x root 2 for 45-45-90 triangles and x – x root 3 – 2x for 30-60-90 triangles.

In addition to the exploration of existing patterns, students should come up with their own patterns because “making patterns for oneself is a lot more fun than memorizing” (Root-Bernstein, 1999).  I noticed that the some of the numbers and vocabulary terms with special right triangles rhymed so wrote a little chant or poem.  It has patterns in the way I decided to write it as well as what it represents.

This process of patterning is can be difficult, but is important for any learner.  Too many times students are just memorizing information to get by and pass the test.  As teachers, we need to foster deeper learning and understanding through cognitive tools like patterning.  It is natural to look for patterns all around us, let’s not lose that when teach our students.

Abstracting

Abstracting is not looking at something in its entirety, but focusing on one feature or viewpoint of it.  An abstraction may represent specific properties that are not obvious when viewing a whole object.  The goal of abstracting is to find “minimum visual stimulus that can be put on paper or canvas and still evoke recognition without spelling everything out” (Root-Bernstein, 1999).

Abstracting plays a very large role in the field of mathematics.  Although we always say that math is “real”, much of the work we do is not obvious.  We use abstract symbols, numbers, and equations to represent concepts.  I created some graphic art expanding on the basic ideas that Pythagoras used from the tiles. By narrowing my focus to the hypotenuse of right triangles I could think of the Pythagorean Theorem in a new way.  Abstracting allows students to deepen their understanding by viewing specific parts of something instead of the whole thing.  They may see new relationships, create images, develop meaning, or relate to a content area in a way that is not possible otherwise.

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Embodied Thinking

Embodied thinking is when we do not have to consciously think of the actions that are needed; our body just automatically knows how to do them.  However, not all embodied thinking involves physical movement.  Empathizing is understanding and sharing the feelings of someone.  This emotional feeling and connection is another great means of embodied thinking.  Empathizing may come into play when you are reading a book and you feel yourself becoming a character and sharing what they are experiencing.  Embodied thinking and empathy are important to use in the classroom as many students learn kinesthetically.  Making the content available in a variety of ways will offer more opportunities for students to succeed.

 It may be difficult to incorporate embodied thinking in some courses that students are taking.  Most mathematical concepts are abstract and students may have a hard time “becoming an equation” or “thinking like a square”.  I had to take time reflecting on some geometric concepts before figuring out how I could use embodied thinking in my classroom.  In Geometry, there are several new terms for students to know throughout the year.  To grasp the vocabulary, I would have them make connections to the word through their bodies and physical movement.  This could be done in a variety of ways: charades, gestures, Simon Says, or a dance.  I would choose to use motions or gestures and have the high schoolers display the term with their bodies.

Although this type of thinking may seem elementary, there are huge benefits to using it.  It would engage some of the students who are kinesthetic learners or “bored” in geometry class because they would be up and moving.  It encourages math conversation, creative thinking, and could be a game changer for some of my special education students who learn differently.

Modeling

Dimensional thinking “involves moving from 2-D to 3-D or vice versa” (Root-Bernstein, 1999).  It also involves scaling which is altering proportions within one set of dimensions.  Typically, we introduce the Pythagorean Theorem after proving triangles congruent.  Triangle similarity and dimensional analysis of areas/volumes of similar figures is not covered until second semester.  That is also when we go over different polygons and find the area/volume of them.  Even though these topics are found in different chapters, they are all intertwined together.

In order to incorporate more dimensional thinking, I began to explore through modeling.  Modeling involves the representation of an idea or concept to be better visualized or understood.  Not only are these ways of thinking helpful in making the ideas stick, but they bring math to life!

Playing

Play involves no rules, no success, no failure, and freedom to do things just for fun.  Play is for the enjoyment of doing or making with no responsibility or accountability tied to it (Root-Bernstein, 1999).  Bringing play into the classroom is important and something that I am passionate about.  Play engages students, reduces anxiety and stress, brings the class to life, and makes the curriculum fun!  Just because teenage students are growing up, it doesn’t mean they can no longer play and have fun in school.

In my Geometry classes I incorporate games and activities to get students up and moving.  To help me figure out a different type of playful introduction to right triangles, I thought back to my childhood and what I enjoyed.  Besides sports and physical activities, I loved to draw and color.  Coloring sparked an idea and I immediately ran with it.  I chose to design an adult coloring page for my students.  There is a huge boom in our culture with the “adult coloring book” market, as more people are recognizing the positive effects of coloring.  It is utilized for reducing stress, anxiety, and for relaxation.

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This activity would be fun for them and meaningful because it helps develop their visual skills, recognize patterns, shapes, and give them a chance to talk with their peers.  I can see students who are quiet and more talented in the arts loving this activity and sharing it in front of the class.  During the next chapter I could use this image again to talk about the different parts of a polygon and how we classify shapes: triangle, hexagon, square, quadrilateral, convex, concave, etc.

Synthesizing

Synthesizing involves “synthetic understanding, in which sensory impressions, feelings, knowledge, and memories come together in a multimodal unified way” (Root-Bernstein, 1999).  Synthesizing is not only experiencing, but understanding things at a much deeper level.  Our future will depend on synthetic minds to be innovative across curriculums.

As Steve Jobs puts it simply, “Creativity is just connecting things” (Henriksen & Mishra, 2014).  It is not something give, but something to be nurtured and developed.  It is important for educators to develop lessons and activities that support the growth of creativity in young minds today.  This does not require changing what they are teaching, only how they teach.

Henriksen, D., Mishra, P., & the Deep-Play research group (2014). Twisting knobs and connecting things: Rethinking Technology & Creativity in the 21st Century. Tech Trends, (58)1, P. 15-19

Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.

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Architecture of Space

Module 6/7: Assignment #2

I chose my classroom at South Lyon East High School as my most creative space.  I spend most of my time throughout the day in other classrooms because I co-teach all of my classes.  My room is used for small group testing in our classes as well as small group reviews or activities.  Since I spend my teacher consultant hour and prep hour in my room, this is my special place.

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Welcome to Room 3202!

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This space is engaging for many reasons.  As you can tell from the pictures, there is a lot to look at. When I was first hired, I couldn’t handle the blank brick walls and no windows; I had to spice it up.  Sports are a huge part of my life and I love sharing that with my students.  I have quotes displayed around as sources of inspiration for my students and myself.  These quotes and student letters/artwork really help pick me up when I am feeling down.  This room is home to me and I feel inspired when I am there.  I enjoy working with my air freshener and Pandora going, researching new lesson plan ideas or creating activities for my students.  My round table is nice and big when I need space to work on a project.

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There is no window to the outside and my initial disappointment has become more of an acceptance.  I have grown to like not having a window because I have less distractions as I work. Students are more focused while taking their tests or quizzes as well.  Some high school teachers may think decorating is elementary or distracting, but I find that it only brings me closer to my students.  They enjoy having things to look at and connect with.


Throughout my undergraduate study of education, I always thought a classroom environment should be welcoming, safe, and a space where students feel comfortable.  After completing this assignment, I still believe that is important. Your creative space is influenced by what you make of it.  You wouldn’t recognize my classroom if you saw it before I was hired in.  The true essence of the room is the positive atmosphere that is created with myself and my students.  My space is limited and technology is not abundant, however I choose to make it efficient for my students.  When someone is designing a learning space, they need to keep the users in mind.  “Designs must be created flexibly, with sensitivity and attention to context” (Mishra, Cain, Sawaya, & Henriksen, 2013) which is why I think of my students before I choose to make any changes to my room.  When I was hired I only had half of a round table in my room.  I knew that a full circle table would be beneficial for all users and I requested the change.  This table is now the most used piece of furniture in my classroom and the host to all of my IEP meetings.

Mishra, P., Cain, W., Sawaya, S., & Henriksen, D. (2013). Rethinking Technology & Creativity in the 21st Century: A Room of Their Own. TechTrends, 57(4), 5-9. doi:10.1007/s11528-013-0668-7

How Do I Love Thee? Playing

Module 7: Assignment #1

“Go play” is something you may hear a parent tell their young child or a teacher tell her second grade class at recess time, but what about a high school student in Geometry class?  As children get older and classes become more complex there is less time to just “go play”.  These words seem to connect only to sports in high school, not the classroom, especially in math class.  Play involves no rules, no success, no failure, and freedom to do things just for fun.  Play is for the enjoyment of doing or making with no responsibility or accountability tied to it (Root-Bernstein, 1999).  Bringing play into the classroom is important and something that I am passionate about.  Play engages students, reduces anxiety and stress, brings the class to life, and makes the curriculum fun!  Just because teenage students are growing up, it doesn’t mean they can no longer play and have fun in school.

In my Geometry classes I incorporate games and activities to get students up and moving.  To help me figure out a different type of playful introduction to right triangles, I thought back to my childhood and what I enjoyed.  Besides sports and physical activities, I loved to draw and color.  Coloring sparked an idea and I immediately ran with it.  I chose to design an adult coloring page for my students.  There is a huge boom in our culture with the “adult coloring book” market, as more people are recognizing the positive effects of coloring.  It is utilized for reducing stress, anxiety, and for relaxation.

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This is an introduction activity for our study of the Pythagorean theorem and right triangles.  Each student receives a picture and colored pencils to color it in any way that they desire, no rules.  Afterward I would have them explain to their group why they chose to color the way that they did.  No wrong answers, just looking for their thought process.  Some students may have colored specific shapes certain colors, made a pattern, or just colored to color.  Next, I would have students try to split up all of the polygons into triangles with their pencils.  Individuals would come up and share their pictures on the Elmo, discussing which shapes use right triangles.  Hopefully they see that each polygon could be split up and there were different ways you could split them up.  This activity would be fun for them and meaningful because it helps develop their visual skills, recognize patterns, shapes, and give them a chance to talk with their peers.  I can see students who are quiet and more talented in the arts loving this activity and sharing it in front of the class.  During the next chapter I could use this image again to talk about the different parts of a polygon and how we classify shapes: triangle, hexagon, square, quadrilateral, convex, concave, etc.

Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.

How Do I Love Thee? Modeling and Dimensional Thinking

Module 6: Assignment #1

Geometry is a class full of drawing shapes, polygons, cubes, constructing 3-D shapes, 2-D nets, and calculating the volume/area of a figure.  Students are always drawing pictures to solve problems, talking about relationships, and calculating answers based on dimensions.  With that said, I pushed myself to find a way to use dimensional thinking in the study of the Pythagorean Theorem and triangles.  There are many different types of triangles and as I drew them out on my paper I started to think past 2-D.  I thought about adding a third dimension and thought about triangles creating 3-D figures.

Dimensional thinking “involves moving from 2-D to 3-D or vice versa” (Root-Bernstein, 1999).  It also involves scaling which is altering proportions within one set of dimensions.  Typically, we introduce the Pythagorean Theorem after proving triangles congruent.  Triangle similarity and dimensional analysis of areas/volumes of similar figures is not covered until second semester.  That is also when we go over different polygons and find the area/volume of them.  Even though these topics are found in different chapters, they are all intertwined together.

In order to incorporate more dimensional thinking, I began to explore through modeling.

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This had me thinking, why not let students play with various manipulatives and create shapes?  Through this exploration and construction of 3-D figures, they will discover a lot of the geometric concepts.  It may sound crazy, but allowing students to play with manipulatives would be very powerful.  Modeling allows them to look at the figure from all different angles and experiment with how changing lengths or angles affect the shape.  Students could use magnetic balls and plastic pieces, spaghetti noodles and marshmallows, or even toothpicks and pieces of clay.  After some play, the teacher could give directions to create different triangles, right triangles, equilateral, isosceles, etc.  From a triangle comes larger 2-D shapes and 3-D shapes.  You could even challenge them to create a shape with the largest volume, or largest surface area.  They would begin to see the concepts we cover at work and in real life.  This hands-on experience would be powerful for kinesthetic learners, students with special needs, and anyone who struggles with visualizing in Geometry.  They can create similar figures by measuring certain parts and comparing models.  This would lead right into dimensional analysis, area, and volume discussions.  I could also see this modeling and dimensional thinking being useful throughout the chapters when we cover these topics, or as a challenge activity towards the end of the chapter.

My geometry classes already do some activities with various spheres and cylinders to calculate surface area and volume.  I have found it powerful in building up their estimated skills and accuracy in measuring as well as deepening the concepts.  We also do a container water project where students calculate the capacity of different shaped containers before filling them with water to win a competition.  Not only are these ways of thinking helpful in making the ideas stick, but they bring math to life!

Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.

How Do I Love Thee? Embodied Thinking

Module 5: Assignment #1

Embodied thinking is when we do not have to consciously think of the actions that are needed; our body just automatically knows how to do them.  One example of this would be tying your shoe.  After tying thousands of shoes over the years, we don’t have to think about finger movements or steps, we just do it.  However, not all embodied thinking involves physical movement.  Empathizing is understanding and sharing the feelings of someone.  This emotional feeling and connection is another great means of embodied thinking.  Empathizing may come into play when you are reading a book and you feel yourself becoming a character and sharing what they are experiencing.  Embodied thinking and empathy are important to use in the classroom as many students learn kinesthetically.  Making the content available in a variety of ways will offer more opportunities for students to succeed.

It may be difficult to incorporate embodied thinking in some courses that students are taking.  Most mathematical concepts are abstract and students may have a hard time “becoming an equation” or “thinking like a square”.  I had to take time reflecting on some geometric concepts before figuring out how I could use embodied thinking in my classroom.  In Geometry, there are several new terms for students to know throughout the year.  To grasp the vocabulary, I would have them make connections to the word through their bodies and physical movement.  This could be done in a variety of ways: charades, gestures, Simon Says, or a dance.  I would choose to use motions or gestures and have the high schoolers display the term with their bodies. 

In our study of triangles, I would separate them into groups, brainstorming ideas for the different types: isosceles, equilateral, right, acute, obtuse, 30-60-90, and 45-45-90.  This embodied thinking pushes students to think beyond the looks or definitions of the terms and actually become the term.  Looking at it through a new lens, and peer discussions, would enlighten them to a deeper understanding.  They would think about the relationship of sides, vertices, lengths, angles, and properties of the triangles.  Another idea would be to have students partner up and take a picture of them creating the vocabulary term with their bodies.  Embodied thinking in this type of class would support creativity which is usually not a focus.

I could add some competition into this lesson by rewarding students with the most creative gesture/stance.  The winning movements would be used throughout the rest of the semester when referring to the specific term.  This would build automaticity in the students’ knowledge of the term and its meaning.  Below are examples of some triangle terms.

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Although this type of thinking may seem elementary, there are huge benefits to using it.  It would engage some of the students who are kinesthetic learners or “bored” in geometry class because they would be up and moving.  It encourages math conversation, creative thinking, and could be a game changer for some of my special education students who learn differently.         

   

Variations on a Theme

Module 5: Assignment #2

Below is my version of “Don’t Stop Believin'” by Journey.

My definition of creativity is continuing to evolve after rewriting this song.  My interview with Christen sparked the change in my ideas and now I really feel that creativity is a skill that everyone has the potential to strengthen.  I love how simple Steve Jobs puts it as, “Creativity is just connecting things” (Henriksen & Mishra, 2014).  Creativity to me is not something given, but something to be nurtured and developed.

Choosing a song to rewrite was a challenge.  I started rewriting a Taylor Swift song and changed to a Backstreet Boys song.  I concluded that I needed a very familiar song in order for me to keep the melody and rhyming similar to the original.  I changed almost all of the lyrics and only left a few words.  I really enjoyed this process and saw potential in using a similar activity with my class.  During student teaching I had my fifth graders rewrite lyrics to any song and relate it to an explorer.  They loved it and I found the music helped the content stick for them.  In Geometry this may be more difficult, but I think it would be worth a shot!

Henriksen, D., Mishra, P., & the Deep-Play research group (2014). Twisting knobs and connecting things: Rethinking Technology & Creativity in the 21st Century. Tech Trends, (58)1, P. 15-19

How Do I Love Thee? Abstracting

Module 4: Assignment #1

How would you define abstracting?  This complicated topic can be boiled down into one sentence for me.  Abstracting is not looking at something in its entirety, but focusing on one feature or viewpoint of it.  An abstraction may represent specific properties that are not obvious when viewing a whole object.  The goal of abstracting is to find “minimum visual stimulus that can be put on paper or canvas and still evoke recognition without spelling everything out” (Root-Bernstein, 1999).

Abstracting plays a very large role in the field of mathematics.  Although we always say that math is “real”, much of the work we do is not obvious.  We use abstract symbols, numbers, and equations to represent concepts.  Before practicing this cognitive tool, I chose to keep working with the Pythagorean Theorem as the formula is very confusing and foreign to most students.

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To many, this abstraction is just a photo of the famous, “Sparty”, found on the campus of Michigan State University.

I focused on the hypotenuse in a right triangle and how it is formed.  I considered the “real life” problems where students solve for the hypotenuse of a tree’s shadow or the distance between two points.  As I searched through my phone, I looked for something I could connect those ideas to.  I stopped when I got to a picture of my MAET group picture from this summer.  Whenever I look at this statue I am drawn to his eyes.  If that were one of the endpoints of the hypotenuse you could put a point anywhere around him to create a hypotenuse.  You could put one on the ground, a person, a piece of grass, etc. and calculate the distance using the Pythagorean Theorem.  You would just need to know the height of the statue (from ground to his eyes) and then measure from the endpoint to the base.

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My second abstraction took a long time to come up with.  I know that the idea of the Pythagorean Theorem came to Pythagoras as he was looking at a tile pattern.  I chose to create some graphic art expanding on the basic ideas that Pythagoras used from the tiles. I started with my graph paper and only used 45-45-90 triangles to keep it consistent as each hypotenuse is double the two legs.  I placed my focus on that and traced only those lines, not the triangles themselves.  As I worked I thought of Tetris and wanted to flip my figures around to piece them together.   I traced my final image and highlighted the triangles to show others where the figures came from.  I am curious to see what images I could produce using 30-60-90 triangles.

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By narrowing my focus to the hypotenuse of right triangles I could think of the Pythagorean Theorem in a new way.  I am proud of my work and realize how this may help my students.  Abstracting allows students to deepen their understanding by viewing specific parts of something instead of the whole thing.  They may see new relationships, create images, develop meaning, or relate to a content area in a way that is not possible otherwise.

Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.

How Do I Love Thee? Patterning

Module 3: Assignment #1

Right triangles are a key topic in Geometry and relate to many other concepts that we cover including the Pythagorean Theorem, volume, area, proofs, and trigonometry.  It is important that students see patterns in figures in order to solve problems and proofs in Geometry.  When I thought of existing patterns with right triangles I immediately thought of special right triangles.  We usually cover this idea after learning the Pythagorean Theorem with some direct instruction on the shortcuts to the figures you see on the left below.  The shortcuts are x – x – x root 2 for 45-45-90 triangles and x – x root 3 – 2x for30-60-90 triangles.

We don’t spend a lot of time going over where the shortcuts came from.  Students are just expected to memorize the shortcuts and be able to use them, which is really hard for some students.  I think it would be even more effective to have students explore the patterns themselves.  In the chart below I displayed these patterns that the shortcuts come from.  For example, since the Pythagorean Theorem states that a squared plus b squared equals c squared we know that in a 45-45-90 if each congruent leg was one unit long, the hypotenuse would be the square root of that sum, 2.  This continues for any 45-45-90 triangle.

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In addition to the exploration, students should come up with their own patterns because “making patterns for oneself is a lot more fun than memorizing” (Root-Bernstein, 1999).  I noticed that the some of the numbers and vocabulary terms with special right triangles rhymed so wrote a little chant or poem.  It has patterns in the way I decided to write it as well as what it represents.

It was very difficult for me to explore and find some new patterns using right triangles and the Pythagorean Theorem.  I had to really push myself to plug in some numbers and play around with the theorem.  Using the chart below I plugged in the same number (1) for the a value in every triangle.  I then took my previous c value as my b value for the next triangle. To be completely honest, I saw there was a pattern, however I didn’t know what it meant.  I went to Google and found out my answer within a few minutes of searching.  There were tons of images, like the shell I drew below depicting the exact pattern I had found.  Amazing!

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This process of patterning is can be difficult, but is important for any learner.  Through this assignment I not only gained experience patterning, but gained a deeper understanding of my content as well.  I think too many times students are just memorizing information to get by and pass the test.  As teachers we need to foster deeper learning and understanding through cognitive tools like patterning.  It is natural to look for patterns all around us, let’s not lose that when teach our students.

Root-Bernstein, R. S., & Root-Berstein, M. (1999). Sparks of Genius: The 13 Thinking Tools of the World’s Most Creative People. Boston, MA: Houghton Mifflin.

Defining Creativity

imagine-creativity-16636424-400-300Module 3: Assignment #2

I chose to interview my friend, Christen, an art teacher in Rockford, Michigan.  Last year she taught art to students in grades K-12th.  This year she is teaching Pottery 1 and Design 1 at Rockford High School.  Design 1 is a pre-requisite art course that offers a mix of experiences with clay, drawings, painting, and sketching.

Christen believes creativity is the ability to make something, our human instinct.  Since the beginning we have been makers and creativity is us expressing ourselves, “adding our own flair or originality”.  Christen’s creative process involves drawing a series of sketches before painting, drawing, or making a ceramic.  For her students, Christen allows for this “planning” part of the creative process.  Students are expected to create 4-8 sketches since this brainstorming of different ideas may uncover a better idea.  She has conversations with her students in order for them to think their ideas through.  Communicating ideas before starting with clay or another material may spark something new.

Christen said that, “planning and thinking are more important than doing and making” which echoes Mishra’s value of the process not the product.  There are requirements for assignments, however students are encouraged to make their project their own and go above and beyond.  She uses a rubric, pictured below, for almost every assignment in her classes.  This echoes the idea that “as educators we have to develop better measures and rubrics to speak coherently and systematically about the creative products that students develop” (Mishra and Henriksen, 2013).  Rubrics allow for flexibility, self-evaluation, and improvement.

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Photo Credit: Christen Woodruff

She also enjoys photography and watercolor painting because you go with the flow and make your mistakes fit.  Christen thinks outside of the box when planning events and uses different perspectives when working with people, especially her.


After our interview I think creativity has a larger role in my life as a teacher than I had realized before.  I consider myself a very logical, mathematical thinker most of the time.  With that said, I enjoy art, calligraphy, and other crafty projects where I can be inventive.

I could relate to Christen when she spoke of bringing new ideas and perspectives to a situation in her personal life.  Working with the special education population, especially in math, I am constantly trying to figure out new ways to teach unclear concepts.  I look at it from different angles, write it different ways, and draw pictures until I find something that makes it click for them.  Similarly, as the “problem solver” in my group of friends, I put myself in other people’s shoes to see different perspectives.  You may need to be creative to find a solution to an issue.  It never dawned on me that helping students solve problems (math and personal) would connect to creativity.

I am starting to view creativity as more of a skill that everyone possesses.  It is not something you have or don’t have, but something that can be developed or improved over time.

Mishra, P., Henriksen, D., & the Deep Play Research Group (2013). A NEW approach to defining and measuring creativity. Tech Trends (57) 5, p. 5-13.

How Do I Love Thee? Perceiving

Module 2: Assignment #1

For this project I needed to choose something well-known or familiar from the content we teach, observe it, and re-image it in a new form.  I thought right triangles would be a great image to observe and re-imagine.  Right triangles are a crucial part of Geometry and connect many different topics and ideas together.  Learning about right triangles dates back to elementary school math class, however they still tend to be a tricky concept for students to grasp.  There is so much to learn with their properties including their angles, names of sides, and how to apply various theorems and postulates to them.  As I observed my topic I found it easy to list characteristics and examples, but hard to describe the triangle with “non-mathematical terms”.  As I continued observing I tried to use all of my senses and although this sounds crazy, imagine what it would be like to be a right triangle.

At first I really struggled with re-imagining a right triangle.  It was difficult to “see” the image in another way other than what was in front of me.  As a former college athlete and huge sports fan, I started to imagine myself becoming the right triangle in sport.  I chose to write a basketball poem where I was the right triangle and detailed my multi-sensory experience.  It describes the last few plays of an exciting basketball game where I end up completing a right triangle as the hypotenuse to win the game.

For some readers, this piece may seem to have nothing to do with math or triangles.  I wrote it purposely without any math terminology to give a real life experience.  I sketched a picture of triangle that I see in case someone has trouble visualizing it.  The highlighted portion is the hypotenuse of the right triangle (c).

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This re-imagining process forced me to really step back and look at something that has always been familiar to myself and my students in a completely different way.  By presenting the material this way, I may reach more students and bridge some gaps in understanding.  My head is spinning as I see several possibilities for lesson plans relating the Pythagorean Theorem and right triangles to sports: baseball, soccer, basketball, and football.  The most common question I am asked is, “when will I use this in real life?”  By using re-imaged right triangles for problems in math students will discover that they use this content without even realizing it.  I could have students go to the gym/field and act problems out, or create their own word problems.  Word problems are very difficult for them to understand when no diagram is given.  They also seem fake or scripted in the textbook.  By perceiving and re-imagining we can make math real and bring it back to life for our students.  Perceiving is a powerful cognitive tool that we need to bring into the classroom more often.  By using all of our senses we can discover new meanings, experiences, and a deeper understanding beyond what is there on paper.