CEP 812: Problem of Practice

This week our task was to choose a problem of practice and illustrate how a digital tool would address the problem. The problem of practice I chose to address in my geometry classroom is classifying and proving quadrilaterals. I believe this is an ill structured problem because there are several important variables that need to be considered, in context, at the same time. That is, students must make connections to prior learning and using reasoning skills to formalize definitions, make conjectures, and write proofs. In the screencast below I will show how using the interactive math software, Geogebra is much more effective for teaching quadrilateral properties and how it allows learners to explore more diverse learning scenarios.

Maker Kit Lesson #2 UDL

Part #1: This week we spent a significant amount of time learning about Universal Design. After we read the UDL guidelines and explored free tools online, we used what we learned to modify our  original Maker Kit Lesson Plan to include elements that support the UDL framework . The revision process entailed focusing on how I could minimize barriers and maximize learning by implementing multiple methods of representation, expression and engagement in terms of what I wanted my students to learn and care about. Embedded you will find my modified lesson plan. To see what changes were made, check out my original lesson plan and read my reflection underneath the document below.

Part #2: Reflection

After reading the UDL Guidelines published by CAST Center, I felt slightly overwhelmed by all of the details. For each of the three principals there were several guidelines and within those guidelines there were several checkpoints with various implementation examples. However, after analyzing my notes and original lesson plan, I found that I had actually included several of the UDL components in the activities I originally planned; I just hadn’t specifically stated them as supports. I was surprised to find I could show evidence for at least two of the teacher implementation examples on most guidelines. With that said, UDL is intended to increase access to learning for all students by reducing physical, cognitive, intellectual, and organizational barriers, and although I am confident I provided options and supports, I did realize that I hadn’t considered all learners while planning. I left out supports for HI students, CI students, and ELL students. So, the goal for my lesson plan rewrite is twofold: to go back and add specific details regarding the options and supports that I already have in place and to implement tools and supports for students who are CI, HI, and/or ELL (because I teach students with those specific impairments I am choosing to focus on them).  Moreover, I believe that the changes made for those specific impairments will actually help students without disabilities as well, kind of like how wheelchair ramps also service individuals with strollers or luggage.

My lesson plan is A LOT more detailed and looks different in format. I started by downloading the UDL lesson plan format and copied what I had from my original lesson plan into their design. I added a few boxes to their design that they didn’t have because I felt they were important components and the UDL Guidelines did stress the importance of short and long term goals, which is why I added a box that shows what they learned, what they are currently going to learn, and what they will learn in the future. I also added a box for materials because it is a cooperative learning lesson and the materials were improved to provide supports that would remove barriers, such as headphones for text-to-speech. Aside from that, my lesson plan is true to their format. I really believe this helped me refocus my planning and re-writing because I had to consider what background knowledge my students should have and how I could help them make connections.

In my original lesson I planned for an exploratory cooperative learning lesson & as explained in my original post, the content actually allows for students to learn in way that it makes sense to them.  Moreover, by focusing on constructivism and choice theory, I found that my original lesson actually covered most of the 3 principals in the UDL guidelines. By paying close attention to the teacher implementation examples for each guideline I naturally began to consider small details that I may have left out, such as print documents for all auditory components I use or visuals to support vocabulary and/or instructions. By exploring online resources and reading about UDL before rewriting my lesson, I was able to easily identify barriers that existed in my original plans and I had a better handle on the supports available to remove those barriers. If you read through my new lesson, you will see I added a ton of support for hearing impaired students, ELL, and students who are cognitively impaired. I used the ideas I learned about on the free resources page we explored. Read my tweet!!

In terms of multiple means of representation, the goal of my lesson is to learn how to write a two-column proof, so there isn’t much autonomy in the structure of their written proofs. However, as I stated in my original post, the path that each learner takes to complete the proof is NOT linear. There are choices each step of the way…that is the beauty in mathematical proof. With that said, to help learners understand that there is not one right method to write a proof, even if it regards the same exact visual element, I added the “driving directions” analogy to my lesson plan (you can read it in my new and improved plan). The UDL guidelines suggest that analogies and metaphors help learners make connections and assimilate new information. I did, however, add additional presentation options, different methods of taking notes for reflection, different methods of communicating and receiving feedback, and alternate methods for viewing and playing with circuits (online switchboard/drawn out circuit). I believe that the original lesson plan included appropriate levels of challenge and support, so, in the rewrite, I focused on providing more options and descriptions that would make the existing challenges and supports explicit and accessible to all learners.

By learning about the three primary principals that guide UDL, I was able to rewrite my lesson plans with improved goals that were specific to the purpose, with differentiated teaching methods that provided support and matched the goal, with materials necessary for learners to access, analyze, organize, synthesize, and demonstrate understanding in varied ways, and with informed assessments that accurately measured learner knowledge, skills, and engagement. You can read about each of these specific changes in the actual lesson plan above. 

This weeks activities helped me re-think my teaching practices and supports. I have hearing impaired students that I wear a microphone for, but I hadn’t really considered all of the other supports they could potentially need that would help their classmates as well. The same idea goes for my ELL and CI students. I have some curriculum redesign ahead of me!!

References

CAST (2011). Universal Design for Learning Guidelines version 2.0. Wakefield, MA: Author.

Ultra Micro MOOC: Knitting a Scarf

Our task this week is to design an “Ultra Micro MOOC” that teaches a specific skill or technique to a target audience.  MOOC stands for Massively Open Online Courses. These courses, offered on websites like P2PU, are changing the face of education and learning. The courses are free to virtually anyone who wants to participate and has internet access. Certificates of completion are award to individuals who complete the course requirements. Although I wasn’t able to actually create a MOOC, I have put together an outline of what one would look like if created. Enjoy!

In my “Keeping Warm One Stitch at a Time” course, my peers will master the basics of knitting a scarf by progressing through a series of mini lessons and sharing updates on their progress and problem solving techniques with their peers online.

Course Topic: Introduction to Knitting

Course Title and Photo: Keeping Warm One Stitch at a Time

Untitled 2 copy

Photo: Licensed Under CC License 3.0

Who is coming to your course? Why would they want to participate in this experience? This course will attract individual of all ages who are interested in a creative outlet for a multitude of reasons, no experience necessary. When people hear the word “knit” they often envision a group of grandmothers, sitting in rocking chairs, knitting pastel colored snowcaps, complete with a fluffy pom on top. However, knitting has been redefined in the 21st century as a creative-DIY outlet for all individuals: old, young, male, female; no experience necessary. Learners will be attracted to the experiences this course will provide for a multitude of reasons unique to their individual motives. While the final knitted product is often the goal, it is typically not the reason why individuals choose to learn to knit. Knitting is not a one-size-fits-all hobby. Some knit to give: to charities, babies, people in need, friends, etc. Others knit for themselves: for social networking, for fashion, for therapy, for accomplishment, for tradition. Regardless of whether you are knitting angry knots or joyful knots, knitting is a timeless, creative outlet and/or hobby that fulfills the various needs of learners on an individual level- it’s comfort food without the calories. Knitting is a creative problem solving process that turns boring things into interesting things and often provides feelings of contentment along the way. This course provides an entry point into the creative world of knitting. In this course learners will learn the basics of knitting by creating a scarf thus increasing their skill level and interest to a point where they can seek other creative knitting options.

What do you want learners to be able to do when they are done? The learners will be able to knit a scarf by the end of the MOOC. More specifically, by the end of the course, participants will be able to cast on the stitches that are necessary to begin their scarf making process, knit additional rows to create a desirable length-counting stitches along the way to ensure they haven’t dropped any stitched, cast off their stitches to complete their scarf, and add fringe for as a creative touch. Each lesson is scaffolded (Vygotsky, 1978) to help participants reach mastery learning, as discussed by Bloom (1974). Knitting is a great example of mastery learning because individuals must master individual skills in a logical, planned progression, such as casting on, knitting rows, casting off, then adding fridge, which when put together create their final product (Yelon, 2001).  One great thing about knitting is that no matter what your skill level may be, once you have mastered the basic stitch, it is possible to knit an entire scarf. Through practice and experience, the skill can be mastered.

Knitting is a learning activity that is grounded in constructivist principles (Piaget, 1971).  It requires learners to problem solve as they progress and create.By allowing students time to experiment and observe before they analyze and deduce, the learners will be able to see the “big picture” and how their progression relates to the overall goal (Dienes, 1969, p.32). This idea can be see in the work of Dienes (1969) and his theory for learning mathematics. Moreover, the lessons in m MOOC are set up with the end in mind. That is, the lessons are laid out in the most effective way for achieving each specific goal along the way in terms of how they relate to the final goal: a knitted scarf (Wiggins, 2005). The logical progression will help students see the purpose for each lesson and how to appropriately problem solve when they make a mistake. For example, it is typical for beginners to drop stitches as they knit; however, since they are actively engaged in their learning process, they are aware of their overall goal, and because the lessons have been scaffolded to support such errors, they will learn how they can fix their mistakes without starting over completely (Piaget, 1971).  By planning each lesson this way, the teacher is able to predict misconceptions and plan activities accordingly (Wiggins, 2005, pg. 13). The lessons in my MOOC also provide periods of reflection and online discussion that allow individuals to learn from their peers, provide feedback to their peers, ask for feedback, and share their work. Through this process, thee learners will make connections within their observations and their peers’ feedback in terms both relate to their experiences and their overall progression towards the end goal (Polya, 1957).

What will peers make? The final product for this MOOC will be more than a scarf. The peers will be required to make a video reflection that shows they have mastered each individual task (casting on, casting off, basic stitch, fridge) necessary to reach the final goal: their completed scarf. They will reflect on the problem solving progress along the way. The video will be posted to the course discussion forum and members of the group will provide feedback on at least one other person’s video reflection.

How do those activities hang together as a course? How long is your course experience? This course is a self-paced course that runs for approximately 6 weeks and is driven by the learning theories and practices discussed above.  Tasks and projects will be implemented to ensure learners master the following skills: casting on stitches, knitting using the basic stitch, casting off stitches, and adding fringe. Moreover, practice of new skills will need to occur between each lesson to ensure the learner has reached mastery and can use the skill as a foundation for the subsequent skill (Yelon, 2001). The course will consist of diagrams and videos to support students as they learn how to knit a scarf. The course will also utilize a discussion board as means to: ask questions, post assignments, reflect, seek feedback, and provide feedback. The tasks for each week of the course are outlined below.

Course Outline

Introduction: There will be a video introduction that discusses the various purposes for knitting. The learners will be exposed to the final goal, the steps they will take to reach the goal, and the final product of how they will present their learning and mastery. This lesson will discuss the materials needed to knit a scarf: yarn, needles, & Internet access and will briefly discuss the time commitment for each lesson.

 Lesson 1: Setting Goals

This lesson will begin by having learners choose the size of their needles, the type of yarn they would like to use, the length they would like their scarf to be and the width they would like their scarf to be. The lesson will provide information on how the size of the knitting needle affects the scarf. The lesson will also briefly discuss types of yarn and where supplies may be purchased.

Lesson 2: Casting on Stitches

This lesson will teach learners how to cast on stitches using the “backwards loop cast on”, which is often the most difficult task for beginners learning to knit. Casting on is the process of adding the very first stitches onto the knitting needle before starting to knit. The lesson will provide diagrams on how to successfully cast stitches on to a knitting needle using the backwards loop method. The steps show learners how to create a slipknot, how to place the knot on a knitting needle, how to hold the yard and the needle, and how to add additional stitches. The learners will be required to take the stitches off and practice the task several times. They will decide how many stitches they want for their scarf (depends on how wide they want it). By the end of this lesson the learner will have mastered casting on stitches and will be ready to add additional stitches next week. There will be a discussion board forum where learners will post a picture of their stitches on the needle. Learners can also use this forum to seek feedback from the instructor or their peers.

Lesson 3:  The Basic Stitch

This lesson will show learners how to add stitches to the row they added in the previous lesson. There will be a video tutorial and diagrams. The learners will be required to drop a stitch, which is a typical error when knitting, and learn how to fix it. They will practice unraveling the bad row of stitches and fixing it. The learner will provide a video that shows they have mastered the basic stitch and can fix a dropped stitch.

Challenge Lesson: Adding Stripes or Colors

This lesson extends the technique of the basic stitch by adding color (doubling up yarns) or adding stripes (switching out yarns). This lesson is intended for learners who are confident in their knitting, have mastered the previous skills, and are looking to add a creative touch. There will be a video tutorial for this lesson. This lesson is not required.

Lesson 4: Casting Off

This lesson will teach learners how to successfully cast off their last row of stitches to create an edge that will not unravel. If done incorrectly, the scarf will unravel. The task will require learners to create a swatch that they will practice casting off on. This will ensure they have mastered the task before they attempt to do it on their scarf. The learners post a photograph of the swatch on the discussion forum and reflect on their problem solving process.

Lesson 5: Your Creative Touch- Adding Fringe & Reflecting

This final lesson will show learners how to add fridge to their scarf through diagrams. All learners will add fringe, but will understand that it is not necessary for their future projects. The learners will post an overall reflection on the discussion forum, they will respond to their peers reflections, and they will begin putting together a plan on how they will complete their final project.

Final Project

The learners will create a video reflection that shows they have mastered each individual task (casting on, casting off, basic stitch, fridge) necessary to reach the final goal: their completed scarf. They will reflect on the problem solving progress along the way and how their mastery of each lesson helped them on the subsequent lesson. They will also share insights and tricks they learned during the process. The video will be posted to the course discussion forum and members of the group will provide feedback on at least one other person’s video reflection.

“Staying Warm One Stitch at a Time” by Kristen Dyksterhouse is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Resources

Bloom, B. S. (1974). An introduction to mastery learning theory. In J. H. Block (Ed.), Schools, society, and mastery learning. New York: Holt, Rinehart & Winston.

Dienes, Z. (1969). Building up mathematics. (rev.ed.) [Print]. London: Hutchinson Educational.

Piaget, J. (1971). The psychology of intelligence. [Print].  Boston: Routledge and Kegan.

Polya, M. (1957). How to solve it. (2nd Ed.). New York: Doubleday.

Vygotsky, L. (1978). Interactions between Learning and Development. In Mind In Society (M. Cole, Trans., pp. 79-91). Cambridge, MA: Harvard University Press..

Wiggins, G. and McTighe, J. (2005). Understanding by Design, Expanded 2nd Edition.  Prentice Hall.  pg 13-33.

Yelon, S. L. (2001). Goal-Directed Instructional Design: A Practical Guide to Instructional Planning for Teachers and Trainers. Michigan State University: Self-published, Not in electronic format.

Maker Kit Lesson Plan

This week our goal was to create a lesson plan that connects learning theories with our Maker Kit. Right off the bat I had no problem connecting Choice Theory (and other learning theories) with my Maker Kit, Squishy Circuits. However, the biggest problem I faced was the interdisciplinary connection between science and mathematics, which seems weird because the two are so closely related. After tinkering and imaging how I could use my Maker Kit in my classroom last week, I came up with several possibilities of how I could implement Squishy Circuits into my curriculum. If I had more tools in my Maker Kit I could build a logic circuit and have students explore truth-values for conditional statements, which would be my first pick. Also, if I had a better handle on circuits, I could’ve had students explore graphing shapes and translating them on the coordinate grid, since we will re-visit coordinate geometry in the near future. I also tried to explore Graph Theory using LED lights as vertices, but I couldn’t figure out how to make it work & make sense. While I managed to come up with a game, I felt like it was a stretch and that I could play a similar game in class without circuits that was just as beneficial but took less time to set up. With that said, after reflecting on my learning process, I decided that making circuits is a lot like constructing a proof.

A mathematical proof is an argument that begins with known facts, proceeds from there through a series of logical deductions, and ends with the thing you’re trying to prove. There are several intermediate conclusions—if I do this, then I get this—that lead to the final conclusion. Similarly, when building circuits, we are given a battery pack, a light emitting diode (LED), a motor, and two buzzers (similar to the picture we receive in a geometric proof). Along with the given materials we have to make sense of circuits using with background knowledge or basic facts: conductive dough lets electricity pass through it, insulating dough does not allow electricity to pass through it, electricity is directional-the current runs from positive to negative, the LED, motor, & buzzers are directional- they have a positive side (the longer leg on the LED) and negative side (shorter leg on LED), and a circuit has to be closed (a continuous loop). From here, we have to have to use what we know to create logical steps that help us reach our conclusion or what we are trying to prove.

As I was building my first simple circuit, I realized that if I did something wrong, like put my LED in backwards (so the positive and negative leg were flipped), the LED would not light up because the circuit was not closed. Likewise, we can use unnecessary information in mathematical proofs that direct us away from our conclusion. Building a circuit is a procedural, logical process much like geometric proofs. Thus, for my activity, as an introduction to proofs I would have my students play with circuits and write a two-column proof for each of their steps towards creating a more complex circuit using the motor, several LEDS, and both buzzers.  This activity seems more practical than the game I created last week and it fits better into my curriculum.

Connection to Learning Theories:

The guiding principles explored in my lesson plan [above] are driven by Diene’s Theory of Mathematics Learning, Choice Theory (Glasser), and constructivist principles. This framework allows learners to take learning from a noun to a verb. It compels learners to think critically within a metacognitive framework that requires them to formulate the problem and reflect on their thinking. Further, by blending progressive pedagogy with modern tools and resources, such as Squishy Circuits, my learners will achieve the skills they need to become innovative, original thinkers.

Writing geometric proofs is about connecting the dots. We have a starting point and an end goal, yet we somehow have to logically fill in the middle so that it gets us to the end (Ryan, 2008, p.49). It’s kind of like giving a friend directions to your house. The coolest thing about proofs is that there isn’t one correct way to reach the destination. You can have them take the back road shortcut, the city streets, or the scenic route. However, regardless of the route you give your friend, if you leave out a step or are too vague, you risk them getting lost. If you think about it, it would be nearly impossible to give someone directions to your house if you have never driven there yourself. You have to experience and understand what you are trying to communicate before you can write it in a logical organized manner. So, you have to play and experiment, make note of your observations, then order your findings logically, filling in the gaps as you go. The squishy circuit activity allows students to do just that. The lesson allows for students to experience different ways of building circuits, make conjectures and observations about how circuits behave, and then go back and write their findings in such a way that not only shows why their process is true, but also allows others to see why their process is true.

This process, in accordance with my squishy circuits lesson plan, is supported by several learning theories. In terms of learning math, Dienes’ Constructivity Principle simply states that ‘construction should always precede analysis’” (Dienes, 1969, p.32). Likewise, in the lesson with squishy circuits, learners are given “play time” to experience and observe before they begin to analyze and deduce. This process allows students to see the “big picture” in a way that fits their unique needs and abilities. Similarly, Dienes’ Theory for learning mathematics states: “When children experience a concept in more than one embodiment, they are more likely to conceive the mathematical generalization independent of the material” (Dienes & Golding, 1971, p.47, 56.). By allowing students to play with something tangible, like squishy circuits, they will be able to form an informal process for writing proofs that is unique to their personal needs. That is, the learners will gain an understanding of how to construct a proof before they actually get a formal definition of what a proof is.

In lieu of learning the learning process, Dienes’ Constructivity Principle (1969) closely aligns with Piaget’s work in that they both imply learning requires embodied experimentation, play time, group work, individual reflection, teacher as facilitator, and student responsibility/ownership. Learning is not a spectator sport. In order to gain conceptual understanding learners must experience diverse learning and make connections between old and new. By using the constructivist approach as a foundational framework in my planning, I was able to ensure that my squishy circuits lesson gave each learner the opportunity to explore and create his or her own understanding through differentiated instruction at a level that makes the content meaningful (Piaget, 1971). For example, as creative problem solvers they will make qualitative and quantitative observations as they build the circuits. Then, they will organize their observations to make sense of their findings through tables, graphs, or other visual representations, which equates to the activity where they write steps with explanation. Finally, they will make connections within their findings and to their previous knowledge by reflecting on the experience (Polya, 1957). In essence, their learning will build on what they already know and will establish new or more extensive relationships within their mental frameworks. Consequently, as learners begin to write mathematical proofs, they will make connections to their squishy circuits proof writing process and use that experience as a foundation that they can build from. This problem solving process is not only relevant to material in the mathematics classroom, it also relates to problem solving skills needed in real life situations and is highly associated with critical thinking skills.

Further, this theory suggests that if the student is given the opportunity to interact with others and question new ideas, they will move from the known to unknown. I personally experienced this during my playtime last week. I really started making progress and understanding circuits when I had my roommate and her boyfriend there to discuss ideas and complications with me. For this reason, my squishy circuits lesson allows the learners to play with the circuits and collaborate in cooperative learning groups, which will help them build of each other’s experiences. Perhaps they will make mistakes within this process, but by accommodating what they thought to be true with what they have found to be true, they are learning from their mistakes and experiences. Moreover, during the creative problem solving process (circuit making) I will act as the facilitator. I will be passive and the learners will be active. By implementing carefully designed partner activities and periods of reflection throughout my lesson, I will be able to create a classroom climate, a “math lab” if you will, that supports experimentation, discovery, and play, while providing learners with choice, which leads me to my final point (Reyes & Post, 1973).

Lastly, this learning model suggests that learners need to have choice in the process. In the squishy circuits lesson, learners will have choice to construct and play with circuits as they please, choice to write their process as it makes sense to them, and choice to create a “masterpiece” that interests them to present to their classmates. In turn, students will feel empowered and will be intrinsically motivated, which aligns with Glassner’s Choice Theory (Corey, 2012, p.402). When learners have a say in what and how they learn, they take control of their learning and achieve a sense of ownership. They will become the teacher when they explain their final product to the class. Their demonstration will show how they consolidated several concepts throughout their playtime and will convey their new understanding of the material.

By using these theories as a foundation for my lesson, I am confident I will be able to appropriately respond to the diverse, intellectual needs of the student body as well as the needs of individual learners who are culturally, socially, and economically different, too. The most rewarding thing that a lesson like this has to offer is seeing the creativity learners bring to mathematics. Processing information, making connections, reflecting, and learning through constructivism are qualities of creative problem-solving mathematicians and innovative learners and defines the educational ideology of the 21stcentury.

References

Corey, G. (2012). Theory and practice of group counseling. (8th ed.) [Print]. Belmont, CA : Brooks/Cole

Dienes, Z. (1969). Building up mathematics. (rev.ed.) [Print]. London: Hutchinson Educational.

Dienes, Z., & Golding, E. (1971). Approach to modern mathematics. [Print]. New York: Herder and Herder.

Piaget, J. (1971). The psychology of intelligence. [Print].  Boston: Routledge and Kegan.

Polya, M. (1957). How to solve it. (2nd Ed.). New York: Doubleday.

Reys, R. & Post, T. (1973). The mathematics laboratory: Theory to practice. [Print]. Boston: Prindle, Weber, and Schmidt.

Ryan, M. (2008). Geometry for dummies (ed. 2). [Print]. Hoboken, NJ: Wiley Publishing, Inc.

The Squishy Circuits Lesson Plan may be distributed, unmodified, under the Creative Commons Attribution, Non-commercial, No Derivatives License 3.0. All other rights reserved.

21st Century Lesson Plan: Surface Area & Volume of 3-D Figures


PowerPoint for Lesson:

http://portal.sliderocket.com/BQZYU/Volume_S_A_Pop

Lesson Plan:

___________________________________________________________________________________________________________

(Rationale & Connections to Reading are included in the Lesson Choice & Technology Paragraphs)

Lesson Choice: I chose to create a lesson for my Geometry Support class. The curriculum we use for our Geometry classes doesn’t allow for much implementation outside of the program and the pacing is already pretty fast, so I opted to go with the course that allowed me the most flexibility. The common core standards are aligned to grade 8; however, the 8th grade standards provide a foundation for the high school standards, which address more complex ideas using 3-D figures. This lesson will help the students consolidate their learning, prepare them for the geometry lessons to come, and provide them with a real-world problem finding/solving scenario.

About the Lesson: I chose to do a three-act math lesson plan. Dan Meyer (2013), one of my all time favorite math bloggers, created the curriculum idea. His rationale is that math is a lot like storytelling, and most stories divide into three acts, each of which maps onto a mathematical task. This is how it works:

  • Act 1: Introduce the central conflict of your story/task clearly, visually, viscerally, using as few words as possible. Students will become problem finders. They will be curious and pose a question about what they are wondering.
  • Act 2: The protagonist/student overcomes obstacles, looks for resources, and develops new tools. Act 2 is not the teacher’s job; the student takes control. However, the teacher may become one of many resources or tools students choose to utilize.
  • Act 3: Resolve the conflict and set up the sequel. The third act must answer the motivating question in act 1 and pay off the hard work in act two.

Dan also talks about the importance of extension problems and the “what’s next” in terms of a sequel (Meyer, 2013). I think the sequel is really the best part of this lesson. I came up with an extension activity where students would create a new package for a product to present to a company; however, students may also come up with great extension activities. There are endless opportunities for the sequel, which opens the door for great classroom discussions.

The ideas behind three-act math lessons were the building blocks, or driving forces if you will, for my lesson plan on surface area and volume. Bransford, Brown and Cocking (2000) address the importance of providing learning opportunities that spark learners’ curiosity in such a way that they want to further explore the ideas (p.18). I believe that act one of this curriculum design does just that. It captures the students’ attention and naturally allows for them to wonder about the problem at hand. They are not handed over the problem; they identify what the problem is. They become innovative thinkers and problem finders. Act two requires learners to be aware of what they know and how they may use it. It also scaffolds learning in such a way that they know when more information is needed and how to find (Vygotsky, 1978; Palinscar & Brown, 1984).

The best part about three-act math is that the video does much more than a textbook problem can. Even the greatest textbook problems have to provide or pose a question at some point. By using a video, I can provide a concrete scenario that forces students to inquire about something or establish a problem. Textbooks, at best, could provide a problem about volume and pop cans where the problem has already been abstracted, which robs students of the skills needed to formulate and solve problems. Traditional textbook problems don’t really even ask students to solve a problem at all. Generally, they provide a question and scenario where all of the information is given, it just has to be plugged into a formula (found two pages back) and computed. The trouble with this approach is it doesn’t require learners to think critically. Really, can you think back to a time where you solved a meaningful, worthwhile problem where you knew all of the necessary information beforehand? Probably not, because in most meaningful problems we encounter, identifying what the actual problem is is half of the battle (Meyer, 2013).  For these reasons, I believe this three-act math lesson encompasses each of Renee Hobbs’ five core competencies as fundamental literacy practices (Hobbs, 2011, p.12).

Three-act math also aligns with the learning environments discussed by Douglas Thomas and John Seely Brown (2011). Specifically, in act two, the students are generating content that represents their learning. Then, in the sequel, students are using play and creation to explore packaging efficiency and costs. Ideally, they would go on to create a package for a company (p.91-99). They are being innovative and creative. In the article, Need a Job? Invent It, Thomas L. Friedman (2013) interviewed Tony Waggoner, a Harvard education specialist. Waggoner discussed the idea solving problems or bringing new possibilities to life and/or companies as what will bring new generation employees from the disappearing middle-class job to the high-wage, high-skilled job of the 21st century (Friedman, 2013). I believe that the mathematical tasks within each act contain the skills needed to successfully live and thrive in an ever-changing world.

Technology Incorporation: Although I didn’t plan for it, this lesson uses several of the digital technologies listed on The Center for Learning and Performance Technologies list of the 100 Best Tools for Learning. I used iMovie to create Act 1 & Act 3. iMovie is something I have worked with before, so it wasn’t new. However, I felt like it was the best option for combining short video clips, pictures, and sounds to create the videos I needed for my lesson plan. I used PowerPoint, SlideShare, and SlideRocket to create and embed this presentation into this post. I used PPT to create the presentation; however, since I had videos in the presentation, the online uploading and sharing became difficult. I initially was going to use SlideRocket, but it told me my account and files would be deleted in 80 days because they were upgrading, so I decided to create a SlideShare. Creating a SlideShare was easy and quick, I just had to upload my PPT file. After previewing the presentation on SlideShare I noticed it didn’t preserve the video properties, it turned them into pictures. I read that SlideShare didn’t have video capabilities, so I went back to SlideRocket. At least I have 80 days to find an alternative. SlideRocket is great for uploading presentations that have sound, videos, and other forms of multimedia. It is something I used once in the past and it worked great for this presentation. I am sad to see the site go away. Within the presentation, I used Google Conversions to provide content necessary for the students to complete the task. Douglas Thomas and John Seely Brown (2011) suggest that students must focus on knowing where to find information rather than knowing the information (p.91-99). While planning my lesson, I reflected on what information I should give my students, information that is widely available, and what information I wanted them to know and build on. This forced me to identify what the real purpose for the lesson was. Did I want my students to memorize or recall formulas? Or did I want my students to know when and how to apply formulas. Going with the latter of the two, I decided to give them the conversions and formulas they needed, but only after they realized the need for them. That is, I didn’t tell them this is the formula you need to use now, but instead, when they realized they needed to make a conversion or use a formula, I provided the information for them.  The last piece of technology I used was Scribd. Since most websites do not preserve formulas, I saved my lesson plan as a PDF and uploaded it to Scribd, which was easy to embed right on my site.

References

Bransford, J.D., Brown , A.L., & Cocking, R.R. (Eds.). (2000). How people learn: Brain, mind, experience, and school. Washington, D.C.: National Academy Press.

Friedman, T. L. (2013, March 30). Need a job? invent it. New York Times. Retrieved from http://www.nytimes.com/

Hobbs, R. (2011). Digital and media literacy: Connecting culture and classroom. Thousand, Oaks, CA: Corwin/Sage.

Meyer, D. (2013). The three acts of a mathematical story [Blog Post]. Retrieved from http://blog.mrmeyer.com/?p=10285/

Thomas, D., & Brown, J. S. (2011). A new culture of learning: Cultivating the imagination for a world of constant change. Lexington, Ky: CreateSpace.