Personal GAME Plan

“Learning to teach generally, and to teach with technology specifically, are lifelong journeys” (Cennamo, Ross, & Ertmer, 2009, p. 1) As teachers, we must be self-directed learners as we constantly learn about new teaching strategies, new content, and how to incorporate technology in our lessons to prepare our students for their technology based futures.  Our text, “Technology Integration for Meaningful Classroom Use:  A Standards-Based Approach, suggests using the GAME Plan for self-directed learning, which involves setting goals, taking action, monitoring and evaluating professional growth (2009).

The International Society for Technology in Education has identified five standards for “evaluating the skills and knowledge educators need to teach, work, and learn in an increasingly connected global and digital Society” (ISTE, 2012).  Although I feel I have room for improvement in each area, the two areas I will focus on at this time are standard two, and standard five.

Standard Two states that, “Teachers design, develop, and evaluate authentic learning experiences and assessment incorporating contemporary tools and resources to maximize content learning in context and to develop the knowledge, skills, and attitudes identified in the NETS-S”.  It has been a personal goal of mine to incorporate more authentic experiences in my classroom to help my students to make connections with the content we are covering in class to how it relates to the real world.  Herrington and Kervin argue that, “Technology use in classrooms is often employed for all the wrong reasons” (2007, p. 219).  They go on to say, “Technology presents the opportunity to employ powerful cognitive tools that can be used by students to solve complex and authentic problems” (Herrington & Kervin, 2007, p. 219). 

 

Standard Five states:  “Teachers continuously improve their professional practice, model lifelong learning, and exhibit leadership in their school and professional community by promoting and demonstrating the effective use of digital tools and resources”  (ISTE, 2012).

The action I plan to take to accomplish these two goals involves a number of steps.  First, I will continue my Action Research Project I have started through my Walden courses which also covers other areas of the GAME plan.  According to Cennamo, et al, “Action research appears to be a particularly effective way to monitor and evaluate classroom innovations, such as new technology uses” (2009, p. 11) This project focuses on adding more authentic experiences to my teacher repertoire by researching online, connecting with other educators, and attending conferences.  In addition to this, I plan on working closely with my technology department to learn new ways to incorporate technology into my classroom.  I meet with our tech guys on a weekly basis to share what I’m doing and to see if they have suggestions on more effective ways, or ways to extend my lessons. I am also a member of our school’s technology team and as a result, I get the opportunity at least once a year to visit other schools to see first-hand how other teachers are using technology to support their instruction.  This has proven to be very informative and I always find myself rejuvenated and excited to get back into my classroom to try out the new things I have learned. 

In addition to furthering my own professional development, I also strive to share what I have learned through my Walden classmates and professors, as well as my own discoveries, with my technology-timid co-workers.  To convince my co-workers of the positive impact technology can have on teaching, I often share what we are doing in class.  I also work with teachers to see what skills they want to cover, and I suggest ways that they can gradually incorporate technology into their lessons.  With each co-worker I first assess their comfort and skill level and I try to make suggestions that will allow them to be successful, allowing them to gain confidence and excitement for incorporating more technology in their lessons in the future. 

 

In order to stay focused on this goal, I find it is helpful to have a timeline in place. The timeline can help me to identify which months we have professional development, conferences, or a visit to other schools.  My goal is to acquire one new strategy or resource each month and to implement at least one authentic experience each semester.  On the off months I will need to set aside time to research for resources online, or to meet with co-workers either to share ideas, or to assist them with developing lessons with supporting technology.  As I get more of these under my belt, I will increase the frequency of these lessons.  Since I plan to acquire these skills through a variety of methods, it is easy to lose focus at times, so I find keeping a journal is helpful.  “The key to effective reflection is the ability to go beyond a simple description of what happened to consider why it happened, how it is connected to other events, and what adjustments should be made to subsequent actions based on this understanding”(Cennamo, et al, 2009, p. 11).   These reflections will help me to remember the entire process and it will allow me to identify my successes as well as areas that still need strengthened.

As an educator, it is crucial to stay current on technology and how to incorporate it into the classroom effectively.  The GAME plan is a great way to facilitate this process by organizing the steps that teachers take, while helping them to focus on their goals and the steps to achieve them. 

References

Cennamo, Ross, & Ertmer.  (2009).  Technology integration for meaningful classroom use:  A standards-based approach.  (Laureate Education, Inc., Custom ed.).  Belmont, CA:  Wadsworth, Cengage Learning.

Herrington & Kervin.  (2007).  Authentic learning supported by technology:  Ten suggestions and cases of integration in classrooms.  Educational Media International, 44(3), 219-236.  Retrieved from the Academic Search Complete database.

International Society for Technology in Education.  (2008).  National education standards for teachers (NETS-T).  Retrieved from http://www.iste.org/standards/nets-for-teachers  

Wanted: Real-Life 5th Grade Math Activities

Do you have great ways you use real-life activities in your math classroom, or would simply like to learn more about how others do this?  If so, this posting is for you.  

I'm currently a 5th grade math teacher in northeastern Indiana and I'm also pursuing my Master's.  For my graduate courses I must conduct action research and I have chosen to focus on how I can incorporate real-life activities into my classroom to provide meaningful and engaging learning experiences, but I need your help.  

Hopefully, we'll compile a number of great resources we all can use.  

Please reply to this posting to share your lesson/activity idea.  If possible, put the standard/skill in the subject area (or at the top of your message) to facilitate the searching process.  Also, if you have links to sites that already have a number of great resources aligned to 5th grade content and the common core, please list those as well.  

Here is an Overview of the 5th Grade Common Core Standards 

(Additional descriptions can be found at:  http://www.corestandards.org/assets/CCSSI_Math%20Standards.pdf)  

Operations and Algebraic Thinking

• Write and interpret numerical expressions.

• analyze patterns and relationships. 

number and operations in Base ten

• Understand the place value system.

• Perform operations with multi-digit whole 

numbers and with decimals to hundredths.

number and operations—fractions

• Use equivalent fractions as a strategy to add 

and subtract fractions.

• apply and extend previous understandings 

of multiplication and division to multiply and 

divide fractions.

measurement and data

• Convert like measurement units within a given 

measurement system.

• represent and interpret data.

• Geometric measurement: understand concepts 

of volume and relate volume to multiplication 

and to addition.

Geometry

• Graph points on the coordinate plane to solve 

real-world and mathematical problems.

• Classify two-dimensional figures into categories 

based on their properties

Make sure to click on the comment section to share any ideas and to view lessons others have shared. :)

Final Reflection for EDUC-66711I-1 Bridging Learning Theory and Technology

Created at abcya.com/wordcloud/ 

     As my fifth Walden class, EDUC-66711I-1 Bridging Learning Theory and Technology comes to a close, it is time to reflect on how my personal theory of learning has changed since writing it during the first week of this course.  I can't say that my personal theory of learning has changed much, if at all through this course, but I have learned new ways to integrate technology to make learning meaningful and engaging for my students.  

    In my own classroom I incorporate a variety of learning theories and teaching techniques to meet my students' unique needs and to increase the number of times students are exposed to the content.  I put great effort into teaching math concepts to my students using a variety of strategies such as modeling, explaining, using music and kinesthetic movements, along with scaffolding learning to meet the multiple intelligences of the students in my classroom.  I agree with Dr. Patricia Wolfe who states, "The more modalities you use to enter information into the brain, the more avenues you have to retrieve it"  (Laureate Education Inc., 2011 Brain Research).

The learning theory I most closely relate to is the constructivist theory.  It states that knowledge is unique to the individual who constructs it and it relies on the cognitive concepts of inquiry-based learning and social interaction (Lever-Duffy & McDonald, 2008).  Although this is the theory I relate to most, I have found it challenging the past few years to utilize it in my teaching due to changing standards, time limits, and switching grades.  I have had the personal goal to work towards creating more hands-on experiences based on my fifth grade math students' interests to allow them to interact with the content and construct their own meaning.  "Lessons in which students are engaged and invested in goals they helped to create have potential to stimulate and restimulate networks of new memories as students actively process information in the construction of knowledge"  (Willis, 2008, p. 427).

Although I already valued the use of technology in the classroom, this class has supported my opinion that technology plays an important role in the classroom.  "Technology is best viewed as a robust set of instructional tools that help you accomplish the objectives of the teaching-learning process" (Lever-Duffy, & McDonald, 2008, p. 9).  Technology should allow us to do different things instead of just doing things differently.

Research shows that we are limited to approximately seven pieces of information to process at any given time (Laureate Education, Inc., 2011).  Technology can facilitate the learning process by allowing students to focus on the content.  For example, spreadsheets allow students to focus on the solution of a problem allowing for more accurate comparisons instead of expending all of their energy towards accessing the data or making complex calculations.  By participating in a WebQuest students can focus on the content instead of the process of finding the information.  

This course introduced me to a variety of new ways to include technology to enhance my lessons including voice threads, blogs, podcasts, concept maps, virtual field trips, and simulations.  I also attended a conference at the Indiana Association for the Gifted and learned effective uses of voice thread, iMovie, and prezi.  I was most fascinated by how the presenter at the conference uses voice thread as the way his students submit work.  This allows him to grade essays at home without taking home stacks of papers and it also creates somewhat of a portfolio of his students' work, including his video comments.  Although it will take some time to fully implement each of these new technologies in my classroom, I strive to utilize each of these in the coming years, and found myself once again, excited about teaching.  

Our text, Using Technology with Classroom Instruction that Works focuses on nine clusters of instructional strategies.  These strategies are:  identifying similarities and differences, summarizing and note taking, reinforcing effort and providing recognition, homework and practice, nonlinguistic representation, cooperative learning, setting objectives and providing feedback, generating and testing hypotheses, and cues, questions, and advance organizers.  These are common strategies that are utilized in every classroom but are not effective unless students are proficient in using them.  According to the research, identifying similarities and differences was the instructional strategies witha percentile gain of 45 points and Marzano's original meta-analysis, using graphic representation had one of the highest impacts on student achievement (Pitler, Hubbell, Kuhn, Malenoski, 2007).  As a result, I plan to focus on utilizing nonlinguistic representations, and identifying similarities and differences, along with cooperative learning in my classroom.  Once my students and I have mastered these, I intend to extend my focus to some of the other instructional strategies.  

The immediate changes I will make is incorporating and focusing on the mastery of nonlinguistic representations and identifying similarities.  I will also use our Edmodo site as a collaboration tool.  The last few months of school my students and I dabbled with Edmodo and learning of its uses in the classroom.  I posted links and assignments but the students were not using it for classroom discussions.  I would love to use this as a tool to get students to communicate their thinking and to reflect on how what we are learning applies to real life.  "Research indicates that online discussions have numerous advantages-such as promoting students' critical thinking and knowledge construction, and improving students' relationships" (Wang, 2008).  "It is the conversations that the students engage in that really help concretize and help them understand something"  (Laureate Education, Inc., 2011b).

The resources throughout this course have inspired me to improve my teaching by incorporating more technology, so selecting only two long term goals seems very limiting.  Two things I would love to use in my classroom are simulations and robots.  However, it is hard to find math simulations at the elementary level for anything other than money based economic activities, and we simply don't have the funding to purchase robot kits or the software to program them.  So, at this point I would say that my two goals will be promoting technology with colleagues, parents, and our technology department and creating an online math journal or notebook.  

As an educator, it is not only important to utilize technology in the classroom, it is also crucial to be an advocate for educational technology.  Colleagues, and parents need to be shown how the new technologies actually enhance learning.  They need to see how it enables students to do different things that would not be possible without the use of technology.  In addition to colleagues and parents, some technology departments also need some convincing about technologies that are appropriate for students.  For example, our tech representative made the comment to me, "Why do kids need to access the cameras built in the netbooks?"  I was shocked!  I immediately rattled off a number of ways this can be a beneficial learning tool including skyping with experts, or other classes, collaboration, demonstrating knowledge for those who struggle with writing papers or performing in front of the class, and for the creation of voice threads.  

For years I have been trying to figure out how to incorporate math journals in my classroom, but have not found a way to make them organized or fun.  During this class I came up with the idea of having students create an online math journal by creating a group wiki.  This will allow them to add pictures, links to videos or games, and it will allow them to organize the information neatly.  Students can create a page for each standard, such as number sense, or data analysis, and will be able to manipulate the information with ease.  It will also allow them to access the content, provided they have internet access, instead of being out of luck when working on homework and their journal is in their desk at school.  

"Teaching is a systematic, planned sequence of events that facilitates the communication of an idea, concept, or skill to a learner.  The act of teaching requires an understanding of learning and an understanding of the individual and environmental factors that affects the learner" (Orey, 2001).  To best meet our students needs teachers need to incorporate a variety of learning theories, instructional strategies, and technologies in the classroom.  They also need to change their view of mastery from students working independently, to allowing students to collaborate to solve complex problems and construct artifacts.  "To be prepared for the fast-paced, virtual workplace that they will inherit, today's students need to be able to learn and produce cooperatively"  ("Pitler, et al, 2007, 139)

References

 Laureate Education, Inc. (Producer). (2011a).  Program eight:  Social learning theories [Video webcast]. Bridging learning theory, instruction and technology.   Retrieved from http://laureate.ecollege.com/ec/crs/default.learn 


 Laureate Education, Inc. (Producer). (2011b). Program two: Brain research and learning [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from http://laureate.ecollege.com/ec/crs/default.learn?CourseID=5700267&CPURL=laureate.ecollege.com&Survey=1&47=2594577&ClientNodeID=984650&coursenav=0&bhcp=1 


Lever-Duffy, J., & McDonald, J.  (2008)  Theoretical foundations (Laureate Education, Inc. custom ed.).  Boston, MA:  Pearson Education, Inc.  


Orey, M. (Ed.).  (2001).  Emerging perspectives on learning, teaching, and technology.  Retrieved from http://projects.coe.uga.edu/epltt/index.php?title=Main_Page 


Pitler H., Hubbell, E., Kuhn, M., & Malenoski, K. (2007). Using technology with classroom instruction that works. Alexandria, VA: ASCD. 


Willis, J. (2008, February). Building a bridge from neuroscience to the classroom. Phi Delta Kappan, 89(6), 424–427. Retrieved using the Academic Search Complete database. 

VoiceThread

https://voicethread.com/share/3141170/

This was my very first experience with VoiceThread, I hope it worked.
I decided to pose a current problem for my students.  This is actually something we are discussing at this time.  Once this activity is done, I would also like to extend it to get the students' feedback on how we can improve our playground and explore pricing and other factors.
I believe my VT is set to public, but please let me know if you are unable to view it.
I enjoyed watching the how-to videos teaching us how to get the link to our VT and how to set it to public.  How would I make a similar VT?  I would love to have a video showing the live onscreen steps as I explain how to do something on the computers.  For example, I would love to have little tutorials like how to format a picture in Word so they can move it around and select the exact location in the document.   Does anyone know where I can get more information on how to do this?

Connectivism and Social Learning in Practice

This week’s resources focused on social learning theories and how to implement technology effectively with this way of teaching.  “Social learning theories state that students actively engage in constructing artifacts and converse with others.  It’s the conversations that the students engage in that really help concretize and help them understand something” (Laureate Education, Inc., 2011).  The idea is that students can learn from one another, and the discussion component allows students to view the information differently, increasing the potential to internalize and retain the information for future use.  As Dr. Orey and our other resources said, ““One of the best ways of learning content is to teach it” (Laureate Education Inc., 2011). 

With our technology filled world we are become more and more social.  The definition of what social means will continue to change, as it used to mean people who spent time with others and were friendly and engaged in discussions.  These days a social person may be texting, emailing, replying to blogs to people he or she has never met.  Some friendships have been established without ever seeing the other person or even hearing their voice.  We are a connected society, we are glued to our devices and we thrive off posting updates about our lives or reading about others.  These changes convince me that we as teachers need to make our classrooms more social as well to meet the needs of our students.  “To be prepared for the fast-paced, virtual workplace that they will inherit, today’s students need to be able to learn and produce cooperatively”  (Pitler, Hubbell, Kuhn, Malenoski, 2007). 

This week’s resources provided numerous ways to help students learn in a social environment.  Although this is the second time I’ve been asked to read this chapter, I learned or was reminded of great resources and plan to revisit this information in the future.  The main premise is that “technology can facilitate group collaboration, providing structure for group tasks, and allowing members of groups to communicate even they are not working face to face” (Pitler, et al, 2007).  The use of technology has greatly increased the number of people students can collaborate with during a learning activity as well as the number of ways students can interact with others.  Students are now able to collaborate with students in other classrooms, experts in a field, or with anyone in the world.  Through the use of email, instant messaging, texting or even video chats through Skype, students have increasingly more ways to collaborate than even 5-10 years ago. 

Our resources discussed using technology to conduct WebQuests, create web sites, use collaborative documents like Google Docs, shared bookmarking and more.  These are all great ways to allow students to communicate and collaborate to create an artifact but what really grasped my interest was the idea of web-enabled simulation games. 

As quoted in our text Using Technology with Classroom Instruction that Works, “Gaming simulation is an interactive learning environment that makes it possible to cope with complex authentic situations that are close to reality”  (Pitler, et al, 2007). 

The text suggests a simulation based upon the Revolution (http://educationarcade.org/revolution) which is a multiplayer 3D game that gives students the opportunity to react to various events that foreshadow the coming of the American Revolution.  (Pitler, et al, 2007).  What a great way to get students engaged in a social studies; I only wish my teachers had used these.  “Since knowledge is contextualized to the students’ real life and the world is brought to them in a unique way, it is more engaging to them than simply reading tables in a textbook.  And interacting in a virtual world offers the potential for different personalities to be heard”  (Czarnecki, K., 2008).

This weekend I dedicated a considerable amount of time to finding simulations that could be used in my 5^th grade math classroom.  Here are some that I found:

Brain Nook http://www.brainnook.com/play.php

*requires a registration but is free

Virtual Math Club http://virtualmathclub.wordpress.com/

Virtual Worlds Designed for Elementary Students  http://vworld.fas.org/wiki/Elementary

*This provides a list to other virtual worlds for multiple content areas, not just math.

JumpStart Video

http://www.youtube.com/watch?v=MkcHlWhGI7I

*Have you used the JumpStart Software with your kids?  This program is designed for Preschool-2^nd grade and is available for purchase.  The link should direct you to a video to explain about the JumpStart learning tools.

SuperMathsWorld

SuperMathsWorld

http://www.supermathsworld.com/

This site allows users to play as a guest or create a login.  There are a number of activities to chose from and some require students to “unlock” previous levels before advancing. 

MinyanLand

MinyanLand  http://minyanland.com/

This is a great place to learn about earning, saving, spending, and giving money while students play games and make friends. 

Bank of MinyanLand

Mathmovesu  http://www.mathmovesu.com/#/home

(Raytheon)

One of my favorite blogs, ilearntechnology describes this site like this:  What it is: MathMovesU is an interactive virtual world where middle school students can interact with algebra, geometry, decimals, fractions, and word problems through topics they are passionate about like sports, music, and fashion.  As students navigate through MathMovesU they will encounter math problems delivered through games, polls, and fun facts.  The site is a great supplement to curriculum and will help students practice and improve their math skills in a fun, engaging manner.

Check out their full review at:  http://ilearntechnology.com/?s=mathmovesu&x=0&y=0

Another great site by Raytheon is the Sum of all Thrills  http://www.mathmovesu.com/sum-of-all-thrills.aspx?grade=Six

 

These virtual environments allow students to apply the skills they learn in their math classes to real-life applications.  It allows them to see how various topics are related and why learning specific skills are beneficial.  The gaming atmosphere is sure to grab students' attention and motivate them to develop or perfect the skills they need in order to move to the next level.  

Communication software is also a great tool to facilitate discussions among students, which is a major component of social learning theories. “Technology allows students to collaborate on projects without the constraints of time or geography.  Blogs, wikis, instant messaging, social networking sites, and Skype provide the means for students to communicate and share ideas as they work cooperatively” (Pitler, et al, 2007).  These sites make it possible for students to share their ideas, check for understanding, and elaborate on the subjects at hand, even if they are not working in the same room.  These also have protective features to help us monitor those in which our students are communicating. 

Edmodo is a site that allows schools to create a free domain for their school, giving teachers more administration rights regarding who can access material and the abilities to block or shut down users if needed.  The format is very similar to Facebook I’m told (according to other teachers and students) and that alone has my students begging to log on and get busy with their math assignments. 

I have used Edmodo to post descriptions to projects which really helps those unorganized students who always seem to lose the directions or expectations.  I post the rubric for tasks, and I even post links to get them started.  Students are able to communicate with one another by posting comments or replying to other student's posts.  They are also able to upload their final projects such as a graph, a word document or powerpoint for others to see, comment on, and collaborate.

The idea of Skype may be fascinating but how do you know where to start?  The link http://education.skype.com/ is a place to connect with other educators.  Who knows, you just might find the perfect support system here. 

A classroom blog can also be a great place for communication.  Students can post questions about an assignment, offer feedback to peers or even post links to resources they found beneficial.  

Wikis are also a great tool that give teachers the option to monitor their students and see who has contributed to a project.  Within the wiki there is a discussion forum that allows group members to post questions for others in their groups, or to post updates if they are unable to communicate in person. My students loved creating their March Madness Wikis this past spring.  Not only were they calculating fractions, percents, and more, they were also able to present what they learned on their group wiki to an audience, which increased their participation and effort in the project.  This feature alone allows students to create something, to collaborate, to discuss, and refine.  It seems it is one of the ultimate social learning tools.  

Education is becoming more and more social.  Students are no longer expected to show what they know by taking a test independently.  They are now able to apply what they've learned to gain a full understanding of the material and how it relates to real-life.  The social learning theory provides students with multiple exposures to content through research, construction, and discussion.  By the use of technology students are able to discuss content, check to see if their understanding matches that of their peer, and collaborate in multiple ways to complete the learning experience.  

References

Czarnecki, K.  (2008, October).  Virtual worlds for educators.  District Administration, 44,(11), 48-52.  Retrieved using the Academic Search Complete database.

Laureate Education, Inc. (Producer). (2011). Program eight: Social learning theories [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from http://laureate.ecollege.com/ec/crs/default.learn?CourseID=5700267&CPURL=laureate.ecollege.com&Survey=1&47=2594577&ClientNodeID=984650&coursenav=0&bhcp=1

Pitler, H., Hubbell, Kuhn, Malenoski.  (2007). Using technology with classroom instruction that works. Alexandria, Va: Association for Supervision and Curriculum Development.

Thatquiz.org and Edmodo

The last few months I have been exploring how to use Edmodo effectively in my classes and I stumbled upon a site called thatquiz.org.  This site offers many quizzes for students to take and the number of questions, types of operations, and other settings are totally customizable.  I simply post an assignment telling my students what type of test they are taking (fact test-click arithmetic under the first heading, fractions-click under a different heading), the number of questions I want them to take (this is adjusted on the left side), and wah-lah.  There is a timed mode, but even if students select "no time" it keeps track of how long the test took them.  The site even offers feedback so students know instantly how they did.  At the end of the quiz a graph appears with their score information.  If students missed any questions, it shows these off to the right.  I simply have my students copy this graph (and info about the questions the missed) and paste it into their Edmodo submit assignment section.
This has worked great for those days I simply didn't have time to make a customized test.  It also has helped to keep my 5th graders honest about their scores.
I also LOVE the quiz/test feature within Edmodo that can score quizzes for you.  I use this when I have time to create my own tests.  I do a fill in the blank style test so students must type their answer instead of just clicking on a multiple choice question and the computer grades it and enters it into their edmodo gradebook.  What a breeze!  :)

I recently had students search to find good sites to help us practice our skills and they loved posting games and video clips they found useful.  This teaches them how to use the internet to find resources, and it gave them a huge list of great sources to select from while mastering that skill.

If you have other suggestions for using Edmodo in your math classroom, I'd love to hear them!

Music & Math

I love using songs in my math classes.  Do they drive my students crazy?  Sure...but I also caught them singing them quietly during our state testing and they said, "Hey, those really work!"  The key is to sing them and have fun with the kids.  When learning a new song/skill I have the words in my Smart board presentation every few slides or so and I make sure to sing along with the kids.  We've even been known to sing them in the cafeteria or even once we've lined up after recess.  The kids love the fraction cadence and love to lead it for the teacher if they have a copy of the words or have memorized it.  I also don't tell the kids but do random "pop quizzes" the first few days songs are learned.  Whoever can sing them without looking earns a treat!   I'm not sure who wrote the original versions of the songs but I'm very grateful they did!

Rounding

Find the place value and circle that digit

Move to the right and underline, get it

0-4 circle stays the same

5-9 add one is the game

Now flex your muscles, like a hero

Digits to the right turn to a zero

All other digits remain the same.

Yo, you're a winner in the rounding game.  

Fractions

Adding and subtracting is plain to see,
you match the bottoms perfectly.

Multiplying fractions is no big problem,
it's the top times the top, and bottom times the bottom.

Dividing Fractions is easy as pie,
just flip the second fraction and multiply!

Fraction Cadence (For most lines the teacher should say it first and the kids should repeat it after the teacher, one line at a time)

**This is one of our favorites!

I don't know what you've been told (kids repeat)
Fractions are the way to go (kids repeat)
Fractions, fractions, don't you know (kids repeat)
Each operation has a different flow (kids repeat)


Sound off (teacher says)   7/8 (kids say)
Knock it on down (teacher says)  3/4 (kids say)
All the way down (teacher says)  5/8, 5/8, 1/2, 3/8, 1/4! (kids say)



Adding and subtracting are so cool
It’s quite easy, here’s the rule
Change the denominators so they match
Then add the numerators, that’s the catch


Sound off, 7/8
Knock it on down , 3/4
All the way down, 5/8, 1/2, 3/8, 1/4!


Multiplication rules, we can name
The denominators aren’t the same
Multiply the tops and then the bottoms
Simplify and then you got ‘em!


Sound off, 7/8
Knock it on down , 3/4
All the way down, 5/8, 1/2, 3/8, 1/4!


Dividing fractions, that’s the test
It’s more confusing than the rest
We don’t divide we multiply
By the reciprocal, and that’s no lie!


Sound off, 7/8
Knock it on down , 3/4
All the way down, 5/8, 1/2, 3/8, ooh rah!

Mean, Median, Mode

Mode shows up the most,

Average is the mean,

Median, median, median, median,

a number in between

Mean, Median, Mode, and Range  **Another FAVORITE!

Mean is just an average, average, average,

Mean is just an average, you add and then divide

Median is in the middle (we clap our hands to demonstrate middle), in the middle, in the middle,

Median is in the middle and never left or right (we shake our heads no and put our left hand up and then our right hand when we say the corresponding word)

We see the mode all around, all around, all around,

we see the mode all around, it shows up lots of times

(For this one we either make a circle with our finger in the air, or we make glasses with our thumb and pointer and circle around from the waist up.....this gets you VERY dizzy at times!)

Range is the difference from least to greatest, least to greatest, least to greatest

Range is the difference from least to greatest, subtract the low from the high.  

(Squat down for "least" and stand up for "greatest".  Also squat for "low" and stand for "high")

Simulations

http://www.classroominc.org/node/101
This site has a number of simulations.  It has short video episodes to go along with the topic.  Check it out to see if any of the topics meet your needs.

http://eclassresources.wikispaces.com/Simulations
This site has a number of simulations sorted by topic.

http://www.interact-simulations.com/c/featuredproduct.html?subject@Writing_2FEnglish+s@AAAHLzXvGfpe2
This site has resources for purchase to create simulations in your classroom.
I have used three of these in my social studies classroom and my kids loved them!  The copies I have are old and do not use technology but they are still good.  I even adapted some of them to use technology.  They are extensive and can last for weeks if you want them to.  I usually selected a few parts to allow my students enough time to get a good grasp on the material while saving time for other activities and lessons as well.  But, like I said, these are not free.

Constructivism in Practice

This week we were asked to discuss how the instructional strategy, generating and testing hypotheses, correlates to the constructivist and constructionist learning theories.  Before addressing this correlation, it is necessary to first discuss these two learning theories.

Constructionism and Constructivism are terms that are often used interchangeably in the schools in which I have worked or volunteered.  If you were to conduct a search online for one of these terms, you will also get numerous hits for the other as well.  The reason is because these two learning theories are closely related to one another.  “Constructionism builds on the Constructivist Theories of Jean Piaget, asserting that knowledge is not simply transmitted from teacher to student, but actively constructed in the mind of the learner.  (Orey, 2001)  Both learning theories state that learning takes place, and connections are made when students are actively involved in an activity, but the constructionist theory goes a step farther and states that, “Ideas are more likely to be created when learners are actively engaged in building some type of external artifact that they can reflect upon and share with others.  (Orey, 2001)

I believe in these two learning theories and I try to conduct lessons based on these models.  Think back to your school days?  What are some of the things you remember learning about?  I always remember the big projects, the science fair projects that I spent countless hours on, or the wooden end table I made and everything that had to be done to make it correctly.  The projects that stand out in my mind were the ones in which a great amount of my time had been invested, striving to find my own answers and make a display or object to demonstrate what I had learned.  These projects incorporated numerous subject areas and the knowledge I gained has stayed with me always. 

Generating and testing hypotheses is very similar to the constructivist and constructionist learning theory.  It too, involves putting the students in the driver’s seat, so to speak.  It allows them to generate a question or hypothesis, and then actively research to support or decline their original hypothesis (Pitler, Hubbell, Kuhn, & Malenoski, 2007).  As they research they are strengthening connections in their brain, helping them to really understand the task at hand.  Even though their hypothesis may be wrong, students will discover this on their own and have an understanding why, instead of just getting feedback from their teacher, and being left to wonder why the hypothesis was incorrect.   Learning that one’s initial thoughts were incorrect causes a disequilibration for the student.  (Laureate Education, Inc., 2010).  The student must then alter their thinking processes in order to make sense of the new material and to understand it fully. 

Technology can really facilitate the testing hypothesis process.  The Internet is a wealth of resources including text, video, and even the capabilities to chat with experts in a field.  Technology can also help students to organize the data they have collected.  In our text, Using Technology with Classroom Instruction that Works, it discusses how the use of spreadsheets can be a beneficial data collection tool.  Spreadsheets allow for students to organize their data and to manipulate it with ease.  It allows for students to use features such as the formula feature to complete computations, allowing students to focus on other aspects of the activity instead of the tedious computations.  It also increases accuracy with answering computations, increasing the likelihood that students’ revised hypothesis will be accurate since the calculations will likely be free from error (Pitler, et al, 2007). 

Technology can also be used to participate in simulations.  “Students can see the outcome of their hypotheses, often in virtual situations that would be impossible or financially unfeasible in real life” (Pitler, et al, 2007).  Although it does take some time to search to find the simulation that really meets your needs, “simulation software also can provide incredibly engaging learning environments, resulting in increased motivation and retention in learning” (Pitler, et al, 2007). 

One simulation I have explored briefly with my high ability students this year is http://mathbydesign.thinkport.org/.  It is a simulation that allows students to create a park or an environmental center.  There are a number of tasks that must be completed, such as determining the location for the concession stands based on certain criteria.  Although this simulation is higher level and challenging for the majority of the grade, my high ability students loved the challenge and often asked to play the game in their free time. 

Another site I found was http://www.explorelearning.com/.  This site has over 450 math and science simulations for grades 3-12.  This site does require a paid membership but it does offer a great free 30-day trial period. 

The instructional strategy, generating and testing hypothesis really reflects the key components of the constructivist and constructionist learning theories.  It allows for students to be an active part of their learning experience.  The teacher’s role is to act as a facilitator and provide guidance to the students to help them successfully reach their own conclusions.  Generating a hypothesis is focusing on the big picture, or is similar to the top-down model.  Instead of learning each component and then understanding how they fit into the big picture, the students are focusing on the main topic while experiences the subtopics along the way.  The main component of each of these is that the students are constructing their own understanding of the material, making neural connections, increasing the likelihood of students retaining the content. 

References

Laureate Education, Inc. (Producer). (2011). Program seven: Constructionist and constructivist learning theories [Video webcast]. Bridging learning theory, instruction and technology. Retrieved from http://laureate.ecollege.com/ec/crs/default.learn?CourseID=5700267&CPURL=laureate.ecollege.com&Survey=1&47=2594577&ClientNodeID=984650&coursenav=0&bhcp=1

Orey, M. (Ed.). (2001). Emerging perspectives on learning, teaching, and technology. Retrieved from http://projects.coe.uga.edu/epltt/index.php?title=Main_Page