Student thoughts about Math

This is my first entry for the course offered by Jo Boaler through Stanford University.  She had interviews with some of her university students about their thoughts on math. Here is my concept math highlighting the thoughts from those interviews.Math concept map

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Reflections on Wii Olympic Math

Last week I submitted my lesson plan about using the Wii, and Mario and Sonic Winter games, to teach a combined unit on decimal operations and central tendency.  Reading that post first will put this post in context and is probably important to have this post make sense.  You can read that post here and then come back for my reflections on the whole process.

Due to time restraints, I was not able to create the introductory iMovie trailer to describe the project, nor to have the student do the project about designing their own event.  I know that this component is important so I will have it ready for the fall when I use this activity again.   I decided that for this run it was more important to have the students learn the basic skills rather than have them focus on the bigger picture and come out of the unit unable to perform the basic skills of the unit.  Teaching is all about time, and although I was able to start this early by looking ahead in what was to come, there was still not enough time available to include all the components I wanted.

The students pulled together to cheer on their classmates.  It was refreshing to see how they cheered on every student even the one coming in fourth. My room has 8 tables so we designated 4 tables as front tables and 4 as back tables.  The students kept track themselves of which tables needed to be up and who had not had a chance to go, without any arguing or students trying to take extra turns.  Many students wanted extra turns but no one took one, which really impressed me.  It was also great to see some students who do not excel academically shine in their use of the Wii and this pride translated into them being more willing to try during the math components.  I had students who do not have regular attendance show up every day during the Wii Olympic math and students who are usually late for class sprinting to ensure they were ready to go.  It was also exciting to see those students who had no experience with the Wii become more proficient and begin to take part in discussions about the Wii.  The team building and excitement that this unit inspired made me decide to start out my new classes in the fall with this unit to try to help foster class cohesion.

I learned something very important about the integrating of technology into a classroom as well as I started this project.  I learned that one should never only include the technology in the first day of the unit, the content needs to be there as well.  The first day I worked on activating prior knowledge and demonstrated how to use the Wii.  We then started gathering our first set of data by playing the team bobsled.  It took the whole class to gather the data with 32 students so I told them that we would use our data the following day.  Needless to say, my students went home and told their parents we did nothing but play the Wii all class, true but out of context, so I had some angry parent phone calls that I needed to return.  The parents were all fine after I explained the purpose of the Wii but the initial contact was not very happy due to their students playing video games in class.

The unit itself went very well.  There were a few occasions when a mode was presented in the data and only one occasion of an outlier when I elected to not have a student fill an extra seat in a run to allow the time to be much slower than all the rest.  I was a bit concerned that once we left the team events we would have 30 or 32 pieces of data to work with, but with scaffolding all students were able to work with the measures of central tendency.  All four classes decided they would rather work harder with many pieces of data if that meant everyone had an opportunity to try all events, than work with fewer data points because fewer students got to try.

One of the most wonderful unexpected things that happened in this unit was that the unit ran itself.  The students took charge of making sure the game was ready, making sure everyone had turns, making sure that all parts of central tendency were calculated that it freed me up to work with those students who needed extra support.  I was able to just check in with those students who needed reassurance but was also able to sit and work in a small group with those students who were struggling to ensure they understood what they need to do.  By the end of the unit, all students were able to demonstrate at least a basic understanding of decimal operations and central tendency.

Some issues that came up due to the nature of the data revolved around the concept of mode.  There were very few times where mode occurred and it only every had the number show up twice.  This created the misconception for some students that mode meant a number that happened two times, even though they could tell you it was a number that happened the most.  As a result, these students would write down the number that happened twice as the mode for a set of data totally ignoring numbers that happened more frequently.  I know it isn’t possible to force the game to create modes with higher frequency so I will have to address that concept through my entrance or exit tickets in the fall.

Overall, I believe that this unit plan did the two major things I wanted it to do.  The first thing it did was to combine units together to allow more time for students to consolidate their knowledge about the concepts in questions.  Many students need more practice in order to be able to consolidate their learning and combining units together made it possible to provide those students with the time they needed.  The second thing it did was to excite students about learning math, students were engaged, on task, and accomplishing what I needed them to do with little fuss or complaints.  Using the Wii allowed me to provide my students with a context for why these skills could be important outside the mathematics classroom.  One thing I did not expect was the sense of class that this activity produced.  The students all worked together to accomplish something and encouraged each other resulting in the ability of the class to do more.  As a teacher the idea that your class can become more than the sum of its parts is an awesome one.  To experience it was really awe-inspiring.   It has made me excited to start school again in the fall even as this school year draws to the close.  I can’t wait for the improved version of this activity.

Wii Olympics Math

The goal of this week’s assignment is to create a lesson plan that uses technology to teach something with which students have misconceptions.  I chose something that students have trouble learning due to their lack of interest.  My plan is actually for a full unit as that is how I plan.  I start an activity with my students and then interject the teachable moments as they come to allow them to link to the experience.  I try to be as responsive in my teaching as I can so planning a single lesson is no longer how I view teaching.  My project comes in two parts, my unit plan and then the section answering the questions posed for this assignment.  I tried to include as much from the questions in the unit plan but some questions didn’t seem to fit, so you will find those answers after the plan.

Olympic math 1 Olympic math 2 Olympic math 3

If the images are not large enough to read, click on the link below for a PDF version you can save.

Unit Plan for Wii Olympic Math CEP800

Creative Commons License
Wii Olympic Math by Amy Tetz is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

  1. Content:

This unit is not as much about challenging misconceptions, even though there are a few that occur, as it is about getting students to want to learn the information. In the past, this has been the most difficult concepts to teach, as students see no use for them. I am hoping that if students are engaged, they will have more desire to learn the information thus retain more of it.

  1. Pedagogy:

The students will be working in groups of four during this unit. These groups are chosen by me by looking at learning needs previously presented so that each groups experience can be tailored to them. As the students are working in groups, their knowledge will be socially constructed. The calculations are required to move on to the next event so this creates the behaviourist idea of intermittent reward. I am also applying Dweck’s idea of motivation being important to learning and am also applying Vygotsky’s idea of scaffolding to allow all students to participate.

  1. Content & Pedagogy: I would love to be able to have each group work on their data independently or in smaller groups than the whole class but I only have one Smartboard in my room and only one version of the game. Thus, the knowledge has to be socially constructed. I decided on not allowing students to move on before playing due to the large number of my students who will do nothing unless getting something done is in their best interest. When those students are actively involved in their learning, or motivated to learn, they retain more of the skills that they are presented. I hope that with the Wii game their engagement and thus their retention will be increased.
  2. Technology:

I will be using the Wii Console with four remotes. I will be using the Game Mario & Sonic at the Olympic Winter Games Vancouver edition. I have chose to use this technology to help increase engagement with the topics. It is possible to teach these units with the Wii as I have done in the past, but I have struggled with having students want to learn the skill and have retention beyond the test. I am hoping that using the game to generate data will help to increase engagement. As well, many of my students are new to Canada and are new to winter sports in general as they are coming from places where the weather is usually warm. Using the Winter Olympic Games allows students some understanding of what the different winter sports are like and can learn some of the vocabulary and understanding of how the sport works. The Technology is a springboard or “twist” that allows students to view the math in a different light. To link the experience of many outside of class to their work at school and more importantly allow those students with no experience the chance to be able to converse with their peers with understanding of how to play a game on a Wii.

  1. Technology & Pedagogy:

The Winter Olympic Game provides just-in-time tutorials to help students learn how to play the event. The game also provides a target line to help students to stay on track. The remotes contain a function that causes the remote to vibrate if the player has gone out of bounds to remind plays to correct their path. The route and out of bounds are clearly marked and a mini map is provided so that students can prepare themselves for what is to come. The game provides images on the ground to remind students of what to do, for example lines that indicate a jump is to happen.

  1. Technology & Content:

The technology I have chosen provides the context for why the skills in question could be useful in the real world. It is also more engaging than pages in a textbook or other artificially generated numbers. I believe students will take more ownership for the learning due to the fact that they had a part in generating the data. In the past, the skills have been very difficult to teach due to student resistance. I am hoping by adding the novelty of playing Wii in class, linking to prior knowledge, and providing context for when these skills will be useful that students will be more receptive to practice these skills.

  1. Assessment:

I have not figured out a way to use the Wii during the summative assessment, only the formative ones. Assessment is discussed in the formal unit plan.

 

Quest to Master Algebraic Division

This week’s project to create a digital story has been fraught with difficulties.  The first issue that arose was the idea of having images and video of my students at work.  In Calgary, I am bound to protect the identity of my students through FOIP legislation.  That meant no video or pictures of my students, so I was left with the quandary of how to  portray their learning without them in the picture.  I decided to go with showing their pre and post test examples with the component parts of this part of the unit.  That is, it became more of a chronicle of how I tried to elicit learning in my students, not a chronicle of their learning in and of itself.

The next hurdle was imovie.  Since I started using imovie trailers I find that imovie themes are just not exciting enough.  If I am not excited to what what I make, who else will be?  However, the trailers run about a minute long and I knew my movie would be about 5 minutes.  So I converted my trailer to a project, added what else I wanted to include, then looped the audio and recompiled the extended imovie trailer.  To accomplish this project I ended up using imovie, Comic Life, Dropbox, Youtube, Audacity, and Windows Live Movie Maker.  Each tool had something that the others didn’t but combined they worked to create a project I am proud of.

The last problem of the week was that I got very sick and due to coughing lost my voice.  No narration for me!  As a result, I had to find alternative ways to express my thought processes without overloading the presentation.  I know auditory and video work better together than video and text but one does what one has to when overcoming challenges.

I hope you enjoy the journey through the mastery of Algebraic Division.

Podcast on identifying student understanding

So I signed up to finish my Masters of Arts in Educational Technology at Michigan State University instead of stopping at just a certificate.  As a result, here is the my first assignment in CEP 800 Learning in Schools and Other Settings.  This first assignment proved challenging, not because I found creating a podcast challenging nor that choosing a topic was difficult, but because of the government legislation FOIP (Freedom of Information and Privacy) which means that I cannot record any students without parental permission.  To get the paperwork approved by my principal, then up the chain, then to get it out to parents would well exceed my week allowed, so I needed to get inventive.  I have tried to link all possible assignments in my work at MSU to my classroom because my main reason for completing the program is to improve what I do in the classroom, so changing my topic was not a option.

During my Masters’ program at University of Calgary I was introduced to the work of George Lakoff and Rafael E. Núñez.  We read many articles but the majority of our exploration was around the 4 grounding metaphors of addition as discussed in their book Where Mathematics Comes From(2000).  Lakoff and Núñez believe that all 4 grounding metaphors are necessary for students to understand later iterations.  For those unfamiliar with the 4 grounding metaphors, I included a brief summary in the podcast.  During the student interview, I looked for examples of where they are using the grounding metaphors to explain their understanding of addition.  This topic lends not to identifying misconception per say but to finding where the students’ understanding of addition is incomplete and therefore needs remediation.

Below is a picture of what manipulatives were available for the 2 students I interviewed.  I thought seeing them may help with the visualization of what they said.

podcast manipulatives

 

Here is my podcast which exaimines which of the 4 grounding metaphors a student at the end of grade 3 and a student at the end of grade 4 are able to access, when asked the question “how does addition work?”.

References

Lakoff, G., & Núñez, R. E. (2000). Where Mathematics Comes From. New York: Basic Books

“The Complex” Kevin MacLeod (incompetech.com) Licensed under Creative Commons: By Attribution 3.0 http://creativecommons.org/licenses/by/3.0/

Reimagining Online Learning

During the course CEP812 I was introduced to the concept of wicked problems or problems that are so complicated it really isn’t possible to create a solution to.  The new Media Consortium created a white paper that highlights 5 of the top wicked problems facing education today.  Working with Nathan Jacques and Kaitlin Rhonda we decided to work on brainstorming possible ways to reimagine online learning, on of the top 5 wicked problems in education today.  Here is what we came up with during our brainstorming sessions.  I especially want to thank Nate for all his wonderful artwork, the project turned out better than I had imagined it could.

RSA style summary

White Paper

It is no secret that there are many problems in education today. Some problems can be solved easily, while others take some work. And then there are problems, the wicked problems, that seem impossible to tackle.   Koehler & Mishra (2008) define wicked problems as a problem that has

incomplete, changing, and contradictory requirements. Solutions to wicked problems are often difficult to realize (or maybe even recognize) because of complex interdependencies among a large number of contextually bound variables. Wicked problems, they argue, cannot be solved in a traditional linear fashion because the problem definition itself evolves as new solutions are considered and/or implemented. (p.10)

Lately, online learning has been a focal point in education reform, but online learning is not always successful. Why is this the case? Reimagining online learning is a wicked problem, one of the top five affecting education as identified by the New Media Consortium (2013). They challenge educators to re-imagine online learning.  However, there is no one way to reimagine online learning in a way that will be successful in every school district. The formula has to change with each particular classroom. Online learning is also constantly changing and it is difficult to stay on top of the latest trends. It’s even more difficult to determine if these latest trends are indeed effective means of teaching! Finally, the success of online learning has so many different variables, that there could literally be thousands of different successful approaches.

Different districts have different policies regarding which devices, technology, and programs are usable, which also makes this problem a little more wicked.  Many schools allow the use of cellphones or other personal devices for the purpose of text message polling, social media in the classroom, and other forms of educational communication. Other school districts have banned the use of cellphones and other personal devices for reasons from abusing the privilege to violence issues. Regardless, it is up to the school district to determine how and what technology can be used, which greatly affects the success of online learning.

 Our potential solution to this wicked problem revolves around the idea of getting students plugged into their own learning! What does this mean?

 We love the idea of “digital gaming” in education. What is gaming in education. Gaming or the “gamification” of lessons use game-like mechanisms to increase motivation and involvement. These mechanisms include, earning experience points/badges, having “lives” in an activity, and a video game element where students have to work through a series of tasks in order to “win” or be successful. Digital gaming allows for students to work at their own pace.  By allowing students to work at their own pace, all students can achieve to their highest potential not falling behind because the class pace is too quick for understanding or bored due to the class pace being too slow.

Digital Gaming also creates an environment where students can make mistakes and try again until they are successful. In a typical video game, a player can make a mistake, die, and come back to life to try again. In a classroom setting, students should be able to make mistakes and build off of that to be successful.

Digital gaming also adds an element of entertainment that is similar to what they are doing outside of school. Developing a gaming lesson that gets all students actively involved can be a wicked problem in and of itself. However, the chances of students being more involved in an interactive learning game over taking traditional pen and paper notes on a lecture is highly probable. Many students who put in little effort into their school days will go home and spend a lot of time and effort into learning new information to be successful in the online environment.  We think education needs to tap into the potential for student motivation found online.  The idea of gaming appeals to student interest, even those who may not be “gamers” by definition. Gaming can be individual, for those who like the challenge of accomplishing goals/tasks. It can also be group-oriented, for those who thrive off competition and teamwork.

Within this, online learning needs to matter to students. It is also important that learning is connected to the real world. Gee (2013) says, “Often students can see no clear and compelling goal for learning in formal classrooms beyond grades and graduation. They often do not care about the material in any deep way.” (p. 16) Students need to be able to find meaning in what they are learning. If students don’t see a real world connection, it is likely they won’t put effort into learning it long-term. If we make online learning fun and realistic, online learning can be a powerful thing.

 What that experience will look like for every student, is still a wicked problem that needs to be solved.  With the circumstances of each student being different from access to technology, teacher comfort, teacher knowledge, school policy, board policy, state or provincial mandates, it is improbable that a single vision for what online learning looks like is possible to create.  What may be possible is an amalgamation of practices that are anchored to educational research from which teachers could choose from to suit the needs of their particular students. Here is the start of a possible list of strategies to keep students highly involved throughout a gaming scenario:

 1) Daily reflection and Debate through Twitter, Blogs, Posts, and Surveys

2) Conscious implementation of devices into assignments and projects

3) Project based learning through the maker culture. Innovation through mistakes

4) Sharing Web 2.0 applications and attempts to fit into content delivery

5) Learning through teaching. Use technology to research and then return information to peers

In the end, the only thing that matters is the students.  Something that needs to be at the forefront of all interested in educational reform.

References

Gee, James Paul (2013) The Anti-Education Era: Creating Smarter Students through Digital Learning [Ibook edition] New York, NY: Palgrave MacMillan

New Media Consortium (2013) The Future of Education: The 2013 NMC Horizon Project Summit Communique Retrieved from http://www.nmc.org/pdf/2013-Horizon-Project-Summit-Communique.pdf