Whenever my wife attends chiropractic conferences or workshops, she always comes home with these great quotes that she hears from the speakers that I always try to apply to my role in education. Last week, she came home with another great one, “You can’t fight the darkness. You can only turn on the lights.”
When I heard this quote, I thought of an issue that is consistently brought up when I present to large groups or work with small groups of teachers; the limited access to technology in their classrooms. It’s very easy fall into the trap of “fighting the darkness” when it comes to not having access to technology. You can swing your fists as much as you want but it’s still going to be pitch black. Sure, it can be frustrating being in a classrom with only one computer and no wireless internet (I’ve been there) but having a classroom filled with expensive technology does not automatically increase engagement and achievement. Rather than “fighting the dark” and focusing on what your classroom lacks in terms of technology, “turn on the light” and take an assets-based approach. What does your classroom have and how can it be effectively be used to develop 21st century fluencies?
As a math teacher, I often became frustrated when I gave a math problem to my students only to have a small percentage of the whole class be able to answer the question correctly. Naturally, many of my students became frustrated too. Consider the following problem:
The word problem above is a very specific problem that only has one answer. The fact that there is only one answer is not a serious issue for me or for the students that need to solve it. The issue with a problem like this is the fact that there is only one way to answer it.
This is a very specific problem that requires a very specific solution. If I gave this problem at the beginning of a grade 6 transformational geometry unit or TLCP cycle (Teaching Learning Critical Pathway) there is a good chance that only a handful of students would be able to solve it correctly. This is the kind of problem that I would give at the end of the unit or TLCP cycle since it is a really good assessment OF learning type of problem. Then it should come as no surprise that this problem was taken from the 2008 EQAO math assessment.
But what if I wanted to use this problem to begin my transformational geometry unit? Well, maybe not in its current form but what if I could “open up” the problem so that it wasn’t so narrow and specific and that a lot more students could solve it. Consider the same problem but with some modifications:
This is an example of opening up a very specific math problem. This open problem has more entry points for students than the previous problem since students have a choice in how they can move and manipulate the mat. Open questions are questions that have more than one answer and are great for differentiating instruction in the math classroom. Open questions allow students to solve problems based on where they are at in their math development.
I actually used the “open” gym mat question last year when I helped a grade 6 teacher introduce her transformational geometry unit. At first, the teacher was hesitant. This approach was drastically different from how she usually introduced the unit. In years past, she would introduce each transformation in isolation. First, a note on translations. Second, examples and demonstrations of translations. Third, practice problems involving translations. The three-step process would be repeated for rotations and reflections (This is also how I used to teach math). Therefore, the notion of giving an open problem to her students that allowed them the opportunity to investigate and use any transformation without defining, modeling or practicing them was pretty daunting. However, the results were very eye-opening and informed the teacher’s next steps for the next few lessons. Here are a couple of the student solutions:
All of the students in the class participated and solved the problem in small groups. As you can see from the gallery, there was a range of solutions from the class that brought up some really good discussion during the reflect and connect portion of the lesson where groups were able to explain their solutions to the class and answer any questions about their transformations. Some topics/questions that were discussed were:
efficiency in transformations.
What is the most efficient/fastest way to get the mat to the desired position?
What’s the purpose of the dotted line AB?
points of rotation.
Can an object/shape have more than one point of rotation?
This rich discussion was able to occur because of the openness of the question and the fact that students had the freedom to investigate and use their own math thinking to come up with a solution. It was also very powerful for the students to see that none of the groups came up with the same solution to the problem. The range of students’ solutions also allowed the me and teacher to determine appropriate action for the next couple of lessons.
For more information on differentiating math content using open and parallel questions please read the following article. (A very good read!)
I thought I’d try something different with this post. It’s more of a screencast/blog of a recent session I co-presented with @misterpuley with grade 5 students. The focus of the session was digital footprints.
This is my daughter Ava teaching me a very important lesson (yet again) with her child-like genius.
Last week, I was in the kitchen with Ava sitting at the counter having our usual father/daughter morning conversation. Ava started off sitting in the chair on the left as I was getting breakfast ready. However, the chair on the left is not her usual spot at the counter and she explained to me that she didn’t want to sit in “that” chair and wanted to switch. I automatically said, “Just climbed down that chair and climb back up the other one.” but Ava didn’t seem satisfied with my solution. Instead of taking my advice, she climbed up on the counter and crawled across the countertop to the chair on the right and sat down. My instant reaction was to remind Ava of the dangers of crawling across high places but afterwards, I thought about what she did and began to look at her actions in a different perspective.
Ava is three years old. So to her, climbing up on the counter is a perfectly reasonable solution to switching chairs. In fact, for a petite three-year old, it is probably easier to crawl across the counter than it is to climb down her chair and climb back up the other chair.
As an adult, I would have never thought to climb up on the counter and crawl across it to switch chairs. Why is that? Maybe it’s because I’d probably fall off and smoke my head off the edge OR maybe it’s because I’m an adult and I have preprogrammed perceptions in my subconscious mind telling me that crawling on countertops is inappropriate and dangerous. Do these preprogrammed perceptions embedded in my subconscious limit my ability to think creatively and outside the box?
Ava is not limited by these perceptions (yet). To me, this was an excellent example of creativity and thinking outside the box. To her, this was a perfectly normal and reasonable solution to her problem. The reason why are children are entering kindergarten with genius-like skills is because they aren’t held back by downloaded perceptions that us grown-ups have of right/wrong, appropriate/inappropriate, good/bad, possible/impossible which are pretty well established. Children’s perceptions are not set in stone. For them, anything and everything is possible.
Malcolm Gladwell, author of Blink, writes about the power of our subconscious and the impact that it has on our thinking and behaviour. Bruce Lipton, biologist and co-author of Spontaneous Evolution, states that 95% of our thinking and behaviours are controlled by our subconscious mind which is already established by age six. However, he also argues that the perceptions that are programmed in our subconscious can be deprogrammed. Lipton’s argument is very encouraging for the students that are currently in our education system.
So what does this mean for us educators? How do we keep and develop the innovation, the creativity, the imagination in our students who are moving through our education system? We give them a voice and listen. We allow them to think and use their own invented strategies to solve problems. We guide them to think critically about their strategies and other students’ strategies. We let them be active-participants in their own learning. We learn with them as opposed to teach to them. We look for limiting perceptions that hinder and handcuff our students’ genius and guide them to the realization that they can succeed and that anything is possible.
I went back to Ava that morning and told her that she used a very creative way of getting to the other chair that I hadn’t even thought of and that she taught me something new. She was so proud and gave me the biggest smile. It was a “Kodak” moment that was captured in the picture at the beginning of this post.
I thought I’d leave you with an amazing video that also inspired this blog post.
I just read a fantastic blog post by Zoe Weil called Reflections on Competition in School.The post sparked great conversation about cooperation vs. competition and I felt compelled to join the conversation. The following was my comment on Zoe’s blog post:
Bruce Lipton is a leading researcher on “new biology” and author of Biology of Belief and and Spontaneous Evolution says that our preoccupation with competition stems from the world’s “myth-perception” of how evolution occurs based on Darwinian theory where nature eliminates the weak in a battle for survival. Consequently, life is basically a competition with winners and losers.
Here is an excerpt from one of his interviews from Planeta Magazine explaining his view on cooperation vs. competition.
Darwinian theory further emphasizes that life is based upon a “survival of the fittest in the struggle for existence,” implying that it is a “dog-eat-dog” world where we must struggle to stay alive. This idea of “struggle” was originally based upon Thomas Malthus’ theory that predicted: “Animals reproduce so quickly that there will come a time when there will be too many animals and not enough food.” So life will inevitably result in a struggle and only the “fittest” will survive the competition. This idea has carried over into human culture so that we see our daily lives as one long competition driven by the fear of losing the struggle. Unfortunately, Malthus’ idea was found to be scientifically incorrect, consequently the competitive character of Darwinian theory is basically flawed.
New insights offered in biology are now revealing that the biosphere (all the animals and plants together) is a giant integrated community that is truly based upon a cooperation of the species. Nature does not really care about the individuals in a species; Nature cares about what the species as a “whole” is doing to the environment. Simply, Nature does not care that we have had an Einstein, a Mozart or a Michelangelo (examples of humanity’s “fittest”), Nature is more concerned about how human civilization is cutting down the rain forests and changing the climate.
The “new biology” emphasizes that evolution is 1) not an accident and 2) is based upon cooperation, these insights are profoundly different than those offered by conventional Darwinian theory. A newer theory of evolution would emphasize the nature of harmony and community as a driving force behind evolution, ideas that are completely different than today’s notion of life/death competition.
Most of us are of the belief that we need to have competition in education because that is the reality of the world that we live in and we have to prepare our students to survive in that “dog-eat-dog” world. However, it is evident that this notion of “survival of the fittest” is not doing our world any good and there needs to be a change of mind. I think this change of mind needs to start in our education system. It’s not about preparing our students to compete in the “dog eat dog” world. We need to focus on cooperation in education so that we can prepare our students to change the “dog eat dog” misperception that the world currently holds.
I was introduced to concept of “Whiteboarding” when I read Frank Noschese’s fantastic blog post titled, “The $2 Interactive Whiteboard” As a former math teacher and math facilitator I was drawn to whiteboarding and socratic dialogues. The whiteboard is such a simple, low tech tool but promotes collaboration, problem solving, communication, basically all of the 7 mathematical processes that I blogged about a few months ago. If you have a few minutes to spare, read the following 5 pg. article on whiteboarding.
There are so many benefits to whiteboarding in the classrooms. I won’t go into details since you can read them on Frank Nochese’s blog mentioned above. However, one question I brought up to Frank on his post was what the difference was between using a whiteboard and just plain chart paper (which up to this point I used very frequently). Other than the obvious benefit of saving paper and trees, he refered to a researcher Colleen Megowan who studied different types of whiteboarding and the affect on student dynamics. Althought it didn’t actually make it into the research paper, she did look at the differences between chart paper and whiteboards and her observations make perfect sense.
When students collaborate using a chart paper most of the thinking and reasoning usually happens before the marker actually touches the paper. This may be due to the fact that students don’t want to make mistakes. Therefore, when students do start writing on the chart paper, it is a summarization of the conversation and the thinking and reasoning that took place before. In addition, Colleen spoke of the “power of the marker” and the fact that usually it is the same student that ends up with the responsibility with writing on the chart paper. Maybe these students are leaders of the group, have the neatest handwriting, or just get to the marker before everyone else but what these students write is their interpretation of the group’s conversation and may not necessarily represent the group’s collaborative thinking.
When students use whiteboards, the writing usually happens as the students converse, reason, and think collaboratively. The ideas written on the whiteboard evolve as the conversation unfolds and is a better representation of the group’s thinking than if written on chart paper. Because the markings can be easily erased, students are immediately inclined to write without hesitation. Whiteboards are also less intimidating for students and encourage multiple students to contribute and write. In addition, Megowan spoke about the “power of the eraser” and the fact that writing can be erased changes the group dynamics and allows a new role (the eraser) to emerge within the group.
After reading more literature on whiteboarding and socratic dialogues, I was hooked and immediately saw the benefits not only for math but in all subject areas and needed to have a set of six whiteboards for myself to try out. I wanted whiteboards with similar dimensions to standard chart paper (24″ x 32″). I looked into getting whiteboards from Staples but the cheapest whiteboards with the dimensions I was looking for cost about $28 each (with tax, close to $200 for six). I needed a cheaper alternative and Frank mentioned on his blog that educators were going to homedepot, Lowes, or Rona and purchasing 4′ x 8′ tileboard and cutting them into six smaller sections (24″ x 32″). However, my online searches on these stores’ websites for tileboard came up with nothing. I phoned multiple home depots and Rona’s in my surrounding area and several phone calls later, I finally found a Rona that had one panel of 4′ x 8′ tileboard in stock. With my school board discount, I was able to purchase the panel for $37 and didn’t have to pay for the cutting since Rona gives you the first 3 cuts for free. So all in all, each whiteboard came to approx. $6.17. Not quite $2 whiteboards but I am very happy with my whiteboards and I’m very excited to implement and share the whiteboarding strategy with the teachers in my school board.
I’m not advocating that we abolish chart paper from the classroom. Chart paper still has it’s place for ideas that need to have a permanent fixture in the classroom. (anchor charts, learning goals, success criteria) However, there are situations in the classroom where using whiteboards would be more effective for collaboration, thinking, and reasoning than chart paper. The benefits of whiteboarding shouldn’t be ignored and should have a place in the classroom as well. I would love to hear your comments on how you use the whiteboarding strategy in your classroom.
In my next blog post, I will be looking at various websites that offer online whiteboards that allow students and teachers to collaborate online and see if the whiteboarding concept can be implemented in a digital environment. Perhaps the digital environment would have an effect on group dynamics not seen in typical face to face whiteboarding interactions or perhaps new roles would emerge from collaborating online.
This past Friday morning at 6:00 am, I was stirred awake by loud unusual noises from outside my bedroom. At first I thought I fell asleep while watching T.V. however, when I opened my eyes the bedroom T.V. was off but I noticed that the hall light outside my bedroom was on. I found this very odd since the lights were turned off before I fell asleep. I curiously got out of bed to see what was going on and this was what I saw:
I have a three-year old daughter named Ava and she apparently decided that it was time to wakeup but didn’t feel it was necessary to wake-up the rest of the family (bless her heart). She didn’t like the fact that it was dark upstairs so she decided to take it upon herself to turn on the lights. I didn’t have to look very far to find her because this is where she was:
She independently turned on the computer, opened Internet Explorer, clicked on the address bar and found one of her favourite websites (Disney Princesses) to play by finding the little pink icon beside the url.
This is my digital daughter and she amazes me everyday. In this case, she demonstrated her problem solving skills by instinctively grabbing her step stool to turn on the light switch when she couldn’t reach it. However, this isn’t really surprising considering that she also uses it for a variety of other uses:
She demonstrated her developing solution fluency by defining a problem (I’m the only one awake and I’m bored), devising and applying a plan in real-time (turn on the lights and find my favourite website to play). According Angela Maiers, Ava and many other preschool/kindergarten students are geniuses in the sense that they possess genius-like skills. At age three, Ava is imaginative, curious, and courageous. She can adapt to any situation, perserveres through many challenges and has an unsatiable appetite for learning. She is my very own genius growing up in a fast-paced, everchanging, and exciting digital world and I know that in order to be successful and to be able to contribute in this 21st century world, she will most definitely need these skills.
This September, she will be entering junior kindergarten and I hope that the public education system will accomodate her needs as a digital learner and allow her to be an active participant in her own learning rather than a passive observer. I hope that the education system will not only maintain her genius-like skills but develop them and allow them to flourish. But more importantly, I hope that school and the classroom will be a place that allows Ava to be a life-long learner, discover her place in the world so that she can make her contribution.
In one of my previous posts about the 3 part problem based lesson, I referred to the third part (reflect and connect) as the most important part of the math lesson since the learning comes from the student work. Students are given the opportunity to explain their math thinking, pose questions, defend their ideas, and make connections with other solutions. The teacher is the facilitator of the discussion as well as a participant. The learning comes from the math community.
The following article describes three approaches to the Reflect and Connect: 1)Math Congress, 2) Bansho, and 3) Gallery Walk.
In this post, I wanted to focus on the gallery walk because to be honest, this is an approach that I don’t use very often when consolidating a math lesson. This is an approach that requires a lot of movement of students in the classroom and could possibly take some time and good management skills to facilitate. In most gallery walks, student solutions are posted around the classroom, and students circulate with sticky notes writing down questions and comments and placing it on the solutions. The idea is for students to read the comments and questions on the stickies about their own group’s solutions and use that feedback to help them prepare the explanations of their work to the class. Problems can arise if students aren’t given enough “wait” time to think of questions or comments to write down on their sticky notes. This can result in comments like, “You spelled multiply wrong.” or “I like how you used the colour red to write your solution.” The goal is to promote higher order thinking and questioning but if students aren’t familiar with a gallery walk or need more time to reflect on the student solutions then perhaps an online gallery walk could be a worthwhile alternative.
Lino it is a great web application that provides you with an online canvas and allows you to post online stickies, pictures, videos, and attachments. You can also share your online canvas with others by sharing its URL. Sharing the URL would allow others to post stickies as well. You can probably see how Lino it could be used to conduct an online gallery walk. To give you an idea of what it could look like, I inserted an screenshot of an online canvas with pictures of four multiplication solutions and stickies with questions and comments posted around them.
The comments/questions were generated by a team of math facilitators when I shared the link with them, which should also give you a good idea of how Lino it could be used for teacher moderation of student work.
By using an online gallery walk, students could post their comments/questions in class or at home and have time to reflect on student work and pose thoughtful questions and comments. Groups could review the feedback the next day and prepare the presentation of their solution to the class.
I would love to hear your thoughts about this alternative approach to communicating in the classroom.
I finally finished reading my book (which I loved), Spontaneous Evolution by Bruce Lipton and Steve Bhaerman after being sidetracked by so many fantastic blogs. In this book, Lipton and Bhaerman make reference to Johan Galtung, a Norwegian mathematician and sociologist and founder of TRANSCEND International, a peace development environment network. Galtung is most known for his ability to transcend conflicts and find what he refers to as the fifth way, or fivers. He recognizes that every conflict has five possible resolutions:
I win. You lose.
You win. I lose.
The conflict is resolved by avoiding it completely.
Compromise where all parties are dissatisfied.
Transcendence where all parties feel like they win and resolution is above and beyond the problem.
After reflecting on this portion of my book, I believe educators need to implement the power of Galtung’s fiver approach in education and seek ways to solve issues with resolutions that are above and beyond the problems so that all parties (students included) are happy with the outcomes. Lipton and Bhaermann explain that the first step to creating a fiver solution is for opposing parties not to settle and meet each other halfway but to work together and progress forward towards an ideal resolution.
This notion can be applied directly to the classroom where conflicts often arise between teachers and students. Often, the labels “teacher” and “student” create a separation, a polarity in the classroom. It’s the teacher vs. student mentality which results in disengaged students, late assignments, students doing the bare minimum to get a “level 2” etc.
Here’s my fiver solution for the teacher vs student power struggle that exists in many classrooms. Get rid of the labels “Teacher” and “Student” and “classroom” replace them with “learners” and “community”. It shouldn’t be about the teacher as the holder and controller of all the knowledge and the student as the observer waiting to be educated. As Angela Maiers would say, It’s about a community of learners each with valuable knowledge and skills working collaboratively to achieve their full potential so they can make their contribution to the world.
Last Friday, I happened to come across a webcast on edtechtalk.com via Twitter when @AngelaMaiers tweeted about it right before she went on. It was a very inspiring discussion that didn’t really focus on technology at all. In fact, the topic of conversation was more about “seeing” students and helping them find their gifts so that they can make their contributions to the world.
Towards the end of the webcast (45 minutes in), Angela recalled a conversation she had with a group of students and she asked them what they thought about technology integration in education. One of the student replied, “If I have to do another Glogster, I going to jump off a cliff…Seriously, I wish teachers would lay off this technology stuff because it’s painful to watch, they’re trying too hard…If they just saw me, If they could just let us talk, If they could just let us share…” She went on to say that integrating technology in education is not that complicated. It doesn’t have to be a fancy project or a unit that is infused with technology, it’s about time, attention and getting students to feel they are valued and seen by their teachers.
After listening to this inspiring webcast for a second time, I realize that it’s not just about integrating technology in the classroom. It’s about establishing a community in the classroom and letting students become active participants in their own learning. Technology just happens to be a great tool to make this happen.