Below are the slides I used during my presentation entitled “Flipping Math Upside Down” at WestCAST 2012 at the University of Calgary in Calgary, AB.
If you attended and would like to know more, please feel free to contact me (in the comments, on Twitter, or email)!
Next week, I will be attending the WestCAST (Western Canadian Association for Student Teaching) 2012 conference being hosted by the University of Calgary. I attended the conference last year when it was in Brandon, Manitoba and shared a session called “Google 2.0 – More Than a Search Engine” and met many other student teachers from across western Canada.
This year, the conference challenge is “How might we rethink the focus and practices of teacher education to explore emergent insights into learning?” and I’m excited to hear what other universities are doing to investigate this.
In Calgary, I’ll be involved in two different sessions. The first workshop is called “Using POEs with K-12 Students to Develop Scientific Concepts” where my Science Education classmates will be sharing and demonstrating various POE (Predict, Observe, Explain) activities. We’re sharing a wiki using business (front and back) and you can find it at bit.ly/urpoes.
The second session I’m running is called “Flipping Math Upside Down” where I am planning to share my use of the flipped classroom over my internship. I’m still working on the finer details of the presentation, but I’m hoping to share my story, show other examples and discuss some pros and cons about the flipped classroom before opening the floor to questions and having a conversation. I haven’t decided yet how I’ll share my presentation with those who attend, but I’m likely going to just use a GoogleDoc and Slideshare (unless you hav ea better suggestion, let me know!)
I’m planning on live-tweeting using the hashtag #westcast2012 * throughout the conference, and I hope others in attendance do the same. It has been a while since I blogged, and I’m hoping that the sessions and conversations can be a spark to get me back into the groove of sharing.
*Edit (Feb 19, 2012): The Faculty of Education at the University of Calgary has recommended using #WestCAST2012, instead of the #westcast I was planning on using. http://educ.ucalgary.ca/node/1171
(Click image to enlarge.)
I don’t know where this image originated, but if you do, let me know so I can give credit where credit is due.
This was a message shared with me by a classmate of mine who is currently doing her internship. I know she is not the only one to encounter this, as I have myself. I’d like this post to serve as a place for you to share any advice/widsom with us if you have any.
I am part way through marking a grade 10 assignment (began with measuring a pop can, ended with finding the cost of producing a certain amount of aluminum) that my class had to do that incorporated everything from the last unit they learned, and the lack of effort put into this is blowing my mind.
Almost every student in my class should have been able to complete this assignment 85-100% correctly, had they even used the class time I had given them. The language was simple, it was divided into small steps, and was EXTREMELY straightforward (almost ridiculously so, for a grade 10 class).
I am finding that one of the things I am most frustrated with is many of my students just DON’T CARE.
Are any of you facing this challenge? If yes, how are you dealing with this? (I’m not looking for a discussion on grading and grades as a non-motivator, because frankly, the fact that this assignment was one of the few graded this unit still wasn’t motivation for my students.) So, how are you motivating your students? Please share.
How do you deal with students who seem to just not care? Any words of wisdom?
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Some rights reserved by Orange42
This past week I attended the NCTM Regional Conference held in St Louis, MO. At the conference, one of the sessions I attended was by Rita Barger from the University of Missouri-Kansas City about commons myths about learning and succeeding in math. This series of 5 posts will share what I learned from the session.
What is it?The “math is only computation” belief is the belief that all math is formulas and just working through numbers. In this belief, it’s safe to say you also believe calculators can solve nearly every problem. To be completely honest, I bought into this belief until approximately a year ago. I didn’t even know “other” math even existed.
What causes it?
Our testing methods lead give this belief life. Our assessments primarily consist of solving problems that involve our students to work their way through questions. Our homework is typically very similar. We have failed to show our students that math is more than this. How often do we take a step back and talk about the logic and thinking processes involved in math? Not nearly enough. To be fair, our traditional curricula hasn’t really allowed much breathing room for such conversations.
There have been many times where I have heard people, other teachers included, say they love math because it’s so “black and white” (I’m sure just as many people hate math, by that same train of thought). You either get it right, or you get it wrong. All of the math I recall taking in school fit under this category. In a math assessment class I took last year, we discussed that reading skills and pattern recognition are the best predictors of success in mathematics. I don’t think we help students with either of these nearly enough.
When all of the math our students see is computation based, why would they have any reason to think math is ever any different?
Students may not see the value in non-computational math. If you choose to do brainteasers with your students, they may enjoy them, but not see the point in doing them. The few brain teasers I have done with my students, have ended with: “Now let’s get back to real math”. Our students don’t see that skills like recognizing patterns and developing game strategy is considered math. I wonder, if we began to use more this kind of math in our classes, if students would start enjoying math class more.
Rita talked about having a game day every now and then in her math classes. These days would encourage problem solving and building strategies that would give you the best chance at being successful in the games. She mentioned the game of Nim, which I have never seen before but I am interested in trying to play it with someone as soon as I get the opportunity.
Using sequences or analogies that don’t use numbers in them may allow students to start looking at math as not only computational. We should encourage our students to look for patterns in absolutely everything. It could very well be the most valuable thing we teach students in math, but I think it is often overlooked.
It might be valuable to discuss what real mathematicians do. You’re students might be surprised to find out that they don’t just show up work and get given a sheet of problems to solve for the day. Students seem to know very little about math beyond high school.
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Some rights reserved by ZeRo`SKiLL
Five unhealthy beliefs in math that exist today are:
This past week I attended the NCTM Regional Conference held in St Louis, MO. At the conference, one of the sessions I attended was by Rita Barger from the University of Missouri-Kansas City about commons myths about learning and succeeding in math. This series of 5 posts will share what I learned from the session.
The “math is mostly memorizing” belief is the belief that you can be good at math by just memorizing a few things. If you simply memorize a few formulas and the step-by-step process that your teacher uses, you can get through math easily. Unfortunately, I think this is a belief that many of our students buy into, even though they may not find much success with it.
This belief is, once again, largely caused by our current teaching methods. When we just emphasize teaching skills, students see this as opportunity to follow a step-by-step checklist to arrive at solutions. We tell students to “do what we do” and, if they do, they will see success in our classes.
It might also stem for our questioning as teachers. Typically, when we’re teaching students to replicate what we are doing, we only engage them in low-level thinking questions. Instead of asking our students to think about what we’re doing in a problem, we’ll ask them to tell us what comes next. Students can easily get by knowing the step-by-step and not having a clue as to why we progress throughf problems the way we do.
Additionally, teachers may cause this by creating assessments (tests or quizzes) that replicate the questions done in class or completed by students for homework. If a teacher consistently does this, students could very easily get through math without ever actually understanding the questions they are “solving”.
One of the most noticeable ways we see students believing this is when we hear them respond to questions with “You said…”. Right away, this shows us that the student has tried to memorize what you had said at an earlier time. I have run into this many times and I have usually found that the students haven’t memorized it properly, or have mixed it up with another similar concept.
Students also have difficulty generalizing or applying the concepts to different situations. They may struggle to make new connections between concepts or use the concepts in real world situations. If you were to present them with a WCYDWT problem, I would imagine they would have difficulty making the connections between the real world aspects of these problems.
One of the best ways to address this memorization is derive any formulas we use in class, instead of just telling students to memorize it. I like this idea, but I wonder if students that believe math is memorizing will just zone out during the derivation and memorize the final formula. There has to be a better way to do this. Maybe some sort of inquiry-based activity is the answer here.
Rita also suggested that once a concept is derived, let your students name it. This will allow students to take some ownership of the formula and maybe they’ll be more inclined to understand where they got it from. Over time, you can begin to explain that the math community actually calls it something else, opening the door the “correct” math vocabulary.
Image from Flickr: Some rights reserved by Pragmagraphr
Five unhealthy beliefs in math that exist today are:
This past week I attended the NCTM Regional Conference held in St Louis, MO. At the conference, one of the sessions I attended was by Rita Barger from the University of Missouri-Kansas City about commons myths about learning and succeeding in math. This series of 5 posts will share what I learned from the session.
The “you have to be taught how” belief is the belief that you can’t do anything mathematical until someone shows you how. When I think about this belief, I wonder if it were true, how math would even exist to the extent it does today? Clearly, the mathematicians who have established the mathematics we teach our students, weren’t held back by this belief. That being said, I know that not every student that steps into my classroom will be a mathematician. Maybe none of them ever will, and that’s okay. I’m not in the business of generating math Phd’s, but rather, I hope my students can think critically and not be afraid to approach problems they might not yet understand. And, if students feel that they need to be taught how to do something before trying it, we have a big problem.
Me. You. Teachers everywhere. When we require students to do things a certain way, we lead our students to believe this, completely unintentionally. If a student tries to solve a problem, and arrives at the answer in a different way than we’re expecting, we might thank them for approaching the problem this way but encourage them to look at it from a different approach (our approach). I’m certain this is largely to make our assessment easier. It’s much easier to assess process when students are supposed to fit a specific template of process. Why would a student continually try to do things their own way? We’re just going to “fix” them later anyways. We like to encourage students into solving our way by asking them to “show their work”. Sometimes, teachers may refuse to give full grades if work is not shown.
Rita says that when we teach shortcuts, we can build on this belief. Often in math classes, we teach students an idea a certain way and then a few days later we make that idea obsolete by showing them a quicker, easier way to do the exact same thing (the concepts of polynomial long division and synthetic division come to mind). I struggle with this idea, because I know why it is valuable to show students the longer, harder way of doing things so they can appreciate and understand the shorter, easier methods we introduce later. But if we can do something quicker and easier, why wouldn’t we just teach that?
I think that the curriculum we are expected to deliver to our students also contributes to this belief. We have so many topics and concepts we are expected to get through, it doesn’t leave much time for students to inquire and discover math on their own. So, to make up time, we take some shortcuts, show some quick tricks. These quick tricks don’t teach our students how to think about math. If we are going to show them these tricks and shortcuts, there is no motivation to make connections on their own and find their own shortcuts.
If students buy into this belief, they likely won’t even attempt to solve a problem until you tell them how to. They may simply skip problems they haven’t been taught how to solve, with the expectation that you will come back to teach them how to do it later. This belief becomes a big problem when students begin to miss class time or stop paying attention for any length of time.
Once again, Rita suggests brain teasers as a way to counter this belief. Since the teacher doesn’t just provide a solution, students will need to find a way to solve it themselves, hopefully allowing them to realize that they don’t need to be taught to how to solve a problem.
Another idea is to get your students to solve problems in more than one way. This will show them that there is no one “right” way to do arrive at a solution. And, if you have a student who finds a solution in a way you have not seen, or did not expect to see, make a big deal about it and acknowledge that extra thinking and creativity that was used to find it.
We need to find a better to get our students to “show their work”, because we want to into their minds and assess the process of their problem solving. Instead, maybe we could ask students to “show their thinking”. It might seem like a very little difference, but it could open the door to allow our students to be creative in explaining themselves. Some may draw pictures, use diagrams, or even write sentences to describe what they’re doing. I would be very interested to see how students would choose to do this. This is a very simple change that I hope to make immediately.
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Some rights reserved by Jiuck
Five unhealthy beliefs in math that exist today are:
This past week I attended the NCTM Regional Conference held in St Louis, MO. At the conference, one of the sessions I attended was by Rita Barger from the University of Missouri-Kansas City about commons myths about learning and succeeding in math. This series of 5 posts will share what I learned from the session.
The “five minute” belief is believing that if you can’t figure out a problem in five minutes or less, you won’t be able to figure it out. I think it’s safe to say, that many people give it much less than five minutes. There are times where I wish students would just try it for five minutes. How often have students tried a problem and gave up after only a moment because it has become challenging? I see this belief every day I teach.
Our traditional teaching methods, where we tell kids how to do something before allowing them to try it on their own. By telling our students how to do everything before they even try, we kill the curiosity in our students that would allow them to try to find their own way to solve a problem. In many cases, they have never had a true opportunity to find, or try to find, solutions on their own. And, if this is how we are going to teach our students, why would they bother to try to figure it out? We’re just going to tell them the answers anyways, right?
I think this belief might also stem from our students fear of failure and fear to make mistakes. If every time they make a mistake, we are lowering their grades, why would a student take a risk to figure it out on their own? When students are only trying to get the highest grade possible (and who can blame them with the education system we find ourselves in today), why would they care about learning if they can find an easier way to get the grades they need (mimicking and copying you, the teacher). This is another topic in itself that I’ll save for another day.
Rita also suggested that students have come accustomed to seeing problems solved very quickly, through current TV shows that solve numerous problems in under 30 or 60 minutes. Maybe it’s not just TV shows, maybe seeing us (the teachers) work so easily and quickly through example problems make things look as if they should go much quicker and smoother. Maybe, as teachers, we need to make mistakes and display struggles more frequently to let our students know that it is normal and acceptable. I have a hard time picturing how I would do that, but it’s something I’m thinking about now.
A student might give up on problems quickly, before you even feel they’ve given it an honest effort. Sometimes, before beginning a problem, hands will shoot up in the air, asking where to start. Other times, it might be an “I don’t get it” before even reading or looking at a problem. And instead of asking valuable questions, they simply expect you start it for them and work through it “with” them.
I would also doubt that students who possess this belief ask a classmate, a friend, a family member at any point. They probably also don’t look back at any resources they have to help them out. They didn’t get it in the first five minutes, it’s hopeless. Why bother trying at all?
Rita suggests that teachers can generate a “did you?” list. A “did you?” list is a checklist that students would need to go through before getting help from you, the teacher. It would include items like “did you ask a friend?”, “did you check your notes?”, and any other “did you…?” questions that you feel appropriate for your students. The hope is that over time, students should get used to going through this check and internalize this checklist.
She also suggested that brain teasers can be an effective way to counter this belief. They can encourage students to think in various ways to try to approach a problem. The brain teasers may get students in the habit of thinking and trying, instead of giving up. When you give students a brain teaser problem, you do not give them the answer. Even if they can’t arrive at a solution in the time you give them. Rita told a story about one brain teaser that stayed on her board for over a month before a student was able to solve it. This helps illustrate that the math done by mathematicians (and arguably anyone else on a day-to-day basis), is never complete and answers don’t always come quickly or easily. Rita suggested that talking about the Four colour theorem, and the history of it, would be a great way to further illustrate this point.
Have you seen this belief in your class? What have you done to counter it?
Image from Flickr: Some rights reserved by * hiro008
Five unhealthy beliefs in math that exist today are:
I’m currently 7 weeks into my student teaching. Recently, I have drastically changed things in my classroom.
My classroom used to look like the classroom I had when I was a high school student. Students would sit in their desks and take notes (maybe) as I stood up front speaking to them or worked through a problem on the board. A few students would give me their undivided attention and build a decent understanding of the concept. A few students wouldn’t pay any attention at all and secretly text under their desk or have Facebook pulled up on their tablets. And most students would pay attention for as long as they could, lost attention for just a moment or two, and be lost the rest of the lesson. I would employ all sorts of classroom management strategies to keep my students quiet and paying attention. Then I would wrap things up, maybe give them a few minutes to try some problems, if I had finished things quicker than planned. Most of the time, however, I sent them home to try to tackle problems that they should have learned about during class (and some beyond that).
The result? I would end up spending the majority of the beginning of the next class reviewing the problems that students struggled with. Half of the students wouldn’t do the homework, some because they didn’t even try, some because they simply didn’t get it. Then I would move on, and start the cycle again, leaving many students with a weakly developed skill set that they’re expected to build upon in the next section.
In an effort to get out of this rut, I’ve flipped everything upside down.
Now, instead of struggling through the homework, and reinforcing bad/incorrect habits, my students are given a short video to watch and a couple of simple questions to respond to for homework. The questions are designed to allow students to think about what they’re actually watching, and why things are done the way they are. My favourite question so far has been “If you’re going to make a mistake doing this, where will it be and what is your plan to avoid it?”. The homework should usually take 10-20 minutes, much less than the “old” way.
Class is a completely different environment now. We start class by discussing a few of the points from the material the night before. I can then set students loose on a sheet consisting of a variety of questions related to the concept we’re covering. Students try things out and when they encounter problems, they can ask a classmate or they can ask me for help before they just begin to develop bad habits. I also have all the solutions posted on the wall for any student to see, and compare their answers to. By doing this, I have nearly eliminated the “Is this right?” question and replaced it with students trying to find their own mistakes and the odd “Where did I go wrong?”. The students who don’t need my help fly through the material and I have higher difficulty problems ready to challenge them when they do, and the students who need a little more help get extra one-on-one time they wouldn’t have had otherwise.
In my old classroom, if a student “forgot” to do the homework, they slowly fell further and further behind, unable to build upon previous concepts. Now, if a students “forgets” to do the homework, they either put in headphones or go into the hallway to watch and catch up. They return to class in no time, and start working with their peers.
Although I don’t think a “flipped” classroom should be chosen over quality inquiry-based or problem-based learning, it has proven to be a very effective way to teach concepts effectively, especially concepts like exponent laws and polynomial operations.
Note: all my current students have their own school-supplied tablet computer and access to internet in class and at home.
Image from Flickr: Some rights reserved by Hani Amir
I’m only six weeks into my student teaching and I’m slowly starting to get the feel of how a classroom works. I am starting to better understand what to expect in different situations, although there always seems to be something that surprises me.
However, there is one constant I have found in every class. No matter what we are working on, one question will always be asked a number of times:
“Is this right?”
It’s a simple yes or no question, right? Yet, I struggle with it.
I don’t want to tell them if they are right or wrong. I want them to know themselves. I want my students to be able to look at what they’ve done and be able to do some sort of self assessment. I want them to be be able to pick out their mistakes, and make the corrections. I want them to be confident in what they’ve done and not need me to tell them whether or not it’s “right” or “good”. I want them to see the value in making and then learning from mistakes.
I want them to do all these things. Then I expect them to write an quiz or a test where I will be the judge whether they’re right or wrong. Maybe I should ask myself: “is this right?“. No wonder they want me to tell them if they’re right or wrong…
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