Ok so its been a while for blogging but here goes.
Introducing Linear programming to my yr 13 alternative stats class tomorrow. Its one of the most authentic maths we do. Completely connected to the real world and yet most of us still teach it by skill first then context.
Last year I changed it up a little but this time I am going to completely change how I do it.
I found this great video. Introduction to Linear Programming
This guy does a great job of introducing a real world problem using a belgium chocolate business example. I could flip this lesson which I would do if I had a mainstream group but I am going to watch the video with the girls and work through it with them.
I have used a video website " teachem"that allows me to insert questions as we watch the video. I will give the girls a worksheet to fill in as a they watch TEACHEM VIDEO. Place this on Moodle so anyone can watch it again if they want.
I am hoping that I won't need to introduce separately the idea of an inequality as it will be a non-issue from the context. What making an expression into an inequality means and why we do it.
So this lesson will be only about writing the constraints, identifying the variables, and creating an objective function from context.
THEN the next step is all about the graph work. Here is where I do the skill work around using graphing calculators to create graphs and tables of points. But my hope is that they have something to hang it all on and understand why they need these skills.
If I had my choice I would use Desmos to do all the graphing work...its so good for this but they can only use graphing calculators so they need to get really good at rearranging and using x and y intercepts.
I will let you know how it goes.
Monday 23 March 2015
Tuesday 29 July 2014
Designing a multimedia learning tool for maths using google docs, desmos and video
So today was the first day of the girls working on the google doc that I had created on exponential graphs.
If you are interested in the resources its in my previous blog. It was a surreal kind of experience. They were quietly working, headphones on as they listened to the videos, then working on the doc, using calculators to assist their working. There was discussion, although somewhat minimal, with very few questions. I had spent a lot of time making the resource a comprehensive guide that could be completed without me present. It certainly seemed to be successful in that regard.
I had very little to do. The creation of the document was labour intensive, but implementation was a non-event. I really struggled as to what to do with myself. Normally I would have expended enormous energy with the proverbial song and dance of the Sage. The girls were quietly engaged and my hope is, that because they are having to think as they go, their inquiry around the topic and their understanding will be enhanced...time will tell.
Tomorrow I will have a wrap-up session to be sure that all students came away with similar messages and to answer any questions. Then there will be practice to help consolidated their knowledge.
I don't necessarily see flipping a lesson as a viable strategy simply because if all classes were doing it it would mean students would be spending incredible amounts of time at home on their learning. I still believe that school is the place and time for learning of new material. But with this approach 3 things happen. It frees me up to address every student's concern immediately, and it gives them and anyone missing the lesson a complete interactive resource on a particular topic. Lastly it allows students who need to see instruction more than once, an opportunity to do just that.
I won't have the time to make an entire unit of work in this frame, but I can see its true merit, and I will be doing more of this type of structuring of my class ......it was fascinating to watch.
Next, student feedback on the process.
https://docs.google.com/document/d/1VCqGiNPh00cEQqEZv6zQuY7GTSgun_f5j8sKqz5-CbY/edit?usp=sharing
If you are interested in the resources its in my previous blog. It was a surreal kind of experience. They were quietly working, headphones on as they listened to the videos, then working on the doc, using calculators to assist their working. There was discussion, although somewhat minimal, with very few questions. I had spent a lot of time making the resource a comprehensive guide that could be completed without me present. It certainly seemed to be successful in that regard.
I had very little to do. The creation of the document was labour intensive, but implementation was a non-event. I really struggled as to what to do with myself. Normally I would have expended enormous energy with the proverbial song and dance of the Sage. The girls were quietly engaged and my hope is, that because they are having to think as they go, their inquiry around the topic and their understanding will be enhanced...time will tell.
Tomorrow I will have a wrap-up session to be sure that all students came away with similar messages and to answer any questions. Then there will be practice to help consolidated their knowledge.
I don't necessarily see flipping a lesson as a viable strategy simply because if all classes were doing it it would mean students would be spending incredible amounts of time at home on their learning. I still believe that school is the place and time for learning of new material. But with this approach 3 things happen. It frees me up to address every student's concern immediately, and it gives them and anyone missing the lesson a complete interactive resource on a particular topic. Lastly it allows students who need to see instruction more than once, an opportunity to do just that.
I won't have the time to make an entire unit of work in this frame, but I can see its true merit, and I will be doing more of this type of structuring of my class ......it was fascinating to watch.
Next, student feedback on the process.
https://docs.google.com/document/d/1VCqGiNPh00cEQqEZv6zQuY7GTSgun_f5j8sKqz5-CbY/edit?usp=sharing
Thursday 24 July 2014
A little bit of Flip and a little bit of That.
Ok so have spent some time putting together an inquiry maths task on yr 12 graphs mixed in with some guided teaching. My goal is to have the students work through the google worksheet by going to the linked sites and working it through with each other so I am not at the front of the room directing. My students have found this model quite unsettling but I am going to keep pushing them.
I have set up links to desmos a graphing online site( love it) and I have also linked in some video to help guide the students through the important points to focus on.
If anyone is interested here is the google doc
https://docs.google.com/document/d/1kRJpk1jiTFz3lgbi3c5k1mnJks5svM2yp3FR8okHK00/edit?usp=sharing
Here is one of my desmos prepared sites.
https://www.desmos.com/calculator/dyee1raieq
Saturday 5 July 2014
"Change" expecting the joy , living with the uncomfortable outcomes.
This past week I spent a fair bit of time designing a few lessons for my year 12 maths class around graphing functions. I decided to use a lovely online graphing website called Desmos to offer up the introduction to the topic. I started with quadratics, a topic the students are quite familiar with. My expectation was that students would be happy to engage in an exploration on a function that they already knew something about.
I was so pleased with myself. I had designed a google worksheet that lead them to the outcomes they needed and links on a google doc that allowed them to go to pre-prepared desmos graphing sites which would help them with their exploration. How clever was I!
What I was expecting was a happy engaged group of girls where I could be out of the main fray and have the learning in the hands of the students with sprinkles of my intervention when they got lost.
What I witnessed was 40 minutes of uncomfortable activity by a group of girls who blinked lot and kept looking to me like I had just thrown them into a den of goblins. Really?? It was so disappointing. Where was the wow factor, the joyful chatter of collaboration, the grateful recognition that Ms Crabbe had stopped talking at them and allowed them to think and work independently, to explore and consolidate in their own time the features of this concept.
I reflected that night on this, looked at my clientele and realise that this structure was a foreign land for these students in maths, a subject they lack confidence in. Although I try to change it up as much as possible, their model of learning maths has never looked like this. Its always been a teacher showing a process and then having the students mimic that process. Its never been about finding their way with a minimum of teacher input. When we went over what they had learned the next day , they had indeed come to most of the right places, and more importantly I discovered their misconceptions, the things they understood and could add clarity where it was needed.
So the next day I gave them something similar to do, no blinking, no fear, they just got on with it confident that at the end of the trail the destination would be made clear.
What did I learn?
That changing pedagogy and how learning happens it not just difficult for teachers, but students as well. That not all students will embrace this different approach and that you must be gentle in the implementation. That one must persist but be willing to go back and forth between the new and the old to get where you need to be. To remember the journey of learning is not about how flash the tool, how thoughtful the preparation, its about the students, its about getting them to think, to challenge, to do deliberate and meaningful practice. And sometimes it has no wow factor, sometimes it just about, as a teacher, being able to sit still, amongst the uncomfortable, puzzled expressions that plead silently for rescue...... and do nothing.
I was so pleased with myself. I had designed a google worksheet that lead them to the outcomes they needed and links on a google doc that allowed them to go to pre-prepared desmos graphing sites which would help them with their exploration. How clever was I!
What I was expecting was a happy engaged group of girls where I could be out of the main fray and have the learning in the hands of the students with sprinkles of my intervention when they got lost.
What I witnessed was 40 minutes of uncomfortable activity by a group of girls who blinked lot and kept looking to me like I had just thrown them into a den of goblins. Really?? It was so disappointing. Where was the wow factor, the joyful chatter of collaboration, the grateful recognition that Ms Crabbe had stopped talking at them and allowed them to think and work independently, to explore and consolidate in their own time the features of this concept.
I reflected that night on this, looked at my clientele and realise that this structure was a foreign land for these students in maths, a subject they lack confidence in. Although I try to change it up as much as possible, their model of learning maths has never looked like this. Its always been a teacher showing a process and then having the students mimic that process. Its never been about finding their way with a minimum of teacher input. When we went over what they had learned the next day , they had indeed come to most of the right places, and more importantly I discovered their misconceptions, the things they understood and could add clarity where it was needed.
So the next day I gave them something similar to do, no blinking, no fear, they just got on with it confident that at the end of the trail the destination would be made clear.
What did I learn?
That changing pedagogy and how learning happens it not just difficult for teachers, but students as well. That not all students will embrace this different approach and that you must be gentle in the implementation. That one must persist but be willing to go back and forth between the new and the old to get where you need to be. To remember the journey of learning is not about how flash the tool, how thoughtful the preparation, its about the students, its about getting them to think, to challenge, to do deliberate and meaningful practice. And sometimes it has no wow factor, sometimes it just about, as a teacher, being able to sit still, amongst the uncomfortable, puzzled expressions that plead silently for rescue...... and do nothing.
Saturday 21 June 2014
Engagement takes a little change in scenary
I continue to try changing the way I do things. Trying very hard to limit the time I spend at the front of the room. Its not always possible.
Yesterday i was teaching year 13 stats class about solving simultaneous equations. This is a alternative class so students range in ability and intrinsic motivation. I did a fairly traditional period of teaching around this because these students really need the basic ability to follow a procedure when solving. Some students got it but many struggled and shut down. Today I wrote down 5 questions on sticky notes and placed them on my wall white board, my interactive board and , and 2 small mobile whiteboards. I gave them pens, told them to work in 2s or 3s and complete 3 of the 5 questions..some did all of them.. I was able to go around and coach the group that was really struggling but the change in engagement was exponential. Those students who sat in chairs yesterday blinking continually, were up and writing.
It was very unstructured a bit chaotic but very enjoyable...and the girls came away with a lot more confidence that they could in fact do this. Sometimes its just a little change, a subtle, low tech hack that can be very effective.
Yesterday i was teaching year 13 stats class about solving simultaneous equations. This is a alternative class so students range in ability and intrinsic motivation. I did a fairly traditional period of teaching around this because these students really need the basic ability to follow a procedure when solving. Some students got it but many struggled and shut down. Today I wrote down 5 questions on sticky notes and placed them on my wall white board, my interactive board and , and 2 small mobile whiteboards. I gave them pens, told them to work in 2s or 3s and complete 3 of the 5 questions..some did all of them.. I was able to go around and coach the group that was really struggling but the change in engagement was exponential. Those students who sat in chairs yesterday blinking continually, were up and writing.
It was very unstructured a bit chaotic but very enjoyable...and the girls came away with a lot more confidence that they could in fact do this. Sometimes its just a little change, a subtle, low tech hack that can be very effective.
Vulnerablility leads to Powerful Learning Moments
So the other day I was having a math lesson similar to so many . I was at the front of the room we were engaging with an excellence level question on discriminates when a funny thing happened. The students were struggling so I jumped in to rescue as I always do. I hadn't done the question in a while and I got the wrong answer. I had made a mistake along the way and initially I couldn't find it.
I heard some murmuring and could feel the uncomfortable shifting of students. I could hear their silent voices saying, she can't do the question, so how can I do it?
It's a difficult place to be as a teacher you are suppose to be the expert, everything mathematical should be easy to you, you are completely exposed. Your brain is screaming with tales of lack of preparation and lack of expertise. And then something amazing begins to happen. We start to have a discussion, the students start to lead that discussion. We work together to find the mistake.
The room becomes a collective of humans searching for a solution and trying to find meaning. They help others understand what happened and where the work should go. I step back , take a deep breath and let go of my ego and realise what is happening and move with it. When we are finished, my image as "the expert " may be tarnished, but the students understanding of a difficult question is completely cemented in most students brain. There are still some rumblings of discontent at the uncomfortableness of not having someone at the front who can rescue them from confusion but I realise what just happened is ten times more powerful then if I had smoothly jumped in and rescued them. They would never have seen the pitfall , the potential errors, grasped the understanding of what lead to the error in the first place.This not the first time this has happened, I am not a trained maths teacher, I am a person that over time has evolved into this role. It often requires hours of sitting down with content and learning the skills myself . I have at times found this to be both a blessing and a curse, but it enables me to work with great empathy and to understand what a growth mindset is all about. I am a poster child of that growth mind set, something to be proud of, and something to continue to encourage in my students.
What at one time I would have identified this as a "bad lesson", became this powerful epiphany of learning. I am sure many students left with a sense of uncomfortableness, but I am equally sure that many students went away with a sense of empowerment and confidence that they really understood the question on a much different level.
So I think the next step will be to have a conversation around that experience and have them discuss that situation as a learning model and as a model that sets them up for life after high school. There will seldom be that " expert" willing to rescue, so what will you do then?
Friday 30 May 2014
Beginnings
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