So I've kept creating my geogebra files after spending two days figuring out how to upload them. I'm going to use this one next monday for my calculus students. 5 examples showing off the exponential, sum, and constant shortcuts of derivitives. Thanks to my mentor teacher I've a set of notes that goes over why we would ever want to use these rules and how we came to find them.
Not sure if I will spend any time whatsoever proving those rules but I will bring my calculus textbook just in case somebody wants to see the proof after the lesson.
In other news, I am super pumped about our whole school project as well, it should be pretty awesome but all we have so far is an idea in our heads. Look out world, here come the student teachers! I've been super lucky in finding friends in my colleagues and am looking forward to working with them more! Look forward to a report on what we have planned and how it went!
This took way too long to figure out... and yet... I did it.
Explanation: Export as dynamic webpage, change advanced setting to whatever you like, under advanced/files go clipboard: google gadget, press clipboard. Copy code to the file that comes up, save it as a file, press publish, then get code, copy the code, put it in blog html, publish to blog. Ta da!
My mentor teacher is awesome and let me design one of his calculus labs! With the help of John Scammell and the Twitter Community, and a little push from the school chemistry teacher, this is what I've come up with!
My school just got a set of CBL probes and I am totally excited to use them! I'll let you know how it goes!
By popular request I have asked my friend Christine if I could post her lesson on Settlers of Catan and she said yes! So here it is!
The worksheet she used for us to record our observations and predictions:
And finally here is the excel worksheet! This is probably the most awesome part of this great lesson!
I think the only thing I might do is add this to the logic and puzzles unit somewhere and have them actually play the game afterwards! Thanks Chistine!
I want to put out a special thanks to John Scammell for providing me with this lesson! It was amazing and quite honestly, very entertaining! Some of the images are his, one of them is Dan Meyer's, and I sort of mashed everything together to recreate a lesson that John taught to a class somewhere here in Alberta! It was fantastic!
Here is a link to the notebook file I used: honestly, the activity was not tech based at all and the students still loved it!
Finally, the activity sheet I used so students could record their observations, measurements, and calculations!
Was this activity successful? Absolutely. One student said “it managed to be applicable to real life.” Another said it was “interactive, engaging, and inquiry based.” Yet another said that it “showed an application that 20-3’s will be excited to complete and learn.” However, in my opinion, the most useful comments are the ones that will make this lesson stronger and more memorable for students. One of my peers pointed out that “in order to be [more] accurate you need to be farther away” when using the clinometers. “A thorough discussion of error” is needed, and “spending more time on some of the strategies and how to measure more accurately using the clinometers” both came up several times in the feedback. Quite frankly, I agree with them.
The time provided to introduce this activity to my peers was not quite enough to fully appreciate what they encountered. Our opening exercise would have included more than identifying trigonometric ratios and the introduction to the clinometers would have included building them and measuring the angle to an object at varying distance had there been more time available to enjoy the activity. With more hands-on experience and more time to explore the use of the clinometers students would have observed the rules of the clinometers on their own and would have begun to think about how else these tools could have been used. I have often felt pressured to perform while teaching in a classroom and the results during these times are always poor. When teaching my grade eight class last year I was told that I was speaking far to fast for anyone to keep up. Making a small leap in logic here, I can assume that it is also possible to move a class too fast through an activity. Without the proper amount of time available to students they will have trouble making connections.
A lot of the students forgot to add their own height to their estimate while measuring the height of the Education Cafeteria. Others didn’t use angles at all, preferring to measure the height of the windows and multiply that by three, estimating for the difference in height of the windows. What is really interesting though is that some students preferred to use meters in their answers instead of feet. When the answer was given in meters some of the groups cheered about how close they came and others ran to google to convert the measurement into meters. Kieren talks a lot about teaching mathematics with a focused, yet open mind. Not looking for a specific answer and yet keeping the class moving towards the final goal, ie. the program of studies. We need to think about teaching with respect to how our students are thinking about the subject. A good discussion to add to this lesson is one that explores the way that different groups found their answer and the strategies that they used.
While teaching during my IPT, I gave students an assignment to explore the NASA website. However, after looking at the assignment, two of my students decided to write their own fictional story and base their calculations on the scenario that they described. Their zeal for the assignment went from nearly no interest to extremely interested when they were allowed to explore the material in a manner that appealed to them. I find the same thing often happens to me while completing assignments. Pedagogically, this lesson became an inner argument of control in the classroom. Allowing the students the freedom to leave the classroom and giving them the responsibility to return to the designated meeting spot can motivate students who would otherwise feel micromanaged and creates an atmosphere of open ideas and solutions. This can be the basis for building mathematically confident and inspired learners. Students who feel empowered within a classroom are more likely to share, communicate, and practice the skills that they’ve learned; which will in turn creates a healthy student/teacher relationship with my students!
I worked on this for a while. I guess I am hoping for it to become a regular part of the Math 20-2 or 30-2 classes I teach! But I know it hasn't been tested and that I haven't exactly been teaching very long at all!
Grade Stream & Strand: Math 30-2
Topic: Mathematics Research Project
I have a start up activity you could use for this particular lesson but I really wanted to introduce the meat of the material. So let me preface this with my belief that mathematics is a language and that if we want to practice this language we really need something to talk about. So I let the students watch this video in class, probably just after our warm-up activity:
America’s native prisoners of war: Aaron Huey on Ted.com (15:28)
The material is fairly heavy and, in my opinion, should not be shown without giving the students a chance to reflect on what Aaron has to say. He talks about how the entire history of the indigenous people of the Black Hills have been, and are still being, taken advantage of! He talks about their history, about their fight for independence, about their lives, and about their sufferings. Now, I wouldn't want to force students to talk about something like this but I am sure that they would be more than curious about the history of the Lakota people as presented by Aaron Huey and will need very little prodding to have an in depth conversation after watching this video. Some conversations that might happen?
Maybe start off with "What are your initial reactions?" or "Has anyone heard of this before?" or maybe even "Wait, this stuff is really happening?"
Perhaps that will lead into something like this, "How do we know he's telling us the truth?" or "How can we tell he's telling us the truth?" and thus: "Where did these statistics come from?"
Or, maybe it would lead this way: "Is their any reason to believe this man is lying to us?" or "What bias does the man have?"
These questions, I believe, would be the crux of the lesson. They would be the real reason for exploring any further! Or perhaps this question would be: "What are the solutions to this issue?" or "Can the problem be solved?" And it would become my job to allow students to begin exploring different sources! I suggest something like Stats Canada but depending on the direction your students feel like taking it would be impossible to predict the sources they might need. They might even want to research the history of the Aboriginal people in Canada and the domestic statistics! Who knows! And it begins...
They research, they think, they probably scream a little because they can't find anything relevant or none of their information is consistent with any other information they find. They begin to see different sides of the story and start to connect Math with their Social Studies class, wouldn't it be great to see them ask their Social Studies teacher for help regarding their Math assignment!?
Questions like "Is this stuff for real?" or "Could you make sense of this for me?" or "How does this even happen in Canada?" or "How many different versions of history are there? Can you tell me about this one?"
Of course I am not at all prepared to lecture on the history of indigenous people in Canada but I do feel quite prepared to engage in conversation about indigenous history in Canada. This may even be a good entrance point for an Elder in the local aboriginal community to come and take part in the conversation!
From here on the only natural thing to do is to learn more about these topics! So with the program of studies in mind I would ask students to collect all of their learning into one grande presentation to share with the class. Ask students to include how they found their information, to create unique ways of presenting their data, and to discuss how they verified the data that they found.
And have fun! There is nothing more boring than a teacher who doesn't want to be teaching. Encourage conversation, wait for responses, give your students a lot of time to reflect on what they see and include everyone in the activities. Above all else I would say, be excited for what you are about to learn! You do not know everything! So don't act like it! When we are learning alongside or students we tend to reflect our strongest learning characteristics. I've found that students often need to learn how to learn, and that can't be shoved down their throats; it's gotta be from watching us learn.
Here are the files. Take a look at them, enjoy them, try them! I know I certainly will!
