Derivitive Shortcuts

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!

Understanding Tangents as Limits of Secants.

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!

Which cup is better?

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!



Hopefully it's not a complete bomb!

Lesson Starters!

So I've been working on some lesson starters in class every day and here are the results!  We were practicing different problems and then marking them holistically.  They are for a bunch of different classes  and stretched our thinking a lot! Have fun trying them for yourself!

Math 30-1: Settlers of Catan!

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!

Polynomial Engineering

This was presented to me by Renee Jackson and is absolutely incredible.  I want to develop it further to include negative tiles!

Here are the templates for the algebra tiles! It will probably take a while to make a class set so start early!

I should just say, for about an hour and a half about thirty math teachers were entranced by this!

Algebra Tiles - A Developing Concept Plan

This isn't a particularly useful outline of an activity we presented.  However, there are very useful resources attached throughout the paper and the papers we researched and included in the bibliography are incredible!  Plus, all the research we did gave me an idea about how to teach negatives in algebra through area explorations, rectangles, and squares!  I'm really excited to develop it and will post it when I finish putting it together!  I promise it will be awesome!



Right from the start of our presentation we had some pretty big issues with the technology we wanted to use. One of the problems with setting up on the spot is that there is no time to test and make sure everything is going to function properly. Initially, the Notebook software we needed would crash every 15-30 seconds after opening it, so our SmartBoard aspect was almost completely useless. Fortunately we got it to function just as we needed it, but the SmartBoard was out of calibration and it wasn’t calibrating properly. Overall though, once we got past these couple bumps and bruises with the technology, it all worked smoothly for the most part. It definitely would have been helpful to have a backup plan for a scenario such as this, as technology can at times be finicky, and there is not always time to fix it.  

Our peers were already well versed in algebra tiles thanks to the previous days activities.  The time that they spent exploring squares and their properties was invaluable to our presentation.  After some reflection I could not help but think the concepts that we presented were far too vast for a 45 minute presentation.  However, if we were to have split the activities that we had into four different presentations then the product of our presentation would have been far more effective in teaching our peers about the properties of algebra tiles.  A more focused exporation of positive algebra tiles, a more intense activity involving the properties of negative tiles, and a single activity exploring the properties of lattice multiplication that tied into a factoring activity later on would have created an atmosphere that allowed the students to explore the tiles themselves later on.  Concerning the properties of positive tiles, there was a need to allow students to further explore the concept of multiplication as represented by area.  Adding further tiles of different shapes and sizes to this activity would have expanded the learning potential.  However, having students build squares and rectangles from predetermined sets of trinomials allows them the opportunity to get comfortable and familiar with the materials before getting into the more difficult ideas of negative area and factoring.

In regards to teaching students about trinomials containing negative terms, we found that it would be useful to review the concept of operations involving integers.  During our presentation is was somewhat difficult even for our classmates to understand why it is needed to keep all negative algebra tiles together along one side of the trinomial representation and all positive tiles along the other side.  Renée brought up a great point which we could have explained.  That is, when multiplying a negative integer with a negative integer we get a positive product (same with a positive integer multiplied by a positive integer).  But when we multiply a negative integer with a positive integer we get a negative product.  If we were to represent our trinomial with negative and positive tiles interspersed, even if the tiled representation generates a square or rectangle, the placement would not satisfy our mathematical rules for integer multiplication.  This would have aided in addressing any confusion that our students may have when investigating with algebra tiles.

After using tiles to build squares and rectangles to factor since grade nine I have only one new suggestion.  The idea of negative area, as presented by Andrew and expanded upon using tile activities, would allow students the opportunity to explore the concept of algebra tiles even further.  Using black negative tiles, colored positive tiles, and a black backdrop could enable us to teach about polynomials using direction.  Statements such as “the black negative tiles cover up portions of the grid that we don’t want to find the area of” would be possible and the need for integer multiplication of negatives would not be needed to determine which color tile is needed to complete the rectangle students are building.  Instead we could use questions such as “do we want to find this area or is this part of the section we don’t want to find the area of?”  However, consistency is important in mathematics and allowing students to use integer multiplication in order to factor is a useful and familiar tool that students can use without too many misconceptions being made.

When working in a group it is hard to have a proper flow. In group work, I think there needs to be more practice on the actual presentation, to ensure timing and flow of thought is clear. This is also true in individual teaching. It may take more then one try to present a lesson properly. This is why it is important to have a detailed lesson plan to follow, or for others to follow. It may also be helpful when presenting a new topic/lesson on the first time it might be helpful to have notes or an outline handy. It is important to remember that a concept may take more/less time then you had originally thought to cover in a period. It is important to remain flexible and allow for some changes. Having problems or an extension activity is a great idea for making up for any shortcomings. Also, keeping an eye on the clock and managing the time properly is very important.


Written by Christine Crowe, Andrew Johnson, Kim Simon, and Darcy Bundy

A Math 10C Resource Analysis!

We put a lot of work into making this a real, viable resource for any teacher's using this textbook!  Included is an analysis of the textbook, its strengths and weaknesses, and links to supplemental resources to compliment the textbook where it falls short of the curriculum!

Mathematics 10C on Prezi

Enjoy!



And a quick look at how exactly the textbook matches the curriculum along with more resources!

Angle of Elevation and Depression!

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!

Information

My grade 8 math class had been studying percentages, fractions, and ratios for several weeks.  Each day I would try to find some sort of real life application of fractions; my thought being that if students were familiar with real life ratios and fractions then they would be more comfortable talking about them abstractly in the classroom.

Some days I would show something extremely simple.  Such as juice:water ratios, and some days I would simply show them pictures of really cool things such as people hanging from the space needle cleaning the side of the tower.  But one day I showed them this:

How much revenue was there in the food sales industry? 

Not exactly your typical Grade 8 Math problem.  Not exactly a math problem at all... just a snipet from a newspaper somewhere on the internet.  You'll have to forgive me for stealing it.  It isn't the problem that is interesting though but the reaction from the students.  

See, I've been studying online learning communities and their seemingly addictive nature.  Places like WoW online communities, Starcraft, eduBlogs, pinterest, technology problem solving forums, and basically any other site which gives users the ability to access any information they want to access regardless of their learning ability.  These places let novices and advanced learners alike interact with each other without discrimination.

My students first reaction was "Could you maybe just tell us how to find it?" when I introduced a more advanced problem for students to ponder and told them we weren't going to solve it that day.  I could have said "We don't have the time for that." or "We might come back to it later."  But instead I asked myself what I would honestly do if I was so curious about something.  Honestly, I would probably tune out, ignore my teacher, talk to some friends about a solution, roll it around in my head for a while, and then wake up in the middle of the night with a whole "ah hah!" moment.  Well... I've only ever made it to the "ah hah in my sleep" moment twice in my life.  

So I took a minute in my classroom and appeased their curiosity for their sake and my sanity.  Seriously, access to information in a classroom is often extremely limited!  And that is not what I want in my classroom.  Students should be able to ask, explore, and even be satisfied and comfortable with an topic, or at least informed enough to access the information on their own later on.  

Teaching Video October 2010

Darcy’s Teaching Video (Produced on November 2nd of 2010)

This video was produced as a tool for self-evaluating my teaching.  It includes key portions of the lesson that I presented in Math 337 to a group of my peers.  The entire lesson is available in the post named “Lesson plans I Approve Of” and can be viewed at your convenience.  It is a teacher-directed approach to the transformations chapter in the Relations and Functions unit of Math 30-1.  In summary, the lesson began with an introduction and continued with a lecture, class discussion, coached work, a conclusion, and independent work.  The lesson that was presented in class was meant to be a supplement for students who had finished their independent work.  Far to often teachers give advanced students more work to complete.  This project is designed so that students do not feel as though they are being punished for their efforts in my classroom, rather they are rewarded with a meaningful experience.

Upon viewing the video I quickly noted a desperate need to ditch the white belt.  The teaching implications of the video are two-fold.

First, there should be a focus on increasing student participation in my lessons in the future.  No one likes getting lectured to, even University students.  Definitely not high school students.  I feel that this activity is fine for a class that is teacher directed, such as this lesson, but I would like to create classes in which the students discover the material in a more meaningful way.  The alternative lesson plan that we created incorporates this concern into the design with a constructivist approach to the chapter.  It is available here:

http://eportfolios.ctl.ualberta.ca/nyoung/category/a-mathematics-for-teaching/mathematical-activities-for-the-classroom/

Second, I feel that the time I allow between student responses and my clarifications should be longer.  Students may perceive my knee jerk reactions as inconsiderate or rude and may begin to take advantage of it if I begin to give away answers.  If I can begin to slow down my responses it will give other students in the classroom a chance to evaluate the answer given before being spoon-fed the logic behind the answer.

Math 30-1: 2.2-2.3 Transformations

This is a lesson from Mathematics 30-1 ‘Relations and Functions’ that my partners and I created!  Feel free to peruse it at your convenience!

Horizontal & Vertical Stretches Worksheet

Horizontal & Vertical Translations Worksheet

Tessellation Project

Transformations Lesson Plan

Transformations Powerpoint Day 1
Transformations Powerpoint Day 2
Transformations Powerpoint Day 3

Rationale for Transformations Lesson

Our colleague David Adams produced this lesson as a wonderful addition to the Math 30-2 ‘Logical Reasoning’ unit:
Logical Reasoning Lesson Plan
Logical Reasoning Lesson Plan Version 2

Big Ideas Reflection of Math 20-1

My colleagues created a poster to portray the big ideas of Math 20-1:

The most interesting and informative big idea presentation was the Math 20-1 poster by far.  The connection between the curriculum and the big ideas presented was very explicit.  Your eyes were caught by the 3D-effects and pulled into the center where the main units of the curriculum were located.  On the edges of the poster there were small pull-outs so that anyone who was interested could sneak in close and read about the units in more detail.

The poster reflects the values of the Charles article and was very informative.  If I were to dissect the more in depth pieces of the poster (ie. the leaves) I would find that I could determine exactly how the course is laid out, what the big ideas of the course are, and the focuses of the course as it applies to the values of mathematics as defined in the program of studies.  Students who proactively become involved with this poster would benefit from a greater knowledge of the course and a more holistic view of the teacher’s expectations.  Onlookers can get a sense of what is involved in the course even though the Big Idea’s of the course have not been explicitly provided.

From the poster I would determine the Big Ideas of Math 20-1 to be:

1) Students will become familiar with and begin to use different expressions involved in algebra and numbers.

2) Students will develop their understanding of functions and equations as they relate to the cartesian plane.

3) Students will use the basic trigonometric ratios, as well as the sine and cosine laws, to solve problems.

It would have been more useful if the students did not have to determine these ideas for themselves.

The Big Ideas of Math 20-3

A short reflection about my experience with the big ideas of Math 20-3.

Big Ideas of Math 20-3