Well today is our last day of regular classes, the final game of the NHL and will also mark the last blog for this school year.

I want to say thanks to everyone who helped me have the most professional developmental year ever!!! This year, I feel I have engaged my students through authentic assessments, and also with true lessons of discovery.

I will start back up again August 30th.

Below is the final compilation of how my students demonstrated their learning in my calculus class.

Coming together to create a real learning environment for students

## Wednesday, June 15, 2011

## Tuesday, June 14, 2011

### 65 year plan when a student is 14?

Here is a post from Lisa, an ex student of mine about having students plan 65 years into the future.

For all those who are graduating or or all those who have already gradated from high school, you probably know what I’m talking about. Everyone tries to convince you that you need to have the next 65 years of your life planned out. No joke, I had to make a 65 year plan for a CALM assignment. In reality though, everyone’s wishing they could go back to the days when the world was before them and they had time to make mistakes and choose something different. So why is everyone trying to get us kids to rush into something if they’re not even sure what they wanna be when they grow up? I get that going to school, getting a job and making money are all important. But so are things like maintaining relationships and gaining life experience. Some people think I’m foolish because I haven’t got it all figured out yet. Personally, I think the most foolish people are those who pick something to do because they feel obligated to, instead of living life to the fullest while you’re still young.

## Wednesday, June 8, 2011

### Samples of work for Integration Project

Below are some samples of the work completed by various students for the Integration Project

Part 1:

Part 2:

Part 1:

Part 2:

Video for Part 3:

Work

## Tuesday, June 7, 2011

### Call of Duty and Vectors

I have shown how Call of Duty can be used in Calculus, and here is how it could be used in Vectors.

A student found this video and she demonstrated her knowledge of vectors:

Playing capture the flag, Johnny was camping at a bearing of [043º] and noticed an enemy 52m away running towards Johnny’s flag approx, only 27m away from the flag. What degree does Johnny have to turn to shoot the enemy when he reaches the flag and what is the magnitude of the shot?

A student found this video and she demonstrated her knowledge of vectors:

Playing capture the flag, Johnny was camping at a bearing of [043º] and noticed an enemy 52m away running towards Johnny’s flag approx, only 27m away from the flag. What degree does Johnny have to turn to shoot the enemy when he reaches the flag and what is the magnitude of the shot?

Vector one = 52m @ [043º] Vector two = 27m @ [134º]

90-43 = [047º]

134-90 = [044º]

47+44 = 91 = 180 – 91 = [089º]

52^2+27^2-2(52)(27)Cos89 = 58.2

The magnitude of the bullet is going to be 58.2fm.

58.2/Sin 89 = 27/Sin(y)

Sin(89)*27/58.2 = [028º]

johnny is going to have to turn 28º.

## Sunday, June 5, 2011

### Appreciate don't crticize

Students do not like to be told what to do, but instead are motivated by getting what they want. There are no tricks, no manipulations, or deals that work endlessly. As teachers, we need to use the interests of students, their passions and desires, to show how our curricula can relate to their everyday life. Students want to be important, great and have a true desire to succeed. I believe it is the responsibility of the education system to show every student that this is a real and attainable possibility.

William James said “The deepest principle in human nature is the craving to be appreciated”. As I reflect back into my classes, I believe I have failed my students on this. Lately, I have been showing how I appreciate every single student. From the ability to use calculus on Call of Duty to being able to draw a line graph, each student must feel as they are contributing to my class in a specific and identifiable way. Too many classes, in the past, I stood at the front of the class, lectured only in a way a mathematical mind would understand, and then sat at my desk worked. This had to change!

What happens when people don’t feel appreciated enough?

I have seen this too many times. Some call it disobedience or insubordination, but it might just be the student saying “Look at what I can do!”. In some cases, people have actually gone insane to allow them to live in a world of their own creation. Carnegie said, “Imagine what miracle you and I can achieve by giving people honest appreciation this side of insanity”

Two years ago, I had a student in my class who was truly bored and wanted to be challenged beyond the scope of the course. What I saw was a boy in the back of the class who would rather play on his calculator drawing weird diagrams than pay attention to me. Days went on where I would walk to the back of the room and delete all his graphs to keep him on task. I am sickened, now, by my actions! I was criticizing his amazing ability to transform math into art. There is even more disgust; this student saw me as his “math guru”. I was condemning a student, who idolized me, on his math ability.

Charles Schwab stated:

“There is nothing else so kills the ambitions of a person as criticisms from superiors. I never criticize any-one. I believe in giving a person incentive to work. So I am anxious to praise but loath to find fault. If I like anything, I am hearty in my approbation and laving in my praise. I have yet to find the person, however great or exalted his station, who did not do better work and put forth greater effort under a spirit of approval than he would ever do under a spirit of criticism”

Lately, I have taken this quote to heart and truly been communicating my appreciation of students daily. Students crave appreciation as they would crave food, or air. It would be outrageous for a teacher to deny a student appreciation for an entire semester, as it would be to deny them a plate of food.

## Friday, June 3, 2011

### The math behind the lotto 649

In my Math 30 Applied Class, we had to cover probability. Instead of using context questions around dice, spinners, and marbles, I allowed students to research any topic they found interesting around probability. I would like to show you: "The math behind the Lotto 649" by Christine, one of my students.

Many people in the world play the lottery each year. You might believe in faith, chance or luck but I believe in math. As you already may know, the chances of winning Lotto 6 49 is not very likely. So why do people play? I can’t really answer that question but for those who are sceptical I can convince you on why you shouldn’t play.

The probability of winning the Lotto 6 49 is 1 out of 13,983,816. The probability of losing the Lotto is 13,983,815 out of 13,983,816.

I’m going to make a scenario about a man named Dave who started playing 6 49 at the age of 18 until he was 80 years old. He bought a ticket twice a week. Each ticket consists of two rows, so technically he is playing four times a week. What is the probability of Dave not winning in his life?

Dave played the lotto for 62 years in his life.

There is 52 weeks in a year.

4/week x 52/year x 62 years = 12896

The total amount of times Dave played is 12896.

13983815/13983816 = 0.9999999999999…..

0.99999999999……^12896 = 99.9%

The reason why you shouldn’t play the Lotto 6 49 is that the chance of you not winning is 99.9% in your life time.

How much money would you spend on buying the tickets?

Each line is 2 dollars and you played 12896 which is 25792$.

## Thursday, June 2, 2011

### Using Video Games as Assessment Tools

Here is an article from Jennifer Kotler, and the link to her blog here.

In January, I attended a workshop dedicated to games, assessment and learning hosted by the MacArthur and Gates Foundations and the USC Game Innovation Lab. The workshop brought together game designers, educators, and researchers to work together on designing games around various curricula topics that would be engaging, educational, and contain features to allow for the collection and feedback about how players were faring when engaged in the game. The conversation went beyond what players could learn from games: We also focused on the valuable information we can gather from patterns of game play, such as

This kind of thinking always reminds me of math class tests where we were asked to "show our work" so that the teachers could see how we went about solving a particular problem. A wrong answer to a division problem that had more to do with a simple subtraction error is very different from getting the wrong answer because of a fundamental lack of understanding of how to approach the problem. Patterns of responses can provide much more specific information than whether children get the answer right or wrong (as many standardized assessments generally report). Game play data may indeed provide another valuable way to assess patterns of children's understanding in a less threatening way than common testing conditions.

Not only might such games be useful in formal learning situations for assessment, but they might also encourage parents to become more engaged in children's learning. As part of some recent research around

I assumed that perhaps only a third of parents would be interested in receiving information on how well children were doing on the game. Surprisingly, the vast majority of parents (over 70%) said would be

Before we rally for more widespread use of games as assessment tools, we likely need more investigation as to whether scores, errors, and successes in games are indeed highly correlated with the very same things that success on standardized or classroom tests are supposed to predict. Clearly, this assumes that standardized measures or classroom tests are the "gold standard" for information about what children "know" and that, of course, is the topic of much debate. Still, at this point in time, children are often classified or assigned to particular learning interventions based upon standardized assessments.

Games might provide a less "frightening" testing environment. Perhaps games might indeed reduce what Dr. Claude Steele termed "stereotype vulnerability." Girls and children of minority status might do better under conditions that don't seem test-like because they have been unfortunately conditioned to believe that children like them do not do as well as others on academic tests. Games might provide a neutral playing ground as well as reduce test anxiety.

On the other hand, perhaps children take more risks in games that they would not do if they were being tested, which may in fact be what educators encourage, but might interfere with their scores. Furthermore, I have seen situations where some children may actually choose wrong answers every so often just because the wrong answer feedback was funny, or perhaps they were just interested in seeing what would happen with a wrong answer choice.

Nevertheless, games provide a very efficient and engaging way to collect valuable information about performance. To be most useful as an assessment tool, however, game designers should work with educators and experts in assessment to ensure that information is captured in meaningful ways. Using the data in ways to support further learning is critical. Providing additional opportunities to practice skills and expand learning through additional gaming or materials for parents can only help make gaming experiences richer for children.

In January, I attended a workshop dedicated to games, assessment and learning hosted by the MacArthur and Gates Foundations and the USC Game Innovation Lab. The workshop brought together game designers, educators, and researchers to work together on designing games around various curricula topics that would be engaging, educational, and contain features to allow for the collection and feedback about how players were faring when engaged in the game. The conversation went beyond what players could learn from games: We also focused on the valuable information we can gather from patterns of game play, such as

*where*players might make errors and the*kind*of errors players might be making so that either the game or another knowledgeable player can help provide the necessary support to improve game play and therefore, learning.This kind of thinking always reminds me of math class tests where we were asked to "show our work" so that the teachers could see how we went about solving a particular problem. A wrong answer to a division problem that had more to do with a simple subtraction error is very different from getting the wrong answer because of a fundamental lack of understanding of how to approach the problem. Patterns of responses can provide much more specific information than whether children get the answer right or wrong (as many standardized assessments generally report). Game play data may indeed provide another valuable way to assess patterns of children's understanding in a less threatening way than common testing conditions.

Not only might such games be useful in formal learning situations for assessment, but they might also encourage parents to become more engaged in children's learning. As part of some recent research around

**Prankster Planet**on*The Electric Company*website that Mindy Brooks wrote about in**last month's blog post**, we asked parents (about 40 of them) to fill out a survey. The survey included questions about parents' interest in receiving feedback about how well their children were doing on the math and literacy activities within Prankster Planet.I assumed that perhaps only a third of parents would be interested in receiving information on how well children were doing on the game. Surprisingly, the vast majority of parents (over 70%) said would be

**very likely**to use information about how well their children were doing on the games. Furthermore, even more said they wanted specific feedback as to how to support the activities that the children were doing in the games even more so than general suggestions how to work on math and reading skills with their children. Parents said they would be most receptive to receiving this information through an email (rather than a text message or in a password protected site). This might be a particularly interesting opportunity to engage more parents and provide very specific information about how to extend children's learning based on children's individual game play patterns.Before we rally for more widespread use of games as assessment tools, we likely need more investigation as to whether scores, errors, and successes in games are indeed highly correlated with the very same things that success on standardized or classroom tests are supposed to predict. Clearly, this assumes that standardized measures or classroom tests are the "gold standard" for information about what children "know" and that, of course, is the topic of much debate. Still, at this point in time, children are often classified or assigned to particular learning interventions based upon standardized assessments.

Games might provide a less "frightening" testing environment. Perhaps games might indeed reduce what Dr. Claude Steele termed "stereotype vulnerability." Girls and children of minority status might do better under conditions that don't seem test-like because they have been unfortunately conditioned to believe that children like them do not do as well as others on academic tests. Games might provide a neutral playing ground as well as reduce test anxiety.

On the other hand, perhaps children take more risks in games that they would not do if they were being tested, which may in fact be what educators encourage, but might interfere with their scores. Furthermore, I have seen situations where some children may actually choose wrong answers every so often just because the wrong answer feedback was funny, or perhaps they were just interested in seeing what would happen with a wrong answer choice.

Nevertheless, games provide a very efficient and engaging way to collect valuable information about performance. To be most useful as an assessment tool, however, game designers should work with educators and experts in assessment to ensure that information is captured in meaningful ways. Using the data in ways to support further learning is critical. Providing additional opportunities to practice skills and expand learning through additional gaming or materials for parents can only help make gaming experiences richer for children.

## Wednesday, June 1, 2011

### Open ended project on Integration

In the past, in my Pre-Calc Class, I have used traditional exams to assess the knowledge of integration techniques. This year I plan on using the following open ended project.

Integration Project

1. Create an equation for the velocity of a particle at any time

*t,*stating the initial position, which cannot equal 0. The equation must include all of:· A polynomial function

· Rational function –Chain rule must be applied

· Trigonometric function

a. Determine what must be true about a function so that it is able to be integrated.

b. Determine the distance of the particle at any time

*t*. – must use*u*substitution for the rational term.c. Create a velocity-time graph, as well as a distance-time graph on the same grid.

d. Determine, using appropriate sums of rectangles, an over and under estimation of the displacement of the particle in the first 10 seconds.

i.

**Explain**how this estimation could be made more exact.e. Determine the

**exact**displacement of the particle for the first 10 seconds, and then determine the**exact**location of the particle after 10 seconds.f. Determine the average acceleration of the particle from 0. Illustrate how your answer could have been determined by the graphs.

2. Create two functions, one representing the revenue of a company while the second will represent the costs of a company over a 12 month period. The curves must intersect and cross each other. Determine the area between the two curves, for the 12 months and interpret your answer.

3. Knowing the gravitational pull on Earth is 9.81m/s

Other ideas can be found here:

2007-08 Problem 8 Chebychev polynomials

^{2}, create a video an object in free-fall. You must throw your object, and calculate the velocity of the object when it left your hand. Appropriate measurements must be included.Other ideas can be found here:

2010-11 Problem 7 The Lanczos derivative (which is defined as an improper integral)

Problem 8 What is the average value of all possible averages?

2009-10 Problem 7 Non-Fundamental functions (just a curiosity)

2008-09 Problem 10 Introduction to Fourier series

A MISSION POSSIBLE…

Your mission, should you choose to accept it …actually you don’t have much choice…will consist of mathematically explaining everything you know about an irregularly shaped symmetrical object such as a bottle or a vase. Include detailed drawings and calculations.

Thank you to the Calculus Discussion Board for the ideas!

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