Why I Blog

Chiming in a little late, but I wanted to share my journey into blogging . . .

I still remember the day when I discovered math teacher blogs. I had been teaching for maybe eight years and I was in a rut. I had gotten to the point where I pulled out the folder of unit whatever from last year and wash, rinse, repeat. I was doing an adequate job, but I was bored.

On THE day I was sitting at my computer and I wondered if there were any math teachers out there blogging about teaching math. I started to search. I found Kate’s blog and Sam’s and a few others. Their blogrolls lead me to others. I started reading and I could not get enough. I tried log war and row games and other stuff. I got creative inspiration and I started to enjoy teaching again. My learning of new things was no longer limited to a rare conference here or there or from conversations with my two colleagues.

I started to recognize that I was a pretty mediocre teacher, and I stopped being content with mediocrity.

It was less than a year later that I started a blog of my own. Initially, I felt that I had gained so much from others that I wanted to contribute something to the community. It didn’t take me long to realize that what I had to share was just a drop in the pool of resources out there, but some people seemed to find what I had shared to be helpful and that felt great. I also wrote about what was on my mind and I was able to solidify many of my thoughts about teaching and learning through thinking them out in writing.

The real hook for me came when I started receiving feedback from others who were reading. I found that even when I posted something that I thought was super amazing, someone would give me an idea to make it even better. I asked questions when I wasn’t sure where to go with a topic, and I got answers. I am so very thankful to those commenters who have made me a better teacher.

I have subscribed to Sam’s philosophy about blogging – it shouldn’t be a chore. But while I refuse to let blogging be stressful, it has provided me with some motivation to produce share-worthy moments in my classroom.

I still mess things up all the time. I still spend too much time talking at the front of the room. I still have so much to learn . . . but there is no question that I am a better teacher than the blog-less version of myself.

And I’m definitely having more fun.

Programming Part 3

Day 3, for documentation purposes . . . I now have so many questions swimming around in my head related to how & when I would use programming in the future. But that's another post.

For Day 3, students were introduced to loops. This was a little more difficult for all of us, but the students were still super interested in the process.

Chris gave us these programs to try:

1. Use a loop to write a program that prints all multiples of three from 3-42.

2. Primality testing: Write a program that lets the user input a number and then checks if it is prime.

3. Number of numbers divisible by 3: Write a program that will let the user input a number, and then the program searches for and counts the number of numbers up to that number that are divisible by 3.

4. Product of first n numbers: Write a program that will let the user input a number, and then it will find the value of the product of all the integers up to that number.

5.  Averaging test scores:  Write a program that asks the user how many test scores they want to average, and then prompts them for each test score and finds the average.

Harder ones:

6.  Reducing Radicals:  Write a program that can reduce a radical. For example, if the user enters 20, it should return the numbers 2 and 5, representing 2 root 5.

7.  Finding perfect numbers:  A perfect number is a number that is equal to the sum of its divisors, besides itself. Example:  6 = 1 + 2 + 3. The first 4 perfect numbers were known in antiquity. Write a program that can find all perfect numbers up to a number inputted by the user. You will most likely need nested loops.

These were tough! I did not get through the list of programs today (or past #3).

The activity is still a hit with students. They are seriously begging for more!

Tomorrow they are each going to present one of their original programs.

Programming Part 2

For Day 2 of my introductory adventures in programming, we (I mean Chris, the amazing student teacher) did this:

1. Introduce students to test and logic commands (2nd MATH). We practice writing logic statements and identifying if they were true or false.

2. Introduce students to "IF" statements. Together we wrote a program that asks the user to input an x and y coordinate, then identify its quadrant.

3. For homework, students worked on these:

*A program that asks the user for 2 numbers, and then displays the larger number.

*A program that asks the user for the center point and radius of a circle, as well as an additional point, and will display whether the point is inside the circle.

*A program that asks the user for A and B from a function in the form Ax^B, as well as an x-coordinate. It then displays the slope of the function at that point.

*A program that asks the user for the slope of 2 lines, and then displays if they are parallel, perpendicular, or neither.

*A program that takes in a number from the user and displays whether it is even or odd. (Hint:  use fPart command).

Day 2 was just as much fun as Day 1! A few students have been enamored with the idea of a guessing game program where the computer generates a random value between 1 and 100 and coaches the user's guesses with "too high" or "too low" until the value is found. They've been working on it even though they don't have quite all the tools yet, and some of them are figuring it out.

Diving Into Programming!

This post is 100% inspired by Jasmine's TMC13 presentation-turned-blog-post. I thought it was a great idea from the beginning, but I honestly didn't take it very seriously for myself. I guess I just didn't think it would work for me. And I don't teach geometry. I passed Jasmine's post on to our geometry teacher and her student teacher. Chris (student teacher) got really excited about it. The more we talked, the more I started to see the potential for any of the classes I teach.

So, Chris and I decided to join forces and introduce our combined Calculus & Pre-Calculus classes to simple programming. I have almost zero knowledge about programming. So by "join forces", I really mean that he taught the class and I'm over here learning along with the students.

This was sort of a spur-of-the-moment interruption-to-your-regularly-scheduled-math-class-kind-of-activity. We have flexible schedules, so we decided to jump in and try it and I am so glad we did! I am feeling confident about doing this on my own in my other classes now.

I am sure this is all painfully simple to anyone who knows anything about programming, but it was mostly new to me. I wanted to document here for my future self. Maybe someone reading is like me and never thought you could do this sort of thing. You can! If you don't have a stellar student teacher to help you out like I did, just follow these steps.

Day 1 looked like this;

1. Distribute TI-83 calculators. Some kids had them already, we had enough for the rest to borrow.

2. Demonstrate the location of the PRGM button, the NEW tab, name a program, and locate all the commands within the program menu.

3. Demonstrate the ClrHome and Disp commands. Write a program to display the word "HELLO".



4.  Demonstrate the Input command. Show students how to store a value, calculate and display a result. Write a program to request someone's age and tell them how old they'll be in 20 years. (I did not like my number).



We also did a pythagorean theorem program together.

5. Send them home with some programs to try:

*Write a program that asks the user for the year they were born, and then displays approximately how many years old they are.

*Write a program that asks the user for 2 x-coordinates and 2 y-coordinates and then finds the distance between the points.

I cannot tell you how much fun this was for me, mostly because I got to learn along with my students. I saw several of them later in the day, and we couldn't put our calculators down. We had to stop and compare distance formula programs. We exchanged calculators and tested each other's programs. Students started coming up with their own ideas for programs and asking me to test them out.

It was a super fun day to be a teacher  student.

I am pumped for my next lesson!

Stay tuned for Day 2.

This Lesson Cost Me $1

Zero product property today, only the students don't know that yet.

For them, its a game-show-style guess-the-number game.

I want a fun prize for the winner, but all I can come up with is a couple of quarters. That will have to do.

Before class, I write a bunch of numbers on this board and cover them with index cards. I'll even give a hint about the first two.

The students are totally into it . . . 2! . . . 3! . . . 6! . . . 1! . . . 

Someone decides to try negatives . . .  -1! . . . -2! 

Finally, someone else tries 0.5. . . Fancy. But wrong.

I let this go on for a bit.

Then I break the bad news. Sorry guys. It was 6000 and 1/1000. Better luck in round 2.

And there are more guesses . . . 1! . . .  -1!  . . . 12!

Someone is on to me . . . "Guys, this could be ANYTHING!" 

So you give up? It was 58 and 1/58. Okay, on to round 3.

At this point I am expecting all hands to go up. In a perfect world, everyone would want to guess zero! Right? Wrong.

That's where I am surprised. One lonely hand goes up . . . Zero? He asks hesitantly. My first two examples raised enough skepticism that students are sure there must be a catch.

This isn't how it worked in my head but that is okay. I can adjust.

Is Tyler right? Can we know for sure that one of the numbers is zero? Discuss at your tables. 

I walk around and listen and most seem to be figuring it out. Someone suggests 5 and -5 but quickly realizes that won't work. For those who aren't convinced, I challenge them to come up with a number other than zero that will work.

We conclude that Tyler is right and move on to the final round.

Zero!!!

 Not exactly. I tricked you this time by using variables. But tell me what you know . . . 

"x minus 3 or x plus 2 equals zero". 

Yep. That is all.

P.S. Next time I am giving everyone a white board to write down their guesses for each round. I had a lot of participation, but definitely regret that I didn't get a response from every single student.

Homecoming Balloons

Me: Okay, the balloons are in my closet. Now, there are 50 pink and 50 silver but only 25 of the black. Remember that when you are planning out your rows.

 . . . later . . .

Decorating girl:  We decided to put the rest of the balloons on the floor.

Me:  Oh, I thought you were going to do three rows on the ceiling.

Decorating girl: Yeah, but there weren't enough black balloons to continue our pattern.

 . . . sigh . . .

Desmos Test Question

I am kind of excited about this (bonus) test question I used today . . .

My advanced algebra 2 students just finished studying a few of the basic parent functions and their transformations. Today, they took a test.

First there was a standard paper/pencil part of the test. Nothing unusual here.

Next, they picked up one of these cards containing the description of a parent function and a transformation.

The cards were color-coded according to difficulty level. Students were free to choose. Every card is different, so you won't be working on the same graph as your neighbor. Students were to pick up an iPad and use Desmos.com to create the function described.

Green Cards: Create a graph using a given parent function and animate one given transformation.  
Purple cards: Animate two given transformations.

When finished, students bring me the iPad. I check that the graph matches the description, stamp the card, and clear out the graphs for the next person.

I was really pleased with the results. Almost everyone was successful in creating their graph. I don't feel like this needs to be a bonus question next time. It might even become a regular part of test-taking in my classroom.

Now I am thinking about the possibilities. My head is already spinning with ways I can use this question format for other topics:

Quadratics/Polynomials: Create a function with given vertex or given zeroes. Can you keep the vertex in place while animating the zeroes? Can you keep one zero in place and animate the other(s)? Create a function with given end behavior.
Systems: Create a system with one solution, no solution, or infinite solutions. Create a system with a given solution.
Rational function: Create a function with given vertical and/or horizontal asymptotes. Animate one or both asymptotes.

P.S. If you are wondering what we did in class BEFORE this assessment, here is a quick summary:

1.  We spent several days sketching parent functions and transformations the old fashioned way, using paper and pencil. Students completed tables and plotted points, sketched graphs, looked for patterns, and generalized their discoveries.
2. Once students had mastered the basic functions and their transformations, I spent one class period introducing Desmos.com. I reserved our math department's shared iPad cart. I showed students how to enter equations, create sliders, and click play to ANIMATE (<3). They were as enamored as I was when I saw this a month ago at TMC13! Then I just let them play.
3. Finally, I started giving them a few challenges. Try to make an x^2 that moves vertically while stretching. Can you keep it from turning upside down? Can you restrict its movement to the second quadrant? Can you make it move horizontally along the line y = 2?