Patterns in i? November 29, 2010

You can imagine my surprise at the end of last school year when, on my tutoree’s final online examination, the imaginary number i was everywhere.  “WHAT?” I thought, “There was just one small section of one small chapter on i in the textbook and here it is, on my students’ final exam, EVERYWHERE.”  At best, it was frustrating.  Sure, math is math, but different publishers tend to focus on different topics, and i was not on of those topics Glencoe included much of.

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For five years, I had taught Algebra 1 and loved it.  The kids loved me and I loved all of their “ooooh, I get it!”s.  But this year had been different because I was moved up to Algebra 2.  So I set my mind to teach this slightly more advanced Algebra (at least with Glencoe it’s only slight), brushed up during the summer, got my curriculum down pat, taught a rough year right up until the final exam and….

  

BOOM!  i! 

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Patterns are everywhere, especially in math.  The imaginary number i is no exception.  The number’s value follows an interesting and very distinct pattern, repeating itself every fourth iteration.  The pattern it DOES NOT fit is into a regular one in Glencoe’s Algebra 2 textbook.  I was mad that my students and I had worked so hard only to be sidelined by a final exam not connected to Glencoe at all.  

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So this year I changed.  I taught i first!  We wouldn’t be stopped!  If the “patterns_of_i.xls” sheet over there in the margin for you to download and use in your classes is not enough, I’d be more than happy to email you more.  You can reach me at sdonohue@post.harvard.edu. 

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I quit this year, jumped a sinking ship, really.  It was horrible leaving the kids- like I was going on maternity leave and never coming back.  But it was the decision I had to make so that I could focus on my thesis, my health and on finding a job where I would be respected.  What they say about finding happiness first before you can pass it on is true.  What they also say about not doing school part-time unless your job is also part-time is also true.    

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Now I’m finishing my thesis and looking for a new job, oh, and emailing you files to use in your classes.  I have thousands that I’ve made over the years that I’d love to share with you. 

 

  

Go i!

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Easy Factoring Trinomials…by grouping! November 27, 2010

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When I was a kid in high school, I remember trying seemingly endless combinations of numbers that would factor each assigned trinomial.  Well, you can kiss those hours of work good-bye!  Factoring by grouping is not only faster, it’s SIMPLE!  Just a few steps lie between you and complete trinomial factoring success… 

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Awesome Euclid and his Algorithm November 19, 2010

One of my favorite things that I learned while in graduate school for math education was the Euclidean Algorithm for finding the Greatest Common Factor of two numbers.  If you click on the  picture to the left, you’ll get to a very informative YouTube video on the Algorithm.  It’s a bit boring, but very educational, and it shows exactly how to go about using Euclid’s method to find the biggest number that divides into two numbers.

 (The screenshot to the left will bring you to the YouTube video on the Euclidean Algorithm) 

 

The alternative, but mainstream, way using factor trees and circling primes always confused my students.  “Do I count the 3 twice since I circled it as a factor in both 81 and 57?” 

 

If Euclid’s method was the mainstreamed one, math would be a lot more interesting and one more confusing topic could be checked off the list.  Euclid, you rock!

  

(The screenshot here of the kids is a funny video about Euclid and his algorithm)

 

 

 

 

 

 

 

 

 

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Small Schools, SUPERSIZED Classrooms: Thanks a bunch, Bill Gates September 3, 2010

School for Boston Public School teachers starts on Tuesday.  The kids come back Wednesday.  Three chairs at a table, eight tables, I have 24 seats in my classroom.  The class size limit in Boston is 31 per class.  -

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37 students + 24 seats = success.  Solve for HOW.

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So that I could get an idea of who I’ll be seeing on a daily basis and when, since I had many of the students I’ll have this year two years ago when they were 9th graders, I went onto mybps.com to download my class lists.  This will be the first year that all students get electives after four years of none (Thanks again, Bill Gates.  My students thank you too for the opportunity to go to a small school where they get to know each other so well that they fight like siblings and miss out on things like art, music, and… computer classes.  But to have computer classes would mean we’d need computers, so thanks for dropping the ball on that one, too.  “Good looks” as my kids would say, only I say it to you sarcastically, you mad scientist, you!)

 

side: What’s the difference between a real scientist and a computer scientist?  Real scientists can admit when they’re wrong and try, try, try again until they get it right.   You can’t Ctrl/Alt/Delete this one, Bill.

 

Anyway, so I downloaded my class lists and I see the following:

 

Math elective, period 3:            37 students

Algebra 2, period 4:                33 students

Algebra 2, period 5:                25 students

Algebra 2, period 6:                24 students

 

By my schedule, you can see I’m a math teacher.  As hard as calculus was, I got through it.  I even got through a java programming class that sucked 15 pounds out of my body.  But I just can’t seem to do the following problem:

 

37 students + 24 seats = success.  Solve for HOW.

 

I appreciate any and all suggestions on how to pull this one off.  These are the kinds of things people forget about us teachers.  We “get summers off”, we “only work 6 hours a day”, we “have tons of vacations”, we are “failing our kids”.  But no one ever comments on how we’re sometimes set up to fail before we even begin. 

 

I’m scared for Wednesday, not because I don’t think I can teach 37 kids at a time but because I don’t know how to choose who gets a seat and who sits on the floor.

 

One More to Graduate. Make that 50.000001% June 7, 2010

With a graduation rate in the US hovering at 50%, getting every kid to graduate from high school should be our #1 prority.  Alex wasn’t a student of mine but he took precalculus in my classroom during my off period. Because our school is a small school, classrooms are shared. One day, Alex asked to use my computer to work on his credit recovery for the Algebra 2 class he had failed the year before. I let him use it, and sat with him as he worked on the problems. I taught Algebra 2 that year so it seemed only natural I help him.  Alex needed to get through just this one course to graduate high school. 

 

Before I knew it, I was helping Alex every day during my off period, and when the school year began to wear down, Alex began staying in my room all day working to get through the program. The program was difficult; much of the material isn’t covered in the Boston Algebra 2 curriculum. It started to become clear that Alex was exceptionally smart, but the program involved a lot of difficult work that would give even m top Algebra 2 students difficulty.

 

On Thursday June 3, 2010, Alex and I stayed at school until 10:30 PM when the custodian politely asked us when we’d be leaving. The credit recovery program deadline was at midnight and we weren’t going to be done. We were on section 10.5 and had to get to 11.11, and it was clear there wasn’t’ enough time. Alex was devastated. I was devastated. After all that time, we were defeated. Worst of all, there were errors in the program that had wrong answers as correct answers and not achieving a 75% or better on each mini quiz (there were approximately 20 in each section) meant we couldn’t move on to the next subsection.

 

The next day was field day. As I was waiting in my classroom for our bus to come, the director of credit recovery came to tell me he’d give Alex another day because he had gotten so far in the program. He had been given another chance! WE had been given another chance! Hard work does pay off! I called the phone number I found in the office fir Alex and told him to come in immediately to continue working.

 

Because I wasn’t allowed to stay behind from the field day trip, I asked another teacher to work with Alex. Alex began working again at 9AM. When I returned from field day at 1:30, Alex had gotten through just one more subsection. I was so exhausted from staying so late the night before, from field day, and just from a week of work in general, that the thought of staying late on a Friday almost brought me to tears. Still, we had to take the chance. I had to be there for Alex. He was so close to graduating that I couldn’t give up. We worked from 1:30PM to 5PM and got to section 11.5 when we ran into the advanced probability questions. Probability has never been strength of mine. I can do problems that involve using formulas, but these problems were less “marbles in a bag” or even “out of 10 people, you need to choose a president, vp, and secretary” and more “If Monty Hall opens one of the doors with a goat…” We were on section 11.5, we needed to get to 11.11, and we were stuck. I was stuck. I felt like a failure. We had been given another chance and it seemed we were defeated again. Alex wasn’t going to graduate because I couldn’t grasp that the Monty Hall probability is 2/3.

 

I couldn’t imagine what Alex’s weekend looked like. If I felt defeated, he must have felt devastated. If I felt frustrated, he must have felt destroyed. To get that close and have it count for nothing.

 

Then came Monday June 7, 2010, two day before graduating seniors were scheduled to sign out of high school forever. I was concentrating on final exam review for my juniors when the credit recovery director came back in. He has overridden the last half of chapter 11 so that Alex could take the final exam. I immediately called the phone number I had for Alex and left a message for him to come in. I had assumed Alex wasn’t in school, but he was. Maybe Alex had ore hope that I did. About 3 hours after seeing the director of credit recovery, Alex was at my door. He took the final exam. He was graduating. I called his mom to let her know, as I promised I would. I had never heard a parent so excited. It was then that it was reaffirmed in my mind and heart that hard work, as painful as it often is, always pays off. Thanks Alex.

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UPDATE:  Alex was shot and killed on September 3, 2011 on his way to a barber shop in Boston.  

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YouTube… BLOCKED. Learning Today… BLOCKED! June 6, 2010

 

Sure, there are a lot of videos on YouTube that we don’t want kids watching at school.  But there are a countless videos on the site that can teach in 3 minutes what it would take a teacher a week to teach.  Our kids are visual learners, learning through video is most effective.  

 

For teachers like me who use their LCD projectors extensively to reach our visual learners, having access to YouTube in school would be extremely helpful.  This year, I could have shown videos on solving systems of equations, finding the equations of circles, solving triangles with the trigonometric ratios, and this says nothing of how much I used YouTube myself to get through my graduate Java and Calculus classes! 

 

But because someone made the executive decision that all of YouTube should be banned from everyone within the walls of BPS, I have to hope that TeacherTube- the ungroomed toenail of YouTube- has a video on the topic I am looking for, and moreover, has their search feature organized in way that a search for “algebra” doesn’t bring up “Mrs. Valentine’s Kindergarten field trip to the Museum of Science”.  TeacherTube is not YouTube, it never will be, and it’s a real shame that teachers in BPS cannot log into YouTube to access its wide range of useful educational videos. 

 

In any case, I have posted videos on TeacherTube at the ridiculously long address: http://www.teachertube.com/members/viewProfile.php?user=Shanadonohue

 

They can be watched in school, even if they take 5 minutes to load.  There’s also one other option that[sometimes] allows you to convert YouTube videos to video files to save onto your computer and then show in class.  I stress, though, that it SOMETIMES works:  http://www.forinside.com/  In fact, it’s not even working now.  Blah!  Maybe this one works: http://www.zamzar.com/url/

 

UNBLOCK YouTube!!!  Please!!

 

 

 

Webpage blocked! [possibly] May 25, 2010

 

I found a great video at http://adgonzalezmath.wordpress.com/ in the “February 2010 archives” that lead to what could [possibly] be the greatest collection of math videos on all of the interweb superhighway: http://justmathtutoring.com/  I say “possibly” because, like many things that could be useful to students, the site is blocked here at school!

 

So I’ll check it out at home.  My bet is, based on the video I saw on adgonzalezmath’s page, the videos are going to be nice.  So if you know how to save videos from the internet onto your computer, I’d love to hear from you.  I know of one site that may [possibly] do this, but it’s blocked here.  Though even if it weren’t, I’d have nothing to upload!