In Search of a Good Teacher

If we, teachers, only listen to our students, they could teach us a thing or two.

Karidme Rocha and Shawn Klesel are both wonderful students of mine in Geometry. Like a host of my former and current students, they're both on my Facebook friends list.

The following is part of a thread that stemmed from Kari's status that she posted on December 30th:

Kari:      In search of a prince charming:)
Shawn:      im a prince and im charming but i aint no prince charmingXD
Kari:      o wow Shawn lol you need to be both at the same time lolXD
Shawn:      hahaha only to certain ppl at certain timeXD

Upon reading this thread, I reflected. Face to face, I looked intently at this teacher that they call Mr. Jope.

You are a teacher, and you are good. But are you a good teacher?
Sometimes? All the time?

Good teacher TO WHOM?

Classroom Economics: Saving for Rainy Days

Holt Geometry, the textbook my students use, defines postulate as "a statement that is accepted as true without proof." According to Reader's Digest Oxford Complete Wordfinder, postulates, or axioms, are used as "basis for mathematical reasoning." Geometry, in fact, is built on a strong foundation of postulates that include the following: There is exactly one line that passes through any two points. I am not quite knowledgeable in the science of finance, but I would assume that one of its postulates must be the following: There'll be nothing for one to withdraw if there was nothing deposited in the first place. Postulate or not, I use it to strengthen the foundation of my own teaching.

At the beginning of each school year, making deposits is on top of my priority list. Like a hungry eagle looking for food, I scour for and swoop on every opportunity - big and small- to make a deposit.

Giving generous compliments is making deposits. While I strive to get to know my students, I make sure that I give each one of them appropriate and hopefully nurturing compliments. Lots of them. I compliment anything about the individual that I can safely and appropriately compliment on. I celebrate every little positive thing I see.

Greeting and wishing them well on their birthdays is making deposits. So are grieving with them when someone in their lives perished, listening to them when their bffs break their hearts, and celebrating the genius behind each academic mistake.

Shaking it in the middle of the dance floor during school dances and being a kewl teacher the right way are making deposits.

Calling parents to tell them positive things is an example of making multiple deposits. With one single deposit, I get to  increase my deposits in two accounts instead of just one.

Sharing my own life stories, whenever appropriate, allows me to deposit to a host of accounts, not just two, with one transaction.

Although I am a sucker for making deposits, I am well-aware that my deposits, like bank deposits, are limited to certain currencies, and because I'm just a teacher, I cannot just deposit large amounts whose sources I cannot justify. Certain amounts of deposits are certainly going to raise alarms. I certainly do not want my students to feel uncomfortable with me.

We do not like to withdraw monies we have saved, but rainy days are bound to come. It is for this reason that we save in the first place.

Making withdrawals is getting after my students for a host of reasons, such as misbehaving, failing to turn in homework or project, violating school or classroom rules, and failing to perform in class satisfactorily or according to certain mutually accepted higher expectations. Sometimes, I withdraw before it becomes necessary to withdraw.

Just like in real banking and finance, my withdrawals have limits. But unlike real banks, my banks, which in this case are my students, are not "financially" stable and well-founded. They are kids, and they are volatile. Sometimes, I withdraw as much as I needed. But most of the time, I withdraw according to the conditions that my banks are in.

No matter what the state of economy is, it is deemed wise to always save. In fact, it is a value we are encouraged to teach our youth.

My classroom economics is always a winner. I may fail to help all students of mine achieve academic mastery. But with my classroom economics, I fervently hope to touch their lives with mine.

When the Devil Talked Back

It's two days yet before Christmas, but I already received a very nice gift!

Around four this morning, I received an email from an editor of PhilStar, the internet site of the Philippine Star, one of the leading national newspapers in the Philippines. Here's Mr. Dino Maragay's message:

Congratulations! Your story has been chosen for publication in our website. Here is the link to your story:

http://www.philstar.com/community/Article201005.aspx?articleId=642058&publicationSubCategoryId=503

Meantime, please wait for our staff's email on how to claim your contributor's fee. Thanks a lot for joining and please continue visiting philstar.com.

Cheers,
Dino

Dino was referring to PhilStar's writing contest that I didn't know about till just the other night. Then, the contest, which opened on December 1, 2009, was going to end in nine days. I thought I would still give it a try.

I wrote When the Devil Talked Back that same night. The following day, I submitted it online, along with the required signed entry form and photocopies of my passport and Texas I.D. Just about twelve hours later, I received the message above.

When the Devil Talked Back is about a traumatic teaching experience of mine in the spring of 1996. I was then an 8th grade mathematics teacher in another school district. Read it here. Don't skip the readers' comments at the end of the article. They're quite interesting.

Words to Live By

I was already late to our faculty Christmas party that was being hosted by our quite endearing school principal at her home for the first time since I joined our school less than two years ago. I had a vague idea where she lives, but I was pretty sure I'd get there.

Got a great excuse for being late. Check. Got my "Grinch Better Have My Presents!" shirt on. Check. The trays of Filipino-style beef lumpia (eggroll) and puto (rice cake) that I ordered from Cabalen restaurant. Check. My videoke microphone. Check. The Christmas carol lyrics sheets? Hhmmm...

As I quickly browsed this pile of papers on the second ledge of my white book case to look for the lyrics sheets, I chanced upon this piece that looked familiar. I had not seen this in so many years. I didn't even know I still have it. I thought my colleagues were probably waiting impatiently for me, but I just had to read it one more time. As soon as I had put on my reading glasses, the words touched my heart anew. This was the short speech delivered by class valedictorian, Alam Quintero, who was born and raised in Mexico, in a banquet meant primarily to honor the top ten students of Hidalgo High School's class of 2003.  

"There is this special individual I would like to recognize tonight. A unique human being whose hard work, intelligence and integrity as a man impacted the life of many students around him as well as my own. His honesty, loyalty, and always-appropriate advice are only a few characteristics I have come to praise here. The respect I owe this teacher, this better called doctor in life education, is something I cannot possibly describe, for in fact it can only be experienced rather than seen. This individual I am speaking of tonight, has passed through several tribulations. Yet no matter what hardships have befallen him, he always surpassed them all with courage and maturity. That is certainly his way of standing out from everyone else."

"Regardless of where life may take him, he will undoubtedly influence those who can be reached by his grace, and those who can be touched by the kindness of his being. Yes, there may be quite a few individuals who can fulfill some of the above-mentioned qualities. Yet there is only one who meets them all and who in fact has been close to me throughout these past high school years. He has been my coach, my teacher, and my friend. This is the individual who has helped me not only the most, but also the best. Mr. Jope."

I carefully placed the sheet back. I grabbed my jacket and was finally on my way sans the lyrics sheets. It was easy to find Mrs. Cavazos' house. When I finally showed up, it didn't matter that I was late. The greetings were warm. The most important teacher in the world had just arrived from a glorious chapter of auld lang syne.

Mitsuo's Magic

Before after-school tutoring commenced yesterday afternoon, I found freshman Mitsuo at my door. I had left it open to let the cool December breeze in. He hesitated for a moment when he realized I was chatting with Ashley, one of my talented sophomores. I quickly sensed that he was anxious to tell me something. Before he had the chance to excuse himself and turn away, I asked him to come in.

Although Mitsuo, who's still taking Algebra 1, is not a student of mine, he has warmed to me. A few months earlier, while I was on after-school duty, the boy, then a stranger to me, approached and impressed me with his magic card tricks. He left a really good impression when he thanked me profusely for indulging in his magic.

When I realized that his concern was about a math idea he had conjured up, I motioned him to approach the white board. He grabbed a marker and wrote the following:

[90^(1-3) + 80] /4

I initially didn't understand the part that appeared to be the exponent of 90, but I assumed that it had something to do with the first, second and third six-week periods. Earlier that afternoon I had discussed semester grades with some of my students. The semester grade is the average of the three six-week period grades and the semester exam.

I also wondered why he didn't multiply 90 by 3.

"It looks like you want to determine your semester grade." He said yes.

As if he read my mind, he said, "I'm sorry, Sir, I know I didn't write it right, but I want to show that this 90 is the average for the three six-week periods."

I decided to not call his attention yet to his failure to multiply 90 by 3.

"You see, Sir, I was told that, to get the average..." He stopped. Suddenly I had a feeling that he had shown his idea to other people and it was dismissed. "But I was explaining that the way it's done is harder for me, because it's harder when you multiply and then divide. Right?"

"What do you mean?"

I thought that he probably just didn't like to work with bigger numbers.

"I have an easier way to get the semester grade." He now looked more determined. "All I do is get the difference between 90 and 80, which is 10. Then I divide 10 by 4, which I then multiply by 3."

I felt relief when he mentioned multiplying by 3!

He wrote 10/4 x 3 = 7.5.

"It's right, right?" I nodded. I now realized that the boy was on to something.

Although I already knew that 7.5 must be added to 80 to get the correct average of 87.5, I had to ask how he's going to use it.

His last step turned out to be wrong, but I did not point it out to him. Not the right time.

I knew in my heart that, despite the careless mistake at the end of his solution, Mitsuo deserved to be congratulated for bravely pursuing his unconventional yet intelligent method of determining the semester grade. He made a careless mistake, but his investigative mathematics is the sort that we hope to see in our students. Clearly, he's been empowered!

To assure him that his mathematics was right, I asked him to demonstrate the conventional solution, i.e. [90x3 + 80]/4, and then pointed out to him where I see his 10, the 10/4,and the (10/4)x3 in said solution.

It was only then that he realized his last step was wrong!

But even to him, the little mistake didn't matter. He was just too happy to know that, after being dismissed for his unconventional method, he got validated.

I promptly attended to my older students when Mitsuo left. There were seven of them already who needed some assistance with their circumcenter constructions.  It didn't matter that I was really tired and hungry. Mitsuo got me under his math spell!

Despised Babies Are Eaten by Illogical Crocodiles

Lewis Carroll, who wrote Alice in Wonderland, was a mathematics professor at Oxford University in England. Besides his popular books, he is also known for his puzzles.

Today, our second and last day of the THSP mathematics conference, Job for the Future's Robert Knittle, our presenter, included sample Lewis Carroll puzzles in a booklet he gave us this afternoon. Puzzle #1, supposedly one of the famed professor's simpler ones, aroused my interest.

The puzzle has three implications:

1. All babies are illogical.
2. Nobody is despised who can manage a crocodile.
3. Illogical persons are despised.

Using the three implications listed above, what is the "inescapable" conclusion?

The same booklet offered a solution, but I had the urge to work on it myself. I teach my geometry students about conditional (if-then) statements. Instinctively I thought that the so-called implications are but conditional statements waiting for a proper makeover. I would love for them to know that everything that I had taught them on conditional statements was enough to solve a Lewis Carroll puzzle. :p

Here's how I played it:

I rewrote all three implications into the following if-then statements:

4. If it is a baby, then it is illogical.
5. If you can manage a crocodile, then you are not despised.
6. If you are illogical, then you are despised.

I applied the Law of Syllogism on statements 4 and 6, and it resulted to:

7. If it is a baby, then it is despised.

I compared statements 5 and 7. Since the contrapositive of a conditional statement is logically equivalent to the statement, I decided to write the contrapositive of the former:

8. If you are despised, then you cannot manage a crocodile.

I applied the Law of Syllogism, once again, on statements 7 and 8 to arrive at my "inescapable" conclusion:

9. If it is a baby, then it cannot manage a crocodile.

It is the same as the one presented in the booklet. Yayyy!

In Lewis Carroll's words, that would probably be rephrased as:

No despised baby is spared by illogical crocodiles.

Not really! :D

Collaborative Group Work

To model collaborative group work, our THSP math conference presenter divided us into groups of three or four and gave us the following math problem:

"Farmer Brown sent her children to the field to count the number of horses and ducks. Her son returned with the count of 30 heads while her daughter came back with the count of 94 legs. How many horses and how many ducks does Farmer Brown have?"

The objective was for each group to, not just solve the problem but, determine multiple solutions and to make sure that each member will be able to explain correctly all solutions that the group finds. Our presenter, Robert Knittle (University Park Campus, Worcester, Massachusetts), had indicated earlier that research supports activities such as this that require collaborative group work, one of six components of THSP's common instructional framework.

We all thought we knew the problem well, so we proceeded with less interest.

Tonya Milburn of Early College High School, Galveston, Texas suggested that we solve the problem using a system of equations and solve it using three different methods: by graphing and by using both processes of elimination and substitution.

I volunteered to do the latter. Angelica Vega, the dean of instruction of East Early College High School in Houston, Texas said she will use guess-and-check in tabular form.

While we were all preoccupied with our individual tasks, our fourth member, Canary Branch Bui of Empowerment Early College, also in Houston, remembered something from her younger days back in Vietnam.

"I have solved a similar problem when I was in the elementary," she announced.

Well, I wasn't the only one who got intrigued. Everyone listened intently as Canary explained her unconventional solution.

"Assume that all thirty heads are horses. Okay?" The three of us nodded.

"Since each horse has four legs, then we have 120 legs altogether. But there are only 94 legs according to the farmer's daughter."

Canary proceeded to subtract 94 from 120 to get 26. Then she announced that these 26 legs mean that there are 13 ducks, and there are 17 horses.

Initially, I didn't understand her explanation why the 26 legs mean that there are 13 ducks, but I thought that out of those 30 four-legged animals, there will be 13 of them that should lose two legs each. These 13 must be the number of ducks.

We were all excited to have found a "new" solution to an extremely familiar problem situation.

Angie, whom I met at the Park City Mathematics Institute in Park City, Utah about five years ago, promptly raised an intriguing question. "Will it work if all 30 heads are assumed to be ducks, instead of horses?"

Here's how I convinced my group mates that said method works:

Thirty ducks give us a minimum number of 60 legs. Since all 30 animals have a combined total of 94 legs, then there are 34 legs that are unaccounted for. This means that there are  17 (34/2) heads that require two more legs each. Note that only horses have four legs, therefore there must be 17 of them and the rest are ducks as our other conventional solutions prove.

Canary was requested to show her crowd-pleasing method to everyone in the room, and I volunteered to show my sweet "corollary" to her "theorem."

A problem-solving exercise meant for our classroom use with our students turned out to be a tremendous learning experience even for us!

Without a doubt, subjecting our students on a regular basis to collaborative group work activities such as the one given above is not such a bad idea after all.

Cursing Students

Today, the first day of the two-day Texas High School Project (THSP) mathematics conference here in Dallas, Texas, our presenter, Robert Knittle (University Park Campus School, Worcester, Massachusetts) read to us the children's illustrated book "Math Curse" (1995, Viking Press)  written by Jon Scieska and illustrated by Lane Smith.

Here's the book's plot according to Wikipedia: "The book, which is told by a nameless female student, begins with a seemingly innocent statement by her math teacher- "you know, almost everything in life can be considered a math problem." The next morning, the heroine finds herself thinking of the time she needs to get up along the lines of algebra. Next comes the mathematical school of probability, followed by charts and statistics. As the narrator slowly turns into a "math zombie", everything in her life is transformed into a problem. A class treat of cupcakes becomes a study in fractions, while a trip to the store turns into a problem of money. Finally, she is left painstakingly calculating how many minutes of "math madness" will be in her life now that she is a "mathematical lunatic." Her sister asks her what her problem is, and she responds, "365 days x 24 hours x 60 minutes." Finally, she collapses on her bed, and dreams that she is trapped in a blackboard-room covered in math problems. Armed with only a piece of chalk, she must escape-and she manages to do just that by breaking the chalk in half, because "two halves make a whole." She escapes through this "whole", and awakens the next morning with the ability to solve any problem. Her curse is broken...until the next day, when her science teacher mentions that in life, everything can be viewed as a science experiment."

After the book reading, we were asked to write how we "curse" our students.

In my table, there were two gentlemen whose responses caught my interest.

Gustavo Alvarado (Cotton Valley Early College High School in El Paso, TX) wrote: "Everything in your daily lives is a function."

Andrew Waxman (Mission Early College High School, El Paso, TX) wrote: "Life is (full of) word problems."

I didn't understand the question then, so my response was totally off. But now that I do, I say that I "curse" my students by telling them, "Finding something difficult to do means that you are about to learn something new."

How do you "curse" your students?

I Beg Your Pardon, Sir?

I had sworn to myself many years ago that I'll never make the same mistake again, yet, with so much regret, I still do. I guess it's a hard habit to break.

Although just occasionally nowadays, I still read numbers in decimal form improperly.

For example, I still read 0.34 as "point thirty-four" instead of "thirty-four hundredths." And I admit it is easier to read 0.2345 as "point two, three, four, five" than to read the number as "two thousand, three hundred forty-five ten-thousandths." The longer the decimal, the easier it is to read it improperly.  

This practice seems harmless at first glance but unfortunately it's not! 

We teachers who have the habit of reading decimals improperly are not helping our students mathematically by not helping them master their vocabulary.

As we all know, students, who know very well that 0.34 is thirty-four hundredths, have better facility at being able to express the number as 34/100, its fractional equivalent which they could easily simplify into 17/50.

This failure in number sense is prevalent even with native high school kids. Add that to the fact that the number of non-native English speakers keeps on increasing only makes it even more urgent to change this practice. These immigrants have lots of potential and they need our unwavering commitment in helping them learn the English language so that they can already promptly engage in learning with academic rigor and achieve mastery.

I now know better, but I wouldn't be able to say I've done the right thing until I've completely stopped doing this unfortunate teaching malpractice myself.

Reading decimals improperly is not a good practice at all. Not to stop doing it is downright irresponsible.

Beat #2

One cannot call his journey sweet
When brothers fall and claim defeat
For we are words in a story grand
No tale no poetry a single word commands!

Term of Endearment

Early on my teaching career, I observed that the bulk of my young Hispanic middle-school students, when asked, "What do you think of the test?", responded in a peculiar way. 

They tilted their heads to the side, squinted their eyes, pouted their lips, showed me a rocking hand, and said, "mas o menos." More or less. 

Well, all these English language-challenged kids just wanted me to understand was that the test wasn't easy, and at the same time, it wasn't hard.

Light bulb! Got me an idea to coin a word!

If it's not easy, facil, but at the same time, it's not hard, deficil, then it's...

DEFACIL!     :D

After almost two decades, I still use the word, and each time I did, I saw grins.

Intrinsic Beauty

My mother, Genoveva, used to say, "If you put me in hell, I'd still choose to smile. I'd still look beautiful."

I believed her.

I Am!

There were numerous times that, as a young boy,  I resented the fact that my family was economically disadvantaged. Regretfully, many of those times I failed to keep my frustrations to myself and keep my actions in check.

During one of such unfortunate outbursts, Nanay (pronounced na-nigh, mother) listened with patience and understanding.

"I'm sorry that you resent that your parents are poor."

I sobbed harder.

"Your Tatay and I are the best parents for you."

I stomped on the wooden floor in protest while I continued to sob.

"If we're not the best parents for you and your three sisters, why did God allow me to conceive all four of you?"




Whenever appropriate, I'd tell my students, "If they're not the best parents FOR YOU, why did God allow you to be placed in their care?"

And at times that I found myself vulnerable, my message to my students has been the same: "I am the best math teacher FOR YOU. Why did God allow you to be placed in my class?"

Teaching is my vocation. "Trying to do my best" is not enough.

Who is the best math teacher FOR MY STUDENTS?

I AM!

My Lexical Crime

Ingenuity. Creativity. Or just plain eccentricity. I'm not sure what led me to mangle a perfectly fine expression.

So far, nothing bad has happened to me since I committed this verbal crime for the first time more than a decade ago. And I've been committing said crime over and over again without letup.

No rehab. No therapy. Nothing could ever cure me!

Here it is. Calm down. Instead of "Excuse me," I say "Squeeze me." :P

I say "Squeeze me" when I want my students to hush.
I say "Squeeze me" to remind preoccupied late-comers to sign my tardy log.
I say "Squeeze me" when my students talk to me using their "normal" voice.
I say "Squeeze me" when my students tell me their parents used their homework to start the barbecue fire.
I also say "Squeeze me" when I confiscate a student's cell phone that's in use while in class because the parent called from the mental hospital.

Am not sure what my students really think of me, but my mangled version seems to work just fine. Same two words. Two innocent words uttered with varying tones of voice or facial expressions.

The fact is it causes excitement that "Excuse me" couldn't draw.

There's magic in "Squeeze me."

It never fails to elicit knowing smiles.

It also disarms those who came to class loaded.

This has been a fixture in my classroom this school year.

Drawing by Samantha Roy Gutierrez.

Draw and Use a Gallon Square

Materials needed: small piece of paper ( a 3 in by 3 in Post-it note will do) and a pencil or pen

Draw a square. You do not need to do this step if you're using a Post-it note. (Are you sure what you drew is a square? :P) This square represents one GALLON.

Cut this square into 4 smaller squares. Write Q, for QUART, inside the top right square.

Horizontally cut the top left square into two small rectangles. Write P, for PINT, inside the top rectangle.

Now cut the second rectangle into two even smaller squares. Write C, for CUP, inside the one on the left.

Lastly, cut the second little square into 8 equal parts. Write O, for OUNCE, inside one of them.

You've just created your GALLON SQUARE!

Let's use it to convert between gallon, quart, pint, cup and ounces.

Fill in the blanks. Mentally!

___quarts =1 gallon
___pints = 1/2 gallon
3/4 gallon = ___pints
1 quart=___cups
1 pint = ___ounces
3 pints = ___ounces
1/2 gallon = ___cups
5 cups = ___ ounces
5 quarts = ___gallons
1 1/2 cups = ___ounces

Carry a mental picture of this gallon square with you. Amaze your friends with how quickly you convert between gallon, quart, pint, cup and ounce.

Proof of Joy

The tutoring period had already started. There were four students in the room who were already busy working collaboratively on exercise problems I have assigned to them.

I was erasing the doodlings Berenice and Leslie did on the dry-erase board during advisory period earlier when Danny came in. He was panting.

"Sir, I do not know how to do proofs, and I want you to help me." There was urgency in his voice.

I handed him the list of exercises we used in class earlier. "Choose any one that you think you could or want to do, and do it on the board."

"Okay."

As Danny copied his chosen problem on the board, he read aloud every word and symbol. He also said out loud what he was thinking about the problem.

"For my first step, I'm gonna write in the first given which is..."

He took a few steps away from the board, knelt on one leg, wrapped his left arm around his chest, and touched his chin with his right hand.

I took a quick check on the four students. Kari had a grin on her face. She had been watching Danny since he came in.

"You always say that it is a good thing to write the last step and just fill in the middle steps afterwards." He mumbled.

"Okay, I think the second step is..." He started writing again.

"Is it right, Mr. Jope?"

"No." I said. But before I had the chance to explain myself, he erased what he just wrote.

"No? Then it must be this... I must be right this time."

"Yes, you are."

He continued on his own while still talking to himself aloud. Occasionally, I made comments on what I was hearing.

"I'm done. Sir, did I do it right?

While I took a moment to review the two-column proof he had written on the board, I could tell he was intently studying my face for any trace of approval.

When I said yes, the young man threw his arms up, his face glowed like the neon orange shirt he was wearing.

"Oh, my God! I can do proofs now!"

I asked him to do two more problems, which he happily solved with minimal errors.

That afternoon, Kari and I had complimentary front row seats to the most entertaining geometric proof presentation we both have ever witnessed!

Daniel's joyful feet and Kari's beguiled face: priceless!

Itzel's Dream

I am the proud founder of Feet2Miles, a charitable organization. My former student, Dr. Leonardo D. Lopez, and his girlfriend, Norma H. Morales, are my co- founders. Among its main objectives is to donate slippers (chanclas) to indigent Filipinos.

Initially, I formed Feet2Miles as a group on Facebook on Mother's Day in May this year. The overwhelming support of my Facebook friends inspired me to take this endeavor seriously.

During my vacation in the Philippines this past summer, with the help of my sister Helen and some of our friends, we bought the first 200 pairs of rubber slippers and gave them away mostly to needy kids in the small isolated village called Aspang in the outskirts of the city of General Santos. The joy that I felt then virtually sealed my commitment to the organization. Upon my return here in Texas in August, I promptly registered Feet2Miles with the Office of the Secretary of State, with my friends Dr. Leonardo D. Lopez (US) and Ariel Marco T. Oclarit (PH) and myself as directors.

The first one to sign up with Feet2Miles on Facebook was a former student of mine, Itzel Garcia.

Just recently, Itzel posted on the most popular social networking website an invite to "like it and I'll tell you what I like about you." I did, and the following was her response:

"sir, i like how youu started that feet2mile,
when i get a real job, i wan helppp moree!
I want for feet2mile to go worldwide, and be
famouss & we'll be helping all the kidss
everywhere in the world. My dream come truee!"

Since then, Itzel has communicated to me her desire to help the organization. She is teaming up with our student council to launch a penny-drive to benefit Feet2Miles.

As teachers and educators, we hope to inspire our youth to be good citizens when they grow up.

Interestingly, when we do, we all feel blessed.

Touchdown!

T-G-I-F!

I felt relieved that the week was over and that I could go home finally to celebrate my birthday. As usual I had planned nothing special for myself. I just looked forward to having a hearty microwaved dinner and enjoying it while watching my favorite shows on cable TV.

It was only October, but I was already looking forward to the five-day thanksgiving break. That year, I added yearbook advisory to my already insane daily work at our high school. So T-G-I-F, indeed!

“So, Mr. Jope, will you be there at the game tonight?” It was Matty, a junior student. I almost forgot that he was still in my classroom. Although I knew he’d be playing football that evening, I made him stay after school to practice for his math competition the following day, Saturday.

“I don’t think so, Matty. I don’t have any energy left in me,” I said to him. “Thanks for inviting me.”

Matty had been an active member of my math team since he was in 6th grade. He also did advance Algebra 1 with me when he was in 8th grade. Despite his successes in sports (he was his varsity football team’s quarterback and his baseball team’s pitcher), he always found time to practice for his math competitions.

This hardworking young man, who was adored by his teachers and peers, continued doing his work for a few minutes more as I quietly waited for him to finish. When he did, I reminded him to wake up early in the morning to catch the bus.

“You have to go to the game, Sir,” Matty insisted. Before he ran out to report to the field house, he added: “Don’t forget to take good pictures for the yearbook. Bye.” 

He only needed to mention the word “yearbook” to convince me to see his game. Now I thought (1) I had to take advantage of the fact that it’s a home game and (2) the football varsity pages would be due in a week!

So I was there at the football stadium that Friday evening, standing close to our mighty Pirates. Not one of my yearbook students was in the crowd to help me take pictures. With two cameras to use, I was hoping to take good action shots, including one of a much-coveted Pirate touchdown. 

The night grew weary, and the game started to deplete me. As an immigrant from a country that never played football, I didn’t appreciate this peculiar American sport. The only thing that kept me interested in the game was the fact that some of our players were my past and present students. As my hope for a good shot of a touchdown started to wane, I also started to feel sorry for myself. It was my birthday after all and I wasn’t even celebrating it!

I decided to leave. I thought I got enough shots for a decent spread. I already had retreated from the field when the home crowd started to get energized again. Our team was gearing up for the long-awaited touchdown. I quickly retrieved the smaller camera from my bag and positioned myself near the end of the field.

Boy, oh, boy! As soon as I found my spot, player No. 10 darted across and scored a touchdown. It was Matty! I was so excited that I forgot to shoot! 

I was about to hurl invectives at myself for failing to capture the lone touchdown when I noticed that Matty held the football in my direction. 

“That was for you, Mr. Jope. Happy birthday!” Matty shouted.

Just when I was almost sure that I wasn’t going to have a happy birthday anymore, I got a surprise. And it was --oh, yes! -- priceless!

The Class Clown

More than a decade ago, as I recited last-minute reminders to my 8th grade Pre-AP Algebra 1 class, one of my female students asked me if I was married. The classroom fell silent and all eyes were on me. Awkward! 

"I'm married to all of you," I said, as the bell finally rang.

Well, that was a slip. I had meant to say "I am married to my job," but somehow I said it the way I did.   

I didn't bother to scour their faces for any reaction, but I did hear Diego, the class clown, say it loud in a sing-song manner, "My teacher is a perveeert," and as soon as he got my attention, he ran away, saying, "See ya tomorrow, Mr. Jope."

Time passed by, and now it was time to gear up for the state end-of-course Algebra 1 exam. Just a couple more days before testing, Diego had more energy than usual, and he did manage to get on my nerves. I made sure that he knew that I did not appreciate his behavior. At the end of the period the boy apologized to me. He said he'll never do it again. 

"I accept your apology, Diego."

I thought I had said enough, but to my surprise, he looked more worried than I thought.

"We're still married, right?," he asked, partly joking.

Until that day, I didn't know that the boy's parents' marriage had recently crumbled. Apparently, our "marriage" was important to him.

The Exotic Teacher

Once upon a time, there was this young Filipino teacher who bravely travelled to America from southeast Asia. Lady Luck quickly found him a middle school math teaching job at a small school that sat very close to the Rio Grande River just across from Reynosa, Mexico.

One day, as the new immigrant wrote sample math problems on the chalkboard, he heard one of his seventh graders say out loud a word that sounded so familiar. The teacher turned around and saw Noe (not his real name) tentatively say the word again as he addressed another boy who promptly hurled the word back.

Instinctively, he thought that both students had  just learned about the delicious Filipino rice cake, called puto, and that they were trying to impress the whole class and their exotic teacher with what they had just learned.

"So, Noe, how did you learn about puto? Did you get to taste it?"

"No, sir! Why, sir, have you eaten puto?"

"Yes, Noe. It's one of my favorites!"

Somehow, the teacher quickly earned a new title: the teacher who liked to eat putos.

A few days later, he brought a tray of the now-notorious rice cakes to be sampled by all his students. Suddenly, to his relief, he wasn't the only one who liked to eat putos anymore!

In this corner of immigrant-friendly America, puto is Spanish for male prostitutes.

The exotic teacher was... me. :D    

Nick's Trick to Find Integer Factors

Students usually struggle with factoring trinomials of the form x^2 + bx + c. But I learned that, most of the time, the problem is in the failure to include the right pair of factors in their list.

As their teacher, I've always asked my Algebra 1 students to list down the integer factors from memory, which needless to say, didn't help everybody.

One day, as I showed my frustration for my students' incapability (Shame on me!), Nick Schaaf, one of my stronger students in his class, grabbed his TI 84 calculator, jumped out of his seat, and volunteered to show his unique method of finding the right pair of factors.

To find all the possible integer factors of, say, -36, all Nick did was enter the equation y= -36/x on his graphing calculator, and then he proceeded to look at the resulting table of values. He scrolled up and down the table, ignoring the pairs of factors that involved non-integers. From his integer factors, he picked the pair whose sum equalled the numerical coefficient of the middle term (bx) of the given trinomial.

Nick was an instant hero. His classmates really appreciated his method, and I started liking the test scores that immediately followed.

As a result of that experience, I have made it a point to facilitate and encourage classroom talk and collaborative group work whenever possible and whenever appropriate.

I still look forward to learning from my students.

Greatest Angle in a Triangle

Our adopted textbook, Holt Geometry, has the following definitions:

"Acute triangle is a triangle with three acute angles."

"Obtuse triangle is a triangle with one obtuse angle."

"Right triangle is a triangle with one right angle."

Using the triangle sum theorem, one would see that there can only be one right angle or one obtuse angle in any triangle.

In my class, I don't see any problem if my students would come up with the following definitions:

Acute triangle is a triangle whose greatest angle is acute.

Obtuse triangle is a triangle whose greatest angle is obtuse.

Right triangle is a triangle whose greatest angle is right.


And what do you think of this take on equiangular triangle:

"Equiangular triangle is a triangle whose greatest angle is 60 degrees"?

A Classifying Triangles Activity

Here's an activity that I have been using to help my students achieve mastery on classifying triangles by side lengths and angle measures.

The primary objectives of this activity are (1) to master vocabulary, and (2) be able to correctly relate the different triangle classifications with each other.

The activity involves a 4 X 5 table. The top row will feature the triangle classifications based on angle measures: acute, right, obtuse, and equiangular. The left column will feature the triangle classifications based on side lengths: scalene, isosceles, and equilateral.

In this activity, the students, individually or in groups, will determine if triangles can fall under two such classifications. For example: Is it possible to draw a triangle that is both acute and scalene? If so, the students will draw that triangle and label it appropriately. If not, then they may write NP for not possible.

I find this activity great for reviewing vocabulary (scaffolding). It is also great for classroom talk and more questioning.

What I like the most about this activity is its "friendliness" to diverse learners, from the learning-challenged to the gifted, and from the color-blind to the most artistic.

This poster was created by Kendra Cobos, Edgar Devora,

Vincent Grimaldo and Rey de Leon in my Geometry class.

Freshmen Irma Mata, Alex Tenopala, Kaela Garcia and Amber

Hernandez created this poster in my Geometry class.

Poster created by Dalia Gutierrez, Victoria Gomez and Berenice Pacheco.

Mnemonic Devices for Points of Concurrency in a Triangle

I have new terms to add to the already-crowded vocabulary bank of geometry.

The terms are PuBliC, BAsIN, CEmeNT, and ALTo.

These four terms I have coined myself are but mnemonic devices to help students and teachers remember the points of concurrency involving a triangle.

The P and B in PuBliC stand for perpendicular bisector. Each of the three sides of any triangle has a perpendicular bisector. All three perpendicular bisectors intersect at a point of concurrency, called circumcenter, the C in PuBliC.

Angle bisector, or bisector of an angle, is represented by B and A in BAsIN. Each of the three angles in any triangle has an angle bisector. All three angle bisectors have a point of concurrency, called incenter. The IN in BAsIN represents incenter.

Together, CE and NT in CEmeNT represent centroid. Centroid is the point of concurrency of a triangle's three medians, the "me" in CEmeNT. The word "middle" is associated with the word median, so I was very excited to find a term that has "me" in the middle.

ALT in ALTo simply means altitude. The lines that pass through each of the three possible altitudes of a triangle have a point of concurrency also. This point of intersection is called orthocenter, the "o" in ALTo.

I came up with these mnemonic devices on my second year of teaching Geometry. I realized it wasn't only my students who had difficulty remembering and associating the points of concurrency. "Mr. Jope" had the same problem, too! :D

Kaela Garcia, one of my freshmen, made this

poster as a project in my Geometry class.

This was my student Samantha Cerda's project.

This was done by Alexis Siller, one of my students.

Victoria Gomez turned in this poster as a project in my Geometry class.