Mr. Hope

Here's an essay Roxie Torres, one of my former students, wrote in her English class last week of September. Her teacher, Mrs. Nelly Limas, forwarded it promptly to me.

I have met many different types of people in my lifetime but during my high school years, I met one specific person who was genuine in his own way. That person is my geometry teacher Mr. Jope.

Mr. Jope is a benevolent person. He has demonstrated to many people, including myself,

how the greatest gift that anyone could acquire is to bring bliss to those around you. He himself has conveyed many wishes to those who are less fortunate. He sends a spark to those who feel lost and hopeless just by showing them care and support. When I look at the impact Mr. Jope brings to others, I feel driven to give a light, a reason, for people to not lose the optimism that can bring a difference to society. In this type of society we live in nowadays, I believe we need more people like my geometry teacher. People who can push others and drive them to the goals of life just by giving them a few words of wisdom and multitudes of support. I have grasped the reason why he wants everyone to succeed. He, like myself, wants the world to be a better place to live in. He craves for everyone to have a chance in the limelight and realize that all their hard work has been worth every blood, sweat and tear.

Although Mr. Jope is still a human who has surely made many mistakes and has had his own fair share of agony like every other human being in this world, he still continues to fight and not let his regrets and decisions in his past haunt him. He has presented to me that the answer to conflicts is not to cower away from them but to run towards them with your head held up high. While facing the challenges that the world may bring, one should consider having a positive attitude. Don’t let the problem overcome your whole life; that is one thing that I still have to master from my mentor.

Mr. Jope has given a sense of hope and accomplishment to everyone he knows. He never leaves any person behind or makes them feel isolated. He has truly made a difference to many lives and he holds pride to his accomplishments. He is a giver not a receiver. I believe it's time for me as his pupil to start using my notes and to start teaching others what I have learned.

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?

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.

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!

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.