Monday, December 29, 2008

Do you always believe other people's claim?

We often have to make decisions based on what other people state or claim. However, how do you know if their statement or claim is a solid and valid argument? For example, we all enjoy going out for dinner with family and friends. When you pick up and look at the restaurant's menu, you notice there is a significant automatic charge for service that will be included in your bill. You question this charge with the owner of the restaurant, who tells you the charge is due to the trend in which large parties often pay less in tips than small parties. Would you take as a fact what the owner claimed?

Mathematics is a useful tool to prove or disprove someone's claim. The excerpts clipped to this post came from an interesting article from Plus Magazine web site (i.e. Issue 49), which explains how Statistics is used to make sense of all the information we receive from different sources. I encourage you to read the article and become aware how mathematics can help you make informed decisions.
clipped from plus.maths.org
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We live in a world full of information and it's a statistician's job to
make sense of it. This article explores ways of analysing data and shows how
they can be applied to anything from investigating diners' tipping behaviour to
understanding climate change and genetics.

Have you recently sat down in a lovely restaurant, picked up the menu, and read
"12.5% discretionary service charge will be added to your bill"? In the UK this
is now a common occurrence. In the USA the extra service charge is often made
dependent on the size of your party: if you're more than six people, the charge
will be added automatically. So what is the connection between party size and
service charge?
One reason for this fairly recent change in procedures is that restaurant owners
and workers collect data on their diners, and it has been discovered that larger
dining parties tend to tip less.
The model says that the tip rate decreases by a little under 1% for each
additional diner in the party.
 blog it

Saturday, December 13, 2008

Almost Fooled on Black Friday!




People take the opportunity to do most of their Christmas shopping the day after Thanksgiving Day, which the media and retailers call "Black Friday, since almost everything on sale have considerable discounts. People arrive way before the stores are open, waiting in line for hours to be the first ones buying the best or most popular items at bargain prices and before it sold out. My wife was one of those early shoppers, leaving at 4 a.m. to the mall.

During Black Friday, people should be very careful not being tricked when purchasing items they may think are at bargain prices. The shopping hype or frenzy of such day could easily distract people for using their critical thinking skills or skepticism when something looks too good to be true. This is exactly what happened with my wife when she tried to buy a nice golf shirt as my Christmas gift. The regular price of the golf shirt was $32 but with a 25% discount, which my wife thought to be good deal even though she did not know the exact amount she was going to pay for the golf shirt.

Like many people, my wife had always questioned the reasons for learning mathematics other than the basics, even though she did fairly well in math courses during her schooling years and college. She was one of those students who did not see any practical reasons for learning advance math topics, such as Algebra, Geometry, Statistics, etc. since she was not going to be a scientist, engineer, or any career that involves mathematics. My wife was one of those students who believed that Algebra made simple problems too complicated. In summary, she was not fully aware of the usefulness of learning mathematics for her daily life activities.

However, it was the experience she gained in the mathematics courses that helped her develop the ability to make sense of numbers. And it was this ability that helped her decide not buying my Christmas gift when the cashier notified it was $30 for the purchase. Probably, many people would have paid the $30 for the golf shirt due to their excitment of being part of big event such as Black Friday, in which the belief is that all purchases are the best bargains. Fortunately, my wife did not get caught in the hype of Black Friday and she questioned the purchasing amount for the golf shirt. The cashier explained the purchase amount was a good bargain even after the discount and sales tax were applied to the purchase.

For a few seconds, my wife hesitated to follow her common sense or number sense since after all, she wanted to give me a gift. However, she told the cashier to cancel the purchase since she was convinced the purchase amount was too high for an item that was a 25% off and a sales tax of 7%. In the way back home, my wife was regretting her decision for not buying my gift. When she got home, she immediately asked me if her decision was correct or not since she did not remember how to calculate the discount of 25% and the sales tax of 7%. I showed her the computations: 25% of $32 is $8, so the sale price should have been $24. The sales tax of $24 is $1.68 (7% of 24), so the purchase amount should have been $25.68. My wife felt relief about her decision! My wife's common sense about numbers was something she developed from taking math courses. A great benefit indeed for learning mathematics!

Wednesday, December 3, 2008

Aha! Cops need math too!




In the episode "Falling" of season 19 of Law & Order, detective Lupo said "Who needs math?, I told my teachers. I'm gonna be a cop." Detective Lupo was studying financial reports to find out a possible motive to solve a murder case. He was having difficulties understanding the mathematics involved in the financial reports and he was regreting the fact that he did not pay careful attention in math classes during his schooling years.


Why I find interesting this scene of Law & Order? Well, this scene demonstrates the typical attitude many students show when learning mathematics. Many students quickly become desinterested learning mathematics if they cannot find an immediate practical use or real-life application for what they are learning. Unfortunately, not every math concept or skill has a practical or real-life application. In many instances, there will be math concepts and skills that are only necessary to grasp more complex or advance math concepts.


There are also those students who often assume there are certain careers (e.g. law enforcement) that do not require mathematical knowledge to perform and excel. However, students who can develop their mathematical skills will also be developing their ability to be critical thinkers and problem solvers. To my knowledge, there are always problems or issues to solve in every career or job, and employers are always looking for those who can solve these problems and issues. Let's not forget that life is also full of challenges that we need to overcome, and those with the critical thinking and problem solving skills are usually the ones who struggle the least overcoming the challenges. They work smarter not harder!


We should avoid minimizing the critical role that mathematics play in our lives solely based on if we can apply it in real-life or not. It is not always possible to forsee the ramifications and uses of the math knowledge we acquire. Today, it may seem useless to learn about a particular math concept or skill, but tomorrow, that same concept or skill could be the difference for becoming successful or not in whatever endeavors we pursue. Therefore, we should view learning mathematics as an important exercise to become better critical thinkers and problem solvers. Otherwise, we will probably regret (the same way as detective Lupo did in the Law & Order episode) for our poor decisions to minimize the role mathematics play in our lives.

Thursday, November 20, 2008

Why we need to learn this?!


Recently, one of my students in my basic skills math courses (college level) asked the question that most math instructors dread answering, "Mr. Diaz, why do I need to learn this?" I have been asked this question so many times before, but I always had the impression that my responses were not convincing enough for my students to see the importance of learning mathematics. My usual responses were "You need a solid foundation to succeed in the higher level math courses" or "What you are learning may not make sense or seem useless right now but at some point you will need it for your career." However, I decided to use the socratic method and an analogy this time around to convince my student about the importance of learning math. For the sake of making easier to follow the discussion that happened in my class, I will call "Z" for the student who questioned the purpose for learning math and "B" for another student who took interest in taking part of the discussion. Here is the dialogue that took place in my classroom.

"Z" asked at loud, "Mr. Diaz, let's be real, why do I need to learn all this Algebra?!"
Mr. Diaz responded, "Well, let me answer your question with another question. What you prefer to be, an intelligent or ignorant person?"
"Z" answered back but with a not convincing tone, "You're right, I prefer to be considered an intelligent person."
Mr. Diaz then said, "Z, when people want to join the Marines, Air Force, Navy or the Army, what are they required to do first?"
"Z" said, "Well, they teach them how to shoot."
Mr. Diaz replied, "Before they are taught how to use a weapon, what these people have to experience first?"
"Z" said, " Oh! They go to basic training."
Mr. Diaz asked "Why they need to go basic training? To use a weapon, they do not need to do push ups, pull ups, running a mile, and so forth!"
"Z" was perplexed with my question and was not able to give an answer when "B," another student, shouted "They go to basic training to build up muscles and become fit for battle!!"
Mr. Diaz excited said "Exactly!!! For the same reason, you are taking this class. Your are building up the muscle you have in your head...the brain!," while pointing his index finger to his head.
Mr. Diaz added "You are training your brain to think and problem solve. You are training to work smarter, not harder."
The discussion ended with "Z" smiling at me and acknowledging that I had a good point that he could not argue anymore. "Z" continue doing his math work.

What do you think?

Saturday, October 4, 2008

Have you ever experienced math anxiety?


According to the site Platonic Realms, math anxiety is "a feeling of intense frustration or helplessness about one's ability to do math." From my experience as a math instructor, I have seen many students feeling incapable of doing mathematics, no matter what they try to overcome it (e.g. studying more hours, tutoring, interactive course materials, etc.). It is unfortunate seeing undergraduate students who cannot finish degree requirements due to their math anxieties. I often cannot believe how students allow their fears and dislikes about math hinder the pursuit of their goals and dreams.

One of the possible causes for math anxiety is unpleasant learning experiences students had during their schooling years. Another cause is the disabling belief that learning math is only for the "natutally gifted person." Math anxiety also often occurs with those students who wants to learn and do math in a quick fashion. Students lacking basic skills usually show signs of math anxiety.

I will like to ask my readers to post a comment by answering the following questions: Do you like learning and doing mathematics? Why or why not? Have you ever felt math anxiety? If you did, how you handled it? Can you pinpoint when these anxieties started? If you did not, what are the reasons for not experiencing math anxiety? Do you have any suggestions for those who experience math anxiety?

Wednesday, October 1, 2008

Students talking about fractions!












One of my goals this year is to use journals (at least 3 or 4) in my developmental math courses to encourage students discuss mathematical ideas. Students usually do not see the reason for writing in developmental math courses. However, writing math journals helps students to pause for a moment from their hectic math studies (there is a lot to cover in these courses!), reflect what they have learned so far, and find out how math connects with their lives. If students write about math then they are becoming aware of its existence in their daily routines. Using thoughtful and provoking math prompts, students use their personal experiences, values, emotions, and knowledge to complete the prompts. The goal of the math journals is to view mathematics as a natural part of our lives, the same way is reading and writing.

Using the power of the Internet and Web 2.0 tools to increase students' interest and motivation for writing, I recently scheduled the first math journal in my developmental math courses using a discussion forum from a Facebook group (i.e. Learning about Mathematics and How and Where to apply it?), which was created by a math faculty member of St. Thomas University. Students responded to the math prompt "Fractions should be scrapped?!" which it came from an interesting article I read in the USA Today web site. This article immediately caught my attention since it mentioned how a math professor has been suggesting a delay in teaching fractions at the elementary level and to focus instead on teaching decimals. As a math developmental math educator, I found this suggestion absurd since I see everyday how many of my students struggle understanding math concepts that involves fractions (e.g. rates, proportions, percents, slope, etc.).

However, I recognized this article was an excellent opportunity to talk about mathematics with my developmental math students. I thought "why not ask my students if they agree or not with the professor in the article since they are the ones who often have difficulties working with fractions?" Their input about this topic may help me gain a different perspective from the article. Therefore, I decided to assign the first math journal about this article. I honestly was expecting the majority of my students being in favor of the professor's suggestion in the article. However, it was amazing to find out how most of my students did not agree with the professor's suggestion. My students may not like working with fractions but they clearly see how vital is learning fractions early in their schooling years. Many students commented how they regret not learning well this concept earlier since it is now hindering their opportunities for pursuing their academic and career goals.

I invite my readers to join the Facebook group Learning about Mathematics and How and Where to apply it? and read my students' posts. In addition, the moderator of this group invites anyone to take part of the discussions in the group. As I stated previously, the goal is to start talking about mathematics and gain awareness of its usefulness and practicability in our lives. Join us!

Tuesday, September 30, 2008

I am Blogging Again!



Hello World! Here I am trying for the second time to create and maintain a blog. I created my first blog in Yahoo 360, in which I have posted a few reflections about my experiences as a math educator using technology in my practice. I do not post often there due to time constraints (I have a heavy teaching course load!) but I will continue the blog as a self-reflection exercise of my teaching practice.

However, this blog will have a different purpose than my first blog. I created Be Aware Math is Everywhere! blog as part of a doctoral assignment in one of my specialization courses (i.e. LTM 5005 The Connected Classroom: Curriculum Development and Technology) at Northcentral University. In every doctoral course, I apply the course assignments in my classroom practice to achieve my pursuit of becoming a better educator (That is why I am pursuing the Ed.D.: to become a practitioner-researcher and improve my practice!). For some time, I have been pondering the use of Web 2.0 tools to enhance teaching and learning in my classroom and this assignment provided a great opportunity for trying blogs in my practice.

As a developmental math instructor, I often encounter students who question the reasons for learning mathematics and they request examples of practical real-life applications of the math concepts and skills they are learning in class. Unfortunately, many students believe learning mathematics is just for the sake of meeting degree requirements and not for personal gain. They are missing the bigger picture that mathematics could help them understand a world where numbers are used to quantify and explain every human endeavor and natural event that occurs. These students are giving away their power of understanding and making informed decisions due to misconceptions, inexperience, or reluctance for appreciating the true power of mathematics.

For such reason, I created this blog to promote awareness among my developmental math students of how mathematics is used daily in their lives. To accomplish this goal, I need to make connections of the mathematical concepts and skills my students learn in class with their everyday life experiences. My intentions are to find real-life examples where mathematics play a vital role and explain it in layman terms to my students. From my experience, students find learning mathematics meaningful and useful when is related or connected with their lives. By making connections, students will realize that they have been doing mathematics often in their lives but were not conciously aware it was mathematics.

I am hoping that somehow this blog will generate discussion of the reasons for learning mathematics among my students and visitors. Talking about mathematics is the only way to create awareness of how mathematics is deeply integrated in our lives. Be Aware, Math is Everywhere!