### EP 125: The Correlation Between Music and Math

I can say this with almost 100% certainty (perhaps 99.9%): if you are a person living on this planet, you enjoy listening to music. You may prefer the dark melodies and heavy guitar riffs of punk rock, or you might gravitate towards the light and upbeat sounds of electro pop. Whatever particular concoction of rhythms and sounds you prefer, rest assured that there is something that tickles your fancy.

There is something else you should know. While most folks readily profess a stalwart love for music, they simultaneously describe a deep hatred for mathematics. When thinking about classroom mathematics and modern music, it is natural to initially presume that the two are diametrically opposed, but this line of thinking is incorrect. The two are in fact inextricably connected (to hear more about the connection between math and music, check out my video on the applications of math). Music is simply an auditory extension of mathematics. Making good music mandates that composers adhere to numerical laws of rhythm, timing, and melody. Scales are literally mathematical rules applied to vibrational frequencies that seem be universal across the planet. Many famous composers like Iannis Xenakis openly use mathematical theories to create musical works of art.

But there is another connection to take notice of that is highly relevant to our young math students today. According to an article from Brain Balance, “using specific music and sounds may help to stimulate one hemisphere more than the other and possibly create more balance in the brain. As such, listening to music could improve a student’s cognition and ability to learn math skills. As recently as 2012, one study showed that listening to music during a math test could improve performance by 40 percent.” Translation: music can help you learn math! Moreover, the article purports that upbeat music and major tones in particular can bolster left hemisphere activities, which is directly relevant to logic based tasks like science and math reasoning.
I have known about the harmonious relationship between mathematics and music for some time now. Recognizing the interplay between the two was the impetus for me to begin the creation of a series of math music videos. I try to bridge the gap between music and math by literally singing about math related concepts. Moreover, I use the choruses as a sort of musical mnemonic device to give students the best opportunity possible to memorize tricky formulas and perform well on tests. To check out my latest math music video on special right triangles, click here.

### EP 124: 6 Reasons Why You Should Study for a Math Placement Test

To date, I have worked as a private math tutor, test preparation specialist, 6th grade math teacher, and online video course creator. Part of my duties in these various positions have led me to counsel students who are transitioning to new middle schools, high schools, and colleges. The question that I have received over and over from students and parents is this: should one prepare for a math placement test? It is an interesting question since most folks naturally assume that everyone should study before an exam. So why the confusion? Because most schools tell new students not to prepare for placement tests. The rationale is that placement tests are merely meant to gauge current math skills, and preparation for these tests might muddy the waters. Moreover, there is no passing or failing; these tests will simply be used to determine what level of math a student will enter when school begins. For example, a new 7th grader may either enter pre-algebra, algebra, or geometry based on their placement test results. So, as it stands, most teachers and counselors seem to be advising students to go into these tests without preparation. Do I agree? Of course not, and I will explain why in six simple reasons.

Caveat: I only recommend preparing for placement tests when the desire to do so comes intrinsically from the student. Forcing the issue means the student is not mentally or emotionally prepared to work hard, and that can be a problem if placed into a high math group. If, however, the student is pushing for the preparation, there is no need to fear. Their desire to perform well will carry them. I am in support of introducing the idea to a student, but if they do not latch onto the concept, then my recommendation is to let them be.

Reason 1: It’s easy to forget nuances and lose points even when math fluency and comprehension are strong

Who out there remembers the quadratic formula in its entirety? Who recalls precisely how to take the derivative of sin(x)? Who can still solve a system of linear equations? As an adult who is far removed from the study of mathematics, my guess is that you have completely forgotten all of these protocols and procedures. But guess what… even if you’ve only had a month or two away from these concepts, chances are that you’ve forgotten parts of these processes. Perhaps you remember the bulk of the quadratic formula, but you somehow thought the denominator was 2 instead of 2a. Or maybe you confused the derivative of sin(x) with the derivative of cos(x).

My point is this: it is very easy to forget a small component of these formulas and procedures, even when your comprehension at one time was flawless. Is it then fair or accurate for a multiple choice math placement test to penalize a student for a series of minor mishaps? Absolutely not. Aside from being fair, it is inaccurate. Accordingly, brushing up on these concepts is a must. Just to be clear, I’m not advocating a full on multi-week cram session where you embark upon a quest to learn massive amounts of new information. What I do recommend, however, is a thorough review of all the concepts you learned in the previous year. It will not misrepresent your abilities; to the contrary, it will let your true math prowess shine.

Reason 2: Math knowledge can be substantially ramped up in a relatively short period of time

Math is not like reading. Becoming a solid reader takes years of practice and devotion because it is such a highly complex process. While math can be highly complex as well, middle school and high school mathematics is comprised of a series of relatively simple operations. When I say simple, I do not mean math is easy. What I mean is that much of the individual math concepts taught at these levels can be understood and mastered in a relatively short period of time. It’s the reason why students preparing for standardized tests routinely see a much larger jump in math scores than verbal scores after preparing for a few months. As such, engaging in some focused practice and review in a short period of time can have a significant impact on one’s ability on a math placement test. Translation: the juice is definitely worth the squeeze.

Reason 3: It is very unlikely that you can perform beyond your abilities on a placement test (i.e. if you can get it right on the placement test, you most likely GET IT)

So many math education websites state that you should not prepare for placement tests because you want to be in an appropriate math class for your knowledge and ability level. Well, since final exams are meant to gauge a student’s understanding of class material, should students forego preparation for final exams as well? What about standardized tests? Don’t we want students to be placed at a university that is appropriate for their skill level? The point is that preparation is part and parcel of the education process, and how hard a student is willing to prepare is also indicative of their ability to succeed through perseverance. Moreover, if a student understands a concept to the point where they can provide a correct answer on a placement test, they GET IT. I do, however, concede that students should refrain from guessing on placement tests. That would be counterproductive. Educated guesses make sense, but blind guesses would serve no purpose in assessing placement.

Reason 4: You can always move backwards, but you usually can’t move forward

Let’s play out the worst case scenario of acing a math placement test. Assume that a student going into 7th grade crushes the assessment and is moved into geometry, a very advanced math class for 7th grade. Let’s also assume that the student is now experiencing great trepidation about geometry and feels as though algebra would be a better fit. The parents concur. Is it feasible to move the child from geometry backwards to algebra? Of course! Schools are extremely amenable to moving a student backwards if both the parents and student feel that such placement is appropriate. Going the other way, however, is extremely difficult, especially with prestigious college preparatory institutions. Schools in the upper echelon of academia can be rigid with respect to placement results. I’ve seen many students fall victim to these systems only to end up facing boredom all year long. In sum, shoot for the stars so that you have options.

Reason 5: If you have a tutor, you will be more than equipped to iron out any difficulties that may arise in a challenging math class

For students lucky enough to have access to outside help, there is nothing to fear. Whether it’s a private tutor, parent, or teacher who volunteers after school, having access to extra help should alleviate any stress about being placed in an advanced math class. Any concepts that are troubling can be cleared up in a very short period of time when personalized help is available.

Reason 6: It is better to busy than be bored

Counselors constantly warn students of the dangers of being placed in a higher than appropriate math class. They admonish parents and students alike of how high level math classes can leave unprepared students feeling overwhelmed or anxious. But what about the alternative? What about the dangers of being bored? Boredom can destroy a child’s love for mathematics. Stagnation is a recipe for indifference. Moreover, the likelihood that a child will be completely overwhelmed with no ability to catch up is very small if the child possesses intrinsic motivation. Again, this entire article is premised on the fact that a child is preparing for a placement test because of his own desire. If a student indeed wants to prepare, they will likely embrace whatever challenge may come their way. So, it is with no hesitation or second thought that I leave you with this final recommendation: if a student wishes to prepare for a math placement test, by all means, let him do so.

### EP 123: Review of the NCTM Annual, one of the largest math education conferences

On April 5th, 2017, I landed in San Antonio, Texas, for the very first time. Sure, I enjoy Tex-Mex, and yes, I was excited to roam the River Walk with the looming possibility of meeting Tony Parker, one of my favorite NBA guards of all time. But that’s not why I came to the home of the Alamo. I had embarked on this southwestern journey with a specific purpose in mind: to learn as much as possible about the vast field of math education. I had come, unequivocally, to milk the most talked about math education conference in the United States: the National Council of Teachers of Math’s Annual Conference!

The NCTM is the world’s largest mathematics education organization, boasting a membership of over 60,000 individuals. Each year, the NCTM hosts a massive annual conference that attracts nearly 9,000 math educators from across the globe to share their insights, strategies, and experiences to improve the entire education process for teachers and professors everywhere. Naturally, I had to be there.

I was beyond excited when I arrived in San Antonio. I imagine it’s the same feeling a budding musician experiences when attending the Grammy’s for the first time. The city’s conference center was filled with math wunderkinds and education superstars. I was elbow to elbow with esteemed research professors and secondary school math zealots that had so much to offer. As soon as I set foot in the main hallway, I immediately downloaded the NCTM conference app and began planning my tour of lectures. And let me say, this conference had an insane amount of lectures to choose from. At the end of each lecture, I perused dozens of lecture titles and descriptions before making a selection for my next stop. Of the many lectures I attended during the conference, there were three that stood above the rest. And by the way, this in no way means that the other lectures were not on the same level; this is simply a collection of three lectures that were particularly impactful for me given my ongoing efforts to use technology and games in concert with math education.

The first all-star lecture was given by Tinashe Blanchet, proud owner of a math education blog: http://mrsblanchet.net/.  Mrs. Blanchet is a teacher brimming with passion and enthusiasm for math. But why, precisely, did I find her presentation so powerful? Yes, she is a charismatic and dynamic speaker, but what really intrigued me was her topic: math music videos. Mrs. Blanchet, like me, infuses math with music to maximize student engagement. She posts her math music videos on YouTube and has so far received great praise from students, parents, and teachers alike. Her presentation went through her process and many of her great works in this arena. It was amazing to hear her inspirational story, and I was able to glean a great deal about her methods when creating math music ensembles. Finally, it was especially nice to hear her reaffirm a hunch of mine: math focused audiovisual productions are extremely effective learning vehicles when executed correctly.

The next highly memorable experience was attending a lecture by Mary Kemper, another blogger who runs the website https://agreaterimpact.wordpress.com/. Mrs. Kemper gave a powerful presentation about integrating animation into math education. She made an excellent case for the use of quality video animations to augment comprehension of key concepts. She explained how using basic programs like Keynote and iMotion can provide potent opportunities to develop compelling animations that can drastically improve understanding and retention of all sorts of math concepts.

Finally, the most interesting and interactive of the presentations was given by Ralph Pantozzi, math teacher extraordinaire and recipient of the 2014 Rosenthal Prize for Innovation and Inspiration in Math Teaching. Mr. Pantozzi led a compelling and thought provoking exercise on the probability of flipping of coins in succession. The in-depth explanation of the entire presentation can be found in the podcast episode, but in short, it was an amazing classroom activity that not only engages a class but develops a deep and concrete understanding of probability and how it changes based on action. It was a great deal of fun to say the least, but the best part of the experience is that it gave me some amazing ideas to put into action as my class begins its study of probability.

All in all, it was one of the most useful and enjoyable conferences I have ever attended. I can’t wait until the next one, and I only hope that I too will earn an opportunity to share some of my insights and experiences with the math educators in attendance.

### EP 122: Reflection on my Implementation of Self-Paced Learning

Every teacher must face a tough decision: “do I teach my class at a steady but slow rate to allow for everyone to keep up, or do I plow through the material in order to satisfy the advanced pocket of students while employing a ‘sink or swim’ classroom policy?” Moving slowly might keep the entire class on pace, but doing so risks losing some of the students to boredom. Conversely, while moving rapidly might pacify those eager to learn, it may simultaneously disenfranchise students who need more time and repetition to properly digest new material.

Nowhere in education is this dilemma more pronounced than in mathematics. Some students learn math concepts seamlessly with very little practice needed. Others, while fully capable of deep and thorough comprehension, need a substantial amount of review and repetition before mastery is achieved. While working as both a classroom teacher as well as a private math tutor, I have seen these distinctions amongst students time and again. As a private tutor, I have the luxury of modifying my instruction on an individual basis so that it meshes with each child’s learning style and speed. Teaching a classroom, however, poses a different challenge.

This episode dives into my quest to solve this quandary by way of implementing a self-paced pre-algebra curriculum for my 6th grade class. I discuss the creation and employment of a custom-made online pre-algebra course used in tandem with on-demand individual instruction. In short, the results have been amazing. Not only have my students enjoyed this self-guided journey through pre-algebra, but it has provided freedom and flexibility that has allowed for unforeseen flourishings. Students that have historically experienced struggles in mathematics have suddenly come to life and surpassed many of their classmates. Other highly motivated students have pushed immensely hard and managed to match the progress of the advanced math group. Using this new format has been challenging at times, but the overall benefits for the students have been innumerable.

This episode also discusses the work of Natalie McCutchen, a teacher and self-pacing pioneer who runs a self-paced pre-algebra course at her elementary school in Franklin, Kentucky. Her classroom setup also relies on a confluence of video tutorials and on-demand individualized instruction. One important part of her class is that she reminds her students that working individually is a privilege, and those who use their time inefficiently will be placed into a standard classroom setting to ensure steady progress. To hear all the details, check out the full podcast episode!