## Tuesday, July 20, 2010

### Session 3 - Question 3

The cover of this book has the following quote, “Math is often taught as all scales and no music. This book contains the music!”. After reading this book does the statement regarding the mathematical music found within the pages ring true for you? Support your response with page numbers. Would it ring true for primary gifted students? Why or Why not?

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I love that quote because I think it illustrates what’s wrong with most all of our educational practices today. There is too much rote practice of “scales” (drill and kill) and not enough opportunity for the joyful performance of “music” (skills) through authentic and self-directed activities. I believe Zaccaro’s book contains the “music” because it is designed in a way that a student can pick and choose problems that are at their level and themed to meet their personal interests. There’s something for everyone in this book as the problem complexities (Level 1 to Einstein level), characters (boys, girls, disabled, various races, animals, etc.), and topics are diverse in nature. If you’re into animals (page 204, #5), sports (page 262, #5), cooking (all of Chapter 6), music (page 34, #3 and 5), transportation (page 178, #4 and 5), etc., there’s a problem for you in this book that will allow you to make a connection. The other feature of this book that I think primary gifted students will be attracted to is that each of the problems requires different skills and strategies to solve – it’s not the same basic computations over and over again as many traditional math books contain. Overall, I think this book will be a valuable addition to our collection of PGP (musical) instruments.

ReplyDeleteZaccaro’s book definitely contains the mathematical music. It plays like an orchestra with a plethora of instrumental math concepts hidden inside meaningful real-life situational problems using advanced vocabulary, Einstein (!) as a narrator throughout the book, and clever/humorous visuals. Primary gifted students will love the interesting chapter names; higher level science and math vocabulary (such as amoebas, p. 275, and radicals and square roots, p.233); humorous text and illustrations (i.e., the princely contest that was a royal pain, p. 245) that subtly introduce a complex concept; the opportunity to use calculators as a tool to solve more difficult problems (p. 66); problems with multiple paths to the answer (magic of multiplying chapter, p. 60); magical changing machines to introduce complex concepts and formulas (p. 192, 234); a translation chart to understand parts of a whole (p. 276); higher-level thinking questions giving students an opportunity to extend what they know even further; and the opportunity to discuss and justify students’ answers (Chapter 25, pp. 256-266).

ReplyDeleteIn response to MillieH:

ReplyDeleteI like your characterization of Zaccaro’s lessons as connecting on some level with all students through choice, character depictions, and diverse topics – kind of a Dewey “something for everyone” offering. The book, when combined with the creative blog suggestions for application in the PGP classroom, will be a fabulous resource as we address our math identified PGP students’ needs.

After reading this book I was very curious about "who" Edward Zaccaro is so I Googled him. Oddly, he maintains a very low internet profile. He doesn't have a website or a blog and he's not on Facebook. About only way to get in touch with him is via his publisher.

ReplyDeleteHe is an ex-teacher who started writing when he couldn't find math materials that excited his students. He is also the darling of the Homeschoolers. State Home School Conference after Conference mentioned having him as a speaker or giving a workshop.

That makes sense to me - the book really is perfect for a homes school setting. If you worked through the entire book with your child said child would have a firm foundation in math.

It's also ideal for differentiating (I'm doing the other book study too so I have differentiation on the brain) - if the child can do a couple of level 1 problems, then them let do some level 2 and if they do those move on the genius level.

Actually a classroom teacher could use this book as a quick way to "test" a new student's math knowledge and ability.

Did I answer the question or did I ramble? Music - yes, he shows that math is more than pages of problems and it is an integral part of everyday life. Teachers spend much time talking about the joy of reading but they rarely muse on the joy of math!

To Millie H: Your statement, "I love that quote because I think it illustrates what’s wrong with most all of our educational practices today. There is too much rote practice of “scales” (drill and kill)" resonates with me. For our population north of the freeway we drill and kill because we have to, so they will make it through the TAKS. Our teachers have to work SOOOO hard to get our kids prepared. There is just so little time to have any fun or enjoyment with them along the way. That is one of the things that makes this such a good little math text. It covers a lot of those TAKS bases AND most kids should enjoy learning math in this manner

ReplyDeleteOf Life, Education ... thank you for finding out that information about the author. I find it kind of sad that so often the innovators in education are "ex" teachers. Too bad they can't accomplish all those innovations and creative methods while they are actively teaching. Or maybe they are getting their materials together and just don't have a chance to consolidate and present it until they leave the school system ...

ReplyDeleteSession3-Question 3

ReplyDeleteDoes this book contain “mathematical music”? Yes, every page, from cover to cover, orchestrates this fact. The book is a full orchestra playing a resounding symphony: Kid-Friendly Math in A+!

I give Zaccaro’s music a standing ovation. Would it ring true for primary gifted students? I answer a resounding “yes” for all elementary students. Children have an innate “natural rhythm”! Zaccaro not only “tapped” into the children’s natural assets…he “main-lined” into it.

Too much math is taught to children as if they are all tone deaf! Kudos for Zaccaro’s musical math abilities.

As students learn math from this book, the quote about scales and music would ring true with them if they were even aware of it, or understood the implications if they were aware of it. Part of the magic of this book is that most students would probably be unaware of the “music” they were experiencing while working the problems. They would be experiencing the “music” while learning. The music would take on the form of their enjoyment, challenge and satisfaction. As for me, that quote certainly rings true and I was immediately reminded again of my third grade experience in learning my multiplication facts. I cringe today when I sit down with students and watch them draw and write out that wretched chart they always do with all the math facts: the chart that goes down and across with all the numbers, and then they fill in the boxes with the quotients. It takes them a long, long time. A lot of our students still have to use their fingers to figure out the quotients. No fun, and time-consuming, when you are multiplying nine by nine. My third grade experience was way ahead of its time. We literally used music to learn our facts. We didn’t even know the multiplication facts were coming, and after about a month, we knew them. We watched with interest as our teacher pulled out a record, put it on the player, and started playing these sing-song little chants that started out with one by one, and ended up with nine by nine. I can still sing some of them. We did this every day until the lights came on and those math facts were planted in our heads forever. It was not effortless learning, but it felt like it. Even though this book does not literally use music, it takes learning math to the same level of interest and engagement. Just looking at the chapter titles engages me: Chapter 22, page 221, using algebra; chapter 23, page 233, radical and squaring machines (I am a bit fuzzy on radicals so I will make sure to go into this chapter and look at and work some of the problems). Chapter 26, page 267: Why DO we need decimals? They are not just another way for the teacher to torment students. When my daughter was in elementary school, I tried to teach her a little algebra, and was met with a brick wall. Wish I had had something like this.

ReplyDeleteKHarrell - loved the quote on the front - I think it describes the book well. I wish something like this had existed when I was trying to learn math. It may have made it easier as he just talks through the concepts. Again, the dedication page and table of contents would intice a GT student to step inside and try the activities. It's hard to give an exact page number as all of the chapters engage you in the activities. The use of cartoons and speech bubbles bring the students in to an active part of learning. In chapter 9 and chapter 19 he uses "machines" to help teach the concept. Students love the idea of machines. The title of chapter 12 is the Magic of Math - I'm sure that students of all ages will want to do that chapter.

ReplyDeleteIn response to Millie- Love your thought - There is too much rote practice of “scales” (drill and kill) and not enough opportunity for the joyful performance of “music” (skills) through authentic and self-directed activities. I so agree with everything you stated...Math has become the dreaded worksheet...I'm so glad my school is looking into Singapore math (where you draw out your math problems) I think we need to look at math, rather than just do math.

In response to life... Thank you for doing the research on the author...I can see how this book would be dynamite for homeschoolers (I'll have to share with my friends who have decided to homeschool!). I can also see this being used by a parent who has a child that doesn't enjoy math (me)...it might bring a positive light to the subject. My daughter is home for the summer and we played around with the book together...she usually finished the problems before me...she has a similar fear of math as I do...I wish I had been a student in Zaccaro's class...

As others have already stated, I really wish this had been available for my math teachers in those formative years. My attitude towards math might be different than it is today. The entire book makes sense and I never would have thought I’d say that about a math book! The characters in the explanations are fun and the explanations are easy to understand. The book talks directly to the kids and doesn’t give a script for the teacher to follow, as so many of our math books have done in the past. The illustrations are cute, but not in a distracting way. It just makes it all easy! I appreciate that each chapter is a complete unit. There are few that need to be done in order, such as chapters 21 and 22 about algebra. But even those could be taught at different times. I like that I could choose to do measurement, for example, and pull in all the chapters that deal with measurement. I could even toss in chapter 6 on fractions. It makes sense to teach measurement in a series. For example, I could use chapter 10 for basic measurement, then go to chapter 18 for weight, then move to chapter 24 for circumference and area. It is also incredibly easy to differentiate using this book, as it is already broken down into levels for you. I am anxious to share this with my math SIS and see what she thinks!

ReplyDeleteIn response to MillieH - I agree with your statement about using different strategies and skills for each problem. I think our kids get bored with the same old thing all the time. This is definitely different!

ReplyDeleteIn response to FMoore - I, too, appreciate the introduction of a calculator as a tool. It seems like we don't do that enough. Kids need to know that it's okay to have and use a calculator to figure out the answer sometimes.

In response to Viking, I like your observation that this book allows students to be unaware of the “music” while solving the problems. I think they will be so engrossed by the engaging format of the problems that it is like “unconscious delight” – they won’t realize that actual instruction and learning is taking place! That’s how learning should be – not rote memorization of formulas and math facts like was the case when I learned math.

ReplyDeleteFolks, I am hearing the music here. As I have stated previously, math was always a struggle for me, and even as a 5th grade teacher, I struggled to wrap my brain completely around the dark shadows and corners of teaching mathematical concepts. However, my experiences with this book have been wonderful. Here's a strange thing... I was re-arranging my library office last month and I opened a box of books that I moved from my classroom to the library office when I became a Librarian and never have unpacked (yes, 6 years ago). There in that box was an earlier copy of this book that a parent of a gifted child gave me when I taught 1st grade several years ago. She thought it was a good way for me to work with her extremely brilliant child. The amazing thing is that I could tell that the book had been used... there were markings all over it that showed me that this child and I had worked together on many of the chapters. However, I didn't even remember seeing or using this book before we started our book study. In thinking more about it, I now remember how much my student *loved* working with this type of activity instead of in the traditional 1st grade Math Workshop that we used to teach. I can't wait to use this with my very active group of PGP boys this year. I think it'll be a perfect mix of creativity, movement, activity, action, and expanded learning. In addition, as I can differentiate with it based on grade level and ability level, it's perfect for a multi-age, multi-gift, multi-faceted group of students! Becky Lee

ReplyDeleteIn response to MScales... I love your idea of jumping around to related concepts instead of working this book from "front to back"... I'm not completely sure what everyone else wants to do, but I think it's a perfect book to use alongside the Math 9 week plans from our teachers. I'd love to relate our PGP math study back to what is going on concurrently in the classroom. It would be a perfect piggyback!

ReplyDeleteThat statement on the front cover caught my attention when I first received the book. And yes, it does ring true for me, and I think it will for gifted students as well.

ReplyDeleteRather than drill students with dozens of the same kind of math problem, this book challenges students to do a few problems at different levels of difficulty, rising to Einstein Level! I can see students being competetive about what level problem they have completed. And the problems are fun and mostly related to real life situations. It also encourages students to perform mental math, often missing in the mainstream classroom.

Yes, I think gifted students will hear the music when they can work with this book.

In response to melscales, I agree that the levels make it easy to differentiate with this book. I will have a first grader next year (probably my only PGP student), and think we'll start with level one & work our way up. Language is an issue, so I'm not sure how it will work out, but the levels help. You also bring up a good point about sharing this text with the Math SIS. I plan to do that as well.

ReplyDeleteHead Squirrel,

ReplyDeleteHow funny that you've already had an encounter with this book and with the very kind of student it was intended for!

Viking, I fear the author had to become an "ex teacher" to write the book. While he was a teacher he was most likely held to a "script" or at least had to be sure he was on page 36 on the same day that every other teacher in the district was on page 36.

This is my philosophy for the teaching of literature. Combining the aesthetic (romance) with the efferent (mechanics) makes a good reader. I have never really thought about it for math. But it makes perfect sense. If you can bring out the beauty of any subject while teaching the mechanics you are using both sides of the brain. This book brings out the beauty or aesthetically pleasing side of math in that it uses fun illustrations, witty situational problems, and a format of challenge (crescendo) for the GT student. This takes place while at the same time, they are learning the factual nature of the material. Chapter 9 is a perfect example of this. The percent machine is a fun, creative idea to let students pretend they are actually using technology to answer the problems, when actually they, themselves are the CPU being utilized for the answers. The bubble dialogue also is aesthetically pleasing and orchestrates a social aspect to the problems.

ReplyDeleteI agree with Head Squirrel, that differentiation is the key with GT students. This book allows for just this type of activities. It was confirming to read what Anonymous said about using it with her daughter this summer. This confirms my thinking that the kids will take off with the concepts with little instructional needs from me. I can just provide the challenge and watch them fly with this fun, stimulating math book!

ReplyDeleteTo me, this quote meant a lot because I can't read music. Listen to music? I get it...the emotion, the lyrics, the composer's/songwriter's tone etc.

ReplyDeleteMath texts might be viewed by some this same way. It's just chaos. But learning a concept by applying it to a real life problem might make the math come alive! One example I liked was on page 79 with the rabbit. The illustration shows and encourages the students how to continue working the problem through drawing. Page 63 was another illustration used with multiplying. They could relate the illustration to the speech bubble because of its clear placement.

Would it ring true for primary gifted students?For some, but it would be a challenge for others. Again, I have a small PGP group. One of my students wanted to quit last year because he could not read the material. We put most everything on the MAC and turned on the text-to-speech feature. Honestly, I think the book on the surface would still be all scales. I'd have to think differently to make it into music...a lot of oral reading and partnering.

Melscales and FMoore, I agree with you about the calculator as a tool. Because I can remember my dad purchasing our first calculator, we thought it was the holy grail. Hmmm...we've come a long way. But we've got to get these new devices to the point of being viewed as tools as well. Sometime useful and but not always.

Of Live, Education...thank you so much for the doing the research on Zaccaro. I applaud him on his low-Internet profile. I spent a lot of time with some "techie" friends this summer who make unbelievable $$$$!!! earnings from this technological world. ALL of them maintain low-Internet profiles are very protective of their children and the exposure of their children to hardware, software, Internet etc. They also all homeschool. But that's for another conversation...just my recent experience/connection to our author.

I have not looked ahead at the questions and the whole time, I have looked and pondered about the word “MUSIC”. Maybe the different levels are different kinds of music. I have found myself finding the rhythm as I go through the different levels. There are definitely levels I prefer to TUNE into. But each level links together. There is a NOTE you learned in a past chapter/level that prepares you for a more COMPLEX “piece of music”. For something to be MUSIC TO YOUR EARS, it has to be something you like, enjoy and understand. Ed knows how to RELATE to the student and catches the interest of the student and keeps the student wanting more. The Drill and Kill is like a broken record and we all know that can just go out the window. Think, talk, challenge, explore, discover, laugh make beautiful music.

ReplyDeleteOur PGP students would welcome this “music” class. Ed shows and explains many materials and strategies that can be used to solve problems. Example Pages 88,133, 276 These are like the INSTRUMENTS that are needed to make the music. Put all the notes together and make your own music.

We need to address our students that have been identified in Math and Science. This is th emusic that htey can dance to. In this book taht can find the song/music that they can play and enjoy. They can even learn to sing it in another language, ALGEBRA.

ReplyDelete