## Tuesday, July 20, 2010

### Session 4 - Question 1

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 gifted students? Why or Why not?

Subscribe to:
Post Comments (Atom)

I do agree with the quote on the front cover. Just the introduction alone, helped with seeing that. In the first paragraph of the intro (page 1), it says that "when children first see the wonders of math and science, it is as if they stepped into a room that they didn't know existed." We want all children to feel this wonder when they enter our room for whatever subject it is we are teaching, but even more so for our gifted kids. Many of them, unfortunately, walk into classrooms expecting to be bored or to not learn something that they don't already know. So to give them the music, we must wow them. Even if they already know something, those are the scales. We give them the music when we build on what they know, when we surprise them with what their knowledge of something can actually do, when we push them to do more than what they thought was the limit on a concept.

ReplyDeleteThe analogy that is used in the Introduction of the book is wonderful. "If musicians were not given the opportunity to perform or play music that stirred their hearts, it is unlikely that they would develop their passion for their field." I agree that in mathematics, this is what often happens. For this reason, this book is definitely a tool that helps mathematically gifted children get excited, and develop their "passion." I think that math is one subject where this is a lot harder to do, often because of the spiral-like nature of the way mathematics is taught in our district. Many concepts are often revisited year after year, and for the mathematically gifted child, it does seem like new opportunities for learning don't come as often as they need them. This book, along with other Zaccaro books, help the teacher of the mathematically gifted student with new opportunities for math challenges.

ReplyDeleteWhile "scales" are an important part of learning any subject, including math, it is important to provide useful information (Einstein, p.8, 9, 38, 166, 222, 270, 303), probing questions (Gumbys, p.11, 39, 129, 166, 213, 268, 298), and challenging problems (p.47-52, 133-137, 179-189, 241-246, 277-279, 305-306)to promote mathematical growth. When students (including gt students) think independently and creatively, the "music" comes.

ReplyDeleteIn response to PKassir: I agree with your statement, "I think that math is one subject where this (developing their "passion") is a lot harder to do." But it is rewarding to see the light in a student's eyes when they have solved a problem in a unique or interesting way.

ReplyDeleteAbsolutely!! This book contains a range of problems that meet every scale in math. The setup of the book in chapters starting with the possible teaching point and ending with differentiated questions for that concept allows for teaching and thinking to be met in the entire range of the concept. This would also be true for gifted students in which we as educators will teach the concept and access students on their level with the extension questions. This book allows us to meet the needs of our students and let their creative GTness be met.

ReplyDeleteIn response to tatumt who responsed to PKassir: I agree it is so rewarding to see the light in a studnet's eyes when they have solved a porblem in a unique or interesting way. I feel in order to see that light we need to make math more meaningful. Not just teaching the concept, but connecting on thier prior knowledge and expand on what they already know...while allowing for them to investigate on their own.

ReplyDeletenlopez in response to PKassir on 7/22/10- I have to quote you: "I think that math is one subject where this is a lot harder to do, often because of the spiral-like nature of the way mathematics is taught in our district. Many concepts are often revisited year after year, and for the mathematically gifted child, it does seem like new opportunities for learning don't come as often as they need them." Very well said! I definitely agree that with the the spiral effect we have, there are not as many chances as we would like to introduce NEW concepts, so we must find every opportunity we can to find those windows that will allow us to introduce something new for them as well as stir their passion for learning.

ReplyDeletenlopez in response to sluther on 7/25/10- Yes, I can't wait to use this book as a guide and resourec this year for my entire class. Very exciting.

ReplyDeleteResponse to NLopez,

ReplyDeleteThank you for your reply. This book enables teachers to not only introduce new concepts to students, but also to go more in depth with other concepts that students may have already been introduced. I think it is always a balancing act, on deciding whether to do breadth and/or depth. I've always thought that a combination of these two go hand-in-hand. You do want to go deeper on some topics, but you also want to keep the interest level up by introducing new concepts. After all, there are certain things in math that you can only go so deep.

I would agree with the author's comment for the most part. The book does a great job of giving the overall picture of a topic without getting bogged down in the individual skills. It seems that we often teach skills in isolation without really teaching the entire scope of the idea to the student. I like how some of the ideas are layered throughout the book to make sure that students can apply the knowledge they have learned. I do wish that the author did have a little more focus on a few of the "scales" though. For example, in his section on coordinate graphing, the author gives one example of a point in the first quadrant. From there, the students are then asked to practice graphing points with negative numbers without any examples to use as a reference. Even gifted kids need a little help with the "scales" sometimes so that they can see the bigger picture.

ReplyDeleteIn response to pkassir:

ReplyDeleteI agree that there is a strong balancing act that must occur between depth and breadth. Our curriculum in PreAP calls for a new topic almost daily in order to "fit" everything in. I think this is something we as a district need to focus on--taking a step back and looking at the bigger picture of what kids need to know. Unfortunately, there is so much pressure to "cover" each of the TEKS that skills are presented in isolation without much connections to the bigger picture.

I absolutely agree with the quote at the beginning. Math can be very musical if taught in a way that catch hook the students and make them want more. All the pages within this book capture the idea that math is more than scales, especially with the illustrations and history given about the different concepts. GT students would find this book very exciting and a fun challenge. I am energized and ready to get my GT students this coming year and let them have a go with this book.

ReplyDeleteYes, the statement does ring true! The book gives many ideas for engaging students and tapping into their creativity and imagination (the proportionexample pg 157). The challenging problems and modeling will grab the students interest and encourage them to work collaboratively.

ReplyDeleteIn response to PKassir, I agree that the revisiting, each year of the concepts, is frustrating for our GT kids. While effective for the average learner, spiraling is not usually needed for the GT learner. This book will be great in workstations for those kids who do not need the same reinforcement as the average learner.

ReplyDeleteIn response to Nlopez, You are so right about the prior knowledge being the scales--we have to extend that knowledge to create the music.

ReplyDeleteI completely agree with the quote at the beginning of the book. On page 84, the way in which Zaccaro describes fractions really brings the math to life. As an elementary teacher the latter chapters didn't pertain to what I teach, but this one really did. I think my gifted students would also enjoy the way Zaccaro presents the concepts because he ties them to real life situations so there is a reason to learn the concepts as you will have opportunities to apply them in life.

ReplyDeleteIn response to PKassir: you hit the nail on the head with your response! I really enjoyed it.

ReplyDeleteThis comment has been removed by the author.

ReplyDeleteIn response to ReneeR... I agree with you how relevent this book is. I can't wait to collaborate with you and CynthiaM and use it this year!

ReplyDeleteI absolutely agree with that statement. I can totally see a student who is musically gifted miserably sitting in a music class learning solfage and where the notes are on a staff when they have already mastered teaching themselves how to play Beethoven on the violin or piano. Gifted students often like to teach themselves challenging material. This book provides step by step examples to teach the challenging math concepts, and then lets them loose with very rigorous problems to put the new knowledge to use. Chapter 23- Probability- is a good example of information that is beyond our scope and sequence, but is very interesting, rigorous, and challenging for the gifted student to learn and apply.

ReplyDeleteI agree with the quote about math being like scales if we teach only the fundamentals of math:the how to do it, follow these models, and then practice, practice, practice. This just inspires math to be boring and for students to hate it. The fundamentals are essential to do the math work just as knowing the notes and the scales but the music is in the application of the fundamentals and the inquiry and perseverance to work on a math problem and that comes from working worthwhile problems. Examples of this include the one on p.189 to determine the height of a tree or on p.291 when working on the acceleration of a car.

ReplyDeleteThe beauty of using music as a comparison is that if you combine the instruments to create a piece of music then this also helps everyone

respect the other mathematicians and the sharing of how they solved the problems, or working together to arrive at an answer, etc.

I think this would especially "ring" true for mathematically gifted students as they would be truly bored with just scales and would give up or hate math more quickly.

In response to tatumt, I have to agree that the music will come when students think independently and creatively both. That was succinct but very well worded.

ReplyDeleteThe quote does ring true to me for the same reasons I feel it will ring true for my gifted students. It makes math fun! Cartoon characters found throughout the text question, answer, and discuss the content throughout (pgs. 6-304, give or take). It’s exciting because cool facts found at the beginning, and throughout, each chapter (such as about Eratosthenes on pg. 5) make the content interesting. And, it’s challenging because the children are required to make many mathematical connections, to independently discover many rules. For example, on pgs. 84-86 Zaccaro doesn’t explain that when adding/subtracting fractions, one must only find the sum/difference of the numerators, not the denominators. He does include examples to derive this, but he does not explicitly state this important fact. Finally, the children are also given the option to greater challenge themselves by choosing higher levels.

ReplyDeleteIn response to PKassir and Tatumt:

ReplyDeleteWell spoken, I fully agree! This is an EXCELLENT tool for our gifted children, to really keep them excited about and challenged in mathematics, to nurture and grow their passion. I also agree that these will be phenomenal in stations.

I agree with the author's statement. GT students are often very bored with just learning the math basics.Many times they never get to apply what they learn to a real life situation. The author does a great job of using historical facts to get the students excited about learning the concept.On page 234-235 he explains how Isaac Newton's discoveries are used to find distance, speed, and time. Gifted students love to be challenged and learning more than just a basic formula will inspire them to be more creative and come up with different ways to solve a problem.

ReplyDeleteIn response to ratliffb- I also felt energized by this book. The students will find the problems fun and exciting.I can't wait to use this book with my class!

ReplyDeleteI agree with the quote on the front cover as well. I especially like the author's statement in the introduction that states" Young students must experience intellectual frustration in a positive way. They must learn that challenge and effort are a part of learning and a part of life." I truly believe that teachers needs to take more a role in promoting creative thinking and risk taking within the classroom, and extend the thinking of their students instead of want to " tell" students the answers or give them so much support that both get frustrated. I think that this book really allows the students to tap into their knowledge base and truly practice their problem-solving strategies. I enjoy watching them learn from their frustrating moment because when they solve it on their own- they are thrilled and hooked into the learning.

ReplyDeleteI agree with ndean's comment about our students finding these problems to be challenging yet fun to work. I think that they will try to come up with many different ways to solve them. I want to watch and listen to their thinking- I think it is going to be interesting!

ReplyDeleteI think when the author says "Math is often taught as all scales and no music." he refers to the old school math teaching where the concepts are taught disconnected from each other and real life, then followed by drill practice. As a consequence, students struggle in making connections, and applying their knowledge for problem solving. In that sense, this book differs from the practice above. GT students are given the big picture and connection to real life from the very first paragraph of each chapter. Author uses facts from history, astronomy, science etc. and then leads them to a deeper understanding using steep steps. For example in Chapter 18, he introduces the concept of acceleration with G-forces which I think is a great hook for GT students. Then in the next chapter “Calculus”, he connects graphing equations (chapter 17), acceleration (chapter 18). The sequence of chapters makes learning more meaningful and help GT students hear the “music”, the harmony, in math.

ReplyDeleteIn response to Kohlerj on July 28th, I agree when you said "Even gifted kids need a little help with the "scales" sometimes so that they can see the bigger picture" There are some critical parts that are left unexplored throughout the book. I think author wanted students to discover some of these concepts on their own and experience "intellectual frustration" in a safe environment.

ReplyDeleteAbsolutely, I agree that this book contains the music to teach math to GT students. The interesting introduction stories about the concepts, the funny cartoon characters, the great specific explanations of Einstein, and the variety of the problems are all demonstrations of the music students want to hear during math. I just finished an online GT course with Dr. Karen Rogers about The 10 Options in GT Education-a Synthesis of Research, in where she conveys that GT students want to sense that they have learned something new every day and for this as Zaccaro says we must teach the music of the concept. This book agrees with the options that Dr. Rogers states such as Daily Challenge in Talent Area(s); Opportunity to work independently and be unique; Double or triple-time pacing in Math & Science; Elimination of Excess Drill and Review; Exposure to Content beyond grade level in specific area of talent.

ReplyDeleteIn response to RCampana on July 29th, I think the five options you listed in the last sentence of your response summarizes what Zaccaro accomplished in this book very well. Thank you for sharing your learning experience with Dr. Rogers and how it coincides with Zaccaro's purpose.

ReplyDeleteIn response to Sluther on July 25.. about connecting on their prior knowledge and expand on what they already know...while allowing for them to investigate on their own. I agree with your statement, and this book is a great resource that could be given to students with the responses while we are working with the strugglers. The problems of this book give a rigorous challenge to the gt student.

ReplyDeleteI definitely agree with the quote and the fact that this book provides us with a great resource for helping our students, gifted as well as others, take the scales and create music with them. I love the differentiation that is provided so that even strong math students that are perhaps not identified as GT can experiment and be creative with their math, thereby experiencing the more musical side of their learning! As I've stated previously in the blog, I've used this book in the past as part of the Navigators curriculum, only focusing only on the specific parts referred to in the curriculum, but now that I've studied the whole book I look forward to incorporating other parts of it into my math classroom. I definitely see the GT kids eating it up, but I also believe many of my other students will enjoy the challenge as well.

ReplyDeleteIn response to PKassir on 7/22, I agree with you completely about the spiral nature of our curriculum. Not only is it repetitive from year to year, but even within a grade level, from nine weeks to nine weeks. I know the goal of the district is for mastery and then maintenance of a concept, but sometimes it can seem redundant, especially for our gifted learners.

ReplyDeleteI do agree because when you teach scales to a student learning music it is boring and repetitive Students are required to play the same notes over and over for and hour a day but to a beginner it is just noise. Math at time is taught the same way only a small piece of what they need to know then every problem relates to the process. Students are rarely taught to understand the big picture of what they are learning or how it builds on to other math they know By the time they get to p 280 where they are using acceleration they have built on every other kind of math learned in the book and they can hear their math sing making music and not just solving problems. The book makes math fun.

ReplyDeleteI agree with Sharon G. post all summer long in every training I attended I kept hearing that “" Young students must experience intellectual frustration in a positive way” or that helping students learn to perceiver will guarantee success in the future.

ReplyDelete