This is a professional development blog primarily for teachers in Spring Branch ISD.
Zaccaro does a good job of creating in depth avenues for gt students b/c he makes the learning relevant. He interests students with his introduction scenarios/stories (p.5, 105, 116, 128, 165, 210, 234, 260-261). He shows how to take what you already know (or may have just learned) and take it further, but he also explains how this math is actually relevant in the world and not just in the classroom. His intros also give tribute to many of those fabulous mathematicians who have helped us get where we are today mathematically, but also helps them think "I'm going to be the next big mathematician. I will make a new discovery." His examples and provided questions provide the extra stimulation that the gt kids need.
This book is geared for the upper elementary student as well as the middle school student. The subjects that Zaccaro introduces in this book are not typically found in the elementary classroom. For example, the chapters on Percents, Ration and Proportion, Statistics, Graphing Equations, Acceleration, and Calculus are not usually introduced until later in the math classroom. For a mathematically gifted student to have the opportunity and the joy of being able to discover and work with these concepts, is truly wonderful. When I have presented my gifted students with new, advanced challenges, they absolutely eat it up. This book helps in that effort. Zaccaro also makes the lessons interesting because he presents background information, often in the form of historical notes, and does it in a manner that kids would find interesting and motivating. His use of Albert Einstein throughout the book, not only helps students to pay extra attention to what Einstein has to say, but also makes is alright to be smart, and it's okay to be a little "nerdy." As a society, we don't think twice about recognizing athletic or artistic talent, and giving those students extra opportunities to develop those talents. I just don't see us readily doing the same for the mathematically gifted student. As teachers of gifted students, we all need to be strong advocates for our students, and looking for and providing advanced learning opportunities for them.
The basic structure of the book, which includes interesting, and sometimes historical, introductions of concepts (p.5, 53, 84, 165, 260, 293), "math bites" from Einstein and the Gumbys (p.6, 8, 74, 171, 202, 302), and a plethora of problems which promote higher order thinking (three levels of problems in each chapter and 20 math contests) provide rich, in-depth avenues for all students, including gt students. The introduction of the book states "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." I think that all children should be given that opportunity.
In response to nlopez: I agree with your statement that, when problems are challenging and “real world relevant”, success could engender the thought that “I’m going to be the next big mathematician. I will make a new discovery”. In the words of Ed Zaccaro, “Children who have a special capacity must learn to treasure and value their gift”. It would be exciting to be a guide along the road of discovery for those students.
Zaccaro creates a rich and in-depth avenue for gifted students to learn and experience mathematics by giving students interesting history on math concepts and connecting them to their everyday situations such as on pages 5, 165, 280, 293. Zaccaro is also able to take what the students already know and strengthen and deepen their knowledge through his level of questions.
In response to PKassir: I agree with you in the aspect that the concepts in this book aren't really taught in the younger elementary grades, however I feel that a majority of the concepts can be tied into 5th grade TEKS. I also think the several of the sections can be simplified to meet the younger grade levels of GT students in small groups.
nlopez in response to sluther on 7/25/10 in regards to PKassir- this book is "challenging" for elementary, especially lower elem. As a 4th grade teacher, I did find many opportunities/insights that I will be able to incorporate. Also having experience with 2nd grade, depending on the level of giftedness, I can see some being applied to 2nd and 3rd grade. Definitely easier ti incorporate with 4th on up though.
nlopez in response to tatumt on 7/24/10- My turn to quote you: "It would be exciting to be a guide along the road of discovery for those students." It's these small moments that give us the biggest reward and remind us why we have chosen to be teachers.
Reply to tatumtI'm so glad that you made the statement that Zaccaro's book can be used by children of varying levels. I love presenting kids that do not have the GT label with problems like Zaccaro's. It's a great feeling to be able to introduce challenging problems to them as well. Sometimes, they don't embrace these problems, but when they do, it's so rewarding to see the expression and enthusiasm in their eyes. Thank you for reminding us all that we can present these opportunities to children of many levels.
I think the beauty of this design is that it can be geared to gifted kids of all ages. As a teacher of 7th graders, I felt that a great deal of the material could be used in my classroom. Then I started reading the other posts to see that elementary school teachers like the book and want to use it as well. That is the epitome of a book written to all levels that can challenge students in whatever grade they happen to be labeled by age.
In response to Pkassir:I agree with you that this book is a great resource for all kids and not just the GT ones. My classroom is integrated GT/Pre-AP and I don't have many opportunities to work with just the GT kiddos. However, so many of these questions would be great for all the kids in my classroom to chew on for awhile.
Edward Zaccaro creates rich and in-depth avenues for gifted students to learn and experience mathematics because he makes the content applicable to the real. By sharing the history of the concept and its' inventor, student can see why and how the concept will apply to the real world not just learning it because the teacher said to. The intro to each chapter and the stories that go along with the chapter help make what could be difficult subjects fun to learn. I really like the Einstein boxes that give more insight and reminds you of the important facts to remember.
In response to sluther...I think tat is the key to this whole book for upper elementary. It allows them to experience math they would normally not do until they get older. That is what is so great about this book. Zaccaro really goes in depth at the right level for upper elementary students to be able to really enjoy and understand the concept in this book
The book does a great job of weaving real world applications, historical significance and modeling to create depth. Some examples of this are page 5 and 53, the author uses historical facts to introduce the topic. This creates interest and excitement for the students.
In response to PKassir, You took the words right out of my mouth. Background information, historical notes, etc--They love the new advanced challenges that the book provides.
In response to Sluther, I agree that Zaccaros ability to take what the students already know and strengthen and deepen their knowledge through the high level of questioning is key to creating depth.
Zaccaro provides rich and in depth situations for gifted students to learn math concepts by introducing concepts within stories and relevant situations, as well as have cartoons and thought bubbles throughout the text. For instance, on page 105 he ties the history behind the mathematics when discussing perimeters and circumferences to make the concepts realistic, rather than just learning a theory without the reasoning or real-life example behind it.
In response to NLopez, I agree that Zaccaro provides the extra questions, examples and stimulation that gt kids need.
Zaccaro presents the math concepts in a way that students want to devour it. He hooks them with background knowledge, history, and real world application. Then he describes the steps for solving steps in a rigorous way! He then adds tips to simplify even the most complex concept. Page 108 really breaks the Pythagorean Theorem down after page 105 introduces the facts about perimeter and circumference.
In response to ratliffb on July 28th, I agree with how well the book is written. It is simple enough that anyone could read it to learn the concepts. I think the different leveled problems wouldn't be appropriate for everyone, which is why we differentiate!
Mr. Zaccaro does it logically and somewhat sequentially but he uses the fundamentals with examples and humor and then jumps the student up to application level very quickly.He also provides various levels so that students can progress on their own with any particular type of problem.On page 67 he starts with level 1 problems, then on the next page offers level 2 problems, and then moves on to the Einstein level as he does with each section of new subject matter.He also uses lots of graphics to explain/demonstrate the examples. For example the Venn diagrams on p.30 and the function machines on page 35 alongside the cartoon characters and their speech bubbles.The other thing that is done frequently is in the chapter introductions where he gives background information or examples of application (giving the big idea) before showing the fundamentals. On p.165 he does this with the trig section.
In response to kohlerj, I do agree that the beauty of this book is that it is applicable to various age groups and ability levels. There is such a wealth of problems that it can be tailored to meet class ors tudent needs.
Zaccaro creates rich and in-depth avenues for gifted students to learn and to experience mathematics because he understands their ability to understand concepts quickly and to make connections. He challenges, in a fun way, the children to connect and generalize learned information to new situations. For example: On pg. 110 the children weren’t shown a strategy to make separate polygons out of the overall, original one, but they will discover this through practice and manipulation on their own; On pg. 109 (#3), a radical symbol on a calculator is needed to solve because 20 isn’t a perfect square. The children will either learn to write the answer in its radical form, or they will learn to use that function on a calculator; On pg. 111 the kids have to learn that d = 2r.
The author creates rich and in-depth avenues for gifted students to learn math by making the concepts relevant and challenging. He makes the concepts interesting and fun. He introduces each concept with some history and humor and then gives them different levels to work with either independently or with a group. I like the way the author introduces the Metric System on page 53. He first explains that in the customary system the measurements are based on the human body making it difficult to use. He also explains why the metric system makes more sense and is easier to use.
I agree with Pkassir that alot of the this material is not usually presented in an elementary classroom, and the GT students would love learning something new.I also agree with the fact that many times GT students are not given extra opportunities to develop their academic skills.
I believe the way that he presents information that seems to be so confusing such as Chapt. 19 dealing with Calculus. I never experienced Calculus in high school, but it was in his explanation and connections that made this concept easier for me to understand. I think the kids are really going to be intrigued with all they are learning, as well as searching for ways to apply their knowledge to real life.
In response to PKassir, I agree that much of this content is applicable to 5th grade and I think the history connection is going to give fuel to the fire of getting the kids excited about learning more math/science together.
I think the author did a great job in creating rich and in-depth avenues for GT students. I teach 6th grade pre-ap and after studying this book I feel more confident teaching 8th grade Algebra (which is 9th grade in Academic class) concepts to my GT students. Author makes advanced concepts such as solving simultaneous equations, trigonometry etc. understandable, enjoyable and interesting for GT students. He builds the foundation by helping GT students see the big picture, introduces the concept without repetition and then let them explore much deeper by various levels of challenging questions.
In response to SharonG on July 29th, I agree that the author made calculus easier to understand. The way he present concepts and make connections are very helpful in building stamina needed to tackle advanced concepts such as calculus.
Zaccaro creates rich and in-depth avenues for gifted students in many ways throughout the book such as in chapter 8 about Area. (I picked this chapter because I teach 4th grade and it is one of the most relevant to my grade) In this chapter, Zacarro introduces in a very effective and concise way the area of many objects like rectangles, triangles, circles, and odd figures allowing the student to have a greater depth about the concept of Area. Area is an easy concept to grasp for GT students so this will be a great resource for them instead of doing excess drill and review of just rectangles and odd figures. The real life problems of page 122-127 are great ways to stimulate the brain of the GTstudent.
In response to Kohlerj on July 28, ..Then I started reading the other posts to see that elementary school teachers like the book and want to use it as well. That is the epitome of a book written to all levels that can challenge students in whatever grade they happen to be labeled by age..Indeed, this is a great book to be used to have the gt student experience intellectual frustration in a positive way and enjoy the music of math. After taking the online GT course course with Dr. Karen Rogers about the 10 Options in GT Education-a Synthesis of Research, Im more assured of the treasure of this book because it agrees with several of her statements such as Exposing the GT student to content beyond their grade level in their specific area of talent, and Double or triple-time pacing in Math and Science.
Zaccaro's book is a rich, thought-provoking resource to use with the gifted student. He has accomplished this in many ways by: providing interesting and meaningful background information, discussing famous mathematicians throughout history, predicting questions that might arise and the dialogue that could ensue from those in the "bubbles" throughout the book, giving just enough information on a topic without giving it all or going back to the very basic (he assumes there's some level of understanding), and providing a multitude of differentiated question types and levels to appeal to just about anyone. He also appeals to the GT student by providing information on concepts that aren't a part of our daily curriculum but are, nonetheless, interesting and motivating for the students.
In response to PKassir on 7/22, I agree with you completely about the fact that this book introduces students to concepts that are beyond the scope and sequence at the elementary level, but are still relevant, meaningful, and interesting to the student. Any time that I can tell the students we are learning something that they don't "have" to learn or know yet, I always peak their interest. they love doing things that they think are advanced or, in their words, more "grown-up" math.
Zaccaro creates a rich in depth path for gifted students but getting them started on the basic math concept then drawing them up into the advance thinking. An example is in chapter 17 he starts the students thinking about how to. On page 262 he is checking their understanding and then on 264 he introduces how it works with equations. By page 269 he has the students understanding the slope of the line and on page 279 the students are writing an equation and drawing the graph of an accelerating vehicle which leads the student in to chapter 18.