## Sunday, June 6, 2010

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## Sunday, June 6, 2010

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This is a professional development blog primarily for teachers in Spring Branch ISD.

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I hope I am addressing this question correctly. The strategy being used is what we should all do- model and then have students apply/practice. We have to first give the tools before we can expect any student to use them. Yes, sometimes a student will be so gifted that they just know an answer, but that means nothing if they don’t understand why the answer is what it is. Before giving the students a particular question, we should make sure that they have the background needed for it to help alleviate any possible frustration. I use this method daily in my classroom. I will also address ch. 2: Problem Solving (patterns, sequences and function machines). Functions and patterns are important in 4th grade. Students usually understand them easily enough to find the next number. It’s when the 100th or 500th… is needed that students have a more difficult time finding the solution. I felt this part of the chapter gave me more insight to teach this concept more effectively to my class. Page 33-35 is an example of this.

ReplyDeleteI've used Ed Zaccaro's books in my gifted classroom before. One of the reasons I joined this book group study is to hear how other teachers would use this in the classroom. I take one chapter at a time, and I do whole group instruction on the beginning material. For example on Chapter 3, Algebra, I would do an introductory lesson from pages 37-45. I would use the illustrations, and the speech bubbles to guide students in understanding what is going on. I would scan all these pages into a flipchart, and then use the tools of the ACTIVboard to model for students. Then I would begin with the Level 1 problems, letting students solve anyway they want. Once we have mastered Level 1 problems, I then let them loose with the rest of the problems, letting them challenge themselves, and see how many levels they can go to. Some students immediately go to the Expert level problems, and are successful. I let them have several days to work on the various levels, and then we come together and use the ACTIVBoard to share and have students talk about how they solved the problems, and how they came up with the answers. This part is a lot of fun, because this is where one can see which kids are mathematically gifted, and solving problems comes naturally for them. Since I work with a classroom of all gifted learners, these types of problems are differentiated for the varying levels of giftedness in my students. I really like Ed Zaccaro's books. They are a great tool for teachers of GT students.

ReplyDeleteResponse to NLopez from PKassir:

ReplyDeleteAnytime I teach number patterns and functions to my gifted fifth graders, I strongly encourage the use of tables when they are first starting. The use of tables in demonstrating number patterns, and functions help them to visualize what is going on more easily. Once students have had practice using tables, then I allow them to do these in their head, and not have to show work. Of course the students love it when I tell them they do not have to show their work.

Response to PKassir from NLopez for comment posted on 6/7/10, 9:44 PM: I definitely like your ideas and I may copy you:). I also feel this will be a good opportunity to bring menues into math workshop. Since the questions/problems are leveled already, this would make it easier to create a menu where students have to accumulate a certain number of points and based on the level of questions they attempt, they have to answer more or less from a certain level. Then there's the tic-tac-toe model too where they'd have less to choose from. Thanks for the ideas!!

ReplyDeleteResponse to NLopez.

ReplyDeleteThe menus certainly lend themselves to the Ed Zaccaro problems. I think that copying the problems, and cutting them out onto a Tic-Tac-Toe Pattern would be quite feasible. It would be large, but then one could laminate it, and re-use it with other groups of students. I can also see kids playing against each other using their TTT pattern. I like what you said about menus being incorporated into the math workshop approach. Glad you're onboard. By the way, where do you teach?

The strategy that is being used is the strategy that all teachers should apply in their classroom in any instructional models—show not tell—question the answers—explore on. It allows teachers to show and not just tell. The illustrations model what some of our children may say if questioned and use their gifted ability so it sets the teacher up for success in being prepared for what the small group may lead to. The illustrations also allow for teachers to engage our children in mathematical communication which is crucial to deep understand of math. I also enjoy the factual information given by Einstein about the content or vocabulary such as on page 35. I can see Einstein posted all over my room!!

ReplyDeleteIn response to both NLopez and PKassir—Learning menus are a wonderful way to differentiate instruction for all children. I use them quite often and it allows for my children to have the choice to learn at their level. Laurie Wesital (not sure if I’m spelling it correctly) has written several books on using menus to teach Science, Math, and Language Arts you may want to check out. You can use her method on points and choices as you place these level of questions in them.

ReplyDeleteHis strategy of instruction includes providing visuals, explicit demonstrations, and offering interesting facts embedded in rich problems. As Zaccaro stated in his introduction, it is important to give students a chance to see how math is used in algebra, trig, and physics. Visualizing how the formula for circumference is important in answering in a real life question about space exploration or a run around a track demonstrates the relevance and power of mathematics. The interesting facts are a great way to hook GT students who absolutely intrigued by a knowing how to name a number with 57 zeros.

ReplyDeletePG 27-29: Teaching problem solving strategies is paramount for any math student, gifted or not. Sometimes, teachers do not realize that gifted students need direct instruction in problem solving too. The strategies Zaccaro lists on pg 20 are a great start. The names he gives the strategies are similar to the ones we teach in SBISD, although he has given them different names. For example, making a problem simpler is called “think 1” in the book. Using a Venn diagram is not a strategy usually taught in elementary grades but would be a great way to extend for GT students.

Each chapter contains one topic (Astronomy, Problem Solving, Algebra, Metric, Decimals) and includes interesting tidbits of information given by cute little cookie men (page 7, 21, 39, 59, 73), a plethora of examples/models (page 12, 23, 43, 55, 74) and of course the wisdom of Albert Einstein (page 9, 27, 41, 55).

ReplyDeleteI plan to use material and problems (Level 1,2, and Einstein Level) next year for all my students while studying topics in the Pre-AP curriculum.

ReplyDeleteI teach math by modeling, modeling with students, guided practice, and then independent practice. The book seems to follow this same process, which makes it easy to follow and gives me better ideas at how to teach some concepts. An example is the using the Venn Diagram on page. 30. The problem used with the Venn Diagram comes along in 5th grade math problem solving. It seems students really struggle with trying to solve it. GT kids just solve it and don't think twice about it. That is where the Gt students can sometimes solve these types of problems, but can't really explain how they got the answer. I am big on being able to explain how you got to your answer. I really liked Chapter 2: Problem Solving. Maybe that is b/c the problems were not just regular boring word problems, but they actually made you think about the problem and how you have to go about solving for it.

ReplyDeleteI find that algebra seems to be really confusing for 5th graders b/c of the use of variables. However once they get the hang of it they seems to really enjoy doing algebra. I thought the problems in this chapter were really challenging and fun to solve for Gt students to play with and solve. GT students seems to get this concept fairly quickly, so extending their thinking further using these problems would be great.

In response to tatumt... I agree that these methods could be used with all students not just GT students. My students generally all need to be challenged not just the GT students. I am excited to use some of these strategies with my class next year, especially the Venn Diagram.

ReplyDeleteSession 1- Question 2

ReplyDeleteI think author demonstrate scaffolding strategy where desired learning strategy or task is modeled, then responsibility is shifted to the students gradually. For example in Chapter 3, steps of solving algebraic equations are given with each type of equation, solutions are modeled, and then independent skill practice problems are provided before word problems. There is a gradual increase in complexity level of problems. I also liked how the author modeled thinking process using “think out loud” strategy. On page 40 characters are modeling how to convert a word problem to an algebraic equation perfectly by thinking out loud.

I think all teachers use many of the strategies mentioned in these chapters. I especially like the examples in Chapter 3 where each step is maped out and explained. I do a lot of modeling and think alouds in my problem solving lessons. I also like to use graphic organizers to help kids focus on the important information. I am interesting in trying these approaches more when working with decimals like in Chapter 5. I think if students had a more systematic approach to comparing decimals- they wouldn't be so tricky for them.

ReplyDeleteI like PKassir and NLopez chat about how to make math fun using the Tic Tac Toe method. You can even branch out to a much wider grid and play connect 4 with problem-solving problems. I have used this technique and the kids love it.I let them "capture" someone else's square if problem isn't solved correctly, and it makes the students improve their checking of work. I believe that if Math is fun- kids will take risks in their thinking and learn more.

ReplyDeleteThe strategy of instruction that is being discussed in Chapters 1-5 really just reinforces best practices in teaching. Certainly it starts with teacher input and modeling, some guided practice, followed by independent practice. I have actually used this book before, as some of the material in it is part of the district's Math Navigators curriculum. One of my favorite activities for the students that test out of the Place Value and Operations Navigators unit is Chapter 1, Astronomy and Large Numbers. When I initially meet with the students to give them their contracts and menu of activities, we spend time talking about the introductory material in this chapter. I pose several of the thinking questions to them and we discuss them. They love talking about pi because they feel it is a "grown-up" concept. Then we cooperatively work through the questions on page 12 so they can share their thinking and see how others are able to figure it out. Then I kind of let them loose on the Level 1 questions that they can work on independently while I am teaching. I periodically touch base with them to make sure they are on track. At the end we wrap up and discuss their questions, issues, and anything else they want to talk about. Most students typically get really into this unit because it is fun and gives them many tidbits of info that, while they don't need to know them, are interesting.

ReplyDeleteIn response to the conversation between PKassir and NLopez, the Tic Tac Toe is a great strategy for differentiating instruction. In the book study I did in the spring, Best Practices for Differentiating Instruction (which I think they are repeating this summer), they refer to this as Think Tac Toe and give many examples. It's a great book.

ReplyDeleteTo Sasha Luther, I have also referred to Laurie Westphal's books regarding menus. We were fortunate to have her on our campus this year working once a week with our highly gifted students (like the 2nd grader that came to me for 5th grade math) and I enjoyed visiting with her about her ideas.

I also agree with ADunlap about the gifted students needing instruction in problem solving strategies. Most are excellent problem solvers, but, when faced with something highly challenging, can be as much at a loss as some of the non-gifted students can be with regular problem-solving.

I do think that each topic gave the essentials to the skills needed to complete that type of mathematics. The gifted students can solve problems if they have this much of the mathematical steps to follow.

ReplyDeleteIt is particularly important when they get up to the high numbers which would be laborious and time consuming to solve by guess and check, etc.

The author introduces the concept with some history and facts that grabs their attention first. I like the way that the author gives background information first such as in the “Metric System” section on p.53. My fifth grade students conducted some research this year on that topic and they were fascinated by what they learned. I plan on taking more time to motivate the students with background information first. The author models several types of problems using different strategies in a step by step manner. Then the students work through different levels. I use a similar method and allow the students to work either independently or with a small group.

ReplyDeleteIn response to Susan M and to continue that topic, the Tic Tac Toe strategy is great as it can be applicable to different areas of study.

ReplyDeleteI like the term Think Tac Toe. I've not had the good fortune to do that book study yet, Best Practices for Differentiating Instruction. I've seen the Tic Tac Toe strategy presented before in Saturday District IV GT workshops and it is always a good one to revisit.

I believe the author is using 2 strategies to engage the learner. 1. Speech bubbles are an interesting and eye catching way to get the students attention. 2. Model drawing-pictures, charts, tables-- are an excellent way to get student to visualize steps, patterns, processes, etc. I use model drawing in my classroom consistently and by the end of the year the students are experts at the disaggregation of math problems. I use this method in the same way that the author does in most respects. I do love his input/output method on page 63- great way to teach conversions!

ReplyDeleteIn response to Sharon G.--"I think all teachers use many of the strategies mentioned in these chapters." You are right-- Many teachers already employ some of these strategies in the classroom.

ReplyDeleteIn response to Sharon G.--"I believe that if Math is fun- kids will take risks in their thinking and learn more."-- Again, you hit the nail on the head. Fun and interesting are key to keeping your students engaged!

ReplyDeleteI have used many of these strategies in my instruction, but I really want to focus on the problem solving in Chapter Two. I love this way of organizing the information into a chart, making some of the higher-level concepts more tangible and easy to manipulate and understand. We do this a lot with our model drawing and I have seen plenty of my kids become very successful even though they "don't get math" (their words, not mine).

ReplyDeleteIn response to N Lopez: you mentioned about giving the kids the tools they need to solve the problems and I completely agree with you. I think a lot of that comes from pre-planning and knowing what they need to know before introducing new concepts.

ReplyDeleteI feel that the author takes basic math concepts and shows how you can break it down and then extend it to create complicated, challenging problems. The break down of the problems is the same, but the problems are easily differentiated for the learner. I will use some of the Einstein tips to make the concepts more concrete. The problem solving strategies are very helpful for all learners. This goes right along with our Singapore Math modeled drawing. It is important for gifted learners to learn the steps of the mathematical concepts even though it often comes easy for them. As the math becomes more extensive, they need to be able to explain what they do and be able to justify their answer. I always love when students can problem solve and give a thorough justification- even if it’s wrong. At least I can see their thinking and help get them headed in the right direction.

ReplyDeleteIn response to ndeans: I agree that historical information and pertinent math facts can make a sometimes dry subject more interesting. That, modeling important math skills, and working in small groups are useful tools that will solidify important concepts.

ReplyDeleteIn response to SusanM on June 10. I agree that the GT kids love anything that is considered a "grown up" concept especially in math and science. They really love learning about the history of pi and even learned part of the pi song.They didn't even mind doing math homework the last 2 weeks of school as long as it was about pi.

ReplyDeleteEdward Zaccaro's strategy of instruction is so much fun for the children, and that is why I have used and will continue to use his resources in my GT classroom. I LOVE the three books by him that I own! Zacarro uses three characters to teach the lessons. The comic-like style of his cartoon figures instantly grabs my students’ interest and the more “teacherly” style his Einstein character serves to remind them of important information. Zacarro includes real-life information at the beginning of each lesson and throughout, as seen in chapter one on page 5: Astronomy and Large Numbers. He tells a story of different cultures’ explanations of the “lights in the sky” and he introduces Eratosthenes and other Greek mathematicians. Not only does Zacarro continually supply the reader with cool information, like how to calculate the distance of a storm, the name of our closest star, and the speed of light (pgs. 6-8), he also supplies an easy way for children to visualize difficult concepts. For example, he includes comparisons that are easier for us to wrap our minds around, such as explaining that the speed of light is equal to light circling Earth over 7 times in one second! Zacarro intrigues his readers by adding historical facts, by offering concrete ways to think about difficult concepts, by supplying step-by-step instructions complete with visual representation, by checking for understanding throughout his lessons, and by including differentiated activities. Each chapter includes level 1, level 2, and Einstein level activities that are typically in word-problem format! I use his leveled activities to differentiate appropriate levels of challenge for my different learners. I have used and will continue to use Challenge Math, Real World Algebra, and The Ten Things All Future Mathematicians and Scientists Must Know (But are Rarely Taught) as supplemental resources throughout my curriculum.

ReplyDeleteZacarro demonstrates many strategies of instructions throughout Chapters 1-5 that I can use with my entire class and not only GT students. I like that he first uses background history of the subject being taught so the student can have an idea of how and why the concept was originated. This gives a little more sense to the abstract concept. I will try to incorporate the background history of my math concepts to give them more sense of use and make them more interesting. Zacarro also makes the modeling of its concepts very animated and realistic because they express emotions such as in page 19 Chapter 2, the cartoon states that “There is no way he’ll ever figure these problems out….they make his brain foggy and confused”..then the teacher cartoon patiently states how he is going to solve them by using 5 difft solving strategies. Expressing the emotions are very important to connect and reach all of our students so I will incorporated them more often in my oral teaching and in my active board flipcharts. I teach 4th grade self contained including Math (last year was my first year teaching Math), and I really liked Chapter 2 exercises on Problem Solving. I already incorporate the use of chart/tables in my teaching and I like how Zacarro is very specific and animated in modeling his problems on page 19-22. I like the variety of problems on page 23 and how you have to work backwards on exercise 8 so I can see myself using these problems with my students.

ReplyDeleteIn response to ADunlap on June 9th, yes interesting facts are a great way to hook GT students. Especially when Einstein says “Most people think that…” pg:61, they are hooked for sure. GT students love to learn these facts that their peers may find boring or unnecessary. I guess that is one of the reasons they relate better to their parents, adults or older students than their peers.

ReplyDeleteIn response to S luther and Susan M “learning menus and Laurie Westphal”, I just browsed the book on Amazon and it says that it does not work well with elementary students-4t graders :0( Is that right? Susan, indeed you were fortunate to have Laurie Westphal in your campus and you were able to pick great ideas from her.

ReplyDeleteWe have the Exemplars Math Word Problem Solving, and Challenge Math reminds me somewhat of them because they have three different levels of difficulty to present problems.

In response to S luther and Susan M “learning menus and Laurie Westphal”, I just browsed the book on Amazon and it says that it does not work well with elementary students-4t graders :0( Is that right? Susan, indeed you were fortunate to have Laurie Westphal in your campus and you were able to pick great ideas from her. We have the Exemplars Math Word Problem Solving, and Challenge Math reminds me of them because they have three different levels of difficulty to present problems

ReplyDeleteIn response to ADunlap June 9th, I agree that problem solving strategies is paramount for any math student including gifted students. Given the right tools, gifted students can easily solve complex math problems. It is amazing to see how author explain concept of inversely proportional quantities in a very simple way by using “Think1” method. Similarly, using “Charts and Diagrams” which we all know as Singapore Math or “Venn Diagrams” to organize the information “so that the brain can more easily understand and analyze it” are essential tools gifted students need for math.

ReplyDeleteIn response to NDeans on June 10th , I am glad to hear that your students were motivated by conducting a research about the measurement before covering it in class. I am planning to do the same next year.

ReplyDeleteIn response to PKassir... I, too, have been using Edward Zacarro's books in my GT classes, but have used them more to challenge my kids individually. I use the different levels as a way to differentiate the challenge. Thank you for describing how you use his resources. I haven't thought about using his lessons whole-group, but I will absolutely implement a lesson similar to the on you described!

ReplyDeleteIn reponse to RCampana on June 11th, Laurie Westphal is great! She will be in Spring Branch in August at a G/T update district staff development. While her main experiences are in middle school, her learning menus can be used in lower grades. If you meet her in person, she will send you the templates for you to create your own learning menus. I felt that was very beneficial to adjust them to the specific needs of my students.

ReplyDeleteI like the way that he starts the chapter with the questions that might be new and difficult. I recently heard that it is good to throw out problems that are difficult for every one so that all the students have to work at the problem. Without this there are some students who would wait for those who always know to tell them how to solve the problems. This teaches everyone to think.

ReplyDeleteThen the charters have the discussion time modeling how the students would talk to each other if they were working together I think it helps the students see how working to gather might sound and feel like. Once the students have a solution model they then are set loose on similar problems moving from the obvious to the complicated then the next problem type is introduced.

Finally the Einstein Level is given and the students are challenged, just as the brain is really working, the Einstein observations are added.

I like the patter of independent learning that the students pass through from “I can not get this to oh this is easy “

What impressed me about the author's approach is his use of a "hook." He caters to the interests of students by telling them why the information is relevant. You aren't just learning metric conversions for the sake of the TAKS test--it's a skill that helps with astronomy and avoids multi-billion dollar mistakes. This is the kind of high level interest that GT students need. After the hook, he leads them through the basics of the calculations with some examples. Then students are encouraged to select problems based on difficulty levels.

ReplyDeleteResponse to Nlopez:

ReplyDeleteI really like the idea of a learning menu where students have to accumulate a certain number of points--the more difficult the problem, the more points, etc. It gives students the freedom to choose the level where they feel comfortable and encourages them to risk some harder questions. It would also appeal to the typical GT student who doesn't want a worksheet of repetitive problems when a few more challenging problems will suffice.

In response to Trixie Tatum,

ReplyDeleteI agree that we should be using these types of problems in the 7th grade PreAP classes. As I was working the problems and reading the examples, I recognized that a lot of these meet our TEKS.