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Task:
Please begin by reading the Preface and Chapter 1: Introduction
Reflect on the following questions and comment below:
1. What are your initial reactions to the beginning of this book?
2. How can you relate your own experiences the past few years in regards to teaching "tricks"? What is your favorite math trick?
3. Comment on a colleagues post to engage in a meaningful conversation.
My initial reaction was, “I wish I had seen this years ago!” I have been making a conscious effort to stop relying on math tricks in my teaching. While I think that tricks are good for helping kids remember a process, they have to understand why the trick works. The need to know the process first.
ReplyDeleteI think that the most frustrating trick that I see is with multiplication and division of decimals by a power of 10. Students can explain that they need to move the decimal the same number of places as the zeros, but they don’t understand why the decimal needs to move. Multiplying by 10 is more than just adding a 0 to the end of the number.
I don’t really have a favorite math trick. I have used PEMDAS for order of operations, Keep, Change, Change for subtracting integers, and Cross-Products for solving proportions. I will be making some changes to this after this course!
I agree students need to know the process. How do we get them to show all the work and not just use the trick?
DeleteThat is a great question. Let me know if you come up with a solution!
DeleteMy initial reaction is that I know I will agree, but also disagree with information contained in this book. I believe that students must gain the understanding of the concept, but I don't see anything wrong with giving them a way to remember something. FOIL is infamous to me, as I remember it from high school from a long time ago. The students that I teach in Algebra are advanced 8th graders and they do understand that FOIL is double distribution. But for a lower student, why not give them a way to remember it. I think this is my favorite "trick" because I never forgot it from when I took Algebra. I have found teaching students that subtracting a number or adding it's opposite are the exact same thing to be very difficult for them to understand. It has worked for me to use keep-change-change but I will show them first on a number line to try and gain the understanding.
ReplyDeleteCathy: I think i am thinking along the same lines as you. After the conceptual understanding has been taught are we really doing any harm teaching them ways to remember certain processes?? This can definitely be debatable!!
DeleteKathy I agree. Yes, we should show the students the "why" but then our memory devices and shortcuts work great. I love the idea of showing the kids the "long way" and then having kids discover the patterns for the shortcuts. I'm glad the beginning of the book addresses our time challenge though.
DeleteI agree with both of you! The conceptual understanding is extremely important. I have seen the benefits from the CCLS as it has been implemented over the past few years at LP, but I don't see the harm in teaching a trick or mnemonic device if it appeals to different learning styles.
DeleteI thought I was going to be very skeptical. I heard people saying that PEMDAS should be outlawed. Well then give me a better way to teach students how to remember the order of operations. I do like to teach students the "why" of how short cuts work, but some students have so much difficulty understanding math so I know they rely more on the tricks just as rote memory rather than understanding. My favorite tricks are PEMAS and Keep, Change, Flip.
ReplyDeleteI have to agree that PEMDAS is a favorite and I am guilty of using it. It was how I learned it and I don't know any other way to teach it!
DeleteMy initial reaction to the beginning of the book is…this is going to be great! The basic idea of “teach the concept and then perhaps the trick” is where my CT teacher and I have “lived” the past few years as we have implemented the CCLS and the modules. As we have gained a deeper understanding of the CCLS and the modules, we can see the greater connection students make with the math curriculum (models especially) and understanding math concepts…not memorizing tricks. My favorite math trick is…DMSCB (Does McDonald’s Sell Cheese Burgers). This trick helps students work through the process of long division. However, there is a great lesson in the 5th grade modules that pertains to dividing with decimals. In that lesson, there is a somewhat complicated model to create, but it gives students a greater understanding of what is exactly being divided.
ReplyDeleteBecause I have been working with the modules for several years now, I am very aware of the importance of teaching children to truly understand math. I have always kept an open mind when working with the modules and I feel as though I learn more each year. It is very difficult, however, to completely step away from tricks. I am hoping this book will help me to see things a different way.
ReplyDeleteI likely have several favorite tricks!! I have always used PEMDAS, even as a student myself. I have also used several tricks to teach decimals and place value. My favorite however, would be teaching the acronym: KHDMDCM (King Henry’s Darling Mother Died Christmas Morning) to teach conversions in the Metric System.
Because I am always looking for ways to help my students recall information, I think giving up tricks completely will be difficult. I teach mnemonic devices for other subjects as well. I don’t always believe that tricks are bad. I guess I will have to find a balance.
I agree that there has to be a balance. If students understand the concepts, then I don't see anything wrong with a trick to help them remember. I also use King Henry, but I say dance instead of died. Just a happier word!
DeleteKelly,
DeleteThat acronym is great it reminds of one i learned in 6th grade science. Keep in mind i was in 6th grade but I remember Kill Pretty Cats Or Find Gross Spit (Kingdom,phylum,class,order,family,genus,species)
I love the part in Ch 1 where the author says "Being a mathematician is about critical thinking, justification and using tools of past experiences.... Allow students to grow into young adults who can think" I think with today's modern technology: calculators, GPS, google students fail to learn to think on their own. This is the challenge to not just teach them the short cuts but how to be critical thinkers in the process. Im not a math teacher so I dont have a lot of tricks up my sleeve but i frequently use Ohms Law triangle where you cover up one letter to find what formula and operation to use.
ReplyDeleteYes, I agree that children need to become better problem solvers and critical thinkers overall. Learning tricks doesn't lead them to understanding, however, I'm not ready to give them up completely. Perhaps there is a time and place for them still!
DeletePeter the ohms law just made me think when I teach R-Value and U-value I do the same thing since they are reciprocals of each other but I skip over the why they are in reciprocity part...Thanks
DeleteI find it very frustrating when students cant think their way through problems. Establishing good foundations will be the building blocks for better understanding.
DeleteMy initial reaction was that “What is wrong with teaching the kids a few shortcuts?”. As I read Chapter 1, it did make perfect sense to me why understanding the concepts of math are more valuable than the tricks and shortcuts. When they understand the concepts, they can apply those concepts to other areas of math. Shortcuts are like a “one and done”. Students remember the trick, but that is where any understanding ends. And I really don’t agree with the last section in chapter one~ not enough time. When you take the time to help students really understand the concepts, they can apply those concept understandings to other math areas. This is truly where time is saved. You don’t have to take more time teaching a new short cut! I will be honest, I have taught my students tricks. But to be honest, I only taught them after I made sure the concept was understood. One that I have often used was just multiplying the denominators to get a common denominator when you are adding or subtracting fractions with unlike denominators. They really should understand that finding the least common multiple is the better way.
ReplyDeleteYou hit it on the head...not enough time. If we had enough time to be sure the students really understood the concept instead of plowing along, things would be much better.
DeleteAudrey, good point about spending some extra time with true understanding will allow for less review and more recall at later times in the year.
DeleteAgree, true understanding will make it easier for review and also help with peer to peer review. Students will be able to help teach each other.
DeleteI love this book already! A couple of my favorite quotes are, "It is in the best interest of students everywhere to make the focus of mathematics critical thinking." Math is a very difficult subject for many of our students. They must work at it, if they want to be successful. I also liked the quote, "Being a mathematician is about critical thinking, justification and using tools of past experiences to solve new problems. Being a successful adult involves pattern finding, questioning others, and perseverance." All math teachers need to promote critical thinking and having students struggle to find the answers. Students will not like this method, but it is much more effective that rote memorization. One of my favorite tricks is when subtracting polynomials, think "Leave, Change, Opposite." After reading the first chapter, I regret now building the concept and using the trick in my past teaching.
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ReplyDelete"I think chapter 1 is interesting. It will take a great effort to slowly change the way that math is taught. At times students encounter conceptual logical difficulties that require more than just practice and tricks. Besides I was a terrible at math when i was younger. It takes me a long time to problem solve math in my head.
My initial reactions to this book are feelings of aha moments. I have realized how the concept of math has evolved since when I was a student in the fact that we were taught the concept first then as a way to "enhance" our understanding we utilized the "tricks" especially SOHCAHTOA and FOIL. The best one I remember from Course III math was my teacher taught me that whenever you here the word Bernoulli replace that word with "exactly" and those problems were then easy for me. As for relating in my own teaching I find that I don't spend enough time teaching pythagorean theorem to teach rafter length because I can show them a physical layout method using a framing square which holds the square giving you the hypotenuse every time. However, some students could benefit from the concept of the theorem since it has some many applications such as squaring a wall, floor, roof framing, siding, plumbing etc...
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