http://nixthetricks.com/
Go to the tab "Resources" and choose one of the 4 articles listed to read.
For this task, we are going to use a new Thinking Routine from Harvard's Project Zero. This one is called "I used to think...but now I think..."
1. Which article did you choose and why?
2. Reflect on what you read. Give further insight, clarifications and how this impacts your instruction.
3. Based on this everything you have read and discussed these past two weeks, what did you used to think about tricks? What do you now think?
4. What do you envision as your first steps in implementing what you have learned?
5. Lastly, is there a "Trick" that you currently use or were taught that hasn't been read about that you would like to share and open up to comments?
I chose "Disappearing Act" as that's a trix I was taught in school to cancel out and didn't realize I was being taught inappropriately. Students need to say simplifies to rather then cancel out. Cancel out makes students think numbers magically disappear. Getting students to gain the correct understanding is crucial in the teaching process so we have to watch our terminology. After reading all these examples I see the mistakes I was taught I have passed on to my students. I now feel challenged to come up with better ways to present the problems using the correct terms. For me the first step is making learning fun so that students dont just want to get the correct answer without understanding. That is not always easy to make every lesson fun. Cant remember any Trix that havent already been covered.
ReplyDeletePeter~ I like your statement regarding "The first step is making learning fun". That has such a huge impact on student learning. Everything I've taught the students where I made it fun, they remember it forever! I think that works for adults, too! And yes, it is difficult to make every lesson fun, but I always try!
DeleteI chose Reason Why When You Invert and Multiply because I definitely need to clarify my math language when dividing by fractions. I have never done a really outstanding job of explaining “why” multiplying by the reciprocal works. I think that if I can explain that clearly and students can understand the concept, then it is easier to justify the “trick.” This is another area that I will be working on for next year.
ReplyDeletePrior to the implementation of the CCLS, I used to think the tricks were great! Once we changed our way of thinking when we implemented the CCLS, I tried to get away from many of these tricks on my own. Unfortunately, there are still some that I rely on that help with concepts that are difficult to teach. After reading this book, and getting some fixes for commonly used tricks, I know that they really aren't helpful for depth of knowledge. I do think that they have their place in math instruction, but not until students have gained understanding.
I am going to tackle my most commonly used tricks next year and change the math language that I use. Hopefully I can take care of “cancel” and “multiply by the reciprocal” to be sure that the students fully understand the process.
I can't think of any tricks that I use as a teacher or that I learned as a student that wasn’t covered in this book. I am sure there are more tricks out there. Maybe there can be a sequel!
I chose the article “Disappearing Act”. The reason I chose that article was because that is a concept that I feel applies to elementary students. Some of the others were higher level and are not taught at the elementary level. This is an interesting concept because I always thought that it really helped kids understand what was happening when you cancel out, but I was wrong. Showing students that simplified fractions are equivalent same value and size) rather than reduced (made smaller). When you tell a fifth grader that a fraction is reduced, they think it becomes a different fraction all together. A smaller one. It is the same fraction, just different representation. It mentioned that children need time to explore these ideas and using the right language will help them identify what is what is new and different about fractions. I do worry though, where is the time? That has always been a number one concern for me. I used to think the tricks were helpful, although I am proud to say that I always thought that if they didn’t understand the concept, they trick would be a shortcut but meaningless. I also believe that the concepts, not the tricks, should be taught starting in Kindergarten. When you have some teachers teaching the tricks only, it really is a disservice to the student and following teachers. Sometimes I have to send a lot of time re teaching the concepts for tricks they came onto fifth grade with, and break the trick habits, and that can take a lot of my time. I think the first thing I am going to do is sit down (when I have time!) and start identifying when tricks are being used in the fifth grade math curriculum. I will flag those situations and make sure that those lessons are going to teach the concept. I will also have to clarify with students that some of what they are doing in math is a trick, and they don’t even know what is really happening as far as math conceptualization
ReplyDelete. Maybe I will make posters showing the trick and the real concept on the same poster! The only trick I can think of at this time that wasn’t mentioned, although it may not be so bad, is the nines finger trick when you are learning your multiplication facts of nine. It really is a crutch that doesn’t force them to learn and memorize their nines. Thoughts on the nines finger trick?
Great class, Jessi! Thanks so much for offering it and I learned a lot!!
I think it would great if we could meet to discuss some vertical alignment. I am going to talk to Andy K about that. We might be able to eliminate some of the tricks early on.
DeleteGreat idea!!!!! Its starts at the bottom with tricks...
DeleteI chose "Disappearing Act" that discusses cancelling things out because I would like to lose the habit of saying "those cancel." I think that this is important to make students understand why things cancel by making them say "adds to 0" or "divides to 1" to help them truly understand what is happening. This is important to me and my students because all too often our students want to cancel more often than they are allowed to cancel. If students can say "multiplicative inverse/divides to 1" they are showing the mathematical understanding of their actions. After reading the book and spending time reflecting, I used to think tricks were effective at helping students complete math correctly. I always wanted students to generally understand, but sometimes it is just easier to teach a trick. Now, I will work very hard to get our students to understand the concepts so that it can be applied at later times. My first steps toward implementation will be starting slow and choosing a couple of tricks to work on. I will try to eliminate cancel from my math vocabulary. I also make sure that I am utilizing content vocabulary to reiterate to students the words they should know to be competent in math. A trick that I used to teach in Algebra 2/Trig was the QRS method for evaluating the exact value of trig functions. I used to make students determine the Quadrant, Sign (Using the All Students Take Calc chart) and Reference Angle (again with the formulas 180-theta/180 plus theta/360-theta). Another teacher in my school utilizes triangles in specific quadrants to determine these exact values and I have converted to using this method....even though it is more time consuming.
ReplyDeleteI think this is going to be a challenge for me!
DeleteI would also like to avoid using the term, cancel. Honestly, I sometimes do not even have the opportunity to explain canceling to the students as it is difficult if students have not mastered their math facts.
DeleteThe article I read was “Internalizing the Order of Operations.” Since I read the chapter in Nix the Tricks, I was hooked on using GEMA instead of PEMDAS. Yes, GEMA is still a trick, but it is more accurate and perhaps can be viewed as a mnemonic device to help students. The basic concept before using GEMAS is students need to understand the concept of inverse operations. For example, they have to understand that multiplying by ½ is the same as diving by two.
ReplyDeleteIn the past I did use PEMDAS, but I explained more as multiplication and division are “friends” (inverse operations) and can trade places “in line” depending on who comes first in the problem. Addition and subtraction are also “friends” (inverse operations), so they can trade places “in line” depending on the problem as well.
I do not think it will be a problem to use GEMAS instead of PEMDAS. Since the implementation of the CCLS and the modules, we spend a great deal of time with conceptual understanding and using models to explain the math. I think using GEMAS will make more sense to the students.
I do use a trick that I don’t believe was mentioned in the book. I wrote about it in an earlier post. It deals with inequality symbols. I feel students know what they mean, but struggle to simply remember which one is which. I tell them that as they read the math statement, it should make sense, but also that the less than symbol looks like a sideways capital letter “L”.
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DeleteI use that one, too. I think it is a good trick because it doesn't detract from conceptual understanding. I wouldn't nix that one!
DeleteI also agree Karen! I wouldn't nix that trick either. I also believe GEMA is more of a mnemonic device as opposed to a trick. Children have to have a conceptual understanding to even use GEMA.
DeleteI like how you were teaching PEMDAS with the understanding of inverse operations and their being friends. The relationship is important. The article points out that most powerful operations should be used first so connecting that with friendship, they are peers.
DeleteI chose the article Disappearing Act for two reasons. First, my students use fractions all the time in my class considering their tape measures are 100% fraction. There are so many times when we need to divide a wall in half or thirds and so on to equally space a window or door and they are not usually very good in this application of division. The author mentioned students can say, “Divides to 1” and show that situation on their paper by making a big 1 instead of a slash to cross factors out. This method makes sense to me and doesn't just let them slash and burn. The second reason is she did this article on my birthday.
ReplyDeleteBased on the class my thoughts on using or not tricks has changed tremendously. The old me thought I am going to show you this trick I learned so that we don't have to waste time getting to the answer when all I was doing was cheating them of the math making sense philosophy. The new me is going to try implementing a few of these strategies in my review this year and make these a regular addition to my curriculum from here on out. Lastly, I'm not sure if this a trick or not,however when I am looking to buy something in the store and I have a coupon for say 20% off I simply multiply the total times .8 in my head. It always works and saves steps from having to subtract the 20% from the total.
The article I chose is “Reason Why When You Invert and Multiply”. I chose this article because learning to divide by fractions is part of our fifth grade curriculum and I believe teaching children to simply flip the sign and the second fraction doesn’t lead to understanding. One method we like to use it to show children how to create visual representations. Having a visual model really helps children to make sense of the process. For example 3 divided by ½ would be shown by showing 3 rectangles (we usually refer to them as submarine sandwiches) and then divide each sub in half. That visual will show them that they now have 6 pieces. Teaching children why multiplying by the reciprocal works can be difficult, but I feel if you work through the process with the students they will begin to develop and understanding and may come upon the trick on their own.
ReplyDeleteBy simply telling children to flip the sign and fraction, students often flip the wrong fraction or forget to change the sign. Clearly, learning the trick doesn’t lead to any level of understanding. The author also spoke about over using the word “opposite” This can lead to “further compound errors because the vocabulary is open to interpretation”. Instead, we teach the children to use correct mathematical vocabulary such as inverse operation and reciprocal.
I believe as with anything, making the transition to math with no tricks, is a slow and steady process. One trick that I have used is to help my kiddos remember their multiplication facts for 9s -11s. We use our hands to figure out the 9s, add a zero for the 10s and double the digits for 11s. It does help them recall facts. Maybe this isn’t as much of a trick as a strategy, I’m not sure!
I choose the Disappearing Act because "canceling" is a term I use WAY too much and so do others.
ReplyDeleteThe mathematics used in the Trades involves fractions, proportions and ratios and equations so I am haunted by the dreaded "cancel" all of the time. It is a word used so often that the Tech teachers use it when trying to teach these topics as well so not only do I have to break myself of this habit I will have to try to break others as well.
I was thinking another way to nix this trick is to use the word reduce instead, and just like stated in the article, show the division in to 1 instead of cancel or the coefficient of 1 in algebraic operations instead of cancel.
Honestly I used to think Tricks were the way math is taught. I just thought it was part of the curriculum and it was okay. I think Common Core is trying to reverse that thinking.
I think I saw most of the tricks in this book or on these websites. I can't think of anything more currently.
I choose "Internalizing the Order of Operations" because I still had questions about GEMA vs PEMDAS. This article helped me to greater understand how GEMA is less of a trick than PEMDAS. I have always taken the time to show students how if you change order on solving these problems that you get different answers so hence the need for a standard order of operations for consistency. The article extends this by talking about the more powerful operations being completed first. I found that very helpful. I also like how the author used the example of a problem students in these levels would innately understand "5 pennies then add 3 cups of pennies" and translating that into an algebraic expression. It is very common for 6th graders to say 5 + 3c is 8c. I have used M & M's and manipulatives to demonstrate the inaccuracy of this, but I like the author's example even better.
ReplyDeleteI wonder if students will still confuse multiplication/division and addition/subtraction left to right or if GEMA taught with understanding will help solve this. Without the understanding GEMA could just become another trick. I wonder if I can convince the new 5th and 6th grade math teachers in my building next year to use GEMA. To make life easier on the 7th grade teachers it would help if all the 6th grade teachers were on board. I will bring it up during our June meeting.
During math in-services or meetings, myself and the other teachers become excited when we saw new, creative, tricks. Now after taking this course, I realize that tricks without the understanding isn't actually learning. Tricks should now be used as tools to help memory when understanding has already been built in. I will not be teaching 6th grade math next year, but will be reading remedial math grade K to 6. This course has already impacted how I answer my struggling students questions so I am so glad I took this course.
I chose the article playing with proportions. Not all people are chefs, but we are all eaters. Most of us need to learn how to follow a recipe at some point. To create dishes with good flavor, consistency, and texture, the various ingredients must have a kind of relationship to one another. For instance, to make cookies that both look and taste like cookies, you need to make sure you use the right amount of each ingredient. Add too much flour and your cookies will be solid as rocks. Add too much salt and they'll taste terrible. Ingredients also have relationships to each other in a recipe This is an important concept to understand in cooking and it's also an important math concept. As i said to much one ingredient can cause recipes to not come out properly.
ReplyDeleteI chose "Reasons why you invert when you multiply". I chose this because fractions are such a large concept in math and many students do struggle with complete understanding. I show students that dividing something in half is the same as multiplying by two to help them understand why we multiply by the reciprocal. I use the language "copy, multiply, reciprocal" when teaching the trick. The way they are showing how to do it could be integrated into the classroom, it would require spending a lot more time. A workshop on using models or tape diagrams for fraction operations is something that I know I would benefit from. Prior to taking this class, I was not in favor of teaching tricks, but many work in helping students to obtain correct answers and gaining confidence. From taking this course, it has solidified for me that I need to do a better job of taking the students to another level of thinking. Over the summer, I will process much of this and make some adjustments to lessons. I know an obstacle, as has been mentioned by some, is time. How much time is appropriate to spend on a concept before moving forward. One trick I use that I don't think was mentioned is changing fractions to decimals. I teach the kids to drop down and divide.
ReplyDelete