Read Chapter 6
Reflect on the following questions and comment below:
1. This is one of my favorite chapters because I think I am guilty of using almost everyone of the tricks :-( What are your thoughts of the fixes of this chapter? Will you change your instruction?
2. Think back to your instruction, how does teaching tricks affect what they will learn in the future? Can you give an example?
3. Comment on a colleagues post to engage in a meaningful conversation.
Jessi, I love your honesty that you use most of the tricks in this chapter! I do 6.1 Hungry Inequality Symbols, but mine are alligators for fifth grade. The alligator is hungry and his open mouth will always open his mouth towards the bigger number. I do use the vocabulary “greater” and “less” than, not bigger or smaller. 6.4 is another one that I use~ cancel. This is an interesting shortcut because although it can work, the students are missing out what is actually happening to the numbers. It’s not a magic trick~ Something does happen to the numbers when you cancel out. It’s not like they are disappearing and have no impact on the math problem. I will often solve the problem for them to see without canceling out, so they can see what is really happening, and then compare it to the same problem where we canceled out. As far as teaching tricks and how they will affect what students learn in the future, I think there is a huge impact on what they are able to learn in the future. If they only know the trick, and not what is actually happening, how are they going to understand that same concept in the future in a different set of circumstances? Are they going to be able to make the connection to a concept when they see it later? I doubt it. Maybe another argument for “Nix the Tricks” and teach the concepts!
ReplyDeleteI hate this trick. Students really struggle with naming the sign if there are no numbers involved. They just need to learn that < is read as less than and > is read as greater than and they would be all set. I watched my 4th grade son comparing metric units on his homework today. For every problem he told me which value was the largest. He actually got annoyed with me when I made him read from left to right.
DeleteI agree, I do not allow the language "pacman" or alligator in my middle school classroom. I do make the students read the symbols and I teach them that it is just like reading a book, left to right.
DeleteLove the fact that you admit your guilt!
ReplyDeleteMany of these are above 6th grade curriculum. I truly despise 6.1. I have to tell students that they are not allowed to draw alligator teeth on their homework. I have always felt that if students would learn to recognize < as less than and > as greater than, they wouldn’t need a trick. Many students just want to choose the greater value. Then they start reading from right to left instead of left to right. That is why they can’t read < and > as terms. If I put one of those symbols up without any values, the majority of students can’t name the symbol.
I think there is a huge impact on what/how children will learn in the future. I think that many students rely on tricks to get them through, so they don’t always give 100% to the learning of a new concept. They struggle to make connections when introduced to new concepts, especially when connected to a previous concept that was taught using a trick.
Karen~ I don't "truly despise" any trick, but I'm happy to say that I never taught students to ever draw teeth on an alligator.
DeleteYes, Yes, Yes, as an AIS teacher for 4 years i did anything and every thing to get the kids to learn math. But, the last three years of truly learning the common core standards and conceptual understanding i now know how to teach math correctly. I may have created larger gaps for these kids without even knowing it :-(
ReplyDeleteSometimes i think we all get caught in the fire of trying to do whatever we can to get by... boy has my thought on that changed!!
I also feel that the implementation of the Common Core has forced teachers to do things differently. I think that is why I can say that I don't use a lot of these tricks. I used to! I think that I do a much better job of teaching the concepts without the tricks. I still wish we had more time!
DeleteThat is awesome that you have mastered the common core standards. Can you offer some workshops on how to implement teaching this higher level of understanding in the classroom, preferably middle school? ;)
DeleteMathyCathy I agree I would enjoy that class too even though I teach higher grade levels my students are typically in your grade level math understanding.
DeleteJessi, have any tricks for teaching reading a tape measure? I have several techniques I use and Sarah uses too but they struggle for quite sometime in their first year with me as they typically don't have that ruler since elementary school as they are switched to the metric system afterward
Please share Matt!! You may see some in the open forum for the book we are going to look at next week.
DeleteI can relate! I have always looked for new ways to help my children learn math. Now that we have a few years of modules under our belt, we can see that children are developing a more solid understanding of many math concepts. While we do teach math according to the modules, I admit that I still sometimes sneak a trick in here or there.....hard habit to break! It's always a work in progress!!
DeleteMatt,
DeleteIm ashamed to say that when I was taught metric rulers I forgot my English measurements as Im not a carpenter like you I rarely use a English ruler. Do share your Trix silly wabbit.
When I taught remedial math year ago, I also did whatever it takes to help the kids remember and follow the pattern. I agree with Karen that with the implementation of common core more teachers are teaching for understanding. We often teach how we were taught. Classes like this help us to depend our understanding and help us teach our students deeper understanding.
DeleteWhen I taught remedial math year ago, I also did whatever it takes to help the kids remember and follow the pattern. I agree with Karen that with the implementation of common core more teachers are teaching for understanding. We often teach how we were taught. Classes like this help us to depend our understanding and help us teach our students deeper understanding.
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DeleteMatt
DeleteI didn't remember how to read a ruler until I was forced to. Like when I was remodeling my home. Remember measure twice cut once.
I definitely use 6.5, but at the end of the lesson. And I tell students that it only works if the variable is on the left. 6.7 and above is beyond what I teach. I think equations is such a foundational concept. I teach using the language of inverse operations and to always show their check. I find the biggest struggle is to get students to think outside of the box and problem solve. And tricks have probably contributed to this. If they are not able to see it immediately, many students want to give up.
ReplyDeleteThis chapter doesn't have as much of an impact in my curriculum as ch 7 however I did enjoy seeing the old bag of tricks I was taught. Especially the 6.3 and 6.4 nixes. Repeatedly I like that the author states math makes sense so this why... I had not seen some of these trix before but after reading them I can understand their attempted rationale. I will change how I teach in the future for sure especially avoiding some of these nixes as I stated in previous chapters. For instance, 4.5 explaining the pythag theorem. For many of my students they do not want to see math on a white board or their paper they are always asking me to show them instead. Since this is how I believe math should be taught(applied math) I will try to make models to represent these concepts. As far as teaching vocab one thing I like to do is show them a gable roof and ask them to tell me the geometric shape they see. Then ask if they can tell me the parts of the triangle. Then I like to explain why these parts have a name in carpentry too but show the correlation. For instance hypotenuse is rafter length, half the width of the house is run and the height above the wall to the peak is rise. Well what other way can we find the length of the rafter if we know the base and the height?
ReplyDeleteNow based off of what you read in that chapter as well you can explain the distance formula comes up in context of roof pitch. How the rafter length is the distance from the rise and run of the roof. You use that same situation when trying to make sure your corners are 90 degree.
DeleteMatt, I love that you are able to use the math concepts and show students that it actually applies in the real world! I wish I was able to do this with all of the topics in Common Core Algebra. Many of my students struggle because they do not see the relevance.
DeleteMany of the tricks in Chapter 6 are not concepts we cover in the 5th grade curriculum, although, I admit that a few are familiar to me from my days as a student. 6.2, “Move to the Other Side” and 6.4 “Cancel” are two that I found myself using when trying to help my daughter with her math. I am not at all familiar with high school math modules. I can relate to the difficulties parents have with the common core as I struggle to help my own child. I love the modules and think they have many wonderful attributes, but I have also been immersed in learning them for the past several years and have enhanced my own understanding through the process. Imagine how difficult it is for parents to make the shift when they haven’t truly developed that same level of understanding. We basically grew up learning tricks. It’s a hard habit to break! Teaching only tricks will definitely impact future learning. Math is a series of big ideas and concepts and if children are simply memorizing steps or tricks, they could miss out making important math connections.
ReplyDeleteI agree Kelly...learning the modules and the CCLS has been a process for us as educators. We can relate to the parents frustration, except we have continued to learn more and perfect our understanding. Parents are kind of forced to just help their children to the best of their own understanding.
DeleteI think the pac man or alligator use is not the worst thing in the world to use but you have to really explain why and hit is hard when you get to negative numbers. Students see a "bigger" number and they think instantly it is the larger one, it is the one that the alligator wants. But when you are comparing -5 and -10 like she stated in the book, the students want the alligator to eat the -10 and this is not the case. Students also start thinking this way when they do fractions. 1/5 must be "smaller" than 1/10 because the only number they see is the denominator and they know nothing else other than the alligator wanted to eat larger numbers.
ReplyDeleteI actually use the cross out method when solving algebraically. I do see students forgetting why they did that and then they start getting cross out happy in any situation. I have to remind them that there is still that coefficient of 1 in front of your unknown but because a number multiplied by 1 doesn't change that is why we are able to just not put it there.
Sometimes when I explain the square root canceling the square I tell the students that the square root is actually the 1/2 power and when you raise and exponent to another exponent you multiply the two values so 1/2 timese 2 = 1 and anything to the 1 power is itself. Maybe this isn't the most perfect explanation but it's more then just the cross out!
I see that several of the trix are in regards to canceling out values. It seems good communication is of the utmost importance when instructing math. If a teacher doesn't explain why or how to do it students will thinks its OK to cancel out wherever they feel like.
ReplyDeleteMost of the tricks in chapter 6 are not tricks I use with 5th grade. However, many of them are familiar to me because I used them as a student! When looking at trick 6.1, I guess I can see where the confusion occurs. I do not use teeth on inequality symbols, I have the students say “less than, greater than, equal, or not equal” when working with inequality symbols. As I have stated earlier, math is a language and it is important for students to use math “language”.
ReplyDeleteI am guilty though of using a different trick with inequality symbols. If students confuse the less than and greater than symbols, I tell them that the less than symbol resembles a sideways capital letter “L”. I have some students who just struggle to differentiate the two.
I am very guilty of many of these, as I was an Algebra 2/Trig teacher when I started my teaching career. I have to admit, that many of the "Fixes" were moderately difficult for me to understand, and I am very strong in math. As our students come up through the common core curriculum from the lower ages, I do feel that they will likely be much more able to handle the upper level math. I was taught many tricks, and used many tricks while teaching. I regret using these tricks now, because my students were not truly understanding the material. As a special education teacher, patience is the #1 trait that we have to possess, and at times....I forget this. I have become frustrated with students when they do not understand a concept, and simply give them a trick or give them the answer. I need to focus on helping that student learn the concept-and present it in a different manner.
ReplyDeleteyou got it Kyle! I couldnt agree more! As an Ais teacher sometimes a trick has to be used as a last resort when all else fails! For many of these kids its sad to say but some new concepts may never make it past the test so is teaching a trick all that bad? Something to think about i guess....
DeleteOkay so when I first started teaching I was very guilty of 6.1 I had 2 pre-drawn and colored pacmen and alligators. However now in 6th grade I focus more on the vocabulary. But I have to admit this year to reinforcing the alligator when a student was really struggling to remember the symbols. I really like how the fix has students analyzing the shape of the symbols. It reinforces that math makes sense. I will be using that in the future!
ReplyDeleteCarol i think we may have all been guilty at one point lol
DeleteOkay so when I first started teaching I was very guilty of 6.1 I had 2 pre-drawn and colored pacmen and alligators. However now in 6th grade I focus more on the vocabulary. But I have to admit this year to reinforcing the alligator when a student was really struggling to remember the symbols. I really like how the fix has students analyzing the shape of the symbols. It reinforces that math makes sense. I will be using that in the future!
ReplyDeleteUnfortunately most of this chapter is not included in my Culinary Curriculum. However one of the things I deal with in my class has to do with portions. When my students have to do costing per plate we have discussions regarding covering the area of the plate with alternative foods that may not cost as much as for instance pasta vs. a filet. Meaning proportions. My students struggle with less than equal to type thinking with relationship to food. The Fix for 6.1 will definitely be helpful because i used to say bigger and smaller.
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