Read the Conclusion
Reflect on the following questions and comment below:
1. What are your thoughts based on what you just read? Do you have any further questions?
2. What is one small change that you can make in your math instruction going forward?
2. Comment on a colleagues post to engage in a meaningful conversation.
I agree with the idea of starting off slowly. Many of these tricks are ingrained in us as teachers.
ReplyDeleteMany are also ingrained in the brains of the students. Teachers, students and parents may have been thinking that the tricks worked, but true conceptual understanding was missing. Just because a student can come up with a correct answer does not mean that they understood the concept.
While I have eliminated the majority of these tricks from my instruction, I still need to work on 6.4. I am glad that this book gave the fix for the trick. Instead of saying cancel, I will really have to concentrate on using the mathematical operation. I have already put a post it note in my planbook to remind me that this is something that i need to really concentrate on next year.
Sounds like you are on the right path to helping students gain a better understanding of math concepts. I also will be working on the elimination of "cancel" from my math vocabulary.
DeleteI agree that many tricks are ingrained in the brains of students. Conceptual understanding is missing. I do think, though, that we are all guilty at some point at teaching a trick, and it does not a blame game, but would work best for students if they learned less tricks starting in kindergarten and up through the grades, so there aren't gaps or students coming into your class each year some knowing the trick only and some understanding the concepts.
ReplyDeleteI agree with you Audrey about NEVER learning tricks, from kindergarten and beyond. I still have to work on some tricks that I use with my struggling students. It would be more effective to spend the time and teach the true math concepts.
DeleteI also agree! I believe the more exposure the children have to the modules, the easier it will be to avoid teaching tricks. Children will come to each grade level with a better math foundation and a better understanding of math.
DeleteI think there has definitely been some great progress that has been made in the past few years. Implementation of CCLS (not necessarily the modules) has forced teachers to go deeper for understanding.
DeleteI agree as well, it is a work in progress and it is getting better each year. Students are learning some concepts that I learned being at least two years older than present students. There are days that I am amazed that they are mastering concepts at a much younger age.
DeleteI like the comment "students are resistant because they fear they are not smart enough to do math" We as teachers are the actors on the stage. Do we make our audience applaud begging for more or want to throw tomatoes at the stage ? Although not a math teacher I feel my math classes could have been better if I could have seen the real world applications and not just used the TRIX to get the right answer. I think the key is teaching understanding and that comes by explaining concepts clearly. I think being aware of students strengths and weaknesses are crucial to being a great teacher. I like the idea of slowly removing the TRIX. I have talked to a friend who said he couldnt help his daughter with her math because he knew how to get the answer but not how to explain it and show the work. Perhaps the curriculum needs to improve the quality and decrease the quantity taught.
ReplyDeletetake a walk over to culinary arts and i'll have have some tomatoes you can borrow.
DeleteI have referenced this book several times in the past week. I love the techniques that are used to nix the tricks in common math teaching. I like the suggestions of utilizing the start small tactic. Choosing a couple of tricks to eliminate in the curriculum is a great way to start and avoid being overwhelmed trying to fix everything. I would like to eliminate the use of the word "cancel" in my math vocabulary. Also, I have found myself already changing the way I multiply fractions. I have corrected my former language (top x top, bottom x bottom) to numerator x numerator, denominator x denominator.
ReplyDeleteI have also referenced this book in the past week. I think it would benefit all math teachers to take a look at it. Sometimes we don't even realize the we are teaching tricks and that conceptual understanding is not really happening.
DeleteI shared the book with my class as well. (What they could understand at the 5th grade level). Many of the tricks surprised them because the thought that was the only way the solve some of the examples. We did spend time going over the "fix".
DeleteI agree!! The more we know the better we can be!!
DeleteThere are many skills that must be acquired in order to become a professional Culinarian, but if you are not fluent at these skills it can become very challenging. Math is an everyday part of being a chef. You have to be able to forecast, run labor and food costs. A chef must be able to convert recipes and properly measure ingredients. One cannot become a chef with out the proper math training.
ReplyDeleteJames~ and being able to cook is a life skill! Fractions are such a huge part of cooking!
DeleteYour class is a perfect example where nixing the tricks is extremely important. Every year we review conversions with Volume, percentages with bakers measurements, recipe conversions (sizing up or sizing down) etc. And when we start to manipulate fractions, pounds, and ounces things can start to get confusing. For example if an original recipe calls for 3/4 of a cup and you must cut this recipe in half... You now are stuck with 3/8 of a cup. Of course there is the age old trick with doubling the denominator for halving a fraction but the students are forced to understand that when they need to use it for cooking. Also 3/8 of a cup is not going to be found in the kitchen, they have to think of the tools they have to work with and the elements of a cup in order to get a measurement closest to 3/8th or 0.375 of a cup (which would be 3 ounces or a little over a 1/3 of a cup). Understanding of fraction operations and equivalences has never been so important then in the kitchen! One wrong "trick" and your pie, cake, sauce, soup on so on is going to be a disaster!
DeleteAs with anything new, it is always a process…..a work in progress! When we first began teaching the modules, it was very difficult. Over time I have developed a greater understanding of the benefits to teaching math this “new” way. I think that the more we teach children to become critical math thinkers, the less we will need to rely on tricks. I agree with the author when she states, “I truly believe that every student would rather understand than memorize a list of steps, but some students are resistant because they fear that they are not smart enough to do math.” Once children begin to understand math, their confidence will grow.
ReplyDeleteI agree without about the author's statement. We all want to understand what we are doing in any topic. I think parents and other adults who tell kids that they themselves were never good at math sets students up to believe they may not be good either. With the modules parents are often reacting with more confusion because it wasn't the way they learned it. I teach 6th grade and very few of the parents are able to help their kids with the homework. 6th grade math is a mystery or magical to many. I really like the quote on page 62 that says "Any day where students use something they understand to reason about something new is a great day for mathematics." It certainly is a great day for the math teacher.
DeleteI have a class this year that is very testing and they want to know the WHY WHY WHY behind everything we encounter. This class is the HOT class which is an acronym for Health Occupation Technician. These students are learning/practicing to become a CNA. There is A LOT of math in the medical field and we do A LOT of proportions and converting in the Metric system. I have to say I love teaching the tricks but I have started to make sure to get the WHY in behind the "shortcut" not the "trick." This new Junior HOT class has put me through the ringer with examples and understanding but it has been awesome. I am so happy that this class has done this and now taking this online course it has helped me even further. I am drawing pictures, using tables, bringing out props, whatever it takes to get their questions answered. They see a lot of material in a two year period but my goal is that they will know this stuff because they KNOW it, not because they used a trick to get their and when a medical situation calls for it, they will be ready to go!
ReplyDeleteI will carry this momentum on to the other programs and make sure even with the "small" topics I am avoiding the shortcut before I get to the meat behind the situation. The math is pretty consistent across the programs so if I start off small I can apply it everywhere.
DeleteOn page 62 like how it is written that if students understand the reasoning then its not a trick its a shortcut. I also love the author's stand that "Math Makes Sense." I have found myself saying that phrase in math class lately when a student uses their prior learning to reason through a new problem. One large change is in my philosophy of spending more time on helping student understand and discover the shortcut for themselves rather than prematurely jumping to a trick.
ReplyDeleteI like your point. I think when I student can come up with a shortcut ion their own it generally happens AFTER they have figured out the concept.
DeleteI too liked the author's philosophy "Math Makes Sense" and have found myself using that take. It is so much of a relief to tell a student it's ok the math will make sense. Time sure would be nice to fully delve into helping students which is probably why so many struggle in the first place. Great points..
DeleteIts true math will make sense if student can understand the problem without using the tricks.
DeleteYes...we have to help students "make sense" of the math concepts. Otherwise I feel they are just memorizing and repeating information...they will struggle apply the skills in other situations.
DeleteMy thoughts on what I have read are eye opening. It is re-energized my math instruction. Amazingly, in the last week I have had the opportunity to work with a few students with their applied math and found myself using different techniques to explain things. For instance I had a student who had to calculate the perimeter length of the floor in a 12' x 12' room. This student originally used "x" instead of +. Well since it is a "rectangle" with equal sides he suggested can I multiply 12' x 4 so I used to accept that answer however I took this as an opportunity to rediscover what perimeter means. It seemed like the light went off once i showed an example of 12' x 14' room as to why the "x" method is much more work and doesn't follow the perimeter by definition. So I too will be implementing these changes as I move forward.
ReplyDeleteMy basic thought is that tricks without conceptual understanding do not actually cultivate learning math. Some tricks can make understanding math processes confusing and almost harmful. I think there can be a place for tricks in perhaps checking work, or for those students who may benefit from using a mnemonic device. I do not have any further questions. I have come to the realization through this class that the implementation of the CCLS and using the math modules as curriculum places more emphasis on conceptual understanding of math. They do not provide the opportunity to teach tricks. I feel I have already made some changes to my instruction because we use the modules. I can say I do not use tricks as a main avenue for instruction, but I will probably still use some tricks as needed to best support student learning and individual needs.
ReplyDeleteThis book will be a good reference guide to look back on and I like the advice of picking two tricks a year to eliminate. It will take time, but I think it is achievable and students will be better off in the long run. Applying the math to real life situations helps to engage the students and then they understand that it does make sense. After learning FOIL more than 30 years ago, I think I am giving it up. I showed my Algebra students an array yesterday (they already know FOIL) and they were very receptive to it.
ReplyDeleteThank you for the GREAT conclusion comments! Its very rewarding for me to read and see that we all are on the same page!
ReplyDelete