Before reading Chapter 5, think about some tricks you have used in the past to teach number systems. (Im sure you will find that trick in this chapter!)
Read Chapter 5
Reflect on the following questions and comment below:
1. This will be an open reflection to your past practices and what you just read in this chapter. Will you make changes? Have the tricks you have taught in the past harmed conceptual understanding? What are your overall thoughts?
2. Can tricks still be used to help Special Education and AIS students learn mathematics???
3. Comment on a colleagues post to engage in a meaningful conversation.
I have taught Scientific Notation as a decimal move in the past. When I do lessons with my students usually they are a review of the past. Most of my students tell me off the bat about the tricks they have learned to solve certain topics. Collectively the group said they learned Sci. Notation as a decimal move as well.
ReplyDeleteOn one hand tough I do talk about the reason we traditionally use Sci Not is to rewrite super large and super small numbers so they are easier to work with/read. But I did stress that we are not changing the value of the number we are just changing the way it looks. Like putting make-up on... We haven't changed ourselves as people we just changed our appearance to look a little better! haha
I enjoyed the section on changing the operation when subtracting a negative number. I never used any explanation before when doing this with my students. I guess I just figured since they were already taught this topic the review of it could be using tricks but some of my students I know do NOT know why they are changing the double negatives change to a positive.
Sarah, you are at a completely different level of math than me, but I like that you recognize that if it is review, the tricks can work, but those that do not understand the concept in the first place are going to struggle with the trick no matter what.
DeleteMoving the decimal is a tough one, i think most teachers use it but it becomes a memorization for them and a 50 50 chance of remembering it when it comes to a test. I think its a tough one for teachers to let go of but it definitely needs to be less stressed during instruction. Base ten is the route it should be taught (Modules do a GREAT job of this)
DeleteUnfortunately, I do not teach any of the concepts in chapter 5 in fifth grade. One that I teach part of is 5.5 Move the Decimal. I am guilty of teaching fifth graders to move to decimal to the left or the right, based on how many zeros are in the base ten, and what direction to move it based on if it multiplication and division. That is a short cut~ and really doesn’t help students understand the concept of how the value of the numbers change based on where the decimal point is. The question regarding if tricks can be used to help Special Ed. and AIS students is an interesting one. My opinion is that they should be treated the same as gen. ed. students. Teaching them the tricks doesn’t help them understand the concepts any better than gen. ed. kids.
ReplyDeleteThis is another trick that many incoming 6th graders can do, but they still don't understand what is actually happening. It would be great if 5th and 6th grade teachers could meet to talk about these things.
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DeleteAlthough, we are also guilty of teaching this trick as well, we do teach them the module way. Hopefully, the students coming up to 6th grade next year will have a better understanding. I do believe there would be great benefit for 5th and 6th grade teachers to meet. Do both teams use the modules?
DeleteI am also guilty of teaching this trick. Often students who lack understanding move the decimal the wrong way. If this was merged with the mastering division algorithm along with multiplication and used powers of ten numbers the kids could generalize the patterns and create their own short cut. They always remember better when they discover something for themselves.
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ReplyDeleteI can see how 5.1 could be used, but I always teach that as distance from 0. Students often realize that absolute value has to be positive. I then stress that it has to be because distance can never be negative. You can move in a negative direction, but distance has to be positive. I think a concern that I use is that students just switch the sign and don’t fully grasp the meaning of absolute value.
Prior to Common Core, I was definitely guilty of 5.2. We always taught Keep, Change, Change. (For those of you familiar with Lew-Port teachers, picture Denis Scinta singing, “Keep, Change, Change” to Aretha Franklin’s “Chain of Fools.”
Did that harm conceptual understanding? Probably. Students learned the rule/trick, and never understood the concept. I am guessing that students have a better understanding of the concept now, but I will have to ask if they still use that rick in 7th grade.
As previously stated, I think that tricks can have a place in math instruction. Do they help Special Education students and AIS student learn mathematics? I don’t think they help any students understand the concept any better. So I would teach those students the same way that I teach the general education students.
Oh Memories Karen! LOL i thought the exact same thing!! But did him singing it help? YES, it did because they had a memory of it, so this is where i think tricks can help, and i saw it for myself helping the special ed. kiddos.
DeleteI'll have to remember to tell Scinta that we"talked" about him!
DeleteI use Aretha Franklin's song not when teaching subtraction but subtracting algebraic expressions to help them remember to change the sign of all the terms in the second expression. I am the world's worst singer but the kids love it and they remember it!
DeleteThanks now I'm in a Aretha Franklin loop... I'm not sure I could pull off the singing with my Jr/Sr classes but I bet if I did they wouldn't let me forget as I'm sure they wouldn't either which is why that can be so effective
DeleteKaren...I had Mr. Scinta and I remember this very clearly! He put his dance moves to work as well! Great point about special ed. vs regular ed too.
DeleteAs many of the posts state, we teach students the real meaning of absolute value without any trick. I have found that teaching students integer rules to be one of the toughest things. I always start with the number line, but end up with mnemonics and singing to the beat of row, row, row your boat for adding and subtracting. This probably does harm the conceptual understanding. Going forward to try and change that will definitely take more time. I think as the Common Core continues to evolve, it will get better each year as students are being taught this way from a young age.
ReplyDeleteI agree with you! At the CCLS evolve, the students should be moving through the grade levels more and more prepared...as long as there is consistency within the district.
DeleteConceptual understanding and using tricks would be the same for AIS/Special Ed.
ReplyDeleteThis chapter doesn't apply to the math found in my curriculum except 5.5 moving the decimal. One thing I teach is home energy analyzing so the students need to determine how many BTU's are lost in a typical year and this is measured by how much fuel is burned based off the amount of btu a specific fuel can generate. These are typically extremely big numbers like 180 million btus in a leaky house so I usually try to use exponents to teach the math end of this and therefore moving the decimal. I like the fix for this and want to try this next time. I personally think it is too general to know if this would work for Special Ed as I have had many students who may or may not benefit from tricks. There is certainly an advantage I think in using some tricks in any class as long as it is after the concept is taught.
ReplyDeletePerhaps we can teach a interdisciplinary lesson on BTU's where Sarah teaches the math, you discuss the application to appliances and we do a lab and calculate BTU's of different fuels . If the students are taught the notation 3x or exposed to it three times and see the real world application they will actually learn the concept.
DeletePerhaps we can teach a interdisciplinary lesson on BTU's where Sarah teaches the math, you discuss the application to appliances and we do a lab and calculate BTU's of different fuels . If the students are taught the notation 3x or exposed to it three times and see the real world application they will actually learn the concept.
DeleteThe only trick that I am familiar with is 5.5 Move the Decimal. I am guilty of teaching students to bump the decimal according to the number of zeroes and to determine which way to move the decimal according to whether or not they are multiplying or dividing. Teaching this trick doesn’t help children to develop an understanding. We do, however, teach them the base ten module way so the students are able to develop an understanding.
ReplyDeleteI work with special education students and as I’m sure you can tell from several of my posts, I am still on the fence about whether or not tricks are always bad. I would continue to teach all children the same initial instruction because I see the importance of teaching math conceptually. However, once children have that level of understanding, I don’t believe teaching a mnemonic device, or a trick here and there is necessarily a bad thing. Sometimes it’s the silliest things that can help children to recall information.
The only trick I am familiar with is 5.5. Yes, I have absolutely used it, but as I have stated in several of my posts, using the modules has somewhat eliminated the use of tricks, or the trick comes at the end. I would say, that I did not use this trick this year. Each year I understand more how some tricks could actually be harmful in helping students understand a concept. Instead of moving the decimal, we now talk more about digits moving and numbers being 10 or 100 times larger, or 1/10 or 1/100 of a value.
ReplyDeleteI do think some tricks can be helpful to all students, including AIS and special education students. However, AIS and special educations students are largely part of our general education classes in the CT model, so they will receive the same instruction as the general education students.
I liked the comment about scientific notation that you are not changing the value only the appearance. I think in math class many students just copy what the teacher writes on the board without understanding why.
ReplyDeleteI agree Peter!
DeleteI liked the comment about scientific notation that you are not changing the value only the appearance. I think in math class many students just copy what the teacher writes on the board without understanding why.
ReplyDeleteI have been guilty of many of these. It seems that number sense is one of the most difficult concepts to teach, because of the difficulty in showing/relating it to students' prior knowledge. I have use Keep change change, scientific notation decimal move, perfect children can come out of the house (square roots), etc.
ReplyDeleteAs a special education teacher, the conversation here really made me reflect. Many of us are saying that we would not change the way we teach a concept to special education/ais students. I am happy to hear that. However, I know that I have stood in front of the room and told students, "Here is an easier way, or a trick to this." Reflecting back, I should have helped students visualize the concept and draw diagrams to help understand the math concept.
5.1 is actually the only area that is in my grade level for this chapter. I can't believe someone would teach to absolute value as just taking the positive. I repeat so many times that it is the distance from zero and use number lines. It also conceptually helps students understand distance of two points on a coordinate plane when crossing an axis. It also helps them generalize for operations with negative numbers which they will be learning in 7th grade. I figure I build the concept and background knowledge and the 7th grade teacher extends it.
ReplyDelete5.1 is actually the only area that is in my grade level for this chapter. I can't believe someone would teach to absolute value as just taking the positive. I repeat so many times that it is the distance from zero and use number lines. It also conceptually helps students understand distance of two points on a coordinate plane when crossing an axis. It also helps them generalize for operations with negative numbers which they will be learning in 7th grade. I figure I build the concept and background knowledge and the 7th grade teacher extends it.
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ReplyDeleteStudents need to know how to be able to covert a recipe for large or small parties. This is called recipe conversion factor. To find your conversion factor, simply
ReplyDeletedivide the desired number of servings by the original number of servings. Then multiply each ingredient by the amount.