Read through the entire Chapter 2 devoted to tricks involving operations
Visit the following YouTube Page in order to watch videos that will clarify certain tricks discussed in this chapter: CLICK HERE (you can watch only the ones you wish too "see")
Reflect on the following questions and comment below:
1. What are your thoughts on teaching key words as discussed in the beginning of this chapter? Do you agree or disagree?
2. Pick one trick and discuss your thoughts on it and the fix that is suggested. Offer further insight, clarifications or a new fix.
3. Comment on a colleagues post to engage in a meaningful conversation.
ReplyDeleteI picked the Ball to the Wall trick. I watched the You Tube video that went along with it. The problem with any mathematical trick is it gets students the answer without comprehension. Clearly if students show all work to solve the problem and dont just use an easy fix like Ball to the Wall they will not only solve the problem correctly but gain comprehension. I think many times we are guilty of knowing how to get the answer but not understanding the meaning behind it. If students comprehend then we are making them life long learners :). No more balls to the walls .... Perhaps we need to write a parody song of Pink Floyds.
I definitely feel that early in my teaching career, I was teaching students how to get the correct answers without fully understanding the process behind it. A lot of that comes with experience.
DeleteI definitely feel that early in my teaching career, I was teaching students how to get the correct answers without fully understanding the process behind it. A lot of that comes with experience.
DeleteI learned how to make bread at a very young age of 14. I could go through step by step and tell you we do this then this and then that. In fact I really didn't understand why we had to mix the bread for 15 minutes. Why we had to proof the bread why we had to add moisture in the oven to create a crust. I didn't learn that until I went to culinary arts class. So I was guilty of knowing how to make bread and now I understand how to make bread.
Deletes an elementary teacher, I really don’t feel that teaching the key words is so bad. I try to make sure that students realize that this is not a definate constant. That they have to read all the other words in the problem to make sure the keys words can be used with the meanings we taught them. I like the fix, because because the kids should draw tape diagrams, which I think leads to a better understanding. I teach them to annotate word problems, like we do in reading. I remind them that math is reading, too! We circle the numbers we need to use, underline what the problem is asking us to do, cross out any extra information, etc. Math is reading!! The trick I picked was 2.4 Rounding. I am so guilty of teaching this trick. It was how I learned it! It is usable for kids, but it doesn’t really help them understand what is really going on when and how we round numbers. I’ve also run into kids who say “five or lower, round down, and actually round the number being rounded down, instead of leaving it what it is. I do like the fix because if you use an actual number line to show them what is happening when you round, the are more likely to understand and get it right. Something I teach the kids is to identify what numbers they are working with. I tell them to underline the number that may go up or stay the same, and the number right after it is the “Bossy Neighbor”. The BN tells the underlined number what to do, and everything after it becomes a “big fat zero!”.
ReplyDeleteI have students that want to round down for the 4 or below! They see that trick and think that it has to work both ways haha. I love the Bossy neighbor idea! I also see student trying to leave numbers after they round to a specific place value and I have to remind them that they rest of the numbers are no longer needed and that is why we rounded. I like the number line idea for decimals, fractions and percents. It helps show the connection between them all and it helps students with one of the toughest math "jobs" they will ever have to do which is... Compare fractions! America in general has a tough time seeing 1/3 and 1/4 and knowing which fractions is larger/smaller.
Deletehttp://www.motherjones.com/kevin-drum/2014/07/great-third-pound-burger-ripoff
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DeleteAudrey, I love your comment, "Math is reading!" It certainly is. Helping kids understand the importance of reading and re-reading math problems to figure out what to do is imperative. Key words are important, but they need to be taken in context.
DeleteYES!! The new catch words this next school year is MATH LITERACY!!!
DeleteThe new catch words should be MATH MAKES SENSE. I found myself using that today in math class when students had a problem that in math next year they will learn a trick to, but this year they would have to reason their way through it. I was so impressed how many of the students did well on it and how they explained how they figured it out. Also I think we need to stress math vocabulary like quotient, product, etc...but in 6th grade often those key words are wrong and a different operation is required.
DeleteThe reason that I signed up for this class was to try and gain some strategies for problem solving. Math has become reading and what do you do with a student who is a struggling reader? They could be awesome with math skills but then when they are thrown application problems, they struggle with figuring out what the question is asking, no less getting a right answer.
DeleteI know that everyone has jumped on the "math is reading" comment, but I totally agree!!! When children have reading difficulties, it impacts them in EVERY subject area!!
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DeleteBoth are extremely important for pretty much any career a student chooses. Reading comprehension skills are crucial you cannot strictly teach math with only numbers. Reading really does improve intelligence and can make you a more well-rounded person in life.
DeleteI think key words can definitely help students to remember important mathematical terms or functions but I do agree that they have become a crutch that without some background to the crutch they will use it incorrectly.
ReplyDeleteMy pet peeve is the "Bigger Bottom, Better Borrow." Let me tell you what some of our Seniors and Juniors do when subtracting large numbers now. They are just taking the range between the value in each place value position. for Example 23 - 18 would equal 15 to them!! They see the 3 and the 8 and take the difference and then the 1 and the 2 and perform the difference. They don't remember place value, they completely forgot how to borrow so they just remember that you put the small number on the bottom and do some sort of subtraction in each "spot." They did not spend enough time on learning place value subtraction, moving range, negative numbers etc.
I do like the idea of using pictures to alleviate this misunderstanding but I also like grouping as well. I would show that you are subtracting 0 tens from 2 tens (20-0) = 20 then you are subtracting 9 ones from 3 ones which cannot be done so where can we borrow from?? the 2 tens. So if we borrow 1 ten we now have 13 ones therefore we can subtract off the 9 ones now, leaving you will 4 ones. So 1 ten (10) and 4 ones (4) = 14
Great point Sarah! Its tough when we teach them a trick to get by in our own class and then they never remember it past that test, so really we are creating even larger gaps for the future!
DeleteJessi,
DeleteGreat point on creating more gaps.. I teach 12th grade and nearly all of my students currently are not taking any math at their home school....This to me is un-american. If they are only to take 1 class it should be math no other subject can affect their life thinking at least math for money/measurement to name a few... They cant figure out how much it would cost to split a pizza 3 ways!
I think that key words are important, but again, students need to be sure to keep the words in context. The “in all” example in 2.1 illustrates this perfectly. It depends on the context in which it is being used. When I tackle word problems with my students, we pick the question apart, highlight or circle/underline key words and numbers, cross out extra information.
ReplyDeleteI chose PEMDAS, because that is one that we use in 6th grade. Students come to us with this trick. The problem that I consistently see with this is the fact that M and D need to be performed from left to right and A and S need to be performed from left to right. They get confused and think that they always have to multiply before they divide and they always have to add before they subtract. I think that GEMA is a great fix. I like that it emphasizes inverse operations between addition and subtraction and multiplication and division. I am going to try this out next year and see if it makes a difference.
Hi Karen! When I teach PEMDAS, I also teach the students that multiplication and division and addition and subtraction are "friends" and they can trade places "in line". I think I should also use GEMA in order to prepare the students for you!
DeleteI agree with not teaching key words for operations to solve problems. Solving problems requires understanding. Even in 6th grade students will see the words in all and decide to add when often they need to do a different operation. I treat word problems like stories they need to understand and visualize what is happening. They solve problems all the time. If there's candy available they each now what their fair share is without looking for a key word.
ReplyDeleteIn my opening comment I asked for an alternative to PEMDAS and chapter 2 gives GEMA. I think the students who make the errors with multiplication/division and addition/subtraction still will...maybe even more. I think the G for grouping is better because of what students will encounter in later mathematics. When I write PEMDAS like this:
P
E
MD
AS
and often switch the letters MD and AS. I am wondering if we should use
G
E
MD
AS.
Some of the tricks in chapter 2 are new to me, such as, turtle multiplication and ball to the wall. I am still struggling with Does McDonald's Sell Cheeseburgers being a trick. It seems to be a mnemonic to me and students are taught the mathematical operations that coincide with these words. After watching the video and seeing the fix, it makes sense. But, in a real-life middle school classroom, I can see students being confused by this. When teachers throughout the grades levels are teaching the same strategies then definitely the fixes will work. The fix for 2.4 with rounding is a great idea, because this is where students can gain the conceptual understanding by seeing it on a number line.
ReplyDeleteI have to admit that I am guilty of teaching key words to help determine which operation to use in word problems. Because I work with so many children who have reading difficulties, teaching them to hone in on key words can have its advantages. I do however, know key words aren’t the end all be all. I also tell children to think about the problem and what is happening. I think if they can put themselves into the scenario, they often can think it out more easily. Drawing pictures or tape diagrams has been super helpful with my kids this year. It gives them a starting point. I also think it is super important for children to see if an answer if reasonable. Often times, students omit this step.
ReplyDeleteI know that I have used many of the tricks in Chapter 2. One that stands out to me is Does McDonald’s Sell Cheeseburgers. I have found this helpful for children to recall the order of solving a division problem. I do think the fix would be helpful as long as this method was taught consistently across the grade levels.
Kelly, I see myself doing that as well. Just today I was working with a student, and she was adding her own scenarios and adding the word "week" when the question was about "months." Her biggest problem is reading! As you said though, it is important to think about the whole problem and making sense of the entire thing. I often tell my students to THINK. It is important to remind them of this, because they simply want to "bulldoze" through everything and just get an answer.
DeleteKelly~ I agree with you that teaching key words to help them determine what operation to use in a word problem does seem to help them. Especially for kids who really struggle, especially with word problems. It feels like your giving them a little cheat. Drawing pictures is a great way to get around some of those "cheat" words. I love tape diagrams and they lend well to word problems.
ReplyDeleteI admit that I do teach key words, but they do not work in all math problem solving situations. For example, the word “of”, we typically see as the clue to multiply…as in “If 1/3 OF 12 crayons are blue, how many are blue?” In the next situation of does not mean multiply...”If I have 20 pencils and I give away 6, how many OF them are left?” If we stick to teaching key words too much, it can be confusing and take away a student’s ability to read for understanding. However, key words can be helpful at times for those many students we have who have reading difficulties.
ReplyDeleteI will choose trick 2.7, ball to the wall. We actually show this trick only after we teach students how to create a whole number with the dividend and/or divisor by perhaps multiplying by 10 or 100. The CCLS and the modules have built the conceptual idea of “making equivalent numbers in order to solve problems more easily” into the curriculum. It is the understanding or idea that equivalent numbers will give you equivalent answers.
One of my biggest "tricks" to teaching is emphasizing the importance of keywords and their paired associations! I was very intrigued to see the book discuss not to emphasize these keywords. In different scenarios, I think keywords are very important and will unlock the meaning to a question, if you know the definition of the keyword (science courses, social courses, etc.). That being said, I still think some keywords are essential and should be utiilizing the paired association technique (geometric sequence=multiply, sum =add, etc.). The trick I will discuss is the turtle multiplication. I really like the use of box diagrams for multiplying and it makes like so much easier for our students in algebra if they are aware of this method. I think that our students would do well with multiplying the same problem, 23x18, and breaking it down to (20+3)(10x8) and using double distribution or the box method.
ReplyDeleteTeaching key words can be a debate. I definitely see the importance and have taught just as you all but what happens when a student is then given a problems like this....
ReplyDelete1. A red hat costs $18 and a blue hat costs $6. How many times as much does the red hat cost as the blue hat?
2. Julie has three more apples than Lucy. Lucy has two apples. How many apples does Julie have?
3. Lucy has three fewer apples than Julie. Lucy has two apples. How many apples does Julie have?
4. There are 3 bags with 6 plums in each bag. How many plums are there altogether?
5. Grandma has five flowers. How many can she put into her red vase and how many in the blue vase? Give all possibilities.
Do KEY words help or hurt them??
DeleteI think key words hurt. They are a run around for trying to understand what is happening...actually comprehending the the situation and problem.
DeleteI think key words hurt. They are a run around for trying to understand what is happening...actually comprehending the the situation and problem.
DeleteMy thoughts on key words is the concept should be fully understood before a "trick" is added. I agree with the author in nixing but I am skeptical that some of these concepts can't me helpful especially in my industry time is money so teaching students the pythagorean theorem to square a floor before we put plywood on it would definitely take time so most carpenters just say pull 6' this side and 8' this side and move the floor 'till your tape measure shows 10'...The method is known as 3,4,5 or 6,8,10 depending on the size of the floor....One trick that sticks out is the total means add. Just today I was helping my student with an applied math problem that was asking how much paint was needed to cover a square room 22' and ceiling ht. 9'6" knowing a gallon can cover 210sqft. Wow was I amazed at how much math this student was choosing..He was ok with calculating sqft but had no concept of how to determine gallons so I asked him to look at my whiteboard and said this board is equal to all of the area you need to paint and this square is how much paint 1 gallon can cover... Ding ding ding the association of division became clear to him...
ReplyDelete“Total" means "Add” – Interpreting Word Problems was the video I watched. I thinks it important for students to understand what they are reading instead of just looking for key words. If students are just looking for key words to figure out if they need to add or subtract it can become misleading. The problem could have them adding but in fact they can multiply. The fix is to have students be able to reason and strengthen their sense making skills. Also have students check to see how reasonable their answer is. I remember having a student double a recipe and it called for 2/3 cups of flour. So when I looked at the students answer he wrote 4/6 Cup of flour. So i asked the kid to get me 4/6 Cup of flour for me. Not happening. Then I went on to explain to him what he did wrong and how to fix it.
ReplyDelete