At least the student may answer using a numerical equation. In Everyday Math questions asking to "explain" require a response of at least two complete sentences.
I like this 3rd grade problem from Singapore that my daughter was working on yesterday:
Three tanks, A, B, and C are filled with water. A has three times as much water as B and B has three times as much water as C. A has 48 gal of water more than C. Find the total amount of water in the three tanks.
Schools talk about balance, but the problem is not finding a balance between skills and understanding. It's a problem of low versus high expectations. It would be very difficult (has anyone seen any attempt?) to show that a third grade TERC student "understands" more math than a third grade Singapore Math student.
It seems to me that the only argument that can be made is that Singapore Math is too rigorous (not appropriate for our heterogeneous, low expectation, culture) for many and that kids will "understand" and like math more if you go at a slower pace.
Has anyone seen an argument against Singapore Math based on understanding, rather than pace? Has anyone ever argued that Singapore Math needs more of a balance between skills and understanding? I haven't. The only arguments I have seen have to do with culture or an implied difference in the level or quality of the students, i.e. low expectations.
This is why I see the following trend at my son's (ex) private school and his (soon to be) public school. Keep Everyday Math in the early grades but provide the better math courses to the capable kids in 7th and 8th grades. They don't use Singapore Math in the early grades because it's too much, not because Everyday Math is better. They just can't believe that it's the curriculum or teaching; it has to be the kids.
They think that it takes "math brains" to be good in math, and the schools guarantee that this is the only result. Even Andy Isaacs (one of the authors of EM) says that Everyday Math is not for the "elite". The elite are those who can survive EM or get outside tutoring help.
"Schools talk about balance, but the problem is not finding a balance between skills and understanding. It's a problem of low versus high expectations."
Yes, I feel that is exactly what is happening in my elementary school. They supplement heavily on basic skills without having kids learn to mastery. It is just exposure. The kids will see it next year so no biggie. However, there is one thing I've noticed at our school. The TERC binders are not being used in my son's third grade classroom. I've never seen a word problem worksheet like the one above. The teacher commented that the program wouldn't work for the state test. I wonder if now that is over if they will rely just on investigations.
What I see happening is the faster kids are being pushed to do "algebra" and "investigations" in the top third grade classes. The slower kids are being fed a steady stream of basic skill worksheets (gotta keep up those state scores). Their is no acceleration for the ones who could possibly excel and accelerate if they were just given the chance. They are stuck on the slow track.
I noticed one third grade classroom had to make up a different math problem for every day of the month. It is proudly displayed in the hallway. I thank my lucky stars my kid isn't in that class. This is enrichment. This is fun. I think it is stupid.
So, you have basic skills exposure versus ennrichment using investigations. Which is the worse of the two?
Three tanks, A, B, and C are filled with water. A has three times as much water as B and B has three times as much water as C. A has 48 gal of water more than C. Find the total amount of water in the three tanks.
They think that it takes "math brains" to be good in math, and the schools guarantee that this is the only result.
This is our school in a nutshell.
It's taken me until midway through this year to realize how incredibly low level the accelerated math class is - and yet it's taught as if only a mathematically gifted child is capable of handling the material.
Which is exactly how things have played out, given that expectation.
I don't get these comments. Are the Singapore math questions people cite here supposed to be harder than the TERC questions? They're different -- the Singapore math ones plug directly into equations, and the TERC question requires you to actually read the words to figure out which dimension is being asked for but is it actually true that one is easier than the other? Or, I guess as an alternative, can the kids trained in Singapore Math do the TERC question, while those trained with the TERC problems can't answer the Singapore Math questions?
Has anyone done that experiment?
I'm a grown-up, and I don't know how I was taught math, but I can do both questions. The number crunching takes longer for the Singapore Math question, but they're easier to plug into the equation than the TERC questions.
I'm not sure I could have answered either as a 3rd grader.
"Are the Singapore math questions people cite here supposed to be harder than the TERC questions?"
Yes, but it's more clear when you see more problems. Open the workbooks side-by-side. My son uses Everyday Math, and "everyday" I see the differences in difficulty.
"...the Singapore math ones plug directly into equations, ..."
I'm not sure what third grade equations you are referring to for the three tank problem. I suspect that Singapore wants the student to translate the words into a bar model.
"... is it actually true that one is easier than the other?"
Yes.
"... can the kids trained in Singapore Math do the TERC question, while those trained with the TERC problems can't answer the Singapore Math questions?"
That's the point.
"...but they're easier to plug into the equation than the TERC questions."
Which equation is that?
It sounds like bj is implying that the TERC problems require more thinking than the Singapore Math problems, which only require plug and chug. If so, I would be open to hearing a more complete argument of that position.
I went to see the person in charge of curriculum at my son's (ex) private school today. They are sorry to see our A+ Everyday Math student leave the school. (He is not A+ in Singapore Math, by my standards.) When we got to talking about changes in the math curriculum, she seemed to have it all figured out. (I had loaned her my Singapore Math books.) It's hard for me to characterize the conversation because it was filled with all sorts of generalities. It looks like they will keep Everyday Math.
Why? Well, it seems for all sorts of reasons. Better test scores were mentioned and many approaches to explanation were discussed. The main reason seems to be that they want to keep it. She even referred to What Works Clearinghouse. It wasn't my goal to change her mind. I wanted to hear the arguments. It all comes down to opinion, pedagogy, and expectations. Apparently, there are two types of students; math brains and the rest. Their math program will be selected based on "the rest". They will worry over what to do with the math brains, but you don't base a curriculum on those kids.
At no time was there any attempt to say that Everyday Math was better than Singapore Math.
"-- the Singapore math ones plug directly into equations"
At this level of Singapore math, the children aren't using equations, they are using bar diagrams. There is no "plugging into equations" - the child has to diagram and solve the problem, which takes multiple steps.
"the TERC question requires you to actually read the words to figure out which dimension is being asked for"
Sinapore questions certainly require that the student "actually read the words." Students can't simply pull out the numbers - diagramming the problems requires understanding exactly what has been stated, what remains unknown and the relationship between the two.
Perhaps we should have looked at more examples from 3rd grade TERC since the example cited is probably the most difficult problem that TERC presents. Here are some worksheets from 3rd grade:
"Suppose you can hold 150 beans in your right hand and 217 beans in your left hand. How many more beans are in your right hand? Write down how you figured this out."
Here's another one:
"Solve this problem three different ways. Using a calculator can be one way. Make notes about how you solved the problem. Be sure that others can understand what you did: 42 + 36 + 18 = "
Here's another one:
"Solve this problem in two different ways, and write about how you solved it: 234 + 123 = Here is the first way I solved it: Here is the second way I solved it:"
Oh, and here's something from TERC's 3rd grade manual:
"Birthday: Pantomime holding a newborn baby in your arms. Tell students that the baby was just born, and write today’s date on the board. Explain that this is the baby’s birthday. Sing “Happy Birthday”, and encourage students to sing with you. Ask for volunteers to sing the song in their native languages. Students might also make a poster with the words “Happy Birthday” in all the languages that are spoken in the class. Have each student point to his or her birthday on a calendar. This is also a good opportunity to make a graph of the months of students’ birthdays."
By the time they get to fifth grade, they're doing only slightly harder problem. Here's a scripted lesson from the teacher's 5th grade manual:
"Teacher: Now let’s use the clock face to add fractions. Say the hand moved one third of the way around the clock and then it moved one sixth more. Where will it end up? "Write the problem on the board: 1/3 + 1/6 = "Encourage students to talk together and find more than one way to think about the problem. Some might find it helpful to look at the clock faces on their (student work sheet)."
Singapore provides guided instruction but certainly doesn't prescribe "one way to solve a problem", nor does it prescribe plug and chug. By the time Singapore students get to sixth grade, they are able to solve problems such as:
"Sally is given $5 more allowance than Megan each week. They each spend $12 per week and save the rest. When Sally saves $60, Megan saves $20. How much allowance does each girl have per week?”
It is true that bar modeling is used to get students through such problems, but such technique also prepares students for algebraic type thinking. By the time they finish sixth grade, they are ready to step into algebra. TERC hardly gives the same preparation. TERC students can hardly add or subtract.
The bar modeling techniques not only serve to help solve problems but are linked to the underlying concepts and help explain to the student what is happening mathematically. Basic skills are embedded in problems; they bootstrap each other.
Solve this problem three different ways. Using a calculator can be one way. Make notes about how you solved the problem. Be sure that others can understand what you did: 42 + 36 + 18 =
"The main reason seems to be that they want to keep it." (emphasis added)
It being Everyday Math.
Same thing here.
Massive supplementation required, tremendous teacher training required, hiring of a new math curriculum "consultant" required, but still, see what good results we get?
If you just supplemented, coordinated, and trained to this level with the old curriculum, we'd see as good results. (Not to mention the private tutoring and parental support).
But this is what they want to do, so that's the end of it.
To be fair, implementing Singapore Math would require tremendous teacher support initially because so few of our elementary teachers have enough mathematical background to successfully implement on their own.
Yes, TERC is scripted in the sense that there is detailed guidance given to the teacher in the manual on how to conduct these seemingly open ended lessons. This begs for an example, so I won't let you down.
This is from the teacher's manual for TERC Investigations, regarding the teaching of algorithms and what to do about students who have learned the traditional methods:
"If you have students who have already memorized the traditional right-to-left algorithm (of addition) and believe that this is how they are “supposed” to do addition, you will have to work hard to instill some new values – that estimating the result is critical, that having more than one strategy is a necessary part of doing computation, and that using what you know about the numbers to simplify the problem leads to procedures that make more sense, and are therefore used more accurately."
One way is traditional, one way the calculator, third way 4 tens plus 3 tens plus 1 ten plus the (8+2) = 9 tens plus the 6 or 96.
I homeschool using Singapore. Variations of this third way are taught in level 2 along with the traditional method. The mental math is used when needed and when it is more efficient than paper and pencil.
I tutor kids from a public school that uses Everyday Math. These kids have no idea about efficient and quick solutions as they usually try to do everything mentally. If that doesn't work cumbersome procedures are tried such as forgiving division or lattice multiplication. They, especially the middle school kids, greatly resist Singapore ideas at first. They have been brainwashed to believe these ways are "Old-fashioned and out of date). These students are so lacking in basic number sense and deep understanding that it is unbelievable to me. Especially since EM is suppose to develop those skills.
25 comments:
Those are "riddles"?
It makes it seem so mysterious.
At least the student may answer using a numerical equation. In Everyday Math questions asking to "explain" require a response of at least two complete sentences.
Low expectations = Low performance
And here's a problem from the 3rd grade Singapore Math textbook:
"Abigail is 12 years older than her sister Davinia. How old will Davinia when Abigail is 3 times as old as she is?"
The riddle is how someone managed to get the first one wrong.
I like this 3rd grade problem from Singapore that my daughter was working on yesterday:
Three tanks, A, B, and C are filled with water. A has three times as much water as B and B has three times as much water as C. A has 48 gal of water more than C. Find the total amount of water in the three tanks.
Schools talk about balance, but the problem is not finding a balance between skills and understanding. It's a problem of low versus high expectations. It would be very difficult (has anyone seen any attempt?) to show that a third grade TERC student "understands" more math than a third grade Singapore Math student.
It seems to me that the only argument that can be made is that Singapore Math is too rigorous (not appropriate for our heterogeneous, low expectation, culture) for many and that kids will "understand" and like math more if you go at a slower pace.
Has anyone seen an argument against Singapore Math based on understanding, rather than pace? Has anyone ever argued that Singapore Math needs more of a balance between skills and understanding? I haven't. The only arguments I have seen have to do with culture or an implied difference in the level or quality of the students, i.e. low expectations.
This is why I see the following trend at my son's (ex) private school and his (soon to be) public school. Keep Everyday Math in the early grades but provide the better math courses to the capable kids in 7th and 8th grades. They don't use Singapore Math in the early grades because it's too much, not because Everyday Math is better. They just can't believe that it's the curriculum or teaching; it has to be the kids.
They think that it takes "math brains" to be good in math, and the schools guarantee that this is the only result. Even Andy Isaacs (one of the authors of EM) says that Everyday Math is not for the "elite". The elite are those who can survive EM or get outside tutoring help.
"Schools talk about balance, but the problem is not finding a balance between skills and understanding. It's a problem of low versus high expectations."
Yes, I feel that is exactly what is happening in my elementary school. They supplement heavily on basic skills without having kids learn to mastery. It is just exposure. The kids will see it next year so no biggie. However, there is one thing I've noticed at our school. The TERC binders are not being used in my son's third grade classroom. I've never seen a word problem worksheet like the one above. The teacher commented that the program wouldn't work for the state test. I wonder if now that is over if they will rely just on investigations.
What I see happening is the faster kids are being pushed to do "algebra" and "investigations" in the top third grade classes. The slower kids are being fed a steady stream of basic skill worksheets (gotta keep up those state scores). Their is no acceleration for the ones who could possibly excel and accelerate if they were just given the chance. They are stuck on the slow track.
I noticed one third grade classroom had to make up a different math problem for every day of the month. It is proudly displayed in the hallway. I thank my lucky stars my kid isn't in that class. This is enrichment. This is fun. I think it is stupid.
So, you have basic skills exposure versus ennrichment using investigations. Which is the worse of the two?
Three tanks, A, B, and C are filled with water. A has three times as much water as B and B has three times as much water as C. A has 48 gal of water more than C. Find the total amount of water in the three tanks.
I love this problem!
I noticed one third grade classroom had to make up a different math problem for every day of the month. It is proudly displayed in the hallway.
Are these the faster kids?
Actually, making up a word problem may be a good idea.
Russian Math has kids do it in every lesson, and it's pretty challenging.
There's only one such problem in problem sets of DOZENS OF PROBLEMS, but "write a problem" problems are consistently posed.
They think that it takes "math brains" to be good in math, and the schools guarantee that this is the only result.
This is our school in a nutshell.
It's taken me until midway through this year to realize how incredibly low level the accelerated math class is - and yet it's taught as if only a mathematically gifted child is capable of handling the material.
Which is exactly how things have played out, given that expectation.
The problem are posed as how many times can you think of a way to write 48 x 2. Some division problems, etc.
These are the faster kids, I think. How does TERC help with word problems?
I don't get these comments. Are the Singapore math questions people cite here supposed to be harder than the TERC questions? They're different -- the Singapore math ones plug directly into equations, and the TERC question requires you to actually read the words to figure out which dimension is being asked for but is it actually true that one is easier than the other? Or, I guess as an alternative, can the kids trained in Singapore Math do the TERC question, while those trained with the TERC problems can't answer the Singapore Math questions?
Has anyone done that experiment?
I'm a grown-up, and I don't know how I was taught math, but I can do both questions. The number crunching takes longer for the Singapore Math question, but they're easier to plug into the equation than the TERC questions.
I'm not sure I could have answered either as a 3rd grader.
bj
"Are the Singapore math questions people cite here supposed to be harder than the TERC questions?"
Yes, but it's more clear when you see more problems. Open the workbooks side-by-side. My son uses Everyday Math, and "everyday" I see the differences in difficulty.
"...the Singapore math ones plug directly into equations, ..."
I'm not sure what third grade equations you are referring to for the three tank problem. I suspect that Singapore wants the student to translate the words into a bar model.
"... is it actually true that one is easier than the other?"
Yes.
"... can the kids trained in Singapore Math do the TERC question, while those trained with the TERC problems can't answer the Singapore Math questions?"
That's the point.
"...but they're easier to plug into the equation than the TERC questions."
Which equation is that?
It sounds like bj is implying that the TERC problems require more thinking than the Singapore Math problems, which only require plug and chug. If so, I would be open to hearing a more complete argument of that position.
I went to see the person in charge of curriculum at my son's (ex) private school today. They are sorry to see our A+ Everyday Math student leave the school. (He is not A+ in Singapore Math, by my standards.) When we got to talking about changes in the math curriculum, she seemed to have it all figured out. (I had loaned her my Singapore Math books.) It's hard for me to characterize the conversation because it was filled with all sorts of generalities. It looks like they will keep Everyday Math.
Why? Well, it seems for all sorts of reasons. Better test scores were mentioned and many approaches to explanation were discussed. The main reason seems to be that they want to keep it. She even referred to What Works Clearinghouse. It wasn't my goal to change her mind. I wanted to hear the arguments. It all comes down to opinion, pedagogy, and expectations. Apparently, there are two types of students; math brains and the rest. Their math program will be selected based on "the rest". They will worry over what to do with the math brains, but you don't base a curriculum on those kids.
At no time was there any attempt to say that Everyday Math was better than Singapore Math.
"-- the Singapore math ones plug directly into equations"
At this level of Singapore math, the children aren't using equations, they are using bar diagrams. There is no "plugging into equations" - the child has to diagram and solve the problem, which takes multiple steps.
"the TERC question requires you to actually read the words to figure out which dimension is being asked for"
Sinapore questions certainly require that the student "actually read the words." Students can't simply pull out the numbers - diagramming the problems requires understanding exactly what has been stated, what remains unknown and the relationship between the two.
Perhaps we should have looked at more examples from 3rd grade TERC since the example cited is probably the most difficult problem that TERC presents. Here are some worksheets from 3rd grade:
"Suppose you can hold 150 beans in your right hand and 217 beans in your left hand. How many more beans are in your right hand? Write down how you figured this out."
Here's another one:
"Solve this problem three different ways. Using a calculator can be one way. Make notes about how you solved the problem. Be sure that others can understand what you did: 42 + 36 + 18 = "
Here's another one:
"Solve this problem in two different ways, and write about how you solved it: 234 + 123 =
Here is the first way I solved it:
Here is the second way I solved it:"
Oh, and here's something from TERC's 3rd grade manual:
"Birthday: Pantomime holding a newborn baby in your arms. Tell students that the baby was just born, and write today’s date on the board. Explain that this is the baby’s birthday. Sing “Happy Birthday”, and encourage students to sing with you. Ask for volunteers to sing the song in their native languages. Students might also make a poster with the words “Happy Birthday” in all the languages that are spoken in the class. Have each student point to his or her birthday on a calendar. This is also a good opportunity to make a graph of the months of students’ birthdays."
By the time they get to fifth grade, they're doing only slightly harder problem. Here's a scripted lesson from the teacher's 5th grade manual:
"Teacher: Now let’s use the clock face to add fractions. Say the hand moved one third of the way around the clock and then it moved one sixth more. Where will it end up?
"Write the problem on the board: 1/3 + 1/6 =
"Encourage students to talk together and find more than one way to think about the problem. Some might find it helpful to look at the clock faces on their (student work sheet)."
Singapore provides guided instruction but certainly doesn't prescribe "one way to solve a problem", nor does it prescribe plug and chug. By the time Singapore students get to sixth grade, they are able to solve problems such as:
"Sally is given $5 more allowance than Megan each week. They each spend $12 per week and save the rest. When Sally saves $60, Megan saves $20. How much allowance does each girl have per week?”
It is true that bar modeling is used to get students through such problems, but such technique also prepares students for algebraic type thinking. By the time they finish sixth grade, they are ready to step into algebra. TERC hardly gives the same preparation. TERC students can hardly add or subtract.
The bar modeling techniques not only serve to help solve problems but are linked to the underlying concepts and help explain to the student what is happening mathematically. Basic skills are embedded in problems; they bootstrap each other.
Basic skills are embedded in problems; they bootstrap each other.
Well said. And hard to see if you haven't actually worked on the different curriculums.
I'm still trying to figure out the third way to add 42, 36, and 18.
Solve this problem three different ways. Using a calculator can be one way. Make notes about how you solved the problem. Be sure that others can understand what you did: 42 + 36 + 18 =
I think I just had a stroke.
Steve said,
"The main reason seems to be that they want to keep it." (emphasis added)
It being Everyday Math.
Same thing here.
Massive supplementation required, tremendous teacher training required, hiring of a new math curriculum "consultant" required, but still, see what good results we get?
If you just supplemented, coordinated, and trained to this level with the old curriculum, we'd see as good results. (Not to mention the private tutoring and parental support).
But this is what they want to do, so that's the end of it.
To be fair, implementing Singapore Math would require tremendous teacher support initially because so few of our elementary teachers have enough mathematical background to successfully implement on their own.
But that's another issue.
TERC is scripted?
I'm still trying to figure out the third way to add 42, 36, and 18.
I initially thought that they were referring to the commutative property of addition. So:
42 + 36 + 18
42 + 18 + 36
36 + 42 + 18
But the clue that "Using a calculator can be one way" suggests that they want something like this:
Use a calculator.
Use paper and pencil.
Use blocks
Use a sliderule
Ask a friend
I think ...
-Mark Roulo
Yes, TERC is scripted in the sense that there is detailed guidance given to the teacher in the manual on how to conduct these seemingly open ended lessons. This begs for an example, so I won't let you down.
This is from the teacher's manual for TERC Investigations, regarding the teaching of algorithms and what to do about students who have learned the traditional methods:
"If you have students who have already memorized the traditional right-to-left algorithm (of addition) and believe that this is how they are “supposed” to do addition, you will have to work hard to instill some new values – that estimating the result is critical, that having more than one strategy is a necessary part of doing computation, and that using what you know about the numbers to simplify the problem leads to procedures that make more sense, and are therefore used more accurately."
Third way:
Use Google (of course!)
42+36+18
One way is traditional, one way the calculator, third way 4 tens plus 3 tens plus 1 ten plus the (8+2) = 9 tens plus the 6 or 96.
I homeschool using Singapore. Variations of this third way are taught in level 2 along with the traditional method. The mental math is used when needed and when it is more efficient than paper and pencil.
I tutor kids from a public school that uses Everyday Math. These kids have no idea about efficient and quick solutions as they usually try to do everything mentally. If that doesn't work cumbersome procedures are tried such as forgiving division or lattice multiplication. They, especially the middle school kids, greatly resist Singapore ideas at first. They have been brainwashed to believe these ways are "Old-fashioned and out of date). These students are so lacking in basic number sense and deep understanding that it is unbelievable to me. Especially since EM is suppose to develop those skills.
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