04.03.2014 |
## What are the core numbers in numerology |

To help young kids who struggle with math, well-intentioned teachers often turn to non-traditional teaching methods. A new study concludes that those first-graders who are behind their peers would have learned more if their teachers had just taught them to add and subtract the old-fashioned way.

Average and above-average students learn about as much with either the innovative or traditional approaches.

The researchers found that the higher the number of struggling students, who scored in the bottom 15 percent in kindergarten, in a first-grade teacher’s classroom, the more likely the teachers were to use manipulatives (hands-on materials), calculators, music and movement (See Table 3 on page 12 in the study). Yet, at the end of first grade, the researchers found that struggling students who were given traditional instruction posted significantly higher math score gains than the struggling students who had been taught by the progressive methods.

Understanding why the more innovative methods didn’t work spectacularly is a matter of conjecture.

Innovative methods can also be more challenging to implement properly, and it could be that many teachers aren’t doing them right. The Morgan study will be helpful to disseminate the message that practice is important for all learners.

I had the opportunity to work with first graders this past school year and what research says is true. As and educator for more than 25 years, I enjoyed reading this article and will be sharing it with my 1st grade teachers. I find the original article and the results very interesting, but I would advise caution in making generalizations about the findings from research that relies heavily on survey data and lots of regression analysis. We have idiots administering education systems that force methods on teachers to feed a system whose sole purpose is to spend as much money as possible making as many C students as possible. A study that classifies a calculator as a manipulative along side of tens sticks is seriously flawed. I can’t imagine moving to rote instruction if a child does not have an understanding of a concept.

As the editor who worked with Jill Barshay on this column, I’m fascinated to read these enlightening responses. I think we confuse arithmetic (number facility) with mathematical reasoning to every learner’s detriment. Also, we neglect offering a meaningful connection to numbers and counting and math by not sharing the rich history of their invention. It is so great to see all the arguments against this articles assumptions about teaching learning and struggling students!

I love the comment made about helping (young minds) learn about math being more than numbers but more about problem solving. Math and language development ought to progress at the same time in order for the (mind) to have mobility in it’s understanding and expression of this understanding by communicating this understanding to others both in colourful language or complex math. I totally agree that a reasonable amount of fluency with numbers should help students learn higher concepts more easily, and too much emphasis on precision of facts will quickly lead to boredom and negative feelings. How boring it would be to have to read a story like the three pigs , if you had to read each word perfectly before going to the next page. As I read this article, I found myself wondering if the writer has ever been in a first grade classroom. Follow news on the common core, literacy, math, STEM, social studies, the arts, and other curriculum and instruction topics with two classroom teachers turned Education Week reporters, Liana Heitin and Jaclyn Zubrzycki.

Ratner meant the question as rhetorical—she's an adamant opponent of the Common Core State Standards in math and spends the article arguing that they're making math education in the country worse. However, at a professional development session on the common core I attended last month, held by the Maryland department of education, a small group of middle school math teachers learned how to illustrate these types of equations. Maryland teachers Terry Wheeler and Dawn Caine taught the group four ways to represent division of fractions by fractions—not one of them was the "invert and multiply" rule that all of the adults in the room had been taught. As I've mentioned before, the common core requires more conceptual understanding than most previous state standards. The PD leaders started with division of fractions by whole numbers, and scaffolded from there.

The common denominator model, while not really a picture, demonstrates that the same rules apply to multiplication and division with fractions.

All students have to do is convert the given fractions into fractions with the same denominator. Caine recommended teachers show their class all four methods, and allow students to choose the one that makes the most sense to them.

Having looked over the above ways of introducing fractions division, what are your thoughts?

Pick3Edge has been helping Pick 3 Lottery players for almost 3 years, but needs YOUR help to maintain its "free"ness. If you enjoy Pick3Edge or have had a win, please help us by making a donation of $5, $10, $20 or a $100+?

Now just split the numbers up by dividing them up into 2 Groups of 6 Sets containing 10 numbers each as in the example below. Now using the history file mark the numbers that hit (marked above by the green highlights), tracking the Groups (A or B) and the Sets.

Access to the site is still FREE, however we would like to be able to contact you about new systems, content and site updates. The fewer the struggling students, the more likely that teachers stuck with traditional methods, such as showing the whole class how to solve something one way from the chalkboard and then having students practice the method using worksheets. Gains are measured by how much students math scores rose between kindergarten and the end of first grade. Morgan theorizes that, just as children need to practice reading a lot and become fluent readers before they can analyze texts, math students need to become fluent with basic operations before they can talk about multiple methods for solving problems or arrive at deep conceptual understandings. Too much traditional in math is not good, because first graders need lots of teacher-directed instruction.

Here’s a link to a 1995 journal, Effective Practices, devoted to the aftermath of Project Follow Through. Obviously repetition helps students learn, but simply reciting the words “two plus two equals four” is not synonymous with learning math and attaining a sense of how numbers work together. I had the same initial reaction, why would you lump hands-on materials together with calculators? In my experience of teaching all of the primary grades, some students need more time at the conceptual level of mathematical topics.

And, of course, Lena Green, Theresa Doerfler and others note, correctly that the teacher’s role and skills are of paramount importance. Here are my two-cents: I find this argument to mirror the pushback against using hands on and the use of manipulatives in math. He is struggling in math, which is partially my fault and the school he attended for second grade. Morgan is implying that drilling and rote memorization are better than hands on concepts- but for struggling kids rote memorization may help increase their capacity for learning, whereas, some kids may not need that extra jog?!

I’ve taught first graders for 20 years, and have swung back and forth with the pendulum.

Their entire presentation is available on this site (see M106 - Some Middle School Standards Are More Difficult to Interpret and Understand in Mathematics).

But I'll begin right with division of fractions by fractions (a 6th grade common-core standard).

In order to figure this out, students need to divide the same number line again, this time into eighths. Eventually, the PD leaders said, students can and should learn the "invert and multiply" rule, to save time with more complicated problems. Would you prefer to go straight to the algorithm, or start with these alternate, conceptual representations? Those who dream before cimmerian dark in the dusty recesses of their minds, wake in the date to become aware of that it was vanity: but the dreamers of the hour are rickety men, for they may deception on their dreams with exposed eyes, to create them possible. It employs the right idea of breaking the numbers down into groups and playing in terms of groups. One complicated way could be starting with 10 + 10 and then taking 3 away (because 7 is 3 less than 10) and then taking 2 away (because 8 is 2 less than the other 10).

But any random classroom is likely to have some strugglers in it; for them, the researcher conclude, traditional, teacher-directed instruction generally yields better results. Department of Education data from about 14,000 students across the United States who entered kindergarten in 1998. Six-year-olds are prone to goof around and stick popsicle sticks in their ears, taking away from precious teaching time. I will see you research study and raise you my 40 years plus of teaching to say I seriously doubt that the success you see has anything to do with learning mathematics. I saw teachers integrating manipulatives and small groups, but the students were not staying on task.

Perhaps manipulatives are effective, but calculators aren’t and the calculator negative effect is drowning out the positive manipulative effect? When they don’t get it, their mathematical wall has a crumbly base and is weak from that time forward. I suspect we have all had learning experiences where sometimes we understood the concept first, but other times we didn’t understand the concept well until we could easily perform the procedural operations. Please don’t try to change what we already know about child development to meet the needs of those that designed developmentally INappropriate learning standards in the first place and corporations that are making a mint off of tests and tutoring to support their lies. If we can engage the student about the process of discovering and inventing their own patterns. In second grade I did not know he needed to be learning his multiplication tables, so it set him back.

By timing things we are constantly measuring and it may not actually mean that children aren’t learning what they are being taught. Or do you think this confirms Ratner's claim, in the Wall Street Journal, that under the common standards, "simple concepts are made artificially intricate and complex"? We all want kids to view mathematics as something that’s interesting and engaging and useful,” he said.

When children are on the rug in close proximity of the teacher, and the teacher is giving direct instruction, students can soak up like a sponge.

They come from teachers’ misunderstanding of the innovative methods they have been advised to teach. However, there’s no explanation given for the basis on which the 120 core groups are formed. You drill them enough on something they can repeat it, but do they really understand what they are doing and can they apply it to new situations. Morgan if he thought his findings had implications for the first grade Common Core standards, and we both agreed that Common Core specifies only WHAT students should know, not HOW you should teach it.

They can ask and answer questions about the skill; then go back to their seats and demonstrate what has been taught.

Morgan, he said that teachers who reported using manipulatives also tended to say that they were using calculators.

I wonder if developing a rich number sense involves a certain amount of rote-like repetition, e.g. Then introducing some well known patterns that have become the building blocks of Math, then giving them exercises to reinforce and memorize larger and more complex concepts, they will quite willingly want to move forward to explain and predict parts of the environment in which they live in. Teachers who are good teachers ALL use methods that help kids think about the foundational concepts involved in the mathematics being taught, and they provide intellectually engaging support to the children no matter where they are conceptually. Then the children get on and randomly select what they want to work on from the chosen list.

I have a struggling student who is very slow to learn via common core, probably, I believe, because she needs to really get some good memory practice and it will enhance her ability to grasp the concepts they are trying to teach. We need to show them different strategies for solving problems, and let them decide what works best for them, with guidance from us, of course. My recollection of how this works (from my own grad school stats classes) is that you put all the teachers’ methods in a big metaphorical salad spinner, you start turning and see how the data clumps together. Unfortunately it is our children most in need of opportunities to think and make decisions that get targeted for these misguided and misinformed teaching methods that abandon all thinking for rote instruction. And I always remind myself how much time children are at school versus at home- many people forget this and may fill up their kids schedules with activities and social events and not recognize that the role we have as parents is crucial! I think the problem that has been seen with this type of teaching is that many teachers put it out there and expect the kids to learn it on their own.

If a high percentage of teachers who say they teach one explicit method from the chalkboard also say that they use worksheets to reinforce the technique, that’s another data clump.

But if you work with the child and see what strategies they pick up on, and build on that, the kids are more likely to understand what they’re doing. But there are things we can to do preempt the crisis that it has created- we can find the time to enhance our kids education by attending museums, watching educational programming, go to zoos, seeing science exhibits or visiting planetariums.

Rote memorization is great for fluency and basic facts, but kids who just memorize often have problems understanding why the answer is correct. Researchers found sixth-graders who took an extra math class in a Florida school district performed no better than those who hadn’t by the time they reached high school. Then when they get into higher grades, they have problems because they can’t figure out harder problems. I have expressed my opinions before but the teacher wants to pull him out of Spanish to work with him one on one. I teach math to first graders using different hands-on strategies, while expecting rote memorization to make them more fluent.

I think the teacher should explain the subjects on a whole, then let the class roam free on KA. I have no problem doing that but the teacher sends me text and let’s me know what my son needs to work on. He is not failing math but he lives the subject and I think he is getting discouraged because he feels like he is not advancing in the subject.

Average and above-average students learn about as much with either the innovative or traditional approaches.

The researchers found that the higher the number of struggling students, who scored in the bottom 15 percent in kindergarten, in a first-grade teacher’s classroom, the more likely the teachers were to use manipulatives (hands-on materials), calculators, music and movement (See Table 3 on page 12 in the study). Yet, at the end of first grade, the researchers found that struggling students who were given traditional instruction posted significantly higher math score gains than the struggling students who had been taught by the progressive methods.

Understanding why the more innovative methods didn’t work spectacularly is a matter of conjecture.

Innovative methods can also be more challenging to implement properly, and it could be that many teachers aren’t doing them right. The Morgan study will be helpful to disseminate the message that practice is important for all learners.

I had the opportunity to work with first graders this past school year and what research says is true. As and educator for more than 25 years, I enjoyed reading this article and will be sharing it with my 1st grade teachers. I find the original article and the results very interesting, but I would advise caution in making generalizations about the findings from research that relies heavily on survey data and lots of regression analysis. We have idiots administering education systems that force methods on teachers to feed a system whose sole purpose is to spend as much money as possible making as many C students as possible. A study that classifies a calculator as a manipulative along side of tens sticks is seriously flawed. I can’t imagine moving to rote instruction if a child does not have an understanding of a concept.

As the editor who worked with Jill Barshay on this column, I’m fascinated to read these enlightening responses. I think we confuse arithmetic (number facility) with mathematical reasoning to every learner’s detriment. Also, we neglect offering a meaningful connection to numbers and counting and math by not sharing the rich history of their invention. It is so great to see all the arguments against this articles assumptions about teaching learning and struggling students!

I love the comment made about helping (young minds) learn about math being more than numbers but more about problem solving. Math and language development ought to progress at the same time in order for the (mind) to have mobility in it’s understanding and expression of this understanding by communicating this understanding to others both in colourful language or complex math. I totally agree that a reasonable amount of fluency with numbers should help students learn higher concepts more easily, and too much emphasis on precision of facts will quickly lead to boredom and negative feelings. How boring it would be to have to read a story like the three pigs , if you had to read each word perfectly before going to the next page. As I read this article, I found myself wondering if the writer has ever been in a first grade classroom. Follow news on the common core, literacy, math, STEM, social studies, the arts, and other curriculum and instruction topics with two classroom teachers turned Education Week reporters, Liana Heitin and Jaclyn Zubrzycki.

Ratner meant the question as rhetorical—she's an adamant opponent of the Common Core State Standards in math and spends the article arguing that they're making math education in the country worse. However, at a professional development session on the common core I attended last month, held by the Maryland department of education, a small group of middle school math teachers learned how to illustrate these types of equations. Maryland teachers Terry Wheeler and Dawn Caine taught the group four ways to represent division of fractions by fractions—not one of them was the "invert and multiply" rule that all of the adults in the room had been taught. As I've mentioned before, the common core requires more conceptual understanding than most previous state standards. The PD leaders started with division of fractions by whole numbers, and scaffolded from there.

The common denominator model, while not really a picture, demonstrates that the same rules apply to multiplication and division with fractions.

All students have to do is convert the given fractions into fractions with the same denominator. Caine recommended teachers show their class all four methods, and allow students to choose the one that makes the most sense to them.

Having looked over the above ways of introducing fractions division, what are your thoughts?

Pick3Edge has been helping Pick 3 Lottery players for almost 3 years, but needs YOUR help to maintain its "free"ness. If you enjoy Pick3Edge or have had a win, please help us by making a donation of $5, $10, $20 or a $100+?

Now just split the numbers up by dividing them up into 2 Groups of 6 Sets containing 10 numbers each as in the example below. Now using the history file mark the numbers that hit (marked above by the green highlights), tracking the Groups (A or B) and the Sets.

Access to the site is still FREE, however we would like to be able to contact you about new systems, content and site updates. The fewer the struggling students, the more likely that teachers stuck with traditional methods, such as showing the whole class how to solve something one way from the chalkboard and then having students practice the method using worksheets. Gains are measured by how much students math scores rose between kindergarten and the end of first grade. Morgan theorizes that, just as children need to practice reading a lot and become fluent readers before they can analyze texts, math students need to become fluent with basic operations before they can talk about multiple methods for solving problems or arrive at deep conceptual understandings. Too much traditional in math is not good, because first graders need lots of teacher-directed instruction.

Here’s a link to a 1995 journal, Effective Practices, devoted to the aftermath of Project Follow Through. Obviously repetition helps students learn, but simply reciting the words “two plus two equals four” is not synonymous with learning math and attaining a sense of how numbers work together. I had the same initial reaction, why would you lump hands-on materials together with calculators? In my experience of teaching all of the primary grades, some students need more time at the conceptual level of mathematical topics.

And, of course, Lena Green, Theresa Doerfler and others note, correctly that the teacher’s role and skills are of paramount importance. Here are my two-cents: I find this argument to mirror the pushback against using hands on and the use of manipulatives in math. He is struggling in math, which is partially my fault and the school he attended for second grade. Morgan is implying that drilling and rote memorization are better than hands on concepts- but for struggling kids rote memorization may help increase their capacity for learning, whereas, some kids may not need that extra jog?!

I’ve taught first graders for 20 years, and have swung back and forth with the pendulum.

Their entire presentation is available on this site (see M106 - Some Middle School Standards Are More Difficult to Interpret and Understand in Mathematics).

But I'll begin right with division of fractions by fractions (a 6th grade common-core standard).

In order to figure this out, students need to divide the same number line again, this time into eighths. Eventually, the PD leaders said, students can and should learn the "invert and multiply" rule, to save time with more complicated problems. Would you prefer to go straight to the algorithm, or start with these alternate, conceptual representations? Those who dream before cimmerian dark in the dusty recesses of their minds, wake in the date to become aware of that it was vanity: but the dreamers of the hour are rickety men, for they may deception on their dreams with exposed eyes, to create them possible. It employs the right idea of breaking the numbers down into groups and playing in terms of groups. One complicated way could be starting with 10 + 10 and then taking 3 away (because 7 is 3 less than 10) and then taking 2 away (because 8 is 2 less than the other 10).

But any random classroom is likely to have some strugglers in it; for them, the researcher conclude, traditional, teacher-directed instruction generally yields better results. Department of Education data from about 14,000 students across the United States who entered kindergarten in 1998. Six-year-olds are prone to goof around and stick popsicle sticks in their ears, taking away from precious teaching time. I will see you research study and raise you my 40 years plus of teaching to say I seriously doubt that the success you see has anything to do with learning mathematics. I saw teachers integrating manipulatives and small groups, but the students were not staying on task.

Perhaps manipulatives are effective, but calculators aren’t and the calculator negative effect is drowning out the positive manipulative effect? When they don’t get it, their mathematical wall has a crumbly base and is weak from that time forward. I suspect we have all had learning experiences where sometimes we understood the concept first, but other times we didn’t understand the concept well until we could easily perform the procedural operations. Please don’t try to change what we already know about child development to meet the needs of those that designed developmentally INappropriate learning standards in the first place and corporations that are making a mint off of tests and tutoring to support their lies. If we can engage the student about the process of discovering and inventing their own patterns. In second grade I did not know he needed to be learning his multiplication tables, so it set him back.

By timing things we are constantly measuring and it may not actually mean that children aren’t learning what they are being taught. Or do you think this confirms Ratner's claim, in the Wall Street Journal, that under the common standards, "simple concepts are made artificially intricate and complex"? We all want kids to view mathematics as something that’s interesting and engaging and useful,” he said.

When children are on the rug in close proximity of the teacher, and the teacher is giving direct instruction, students can soak up like a sponge.

They come from teachers’ misunderstanding of the innovative methods they have been advised to teach. However, there’s no explanation given for the basis on which the 120 core groups are formed. You drill them enough on something they can repeat it, but do they really understand what they are doing and can they apply it to new situations. Morgan if he thought his findings had implications for the first grade Common Core standards, and we both agreed that Common Core specifies only WHAT students should know, not HOW you should teach it.

They can ask and answer questions about the skill; then go back to their seats and demonstrate what has been taught.

Morgan, he said that teachers who reported using manipulatives also tended to say that they were using calculators.

I wonder if developing a rich number sense involves a certain amount of rote-like repetition, e.g. Then introducing some well known patterns that have become the building blocks of Math, then giving them exercises to reinforce and memorize larger and more complex concepts, they will quite willingly want to move forward to explain and predict parts of the environment in which they live in. Teachers who are good teachers ALL use methods that help kids think about the foundational concepts involved in the mathematics being taught, and they provide intellectually engaging support to the children no matter where they are conceptually. Then the children get on and randomly select what they want to work on from the chosen list.

I have a struggling student who is very slow to learn via common core, probably, I believe, because she needs to really get some good memory practice and it will enhance her ability to grasp the concepts they are trying to teach. We need to show them different strategies for solving problems, and let them decide what works best for them, with guidance from us, of course. My recollection of how this works (from my own grad school stats classes) is that you put all the teachers’ methods in a big metaphorical salad spinner, you start turning and see how the data clumps together. Unfortunately it is our children most in need of opportunities to think and make decisions that get targeted for these misguided and misinformed teaching methods that abandon all thinking for rote instruction. And I always remind myself how much time children are at school versus at home- many people forget this and may fill up their kids schedules with activities and social events and not recognize that the role we have as parents is crucial! I think the problem that has been seen with this type of teaching is that many teachers put it out there and expect the kids to learn it on their own.

If a high percentage of teachers who say they teach one explicit method from the chalkboard also say that they use worksheets to reinforce the technique, that’s another data clump.

But if you work with the child and see what strategies they pick up on, and build on that, the kids are more likely to understand what they’re doing. But there are things we can to do preempt the crisis that it has created- we can find the time to enhance our kids education by attending museums, watching educational programming, go to zoos, seeing science exhibits or visiting planetariums.

Rote memorization is great for fluency and basic facts, but kids who just memorize often have problems understanding why the answer is correct. Researchers found sixth-graders who took an extra math class in a Florida school district performed no better than those who hadn’t by the time they reached high school. Then when they get into higher grades, they have problems because they can’t figure out harder problems. I have expressed my opinions before but the teacher wants to pull him out of Spanish to work with him one on one. I teach math to first graders using different hands-on strategies, while expecting rote memorization to make them more fluent.

I think the teacher should explain the subjects on a whole, then let the class roam free on KA. I have no problem doing that but the teacher sends me text and let’s me know what my son needs to work on. He is not failing math but he lives the subject and I think he is getting discouraged because he feels like he is not advancing in the subject.

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