Tag Archives: Solving America’s Math Problem

Michigan State University study: Young children can understand large numbers

21 Dec

Mary Niederberger of the Pittsburgh Post-Gazette writes in the article, Formula written for math success:

Mastery of fractions and early division is a predictor of students’ later success with algebra and other higher-level mathematics, based on a study done by a team of researchers led by a Carnegie Mellon University professor.
That means more effective teaching of the concepts is needed to improve math scores among U.S. high school students, which have remained stagnant for more than 30 years….
The study said a likely reason for U.S. students’ weakness in fractions and division could be linked to their teachers’ “lack of a firm conceptual understanding” of the concepts, citing several other studies in which many American teachers were unable to explain the reasons behind mathematical solutions, while most teachers in Japan and China were able to offer two or three explanations. http://www.post-gazette.com/stories/news/education/formula-written-for-math-success-640962/#ixzz1ym9qos5j

Citation:

Early Predictors of High School Mathematics Achievement
1. Robert S. Siegler1,
2. Greg J. Duncan2,
3. Pamela E. Davis-Kean3,4,
4. Kathryn Duckworth5,
5. Amy Claessens6,
6. Mimi Engel7,
7. Maria Ines Susperreguy3,4 and
8. Meichu Chen4Abstract
Identifying the types of mathematics content knowledge that are most predictive of students’ long-term learning is essential for improving both theories of mathematical development and mathematics education. To identify these types of knowledge, we examined long-term predictors of high school students’ knowledge of algebra and overall mathematics achievement. Analyses of large, nationally representative, longitudinal data sets from the United States and the United Kingdom revealed that elementary school students’ knowledge of fractions and of division uniquely predicts those students’ knowledge of algebra and overall mathematics achievement in high school, 5 or 6 years later, even after statistically controlling for other types of mathematical knowledge, general intellectual ability, working memory, and family income and education. Implications of these findings for understanding and improving mathematics learning are discussed.
1.Published online before print June 14, 2012, doi: 10.1177/0956797612440101 Psychological Science June 14, 2012 0956797612440101

Math is important for a number of reasons.

Michigan State University’s Office of Supportive Services succinctly states why math is important:
Why is math important?

All four year Universities have a math requirement
Math improves your skills:
◦Critical Thinking Skills
◦Deductive Logic and Reasoning Skills
◦Problem Solving Skills
A good knowledge of math and statistics can expand your career options
Physical Sciences – Chemistry, Engineering, Physics
Life and Health Sciences – Biology, Psychology, Pharmacy, Nursing, Optometry
Social Sciences – Anthropology, Communications, Economics, Linquistics, Education, Geography
Technical Sciences – Computer Science, Networking, Software Development
Business and Commerce
Actuarial Sciences
Medicine
http://oss.msu.edu/academic-assistance/why-is-math-important

Young children have the ability to grasp large numbers.

Science Daily reported in the article, Kids Grasp Large Numbers Remarkably Young:

Children as young as 3 understand multi-digit numbers more than previously believed and may be ready for more direct math instruction when they enter school, according to research led by a Michigan State University education scholar.
The study, online in the journal Child Development and funded by the U.S. Department of Education’s Institute of Education Sciences, has implications for U.S. students who continue losing ground internationally in mathematics performance.
“Contrary to the view that young children do not understand place value and multi-digit numbers, we found that they actually know quite a lot about it,” said Kelly Mix, MSU professor of educational psychology and co-author of the study. “They are more ready than we think when they enter kindergarten.”
Understanding place value is the gateway to higher math skills such as addition with carrying, and there is a strong tie between place value skills in early elementary grades and problem-solving ability later on.
“In short, children who fail to master place value face chronic low achievement in mathematics,” the study states.
In several experiments, Mix and Richard Prather and Linda Smith, both from Indiana University, tested children ages 3 to 7 on their ability to identify and compare two- and three-digit numbers.
In one task, for example, children were shown two quantities (such as 128 and 812) and asked to point out which was larger. “There was significant improvement in interpreting place value from age 3 to 7,” Mix said, “but it was remarkable that even the youngest children showed at least some understanding of multi-digit numbers.”
Mix said the surprising findings are likely due to the fact that children in today’s society are bombarded with multi-digit numbers — from phone numbers to street addresses to price tags.
Interestingly, children may be developing partial knowledge of the place value system at least partly from language, she explained. Children often hear multi-digit numbers named while also seeing them in print, such as when parents comment on a calendar, ask their child to push the elevator buttons or look for a room number in an office building.
http://www.sciencedaily.com/releases/2013/12/131218112914.htm#.UrVMao_ZKxU.email

Citation:

Journal Reference:
1.Kelly S. Mix, Richard W. Prather, Linda B. Smith, Jerri DaSha Stockton. Young Children’s Interpretation of Multidigit Number Names: From Emerging Competence to Mastery. Child Development, 2013; DOI: 10.1111/cdev.12197
Michigan State University (2013, December 18). Kids grasp large numbers remarkably young. ScienceDaily. Retrieved December 21, 2013,

Jonathan Cohn reported about an unprecedented experiment which occurred in Romanian orphanages in the New Republic article, The Two Year Window. There are very few experiments involving humans because of ethical considerations.

Drury, Nelson, and their collaborators are still learning about the orphans. But one upshot of their work is already clear. Childhood adversity can damage the brain as surely as inhaling toxic substances or absorbing a blow to the head can. And after the age of two, much of that damage can be difficult to repair, even for children who go on to receive the nurturing they were denied in their early years. This is a revelation with profound implication—and not just for the Romanian orphans.
APPROXIMATELY SEVEN MILLION American infants, toddlers, and preschoolers get care from somebody other than a relative, whether through organized day care centers or more informal arrangements, according to the Census Bureau. And much of that care is not very good. One widely cited study of child care in four states, by researchers in Colorado, found that only 8 percent of infant care centers were of “good” or “excellent” quality, while 40 percent were “poor.” The National Institute of Child Health and Human Development has found that three in four infant caregivers provide only minimal cognitive and language stimulation—and that more than half of young children in non-maternal care receive “only some” or “hardly any” positive caregiving. http://www.tnr.com/article/economy/magazine/97268/the-two-year-window?page=0,0&passthru=YzBlNDJmMmRkZTliNDgwZDY4MDhhYmIwMjYyYzhlMjg

Because the ranks of poor children are growing in the U.S., this study portends some grave challenges not only for particular children, but this society and this country. Adequate early learning opportunities and adequate early parenting is essential for proper development in children. https://drwilda.wordpress.com/2011/12/18/jonathan-cohns-the-two-year-window/

Related:

Study: Gender behavior differences lead to higher grades for girls
https://drwilda.com/2013/01/07/study-gender-behavior-differences-lead-to-higher-grades-for-girls/

Girls and math phobia https://drwilda.com/2012/01/20/girls-and-math-phobia/

University of Missouri study: Counting ability predicts future math ability of preschoolers
https://drwilda.com/2012/11/15/university-of-missouri-study-counting-ability-predicts-future-math-ability-of-preschoolers/

Is an individualized program more effective in math learning?
https://drwilda.com/2012/10/10/is-an-individualized-program-more-effective-in-math-learning/

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University of Missouri study: Counting ability predicts future math ability of preschoolers

15 Nov

Jacob Vigdor wrote the interesting Education Next article, Solving America’s Math Problem:

American public schools have made a clear trade-off over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made the curriculum more accessible. The drawback to exclusive use of this more accessible curriculum can be observed among the nation’s top-performing students, who are either less willing or less able than their predecessors or their high-achieving global peers to follow the career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them. Although there is some evidence of a payoff from this sacrifice, in the form of marginally better performance among average students, some of the strategies used to help these students have in fact backfired…

Not all children are equally prepared to embark on a rigorous math curriculum on the first day of kindergarten, and there are no realistic policy alternatives to change this simple fact. Rather than wish differences among students away, a rational policy for the 21st century will respond to those variations, tailoring lessons to children’s needs. This strategy promises to provide the next generation of prospective scientists and engineers with the training they need to create jobs, and the next generation of workers with the skills they need to qualify for them. http://educationnext.org/solving-america%E2%80%99s-math-problem/#.UG25FCk_6rE.email

One way of looking at Vigdor’s conclusions is to ask whether high performance preschool programs and early intervention can affect student achievement?

Science Daily reports about a University of Missouri study about the effect of counting ability in preschoolers in the article, Preschoolers’ Counting Abilities Relate to Future Math Performance, Researcher Says:

Along with reciting the days of the week and the alphabet, adults often practice reciting numbers with young children. Now, new research from the University of Missouri suggests reciting numbers is not enough to prepare children for math success in elementary school. The research indicates that counting, which requires assigning numerical values to objects in chronological order, is more important for helping preschoolers acquire math skills.

“Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,” said Louis Manfra, an assistant professor in MU’s Department of Human Development and Family Studies. “When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.”

Manfra analyzed data from more than 3,000 children from low-income households in order to determine if the children’s reciting and counting abilities in preschool affected their first-grade math scores. He found that students who could recite and count to 20 in preschool had the highest math scores in first grade; however, less than 10 percent of the children in the study could count and recite to 20.

“Counting gives children stronger foundations when they start school,” Manfra said. “The skills children have when they start kindergarten affect their trajectories through early elementary school; therefore, it’s important that children start with as many skills as possible.” http://www.sciencedaily.com/releases/2012/11/121108142808.htm

Here is the press release from the University of Missouri:

News Bureau

University of Missouri

Preschoolers’ Counting Abilities Relate to Future Math Performance, MU Researcher Says

Counting, in addition to reciting, should be emphasized in early childhood education to establish foundation for future academic success

Nov. 08, 2012

Story Contact(s):
Jesslyn Chew, ChewJ@missouri.edu, (573) 882-8353

COLUMBIA, Mo. – Along with reciting the days of the week and the alphabet, adults often practice reciting numbers with young children. Now, new research from the University of Missouri suggests reciting numbers is not enough to prepare children for math success in elementary school. The research indicates that counting, which requires assigning numerical values to objects in chronological order, is more important for helping preschoolers acquire math skills.

Reciting means saying the numbers from memory in chronological order, whereas counting involves understanding that each item in the set is counted once and that the last number stated is the amount for the entire set,” said Louis Manfra, an assistant professor in MU’s Department of Human Development and Family Studies. “When children are just reciting, they’re basically repeating what seems like a memorized sentence. When they’re counting, they’re performing a more cognitive activity in which they’re associating a one-to-one correspondence with the object and the number to represent a quantity.”

Manfra analyzed data from more than 3,000 children from low-income households in order to determine if the children’s reciting and counting abilities in preschool affected their first-grade math scores. He found that students who could recite and count to 20 in preschool had the highest math scores in first grade; however, less than 10 percent of the children in the study could count and recite to 20.

Counting gives children stronger foundations when they start school,” Manfra said. “The skills children have when they start kindergarten affect their trajectories through early elementary school; therefore, it’s important that children start with as many skills as possible.”

Previous research has shown that, in low-income families, parents often think children’s educations are the responsibility of teachers, while teachers expect parents to teach some essential skills at home, Manfra said.

These low-income children aren’t learning math skills anywhere because parents think the children are learning them at school, and teachers think they’re learning them at home,” Manfra said. “This is a problem because it gives parents and teachers the idea that it’s not their responsibility to educate the children, when it’s everyone’s responsibility. This is problematic because, when the children enter kindergarten and are at lower math levels, they don’t have the foundational skills needed to set them on paths for future success.”

Parents and teachers should integrate counting into all aspects of children’s daily activities so they can master the skill, Manfra said.

You can learn anything anywhere, and this is very true for counting,” Manfra said. “When adults read books with children, they can count the ducks on the page. They might count the leaves that fall to the ground outside or the number of carrots at lunchtime.”

The Department of Human Development and Family Studies is part of the MU College of Human Environmental Sciences. The study, “Associations between Counting Ability in Preschool and Mathematic Performance in First Grade among a Sample of Ethnically Diverse, Low-Income Children,” will be published in an upcoming issue of the Journal of Research in Childhood Education.

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education

Related:

Study: Early mastery of fractions is a predictor of math success                                                                                  https://drwilda.com/tag/formula-written-for-math-success/

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Blogs by Dr. Wilda:

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Is an individualized program more effective in math learning?

10 Oct

Moi wrote in Study: Early mastery of fractions is a predictor of math success:

Math is important for a number of reasons.

Michigan State University’s Office of Supportive Services succinctly states why math is important:

Why is math important?

All four year Universities have a math requirement

Math improves your skills:

  • Critical Thinking Skills

  • Deductive Logic and Reasoning Skills

  • Problem Solving Skills

A good knowledge of math and statistics can expand your career options

Physical Sciences – Chemistry, Engineering, Physics

Life and Health Sciences – Biology, Psychology, Pharmacy, Nursing, Optometry

Social Sciences – Anthropology, Communications, Economics, Linquistics, Education, Geography

Technical Sciences – Computer Science, Networking, Software Development

Business and Commerce

Actuarial Sciences

Medicine

http://oss.msu.edu/academic-assistance/why-is-math-important

In Perhaps the biggest math challenge is how to teach math, moi said:

There will continue to be battles between those who favor a more traditional education and those who are open to the latest education fad. These battles will be fought out in school board meetings, PTSAs, and the courts.

There is one way to, as Susan Powder says, “Stop the Insanity.” Genuine school choice allows parents or guardians to select the best educational setting for their child. Many policy wonks would like to believe that only one type of family seeks genuine school choice, the right wing wacko who makes regular visits on the “tea party” circuit. That is not true. Many parents favor a back-to-the basics traditional approach to education.

A one-size-fits-all approach does not work in education https://drwilda.wordpress.com/2012/02/01/perhaps-the-biggest-math-challenge-is-how-to-teach-math/

https://drwilda.com/2012/06/26/study-early-mastery-of-fractions-is-a-predictor-of-math-success/

Jacob Vigdor wrote the interesting Education Next article, Solving America’s Math Problem:

American public schools have made a clear trade-off over the past few decades. With the twin goals of improving the math performance of the average student and promoting equality, it has made the curriculum more accessible. The drawback to exclusive use of this more accessible curriculum can be observed among the nation’s top-performing students, who are either less willing or less able than their predecessors or their high-achieving global peers to follow the career paths in math, science, and engineering that are the key to innovation and job creation. In the name of preparing more of the workforce to take those jobs, we have harmed the skills of those who might have created them. Although there is some evidence of a payoff from this sacrifice, in the form of marginally better performance among average students, some of the strategies used to help these students have in fact backfired.

To some extent, the nation has reduced the costs of this movement through immigration. Foreign students account for more than half of all doctorate recipients in science and engineering, two-thirds of those in engineering. Many of these degree recipients leave the country when they finish, however, limiting their potential benefit to native-born Americans. Immigration policy reform that emphasizes skills over traditional family reunification criteria, much like the policies in place in Australia, Canada, and other developed nations, could change this pattern.

A second possible policy option would be to implement a curricular reform more radical than tinkering with the timing of already existing courses. Many schools have adopted the so-called “Singapore math” model, which emphasizes in-depth coverage of a limited set of topics. There are concerns, however, regarding whether a curriculum developed in a different cultural and educational context could produce similar results here. Singapore’s public schools, for example, use a year-round calendar, obviating the need to review basic subjects after a summer spent out of the classroom. Evidence also indicates that Singapore’s teachers have a firmer grasp of math than their American counterparts.

The United States need not import its science and engineering innovators, however. It need not borrow a faddish curriculum from a foreign context. And it need not sacrifice the math achievement of the average student in order to cater to superstars. It need only recognize that equalizing the curriculum for all students cannot be accomplished without imposing significant lifelong costs on some and perhaps all students.

Curricular differentiation might, for its part, exacerbate test-score gaps between moderate and high performers, if high performers move ahead more quickly. A narrow-minded focus on the magnitude of the gap, however, can lead to scenarios where the gap is closed primarily by worsening the performance of high-achieving students—bringing the top down—without raising the performance of low-achieving students. Society’s goal should be to improve the status of low-performing students in absolute terms, not just relative to that of their higher-performing peers. A growing body of evidence suggests that this type of improvement is best achieved by sorting students, even at a young age, into relatively homogenous groups, to better enable curricular specialization. Recent results from Chicago, cited above, provide evidence that differentiating the high school mathematics curriculum can have long-run benefits, even for students assigned to remedial coursework.

Not all children are equally prepared to embark on a rigorous math curriculum on the first day of kindergarten, and there are no realistic policy alternatives to change this simple fact. Rather than wish differences among students away, a rational policy for the 21st century will respond to those variations, tailoring lessons to children’s needs. This strategy promises to provide the next generation of prospective scientists and engineers with the training they need to create jobs, and the next generation of workers with the skills they need to qualify for them. http://educationnext.org/solving-america%E2%80%99s-math-problem/#.UG25FCk_6rE.email

One way of looking at Vigdor’s conclusions is to ask whether high performance preschool programs and early intervention can affect student achievement?

Moi wrote in Oregon State University study: Ability to pay attention in preschool may predict college success:

In Early learning standards and the K-12 continuum, moi said:

Preschool is a portal to the continuum of life long learning. A good preschool stimulates the learning process and prompts the child into asking questions about their world and environment. Baby Center offers advice about how to find a good preschool and general advice to expectant parents. At the core of why education is important is the goal of equipping every child with the knowledge and skills to pursue THEIR dream, whatever that dream is. Christine Armario and Dorie Turner are reporting in the AP article, AP News Break: Nearly 1 in 4 Fails Military Exam which appeared in the Seattle Times:

Nearly one-fourth of the students who try to join the U.S. Army fail its entrance exam, painting a grim picture of an education system that produces graduates who can’t answer basic math, science and reading questions, according to a new study released Tuesday.

Many children begin their first day of school behind their more advantaged peers. Early childhood learning is an important tool is bridging the education deficit. https://drwilda.wordpress.com/2012/01/03/early-learning-standards-and-the-k-12-contiuum/

Jonathan Cohn’s study about the value of early learning is described in Jonathan Cohn’s ‘The Two Year Window’:

Jonathan Cohn reports about an unprecedented experiment which occurred in Romanian orphanages in the Nw Republic article, The Two Year Window. There are very few experiments involving humans because of ethical considerations.

Drury, Nelson, and their collaborators are still learning about the orphans. But one upshot of their work is already clear. Childhood adversity can damage the brain as surely as inhaling toxic substances or absorbing a blow to the head can. And after the age of two, much of that damage can be difficult to repair, even for children who go on to receive the nurturing they were denied in their early years. This is a revelation with profound implication—and not just for the Romanian orphans.

APPROXIMATELY SEVEN MILLION American infants, toddlers, and preschoolers get care from somebody other than a relative, whether through organized day care centers or more informal arrangements, according to the Census Bureau. And much of that care is not very good. One widely cited study of child care in four states, by researchers in Colorado, found that only 8 percent of infant care centers were of “good” or “excellent” quality, while 40 percent were “poor.” The National Institute of Child Health and Human Development has found that three in four infant caregivers provide only minimal cognitive and language stimulation—and that more than half of young children in non-maternal care receive “only some” or “hardly any” positive caregiving. http://www.tnr.com/article/economy/magazine/97268/the-two-year-window?page=0,0&passthru=YzBlNDJmMmRkZTliNDgwZDY4MDhhYmIwMjYyYzhlMjg

Because the ranks of poor children are growing in the U.S., this study portends some grave challenges not only for particular children, but this society and this country. Adequate early learning opportunities and adequate early parenting is essential for proper development in children. https://drwilda.wordpress.com/2011/12/18/jonathan-cohns-the-two-year-window/

https://drwilda.com/2012/08/08/oregon-state-university-study-ability-to-pay-attention-in-preschool-may-predict-college-success/

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