The hassle of the numbers is so innate to many adults that they may not remember that they have been taught such skills. It is crucial to master more complex mathematical skills such as manipulating factions and decimal signs or solving equations with unknown variables, experts say. Research It shows that the flexible understanding of numbers is highly related to the short mathematical achievements and the ability to solve problems presented in different ways.
Unlike the recent jump of evidence regarding the instructions for reading science, research and the emphasis on the meaning of the number, they do not penetrate schools and classrooms in the same way. Students spend shorter on the fundamental number compared to what they spend on reading; Elementary teachers often receive less How to teach mathematics effectively; and schools use less interventions For students who need additional mathematical maintenance.
Many American students are fighting mathematics. According to 2024 National Educational Progress AssessmentNearly 1 in 4 fourth -graders and 39 percent of the eighth graders put the “under the main”, the largest category of the test. Analysis of State Tests It shows that few countries have recovered pandemic math loser students, with disadvantaged students from low -income neighborhoods being particularly strong.
For those who fight students – including those diagnosed with dyscalculia and the associated challenges of learning – the lack of meaning of a number often plays a significant role.
“For children who have a major weakness in mathematics, 80 percent or 90 percent of the time that will be related to the lack of understanding of numbers,” says Ben Clark, an early mathematics researcher and the head of the Special Education and Clinical Science Department Oregon University. “If we want students to have access to other pieces of mathematics, which are really important, then they must build this fundamental understanding of numbers.”
Doug Clement, the chairman of Kennedy in early childhood at the University of Denver, said many American students are struggling to see relations between numbers. “Children who see 98 plus 99 and arrange them vertically, draw a strip below with a sign of adding, then summarize the eight and nine, carry one, and so on – they do not show relaxation thinking,” says Clement. “The kids who immediately say,” It’s 200, so it takes three, so 197, “show a meaning of a number.”
Even in the first years of school, researchers can notice students who can connect between numbers and use more complex strategies to solve problems, just as there are some students who are starting to read.
As with reading, the gaps between students are present on the first day of kindergarten. Low-income and disadvantaged students arrive at school with less mathematical knowledge than high-income students. Boston college psychologist and mathematics researcher Elida Laski said studies have found differences based on income in the way families talk about mathematics with children before reaching school.
“Families with lower incomes are more likely to think of mathematics as narrow, it’s counting and numbers,” said caresses. “While higher-income families tend to think of mathematics as more conceptual and around everyday life.”
These differences in thinking play in how flexible students are with numbers in the early primary school. In StudyCramps and her team have discovered that a higher-end kindergarten and first-class students use more complex strategies to solve problems than lower-income students, which are more likely to rely on the number. Higher income students also had more basic mathematical facts engaged in memory, with the answer to one plus two.
Memory recall and relatively sophisticated strategies used by higher-income students have created a more effective solution to problems and more correct answers than counting. In addition, when students from high-income families gave the wrong answer, it was often less wrong than students who relied on strategies such as counting.
Cramps said that many low -income students in the study are struggling with the addition, as they have no good understanding of how the basic concepts of numbers work. For example, “when we would ask” what is three plus four “we will receive answers like ’34, said caresses.” Whatever ways to practice arithmetic, they have no conceptual basis to make sense of it. They really didn’t make sense to the number .
Cramps said that classrooms at an early age can be “far more direct” with students in a sense of teaching numbers, weaving explicitly when working on more specific skills such as addition.
Clark, an early mathematics researcher at Oregon University, agreed.
“Our understanding has grown dramatically over the last 20, 25 years for effective teaching approaches,” to help students learn with a sense of number, “Clark said. “If you only get an X number of minutes in kindergarten or first grade to support the development of mathematics students, children who do not respond to the basic instruction – you need to be quite focused on what you do and what you offer.”
But elementary school teachers are often not well trained at the evidence of the best practices in a sense of teaching. A A report of 2022 The National Teachers’ Quality Council emphasizes that while teacher training programs have improved over the last decade, they still have a long way. By its standard, only 15 percent of the programs for primary education at a bachelor’s degree won and for adequate coverage of both mathematical content and pedagogy.
Teachers do not learn often to look at mathematical learning as a whole, a skill progression This leads students through elementary mathematics, starting with learning to count and end with fractions and decimal signs – something that some instructive coaches say that it would help to emphasize the importance of how early numeric meaning is associated with advanced mathematics. Class level standards are the focus that can abandon the larger picture.
Both General basic state standards and Kliment, who served in the National Advisory Council of Mathematics in 2008. Early trajectories of learning in mathematicsOutline these skills progressions. But many teachers are not aware of them.
The instructions coach and Mathematics consultant Neilly Boyd, who is based in Nashville, Tennessee, said he often works with teachers to understand how a skill upgrades another sequentially, how the skills are connected using progress as a jumping point.
“When teachers were trained in both the whole mathematical concept and how the pieces progress from year to year, they are able to learn their piece at the class level in a way that is built from previous pieces and to future pieces,” She said. “Mathematics learning is about expanding and improving the understanding you have already built, not an endless list of seemingly excluded components.”
Young students too Spend a little time with numberswhich often occur only during “mathematical time” than with letters, reading and literacy.
“I will often go to classroom literacy rooms on all walls, but nothing about the number,” says Nancy Jordan, a professor of scientific science at the University of Delaware and the author of “”Interventions with a sensor for numbersS “” In early grades, there are so many ways to build meaning beyond the teaching time – game games, digital lines in the classroom. Teachers can think of other ways to build these informal understandings about mathematics and associate them with official understanding. “
On a recent autumn day at the classic charter school in Nashville, in Nashville, Tennessee, the fourth -grade math teacher Catherine Schwartz went to students with a complex problem with the removal of large numbers: “Light has 2,02 dogs, but it needs 13,400. More treats need Lyle? “
To decide it, students had to “take out zeros” by regrouping from one value to one place to the next. The standard removal algorithm is an important ability to learn, Schwartz said, but it cannot be done well without a strong sense.
The meaning of the number for older students has some of the same ideas for magnitude and relationships, said Schwartz, but the numbers are becoming bigger. Students began the problem of removal, using 13,000 and four hundred to recognize the magnitude of the numbers in each value at each place, for example, but slowly simplify it in the classic stack and maintenance method.
Schwartz, who has been teaching for seven years, does not initially realize how much meaning he has played in calculations as removal as removal with large numbers. “The feeling of numbers or flexibility of numbers, he is never really called” in the curriculum, “Schwartz said. “We are trying to practice it.”
Even something as simple as counting large numbers, including one hundred thousand and millions, some teachers say, can help develop numbers. The census may seem simple, but for young children it is fundamental and essential. “These are really big ideas for young children,” Jordan said.
Contact the editor of this story, Christina Samuels, 212-678-3635 or samuels@hechingerreport.org
