The sense of numbers is so innate for many adults that they may not remember having learned such skills. It is crucial to master more complex mathematical skills such as manipulation of fractions and decimals, or to solve equations with unknown variables, according to experts. Research shows that a flexible understanding of numbers is strongly correlated with subsequent mathematical success and the ability to solve the problems presented in different ways.
Unlike the recent increase in evidence on teaching reading based on science, research and emphasis on the meaning of numbers do not make its way in schools and classrooms in the same way. Students spend Less time on the fundamental numeracy in relation to what they spend to read; Primary teachers often receive Less training In how to effectively teach mathematics; and schools use Less interventions For students who need additional mathematical support.
Many American students have trouble in mathematics. According to the 2024 National evaluation of educational progressNearly 1 fourth year student out of 4 and 39% of the students of eighth obtained notes “below the base”, the lowest category of the test. An analysis of state tests shows that few states have recovered students from the loss of pandemic mathematics, disadvantaged students from low -income neighborhoods were particularly affected.
For students in difficulty – including those diagnosed with dyscalculia and related learning challenges – the lack of sense of numbers often plays an important role.
“For children who have a fundamental weakness in mathematics, 80% or 90% of the time which will be linked to a lack of understanding of the figures,” said Ben Clarke, researcher in mathematics and head of special education department and Clinical sciences in the University of Oregon. “If we want students to access other mathematics that are really important, then they must create this fundamental understanding of numbers.”
Doug Clements, the chair with Kennedy in learning early childhood at the University of Denver, said that many American students have trouble seeing relations between figures. “The children who see 98 plus 99 and align them vertically, draw a bar below with a sign of addition, then the sum of the eight and the nine, bear one and so on – they do not show relational reflection” said Clements. “Children who say immediately:” it’s 200 win three, so 197 “, show a sense of numbers.”
Even in the first years of school, researchers can identify students who can establish links between figures and use more sophisticated strategies to solve problems, just as there are students who are already starting to read.
As with reading, the gaps between students are present on the first day of kindergarten. Students from low -income and disadvantaged backgrounds arrive at school with less mathematics than high income students. The psychologist of the Boston College and researcher in mathematics Elida Laski said that research has revealed differences based on income in the way families speak of mathematics with children before they never reach school.
“Low -income families are more likely to consider mathematics as narrow, it is counting and figures,” said Laski. “While high -income families tend to consider mathematics as more conceptual and in everyday life.”
These differences in thought take place in the flexible students with the figures at the start of primary school. In a studyLaski and his team found that high -year -old pupils and first -year -old students used more sophisticated problem solving strategies than low -income students, who most often relied on the counting. Students with high income also had more basic mathematical facts committed to memory, such as the response to One more Two.
Reminder of memory and relatively advanced strategies used by high income students have produced more efficient problem solving and more correct responses than counting. In addition, when students of high income families produced a bad answer, it was often less bad than students who were counting on strategies such as counting.
Laski said that many low -income students from the study had trouble with the addition because they did not firmly understand the functioning of the basic concepts of numbers. For example, “when we ask:” What is three more than four “, we would get answers like ’34 ‘, said Laski. “Whatever the ways they practice arithmetic, they do not have the conceptual basis to give meaning. They really didn’t have a sense of numbers.
Laski said that early childhood classrooms could be “much more direct” with students in the sense of teaching numbers, by weaving it explicitly when you work on more concrete skills such as addition.
Clarke, the first math researcher at the University of Oregon, accepted.
“Our understanding has increased considerably in the last 20, 25 years on effective educational approaches” to help students learn the meaning of numbers, “said Clarke. “If you will only obtain the number of minutes in kindergarten or the first year to support the development of students in mathematics, children who do not respond to the main education – you must be concentrated enough on what you do And what you offer. “
But primary school teachers are often not well trained on the basis of evidence of best practices in the sense of teaching numbers. A 2022 report From the National Council on the quality of teachers stresses that if teacher training programs have improved over the past decade, they still have a long way to go. According to their standard, only 15% of the undergraduate elementary education programs obtained an A A to adequately cover mathematical content and pedagogy.
Teachers have often not learned to look at the learning of mathematics as a whole, a skills progression This takes students by basic mathematics, starting with learning to count and finds themselves in fractions and decimals – something that certain educational coaches say would help to emphasize the importance of the connection of early number to advanced mathematics. Standards at level are the center which can leave aside the situation as a whole.
Both Common core standards and clement, which sat at the national mathematics consulting panel 2008 and helped create a resource of First mathematics learning trajectoriesDescribe these skills progress. But many teachers are not aware of it.
The educational coach and mathematics consultant Neily Boyd, who is based in Nashville, Tennessee, said that she often worked with teachers to understand how a skill is based on another in sequence, how skills are connected, using progressions as a starting point.
“When teachers were trained both on the whole mathematical concept and on the way parts progress from year to year, they are able to teach their school level in a way that is built at Starting from the previous parts and towards future parts, ”she says. “The learning of mathematics is on the widening and refining of the understanding that you have already built, rather than an endless list of apparently disconnected components.”
Young students too Spend less time with figureswhich often appear only during “mathematics time” only with letters, reading and literacy.
“Often, I’m going to go to classrooms with literacy stuff all over the walls, but nothing in terms of number,” said Nancy Jordan, professor of learning sciences at the University of Delaware and author of “Interventions of meaning of numbers. “” In the first years, there are so many ways to create a sense of numbers outside of educational time – playing games, digital lines in class. Teachers may think of other ways to build these informal understanding mathematics and connect them to formal understanding.
A recent fall day at the Nashville Classical Charter School, in Nashville, Tennessee, the fourth -year mathematics professor, Catherine Schwartz, made the students cross a complicated subtraction problem with a large number: “Lyle a 2 302 dog treats, but he needs 13,400. How many treats does it need? »»
To resolve it, the students had to “subtract through the zeros”, regroup from one place from place to another. The standard algorithm of subtraction is an important competence to learn, said Schwartz, but cannot be well done without a strong sense.
The sense of numbers for older students has some of the same ideas of magnitude and relationships, said Schwartz, but the figures are growing. Students started the subtraction problem using 13 thousand and four hundred to recognize the extent of the numbers in each place value, for example, but slowly simplified in the classic method of battery and sustract.
Schwartz, who has taught for seven years, first said that she did not realize how much a sense of the number of roles had played in calculations such as subtraction with large numbers. “Sense of numbers or flexibility of the number, it is never really named” in the program, said Schwartz. “We try to practice it.”
Even something as simple as having large numbers, including hundreds of thousands and millions, according to some educators, can help develop a sense of numbers. The count may seem simple, but for young children, it is fundamental and essential. “These are very big ideas for small children,” said Jordan.
Contact the editor-in-chief of this story, Christina Samuels, at 212-678-3635 or samuels@hechingerreport.org
