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Can young children learn mathematics?
What is the best way to teach them? Herbert P. Ginsburg, a developmental psychologist at Teachers College, Columbia University, has been studying those questions for more than 25 years. The following questions and answers were mostly adapted from his chapter on early mathematics education in Handbook of Child Development and Early Education (Guilford Press, 2009).
Why are adults often reluctant to consider teaching mathematics to young children?
In the United States, there is widespread fear and loathing of mathematics, which is often based on people’s memories of their own unhappy school experiences.
Many early childhood educators also believe that math is bad for young children because they are not ready for it and will become anxious if they cannot succeed. Developmentally inappropriate math classes would indeed have that effect, but well-designed programs would not.
Can little children really learn mathematics? The overwhelming body of research conducted over the past 25 years suggests that contrary to popular opinion, young children can learn both concrete and abstract mathematics. And what’s more, they often enjoy it. From birth to age 5, young children develop informal mathematical ideas about numbers, shapes, space, patterns, and other mathematical topics.
For example, they can see that one plate has five cookies and another has three, and they understand that five is more than three. They can easily distinguish between a circle and a square, although they may not know the words for these shapes. They can locate objects in space.
How powerful is the math that young children learn?
Modern research has shown that children’s minds are complex. From an early age, they seem to understand some abstractions involving numbers (for example, that the order of counting a group of objects does not matter, so long as you count each object only once) and are even concerned to know what is the “largest number,” clearly a very abstract mathematical issue. They do not simply remember the isolated “addition facts” but instead can spontaneously develop, without adult help, various general methods or strategies for figuring them out.
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At the same time, children display certain kinds of mathematical ineptitude. For example, they have difficulty understanding that a set of seven objects spread out in a long line is the same number as a set of seven objects arranged in a shorter line. Children’s mathematics is a kind of hidden world that adults have to learn to see.
What is the best way to teach mathematics to young children?
The leading professional organizations in the field recommend that early mathematics instruction cover the “big ideas” of mathematics in such areas as number and operations, geometry (shape and space), measurement, and “algebra” (particularly patterns). The research-based expectation is that early math education should involve topics more challenging than those usually taught.
This is not the kind of mathematics early childhood teachers usually teach. Nor is it the trivial mathematics of the drill sheets. It is a more genuine mathematics than either of these, and children can benefit greatly from learning about it under teachers’ guidance.
Does this imply a “push-down” curriculum?
Not at all. That would be a disaster – just as it often is for the children in the higher grades! The proposal is not to give young children textbooks, worksheets, and all the deadly drills that too often characterize (unsuccessful) elementary mathematics education. The goal is rather to engage children in “big ideas.”
What else does early mathematics involve?
Mathematics involves not only the content – the big ideas – but also ways of thinking. Children need to mathematize – to conceive of problems in explicitly mathematical terms. One of the functions of mathematics education is to help children advance beyond their informal, intuitive mathematics.
How can we help children to learn big ideas and to think mathematically?
First, the preschool classroom or child-care center should contain a rich variety of objects and materials – such as blocks, water tables and puzzles – that can set the stage for mathematics learning. Modern electronic toys and computers can be useful, too.
The second important component is play. Children have a good time when they play, and it stimulates cognitive development. We know that children do indeed learn a good deal of everyday mathematics on their own in the course of free play.
Third, projects can help teachers capitalize on children’s natural curiosity and can help them learn that making sense of real-life problems can be stimulating and enjoyable. These three components are most effective if they are part of a well-planned curriculum that covers big concepts – like numbers, shapes and patterns – in the context of specific and exciting activities. To succeed, a curriculum needs to be of high quality and needs to be implemented well.
What does good implementation of a curriculum involve?
It involves intentional teaching of a planned sequence of activities. The early childhood educator needs to teach the material in an intentional, organized manner, while at the same time being sensitive to individual children’s interests. The teacher needs to provide thoughtful but firm guidance. Good teaching is in many ways like good parenting. And like good parenting it does not always produce immediate (or long-term) success!
How can you possibly use a single curriculum with a diverse group of children?
Dealing with varying abilities is always a problem, no matter what the age of the students or the subject being taught. Early childhood mathematics education is no different. It cannot meet the needs of all children, and it often must fail. Teachers must do their best and what is best depends on the individual teachers and on the individual students they are trying to teach.
What should journalists be looking for in the classroom?
I’m not sure that a brief visit to a classroom will do them much good. But they can try to determine if kids look bored, are restricted to chairs, or seem to be harshly disciplined. On the positive side, they can observe how the teacher talks to the kids. Does she try to explain, use reasonably complex language, and try to engage the kids in some kind of dialogue rather than just lecture to them or tell them what to do?
The most relevant story, I think, is about whether a district or some other education authority is trying to promote education – literacy, math, science – for young children. If so, what kind of approach are they taking?
Do they favor drill? Do they rely exclusively on play? Do they try to promote some intentional teaching? Are they trying to use some of the new math and science curricula? And are they trying to institute long-term, intensive professional development for their teachers? What mistakes have you seen in coverage?
I haven’t seen many stories on the topic, at least as far as preschool is concerned. But here are some things to avoid: Don’t assume that any one curriculum or method is a magic bullet. Everything can be done badly. Don’t assume that early math education is simple or easy. It takes a lot of skill to do it well.
Don’t forget that at the heart of education at all levels is the teacher, and that most preschool teachers have not been trained well in doing math education. But they should be, and that requires commitment and resources from the appropriate educational authority.
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I was very interested in reading your article on mathematics and the young child.I have a Montessori school in Wexford Ireland. The Montessori Mathematics materials are used everyday by my 2.5 to 6year olds, I feel they give the children a sence of security and they feel emotionally satisfied after the completion of this work . The preparation for working with the materials comes form working with everyday life skills that complete a cycle of beginning model and end . Sequineing ,matching all work based on the decimal system e.g. ten cubes in the pink tower I have been working with children for over 30yrs and I still am amazed by the natural way they absorb mathematical concepts. I would have considered myself weak at maths a d my grades confirmed this but as I studied to become a Montessori teacher I realized I had a mathematical mind and I feel if I had have been exposed to the Montessori materials as a young child I would have had a totally different view of maths. Have you observed children engaging with these materials?
Clodagh Dunleavy Smythe
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