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Effective Early Math Education: Carpe Diem to Avoid Collateral Damage

Dec 21 2017

Posted In:

General, Parents, Policy Makers, Researchers, Teacher Educators, Teachers

By Herbert P. Ginsburg, Columbia Teachers College

We know that effective early math education (EME) lays the foundation for long-term educational success. As we attempt to develop and implement quality EME, we need to be aware that our well-intentioned efforts may result in unintended and harmful outcomes: pushdown curriculum; teaching to the test; misunderstanding of the Common Core Standards; uninformative evaluation; anxious and ineffective teachers; confused parents; and, most importantly, blindness to the present. Understanding these instances of “collateral damage” helps us avoid them and create the conditions for high-quality EME.

Pushdown Curriculum

Early childhood teachers—and many others, including school administrators—may assume that math can be taught only through direct instruction. After all, this approach is probably what they experienced in school. The typical outcome of this view is the “pushdown curriculum” in which preschoolers are subjected to drill and practice on number facts and the like. This is a mistake. Direct instruction of this type does not work well. It stifles thinking and poisons the excitement that can characterize math learning.

Teaching to the Test

This is a ubiquitous and unfortunate practice in education at all levels. Many readers no doubt have observed elementary school teachers suspend regular instruction in April or May to prepare children for standardized district-wide tests. Fortunately, preschool is spared this kind of testing. But be alert! Standard tests, along with a pushdown curriculum, can result in teaching those limited aspects of mathematics that can be easily measured, like recall of number facts, as opposed to fostering the kind of mathematical understanding and excitement that standard tests cannot accurately measure.

Misunderstanding of the Common Core Standards

The Standards were intended to provide aspirational goals, not a curriculum. The Standards for kindergarten (and state standards for younger children) point to developmentally-appropriate concepts and skills that EME should foster, but do not mandate or explain how to do so (Clements, Fuson, & Sarama, 2017). As a result, implementing the standards is not an easy task, and will fail without extensive professional development in intentional teaching and a rich curriculum.

Uninformative Evaluation

Evaluation of specific EME programs is an educational, scientific, and moral imperative. Clearly we need to determine whether our efforts to promote children’s math learning are successful, and if not, to improve them. The problem is the nature and quality of the evaluation. Young children are notoriously difficult to test; their performance can be variable and unstable; standard tests may not effectively measure important aspects of their knowledge (as opposed to their superficial performance) and motivation (like excited engagement); and the evaluations are usually not designed to provide, and do not provide, actionable knowledge on how to improve the program under consideration.

Anxious and Ineffective Teachers

Preschool teachers often do not want to teach math and have been poorly trained to do so. As a result, they may transmit their math anxiety to the students whom they are tasked to teach. Curricula are not and should not be teacher-proof. Their success depends on knowledgeable, confident, and skilled educators.

Confused Parents

Parents naturally want the best for their children. But not knowing how to promote math learning, parents may employ mind-numbing workbooks that can be obtained at various commercial outlets, and may then quiz children on number facts. Successful implementation of EME requires parent education as well as teacher professional development in order to make sure that young children experience rich and engaging early math.

Blindness to the Present

Finally, we need to keep in mind and honor John Dewey’s (1938) admonition: “When preparation is made the controlling end, then the potentialities of the present are sacrificed to a suppositious future” (p. 49).

Schooling for young children should be improved and made widely available simply because it is a good in itself, whether or not it increases the probability of later academic success. Regardless of what happens later, do we want to have children sitting at home in front of a television or playing digital games all day, as opposed to participating in a stimulating preschool or kindergarten program?

Throughout the grades, we should always keep our eyes on the children we serve at the present moment. What can we do to promote their learning now? What captures their interests and imaginations now? Is our teaching fruitful now? What do they understand and fail to understand now? If we focus on the future, we may not see and nurture what is in front of us, namely children’s informal understanding and enjoyment of math.

The next question is this. Keeping these pitfalls in mind, how can we exploit the potentialities of the present? The answers are straightforward but require great effort and adequate resources to implement.

  • Train adequately-paid teachers to employ a playful math curriculum covering the topics advocated by the standards. Provide ongoing and frequent professional development to help teachers understand the curriculum and children’s learning, and to overcome teachers’ math anxiety.
  • Develop materials to help parents understand EME and contribute to it in a relaxed and enjoyable manner.
  • Train teachers to make extensive use of formative assessment—clinical interviews and observation—designed to uncover children’s thinking and interests and to suggest intentional teaching for the individual child. Standard tests should play a limited role in EME.
  • Evaluate a program of EME by . . . Whoops, no straightforward answer. Stay tuned.

Herbert P. Ginsburg is the Jacob H. Schiff Professor of Psychology and Education at Teachers College, Columbia, and a member of DREME's Parent and Early Caregiver Engagement in Math project and Early Math Resources for Teacher Educators project.

Reference

Clements, D. H., Fuson, K. C., & Sarama, J. (2017). The research-based balance in early childhood mathematics: A response to Common Core criticisms. Early Childhood Research Quarterly, 40, 150-162

Dewey, J. (1938). Experience and education. New York: Collier Books.

Herbert P. Ginsburg
Herbert P. Ginsburg is the Jacob F. Schiff Professor of Psychology and Education at Teachers College, Columbia University.

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