AWM Book Review:
From: AWM Newsletter, January/February 2000.
Reviewed by: Bridget Arvold, Department of Curriculum and Instruction, College of Education, University of Illinois at Urbana/Champaign, Champaign IL 61820; email: email@example.com.
Many reports and articles lead Americans to believe that mathematics education in the United States is a sad state of affairs. Textbook publishers, program developers, teachers, and teacher educators have become targets for attack. In _Math Power: How to Help Your Child Love Math, Even If You Don't_, Patricia Clark Kenschaft not only offers her perspective on a plethora of issues in mathematics education but invites parents to become involved in their children's mathematics education. She addresses parents "who are willing to play with math for the sake of their children." Kenschaft is motivated by her work with children and her concern for the future of mathematics. "As real mathematics struggles for survival in our culture," Kenschaft writes, "it becomes increasingly urgent that parents share real mathematics with their children." She describes Math Power as a guide to parents who, as she noted, "may or may not possess 'mathematical minds.'"
Kenschaft shares her perspectives on the nature and value of mathematics, and on mathematical ability and development. In some cases, however, her incorporation of outside perspectives confuses rather than clarifies matters. She emphasizes the need for parental involvement in the school community and urges parents to promote enjoyable mathematical experiences at home. She suggests that parents help their children view failure and frustration as a natural part of learning. Although the mixed messages about the enjoyable and frustrating nature of doing mathematics might confuse some readers, her messages speak to the complexity of learning mathematics.
Kenschaft reveals how her teaching experiences brought her to the realization that the basics of school mathematics often leave children confused. Her involvement with PRIMES, the Project for Resourceful Instruction in Mathematics in the Elementary School, provided her with insights into early childhood education. She describes the nature of context-free mathematics terminology and shares her feelings: "Pity the poor children trying to figure out the meaning of basic mathematical words." Her frustration spilled over into her graduate level classes and became an important topic of discussion there. Convinced of the power of understanding the basic concepts in mathematics, she pours her convictions about developing math power into this resource for parents.
Although Kenschaft supports the organizational and relational nature of mathematics, her book focuses on coping with conventional school mathematics and downplays mathematical enjoyment. Statements such as, "You must have a resilient ego to live with yourself while learning math" reflect little of the natural "enjoyment" she claims as necessary in parent-child activities. Remarks like, "The U.S. system is so unreliable, we must give our children every possible advantage to endure it," reveal her feelings of frustration with the present system. Parents, especially those who were unsuccessful with school mathematics, might trust the author and follow the suggestions to make their children "smart kids." But they are likely to be confused by messages such as, "Simple math is harder than you thought," and "We all learn that failure is inevitable - but followed by success." While such statements might be true within given contexts, the mixed messages they offer parents may be debilitating. In her effort to help parents thwart children's confusion, she may also incite parental confusion.
The mathematics education literature offers a host of rationales for supporting early mathematical development. Turback (1999) shares a biological research perspective that posits that although babies may be born with neural wiring, most connections form during infancy and childhood. He adds that even while in the womb, humans begin to build connections that form the foundation of language. Moreover, he reports that the analysis of data collected from monitoring human brain activity indicates that specific types of connections are made within small time periods. Findings suggest that if children are not appropriately stimulated during this time, they may never be able to learn a specific concept or skill. From these findings, we might hypothesize that the foundations for the language of mathematics are also formed in a child's earliest years and therefore parental nurturing is crucial to their mathematical development.
In The Language Instinct, Steven Pinker (1994) describes language not as a cultural artifact that is learned --- as, for example, we learn to tell time --- but as a distinct piece of our biological makeup. From this perspective, mathematical language is integral to our very being and complements a natural penchant for organization and inquiry. Pinker adds that much of formative human experience relies on touch, sound, and sight. Thus the construction of the language of mathematics might be enhanced by distinguishing shapes by touching, hearing the cadences of number patterns, and noting similarities and differences. Kenschaft incorporates such approaches to language acquisition --- despite the fact that her perspective on child development is quite different from Pinker's. For example, she believes that newborns are filled with mathematical potential at birth and that diminished potential is due to our corruptive culture. Thus Kenschaft provides parents with a quite different basis for creating a positive learning environment for their children.
Although books of elementary mathematics activities abound, relatively few authors direct attention toward helping parents nurture the mathematical development of their children. Kenschaft approaches this task by focusing on preparation for conventional school mathematics activities. A focus on counting and recognition of number patterns and polygonal shapes, for instance, offers children cultural artifacts that prepare them for conventional school activities. Kenschaft's suggested activities connect to children's worlds, but few build from children's worlds or their parents' worlds. Such building is based on fundamental mental and intuitive processes that are distinct pieces of a child's biological makeup. For example, enhancing story time with children's mathematics literature (see Bresser 1995; Burns 1992) provides parents with subtle ways to expand children's ways of thinking. The mathematics within existing family practices provides learning opportunities for both children and parents.
In a description of mathematics programs involving parents, Kliman (1999) suggests that adults build from natural mathematical processes that are often hidden from view. She describes how the matching and sorting that accompany laundry chores can serve as a basis for subtle mathematical discussion. Kliman, like Kenschaft, promotes skill and concept development --- but Kliman emphasizes relational thinking, reasoning, and problem solving as embedded within story time, outdoor activities, road trips, and household chores rather than as additions to existing activities. Yet both approaches offer parents and children opportunities for extending themselves mathematically.
Descriptive accounts of parents' experiences with a child's mathematics --- although lengthy --- might better enable parents to foster mathematical development. For example, when my three-year old daughter Trina voiced her wonderment about how we would share ten dinner rolls among the four at the table, we asked her to distribute the rolls for us. She passed one roll to each person and then another to each. She broke each of the two remaining rolls into two pieces, and distributed the pieces equally among us. She smiled widely as she declared that we each received "two and a half rolls so we each got the same." My amazement only grew when five-year old Erica piped in with, "No, we did not get the same amount. Actually, I don't have two and a half because halves must be the same size and my half is bigger that your half." She immediately realized that the very words she had spoken, "my half is bigger than your half," contradicted her message and she broke out in a laughter that was contagious.
The messages that parents might accord to this short account are numerous. Parents might learn a strategy for division. They might realize the power of language and children's ability to communicate and think abstractly. Child-initiated mathematical activities are well worth the attention of parents and simple analysis of children's dialogue might help parents learn to recognize and make the most of possible learning situations.
The belief that a young child constructs meaning has prompted the recent focus on student engagement in reasoning, problem solving, making connections and communicating mathematically (NCTM, 1989, 1999). Although Kenschaft uses a riddle and a description of a game called 7-Up to highlight these process standards, her mention of these areas of cognitive and social development is far too brief to adequately prepare parents to ready their children for the classrooms of today. She might have relegated what she termed her "tirade" to a separate publication rather than including it in a motivational guide to parents. Nonetheless, Math Power incites parents to become involved in their children's education and offers them insights into how they might help their children. In this sense, it provides a much needed resource for parents.Works cited:
Bresser, R. (1995). Math and Literature (4-6). White Plains, NY: Math Solutions Publications.
Burns, M. (1992). Math and Literature (K-3). White Plains, NY: Math Solutions Publications.
Kliman, M. (1999). "Beyond Helping with Homework: Parents and Children Doing Mathematics at Home." Teaching Children Mathematics 6, (3), 140-146.
National Council of Teachers of Mathematics (NCTM). (1999). Principles and Standards for School Mathematics, draft for 2000. Reston, VA: NCTM.
National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and Evaluation Standards for School Mathematics. Reston, VA: NCTM.
Pinker, S. (1994). The Language Instinct. New York: William Morrow.
Turbak, G. (1999). "Tomorrow's Brainchild, Part One: The First Years Last Forever." Kiwanis 84 (1), 26-29, 50-51.