Product Description: This book offers clear proof of what can happen when the system is allowed to function at its best. You will see how remarkable teaching and learning, and unprecedented parental involvement, are putting an end to 'mathphobia.'
Conceptual Math No Longer a Mystery! In this book, Susan Ohanian poses some intriguing questions: If we believe in the importance of mathematics, why don't we practice what we preach? Why do we stop taking math courses as soon as we can? She believes that the first issue is that academic attitudes, both positive and negative, come from parents, and "a whole lot of parents have negative attitudes about mathematics". Secondly, teachers pass their own math anxieties on to their students whether they realize it or not. Additionally, many are overwhelmed by the enormity of the task of accomplishing change. It's not enough to come up with good ideas or the newest technology. The bottom line will still be that each individual student needs a smart and sensitive teacher "reacting and prodding and shifting and altering and inspiring". The author maintains that successful schools need to offer courses that develop the mathematical understanding of their staff first, then let the teachers do their jobs.
In 1989, the Curriculum and Evaluation Standards for School Mathematics was published by the National Council of Teachers of Mathematics (NCTM), creating a vision of what mathematical competence should look like as well as outlining a set of goals to guide educators in revising the curriculum. These standards recommended less emphasis on complex pencil-and-paper calculations and more emphasis on making sense of numerical operations, less focus on solitary rote memorization of math facts and rules and more focus on learning to work cooperatively with concrete, manipulative materials, less emphasis on single-answer, one-method problems, and more emphasis on the ability to explain mathematical thinking and writing. This development placed the responsibility for what was achieved in the classroom squarely on the teacher, who would need to be an informed, specialized professional in mathematics in order to effectively implement this plan.
Over the past two decades, there has been increased interest in the many facets of intelligence, which demonstrates that people attack real-life problems in a variety of ways, according to their own unique wiring, their own individual strengths and weaknesses. Even preschoolers have been found to have their own "working styles". Teachers are placed in an unenviable position as they are faced with contradictory expectations. They are expected to observe children's spontaneous behavior and then document skills and attitudes which relate to initiation of ideas, persistence, confidence, introspection, cooperation, and response to frustration in an attempt to nurture each child's unique working style for optimal learning; however, at the same time, the public demands standardized test results, which insist that all children must develop along a set continuum, regardless of learning differences.
This book is the result of a project funded by the Exxon corporation, in which teachers were trained as math specialists, linked up with mentors and colleagues in a supportive network, and then challenged to teach math concepts and skills according to this new, non-traditional method, which asserts that for deep-seated, functional learning, children cannot be taught mathematical processes; they need to discover and invent these processes in an environment created by the teacher. Using these strategies, children as young as first grade are empowered to understand basic mathematical functions using patterns, to develop their own word problems and problem-solving techniques related to real-life situations using activities such as creating measurements, graphs, and Venn diagrams. But this type of teaching is not for the meek or lazy. It requires intensive learning on the part of the teacher, and an ongoing interactive process.
Using the methods recommended in this book, teachers are trained to present problems that enable students of varying skill levels to invent a range of strategies for solving the problem. Part of this process involves the teacher's seeking insight into how each child approaches the problem, which will then determine how the teacher structures her subsequent problems. It is more important to zero in on student strategies than it is to check that the answer is "right". Students are encouraged to work together, to share ideas, so that they learn there is more than one way to view a problem. This method empowers students to be risk-takers and provides ample opportunity for the teacher to make informal assessments.
An example of the process might be along these lines: Initially, students are given a problem, perhaps in a story format. The teacher may elect to write some of the basic information on the board to review the main facts, identify the question, and make them accessible for the children to think about. She may ask questions not related to this particular problem to encourage students who are able to think in larger terms, such as "What other things can you think of that would be difficult to measure?" Often students are given an opportunity to estimate what the correct answer will be before they begin solving. Students work with a partner or in a group, discussing the problem to ensure that they understand all of its parts. Next, they discuss how to solve the problem, and how they will share the work of communicating their findings on paper. Follow up discussion focuses on how close people's guesses were to the final answer, what type of collaborative efforts were used, and groups are given the opportunity to convince their classmates that their answer is reasonable and/or correct. They display their written work and drawings to illustrate their meaning. Students are also required to keep "math journals" discussing what they have learned and how the discovery was made. The author quotes Marilyn Burns in claiming that "a good mathematics lesson is never finished; it offers lots of possibilities". Pivotal to this technique is the teacher's wisdom in holding back the answers so that the students can enjoy their "eureka!" moments, instilling a love for thinking, for questioning, for discovery, and for learning mathematics.
On the other hand, I don't agree with the author that standardized tests are "insanity". I think they have their place in providing a snapshot of where a student's learning skills are most likely to be at a given point in time. They provide valuable data over time, demonstrating student progress in specific skill areas. As a speech/language pathologist, I also utilize standardize tests to precisely determine areas of deficit, so that goals are functional in addressing the individual's needs. What I do think is "insanity" is when parents, teachers, or administrators consider their children's scores on standardized tests such as the SAT to be the ultimate goal of education. Otherwise, I think the information in this book has a lot to offer students in teaching students from a young age to have inquisitive, healthy minds and to love to learn.
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