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Posted by: Topic: Message: In the wake of the Third International Mathematics and Science Study (TIMSS) report, in which the United States placed so poorly in relation to students from other countries, mathematics educators are indeed facing critical issues on many fronts. Some of these issues in problem solving stem from a misunderstanding of exactly what is involved in the process. For a simple example, in a problem like 38 + 26, if a first grader adds 30 + 20 to get 50, and 8 + 6 to get 14, then adds 50 + 10 + 4 to get 64, the first grader is problem solving. On the other hand, if an eighth grader simply adds and carries according to the traditional algorithm, that student is not problem solving. Too many times, plugging numbers into a formula is considered to be problem solving. Because students are so often given formulas rather than asked to develop their own formulas, they often lack problem-solving skills.
Technology tools, such as calculators, can advance the notion that mathematics is about formulas and plugging in numbers, if these tools are viewed exclusively as a means for checking answers. And, even if calculators and computers are used in a teaching situation, they are often removed in testing situations, as if they are an added bonus rather than an integral part of the teaching and learning process.
However, calculators and computers can definitely aid in the teaching and learning of mathematics, if they are used in appropriate ways. (This, of course, gets into professional development issues, as well.) If one can skip the tedious number crunching when looking at an overall concept, concept formation can be enhanced.
The above-mentioned problems with problem solving and technology also impact assessment issues. If the mathematical, problem-solving process is not valued, then assessment often consists of single-answers in a testing situation. In these cases, technology is often deemed inappropriate. Open-ended questions, process-oriented questions, problem-solving activities, and technology-based activities are often not part of assessment.
Oral and written communication should be an ongoing part of assessment to determine if students are thinking deeply or are only skimming the surface of the mathematics. Underlying all of the problem solving, technology, and assessment issues is a general philosophy of the nature of mathematics and the nature of teaching and learning.
Changing philosophies takes time. Teachers must be allowed time for professional development and must be allowed time for new ideas to be nurtured and developed. Rarely are teachers given the time and mentoring needed for change to take place. Rather, they are often given materials and resources and then left to their own devices as to how to fit those materials into an already packed curriculum program.
Professional development opportunities occur in small time slots, and implementation is assumed to be quickly forthcoming. In my own life, change has come in small, steady increments; and professional development opportunities have been the most beneficial, when I have been immersed in them and have then had time to discuss and revise with colleagues.
The above-mentioned are some of the critical issues I see facing education today. Are students allowed to problem solve? Are they assessed in a way that encourages problem solving? Is technology used in a way that enhances problem solving? And, are teachers given professional development opportunities to encourage change in these areas? To reply, please first log into The Knowledge Loom |
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