Using Part-Whole Thinking in Math
The article, "Using Part-Whole Thinking in Math" by Dorothea Steinke, discusses the importance of teaching students this approach to understanding mathematics. The article provides statistical data documenting the improved GED Math test scores of students at the West Side Learning Lab in Denver after using the part-whole thinking approach when teaching mathematics. During the past two years while using this method, the center has seen 92 percent of their students pass the GED math test on their first try. This compares to a 50 percent pass rate with repeated attempts before using the part-whole method.
The part-whole method is discussed in detail in the article. The author provides both written examples and diagrams illustrating the concept. The case is made that without understanding part-whole thinking, students have greater difficulty with problem solving and mental math.
Research on the difficulty children have with part-whole understanding is also cited. In addition, commonly missed numeracy items found on The 1992 National Adult Literacy Survey and the Test of Adult Basic Education (TABE) were analyzed for evidence of a lack of part-whole understanding.
Current numeracy materials assume an understanding of part-whole relationships. The article discusses in detail a number of ways to help students develop part-whole understanding. The examples discussed are from a numeracy math book being developed by the author, and they increase in difficulty as the discussion progresses. Again, the author includes detailed descriptions and diagrams. The author makes a strong case for the importance of teaching students part-whole thinking as a way to improve their problem solving abilities and increase their mathematical understanding.
I am not sure that this can be such an all-sweeping approach to mathematical instruction. While this model does offer students another way of solving word problems, as the author describes, I am not sure that this can be such an all-sweeping approach to mathematical instruction.
The author describes the efficacy of this method in terms of it helping adult learners gain higher scores on the General Educational Development (GED) math test. I would be interested in other measures of its success as a tool with which "…to develop and retain an integrated and functional grasp of mathematical ideas. " (See Ginsburg, Designing Instruction with the Components of Numeracy in Mind) The author states that she knows the part-whole model is working for her students because she sees "…the eyes go wide and hear the inadvertent "Ohhh" of understanding escape from lips." Perhaps this article can be augmented by other literature which carefully assesses the success of this approach, if such studies exist.
That said, there are useful features to this article. The author describes misunderstanding of the meaning of the equal sign, and gives a concrete example of its true role as describing relationship, not "right answer". The author also describes her success in using the phrase, "Different name, same thing" when talking about these mathematical relationships. The author also describes the successive stages of mathematical understanding from the concrete, through representative, (and perhaps) to the abstract. Her examples of part-whole thinking are intriguing.
Finally, this author provides a good model of a classroom instructor who is always exploring ways in which to make meaning of mathematics. Her interest in improving teaching and learning is obvious, and she provides the reader with things to think about, and try.
After reading Steinke's article, I found myself noticing many of the part/whole problems sited in her article with students in my classroom. However, in visiting her webpage, the sample pages seem like the thinking is already done for the student. However, I think many adult education practitioners still would benefit from Steinke's research and at least, build an awareness of the part/whole problems their students might be struggling with.
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