Spatial Orientation

ARTICLE:  Spatial orientation skill and mathematical problem solving...Lindsay Ann Tartre, California State University, Long Beach.

SOURCE:  Journal for Research in Mathematics Education March 1990, Vol. 21, No. 3, 216-229

A review by Claude H. A. Simpson, Nova Southeastern University.

Studies in the specialized field of mathematics all portray one thing in common, and that is, the importance of the subject.  Mathematics is a way of life and presents itself all around us; therefore, everything we see, say or do has much mathematics about it. The volume of mathematics is infinitely large and so there is always room for change of teaching strategies for the benefit of the learners, room for deduction for simplification purposes and room for invention or discovery.  For this reason the learning of mathematics is "key" in this changing, scientific and technological age. 

Every single human-being is born with an intuition to learn. Spatialness as we know, comes to the child by:- playing with toys and other objects; observing roundness, flatness, size in terms of big or small, length in terms of long or short and general space awareness.  As time goes by the child conceptualizes these properties which will eventually leads the child to solve simple problems.  Many children have feelings of anxiety and feel incapable of performing mathematical tasks.  According to Stodolsky (1985), instruction has been cited as the major factor to this problem.  Grouws and Good (1989) argued that for students to gain competence in problem solving then one main issue must be addressed and that is the teaching of lessons that focus on PROBLEM SOLVING as a topic.

If the current mathematics education reform is to have a significant impact on the mathematical development of students, then, the mathematical understandings encompassed by problem solving are paramount. Not only is mathematical problem solving important in the modeling of real world situations, but it forms the basis for student to function effectively in other subject areas. What exactly is problem solving? According to the National Council of Teachers in Mathematics (1991), problem solving is the process by which students experience the power of usefulness of mathematics in the world around them. It is also a method of inquiry and application, interwoven throughout the standards to provide a consistent context for learning and applying mathematics.  Problem situations can establish a "need to know" and foster the motivation for the development of concepts.          

SPATIAL ORIENTATION SKILL AND MATHEMATICAL PROBLEM SOLVING
provides the reader with a useful compilation of much of the important recent research in this field. In describing some of the strengths of this article, I will discuss not only why the article makes an important contribution to understanding the role of spatial orientation skill in the solution of mathematics problem, but also why it serves as an important mathematics education research more generally. I now summarize the strong nature of this work in the following points:

⦁      The author first cites various research to emphasize that for effective mathematics learning and achievement then students spatial skills must be a priority. The author cites many studies that have found spatial studies to be positively correlated with measures of mathematics performance.  This is important with respect to the usefulness of the author's research endeavor as a whole.

⦁          The relationship of theory and empirical work is explicit and the author cites research of other work done to support the existence of spatial ability.  According to the author, McGee (1979) distinguished two major types of spatial skills: visualization and orientation. This of course categorizes the spatial skills.

⦁          The author defines quite clearly what is SPATIAL VISUALIZATION and what is SPATIAL ORIENTATION and this set of definitions helps the reader to conceptualize the differences.  The author's argument was further substantiated with research as cited.  An important contribution according to the author is that of Bishop (1980) who theorized that spatial training might help students to organize a situation with mental pictures during problem solving in mathematics.  This would give rise to the frequent use of tree diagrams, Venn diagram, charts, and other figures.  This is a "positive" in order to use pictures to help in solving problems.

⦁          The work represented by the author's research reflects the real importance of focusing on students' mathematical thinking because certainly, the various research cited by the author in the article stand to show that students success in mathematical problem solving hinged strongly on students spatial orientation skills.

⦁          To reaffirm and consolidate the issue that spatial orientation skill determines how well students are capable and efficient in solving mathematics problems; the author's research article capitalizes on a means of "alternative assessment" using spatial orientation measure (The Gestalt Completion Test) pictorial form; Problem- solving Interview and Observation.  The author states that the Gestalt Completion Test has not been used as much as other tests recently in mathematics education research, possibly because spatial visualization has been studied more and because it is so difficult to describe the process or processes used to solve it.

I give credit to the author for utilizing a most intuitive or insightful spatial organizational process in the research to illustrate ways in which students scoring high or low in spatial orientation skill behaved differently as they solved mathematical problems.

The introduction of the ARTICLE is followed by definition of spatial skills and research that are cited.  The next section deals with the study, outlined in the format:

1•          Method - (Sample, Spatial Orientation Measure, Problem Solving Interview, Interview Procedures and Coding Categories).

2.    Results - Tables to illustrate Means and Standard Deviation of Categories.


3. Discussion of Results and Conclusions.

On the issue of spatial skills and mathematics; The author claimed that spatial skills may be intellectually interesting in themselves but the author was more inclined to attempt to understand part of the nature of the relationship between spatial skills and mathematics. The author posed these two questions:
⦁           Do we use individual spatial skills in specific and identifiable ways to do mathematics?
⦁          Do spatial skills serve as general indicators of a way of organizing information that may help solve many types of mathematics problems?

According to the author many people have speculated about how spatial skills and mathematics might be related and how much research have attempted to identify specific processes used to solve mathematics problems that might be related to spatial skills.

The article highlighted that when the students studied were asked to draw pictures to solve mathematical problems.  These students with low spatial visualization and high verbal skills tend to provide more detailed verbal descriptions of the relevant information in the problems.  However, students with high spatial visualization skill and low verbal skill had more detailed information on picture for problem solved correctly.
The author cited various researchers to bring home the point that spatial skills are general indicators of mentally organizing information for problem solving.

As I conclude this review I realize that the only likely weakness of this article is probably the fact that it needs a little more scope and depth on the cognitive aspect of spatial visualization, spatial orientation and a  step  by  step process of mathematics problem-solving. Hence  to  be  used  as a  tool  for mathematics education.

My closing thought concerns the potential readers of this article.  It portrays a balance between spatial skills and the mathematical problem solving skills.  For instance, it may be that different levels of spatial ability affect students' problem-solving strategies.  Hence a student high in spatial ability and low in verbal ability may tend to use a spatial strategy quite frequently, whereas a student high or low in both (spatial or verbal) abilities might exhibit much more variability in strategy use. This balance or discrepancy may be a key variable in investigating students' problem-solving abilities and strategies especially in the geometric domain.

Finally I wish to conclude that the article is rather informative and those who are directly involved in research in Spatialness re- geometry/mathematics would find the article not only informative but also useful in providing models of effective mathematics education research.

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References

Grouws, Douglas A., & Good, Thomas L. (1989 April).
Issues in Problem-Solving Instruction.  Arithmetic Teacher, 34-35.

National Council of Teachers of Mathematics.  (1991).  Professional Standards for Teaching Mathematics.
Virginia: The National Council of Teachers of Mathematics, Inc.

Stodolsky, Susan. (1985). Telling Math:  Origins of Math
Aversions and Anxiety.  Educational Psychologist,Vol. 20, No. 3.