Wichita State University Wichita. KS 67208
Pictorial Problem-Solving Networks Robin E. L. Waddling Falmauth School Cornwall, England
In a previous article we reported the use of a routine nroblem-solvine network that bas been used to enable stuhents to masteFtitration calculations ( I ) . In this article we shall discuss how problem-solving networks can be incorporated into courses, and report on the development of a new stvle of oictorial network that can assist students in the handlingof experimental data. Problem-Solving Networks Students who have not yet learned to cope adequately with formal operations are unable to select the appropriate pieces of data required to perform calculations. For these students the perceived difficulty of such problems is large. Problem-solving networks can train students in the methodology of logical thinking by listing, in a systematic manner, the desired actions that must he executed in order to obtain a solution. Three stages in the learning of a skill have been identified (2). There is an initial ohase or cognitive stage when the learner is instructed in the task. TI&knowledge or understanding acquired in this stage is usually inadequate for skilled performance. Then follows an associative stage when errors in initial understanding are corrected and connections between the various separate elements required for a successful performance are strengthened. In the final autonomous staee. - , the learner's facilitv in the skill increases. and the desired procedure becomes more automatic. Problem-solvine networks assist the learner to oass through all these stages of learning and lo achieve competence in performing the skill or task. 11is also possible t o use the problem-solving network as a reaching reiource tu support the iirst, cognitive stage of learning. Networks can he used asa basis for the discussion of the underlying principles when introducing a new section of work.
find the chemical formula
I calculate the formula mass I
lncorporatlng Problem-Solvlng Networks Into a Course The introduction of simple oroblem-solvine networks at an early stage of a course increases the student's confidence to use this approach to develop problem-solving skills. In narticular. this techniaue has worked well with mature students attending adult ;ducation evening classes even though thev are less familiar with a flow diaeram mesentation. dalculations involving the compos%ionof compounds and the determination of chemical formulas make a eood starting point. Students can usually easily master percentage composition calculations, and the problem-solving network (Fig. 1) is readily accepted by the student as being a representation of the steps required to complete the calculation. Students tend to find the reverse process of calculating empirical formulas to be more difficult. Such calculations demand a high level of conceptual development, approximatine the 3B or late formal ooerational staee in Piaeet's arrangement of cognitive deveiopment (3). The prohiemsolving network (Fig. 2) has been usefully employed in assisting students to master calculations when given the mass of each element present in a sample of a compound. The Use ol Pictures We have found that students can develop skills to deal with chemical calculations more easily by using a flow chart nresentation than bv iust listine the stens in a series of humbered sentences: w e helievethat the'incorporation of oictures further aids the student in the comnrehension and long-term recall of the material. For example, i t has been demonstrated that pictures are learned faster than words in serial anticipation tasks ( 4 ) , and it has been suggested that when a nonlinguistic representation is encoded, the representation is richer for pictures than for words (5).It has been shown that the ability of children to recall both pictorial and nonpictorial information from a previously presented passage is enhanced if that passage is accompanied by black line drawines. Furthermore. oictures were found to enhance recall evenuwhen they were not required for interpretive purposes (6). I t appears that when the input stimulus is a picture, distinctive clues may be available that add to the representation that is stored by the students. Pictures seem to improve
I \\'hat is the percenlarc
UI
clement present'!
.1
for one of the elements, calculate the total mass present
What is the mass of each element if you have 100 g of the sample?
percentage of element = total mass of element present X 100 formula mass
Calculate the number of moles of each element present. mass of element atomic mass
4
).
reoeat for other elements Figure 1. Calculating percentage composition.
260
Journal of Chemical Education
1
1 Di\,ide hy the -mi~llritnumber t u get the emr~~rical lormula. Figure 2. Calculating empirical formulas
I
weigh
Calculate the number of moles of Mg used: mass No. of moles = 24
mass of magnesium used.
weigh magnesium
Compare the number of moles of each element. Divide by the smaller.
, oxidize
p,
w
I
\
+ cool and weigh
( .,'
I',
Calculate mass of oxygen that combines with magnesium.
Calculate the number of moles of oxygen: No. of moles = 16
Figure 3. Finding Me formula of magnesium oxide
long-term understanding, making use of a student's longterm memorv store or coenitivelv inteerated network of propositions 77). I t has alsobeen suigestei that the presence of pictures promotes semantic elaboration of the material Using Pictorial Networks
The determination of the empirical formulas of oxides using the oxidation of magnesium and reduction of copper (11) oxide as examples is common to many practical courses. Although students may have developed the necessary skills to perform empirical formula calculations, many still experience a ereat deal of difficultv in dealing with their exnerimental>esults. The student is often unable to select' the appropriate pieces of data and to use them in the correct order. Some texts andteachers' worksheets get around this problem by labelling the different weighings with code letters. The student is then instructed to subtract the appropriate values. This surely must be of limited educational value. Instead we have found that the merger of practical details, and the inclusion of pictures, into problem-solvingnetworks
can be both attractive and highly motivating to the student. Two such networks are shown in Figures 3 and 4. The practical details are summarized in a vertical flow diagram in which dotted lines are used to indicate how the appropriate data can be extracted from the experimental procedure. The calculations are set out horizontally and can reveal to the student when similar procedures are followed. In practice, this new style of problem-solving network can be displayed on an overhead projector while the class performs the experiment and the subsequent calculations. Such networks enable teachers and students to refer back to experimental procedures and also make it easier for the student to visualize how a particular result was obtained, thus overcoming any difficulties associated with data selection. In the case of the determination of the formula of magnesium oxide (Fig. 3), the mass of metal used can be readily calculated. The mass of oxygen combining with the metal can be derived once the student appreciates that this is equal to the increase in mass of the crucible and magnesium. The copper(I1) oxide experiment is complicated by the fact that the final weighing is used to calculate the mass of both elements in the compound. Without this guidance,
weigh
*.
1~a I. .. copper oxi e
'\I
Calculate the mass of copper in the copper oxide.
1
I
, I
Calculate the number of moles of copper = mass -
I
64
/
Compare the number of moles of each element. Divide by the smallest
Reduce I I
Hz
,,
I
1
,
*
Calculate the mass of oxygen in the copper oxide.
I
Calculate the number of moles of oxygen = mass 16
I
Figure 4. Finding the formula of copper axi&
Volume 65
Number 3
March 1988
26 1
some students may attempt more complex, and unnecessary, manipulations of the data.
develop cognitive skills and can greatly reduce their perceived difficulty of the subject.
Conclusions Chemistry teachers must not only impart factual knowledge to their students but must also help them to develop skills in thinking creatively and having the confidence to analyze data, The use of pictorial problem-solving networks and longappears to assist students in the term recall of procedures. Their use encourages students
Literature Cited
282
Journal of Chemical Education
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