© 1996: The University of Newcastle: Faculty of Education
A graduated help facility
Figure 4: Nomi's OperationsThe graduated help facility is based upon Wood's (1986) "levels of control", as outlined earlier. Consider the simple software tool developed by the author using HyperCard on the Macintosh as a means for his ten year old daughter to practise her algorithms (Figure 4). The emphasis was to be upon the process, in such a way that any errors would be highlighted where they occurred and support was given throughout the sequence of activities. The format was intended to simulate the way in which the procedures were to be carried out using pen-and-paper. Note the use of bold style to draw attention to the current part of the process (in this case, adding 4 and 7). The student enters the two-digit sum as it occurs (as "11"); upon pressing the ENTER key, the tens digit is transferred to the next place, under the 3. Use of the technology supports and leads naturally to traditional methods. Naomi was assisted to navigate across the zone of proximal development, supported in learning the process, but then encouraged to continue alone and unaided. As any experienced teacher knows, it is not difficult to support students in their learning. The challenge lies in knowing when to withdraw that support. Too soon, and the learner becomes frustrated, too late and independence is stifled. The scaffolding offered by technology must be constructed in such a way as to offer adequate support without encouraging dependence on the part of the learner.
These principles may be applied directly to mathematical problem situations using Wood's (1986) model of contingent learning. The following sample problems illustrate ways in which this might be accomplished for a range of age and ability levels.
A structured solution format.
The restaurant problem.
Last updated: 1st May, 1996
Stephen Arnold
crsma@cc.newcastle.edu.au
© 1996 The University of Newcastle
© 1996: The University of Newcastle: Faculty of Education