Many children who are dyslexic also experience difficulties in arithmetic. This is partly because they struggle to read the arithmetic questions. In addition, however, some of them have comprehension problems, that is, even when the problem is read out to them, they cannot understand it. This indicates a deficit in simultaneous processing, the same cognitive process that is involved in word comprehension.
Comprehension is essential for problem solving in arithmetic; the child cannot choose the correct steps to find the solution unless he or she understands what the problem is. Another requirement for problem solving is planning. Because arithmetical computation has to be executed step-by-step, planning is required, first, to understand the link between the meaning of the problem and the steps that are necessary to solve it and, second, to execute those steps.
It is important, therefore, to distinguish between those whose main problem is comprehension and those whose main problem is planning. It should be mentioned that comprehension may be aided by presenting the problem in more than one way—for example, by using pictures and graphics in addition to explaining the problem in words.
Is it possible, then, to construct a program for boosting the planning process? Such a program would be linked to PREP, but its emphasis would be on planning and its prerequisite, that is, attention.
A beginning has been made (Naglieri and Das, 1997). The following research study was conducted by Naglieri and Gottling (1997). It used prompts and strategies to improve children’s arithmetical problem-solving skills. Children who were weakest in planning were expected to benefit most from the training procedure, and that is exactly what the research showed.
Facilitating the Planning Process: A Study on Arithmetic Remediation
The relationship between planning and instruction was closely examined in a series of research papers beginning with Cromier, Carlson, and Das (1990) and Kar, Dash, Das, and Carlson (1992). The researchers developed a method that stimulated children’s use of planning and had positive effects on their performance. This method was based on the assumption that the children’s use of planning processes should be facilitated by prompts and by exposure to strategies rather than by direct instruction—the same assumption on which PREP is based.
These studies were used as a basis for two applied investigations by Naglieri and Gottling (1997) and also Naglieri and Johnson (2000). Both these investigations demonstrated that intervention designed to facilitate the use of planning significantly helped those with low initial scores in planning, but led to minimal improvement for those whose initial planning scores were high. This finding underlines the importance of matching the instruction to the specific cognitive weakness of the child. The Naglieri and Gottling study was the first to examine the efficacy of facilitation of planning as part of mathematics instruction for learning-disabled students.
The Naglieri-Gottling (1997) Study
The investigators worked with a sample of elementary school students who attended an independent school that specialized in the treatment of students with significant learning problems and who had made minimal progress in public special education programs. The two teachers who provided instruction to the students at the school participated in the study and were consulted every week by the authors about the application of the intervention, the monitoring of the students’ progress, and the facilitation of classroom discus-sions. Over a two-month period, the students participated in seven baseline and 21 intervention sessions.
The intervention sessions consisted of three 10-minute periods— one for completing a math page, one for facilitating planning, and one for mathematics again. During the group discussion periods, self-reflection and evaluation, verbalization of methods used, and discussion were encouraged with the goal of improving planning competence. One student’s comment often became the starting point for vigorous discussion and further development of the idea he/she had raised. Some of the prompts used by the teachers to encourage discussion are listed here. These are quoted to show how planning processes emerge from collaborative learning and how “zones of proximal development” are expanded; both lead to a better performance in subsequent arithmetic tasks.
• Can anyone tell me anything about these problems?
• Let’s talk about how you did the worksheet.
• Why did you do it that way?
• How did you solve the problems?
• What could you have done to get more correct answers?
• What did it teach you?
• What else did you notice about how this page was done?
• What will you do next time?
• What did you think of that?
• I noticed that many of you did not do what you said was important.
In response to these probes, the students made comments such as the following:
• I’ll do all the easy ones first.
• I do them row by row.
• When I get distracted, I’ll move my seat.
• I have to remember to borrow.
• I do the ones with ones, zeros and tens in them—they’re easy.
• If it is a big problem (all big numbers on the top), you don’t have to borrow, so do it first.
• Be sure to get them right, not just get them done.
• I have to stay awake.
• I have to remember to add the numbers after multiplying.
• I have to keep the columns straight.
Note that the teachers made no direct statements, such as “That is correct” or “Remember to use that same strategy.” Nor did they give instruction in mathematics or provide any feedback about the number of correct answers obtained. Their role was to facilitate self-reflection, and thereby to encourage the students to plan, so that they could complete the worksheets successfully.
As mentioned earlier, the results of the intervention showed that the low and high groups benefited differentially from the intervention, despite the fact that the two groups had similar initial baseline scores in math computation. Students who were low in planning improved consistently across the intervention segments, whereas the students with initial high planning scores improved somewhat, but inconsistently.
Planning is at the Center of Remediation
We use many tools for teaching and learning; our most important tool, however, is language. Language not only shapes our thoughts and guides our learning but also enables us to communicate our thoughts to others.
While an animal may remember something by repeated direct experience, humans can use language to remember a vast number of things and ideas. Planning is, similarly, greatly helped by the use of language. This does not necessarily have to take the form of external speech; it may be internalized private speech. How does this work? In remediation, the adult’s directions are often repeated aloud by the child; this is an example of external speech.
However, once the child has internalized the directions, he/she may not need to repeat the directions any more, not even silently in his/her mind; the external speech is transformed to an inner voice which now regulates the child’s behavior. We see this often in PREP sessions. The facilitator asks the child, “How did you do this?”, and the child responds, “I just did it! Don’t ask me how!” This child cannot translate his or her inner speech to external speech, yet the inner speech is guiding and regulating his/her behavior.
Essentials of Planning
What exactly do we try to boost when we set out to help children develop their planning skills? The following very brief discussion outlines the bare essentials (see Das, Kar, and Parrila, 1996 for a full discussion of this issue).
At the center of planning are goals and objectives. Before a problem can be solved or a composition written, we need to establish what our goals are; then we can plan. In the Naglieri and Gottling study (1997), the teacher asked, “Can anyone tell me anything about these problems?” In other words, the children were being asked to define their goals and objectives. Our goals may change as we progress through a task; we may set ourselves immediate, intermediate, and final goals, and make appropriate plans to fulfil the goals at each stage.
Planning has four components—anticipation, representation, exe-cution, and regulation, not necessarily in that order. We anticipate when we try to imagine what will happen if we do one thing rather than another, often using our past experiences in similar situations as a guide; if we can anticipate what is going to happen, we are prepared for it. Representation of the problem is equally important. Essentially, representation involves answering the question, “What is this task all about?” Execution is about carrying out the task step by step, and regulation involves paying attention to the outcomes as we perform the task, and if necessary adjusting our activities as a consequence—in other words, monitoring our activities according to the goals and objectives that we established.