Ang Xin Yi Michelle Group A

(1) CASE 2 - Kim

(2) Area of intervention: To improve existing mathematical concepts and introduce new mathematical concepts to Kim

(3) Journal article: Constructivist mathematics education for students with mild mental retardation

i) The intervention

In this study, two interventions (instructional programmes) are compared: guided instruction versus directed instruction.

Directed instruction (DI)

Lessons in DI will start with a repetition of what was done in the previous lesion. When the students show enough knowledge of the pervious lesson, the teacher will proceed to the content of the actual lesson. The teacher will introduce a new task and explain the process of how to solve the task.

The focus is on the explanation of the strategy used to solve the task. If needed, concrete materials are used to help in the explanation. After one or two examples are presented, several tasks are then practiced and discussed within the group, which is later followed by an individual practice period. This is when students familiarize themselves with the involved tasks and create connections to the mental solutions of the problems.

However, when a child applies a new strategy that has not been taught, the teacher may acknowledge that the strategy is a possible for solving the problem, but will ask the child to apply the strategy being taught. Students using this method learn to work with a strategy decision sheet to aid them in choosing the most appropriate strategy.

DI is an explicit teaching of new strategies and is intended to help students expand their strategy repertoires. The children are instructed to follow the example of the teacher, when a new strategy is taught.

Guided instruction (GI)

Similarly, GI lessons starts with a recap of the previous lesson. However, what the students do and say in this phase is actually taken as the starting-point for the actual lesson. When the students do not fully comprehend the tasks discussed in the previous lesson, the teacher will focus again on those tasks. Otherwise, the next topic will be introduced.

In GI lessons, discussions are always centred on the contributions of the children. This means that topics and strategies differing from the teacher’s may arise. Similar to the DI lessons, GI lessons also has a phase of a group practice, followed by individual practice.

The contrast between DI and GI is; greater attention is given to the discussion of possible solution procedures and strategies during GI lessons. More attention is given to the individual’s contributions. When the teacher presents a problem, the children brainstorm for possible solutions. The teacher acts as a facilitator, asking questions and encouraging the discovery of new strategies by scaffolding. The teacher does not demonstrate a particular strategy.

Therefore, when the children do not discover a strategy, the strategy will not be discussed. However, the teacher does structure the discussions during lessons by helping students to classify various strategies by asking them about the usefulness of the strategies.

(ii) Effectiveness (as reported in the journal article)

The two experimental groups, one using DI and the other using GI, were found to differ significantly from each other. The DI group showed greater improvement than the GI group in multiplication ability and strategy competency. These findings further supported additional research that students in special education benefited best from directed instruction. (Swanson & Hoskyn, 1998; Xin & Jitendra, 1999; Kroesbergen & Van Luit, 2003; Timmermans & Van Lieshout, 2003)

Student in DI group learned how to apply the strategies by modeling the teacher. It is obvious that this is more effective for students with mild mental retardation (MMR). The strategy competency of students in the GI group did not improve. Furthermore, they made more mistakes in the multiplication test as compared to their peers in DI condition.

Nonetheless, the two groups were similar in two measures; automaticity and strategy diversity. It seemed that automatic mastery of multiplication facts can be reached with both methods and is less dependent on the student’s strategy use (Lin et al, 1994).

The students in the DI condition, who learned a specific set of strategies, could apply it competently. Ironically, those in the GI condition who were given the freedom to use as many strategies as they want, did not make us of more strategies. It seemed that most of the students with MMR in both conditions learned only a few (three to four) strategies, and these strategies were enough to meet the test requirements.

This is agreeable with the theory that students with MMR have problems handling a large range of strategies and they benefit most from instruction that involves explicit teaching of a small yet competent range of strategies (Jones et al, 1997; Van Luit & Naglieri).

To conclude, the two groups did not differ in automaticity or strategy diversity. But the DI group improved more in multiplication ability and strategy adequacy as compared to the GI group.

(iii) Personal evaluation how the child will benefit from this intervention

From the reading, I feel that Kim will benefit from the directed instruction method. However, that is not to say that I will totally omit the choice of the guided instruction method. Since Kim has only a very basic knowledge of math, (rote count up to 30, recognize numbers up to 20 and write numbers up to 15), I feel that the DI method will be more appropriate for her at this point of time.

In the case of children with MMR, they will have even more difficulty with reaching automatic mastery of basic facts as their strategy use is still not adequate. When students are unable to retrieve basic facts on their automatically, they have to depend on strategies (Kerkman & Siegler, 1997). Through repetitions, they may become more adept in applying a certain strategy and start to associate problems with their own solutions (Lin et al., 1994).

The DI method will work better because Kim has not yet possess a substantial amount of prior knowledge. Therefore, she might not be able to produce possible solutions or strategies on her own.

(iv) Adjustments to cater to the needs of the child and to facilitate integration of the child / the intervention activity into your classroom

As this was done in an elementary school setting in a Dutch school, the skills and objectives of this intervention might be relevant for Kim’s case. For example, the article used the student’s multiplication ability and strategy competency to assess the two different instructional programmes.

However, I feel that these concepts are too challenging for Kim, due to her limited knowledge of Math at present moment. It would be more appropriate for her to enhance on the concepts she already know, such as rote counting. Once she has mastered that, I would introduce Kim to new mathemactical opeartions such as addition and subtraction.

Another adjustment I would make is to ensure that I adopt both instructional methods, in order to cater to the needs of the other children in the classroom as well. Although research has shown that children with MMR learn better through the DI method, I believe that exposing Kim through the GI method is possible as she will learn more through the years.

Furthermore, the GI method will allow Kim and her classmates to discuss strategies. This will promote interaction and peer learning among the class. This may also help in Kim’s social and communication skills, as she can see how her peers brainstorm for ideas, and she may pick up and model the appropriate behaviours from them.


Reference:

Jones, E. D., Wilson, R. & Bhojwani, S. (1997) Mathematics instruction for secondary students with leaming disahilities, Journal of Leaming Disabilities, 30, 151-163.

Kerkman, D. D. & Siegler, R. S. (1997) Measuring individual differences in children's addition strategy choices, Leaming and Individual Differences, 9, 1-18.

Kroesbergen, E. H. & Van Luit, J. E. H. (2005). Constructivist mathematics education for students with mild mental retardation. European Journal of Special Needs Education, 20, 107-116. Retrieved September 9, 2009, from Academic Search Premier.

Lin, A., Podell, D. M. & Tournaki-Rein, N. (1994) CAI and the development of automaticity in mathematics skills in students with and without mild mental handicaps. Computers in the Schools, 11,43-58.

Swanson, H. L. & Hoskyn, M. (1998) Experimental intervention research on students with leaming disabilities: a meta-analysis of treatment outcomes. Review of Educational Research, 68, 277-321.