*by Mary Land, Graduate Student, Faculty of Education, University of Ottawa and Cheryll Duquette, PhD, University of Ottawa*

## Description of the Strategy:

Students with learning disabilities (LDs) may demonstrate specific deficits in mathematical problem solving. They include difficulties reading the problems, identifying operations needed to solve, inability to set up the problem’s manipulatives, retrieving arithmetic facts, knowing the cognitive strategies to solve the problem, implementing the strategies, and using appropriate metacognitive strategies (Berg & Hutchinson, 2010; Montague & Applegate, 1993; Parmar, 1992). These deficits may lead to impulsive responses when solving math problems, the use of trial and error, and failure to verify solution paths (Rosenzweiz, Krawec, and Montague, 2011). Verbalization has been identified as an evidence-based practice that can be used to teach cognitive and metacognitive strategies to students with learning disabilities. Verbalization, as used in solving mathematical problems, is the act of orally stating one’s thinking processes. It is a component of explicit instruction and can be used by teachers to model a cognitive or metacognitive process used in problem solving through “think-alouds”. A think-aloud allows students to hear what the teacher is thinking as he or she demonstrates how to use a problem solving or a metacognitive strategy (Montague, 2008). The next phase of the explicit teaching of a strategy involves the student working on the task while first verbalizing the process, then whispering the steps, and eventually working without verbal cues. The student is then provided with more opportunities for practice, with the teacher giving immediate guided support and feedback, but then decreasing this support as the student progresses using the strategy. When used as a step in explicit instruction, teacher verbalization scaffolds student learning of problem-solving and metacognitive strategies (Cole & Wasburn-Moses, 2010). Teachers may also ask students to verbalize their thoughts while solving a mathematical problem. Student verbalization can be used in different ways, such as supporting strategy acquisition (Schunk & Cox, 1986) or as a way for teachers to understand the thinking processes of students (Bosson et al, 2010; Parmar, 1992). In research studies, student verbalization is often prefaced by explicit instruction on a strategy or strategies that include teacher think-alouds (Hutchinson, 1993; Rosenzweig, Krawec, & Montague, 2011; Schunk & Cox, 1986).

## Objective of practice, approach or strategy:

### Teacher Verbalization – a component of explicit instruction

Teachers use explicit instruction to teach cognitive or metacognitive strategies. An important step in explicit instruction is teacher verbalization of his or her thought processes (“think-alouds”) as the strategy is modeled. Teacher verbalization helps students with learning disabilities gain an understanding of how that task may be approached (Montague, 2008). The description of research below shows how teacher verbalization, used as part of explicit instruction, is related to improved math performance among students with learning disabilities. Hutchinson (1993) conducted a study involving students in grades 8-10 who had been identified as having learning disabilities. The 20 adolescents were randomly assigned to either the treatment group (12 students) or control group (8 students). Students in the treatment group received explicit instruction on the use of specific cognitive and metacognitive strategies for solving algebraic problems. The researcher modeled the strategies using think-alouds and provided feedback during guided practice sessions. Students in the treatment groups were provided with a prompt card for self-questioning and were encouraged to voice their thoughts as they followed the steps and carried out the operations. Students assigned to the control group did not receive the strategy instruction, but they verbalized their thoughts while solving the same problems. Hutchinson (1993) found that the students with LDs with think-aloud training on the cognitive strategy of problem solving when combined with the metacognitive strategy of checking one’s work experienced greater success than the control group.

### Classroom use:

- Specify the steps in a cognitive or metacognitive strategy.
- Model the steps in the strategy by
**verbalizing your thoughts as each step is completed (think-aloud).** - Students apply the steps and verbalize their thinking related to a task.
- Provide corrective feedback to students and decrease support as the student learns the strategy.

(Adapted from Cole and Wasburn-Moses, 2010)

### Student Verbalization:

This strategy involves having the student verbalize his or her thoughts while solving a problem. The teacher records the student’s words, transcribes them, and analyses the data. The research shows that verbalizing strategies is related to improved test scores (Swanson, 1990) and helps teachers determine the types of cognitive and metacognitive strategies used and errors that are made.

**Task completion**

Students are first instructed on how to use a strategy and are asked to verbalize their thoughts as they solve problems. Descriptions of how student verbalization has been used in research follow. Schunk and Cox (1986) randomly assigned 90 students in grades 6 to 8 with LDs to three groups. After receiving the same explicit teaching of a subtraction skill, one group was encouraged to verbalize their thoughts freely while working on the task, a second group began verbalizing, but eventually stopped, and the third group did not verbalize their thoughts. Their results indicated a direct relationship between explicit teacher instruction, student verbalization, and improved student practice. The researchers concluded that verbalizing each step of the process helps students with LDs remain focused, assists in recall of important information, and encourages a sense of personal control over learning. In Hutchinson’s (1993) study described earlier, it was found that student verbalization resembled the instructional scripts that teachers had used while modeling the strategy, indicating that students with LDs were able to remember and put into practice the information that had been taught. In addition, the verbalizations made by students in the treatment group showed that while solving the problems, they engaged in the metacognitive strategy of self-correction, noticing when their work differed from how the teacher had instructed. Naglieri and Johnson (2000) also reported positive outcomes for students who verbalized a strategy while solving math problems. Their research involved 19 students between the ages of 12 and 14 with learning disabilities who were sorted into 1 experimental group and 4 contrast groups. They were all taught the steps in the cognitive problem-solving strategy, PASS (Planning, Attention, Simultaneous, Successive). Verbalization of the planning and self-reflective components of the PASS strategy was encouraged, and teachers use questions to probe thoughts if no verbalizations were heard after 5 seconds. The data showed that the group of students who demonstrated weaknesses in planning benefited the most from the verbalization process.

**Access and understanding student thinking processes**

Encouraging student verbalization allows teachers to determine the types of strategies students use, and the types of errors they make (Hutchinson, 1991; Montague & Applegate, 1993; Parmar, 1992; Rosenzweig, Krawec, & Montague, 2011). To determine the types of strategies used – Rosenzweig, Krawec, & Montague (2011) recorded, transcribed, and analyzed the verbalizations of 73 eighth-grade students while they solved math questions. The students were divided into three groups: learning disabilities in math (14), low achieving in math (34), and high achieving in math (25). For each student, the researcher modeled the metacognitive skill using a think-aloud, the student practised it, and solved 3 problems. The researcher encouraged the student to say what he or she was thinking while solving the problem. The verbalizations were recorded, transcribed, and classified as metacognitive or not. Notations were also made on how frequently these types of statements were made. The researchers determined that students with LDs tend to use more nonproductive metacognitive strategies (e.g., emotional reactions, negative self-talk) as the math problems increased in complexity than the other two groups. This result points to their increased frustration with the problem, indicating the need for explicit cognitive and metacognitive strategy instruction for students with learning disabilities. Montague (1992) also used student verbalizations to understand students’ use of strategies when solving problems. Six middle school subjects were selected randomly from 14 students who had been identified as having learning disabilities by a school district. The subjects were then randomly assigned to two groups. They reported that cognitive strategy training and metacognitive strategy training improved problem-solving scores. The use of cognitive strategies combined with metacognitive strategies was more effective than either cognitive or metacognitive alone. Through student verbalization the researchers could identify that students knew the strategies and were implementing them correctly. To examine the types of errors made – Parmar (1992) investigated the types of errors when solving math problems that were made by students with 31 participants with learning disabilities aged 8 to 14. In this study, individual students verbalized their thoughts, and the teacher took notes on student verbalizations and behaviours during problem solving. The students were encouraged to talk through the problem and the teacher asked questions. The notes were transcribed and the errors were classified as due to skill deficit or knowledge deficit. Teachers were then able to use this information to inform the next steps in instruction.

### Classroom use:

- Specify the steps in a cognitive or metacognitive strategy.
- Model the steps in the strategy by verbalizing your thoughts as each step is completed (think-aloud).
- Students apply the steps and verbalize their thinking related to a task.
- Teacher records, transcribes, and analyses the verbalizations.
- Teacher uses data to determine future instruction.

## Summary of level of evidence:

A comprehensive search was done to find all research that (a) focused on verbalization with students with learning disabilities in mathematical problem-solving tasks, (b) used an experimental design with a control or comparison group or a single-subject design, and (c) was published in a peer-reviewed journal. Articles were read, and studies meeting the above criteria were retained. In some cases a clear cause and effect relationship between the interventions and the variable under study was found. In other cases, verbalization was a research method used to determine cause-and-effect relationships.

## Additional Resources

Click here to visit the LD@school website and access the evidence-based strategy, “Math Heuristics”.

## References:

Berg, D., & Hutchinson, N. (2010). Cognitive processes that account for mental addition fluency differences between children typically achieving in arithmetic and children at-risk for failure in arithmetic. *Learning Disabilities: A Contemporary Journal 8*(1), 1-20.

Bosson, M., Hessels, M., Hessels-Schlatter, C., Berger, J-L., Kipfer, N., & Büchel, F. (2010). Strategy acquisition by children with general learning difficulties through metacognitive training. *Australian Journal of Learning Difficulties, 15* (1), 13-34.

Cole, J., & Wasburn-Moses, L. (2010). Going beyond the math wars: A special educator’s guide to understanding and assisting with inquiry-based teaching in mathematics. *Teaching Exceptional Children, 42*(4), 14-20.

Hutchinson, N. (1991). The challenges of componential analysis: Cognitive and metacognitive instruction in mathematical problem solving. *Journal of Learning Disabilities, 25*(4), 249-252, 257.

Hutchinson, N. (1993). Effects of cognitive strategy instruction on algebra problem solving of adolescents with learning disabilities. *Learning Disability Quarterly, 16*(1), 34-63.

Kretlow, A., & Blatz, S. (2011). The ABCs of evidence-based practice for teachers. *Teaching Exceptional Children, 43*(5), 8-19.

Montague, M. (1992). The effects of cognitive and metacognitive strategy instruction on the mathematical problem solving of middle school students with learning disabilities. *Journal of Learning Disabilities, 25*(4), 230-248.

Montague, M. (2008). Self-regulation strategies to improve mathematical problem solving for students with learning disabilities. *Learning Disability Quarterly, 31*, 37-44.

Montague, M., & Applegate, B. (1993). Middle school students' mathematical problem solving: An analysis of think-aloud protocols. *Learning Disability Quarterly, 16*(1), 19-32.

Montague, M., & Bos, C. (1986). The effect of cognitive strategy training on verbal math problem solving performance of learning disabled adolescents. *Journal of Learning Disabilities, 19*(1), 26-33.

Naglieri, J., & Johnson, D. (2000). Effectiveness of a cognitive strategy intervention in improving arithmetic computation based on the PASS theory. *Journal of Learning Disabilities, 33*(6), 591-597.

Ostad, S., & Sorenson, P. (2007). Private speech and strategy-use patterns: Bidirectional comparisons of children with and without mathematical difficulties in a developmental perspective. *Journal of Learning Disabilities, 40*(1), 2-14.

Parmar, R. (1992). Protocol analysis of strategies used by students with mild disabilities when solving arithmetic word problems. *Diagnostique, 17*(4), 227-243.

Rosenzweig, C., Krawec, J., & Montague, M. (2011). Metacognitive strategy use of eighth-grade students with and without learning disabilities during mathematical problem solving: A think-aloud analysis. *Journal of Learning Disabilities, 44*(6), 508-520.

Schunk, D., & Cox, P. (1986). Strategy training and attributional feedback with learning disabled students. *Journal of Educational Psychology, 78*(3), 201-209.

Swanson, H. (1990). Influence of metacognitive knowledge and aptitude on problem solving. *Journal of Educational Psychology, 82*(2), 306-314.

## Additional Resources:

Inquire, *Math Think Aloud Click here* *Mary Land is currently a graduate student in the Faculty of Education at the University of Ottawa. She worked for several years as a high school teacher before returning to pursue graduate studies full-time. Her experiences in the classroom have encouraged her varied interests in the field of education, including literacy and language arts instruction for all students. * *Cheryll Duquette’s research in the area of special education reflects her interest in the experiences of students with exceptionalities in inclusive classrooms. As a former teacher, she focuses particularly on strategies that may be used by classroom teachers to facilitate inclusion. Dr. Duquette is also the author of Students at Risk (2 ^{nd} ed.), a book containing practical suggestions for working with students with exceptionalities and their parents. She teaches teacher education and graduate courses in special education at the Faculty of Education at the University of Ottawa.*

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