28May

Promoting Metacognition with Early Math Learners

by Meghann N. Fior, Jac J. W. Andrews, and Michelle A. Drefs

Werklund School of Education, University of Calgary

 

Abstract

This paper overviews the nature and scope of metacognition, presents the importance of developing metacognition within early math learners, and focuses on the importance of language development for the promotion of metacognition. In addition, a metacognitive learning model as well as a framework of instructional steps is provided for teachers interested in developing metacognition within their early math learners.

 

What is Metacognition?

Metacognition is an important part of learning. Generally, metacognition is the knowledge, awareness, and control of one’s cognitive processes and products (Flavell, 1979) and is sometimes referred to as “thinking about thinking” (Anderson, 2002). It allows learners to manage their cognitive thought processes by determining their learning strengths and weaknesses, monitoring their skills with respect to solving problems, and evaluating the outcomes of their learning tasks. Promoting metacognition in young learners begins by building awareness that metacognition exists and that associated learning strategies can increase their academic success. By teaching metacognition and associated learning strategies to young children, we can help them build strategies to use along with the knowledge of when and how to use these learning strategies.

 

The Importance of Metacognitive Development with Early Math Learners

Metacognitive development with early math learners importantly provides a way for students to think about, understand, and describe their own mathematical learning. In other words, it allows students to talk about and express the ways they are thinking about mathematics and their approaches to math problem solving. The ability to verbally describe one’s cognitive processes and products in math is important from an instructional perspective because it allows teachers to assess how best to scaffold young children’s mathematical understandings and determine the types of learning experiences required.

Such assessment is particularly important when working with children who are struggling in mathematics because it helps teachers identify specific areas of misunderstanding a child might have. For example, a child responding incorrectly to a math problem might have used a skillful and creative mathematical approach. Unless the child is able to verbalize this process, the teacher is unable to identify where an “error” occurred based only on the provided response (“product”). Moreover, when young children are able to articulate their strategic mathematical thinking, they are better able to share with and learn from their classmates (i.e., socially constructed learning). For students who have a firm grasp on metacognitive strategies, the academic benefits include an increased ability to plan their approach to problems, seek the information they need, reflect on the progress they make, and make changes when they are not getting the results they desire. These skills are essential in the development of independent and effective problem-solving and learning in mathematics.

Current instructional methods for promoting metacognition in the classroom include modelling, reciprocal teaching, questioning, and direct instruction (Fischer, 1998; Larkin, 2010; Schneider, 2008; Schraw, 1998). Unfortunately, metacognition instruction to facilitate mathematical development remains an underutilized approach within the early elementary grades (Larkin, 2010; Pappas Schattman, 2005), with instruction typically limited to students in the upper grades (e.g., Grades 4 and higher). This lack of instruction is likely due to widespread but inaccurate beliefs within the educational field that the ability to think metacognitively does not emerge until 8 to 12 years of age (Desoete, 2008; Shamir, Mevarech, & Gida, 2009).

More recent research supports children’s abilities to be metacognitive as young as three years old (Kuhn, 2000; Shamir et al., 2009; Whitebread et al., 2009). Metacognitive skills continue to develop during the primary school years (6 to 9 years) with both increasing age and experience (Annevirta & Vauras, 2006; Ozsoy, 2011; Veenman, Van Hout-Wolters, & Afflerbach, 2006). Young children understand that they must concentrate and try hard if they are to be successful at a task. As children age, this understanding further develops and they better appreciate that concentrating and trying hard can vary depending on the task and that different outcomes require the use of different strategies (Berk & Shanker, 2006). For example, elementary school children know that rehearsing or categorizing information is better than just reading; however, older children understand that organizing information (i.e. grouping by similar themes) is better than rehearsing (Schneider, 1986 as cited in Berk & Shanker, 2006).

 

Importance of Language in the Promotion of Metacognitive Development

Some researchers believe young children are capable of greater metacognitive thought than what they are able to articulate. In particular, researchers working with children ages 4 to 6 have found significant differences between the number of metacognitive behaviors children use (procedural metacognition) and what they report using (declarative metacognition; e.g., Shamir et al., 2009). Young children also commonly respond to queries about their thinking by more simply stating "I don’t know" or "My brain just thought of it" (Alexander, Johnson, Leibham & DeBauge, 2004, p. 49). What may account, in part, for such difficulties are the more limited language skills of young children.

Children require language specific knowledge (Pelletier, 2006) to use metacognitive strategies, both in terms of the demands of thinking and of expressing thought (Lockl & Schneider, 2006; Pelletier, 2006). During the primary years, language becomes more elaborate and complex (Bos & Vaughn, 2006) and vocabularies increase substantially (from approximately 10,000 words in Grade 1 versus 20,000 words in Grade 3; Hoff, 2014). Research has also found growing competence with metacognitive language as children progress through the school years. For example, younger children may understand the difference between "know" and "think"but an understanding for words such as "infer," "assume," "confirm," and "predict" does not develop until the intermediate school years (Peskin & Astington, 2004).

To bridge this gap between metacognitive behaviors and the accurate articulation of such behaviors it may be necessary to provide young learners with specific metacognitive training that serves to support articulation of their thoughts. Astington and Olson (1990) propose that using metacognitive terms within the classroom will help children more readily incorporate such words into their vocabulary and to recognize distinctions between these words. Certainly, a number of studies have found that increased exposure to metacognitive terms (e.g., figure outknowguess) results in increased frequency in use (Peskin & Astington, 2004) and understanding (Ruffman, Slade, & Crowe, 2002) of such terms.

 

Present Study

The present study was conducted to determine if it would be possible to generate a list of metacognitive statements young children might be expected to use during mathematics problem solving, with the goal to use this list to develop visual prompts (i.e., Metacognitive Thinking Cards) that could be incorporated into metacognition instruction in the primary grades. This work was based on the previous work of Wilson and Clarke (2004) who specified a 3-component metacognitive framework (awareness, evaluation, and regulation) and then generated a series of Metacognitive Awareness Cards that depicted various metacognitive strategies to be used when solving challenging math problems. When used with 11 and 12 year old children, Metacognitive Awareness Cards resulted in increased accuracy in reported metacognition statements.

As the first step in downward extending this work to younger populations, Wilson and Clarke’s 3-component metacognitive framework was adopted in the present research study. Next, items where then generated for each category (awareness, evaluation, and regulation) based on modified items from metacognitive assessment measures for use with older students (the Metacognitive Awareness Cards [Wilson & Clarke, 2004], Metacognitive Awareness Inventory [Schraw & Dennison, 1994]). A comprehensive list of potential card items was presented to a focus group of six Grade 1 teachers where they identified the most pertinent strategies first grade students should be using, provided suggestions for potentially missing strategies, and ensured that the cards consisted of developmentally appropriate language. Then, the revised cards were further improved through expert consultation. As a final step in the study, the focus group teachers were asked to pilot the use of the cards in their classrooms.

 

Results

The initial focus group work identified the appropriateness of two metacognitive categories for use with young children: Awareness (of the task/problem difficulty or of the student’s perception of their ability to complete the problem) and Regulation-Strategies (possible strategies to aid in overseeing the solving of difficult mathematical problems). In total, two awareness and eight strategy cards were developed (see Figure 1).

 

Figure 1:  Metacognitive Thinking Cards consisting of 2 awareness cards (easy, hard) and 8 strategies

 The six teachers using the Metacognitive Thinking Cards in the class reported the cards and metacognitive vocabulary were easily incorporated into the regular classroom math activities. Overall, the results from this study supported the view that children aged 6 to 7 are capable of articulating metacognitive thoughts and that these thoughts can be increased with access to Metacognitive Thinking Cards.

 

Implications for Practice

Teachers interested in instructing metacognition in the primary grades may find value in focusing on two metacognitive components: Metacognitive Awareness, which refers to the evaluation of the task/problem to determine what skills/strategies may be needed depending on the difficulty, and Metacognitive Strategies, which are procedures and tactics students can use to solve different mathematical problems. Specifically, the two awareness and eight strategy cards detailed in Figure 1 might prove a useful starting place in identifying developmentally appropriate language and strategies to use as external prompts in both teaching and supporting metacognitive development in the first grade classroom.

Although the present study was focused on the development of the Metacognitive Thinking Cards, this work also has implications for the instruction of metacognition with young children. To date, the limited research focused on metacognitive intervention with younger children has tended to be fairly time-restricted, limited to around 5 to 6 sessions (Desoete, Roeyers, & De Clercq, 2003; Pappas Schattman, 2005). The Metacognitive Thinking Cards, in contrast, can be readily incorporated as part of regular mathematics instruction and throughout the school year. Table 1 details the 3-stage approach used by teachers in this study. Key elements of this approach entail the teacher providing students with motivation to learn a metacognitive process and modeling of the required skills (Stage 1), opportunities to talk about the metacognitive process with others (peers, teacher) to strengthen self-talk (Stage 2), and repeated practice using the newly learned strategies across diverse tasks (Stage 3). Throughout all these stages, the teacher provides students with tools to think and express their metacognitive thinking through modeling and the use of Metacognitive Thinking Cards.

 

Table 1:  Metacognitive instructional stages of teacher modeling, guided practice, and student application used with the Metacognitive Thinking Cards

Stage

Specifics

Stage 1. Teacher Modeling of metacognitive vocabulary and processes (i.e., evaluate thinking about the difficulty level of a math problem and the strategy that would be best used).

 

Using a sample math problem, the teacher models:

(1) Awareness Check—self-evaluation of the difficulty level of a sample math problem (e.g., “I find this hard/easy because...”), and

 (2) Strategy Selection—vocalization of strategy selection and reasoning (e.g., “I remember seeing a question like this before, although it was a bit different because ….”).

Stage 2. Guided Practice with peers in use and verbalization of metacognitive thinking (awareness, strategies), with teacher feedback, and opportunity for adjustments in effective use of the process.

Students practice awareness check and strategy selection on novel tasks as a class (e.g., count to 10 then hold up Metacognitive Thinking Card that they would use to solve the given math problem) or in small groups (discussion of different strategies they believe would work best).

Stage 3. Student Application of the learnings to novel or independent tasks to assist with consolidation and transfer of metacognition learning.

Students use the Metacognitive Thinking Cards for the remainder of the math lesson to practice using the cards on their own while solving math problems.

 

Conclusion

There is general support for the viewpoint that children need to be shown effective ways to approach learning to improve their performance, be encouraged to more actively engage their learning, and have assistance in evaluating and improving their learning and thinking. Teaching thinking (metacognitive awareness and strategies) helps children become aware of their own cognitive processes and to be effective managers of their own mental resources. This teaching approach within the classroom context can improve the quality of children’s learning and thinking.

 

References

Alexander, J. M., Johnson, K.E., Leibham, M. E., & DeBauge, C. (2004). Constructing domain-specific knowledge in kindergarten: Relations among knowledge, intelligence, and strategic performance. Learning and Individual Differences15, 35–52. doi:10.1016/j.lindif.2004.07.001

Anderson, N. J. (2002). The role of metacognition in second language teaching and learning. Washington DC, WA: Clearinghouse on Information Resources.

Annevirta, T., & Vauras, M. (2006). Developmental changes of metacognitive skill in elementary school children. The Journal of Experimental Education, 74(3), 197-225. doi: 10.3200/JEXE.74.3.195-226

Astington, J. W., & Olson, D. R. (1990). Metacognitive and metalinguistic language: Learning to talk about thought. Applied Psychology: An International Review39(1), 77-87. doi: 10.1111/j.1464-0597.1990.tb01038.x

Berk, L. E., & Shanker, S. G. (2006). Child development: Second Canadian edition. Toronto, CA: Pearson Education Canada Inc.

Bos, C. S., & Vaughn, S. (2006). Strategies for teaching students with learning and behavior problems (6th ed.). Boston: Allyn and Bacon.

Desoete, A. (2008). Multi-method assessment of metacognitive skills in elementary school children: How you test is what you get. Metacognition Learning3, 189-206. doi: 10.1007/s11409-008-9026-0

Desoete, A., Roeyers, H., & De Clercq, A. (2003). Can off-line metacognition enhance mathematical problem solving? Journal of Educational Psychology, 95(1), 188-200. doi:10.1037/0022–0663.95.1.188

Fisher, R. (1998). Thinking about thinking: Developing metacognition in children. Early Child Development and Care141, 1-15. doi: 10.1080/0300443981410101

Flavell, J. (1979). Metacognition and cognitive monitoring: A new area of cognitive developmental inquiry. American Psychologist, 34, 906-911. Retrieved from http://www.apa.org/pubs/journals/amp/index.aspx

Hoff, E. (2014). Language development (5th ed). Belmont, CA: Wadsworth.

Kuhn, D. (2000). Metacognitive development. Current Directions in Psychological Science, 9(3), 178-181.

Larkin, S. (2010). Metacognition in young children. New York, NY: Routledge.

Lockl, K., & Schneider, W. (2006). Precursors of metamemory in young children: the role of theory of mind and metacognitive vocabulary. Metacognition Learning, 1, 15-31. doi: 10.1007/s11409-006-6585-9

Ozsoy, G. (2011). An investigation of the relationship between metacognition and mathematics achievement. Asia Pacific Educational Review, 12, 227-235. doi: 0.1007/s12564-010-9129-6

Pappas Schattman, S. S. (2005). Fostering kindergartener’s metacognition. (Unpublished doctoral dissertation). Columbia University, Ann Arbour.

Pelletier, J. (2006). Relations among theory of mind, metacognitive language, reading skills and story comprehension in L1 and L2 learners. In A. Antonietti, O. Liverta Sempio, & A. Marchetti (Eds.), Theory of mind and language in developmental contexts (pp. 7792). New York: Springer

Peskin, J., & Astington, J. W. (2004). The effects of adding metacognitive language to story texts. Cognitive Development, 19, 253-273. doi:10.1016/j.cogdev.2004.01.003

Ruffman, T., Slade, L., & Crowe, E. (2002). The relation between children's and mothers' mental state language and theory-of-mind understanding. Child Development, 73(3), 734-751. doi: 10.1111/1467-8624.00435

Schneider, W. (2008). The development of metacognitive knowledge in children and adolescents: Major trends and implications for education. Mind, Brain, and Education, 2(3), 114-121. doi: 10.1111/j.1751-228X.2008.00041.x

Schraw, G. (1998). Promoting general metacognitive awareness. Instructional Science, 26, 113-125. doi: 10.1023/A: 1003044231033

Schraw, G. & Dennison, R. S. (1994). Assessing metacognitive awareness. Contemporary Educational Psychology, 19, 460-475.

Shamir, A., Mevarech, Z. R., & Gida, C. (2009). The assessment of meta-cognition in different contexts: Individualized vs. peer assisted learning. Metacognition Learning, 4, 47-61. doi: 10.1007/s11409-008-9032-2

Veenman, M.V.J., Van Hout-Wolters, B.H.A.M., & Afflerbach, P. (2006). Metacognition and learning: Conceptual and methodological considerations. Metacognition Learning, 1, 3-14. doi: 10.1007/s11409-006-6893-0

Whitebread, D., Coltman, P., Pino Pasternak, D., Sangster, C., Grau, V., Bingham, S., … Demetriou, D. (2009). The development of two observational tools for assessing metacognition and self-regulated learning in young children. Metacognition Learning, 4, 63-85. doi: 10.1007/s11409-008-9033-1

Wilson, J., & Clarke, D. (2004). Towards the modelling of mathematical metacognition. Mathematics Education Research Journal, 16(2), 25-48. doi: 10.1007/BF03217394