Saturday, May 1, 2010

Online Discussion and Self-Regulated Learning: Effects on Intructional Methods on Mathematical Literacy

Kramarski, B. & Mizrachi, N. (2006) Online Discussion and Self-Regulated Learning: Effects on Intructional Methods on Mathematical Literacy. The Journal of Educational Research 99, 4, 218-230

The authors investigated the effects of online discussion embedded within metacognitive guidance on mathematical literacy and self-regulated learning (SRL). They compared 4 instructional methods: online discussion embedded within metacognitive guidance, online discussion without metacognitive guidance, face-to-face discussion with metacognitive guidance, and face-to-face discussion without metacognitive guidance. Results showed that the Online+Meta students significantly outperformed the Face-to-face+Meta students, who, in turn, significantly outperformed the Online and Face-to-face students on mathematical literacy of standard tasks, real-life tasks, and various aspects of self-regulated learning. In regard to Online students, results were mixed; these students outperformed the Face-to-face students on part of the criteria for standard problem-solving standard tasks and real-life tasks. The authors found no significant differences between the Online and Face-to-face students on SRL. In the end the authors result showed that training in metacognitive guidance and SRL strategies greatly improve students mathematica literacy in both environments and there was a greater improvement in the Online environment for those students who received the metacognitive guidance.

This article provides several practical methods for providing metacognitive guidance for students, particularly using the IMPROVE method (Mevarech & Kramarski 1997), which I will need to further investigate. The IMPROVE method uses 4 different question that students use to self-address themselves around the topics of comprehension, connection, strategy and reflection. Using such questioning allowed students to build on prior knowledge and to better understand the problem, process, and solution. This method will play an important role in investigating my research questions.

Some quotes:

PISA assesses mathematical literacy in relation to the content, process, and situations in which mathematics is used. Content refers to curriculum-based knowledge and mathematical big ideas, which indicate general properties, such as change and growth. Curriculum-based knowledge refers to standard tasks that describe simplified situations involving quantitative information which includes readymade algorithms that students must apply to solve a problem. Process refers to mathematical skills like problem solving, mathematical reasoning, argumentation, and communication; situations refer to contexts in daily life. Real-life tasks employ realistic data that often (a) are incomplete or inconsistent, (b) provide rich information about the described situation, (c) include complex mathematical data, (d) are approached in different ways, (e) are based on a wide range of mathematical knowledge and skills, and (f) often ask solvers to use different representations in their solutions. By assigning students tasks based on situations that represent the kinds of problems encountered in real life, educators impart challenging tasks that are relevant to the students’ world (OECD, 2003). (218)

Self-regulation is “a major objective of mathematics education and a crucial characteristic of effective mathematics learning” (De Corte, Verscaffel, & Eynde, 2000, p. 721). PISA describes SRL as a style of activities for problem solving that includes three phases: (a) analyzing tasks and setting goals; (b) thinking of strategies and choosing the most appropriate strategy for solving the problem; and (c) monitoring and controlling behaviors, cognitions, and motivations by enlisting strategies, such as attention control, encoding control, and self-instruction. Research (e.g., OECD) indicates that relationships exist between SRL and academic achievement and that SRL is teachable to students (e.g., Kramarski & Mevarech; Mevarech & Kramarski; Schoenfeld, 1992). (219)

Several reasons may account for the results. First, students who used IMPROVE self-questioning (Online+Meta, Ftf+Meta) actively monitored and controlled their interactions with environment learning. That, in turn, enhanced the students’ knowledge about SRL; students who were not exposed to such guidance (Online, Ftf), however, were more motivationally and metacognitively passive when they received instructions, which, in turn, affected low SRL. (228)

Our findings extend to other research that indicates that SRL is teachable and that students who are exposed to metacognitive guidance have more knowledge about orienting and self-judging themselves than do students in control groups. Researchers noted that metacognitive knowledge is related positively to academic performance. (228)

Moreover, we found that Online+Meta students justified their reasoning mathematically to solve online tasks more often than did Online students. Online students based their reasoning on repeating their final result without explaining how they
obtained it. (228)

When students explain and justify their thinking and challenge the explanations of their peers, they also clarify their own beliefs. (228)

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