metacognition discussion

8/10/2019 Metacognition Discussion

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Promoting General Metacognitive Awareness, Schraw, 1998

1.

Metacognition is multidimensional

Framework of metacognition

Metacognition

Knowledge of cognition-what individuals

know about their own cognition or about

cognition in general. There are 3 types:

Regulation of cognition-set of activities that

help students control their learning. There

are three essential skills:

Declarative knowledge-knowledge about

oneself as a learner and about what factors

influence ones performance

Planning-selection of appropriate strategies

and allocation of resources that affect

performance. Examples: making predictions,

allocating attention selectively before

beginning a task.

Procedural knowledge-knowledge about

doing things, such as heuristics and

strategies. More procedural knowledge gives

rise to more automatic performance.

Examples include chunking and categorizingnew information.

Monitoring-ones on-line awareness of

comprehension and task performance.

Example: periodic self-testing. Monitoring

ability develops slowly and is quite poor in

children and adults.

Conditional knowledge-knowing when and

why to use declarative and procedural

knowledge. Helps students selectively

allocate resources and use strategies more

effectively.

Evaluating-appraising the products and

efficiency of ones learning. Examples-re-

evaluating goals and conclusions.

Knowledge and regulation of cognition are related-knowledge of strategies is related to

self-reported strategy use. College students judgments of their ability to monitor their

reading comprehension were significantly related to their observed monitoring accuracy

and test performance.

2.

Metacognition is domain-general

Knowledge and regulation of cognition are domain-general (span a wide variety of

subject areas and domains) in nature. Some studies have shown that teaching

strategies such as identifying main goals, self-monitoring, self-questioning and self-

assessment can improve learning in all domains and that strategy use and self regulation

are correlated in multiple domains. There is empirical evidence (Schraw, 1995) to

support the conclusion that adult learners possess a general monitoring skill.

Schraws view-cognitive skills tend to be encapsulated in subject areas, where

metacognitive skills span multiple domains.

Acquisition of metacognition does not depend strongly on IQ. Alexander, Carr, and

Schwanenflugel (1995) reported that content specific knowledge was modestly relatedto IQ, but strategies and comprehension monitoring were not related at. IQ constrains

knowledge acquisition initially, but becomes less important as other skills, such as task

specific strategies and metacognitive knowledge come into play.

Well organized instruction of the use of effective learning strategies may in large part

compensate for differences in IQ.

Many researchers believe that metacognitive knowledge is domain specific initially, but

as students acquire metacognitive knowledge in a number of domains, they may


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construct general metacognitive knowledge and skills that cut across all academic

domains.

Swanson (1990) found that metacognitive knowledge compensated for IQ when

comparing fifth and sixth grade students problem solving

While high levels of domain specific knowledge may facilitate the acquisition and use of

metacognition, domain knowledge does not guarantee higher levels of metacognition.

3.

Promoting general metacognitive awareness

Promote the importance of metacognition-teachers should model both cognitive and

metacognitive skills for their students

Students can model metacognitive skills as well and provide a rationale for these skills

within the students zone of proximal development, compared to teachers.

Make metacognitive knowledge and skills explicit- Schraw uses a strategy evaluation

matrix(strategy-how, when and why to use it) to increase metacognitive knowledge in

his students and a regulatory checklist that helps facilitate planning, monitoring, and

evaluation. Similar to Reif- forcing students to go through the process of representing

the problem, initial problem analysis, implementation, and checking work allows them

to be better problem solvers.

Foster conducive environments-Students possess knowledge and strategies that are

appropriate for a task, but do not use them. Students fail to engage and persist in a

challenging task or fail to attribute their success to the use of strategies and self-

regulation. They may believe that low ability makes the extra effort (metacognition)

useless.

Schraw says that the most salient characteristics of successful learners is their goal

orientation. Mastery orientation-students want to improvetheir competence.

Performance orientation-students want toprovetheir competence. Teachers can focus

on increasing ones current level of performance, rewarding increased effort andpersistent, and strategy use to discourage performance orientation.

We discussed goal orientation previously-there needs to be a balance. Getting good

grades is an incentive for students to work harder. But whatwe assess can cause

students to focus on the wrong things, like just getting a final numerical answer. We

can also assess for problem analysis and checking, as well as holistic grading to see if

they are monitoring their learning, such as like what we saw on the QMFPS.

Whats all the Fuss about Metacognition? Schoenfeld, 1987.


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Students in a geometry class spent the most time exploring problem solutions, rather than

reading, analyzing, planning, implementing, and verifying. Its not only what you know, but

how you use it that matters.

An expert mathematician, although he had not worked in geometry for a number of years, spent

more time analyzing, planning, and verifying in addition to exploring.

Schoenfeld also discusses another aspect of metacognition-beliefs and intuitions. Students havepreconceptions and misconceptions about the subject matter, and we should take this into

account.

Question about how many buses are needed to hold 1128 soldiers. 1/3 of students said that the

answer was 31 remainder 12. In Schoenfelds class, 30% of students solve a proof problem

correctly then make a conjecture that flatly violates what they just proved. They dont see the

connection between the two problems.

Students beliefs: Math consistsof mastering formal procedures that are completely divorced

from real life, discovery, and problem solving. They disregard proof because its meaningless to

them. They also believe that all problems can be solved in 10 minutes or less, only geniuses are

capable or discovering mathematics.

Schoenfelds approach to developing metacognitive skills:

o use videotapes. He has students in his class watch videos of students struggling to solve

problems. The students can objectively analyze the behavior when its someone elses

then to see how the analysis applies to yourself. Thus, they are more aware of

metacognitive issues and more receptive to his teaching techniques.

o Teacher as role model for metacognitive behavior-he works through a problem from

scratch, modeling self-regulatory strategies.

o Whole class discussions of problems with teacher serving as control-scribe and

orchestrator of students suggestions, but does not guide students to correct solutions.

Asks for suggestions to solve the problem, and the class discusses whether or not the

suggestion is reasonable, implements the suggestion, monitors whether it is working,checks the final solution and discuss alternative solutions.

o Problem solving in small groups-he describes himself as a coach, watching students as

they practice and giving on-line corrections. He asks the group What are you doing?

Describe it precisely. Why are you doing it? How does it help you? After a while,

students prepare their answers in advance, before he reaches the group. This develops

a good habit of self-regulatory skills.

Post instruction, students spend more time planning, implementing, and verifying. Not as much

as the expert mathematician did, but they were getting better.


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How can primary school students learn self-regulated learning strategies most effectively? A meta-

analysis on self-regulation training programmes, Dignath, Buettner, Langfeldt, 2008.

This analysis only discusses the results of 48 metacognitive interventions with children between

grades 1-6, but I still found some interesting points that might be used for older students.

They looked at the instructional strategy of the intervention-metacognitive (metacognitive

knowledge and skills), cognitive (repetition, organizational, and problem solving strategies) and

motivational (causal attribution and self-efficacy beliefs, action control, and feedback), and

combinations of metacognitive and motivational, cognitive and motivational, and cognitive and

metacognitive. The highest effect sizes were found for:

Metacognitive and motivational (combination)

Motivational

Metacognitive and cognitive (combination)

Within the metacognitive strategy interventions, they found the largest effect sizes to be a

combination of planning and evaluation strategies. Monitoring had the largest effect size on

academic performance overall, but the difference was not significant.

Within the metacognitive reflection groups (impact of promoting students metacognitive

reflection)-found that they largest effect sizes to be a combination of knowledge of

metacognitive strategies and benefit. I found this very interesting because we hope that byhaving student buy in they are more likely to practice using the strategies.


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Im not exactly sure what they mean by reasoning but I think they mean metacognitive self-

regulation skills

Overall, the most effective training programs include interventions with

o metacognitive and motivational aspects.

o knowledge about strategy application and its benefits (learners need to be motivated to

use the strategies-they need the skill and the will to engage in self-regulated learning.)

o

feedback about their learning (learner should be encouraged to ask for feedback and

talk about his learning. Analysis of the learning outcome and the factors which led to

the outcome should offer conclusions about the appropriateness of ones own goal

setting and procedures to attain this goal.)

Knowing what kinds of metacognitive interventions work, we can adapt these for physics and

other natural sciences and help teachers/professors implement these types of strategies in their

own classrooms.


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Enhancing Mathematical Reasoning in the Classroom: The Effects of Cooperative Learning and

Metacognitive Training, Kramarski and Mevarech, 2003

384 eighth grade students from 12 schools

All students studied linear graphs Two interventions-metacognitive training and cooperative learning

Metacognitive training-used three sets of self-addressed metacognitive questions printed in

their worksheets:

o comprehension questions-prompt students to reflect on a problem before solving it,

e.g., what does the x-axis represent? What is the trend of the graph?

o

strategic questions-prompt students to consider which strategies were appropriate for

solving or completing a given problem, e.g., why is the strategy the most appropriate to

carry out task? Some strategies could be adding steps to find the slope, using data

tables, and the algebraic representation.

o connection questions-prompt students to focus on similarities and differences between

immediate problem or previous problems they had completed, e.g., compare different

intervals on the same graph, find similarities and differences between graphs

cooperative learning vs individualized learning- included three parts (teacher introduction,

cooperative or individualized seatwork, and teacher review with the whole class)

o cooperative groups in teams of four-one high achieving student, two middle achieving

students, and one low achieving students

o each student read a problem aloud and tried to solve it

o the team discussed the problem until they reached a final consensus and wrote down

the solution on their answer sheets

Four groups:

o

Cooperative learning + metacognitive trainingo Individual learning +metacognitive training

o Cooperative learning only

o Individual learning only

The assessments included

o a pre/post test of graph interpretation

o mathematical explanations

fluency-number of correct arguments

flexibility-provision of more than one kind of correct argument

o graph construction test (transfer task)

o

metacognitive questionnaire


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Results

The COOP+META group scored the highest on the graph interpretation test (24.4/36) as

opposed to the other groups (around 20/36)

The COOP+META group gave more correct arguments (8.9) than the other groups (around 5-6.5)

o logical formal: based on logical mathematical arguments

o Numerical computational: based on numerical comptations or algebraic formulas

o Visual: based on intuitive, visual analysis of the graph

o Drawing: based on drawings that students added to the graph

More students from the COOP+META group gave more than one kind of correct argument

The COOP+META group and IND+META scored slightly higher on the transfer test as opposed to

other groups Being more flexible and fluent can help students see that math is not a rigid subject where there

is just one path to one right answer, but that there are many ways to reach the same answer.

Also, when elaborating on solutions, students can enhance their understanding.

They reason that because the metacognitive questions were internalized by both groups to such

an extent that students interactions could have only a small additional impact on transfer

performance (graph construction).


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COOP+META outperformed IND+META on the graph interpretation test because learning in

small groups provides a natural setting for students to formulate and discuss questions that they

used in the study (comprehension, strategic, and connection)

It is possible that by explicitly giving students comprehension, strategic, and connection

questions to ask within the group, it directed the group in the right direction. In the COOP

group, the students may have just done the problem and moved on without further questioning(perhaps the high achieving student just did the problem and everyone else agreed without

questioning).

IND+META outperformed COOP students because just placing students in cooperative learning

groups is not sufficient for enhancing mathematical reasoning. Groups need structure, practice,

and reinforcement in metacognitive skills.

I think this is important for us because we expect that students who work in groups engage in

metacognitive dialogue. This might not be the case, maybe one student is doing all the work

and others just agree with him. As Schraw article pointed out, the metacognitive knowledge

and skills need to be made explicitly clear.


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Metacognitive Teaching Interventions

Teachers metacognitive knowledge and the instruction of higher order thinking, Zohar, 1998

In-service training for Teaching in Science curriculum

Do teachers need to have metacognitive knowledge of thinking skills (e.g., identifying a research

question, formulating hypotheses, planning experiments controlling variables)? Yes, becauseo

Essential for introducing metacognitive activities in class

o

Essential for DESIGN of high quality learning activities because it requires thinking about

thinking skills as explicit goals of the learning activity

o

Essential for systematic teaching of higher order thinking. Teaching the same skills over

and over again in different scientific contexts requires that teachers can plan their

teaching for both content and thinking goals. Thinking skills are explicit goals of

instruction.

Data analysis-audiotapes of the in-service courses, notes were taken by the leader, elements

from teachers written work that referred to metacognition were collected.

They found that teachers were teaching for thinking in an intuitive way. After the in-service,

they were conscious of teaching higher order thinking as a distinct educational goal.

Teachers did not have declarative knowledge of thinking skills, e.g., they could not articulate

thinking objectives or thinking skills as a goal of a lesson plan. They were unable to discuss

thinking skills in general terms using names, rules, and definitions and to think of them as

explicit instructional objectives. Once thinking skills were made explicit, the teachers could

effectively design their learning activities.

Discrepancy between procedural knowledge and declarative knowledge- teachers may

intuitively teach for thinking, but they have trouble articulating the skills and making them

explicit goals of lessons.

If teachers have difficulty articulating these skills, they may not necessarily teach them or make

them explicit to their students. They may also have difficulty teaching them across different

contexts in science.


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In 1995 teachers were asked to create learning materials which will apply the goals and

instructional means of the TSC project to new science topics (less teachers addressing thinking

skills in 1995). In 1996, teachers reviewed of thinking skills in several TSC learning activities and

given a written page of guidelines including a request to define the thinking skills in each item

they wrote.

Shulman-absence of focus on subject matter among the various research paradigms for the

study of teaching as the missing paradigm

Thinking skills should be a goal of teaching. When teaching pedagogical knowledge of thinkingskills, teachers need to be taught the subject matter, e.g., thinking skills, before learning HOW

to teach thinking skills to students.

We learn physics before learning how to teach physics effectively. Likewise, teachers need to

learn about thinking skills before learning how to teach thinking skills effectively.

I think this is important for us because we want teachers/professors to teach metacognitive

skills within the context of physics. First, we need to have a coherent vocabulary that describes

and defines the metacognitive strategies we are talking about to ensure that teachers are on

the same page. Then we can talk about the pedagogy-how to teach these strategies,

implement them in the context of physics, and help students generalize metacognitive

knowledge and strategies.

metacognition discussion

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