Metacognition in Elementary Mathematics

Daniel C. Moos, PhD

Objectives:

1. What is metacognition?

2. Why is metacognition important?

3. What are some developmental considerations for metacognition?

4. How can Elementary teachers support metacognition?

5. How can Elementary teachers support metacognition in mathematics?

Opening questions:

1. In your experience, what types of strategies do students use when learning mathematics (i.e. taking notes, memorization, maladaptive help-seeking, etc) and to what extent do they appropriately apply these strategies?

2. In your experience, which of these strategies are effective? Ineffective?

3. In your experience, what instructional practices help students use/learn these strategies?

4. Which strategies (or other learning processes) do you wish your students utilized more often? Why do they not use these strategies more often?

Tall in the the saddle

Guiding Question: What does this activity suggest about the role of prior knowledge and experience in learning?

“Phraseology” example

RED BLACK BLUE BLACK YELLOW BLACK RED YELLOW BLUE BLACK

RED BLACK BLUE BLACK YELLOW RED YELLOW BLUE BLACK RED

As quickly as you can, quietly say the COLOR and not the pronunciation of the following words (from left to right):

Example: Yellow Blue

Guiding Question: What does this activity suggest about the role of “attention” and “perception” in learning? Implications for teachers?

“Color” example

31 5 70 4860 201 4201

Guiding Question: What does this activity suggest about the importance of organization in learning? What does this activity suggest about the maximum number of items we can learn at one time? Implications for teachers?

“Numbers” example

As quickly as you can…

…state the months of the year

…state the months of the year, alphabetically

Guiding Question: What does this activity suggest about the role of how we originally learn in retrieving this knowledge? Implications for teachers?

“Months” example

Information Processing Theory

What is Metacognition?

Cognition refers to… The manner in which information is processed (the

way in which students process, store, retrieve, manipulate knowledge)

Metacogntion refers to… Knowledge about these operations and how they

may be best used to achieve a learning goal

What is Metacognition?, continued

A critical turning point during World War II was…hmm..wonder what I should wear tomorrow…World War II, December 7, 1941….I am really mad at what Sally said to me in PE today….let’s see..I’ve finished the first part of the chapter..

A critical turning point during World War II was…I think we talked about this yesterday …World War II, December 7, 1941...I don’t really understand this paragraph…I better read it again…

What is Metacognition according to Flavell (1987)?

Knowledge-of-person variables Individual understanding (are you better at math

or English?) Knowledge-of-task variables

Knowledge of tasks (which tasks take you longer to complete?)

Knowledge-of-strategy variables Knowledge of effective strategies (which

strategies are most effective for you?)

Age trends in Metacognition Young Elementary (6 yr olds)

Do know: Familiar items easier to remember, small set of information easier to recall

Do not know: Limit to amount one can recall Young Elementary (7 yr olds)

Do know: Interest, familiarity, and story length affect comprehension and recall

Do not know: time of test should affect study time Elementary (9 yr olds)

Do know: Recall is limited (younger children overestimate how much they can store and retrieve)

Begin to understand when they know something well enough to pass a memory test (younger children choose to study something they had already seen)

Supporting Students’ Metacognition

“Self-metacognitive questions”: Creating a Thinking Checklist Comprehending the problem

“What is the problem/task?” Constructing connections between previous and new

knowledge “What are the similarities/differences between the problem/task at hand

and problems/tasks I have solved in the past, and why?” Using appropriate strategies to solve the problem/task

“What are some appropriate strategies?” “When and how should I use a particular strategy?”

Reflecting on the process and the solution “Does the solution make sense?” “How can I solve the task in another way?”

Metacognitive Calibration “How well did you do on the assessment?” (Likert scale)

Supporting Students’ Metacognition

Metacognition in Mathematics: Wild Goose Chase in Problem Solving

• Students generally apply learned procedures in straightforward way• (1) Applies it persistently, even in the absence of success• (2) Haphazardly jumps from one strategy to another, becomes

frustrated and then gives up• Teacher’s response to frustrated students?

• Assume lack of process knowledge and re-teach the skills within context of particular problem

Band-aid (student solves this particular problem, but will end up in a wild goose chase again)

Metacognitive support: • More general process support (Thinking checklist)• Think aloud (teacher and student)

Ending questions:

1. In your experience, to what extent do your students engage in metacognition? How accurate are they in assessing their own knowledge (“metacognitive calibration”)

2. What instructional practices would help your students with their metacognition?

Email: dmoos@gustavus.edu

Website: http://homepages.gac.edu/~dmoos/