The Cognitive Processes Dimension

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Analyzing standards from a cognitive perspective

• Analyzing standards from a cognitive perspective
  can help teachers in three ways
• It can help to gain a more complete understanding
  of their standards (learning).
• Make better decisions about how to teach and
  assess their students (instruction and
  assessment).
• It can help determine how well the standards,
  assessments and instructional activities fit
  together in a meaningful way (alignment).

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Taxonomy Table
Analyzing standards from a cognitive
perspective. Procedure 1) choose a science
standard. In our example it will be 6th grade,
standard 1A. 2) Identify one and only one cell in
the taxonomy table that the standard best
matches. Use the descriptions of the cognitive
processes and knowledge types to identify the
cell that the standard is most closely aligned
with. 3) Create a task(s) that will assess
students understanding of the standard(s). 4)
Identify activities the will build student
mastery of the standard. 5) Repeat this process
for related science standards and standards from
other disciplines.
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The Cognitive Processes Dimension
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The Cognitive Processes Dimension
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Knowledge Table
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6th grade science
Plate tectonics accounts for important features
of Earths surface and major geologic events. As
a basis for understanding this concept 1a.
Students know evidence of plate tectonics is
derived from the fit of the continents the
location of earthquakes, volcanoes, and mid-ocean
ridges and the distribution of fossils, rock
types, and ancient climatic zones. 1b. Students
know Earth is composed of several layers a cold,
brittle lithosphere a hot, convecting mantle
and a dense, metallic core. 1c. Students know
lithospheric plates the size of continents and
oceans move at rates of centimeters per year in
response to movements in the mantle.
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6th grade science contd
1d. Students know that earthquakes are sudden
motions along breaks in the crust called faults
and that volcanoes and fissures are locations
where magma reaches the surface. 1e. Students
know major geologic events, such as earthquakes,
volcanic eruptions, and mountain building, result
from plate motions. 1f. Students know how to
explain major features of California geology
(including mountains, faults, volcanoes) in terms
of plate tectonics. 1g. Students know how to
determine the epicenter of an earthquake and know
that the effects of an earthquake on any region
vary, depending on the size of the earthquake,
the distance of the region from the epicenter,
the local geology, and the type of construction
in the region.
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The Cognitive Processes Dimension

• Remembering - Retrieve relevant knowledge from
  long-term memory

Recognizing Identifying Locating knowledge in long-term memory that is consistent with presented material
Recalling Retrieving Retrieving relevant knowledge from long-term memory.
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The Cognitive Processes DimensionUnderstand -
Construct meaning from instructional messages,
including oral, written, and graphic communication
Interpreting Clarifying, paraphrasing, representing, translating
Exemplifying Illustrating, instantiating
Classifying Categorizing, subsuming
Summarizing Abstracting, generalizing
Inferring Concluding, extrapolating, interpolating, predicting
Comparing Contrasting, mapping
Explaining Constructing models
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The Cognitive Processes DimensionApply - Carry
out or use a procedure in a given situation
Executing Carrying out
Implementing Using
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The Cognitive Processes DimensionAnalyze - Break
material into its constituent parts and determine
how the parts relate to one another and to an
overall structure or purpose
Differentiating Discriminating, distinguishing, focusing, selecting
Organizing Finding coherence, integrating, outlining, parsing, structuring
Attributing Deconstructing
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The Cognitive Processes DimensionEvaluate - Make
judgments based on criteria and standards
Checking Coordinating, detecting, monitoring, testing
Critiquing Judging
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The Cognitive Processes DimensionCreate - Put
elements together to form a coherent or
functional whole reorganize elements into a new
pattern or structure
Generating Hypothesizing
Planning Designing
Producing Constructing
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Knowledge TypesBased on A Taxonomy for Teaching,
Learning, and Assessing (2001, Anderson, L.,
Krathwohl).

• Assumptions
• Non-Behaviorist view knowledge is not best
  characterized as an accumulation of associations
  between stimuli and responses (although some
  surely is) or merely a quantitative increase in
  bits of information.
• Constructivist view - Knowledge is organized and
  structured by the learner but not in stages or
  in a logico-systemic manner as in strict
  Piagetian notions.
• Parsimony There are many different types of
  knowledge along with terms to describe them
  conceptual, conditional, content declarative,
  disciplinary, discourse, domain, episodic,
  explicit, factual, metacognitive, prior,
  procedural, semantic situational, sociocultural,
  strategic, tacit, etc. For simplicity of use we
  use four categories factual, conceptual,
  procedural, metacognitive
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• Defining knowledge types With your neighbor
  come up with a definition of the four types of
  knowledge Factual, Conceptual, Procedural, and
  Metacognitive

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Factual Knowledge - Factual knowledge encompasses
the basic elements that experts use in
communicating about their academic discipline,
understanding it, and organizing it
systematically. Factual knowledge contains the
basic elements students must know if they are to
be acquainted with the discipline or to solve any
of the problems in it. For the most part factual
knowledge exists at a relatively low level of
abstraction

• Knowledge of terminology
• Technical vocabulary - examples
• Knowledge of the alphabet
• Knowledge of scientific terms
• Knowledge of standard representational symbols on
  maps and charts
• Knowledge of the symbols used to indicate correct
  pronunciation of words

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Factual Knowledge

• Knowledge of specific details and elements
• Knowledge of major facts about particular
  cultures and societies
• Knowledge of practical facts important to health,
  citizenship and human needs
• Knowledge of more significant names, places, and
  events in the news
• Knowledge of major products and exports of
  countries
• Knowledge of reliable sources of information for
  wise purchasing
• Create examples for the two subtypes of Factual
  Knowledge

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Conceptual knowledge - includes schemas, mental
models, or implicit or explicit theories in
different cognitive psychological models. These
schemas, models, and theories represent the
knowledge an individual has about how a
particular subject matter is organized and
structured, how the different parts or bitts of
information are interconnected and interrelated
in a more systematic manner, and how these parts
function together.

• Knowledge of classifications and categories
  Includes specific categories, classes, divisions
  and arrangements that are used in different
  subject matters. Classifications and categories
  differ from terminology and facts in that they
  form the connecting links between and among
  specific elements.
• Knowledge of the variety of types of literature
• Knowledge of the various forms of business
  ownership
• Knowledge of the parts of sentences
• Knowledge of the different kinds of psychological
  problems

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Conceptual knowledge

• Knowledge of principals and classifications
  Principals and generalizations tend to dominate
  an academic discipline and are used to study
  phenomena or solve problems in the discipline.
  One of the hallmarks of a subject matter expert
  is the ability to recognize meaningful patterns
  and activate the relevant knowledge of these
  patterns with little cognitive effort. Principles
  and generalizations bring together large numbers
  of specific details and describe the processes
  and interrelationships among the classifications
  and categories. Principles and generalizations
  tend to be broad ideas that may be difficult for
  students to understand because students may not
  be thoroughly acquainted with the phenomena they
  are intended to summarize and organize.
• Knowledge of major generalizations about
  particular cultures
• Knowledge of the fundamental laws of physics
• Knowledge of the major principles of learning
• Knowledge of the principles of federalism
• Knowledge of the principles that govern
  rudimentary arithmetic operations (e.g. the
  commutative principle, the associative principle)

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Conceptual Knowledge

• Knowledge of theories, models, and structures -
  This knowledge includes knowledge of principles,
  and generalization together with their
  interrelationships that present a clear, rounded,
  and systemic view of a complex phenomenon,
  problem, or subject. These are the most abstract
  formulations.
• Knowledge of the interrelationships among
  chemical principles as the basis for chemical
  theories
• Knowledge of the overall structure of Congress
• Knowledge of the basic structural organization of
  the local city government
• Knowledge of a relatively complete formulation of
  the theory of evolution
• Knowledge of the theory of plate tectonics
• Knowledge of genetic models
• Create examples for the three subtypes of
  Conceptual Knowledge

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Procedural KnowledgeWhereas factual and
conceptual knowledge represent the what of
knowledge, procedural knowledge concerns the
how. Procedural knowledge reflects knowledge of
different processes, whereas factual and
conceptual knowledge deal with what might be
termed products. It is important to note that
procedural knowledge represents only the
knowledge of these procedures, their actual use
is included in the apply category of the
cognitive dimensions. In contrast to
metacognitive knowledge procedural knowledge is
specific or germane to particular subject matters
or academic disciplines.

• Knowledge of subject specific skills and
  algorithms Procedural knowledge can be
  expressed as a series or sequence of steps known
  as a procedure. Sometimes the steps are followed
  in a fixed order at other times decisions must
  be made about which step to perform next.
  Similarly, sometimes the end result is fixed in
  other cases it is not.
• Knowledge of the skills used in painting with
  watercolors
• Knowledge of the skill used to determine word
  meaning based on structural analysis
• Knowledge of the various algorithms for solving
  quadratic equations
• Knowledge of the skills involved in performing
  the high jump

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Procedural Knowledge

• Knowledge of subject specific techniques and
  methods In contrast with specific skills and
  algorithms that usually end in a fixed result,
  some procedures do not lead to a single
  predetermined answer or solution. We can follow
  the general scientific method in a somewhat
  sequential manner to design a study, but the
  resulting experimental design can vary greatly
  depending on a host of factors. In this type of
  procedural knowledge, then, the result is more
  open and not fixed, in contrast to knowledge of
  subject specific skills and algorithms.
• Knowledge or research methods relevant to the
  social sciences
• Knowledge of the techniques used by scientists in
  seeking solutions to problems
• Knowledge of the methods for evaluating health
  concepts
• Knowledge of various methods of literary
  criticism

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Procedural Knowledge

• Knowledge of criteria for determining when to use
  appropriate procedures - In addition to knowing
  subject specific procedures, students are
  expected to know when to use them, which often
  involves knowing the ways they been used in the
  past. Though simpler and perhaps less functional
  than the ability to actually use the procedures,
  knowledge of when to use appropriate procedures
  is an important prelude to their proper use.
  Thus, before engaging in an inquiry or solving a
  particular problem, students may be expected to
  know the methods and techniques that have been
  used in similar inquiries. At a later state in
  the process they may be expected to show
  relationships between the methods and techniques
  they actually employed and the methods employed
  by others. Experts know when and where to apply
  their knowledge. They have criteria that help
  them make decisions about when and where to use
  different types of subject specific procedural
  knowledge that is, their knowledge is
  conditionalized, in that they know the
  conditions under which the procedures are to be
  applied.

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Procedural Knowledge

• Knowledge of criteria for determining when to use
  appropriate procedures
• Knowledge of the criteria for determining which
  of several types of essays to write
• Knowledge of the criteria for determining which
  method to used in solving algebraic equations
• Knowledge of the criteria for determining which
  statistical procedure to use with the data
  collected in a particular experiment
• Knowledge of the criteria for determining which
  technique to apply to create a desired effect in
  a particular watercolor painting
• Create examples for the three subtypes of
  Procedural Knowledge

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Metatcognitive Knowledge

• Metacognitive knowledge is knowledge about
  cognition in general as well as awareness of and
  knowledge about ones own cognition. An important
  distinction in this field is between knowledge of
  cognition and the monitoring, control, and
  regulation of cognition. In recognition of this
  distinction we will use only students knowledge
  of various aspects of cognition, not the actual
  monitoring, control, and regulation of their
  cognition. The latter will be covered in the
  discussion of the cognition dimensions.

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Metacognitive Knowledge

• Strategic knowledge This is knowledge of the
  general strategies for learning, thinking, and
  problem solving. The strategies in this subtype
  can be used across many different tasks and
  subject matters, rather than being most useful
  for one particular type of task in one specific
  subject area (e.g. solving a quadratic equation).
  This subtype includes knowledge of the variety
  of strategies that students might used to
  memorize material, extract meaning from text, or
  comprehend what they hear in classrooms or read
  in books and other course materials. The large
  number of different learning strategies can be
  grouped into three general categories
•         Rehearsal
•         Elaboration
•         Organizational

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Metacognitive Knowledge

• Strategic knowledge
• Knowledge that rehearsal of information is one
  way to retain the information
• Knowledge of various mnemonic strategies for
  memory (e.g., pairing, categorizing, procedures,
  patterns or rules)
• Knowledge of various elaboration strategies such
  as paraphrasing, summarizing, questioning,
  predicting, connecting, clarifying, visualizing
• Knowledge of various organizational strategies
  such as outlining or diagramming
• Knowledge of planning strategies such as setting
  goals for reading
• Knowledge of comprehension monitoring strategies
  such as self-testing or self-questioning
• Knowledge of means-end analysis as a heuristic
  for solving an ill-defined problem
• Knowledge of working backwards from the desired
  goal state
• Knowledge of strategies for inductive and
  deductive thinking including evaluating the
  validity of different logical statements,
  avoiding circularity in arguments, making
  appropriate inferences from different sources of
  data, and drawing on appropriate samples to make
  inferences.

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Metacognitive KnowledgeKnowledge about
cognitive tasks, including contextual and
conditional knowledge This includes knowledge
that different cognitive tasks can be more or
less difficult, may make differential demands on
the cognitive system, and may require different
cognitive strategies. For instance, a recall task
is more difficult than a recognition task because
recall requires a search in long term memory
whereas recognition requires discrimination among
alternatives. If one thinks of strategies as
cognitive tools that help students construct
understanding, then different cognitive tasks
require different tools, just as a carpenter uses
different tools for performing all the tasks that
go into building a house

• Knowledge that recall tasks generally make more
  demands on the individuals memory system than
  recognition tasks
• Knowledge that a primary source book may be more
  difficult to understand than a general textbook
  or popular book
• Knowledge that a simple memorization task may
  require only rehearsal
• Knowledge that elaboration strategies like
  summarizing and paraphrasing can result in deeper
  levels of comprehension
• Knowledge that general problem solving heuristics
  may be most useful when the individual lacks
  relevant subject or task specific knowledge or in
  the absence of specific procedural knowledge

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Metacognitive KnowledgeSelf-Knowledge
Self-knowledge includes knowledge of ones
strengths and weaknesses in relation to cognition
and learning. Self-awareness of the breadth and
depth of ones own knowledge base is an important
aspect. An awareness that one tends to over-rely
on a particular strategy, when there may be other
more adaptive strategies for the task, could lead
to a change in strategy use.

• Knowledge that one is knowledgeable in some areas
  but not in others
• Knowledge that one tends to rely on one type of
  cognitive tool
• Knowledge of ones capabilities to perform a
  particular task that are accurate, not inflated
  (e.g. overconfident)
• Knowledge of ones goals for performing a task
• Knowledge of ones personal interest in a task
• Knowledge of ones judgments about the relative
  utility value of a task

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7th grade mathematics
Standard(s) 1.0 Students express quantitative
relationships by using algebraic terminology,
expressions, equations, inequalities, and
graphs 1.1 Use variables and appropriate
operations to write an expressions, an equation,
an inequality, or a system of equations or
inequalities that represents a verbal description
(e.g. three less than a number, half as large as
area A). 1.2 Use the correct order of operations
to evaluate algebraic expressions such as
3(2x5)2. 1.3 Simplify numerical expressions by
applying properties of rational numbers (e.g.,
identity, inverse, distributive, associative,
commutative) and justify the process used.
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7th grade mathematics

• 3.0 Students graph and interpret linear and some
  nonlinear functions
• 3.1- Graph functions of the form y nx2 and
• y nx3 and use in solving problems.
• 3.2 - Plot the values from the volumes of
  threedimensional shapes for various values of
  the edge lengths (e.g., cubes with varying edge
  lengths or a triangle prism with a fixed height
  and an equilateral triangle base of varying
  lengths).

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7th grade mathematics
3.3- Graph linear functions, noting that the
vertical change (change in y-value) per unit of
horizontal change (change in x-value) is always
the same and know that the ration (rise over
run) is called the slope of a graph.
3.4 - Plot the values of quantities whose
rations are always the same (e.g., cost to the
number of an item, feet to inches, circumference
to diameter of a circle). Fit a line to the plot
and understand that the slope of the line equals
the quantities.