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Learning levels

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Learning levels• Construct a concept• Discover a relationship• Simple knowledge• Algorithmic skill• Comprehension and communication• Application• Creative thinking• Affective domain:• Appreciation• Willingness to try

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Construct a concept• Objective: Students achieve an objective at the construct-a-concept learning level by using inductive reasoning to distinguish examples of a particular concept from non-examples of that concept• Stages: • Sorting and Categorizing• Reflecting and Explaining• Generalizing and Articulating• Verifying and Refining

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Discover a relationship• Objective: Students achieve an objective at the discover-a-relationship learning level by using inductive reasoning to discover that a particular relationship exists or why the relationship exists.• Stages: • Experimenting Stage• Reflecting and Explaining Stage• Hypothesizing and Articulating Stage• Verifying and Refining

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Simple knowledge• Objective: Students achieve an objective at the simple-knowledge learning level by remembering a specified response (but not multiple-step process) to a specified stimulus.• Stages: • Exposition• Explication• Mnemonics• Monitoring and feedback• Overlearning

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Algorithmic skill• Objective: Students achieve an objective at the algorithmic-skill level by remembering and executing a sequence of steps in a specific procedure. • Stages: • Explanation of the purpose of the algorithm• EXPLANATION AND PRACTICE ESTIMATING OUTCOMES• General overview of the process• Step-by-step explanation of the algorithm• Trial test execution of the algorithm• Error-pattern analysis and correction• Overlearning

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Application• Objective: Students achieve an objective at the application level by using deductive reasoning to decide how to utilize, if at all, a particular mathematical content to solve problems.• Stages: • Initial Problem Confrontation and Analysis• Subsequent Problem Confrontation and Analysis• Rule Articulation• Extension into Subsequent Lessons

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Application• Objective: Students achieve an objective at the application level by using deductive reasoning to decide how to utilize, if at all, a particular mathematical content to solve problems.• Stages: • Initial Problem Confrontation and Analysis• Subsequent Problem Confrontation and Analysis• Rule Articulation• Extension into Subsequent Lessons

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Comprehension and Communication • Objective: Students achieve an objective at the comprehension-and-communication level by (i) extracting and interpreting meaning from an expression, (ii) using the language of mathematics, and (iii) communicating with and about mathematics.• Literal understanding of mathematical messages• Interpretive understanding of mathematical messages

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Comprehension and Communication • Technical Expressions• Common English words with special definitions• Technical mathematical words• Numerals• Shorthand symbols• Communication or language structures• Stages of lessons:• The Message is Sent to the Students• The Message is Rephrased and Explained• Students Are Questioned about the Specifics of the Message• Students Are Provided with Feedback on Their Responses

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Creative Thinking

• Objective: Students achieve an objective at the creative-thinking learning level by using divergent reasoning to view mathematical content from unusual and novel ways.

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Affective domain• Appreciation • Students achieve an objective at the appreciation learning level by believing the mathematical content specified in the objective has value.

• Willingness to Try • Students achieve an objective at the willingness-to-try learning level by choosing to attempt a mathematical task specified by the objective.

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COOPERATIVE LEARNING

In your group, write a definition of collaborative learning which includes all desirable aspects of it.

Five essential elements:• positive interdependence• individual accountability• face to face interaction• collaborative skills• group processing

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WHY??

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COMPARE

INDIVIDUALLEARNING

GROUPWORK

I must learn this. Someone must learn this.

We must learn this.

Competitive Varies Cooperative

I am responsible for only myself.

They are responsible for me or I am responsible for them.

We are responsible to each other. 

Interaction is with text, teacher, or materials.

Vaguely structured interaction.

Highly structuredinteraction

Learn individually,perform individually

Learn individually,perform cooperatively.

Learn cooperatively, Perform individually.

Grade curve Group grade Positive interdependence, Individual accountability.

COOPERATIVELEARNING

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Norms

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Assign Roles

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How to form groups

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Social Skills

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Teacher's Roll

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Cooperative learning structures

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Assessment

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Appropriate topics for collaborative learning.

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Suggestions for successful cooperative learning experiences:1.  Start cooperative learning with short activities.  Lead up to longer projects gradually to teach skills of working in groups.2.  Have students do some preliminary work at home, then bring it to the group for processing.3.  Use team building activities at the beginning of the year and whenever new teams are formed to encourage team members to know and trust each other.  These should be short, social and meant to build inclusion.4.  Assign jobs within the group5.  Outline tasks specifically, giving clear directions6.  Utilize efficient and routine procedures for making the transition from class to groups.7.  Use rubrics instead of grades to help students check progress.8.  Spot check groups to see that individuals are performing.9.  Demonstrate the finished product10.  Vary the size of groups and the method for grouping

• ability grouping• tutoring grouping• random grouping• student choice11.  Monitor the group activities, not spending too much time with any one group.12.  Plan for closure points, especially for lengthy activities.13.  Follow up group work by utilizing the product in subsequent learning activities14.  Evaluate the team process as well as the finished product.

Suggestions for successful cooperative learning experiences1.  Start cooperative learning with short activities.  Lead up to longer projects gradually to teach skills of working in groups.

2.  Have students do some preliminary work at home, then bring it to the group for processing.

3.  Use team building activities at the beginning of the year and whenever new teams are formed to encourage team members to know and trust each other.  These should be short, social and meant to build inclusion.

4.  Assign jobs within the group

5.  Outline tasks specifically, giving clear directions

6.  Utilize efficient and routine procedures for making the transition from class to groups.

7.  Use rubrics instead of grades to help students check progress.

8.  Spot check groups to see that individuals are performing.

9.  Demonstrate the finished product.

10. Vary the size of groups and the method for groupingby seatingability groupingtutoring groupingrandom groupingstudent choiceteacher choice

11. Monitor the group activities, not spending too much time with any one group.

12.     Plan for closure points, especially for lengthy activities.

13.     Follow up group work by utilizing the product in subsequent learning activities.

14.     Evaluate the team process as well as the finished product.

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Cooperative Learning Evaluation No name necessary

Please answer each of the following questions honestly.  

1. Did you like working with a partner? 1  2  3  4  5  loved

2. How well did you two work together 1  2  3  4  5  great

3. How good was your partner? 1  2  3  4  5  great

4. How good a partner were you? 1  2  3  4  5  great

5. How well did you know your partner before? 1 2  3  4  5   well

6. How well do you know them now? 1  2  3  4  5   well

7. Did you score better than on your own? 1  2  3  4  5   much

8. Who did most of the work? 1  2  3  4  5   you

9. Did you do put in more or less effort on this   unit than on the others we have done? 1  2  3  4  5   more

10.  What did you like best about the experience?  What were the advantages?

11.  What did you like least about it?  What were the disadvantages?

12.  Did you come to school on a day when you might not have so that you would not disappoint your partner?

13.  Did you try harder for the sake of the partner?

14.  What did you learn about life from this experience?

15.  Shall we do it again?

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Cooperative Learning Is:

An appropriately­sized and carefully structured group involved in collaboration, sharing and compromise as they engage in synergistic discussion of a carefully selected task using assigned roles to share perspective as they scaffold, while practicing positive interdependence on the road to a common goal of mutual understanding.

Working together in synergistically supervised structured groups to facilitate learning by communicating ideas to achieve the common goal while demonstrating individual accountability.

Student collaboration and interaction in structured groups working on well­defined tasks where they help each other build their own core knowledge and take responsibility for their learning while heading toward a common goal.

Cooperative learning is a classroom of students in a premeditated group working toward a common goal accomplishing detailed well­defined tasks by sharing knowledge and experience in an enjoyable atmosphere of respect and support from inside and outside the group in such a way that each individual is accountable for themselves and each other.

Cooperative learning is accountable individuals in well­structured groups working together on well­defined tasks to accomplish a common goal in a collaborative environment.

Cooperative learning is a team process coached by the teacher where a small group learns by working respectfully toward a common goal by sharing responsibility and accountability while solving well­designed problems through discussion, analysis and examination of the consequences of the outcome.

2008:A true collaborative learning experience takes place in a safe environment  carefully guided by the teacher, and will include students  synergistically engaged in listening, discussing, sharing and brain­storming, with each assuming personal accountability for their own learning as well as exhibiting an attitude of positive interdependence to see that the experience is mutually beneficial to everyone involved.

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