FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1
Cognitive Information Processing
Function Families
Martha Townsend
G...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 2
Cognitive Information Processing
Function Families
Instructional Goa...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 3
Instructional Goals (continued)
Show students how
to chunk related
i...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 4
Learning Focus for Function Family Lesson
Essential Questions
Key De...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 5
Learning Objectives
Related to Cognitive Information Process
Student...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 6
Learning objectives (continued)
Synthesize, interpret,
evaluate, and...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 7
Standards
(Common Core Georgia Performance Standards)
(CCGPS)
Studen...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 8
Learning Environment
Student Activities Using
Technology-Based
Instr...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 9
Justification for a Technology-Based Module
Students will have a com...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 10
Assessment of Lesson Rubric
Justification of CIP
CIP
Activity
Limit...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 11
Functions Families Lesson Rubric (continued)
PRACTICE
WORKSHEETS
Sy...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 12
Function Families Lesson Rubric (continued)
GRAPHIC
ORGANIZERS
AND
...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 13
Function Families Lesson Rubric (continued)
NOTE-TAKING
GUIDES: NOT...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 14
Justification of Cognitive Information Processing
(Processing, stor...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 15
Justification of Cognitive Information Processing (continued)
Autom...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 16
Justification of Cognitive Information Processing (continued)
♦ Off...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 17
Justification of Cognitive Information Processing (continued)
Rehea...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 18
Justification of Cognitive Information Processing (continued)
(cont...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 19
Justification of Cognitive Information Processing (continued)
Retri...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 20
Justification of Alignment
CIP
Learning
Objective
Instructional Str...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 21
Justification of Alignment (continued)
• Define categories
• Group ...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 22
Justification of Alignment (continued)
Analyze
Students will be
abl...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 23
Justification of Alignment (continued)
• formulate
• generate
• ini...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 24
Figure A
Sample Slidefrom SlideRocketPresentation
MEET BUZZ
Buzz is...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 25
Figure B
Sample Slide from SlideRocketPresentation: Vertical Shift
...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 26
Figure C
Sample Slide from SlideRocketPresentation: Vertical Reflec...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 27
Figure D
Sample Slide from SlideRocketPresentation: Vertical Shrink...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 28
Figure E
Sample Slide from SlideRocketPresentation: Vertical Stretc...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 29
Figure F
Sample Slide from SlideRocketPresentation Introducing “Lin...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 30
Figure G
Sample Slide from SlideRocketPresentation Introducing “Abb...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 31
Figure H
Sample Slide from SlideRocketPresentation Introducing “Cur...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 32
Figure I
Sample Slide from SlideRocketPresentation Introducing “Squ...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 33
Figure J
Sample Slide from SlideRocketPresentation Introducing “Rac...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 34
Figure K
Sample Slide from SlideRocketPresentation Introducing “Qui...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 35
Figure L
Screen Shot of Appletsfor Manipulation of Functions
Multi-...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 36
Figure M
Sample Warm-up Quizon the Basic Behaviors of Functions
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 37
Figure N
Note-taking Guide
Name: Class: Date: Lesson Topic:
Learnin...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 38
FigureO
Sample Chart
Fill in the
organizer
according to the
informa...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 39
Figure P
Sample Chart
According to the
condition of Buzz
below, fil...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 40
Figure Q
Sample Graphic Organizer
Definition Facts/Characteristics
...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 41
FigureR
Sample Practice Worksheet on Writing Equations
Look at each...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 42
FigureS
Sample Practice Worksheet on Writing Equations
Look at each...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 43
FigureT
Sample Practice Worksheet on Writing Equations
Look at each...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 44
Figure U
Sample Practice Worksheet Drawing Graphs
Place a box aroun...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 45
FigureV
Sample Review Activity on Shifting Parent Graphs
Graph
Awak...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 46
FigureW
Activity on Linear Regression Which Serves as an Additional...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 47
Figure W (continued)
Activity on Linear Regression Which Serves as ...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 48
Figure W (continued)
Activity on Linear Regression Which Serves as ...
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 49
FigureX
SampleAssessment Questions
(continued)
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 50
FigureX(continued)
Sample Assessment Questions
FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 51
References
Driscoll, M.P. (2005). Psychology of learning for instru...
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Technology Based Module CIP Using Mobile Apps

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Technology Based Module CIP Using Mobile Apps

  1. 1. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1 Cognitive Information Processing Function Families Martha Townsend Georgia Southern University
  2. 2. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 2 Cognitive Information Processing Function Families Instructional Goals CIP Goals (Driscoll, 2005, p. 71-110) Methods of Instruction Technology-Based Student Activities Gain and keep the attention of students. The students will start each day of class by watching an entertainingSlideRocket Presentation on function families via their iPads or iPhones. This presentation includes a meaningful storywith color, audio, and animation. The teacher will keep students focused on learning usingTeacher's Assistant Pro which allows teachers to keep track of student actions, behaviors, and achievements in the classroom. The teacher will view each student’scomputer screen on the teacher computer and monitor their activities. The teacherwill interact with students through the management software to keep them engaged and on-task. The students will use applets to explore and experiment with functions. These provide interactive entertainment. Incorporate relevant prior learning. The students will complete a warm-up activity each day. The questions on the warm-up will cover the previous lesson on the characteristics of function. The teacher will analyze student responses and use ClickerSchool Virtual Clicker to communicate feedback to the students. Highlight and stress important information. As students watch the presentation they will fill in anote-taking guide with a section labeled “Cues”. In this box they should type in key ideas. The teacher will use the teacher computer and overhead projector to display key words and important facts. Present lesson in an organized manner. The lesson, which is presented in story format, will followa logical sequence as it introduces new concepts and skills. Once students have mastered the characteristics of manipulating the example graph, they will recognize the parent graphs and slowly begin to apply those same properties. Studentswill take each of the parent graphs and shift them up or down in accordance to their equation. Next students will advance to the more complex concept of reflecting a function over the x- axis. Finally,the studentswill combine the steps for vertically manipulating a function. (continued)
  3. 3. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 3 Instructional Goals (continued) Show students how to chunk related information. The graphic organizers and note-taking guideswill allow students togroupthe concepts into categories with manageable steps. The activities and lesson will teach students inductive reasoning as theyconstruct or evaluate general propositions about functions. These are derived from specific examples. Provide activities for students which allow them to elaborate on new information. The students will perform activities that will allow them to connect the graphing of more complex functions to what they already know about the behaviorsof basic functions. The students will perform activities that will allow them to connect the graphing of functions to each other. The students will look for similarities and differences between the functions,their algebraic equations, and their graphs. Show students how to use coding when memorizing concepts and facts. The students will learn what the graph of each function looks like by relating it to an animal that is similar in appearance. The students will learn the names of the functions by giving the corresponding animals a name that starts with the same letter. The students will learn how to algebraically manipulate the graph of a function by relating the aspects of their equations to the behaviors of the animal. Provide students the opportunity for repetition of learning. The students will receive the information and practice on applying the behaviors of functions several times in various ways. The students will collaborate with peers and ask questions or help explain the material. The students will complete homework activities that reinforce the material that was learned that day. Provide activities for automaticity of fundamental concepts and skills. The students will continue to review graphing skills and the basic properties of functions through practice worksheets and the test review. The students will use ClickerSchool Virtual Clickersubmit answer towarm-up activities on the basic concepts involved with functions and receive immediate feedback. The students will access applets on the Internet that will allow them to practice manipulating the graphs of functions in the coordinate plane. Prior Relevant Learning Focus Essential Questions Key Definitions What are the characteristics of a function and how can you implement and apply these characteristics to arrange and illustrate the function in multiple ways? • Coordinate plane • Relation • Ordered pair • Independent variable • Dependent variable • x-coordinate • y-coordinate • x|y chart • Abscissa • Ordinate • Input • Output • Table • Function • Graph • Domain • Range • Vertical line test
  4. 4. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 4 Learning Focus for Function Family Lesson Essential Questions Key Definitions (Should be stressed and highlighted) What are the properties of the parent graphs of linear, quadratic, cubic, absolute value, and square root functions and how can you implement and apply these properties to identify, compare, and illustrate the functions? • Maximum • Minimum • Absolute Value • Parent Graph • Zero • Linear • Quadratic • Parabola • Radical • Infinity • Cubic How can you recognize ifthe parent graphs and equations of linear, quadratic, cubic, absolute value, and square root functionshave been vertically affected? How can you distinguish among, implement, and demonstrate vertical transformations of linear, quadratic, cubic, absolute value, and square root functions? • Coefficient • Reflection • Solution • Increasing • Shrink • Decreasing • Average rate of change • Slope • End behavior • Stretch • Shift Prior Relevant Learning Objectives Students should have already: At the beginning of this lesson students should be able to: Comprehended and interpreted the characteristics of relations and functions. • Develop and illustrate a relation in multiple ways without the use of Quick Graphbut by using tables, x|y charts, listing of ordered pairs, or graphs in the coordinate plane. • Identify and arrange the domain and range of a relation by looking at a table, x/y chart, a listing of ordered pairs, or graph. • Deduce and classify a relation as being a function by looking at a table, x/y chart, or a listing of ordered pairs. • Perform and apply the vertical line test to determine if a graph is a function. • Calculate to develop x|y charts of functions from their equations and illustrate these functions in the coordinate plane. • Demonstrate graphs of functions using Quick Graph.
  5. 5. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 5 Learning Objectives Related to Cognitive Information Process Students completing this lesson will: Students that successfully complete this lesson will be able to: Understand, recognize, evaluate, and analyzethe properties of the parent graph equations of linear, quadratic, cubic, absolute value, and square root functions. • Identify, define, describe, and label the parent graph equations and organize, classify, and summarize this information. • Determine if an equation is one of the parent graph equations. • Differentiate between and compare the equations of parent graph functions. • Develop and produce theparent graph equations from memory. • Recall and recognize the characteristic of the equations of parent graphs. Understand, recognize, evaluate, and analyze the characteristics of the parent graphs of linear, quadratic, cubic, absolute value, and square root functions. • Identify, define, describe, and labelthe graphs of functionsthat are linear, quadratic, cubic, absolute value orsquare root and organize, classify, and summarize this information. • Determine if a graph is one of the parent graphs. • Differentiate between and compare the parent graphs. • Develop and produce illustrations ofthe parent graphsfrom memory. • Recall and recognize the characteristics of parent graphs. Synthesize, interpret, evaluate, and apply the vertical transformations of linear, quadratic, cubic, absolute value, and square root function equations. • Identify, define, describe, and label the vertical shift, vertical stretch, vertical shrink, and vertical reflection of linear, quadratic, cubic, absolute value, and square root function equations and organize, classify, and summarize this information. • Determine if an equation is a parent graph equation that has been vertically transformed. • Recall and recognize the vertical transformations that can be applied to parent graph equations. • Differentiate between and compare the different vertical transformations of parent graph equations. • Compare and contrast parent graph equations to equations that have been vertically transformed. • Develop and produce equations of linear, quadratic, cubic, absolute value, and square root functions by combining, implementing, and executing the rules of transforming graphs. • Explain the different transformations that can be applied to a parent graph equation. (continued)
  6. 6. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 6 Learning objectives (continued) Synthesize, interpret, evaluate, and apply the vertical transformations of the graphs of linear, quadratic, cubic, absolute value, and square root functions. • Identify, define, describe, and label the vertical shift, vertical stretch, vertical shrink, and vertical reflection of linear, quadratic, cubic, absolute value, and square root graphs and organize, classify, and summarize this information. • Determine if a graph is simply a parent graph that has been vertically transformed. • Recall and recognize the vertical transformations that can be applied to parent graphs. • Differentiate between and compare different graphs of functions that have been vertical transformed. • Compare and contrast parent graphs to graphs that have been vertically transformed. • Develop and produce illustrations of the graphs of linear, quadratic, cubic, absolute value, and square root functions by combining, implementing, and executing the rules of transforming graphs. • Explain the different transformations that can be applied to a parent graph equation.
  7. 7. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 7 Standards (Common Core Georgia Performance Standards) (CCGPS) Students will analyze functions using different representations. https://www.georgiastandards.org/Common- Core/Common%20Core%20Frameworks/CCGPS_Math_9-12_Accel-GeometryB- AdvAlgebra_Standards.pdf MCC9‐12.F.IF.7 Characteristics of functions Students will graph functions expressed symbolically and show key features of the graph. They will do this by hand in simple cases and using technology for more complicated cases. MCC9‐12.F.IF.7a MCC9‐12.F.IF.7b MCC9‐12.F.IF.7c Students will graph linear and quadratic functions. Students will graph square root and absolute value functions. Students will graph cubic functions. Lesson Management Day Lesson Activities Homework 1-3 • Warm-up with immediate feedback from ClickerSchool Virtual Clicker • Transition of Buzz Presentation • Graphic organizer • Note-taking guide • Practice worksheet • Applet activity • Post on discussion board • Review lesson presentation • Review notes • Homework practice sheet 4 • Review activity with immediate feedback from ClickerSchool Virtual Clicker • Applet activity for review • Post on discussion board • Extra activity if time • Review all presentations • Review all notes • Review all graphic organizers 5 • Final assessment with immediate feedback from ClickerSchool Virtual Clicker Audience The audience for this lesson is an Accelerated CCGPS Analytic Geometry B / Advanced Algebra Mathematics class. There are 24 students, 16 female and 8 males. This class is taught on a block schedule and meets 1.5 hours every day. The class has been together since the beginning of the second semester of the school year (approximately 14 weeks), and they are comfortable working collaboratively. They are already familiar with Google Groups, Google Drive, and Quick Graph. They have a Google account. They have already set up a folder that is shared with the teacher which is used for submitting their completed assignments.
  8. 8. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 8 Learning Environment Student Activities Using Technology-Based Instruction (Samples of some of the activities are attached.) • Warm-ups • Note-taking guides • Graphic organizers • Student practice activities • Additional-time activity • Manipulative activity • Online discussions • Multiple-choice assessment Function Families Lesson Setting Offers: (Samples of some of the presentation slides are attached.) • Student access to individual computer • Common starting point for all students • Incorporation of prior learning • Technology-based instruction • All material accessible through Google Drive • All material turned in electronically • Audio and video for delivery of content • Differentiated sources (if students do not an iPad or an iPhone for their own personal use, the school will issue them an iPad for classroom use.) o ClickerSchool Virtual Clickeractivities o Teacher's Assistant Pro o Google Groups o Quick Graph o Google Drive o Internet research o Applets • Repetition of learning through a variety of practice • The use of imagery to retain new information • Communication with peers • Additional activity for those that finish early • Appropriate alignment of learning activities with objectives and assessment Assessments Students will be assessed on their attention to the lesson, their ability to complete their note- taking guides, charts, and graphic organizers, practice worksheets, and their collaboration with their peers and teacher (see rubric). They will receive separate grades on their warm-ups and homework assignments based on correctness. Students will take a multiple choice assessment and submit their answers using Google Forms and ClickerSchool Virtual Clicker. Thesefinal assessments cover all objectives on the lesson.
  9. 9. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 9 Justification for a Technology-Based Module Students will have a complete online experience Technology Class Set-up and Activities Google Drive: Shared Documents • The teacher will share a Google document with the class that will have the instructions and requirements for completing the lesson. It will contain all web-links used in the lesson. Google Drive: Shared Folders • The teacher will share a lesson folderwiththe class. Itwill includethe following documents: objectives, rubrics, charts, graphic organizers, practice worksheets, and note-taking guides. These will be read-only documents, but students will make copies of them so that they can edit their own version. • The students should already have a “turn-in folder” set up that is shared withthe teacher. To turn in anassignment, the student will add the completed material to the turn-in folder and it will be available to the teacher. Google Groups • Students will respondtoothers ideas. • Students will provide new resources and ideas related to functions. • Students will elaborate on the material. • Students will offer help to other students. • Students will post responses to teacher questions. Google Drive: Google Forms • Students will submit answers to multiple choice assessments SlideRocket Presentation Software • Students will observe a lesson presentation Internet • Students will perform research required for an “additional time” activity On-line Mathematical Applets • Students will explore characteristics of functions. o Multi-Function Data Flyer: http://www.shodor.org/interactivate/activities/ o Slider Graph: o http://math.hws.edu/javamath/basic_applets/SliderGraph.html ClickerSchool Virtual Clicker • Teachers and students will use this interactive response system app using their iPads or iPhones to submit responses to warm-ups and assessments. Teacher's Assistant Pro • The teacher will keep track of student actions, behaviors, and achievements in the classroom using this iPhone or iPad app. Quick Graph: Your Scientific Graphing Calculator • The student will use this app to graph functions. These results will then be emailed to the teacher.
  10. 10. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 10 Assessment of Lesson Rubric Justification of CIP CIP Activity Limited 1 Developing 2 Proficient 3 Exemplary 4 CLASSROOM ATTENTION Focuses attention on all aspects of the lesson. Focusing attention allows for the processingof important information while ignoring impertinent information. Cannot focus attention ♦ Does not evaluate material when prompted by teacher ♦ Cannot maintain a focus of attention despite cognitive efforts which may cause some level of anxiety Requires redirection ♦ Evaluates material only when prompted by teacher ♦ Requires considerable degree of cognitive effort to focus attention Requires minimal redirection ♦ Recognizes teacher cues to evaluate material ♦ Requires little cognitive demand for successful completion Maintains strong focus and attention on all components of the lesson ♦ Systematically evaluates material without needing the cues from the teacher ♦ Demands self- monitoring or self-regulation of own level of attention PRACTICE WORKSHEETS Makes connections among mathematical ideas and concepts and procedures. When students can make connections among multiple representations they can develop meaning and solve problems. ♦ Has no connection of the concepts or meaning to the facts, rules, formulas, or definitions being learned ♦ Partially identifies similarities and differences between concepts but only by saying they are opposites ♦ Cannot solve problems using procedures ♦ Has no connection of the concepts or meaning to the procedure being used ♦ Identifies some similarities and differences between concepts ♦ Struggles with general procedures and solving problems ♦ Has some ability to make connections between concepts or meaning to the procedure being used ♦ Identifies specific similarities and differences between concepts and makes generalizations ♦ Follows general procedures but requires a lot of thought ♦ Experiments with new information and procedures and uses them in different ways ♦ Identifies specific similarities and differences between concepts and can make generalizations and identify behaviors ♦ Follows general procedures and can do so with ease (continued)
  11. 11. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 11 Functions Families Lesson Rubric (continued) PRACTICE WORKSHEETS Synthesizes or brings together information. When students can retrieve learned concepts, rules, formulas, processes, or definitions it helps them to gain meaning and understanding of new information for final interpretation. Cannot synthesize information ♦ Misunderstands the material Synthesizes a majority of the information incorrectly ♦ Focuses on generating correct responsesrath er thanestablishi ng mathematical understanding Synthesizes the information somewhat precisely ♦ Understands the material, though there may be a few minor errors Provides a highly imaginative and individualized synthesis of the information ♦ Understands all concepts in the material GRAPHIC ORGANIZERS AND CHARTS Organizes and charts so that data and ideasare correctly categorizedand represented When students represent information in multiple ways it is easier for them to encode and store information. Cannot organize information ♦ Creates graphic organizers and charts that are not complete and do not correctly represent the material ♦ Displays no sense of organizationand categorization Requires assistance to select an appropriate organizational strategy ♦ Requires assistance to create graphic organizers and charts that accurately or clearly represent the material ♦ Attempts to showorganizat ion and categorization but struggles Completes organizers withminor problems with organization ♦ Creates organizers and charts that accurately represent the concepts and understanding of the topic ♦ Displays a relatively good sense of organization and categorization Independently selects an appropriate organizational strategy ♦ Creates organizers and charts that accurately depict the concepts and understanding of the topic but can also do it in different ways ♦ Creates highly organized and effective organizers and charts (continued)
  12. 12. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 12 Function Families Lesson Rubric (continued) GRAPHIC ORGANIZERS AND CHARTS Effectively interprets When students analyze the usefulness of information and reflect to develop personal meaning and knowledge. ♦ Grossly misinterprets the information ♦ Makes little or no attempt to determine what information is necessary to complete given task ♦ Makes some significant errors in interpreting the information ♦ Cannot determine effectively what information is needed to complete a given task ♦ Understands and gives interpretation of most of the information ♦ Makes some errors in determining what information is needed for a given task ♦ Interprets all of the information in accurate and highly intuitive ways ♦ Accurately determines what information is reliable and relevant to complete a given task NOTE-TAKING GUIDES: SUMMARY Summarizes information When students process new information it is easier for concepts and ideas to be stored into their memory. ♦Retells findings ♦ Does not put the material in own words ♦ Does not have key ideas nor accurate phrases ♦ Does not setup the material with original examples ♦Summarizes information ♦ Puts some of the material in own words ♦ Has few key ideas and accurate phrases ♦ Sets up material but without examples ♦Creates Relationships; draws conclusions ♦ Rephrases most all of the material ♦ Has most key ideas and accurate phrases ♦ Sets up material and has some original examples ♦Applies learning to new, different situations ♦ Condenses and rephrases all of the material ♦ Has all key ideas and accurate phrases ♦ Sets up material with original examples NOTE-TAKING GUIDES: CUES Identifies and labels key ideas, asks questions that connect these ideas. When students focus on key ideas they determine the importance of new information. ♦ Does not accurately seek out needed information ♦ Fails to use the most critical questioning techniques connecting information ♦ Makes little or to assess beneficial information ♦ Fails to ask significant questions for connecting information ♦ Accurately assesses the lesson to identify beneficial information ♦ Uses appropriate questioning techniques to connect information ♦ Insightfully determines beneficial information and effectively seeks it out ♦ Effectively uses a variety of questioning techniques to connect information resources (continued)
  13. 13. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 13 Function Families Lesson Rubric (continued) NOTE-TAKING GUIDES: NOTES Labels and categorizes notes When students adapt and reorganize information it is easier for them to process new facts. Sorts data ♦ Lists information inaccurately, includes unimportant information, and leaves out important details Orders and ranks data ♦ Processes the information incompletely or includes many errors Classifies information ♦ Processes the information completely with few errors Classifies information and makes comparisons ♦ Accurately and insightfully processes information POSTS Communicates When students collaborate with other students and teachers, it creates situations where they can repeat, elaborate, explain, and self-question. Ignores any form of communication from teacher and other students ♦ Does not offer any feedback ♦ Does not acknowledge ideas and comments ♦ Explains information related to the concepts but only with assistance Responds briefly to teacher and other students comments and ideas ♦ Pays little attention to the details of others ideas and comments ♦ Offers very little feedback with no discussion ♦ Explains the information fromthe concepts but it may not be clear or related to the procedures Explains and gives reasons for agreement and/or disagreement of comments and ideas of teacher and other students ♦ Critiques or supports ideas and comments ♦ Asks simple questions ♦ Explains the information related to the concepts in a clear way that is easily understood Actively seeks out ideas and comments of teacher and other students ♦ Asks questions to clarify ideas and comments and suggests possibilities ♦ Suggests support of ideas and comments ♦ Explains the information related to the concepts and draws conclusions from it which are understandable to another
  14. 14. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 14 Justification of Cognitive Information Processing (Processing, storage, and retrieval of knowledge in the mind) (Driscoll, 2005, p. 71-110) CIP Process Technology-Based Teaching Strategies Student Strategies Selective attention Actively focusing on certain important stimuli while excluding others ♦ Signaling students:The teacher sends messages through ClickerSchool Virtual Clickerclassroom management software alerting students that are off-task. ♦ Moving around:The teacher periodically walks around the computer lab. ♦ Utilizing a variety of materials: The lesson requires students to access several different types of technology: • Google Groups • Quick Graph • Computers • Social networking • Google Drive • Internet research • Applets ♦ Capturing student interest: The presentation contains animation and audio which is captivating to the students. The animals that represent the functions are meaningful, colorful, and attractive. ♦ Highlighting stimulus features: The note- taking guide has students defineand highlight the key words and definitions. ♦ Giving material meaning: The lesson presentation makes the material meaningful to the students by relating the functions to animals. ♦ Keeping the classroomin order: The lesson mandates that students work independently on the computer. The collaboration with peers is totally online via Google Groups. This setting helps to keep the classroom free of noise and distractions. ♦ Encouraging the reduction of student impulsiveness: Teachers reassure students that they have the time necessary to complete the lesson because it is broken down into five days. ♦ Assigning learning objectives: The lesson provides teachers with a new set of learning objectives that they assign to the material and then share with students. ♦ Adhering to cues from the teacher which alerts attention to lesson activities ♦ Recognizing the features of the presentation that signalimportant information ♦ Recognizing the complexity of new information and devoting a greater amount of attention tolearningit (continued)
  15. 15. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 15 Justification of Cognitive Information Processing (continued) Automaticity Devoting little attention to a task because the basic skills that are involved in completing it are habitual ♦ Questioning students about material: The teacher asks students individual questions on the basics of functions through ClickerSchool Virtual Clickerand Google Groups. ♦ Providingstudents with practice of basic skills: Teachers assign warm-up practice exercises on the basic concepts related to the lesson. ♦ Encouraging students to practice extensively: Teachers encourage students to complete worksheets and provide homework that continues this practice. ♦ Overlearning the material by constantly studying ♦ Continuing to practice even though the problemsare correct ♦ Reworking problems presented in the lesson ♦ Completing homework practice assignments Pattern recognition and perception Recognizing familiar patterns as examples of concepts and principles already stored in memory ♦ Providing opportunities for linking information: The lesson requires students to compareand match behaviors and characteristics of the new functionsto the corresponding behaviors and characteristics of the simple functions that were previouslystored in memory. ♦ Requiring thatstudentsgenerate unique examples and non-examples: This lesson supports feature analysis meaning that it shows an example of a function then requires the students to generate a counter-example. Students use their note-taking guides to develop original and alternate examples. They use a graphic organizer to create and fill-in their own non-examples. This activity helps students understand what is meaningful and critical when analyzing a function. ♦ Offering extensive practice:The lesson offers anextensive amount ofpracticeon the graphing of functions usinga variety of techniques.This ensures that students overcome any past experiences or prior learning that might interfere with their ability to process this new knowledge. ♦ Overcoming predetermined perceptions: Teachers monitor students’achievements and give immediate feedbackClickerSchool Virtual Clicker so that they do not judge students based on preconceived notions. ♦ Focusing on the material in the review warm-ups and linkingit to information about the new functions ♦ Paying close attention to the examples in the presentation in an effort to create original counter- examples ♦ Taking advantage of the extensive practice so that any past learning experiences will not interfere with linking previously learned material to new information (continued)
  16. 16. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 16 Justification of Cognitive Information Processing (continued) ♦ Offering opportunities for guided discovery:The lesson usescharts and graphic organizers to help students identifythe relevant and irrelevant characteristics of parent functions and their related vertical transformations. ♦ Presenting situations to analyze conditional situations:The lesson presents students with relatedsets of concepts and procedures dealing with functions and their transformations. It then provides them with worksheets where they analyze graphs to determine if certain transformations have been applied to them (if/then). Chunking 1. Increasing working memory capacity through creating larger bits or taking small bits of information and chunking them together ♦ Breaking down the material: The lesson is broken down into understandable and manageable parts per day to counteract the limitations of short- term memory. Students learn the characteristics of functions bit by bit over the course of five days. ♦ Organizing learning tasks: This lesson organizes the learning tasks according to complexity. First of all students recognize important information and respond to this information by filling in a note-taking guide. Next they follow procedures and apply definitions as they complete their graphic organizers and charts. Finally they form concepts and apply rules as they solve the problems on their practice worksheets. ♦ Promoting inductive reasoning:The lesson provides students with examples of parent graphs and the charts have students derive and discuss theirgeneral characteristics (inductive reasoning). ♦ Following the guidelines of the note-taking guide and filling it in appropriately ♦ Taking the complex information from the lesson presentation and breaking it down into manageable parts ♦ Completing the tasks of the lessons in the appropriate order: note-taking, charts and organizers, then practice worksheets (continued)
  17. 17. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 17 Justification of Cognitive Information Processing (continued) Rehearsal Repeating information in an effort to maintain itso it can be applied ♦Providing students with charts and graphic organizers:This lesson has a variety of charts and graphic organizers that categorizes the same information about functions in several different ways. ♦ Providing opportunities for student practice:The teacher arranges for a variety of practice opportunities. The goal is to help the learner generalize the concepts, principles, and skillsrelated to function families so that they can be applied to different problem situations. ♦ Promptingdiscussions:The lesson provides for discussion posts where students have the opportunity to explain or to help clarify the problems that others are having. This interaction creates situations for students to repeat learned information which will helps them to maintain it. ♦Asking students redundant questions:Because of the use ofTeacher's Assistant Pro classroom management software, teachers have the domain to periodically ask students questions throughout the course of the lesson. This allows students to reiterate the material and express their knowledge. ♦ Filling in several charts and graphic organizers to continually work with the information ♦ Completing a variety of practice problems after each lesson presentation ♦ Completing homework practice assignments ♦ Completing a review assignment ♦ Helping others by asking and answering questions ♦ Answering teacher- asked questions about lesson content (continued)
  18. 18. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 18 Justification of Cognitive Information Processing (continued) (continued) Encoding Relating incoming information to concepts and ideas already in memory so that the material is more memorable ♦ Organizing instruction:The teacher provides students with graphic organizers that help them group related information into categories and lists. Using these aids, students name and define the function, reference it to a category, and define its specific attributes. ♦ Mediating: The lesson uses the story about Buzz and the way he behaves to teach vertical transformations of the graphs of functions and how they relate to specific equations. This way of presenting the material makes the steps and procedures involved in transforming graphs more meaningful and easier to remember. ♦ Incorporating mnemonics: The lesson relates the names of the functions to the namesof the animals representing the functions by starting the names with the same letter. ♦ Incorporating imagery:The lesson provides students with the means to remember what the graph of each function looks like by connecting it to an animal that is similar in appearance.Students also use imagery tricks to help remember how each animal behaves under certain circumstances and relates this back to its corresponding function. ♦ Providing mental scaffolding:The lesson uses charts and graphic organizers to provide students the opportunity to link new material about function families with relevant prior knowledge about basic functions ♦ Providing a frame of reference: The lesson acknowledgesparent graphs as being a frame of reference. Characteristics and behaviors of these graphs are learned first. Then students apply complex techniques, including procedures and visualizations,to these graphsto create the more complex structures. ♦ Using graphic organizers to help work practice problems ♦ Encoding information in more than one way by using mnemonic devices, acronyms, and imagery ♦ Elaborating on new information by providing unique examples of each type of graph on note-taking guides ♦ Self-questioning ♦ Making information meaningful by relating it to personal life (This activity is prompted by discussions on the discussion board.) ♦ Using note-taking guides to take notes using unique words and phrasing ♦ Using note-taking guides to summarize information ♦ Imposing subjective organization ♦ Posting inferential questions on discussion board ♦ Including prompts in notes while filling in the note-taking guide
  19. 19. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 19 Justification of Cognitive Information Processing (continued) Retrieval Bringing back previously learned material ♦ Offering opportunities of recall: This lesson makes recall easier by offering studenta multitude of practice exercises that present questions in a variety of ways. • Cued recall: The students complete practice exercises with the aid of graphic organizers which provide cuesthat help students remember the desired information. ♦ Offering opportunities for recognition: • Yes/no type of recognition: On sections that require students to interpret the vertical reflection of a graph, students must determine if graph is in the normal position or flipped over the x-axis. • Forced choice recognition: On warm-ups, reviews, and the assessments, this lesson requires that students only recognize which answer is correct by presenting them with multiple-choice questions. They must only make a decision or judgment. ♦ Offering opportunities for encoding specificity: The lesson is entirely technology- based with many multiple choice practice exercises. All assessments are multiple choice and technology-based; therefore, cues that are used by students to facilitate encoding will also serve as the best retrieval cues at test time. ♦ Offering opportunities to counteract interference: The lesson provides a lot of practice on previously learned material through the warm-up activities; therefore, retroactive interference (interference from newly learned material) is not of concern to the student. ♦ Offering opportunities to counteract proactive interference: The lesson has students signal key ideas and definitions which counteract proactive interference (interference from previously learned material); therefore, it is not of concern to the student. ♦ Accessing the lesson at home for further study ♦ Reviewing the presentation as needed to ensure that the important concepts will be remembered ♦ Practicing all material using the graphic organizer for guidance ♦ Using the note- taking guide to study and complete practice exercises ♦ Being a state- dependent learners by not taking a drug that might cause drowsiness during learning
  20. 20. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 20 Justification of Alignment CIP Learning Objective Instructional Strategy Types of Assessment Retrieve Students will be able to: • recall • duplicate • memorize • recognize • relate • reproduce • matches • identifies • selects • indicate • choose The Web-based instruction presentation will: • Explain how learners will be expected to recall the information • Draw attention to key features of the material • Provide a meaningful context for effective encoding of information • Provide memorization tricks • Provide cues for effective recall and generalization of information Formative Assessments Questions are convergent • Multiple-choice warm-ups • Homework assignments • Practice worksheets • Teacher questioning Summative Assessments Exam items of the form: reproduce, identify, or select Items are convergent with limited answers. • Multiple-choice objective test Understand Students will be able to: • classify • summarize • compare • explain • restate • paraphrase • define • label • list • name • order • describe • discuss • generalizes • assemble • organize • collaborate • communicate • individualize Google Groups will: • Provide an environment for question- and-answer sessions • Provide an environment where students can review material with others • Provide an environment where students can teach others The Web-based instruction presentation will: • Present a variety of observable,concrete examples related directly to the information • Encourage learners to recall previously learned information • Give examples that illustrate concepts or rules • Relate the information to preexisting knowledge • Present cues to the organization of concepts • Break down the process of performing or applying rules into steps • Present all terms clearly using the fewest number of words to convey the meaning Formative Assessments Questions are convergent • Class discussions • Graphic organizers • Charts • Note-taking guides • Teacher questioning • Posts Summative Assessment Items are convergent Exam items of the form:, label, list, describe, define,explain, or summarize • Multiple-choice objective test (continued)
  21. 21. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 21 Justification of Alignment (continued) • Define categories • Group related terms or units • Present the material into manageable parts • Present information so that it can be made into chunks • Present a variety examples • Present rule applications and highlight the distinctive features of examples, definitions, and procedures. • Encourage the development of graphic organizers and charts • Encourage the writing of well- developed notes • Provide activities for summary and closure Apply Students will be able to: • execute • implement • engage • execute • practice • demonstrate • employ • solve • use • chart • compute • discover • establish • inform • participate • predict • provide • relate • transfer • utilize Lesson format will: • Schedule occasions for practice and spaced review • Encourage the recall of relevant rules and concepts • Provide practice in multiple contexts • Provide guided practice with immediate feedbackClickerSchool Virtual Clicker • Present a variety of practice that allow the students to practice applying the rules or identifying/describing concepts • Encourage guidance throughout early stages of practice using graphic organizers • Provide learners with opportunities to engage with concepts and rules using applets • Encourage the use of mental practice • Arrange repeated practice • Require students to demonstrate problem-solving • Require studentsto demonstrate application of rules, methods, or procedures Formative Assessments Questions may be convergent or divergent. • Warm-ups • Problem worksheets • Homework sheets Summative Assessments Questions are convergent Exam items of the form: apply, use, solve, demonstrate, employ • Multiple-choice objective test (continued)
  22. 22. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 22 Justification of Alignment (continued) Analyze Students will be able to: • differentiate • determine • consider • investigate • analyze • calculate • compare • contrast • differentiate • distinguish • examine • experiment • question • categorize Google Groups will: • Provide an environment for students to respond to others ideas • Provide an environment where students can elaborate on material • Provide an environment where students can analyzeon material Lesson format will: • Activities that require the analysis of important information • Activities that determine how procedures involved in the material work together • Activities that require analyzing a final outcome to see how it was produced • Activities for students to analyze content using computer applets Formative Assessments Questions may be convergent or divergent. • Posts • Practice Worksheets • Note-taking guide Summative Assessment Questions are convergent Exam items of the form: analyze, compare, distinguish, examine, test • Multiple-choice objective test Evaluate Students will be able to: • assess • rate • criticize • rank • decide • assess • calculate • decide • argue • defend • conclude • justify Google Groups will: • Provide an environment for students to self-question • Provide an environment where students critique the comments of others • Provide an environment where students discuss the appropriateness of procedures Lesson format will: • Provide activities for evaluating material to determine if it fulfills given purpose • Provide activities to demonstrate processes for evaluating material • Provide activities torate and rank material Formative Assessments Questions may be convergent or divergent • Posts • Problem worksheets • Charts Summative Assessments Questions are convergent Exam items of the form: evaluate, argue, assess, defend, judge, predict, rate, support • Multiple-choice objective test Create Students will be able to: • develop illustrate • produce • construct • discover • establish Google Groups will: • Provide an environment where students can provide new resources and ideas • Provide information feedback as to the creativity or originality of comments Lesson format will: • Provide activities for generating and constructingnew outcomesbased on rules and procedures Formative Assessments Small group discussions Questions may be convergent or divergent • Problem worksheets • Posts • Note-taking guide (continued)
  23. 23. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 23 Justification of Alignment (continued) • formulate • generate • initiate • originate • perform • give examples • sketch • show • express • Encourage learners to identify and select their own examples and non-examples of concepts and rule applications if possible. Summative Assessments Questions may be convergent or divergent Exam items of the form: develop, plan, prepare, propose, construct, design, formulate, create, assemble • Multiple-choice objective test
  24. 24. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 24 Figure A Sample Slidefrom SlideRocketPresentation MEET BUZZ Buzz is a freshman in High School and lives with his parents. The street that he lives on is the y- axis. f(x) = Buzz Buzz is at his parents' home when his stinger is on the origin. We call this the “origin point”.
  25. 25. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 25 Figure B Sample Slide from SlideRocketPresentation: Vertical Shift BUZZ VISITING FRIENDS Vertical Shift Buzz likes to visit his friends on the street: (y-axis). Buzz visits Bill when he moves his origin point 5 blocks up. f(x) = Buzz + 5 Buzz visits Nancy when he moves his origin point 7 blocks down (-7). f(x) = Buzz – 7
  26. 26. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 26 Figure C Sample Slide from SlideRocketPresentation: Vertical Reflection SLEEPING BUZZ Vertical Reflection When Buzz sleeps, he sleeps upside (vertically flips over his origin point). When we refer to Buzz in this position, we write f(x) = -Buzz. The negative sign in front of his name indicates that he is in the sleeping position. If there is not a sign at all or a positive sign is in frontthis means that he is in the awake position. This is Buzz asleep at his parent's house.
  27. 27. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 27 Figure D Sample Slide from SlideRocketPresentation: Vertical Shrink YOUNG BUZZ Vertical Shrink When Buzz was young he was short and fat. When we refer to Buzz at this age, we put a number between 0 and 1 in front of Buzz. The smaller the number the fatter Buzz gets. f(x) = (¼)Buzz. This is a young Buzz at his parents’ house.
  28. 28. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 28 Figure E Sample Slide from SlideRocketPresentation: Vertical Stretch and Shift YOUNG BUZZ Vertical Stretch and Shift When Buzz gets old he will be tall and thin. When we refer to Buzz at this age, we put a number greater than 1 in front of Buzz. The larger the number the taller and thinner Buzz gets. f(x) = (5)Buzz + 3. This is an older Buzz at a friend’s house that lives 3 blocks up.
  29. 29. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 29 Figure F Sample Slide from SlideRocketPresentation Introducing “Linus” Introduction of Function Animals Animal Name: “Linus” Function Name: Linear Function Graph Name: Line Math Symbol: x Animal Symbol: see below
  30. 30. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 30 Figure G Sample Slide from SlideRocketPresentation Introducing “Abby” Introduction of Function Animals Animal Name: “Abby” Function Name: Absolute Value Function Graph Name: Absolute Value Math Symbol: |x| Animal Symbol: see below
  31. 31. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 31 Figure H Sample Slide from SlideRocketPresentation Introducing “Curt” Introduction of Function Animals Animal Name: “Curt” Function Name: Cubic Graph Name: Cubic Math Symbol: x3 Animal Symbol: see below
  32. 32. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 32 Figure I Sample Slide from SlideRocketPresentation Introducing “Squirm” Introduction of Function Animals Animal Name: “Squirm” Function Name: Square Root Function Graph Name: Radical Math Symbol: Animal Symbol: see below
  33. 33. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 33 Figure J Sample Slide from SlideRocketPresentation Introducing “Rachel” Introduction of Function Animals Animal Name: “Rachel” Function Name: Rational Function Graph Name: Rational Math Symbol: Animal Symbol: see below 2 4 -3
  34. 34. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 34 Figure K Sample Slide from SlideRocketPresentation Introducing “Quinton” Introduction of Function Animals Animal Name: “Quinton” Function Name: Quadratic Function Graph Name: Parabola Math Symbol: x2 Animal Symbol: (see below)
  35. 35. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 35 Figure L Screen Shot of Appletsfor Manipulation of Functions Multi-Function Data Slide Graph
  36. 36. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 36 Figure M Sample Warm-up Quizon the Basic Behaviors of Functions
  37. 37. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 37 Figure N Note-taking Guide Name: Class: Date: Lesson Topic: Learning Objectives: CUES (After class) • Key ideas • Questions that connect ideas • Diagrams and charts • Prompts for studying PRESENTATION NOTES (During class) • Short and concise phrases • Symbols and abbreviations • Labels and categories • Lists and tables • Spaced out facts SUMMARY (After Class) • In own words • Original examples • Most important key ideas • Accurate phrases for quick reference
  38. 38. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 38 FigureO Sample Chart Fill in the organizer according to the information you viewed during the presentation. Animal Name Animal Symbol Math Symbol Function Name Name of Graph
  39. 39. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 39 Figure P Sample Chart According to the condition of Buzz below, fill in the cells using the directions at the top of each column. Follow the example done for you. Description of How Buzz changed Mathematical Operation That Create This Change Mathematical Name of the Change That Took Place Asleep and younger Upside down and fatter Negative number between 0 and 1 multiplied by Buzz Vertical reflection and vertical shrink Awake at his parents Visiting a friend and awake Younger at his parents house and asleep Older at his friend’s house and awake Younger at his friend’s house Older and awake at his parents’ house Asleep at his friends house and younger
  40. 40. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 40 Figure Q Sample Graphic Organizer Definition Facts/Characteristics Examples Non-Examples Definition Facts/Characteristics Examples Non-Examples Definition Facts/Characteristics Examples Non-Examples Linear Function Quadratic Function Cubic Function
  41. 41. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 41 FigureR Sample Practice Worksheet on Writing Equations Look at each graph below and fill in each cell according to the heading at the top of each column. An example is given. Animal Name Awake or asleep Age of Animal Math Symbol Possible Equation Quadratic + 6 X2 f(x) = 6x2
  42. 42. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 42 FigureS Sample Practice Worksheet on Writing Equations Look at each graph below and fill in each cell according to the heading at the top of each column. An example is given. Function Notation = Awake Or Asleep (+ or -) Possible Age Function Symbol + - or “nothing” Vertical Position f(x)= + 5 x2 - 6
  43. 43. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 43 FigureT Sample Practice Worksheet on Writing Equations Look at each graph below and fill in each cell according to the heading at the top of each column. An example is given. Awake + Asleep - Age of Animal Math Symbol Up + Down – # of units Possible Equation - 7 √x - 5 f(x) = -7√x - 5
  44. 44. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 44 Figure U Sample Practice Worksheet Drawing Graphs Place a box around each of the 4 parts of the equations below. Name the animal in the blank provided. Fill in the chart according to the directions at the top of each column. Box 1 Box 2 Box 3 Box 4 Sketch of Possible Graph (in 1,2,3,4 order) Draw Graph Awake or Asleep Draw Animal At Age Draw Parent Graph How many Units Up or Down? 3rd 2nd 1st 4th (example) animal: Quinton . Down 7 y = - (1 /4) x3 + 2 animal_________ y = -5x + 2 animal_________ y = (1 /3) √x - 5 animal_________
  45. 45. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 45 FigureV Sample Review Activity on Shifting Parent Graphs Graph Awake or asleep Possible Age of Animal Shape of the graph Shift up or down 1. A. + B. - 2. A. 1 /2 B. 2 C. 1 3. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 4. A. + 3 B. - 2 C. no shift 5. A. + B. - 6. A. 1 /2 B. 2 C. 1 7. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 8. A. + 3 B. - 2 C. no shift 9. A. + B. - 10. A. 1 /2 B. 2 C. 1 11. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 12. A. + 3 B. - 2 C. no shift 13. A. + B. - 14. A. 1 /2 B. 2 C. 1 15. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 16. A. + 3 B. - 2 C. no shift 17. A. + B. - 18. A. 1 /2 B. 2 C. 1 19. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 20. A. + 3 B. - 2 C. no shift 21. A. + B. - 22. A. 1 /2 B. 2 C. 1 23. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 24. A. + 3 B. - 2 C. no shift 25. A. + B. - 26. A. 1 /2 B. 2 C. 1 27. A. x D. x3 B. |x| E. √x C. x2 F. 1 /x 28. A. + 3 B. - 2 C. no shift
  46. 46. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 46 FigureW Activity on Linear Regression Which Serves as an Additional Activity “Extra Time” Activity Basics of Linear Regression Page 1 If you complete all components of the lesson on Function Families, use the extra time to complete this activity. 1. Before you perform any Internet research, estimate the ages of each of the famous people above. Fill in the appropriate column in the chart (x-value). 2. Using the Internet, research each of the famous people and record their ages in the appropriate column in the chart (y-value). How well were you able to estimate the ages of these famous people? 3. To help answer this question, first of all make a scatterplot usingtheestimate of their age as the x-value and the actual age asy- value. Use the graph paper attached. Be sure to give it a title, use appropriate increments on the axes, and label each axis. 4. If you estimated the age correctly, what istrue about this point? 5. Sketchagraphofthe line of estimates that were 100% accurate. 6. What is the equation of this line? 7. What does it mean if a point on your scatterplot is above this line? (continued)
  47. 47. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 47 Figure W (continued) Activity on Linear Regression Which Serves as an Additional Activity “Extra Time” Activity Basics of Linear Regression Page 2 8. In general, did you overestimate or underestimate the ages of your famous people? 9. How can you tell this from your scatter plot? 10. Plot the points on Quick Graph. 11. Have Quick Graph calculate linear regression and draw this line. What is the equation of this line? 12. Sketch this line on your graph paper. 13. Write a paragraph that discusses the slopes of your lines and the characteristics of your data. What conclusions can you draw? (continued)
  48. 48. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 48 Figure W (continued) Activity on Linear Regression Which Serves as an Additional Activity “Extra Time” Activity Basics of Linear Regression Page 3 Famous Person Estimated Age x-value Actual Age y-value Bill Clinton Tom Cruise Hillary Duff Miley Cirus Carrie Underwood Abraham Lincoln(age at death) Babe Ruth(age at death) “The Rock” George Washington Tim Allen Oprah Winfrey Cleopatra(age at death) Barney Einstein(age at death)
  49. 49. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 49 FigureX SampleAssessment Questions (continued)
  50. 50. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 50 FigureX(continued) Sample Assessment Questions
  51. 51. FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 51 References Driscoll, M.P. (2005). Psychology of learning for instruction (3rd ed.). Boston: Allyn and Bacon

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