Technology based module cip martha townsend
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Technology based module cip martha townsend Technology based module cip martha townsend Document Transcript

  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 1 Cognitive Information Processing Function Families Martha Townsend Georgia Southern University
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 2 Cognitive Information Processing Function Families Instructional Goals 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 entertainingSlide Rocket Presentation on function families with color, audio, and animation. The teacher will periodically walk around the laband redirect students that are off-task. The teacher will keep students focused on learning using SMART Sync™ classroom management software. 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. Incorporate relevant prior learning. The students will complete a warm-up activity each day via Smart Notebook Software clickers. The questions on the warm-up will cover the previous lessons on the characteristics of a function. The teacher will analyze student responses and use SMART Sync™ to communicate feedback to the students. Highlight and stress important information. The teacher will provide note-taking guides to accompany each day’s lesson.Students will receive a hard copy as well as a computer copy using Google Documents. They should fill these in as they watch the presentation. The teacher will use the teacher computer and overhead projector to display key words and important definitions. 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 be slowly introduced to the algebraic parent graphs. Studentswill then take each of the parent graphs and shift them up or down. Next students will move to the more complex concept of reflecting a function over the x-axis. Finally,the lessonwill show students how to combine the steps for vertically manipulating a function.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 3 Show students how to chunk related information. The graphic organizers and note-taking guideswill allow students togroupthe concepts into categories and manageable steps. The activities will teach students inductive reasoning as theywill construct or evaluate general propositions about functions that 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 functions to what they already know about the behaviors of positive and negative numbers. 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 different functions andtheir algebraic equations. 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 animals that are connected to each graph a name that starts with the same letter. The students will learn how to graphically manipulate the graph of a function by relating the aspects of their equations to the behavior of the animal. Provide students the opportunity for repetition of learning. The students will receive the information and practice on 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 throughout the course of the lesson through warm-up activities and the test review. The students will use the Senteofree-response system to access drill and practice on the basic concepts involved with functions. The students will access a SMARTNotebook file that will allow them to practice manipulating the graphs of functions in the coordinate plane.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 4 Prior Relevant Learning Objectives Students should have already: At the beginning of this lesson students should be able to: Learned about the characteristics of relations and functions. • Represent a relation in multiple ways without the use of a calculator using tables, x|y charts, listing of ordered pairs, or graphs in the coordinate plane. • Identify domain and range of a relation by looking at a table, x/y chart, a listing of ordered pairs, or graph. • Determine if a relation is a function by looking at a table, x/y chart, or a listing of ordered pairs. • Apply the vertical line test to determine if a graph is a function. • Create x|y charts of functions from their equations and graph these functions in the coordinate plane. • Graph functions using a TI-83 Plus graphing calculator. Learning Objectives for Function Family Lesson Students completing this lesson will: Students that successfully complete this lesson will be able to: Learn about the properties of the parent graph equations of linear, quadratic, cubic, absolute value, and radical functions. • Identify the parent graph equations of linear, quadratic, cubic, absolute value, and radical functions. • Match the parent graph equations of linear, quadratic, cubic, absolute value, and radical functions with their appropriate algebraic name. • Determine if an equation is linear, quadratic, cubic, absolute value or radical by looking at an equation. Learn about the characteristics of the parent graph of linear, quadratic, cubic, absolute value, and radical functions. • Match the parent graphsof linear, quadratic, cubic, absolute value, and radical functions with their appropriate name. • Identify if a function is linear, quadratic, cubic, absolute value or radical by looking at the graph. • Sketch the parent graph of a linear, quadratic, cubic, absolute value, and radical function by looking at an equation. Learn about vertical transformations of linear, quadratic, cubic, absolute value, and radical functions. • Identify the vertical shift, vertical stretch, and vertical reflection of linear, quadratic, cubic, absolute value, and radical functions by looking at an equation. • Sketch the graph of linear, quadratic, cubic, absolute value, and radical functions by looking at an equation and applying the appropriate transformations. • Match an equation of linear, quadratic, cubic, absolute value, and radical functions with a picture of a graph.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 5 Prior Relevant Learning Focus Essential Questions Key Definitions What are the characteristics of a function and how can you use those characteristics to represent the function in multiple ways? • Coordinate plane • Relation • Function • Independent variable • Dependent variable • x-coordinate • y-coordinate • x|y chart • Input • Output • Table • Ordered pair • Graph • Domain • Range • Vertical line test Learning Focus for Function Family Lesson Essential Questions Key Definitions (Should be stressed and highlighted) What are the characteristics of the parent graphs of linear, quadratic, cubic, absolute value, and radical functions? • Linear • Absolute Value • Cubic • Quadratic • Parabola • Radical • Infinity • Zero • Parent Graph • Maximum • Minimum How arethe parent graphs of linear, quadratic, cubic, absolute value, and radical functionsvertically affected when their parent graph equations are added to and/or multiplied by a number. • Coefficient • Reflection • Solution • Increasing • Decreasing • Stretch • Shrink • Shift End behavior • Average rate of change • Slope
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 6 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. Audience The audience for this lesson is anAccelerated CCGPS Analytic Geometry B / Advanced Algebra Mathematics class. There are 24 students, 16 female and 8 males. 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 already familiar with SMART Notebook software, Senteo free-response system, Google Drive, and TI-83 Plus graphing calculators.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 7 Learning Environment Student Activities Using Technology-Based Instruction (Samples of some of the activities are attached.) • Warm-ups on previously learned material • Note-taking guides • Graphic organizers • Student practice activities • Famous People Graphing Activity (“Additional Time Activity”) • Final assessment via Senteo Clickers 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 • Audio and video for delivery of content • Differentiated sources o Senteo free-response system activities o SMART Notebook software o Social networking o TI-83 Plus graphing calculators o Google drive o Internet research • Repetition of learning through a variety of practice • The use of imagery to retain new information • Communication with peers (Google Groups) • Additional activity for those that finish early • Appropriate alignment of learning activities with objectives and assessment Assessment Students will be assessed on their attention to the lesson, their ability to fill in their note-taking guides and graphic organizers, and their collaboration with their peers and teacher (see rubric). They will receive separate grades on their warm-ups, practice worksheets, and homework assignments based on correctness. Students will take a multiple choice assessment using the Senteo clickers that covers all objectives on the lesson.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 8 Lesson Management Day Lesson Activities Homework 1 • Warm-up Day 1 • Transition of Buzz Presentation Day 1 • Graphic organizer • Note-taking guide • Practice worksheet • Review Presentation from website • Review notes • Homework practice sheet 2 • Warm-up Day 2 • Transition of Buzz Presentation Day 2 • Graphic organizer • Note-taking guide • Practice worksheet • Applet activity • Review Presentation from website • Review notes • Homework practice sheet 3 • Warm-up Day 3 • Transition of Buzz Presentation Day 3 • Graphic organizer • Note-taking guide • Practice worksheet • Applet activity • Review Presentation from website • Review notes • Homework practice sheet 4 • Review activity • Peer collaboration review game • Review all presentations • Review all notes • Review all graphic organizers 5 • Final assessment with immediate feedback Engage • Students will participate in a lesson that has them watch a presentation with animation and audio. • Students will be engaged by using SMART Notebook software to practice manipulation of functions. Explore • Students will explore characteristics of functions by using SMART Notebook software to practice vertical manipulation of functions. • Students will explore characteristics of functions by using TI-83 Plus graphing calculators to practice vertical manipulation of functions. Explain • Students will complete graphic organizers and note-taking guides using their own words. • They will complete practice worksheets and an assessment which will display their knowledge of function transformation. • Students will offer help to other students via the Google Group Discussion Board.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 9 Elaborate • Students will use the Google Group Discussion Board to post new resources and/or ideas related to functions. • Students will elaborate on the material by posting discussions related to new information about functions. • Students will post well-written responses with evidence supporting their position/opinion on the topic.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 10 Function Families Lesson Rubric 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 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 ♦ Student can partially identify Some 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 ♦ Student can identify specific similarities and differences between concepts generalizations ♦ Struggles with general procedures and solving problems ♦ Has some ability to make connections between concepts or meaning to the procedure being used. ♦ Student can identify specific similarities and differences between concepts and make generalizations ♦ Follows general procedures but has to put a lot of thought into it ♦ 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 11 PRACTICE WORKSHEETS Synthesizes or brings together information When students can retrieve learned concepts, rules, formulas, or definitions it helps them to gain meaning and understanding of new information. Cannot synthesize information ♦ Makes little or no attempt to determine what information is necessary to complete given task ♦ Misunderstand s the material Synthesizes a majority of the information incorrectly ♦ Cannot determine effectively what information is needed to complete a given task ♦ Focuses on generating correct responsesrather thanestablishing mathematical understanding Synthesizes the information somewhat precisely ♦. Makes some errors in determining what information is needed for a given task ♦ Understands the material, though there may be a few minor errors- can explain the event Provides a highly imaginative and individualized synthesis of the information ♦ Accurately determines what information is reliable and relevant to complete a given task ♦ Understands all concepts in the material- can explain the answer GRAPHIC ORGANIZERS Organizes data and ideas When students represent information in multiple ways, such as visual diagrams, manipulatives, symbols, and problem situations, it is easier for them to encode and store information. Cannot organize information ♦ Creates graphic organizers that are not complete and do not correctly represent the material ♦ Displays no sense of organization Requires assistance to select an appropriate organizational strategy ♦ Requires assistance to create graphic organizers that are accurate or clear ♦ Attempts to showorganizati on but struggles Completes organizers withminor problems with organization ♦ Creates organizers that accurately represent the concepts and understanding of the topic ♦ Displays a relatively good sense of organization Independently selects an appropriate organizational strategy ♦ Creates organizers that accurately depict the concepts and understanding of the topic but can also do it in different ways ♦ Creates highly organized and effective organizers
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 12 NOTE-TAKING GUIDES Identifies, highlights, and labels key information and ideas When students focus their attention on certain key issues in the lesson,they gain assistance indetermining the importance of new information. ♦ Does not accurately seek out needed information ♦ Fails to use the most important techniques for gathering information ♦ Makes little or to assess beneficial information ♦ Fails to use some significant techniques for gathering information ♦ Accurately assesses the lesson to identify beneficial information ♦ Uses appropriate techniques to gather information ♦ Insightfully determines the types of information that would be beneficial and effectively seeks out that information. ♦ Effectively uses a variety of information- gathering techniques and information resources NOTE-TAKING GUIDES Labels and categorizes notes When students adaptand reorganize information for a specific task, it is easier for them to process new information. Sorts data The processing of the information is not complete or there are many errors Orders and ranks data There are some errors, such as listing unimportant information and missing important details or simply having incorrect information. Classifies information . ♦Analyzes information in detail Classifies information and makes comparisons ♦ Accurately and insightfully processes information NOTE-TAKING GUIDES 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 setup the material with original examples Summarizes information ♦ Puts some of the material in own words ♦ Sets up material but without examples Creates relationships and draws conclusions from information ♦ Puts almost all of the material in own words ♦ Sets up material and has some original examples Independently applies learning to new and different situations ♦ Condenses the material and puts it all in own words. ♦ Sets up material with original examples
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 13 POSTS Effectively interprets When students overlearn basic skills by performing extensive practice it ensures that they can recall these concepts with little thought or attention. ♦ Grossly misinterprets the information ♦ Explains information on a graph, table, or chart but only with assistance ♦ Makes some significant errors in interpreting the information ♦ Explains the information on a graph, table or chart, but it may not be clear or related to the requirements ♦ Understands and gives interpretation of most of the information ♦ Explains the information related to the concepts in a clear way that is easily understood ♦ Interprets all of the information in accurate and highly intuitive ways ♦ Explains the information related to the concepts and draws conclusions from it which are understandable to another POSTS Communication When students collaborate with other students and teachers, it creates situations where they can elaborate and self-question. It also provides opportunities for them to make the information personal and more meaningful. Ignores any form of communication from teacher and other students ♦ Does not offer any feedback ♦ Does not acknowledge ideas and comments 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 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 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
  • 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 Teaching Strategies Student Strategies and Responsibilities Selective attention Actively focusing on certain important stimuli while excluding others ♦ Signaling:The teacher sends messages through SMART Sync™ classroom management software alerting those that are off-task. ♦ Moving:The teacher periodically walks around the computer lab. ♦ Utilizing variety of materials: The lesson requires students to access several different types of technology: • SMART Notebook software • Senteo free-response system • TI-83 Plus graphing calculators • Computers • Social networking • Google drive • Internet research ♦ Capturing interest: The lesson 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 teacher displays the key words and definitions on the overhead. ♦ Giving meaning: The lesson presentation makes the material meaningful to the students by relating the functions to animals. ♦ Keeping order: The lesson mandates that the 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 reduction of impulsiveness: Teachers ensure students that they have the time necessary to complete the lesson because it is broken down into five days. ♦ Students adhere to cues from the teacher which alerts them to focus and pay attention while watching the lesson presentation, taking notes, and working through the practice worksheets. ♦ Students recognize the features of the presentation that signalimportant information. ♦ Students recognize the complexity of new information and devote a greater amount of attention tolearningit.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 15 Automaticity Devoting little attention to a task because the basic skills that are involved in completing it are habitual ♦ Questioning: The teacher asks students individual questions on the basics of functions through SMART Sync™ and Senteo free-response system. ♦ Offering practice of basic skills: Teachers assign warm-up practice exercises on the basic concepts related to the lesson. ♦ Assigning objectives: Teachers share the learning objectives with students. ♦ Encouraging extensive practice: Teachers encourage students to complete worksheets and provide homework that continues this practice. ♦ Students overlearn the material by constantly studying. ♦ Studentscontinue to practice even though they may be getting the problemscorrect. ♦ Students rework problems presented in the lesson to see if they can continue to get a correct answer. ♦ Students complete 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 compare or match behaviors and characteristics of the new graphs to the corresponding behaviors and characteristics of the functions that are already stored in memory. ♦ Providing examples and non-examples: This lesson supports feature analysis meaning that it shows an example of a function then makes students generate a differing or counter-examples. This 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 through the Senteo free-response system and give immediate feedback so that they do not judge students based on preconceived notions. ♦ Students focus on the material in the review warm-ups so that they can link previously learned information about graphs to the new graphs. ♦ Students pay close attention to the examples in the presentation so that they can create their own counter- examples. ♦ Students take advantage of the extensive practice so that any past learning experiences will not interfere with their ability to link new information. Chunking Increasing working memory capacity through creating larger bits ♦ Breaking down the material: The lesson is broken down into understandable and manageable parts 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: The lesson is highly organized so that students can easily chunk the information on their own. ♦ Students follow the guidelines of the note-taking guide. ♦ Students take the complex information from the lesson presentation and break it down into manageable parts.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 16 Rehearsal Repeating information in an effort to maintain it ♦ Providing practice.The teacher arranges for a variety of practice opportunities. The goal is to help the learner generalize the concept, principle, or skill to be learned so that it can be applied to different problem situations. ♦ Students complete a variety of practice problems after each lesson presentation. ♦ Students complete homework practice assignments. ♦ Students complete a review assignment the day before the test. Encoding Relating incoming information to concepts and ideas already in memory so that the new material is more memorable ♦ Organizing instruction:The teacher provides students with a graphic organizer handout that helps them to process the information from the lesson. They name and define the concept to be learned, reference it to a larger category and define specific attributes. Scheme -- an organization of concepts, principles, rules, etc. that define a perspective and presents specific action patterns to follow. ♦ Mediating: The lesson uses the story about Buzz to teach the properties of specific graphs of functions and how they relate to their accompanying equation. ♦ 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 relating it to an animal that is similar in appearance. personal experience (information in stories and analogies) ♦ Providing mental scaffolding:The lesson provides students with the opportunity to link new material with what is relevant prior knowledge. ♦ Offering guided discovery:The lesson uses elaboration and multiple contexts to help students identify relevant and irrelevant characteristics of the parent graphs. ♦ Showing methods of elaboration:The lessons provide students with examples and non-examples and have them create their own. ♦ Promoting reasoning techniques:Inductive (example/experience --> definition) and deductive (definition --> examples) ♦ Presenting propositioning techniques:The lesson gives students interrelatedgroups of concepts and relationships such as when they learn ♦ Students use their graphic organizer to help them work practice problems. ♦ Students encode information in more than one way by using mnemonic devices, acronyms, and imagery. ♦ Students elaborate on new information by providing their own examples of each type of graph within their notes. ♦ Students make information personal and meaningful by relating it to their own life. This activity is prompted by discussions on the discussion board. ♦ Students use the note-taking guide to take notes in their own words. ♦ Students use the note-taking guides to summarize the information. ♦ Students impose their own subjective organization ♦ Students post inferential questions ♦ Students include
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 17 the properties of graphs. It has students fill in and analyze if/then statements. ♦ Teaching scripting:The lessondevelops general information about a series of stepsinvolved in graphing functions and has students apply these steps to attain either a picture of a graph or an algebraic equation. ♦ Providing a frame of reference: The lesson offers complex organizational techniques including concepts and visualizations that provide a reference point from whichgraphs and graph manipulations are analyzed. ♦ Delivering programming: This lesson provides a set of rules that define what students shoulddo when the equations of parent functions have been added on to or multiplied by a number. ♦ Focusing on reality: The parent graphs offer a basic way of perceiving, thinking, valuing, and doing something associated with the real-world. ♦ Modeling:The parent graphs or algebraic equations of function describecharacteristicsof the more elaborate graphs. ♦ Helping learners become "self- regulated":Teachers assist students in selecting and using appropriate learning strategies such as summarizing and questioning by providing note- taking guides and structured guidance on the discussion board. study questions in their notes as they fill in the note-taking guide. Retrieval Bringing back previously learned material ♦ Offering opportunities of recall: This lesson asks students to generate graphs by hand and has them use these graphs to answer questions on the practice exercises and test. This lesson offers lots of practice in a variety of ways which makes recall easier. • In free recall situations, learners must retrieve previously stored information with no cues or hints to help them remember. The practice worksheets offer free recall. • Cued recall tasks are those in which a hint or cue is provided to help learners remember the desired information. Students use their graphic organizers to assist with this type activity. ♦ Offering opportunities for recognition: This lesson requires that students must only recognize which answer is correct by utilizing multiple- choice questions on warm-ups and the assessment. Students must make a decision or judgment. ♦ Because the lesson presentation is online, students have the opportunity to access it at home. ♦ Students review the presentation as needed to ensure that they will remember the important concepts. ♦ Students learn the material on the computer using the SMART Notebook software to help them manipulate parent graphs. They then take the test and complete all activities at the
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 18 Yes/no recognition: Determine if the relation is a function. Forced choice recognition: Multiple choice assessments. ♦ Offering opportunities for encoding specificity: The lesson is entirely technology- based and all assessments are technology-based. Whatever cues 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 lots of practice on previously learned material through the warm- up activities, so retroactive interference (interference from newly learned material) is counteracted. Offering opportunities to counteract proactive interference: The lesson has teachers signal key ideas and definitions which counteract proactive interference or when previous learned material interferes with what students are trying to learn now. computer with the notebook page and graphic organizer at their disposal. ♦ Students use the note-taking guide and elaborately take notes in own words. ♦ Students are state- dependent learners. They do not take a drug that might cause drowsiness during learning.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 19 Sample Slide A Slidefrom SlideRocketfrom Function Families Presentation 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”.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 20 Sample Slide B Slide from SlideRocketPresenting Vertical Shift from Function Families Presentation 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 21 Sample Slide C Slide from SlideRocketPresenting Vertical Reflection from Function Families Presentation BUZZ SLEEPING 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 front means that he is in the awake position. This is Buzz asleep at his parent's house.
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 22 Sample Slide Slide from SlideRocketIntroducing “Linus” from Function Families Presentation Introduction of Function Animals Animal Name: “Linus” Function Name: Linear Function Graph Name: Line Math Symbol: x Animal Symbol: see below
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 23 Sample Slide Slide from SlideRocketIntroducing “Abby” from Function Families Presentation Introduction of Function Animals Animal Name: “Abby” Function Name: Absolute Value Function Graph Name: Absolute Value Math Symbol: |x| Animal Symbol: see below
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 24 Sample Slide Slide from SlideRocketIntroducing “Curt” from Function Families Presentation Introduction of Function Animals Animal Name: “Curt” Function Name: Cubic Graph Name: Cubic Math Symbol: x3 Animal Symbol: see below
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 25 Sample Slide Slide from SlideRocketIntroducing “Squirm” from Function Families Presentation Introduction of Function Animals Animal Name: “Squirm” Function Name: Square Root Function Graph Name: Radical Math Symbol: Animal Symbol: see below
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 26 Sample Slide Slide from SlideRocketIntroducing “Rachel” from Function Families Presentation Introduction of Function Animals Animal Name: “Rachel” Function Name: Rational Function Graph Name: Rational Math Symbol: Animal Symbol: see below 2 4 -3
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 27 Sample Slide Slide from SlideRocketIntroducing “Quinton” from Function Families Presentation Introduction of Function Animals Animal Name: “Quinton” Function Name: Quadratic Function Graph Name: Parabola Math Symbol: x2 Animal Symbol: (see below)
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 28 Sample Warm-up QuizA Warm-up QuizusingSMART Notebook on the Basic Behaviors of Functions
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 29 Sample Note-taking Guide A Note-taking Guide for the Behavior of Basic Parent Graphs 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 • Lists and tables • Space out facts SUMMARY (After Class) • In own words • Original examples • Most important key ideas • Accurate phrases for quick reference
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 30 Sample Graphic OrganizerA Organizeron Google Documents Categorizing Connections Between Functions Animals and Algebraic Functions Fill in the organizer according to the information you viewed during the presentation. Animal Name Animal Symbol Math Symbol Function Name Name of Graph
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 31 Sample Graphic OrganizerA Organizer on Google Documents Categorizing Relationships Between Behaviors of Functions Animals and Behaviors of Algebraic Functions 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 32 Sample Practice WorksheetA Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate One-Step Equation Using Cues from the Function Animals 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 33 Sample Practice WorksheetB Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate Equation Using Cues from the Function Animals 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 Quadratic + 6 X2 f(x) = 6x2
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 34 f(x) = + 5 x2 - 6 Sample Worksheet C
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 35 Practice Worksheet on Google Documents Relating the Graph of a Function to an Appropriate Equation Using Cues from the Function Animals 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 36 Sample Practice WorksheetD Practice Worksheet on Google Documents Relating the Equation of a Function to an Appropriate Graph Using Cues from the Function Animals 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_________
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 37 Sample Assessment Review or Extra Practice Activity A Review Activity on Shifting Parent Graphs Completed with Cues from Behaviors of Function Animals 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
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 38 Sample Additional Activity B, p. 1 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?
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 39 Sample Additional Activity B, p. 2 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 your TI-83 Plus graphing calculator. 11. Have the calculator 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?
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 40 Sample Additional Activity B, p. 3 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)
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 41 Sample Assessment Questions A, p. 1 Sample Assessment Questions for Functions Families Copied from SMART Notebook to be Used with Senteo Free-Response System
  • FUNCTION FAMILIES: COGNITIVE INFORMATION PROCESSING 42 Sample AssessmentA, p. 2 Sample Assessment Questions for Functions Families Copied from SMART Notebook to be Used with Senteo Free-Response System