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# Suppose that you know that a golfer plays the first hole

ISBN: 9780073383095 37

## Solution for problem 2E Chapter 5.1

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition

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Problem 2E

Suppose that you know that a golfer plays the first hole of a golf course with an infinite number of holes and that if this golfer plays one hole, then the golfer goes on to play the next hole. Prove that this golfer plays every hole on the course.

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Module 12 Notes Strategies for responding to individual success: Reinforcement Written by: Krista Anstead April 2016 Learning Outcomes • What Behaviors to Reinforce o Identifying the Reinforcers (What) o Using Reinforcers (How) • Token Economies o Behavior Contracts • Schedules of Reinforcement (When) o Tracking Progress (Is the Reinforcement Working) Readings/References: Scott, T., & Anderson, C. (2012). Strategies for responding to individual success: Reinforcement. In Managing Classroom Behavior Using Positive Behavior Supports. Boston: Pearson. Acronyms: • CRF = continuous reinforcement behavior Chapter 12 Notes Introduction • Head-­‐on approach of trying to stop S challenging behaviors through punishment is: o Ineffective for S o Creates a number of unwanted side-­‐effects • Reinforcing desired behaviors in integral in preventing challenging behaviors because when no behaviors are reinforced, many S will use challenging behaviors to fill the void • Steps to taking control of classroom environment through reinforcement o Identify social and academic behaviors that would benefit the S if they happened more often o Identify the reinforcers that will make S more likely to engage in these behaviors in the future (what) o Identify how and by whom these reinforcers will be delivered to S (how) o Identify an appropriate schedule for reinforcement (when) o Monitor for behavior change as a result of reinforcement procedures (for how long) • First step is deciding what you want S to do and then talk about getting S to do it Selecting S behaviors to target for reinforcement • Begin with choosing the behaviors that T want to happen more often • Throughout the school day, T should constantly confront themselves with this strategy: this behavior just happened. Do I want that to happen more often or less often in the future • Behaviors that we sometimes expect from S may be complex or require considerable effort; in these situations, we need to put 2 reinforcement strategies into place o Break the expected behavior down into steps using task analysis o Reinforce behaviors close to desired behavior we are looking for • When selecting appropriate behaviors to reinforce, we assume that desired behavior and its demonstration are already in S repertoire o Reinforcing S only when they demonstrate behaviors that are not in their repertoire is unfair and sets them up for failure • Teaching or re-­‐teaching is often an important first step to perform before beginning a reinforcement plan • Recruitment reinforcement: equipping S with series of steps to access T attention o S gain attention and praise they desire and improve their behavior and classroom success o Examples: think-­‐aloud strategies, modeling, role playing, error correction, and praise Identifying effective reinforcers for different S and different target behaviors • attention reinforcers should be done subtly and quickly in S direction o Ex: wink, thumbs up, nod • Activities should be things that S can earn as rewards for being on-­‐task in class • Positive reinforcement: adding something to the environment to increase future occurrences of behavior o Advantages: avoiding the use of aversives and allowing T to accentuate the enjoyable aspects of classroom • Negative reinforcement: removing something from the environment to increase future occurrences of specific behavior • Types of direct reinforcers: o Attention, activities, and tangible reinforcers • systems of reinforcers: o token economies – coins/tokens can act as: § backup reinforcers – give S access to three categories of reinforcers § conditioned reinforcers – tokens paired with backup reinforcers • most essential guide to selection and implementation is the use of ongoing data collection to determine whether behaviors are increasing or decreasing based on what the T is putting into the environment • critical to view both the consequence that the challenging behavior accesses and the one that the new desired behavior should access from a functional perspective • portable system to earn reinforcement across all classes is most beneficial • S can cash in tokes at end of day, or maybe a couple times during the day, to use on activities that he/she likes Components necessary to implement reinforcers effectively • Steps to implement token economy o Get a stamp made o Get a series of different colored index cards to represent different levels o As S moves up in levels, they earn fewer points, but privileges cost less, and S have access to additional activities and privileges o Make goals specific and positive o Put S name and date on back of each card o Watch carefully for compliant behavior o Award points by punching holes in card using stamp. Points are spent throughout day for privileges. A point is spent when T circles it in ink. There is no total amount of points for S to earn. Pair token reinforcement with verbal reinforcements • Principles to help determine hot to effectively apply reinforcement for desired behaviors o Immediacy: immediacy with which reinforcer follow the behavior § Longer the time between behavior and reinforcer, the weaker the reinforcer is o Novelty: reinforcers that are new, different, or unexpected are stronger that those that have been used for long periods of time; guards against satiation § Satiation: when an individual receives a reinforcer too much or too often, causing it to lose its previous reinforcing strength § Example of novelty: incorporating “surprise” – S looking inside envelope to finding out clues to reinforcer; prize envelopes with laminated cards of activity reinforcers; act of choice o Consistency: S make connections between behavior and reinforcing consequences, so they should be consistent o Combining reinforcers with choice: strengthens learning connections between behaviors and reinforcers; allows S to decide the tasks they want to complete first, second, or third as well as to choose from a menu of reinforcers § Leads to likelihood of completing tasks and decreases likelihood of satiation § Embedding choices throughout the days helps to reduce the feeling of hopelessness • Token economies: assist in delivery of frequent reinforcement and include indirect or secondary reinforcers o should be items that are not easily stolen or counterfeited and can be awarded efficiently and effectively in quantities o requires that T constantly monitor for appropriate and desired behavior rather than inappropriate behaviors and make it convenient and easy to reinforce desired behaviors when they occur • behavior contracts: systematic, formal, written agreement between T and S of behavior expectations that specify: § clear behavior objectives § reinforcement that S will receive when they meet the objectives § short-­‐term goal statement § review dates to evaluate performance o important to clearly identify the behavior to be increased or decreased in observable and measurable terms and to select as reinforcers the items and activities that the S finds motivating o guidelines: § time interval of the contract should be fairly short, usually the end of the day or even end of a half day § S should experience success and see T living up to their end of the contract with the first behavior contract that is set up • key to using reinforcement is not that we reinforce every single behavior every time, but rather to provide reinforcement systematically on a schedule where T gradually reduce the frequency or fade the reinforcement Different schedules of reinforcement • effects a T can have by strategically planning when to reinforce to a desired behavior: o ensure that reinforcer remains effective • CRF provides reinforcement on a 1:1 basis and is important to strengthen new skills • S will come to expect reinforcement every time they engage in behavior and may cease demonstrating the behavior as soon as the reinforcement is not presented • T should be systematic with how frequently they reinforce desired behaviors • Ways schedules typically divided: o Amount of time (interval) o Number of behaviors emitted (ratio) o Can be fixed or variable § Variable schedules have greater reinforcing strength because S doesn’t know when reinforcement is coming; “next reinforcement is right around the corner” • Use least amount of reinforcement necessary • Continuous reinforcement should be used only during the acquisition of the skill • Reinforcement rule: collect data continuously to determine what, how, and when to provide reinforcement and to ensure that the contingencies put in place truly reinforce the desired behaviors, removing them as soon as possible without decreasing occurrences of the desired behavior • Frequently used token economies based on schedule: o Point sheet: points awarded on a fixed interval § Need to collect data on when S do and do not earn points may require a point sheet o Punch card: T monitors S behavior and provides reinforcement on a variable ratio contingent on average numbers of behaviors emitted Effective ways to track progress of S receiving reinforcement • To determine whether the stimuli that we put into a classroom environment is truly reinforcing, T must monitor S behavior • Ability to manage one’s own behavior is one of ultimate goals of education • Self-­‐monitoring: S are taught to monitor their attention to tasks or their rate of task completion, accuracy, or productivity and to evaluate themselves in comparison to a pre-­‐determined objective o Teaches S to be more consistent with behaviors already in repertoire o Easiest way of charting is to begin with some type of worksheet § To chart behavior, identify S, goal, and context in which charting will be used o Examples of behaviors to self-­‐monitor: engagement with or attention to tasks, in-­‐seat behavior, hand-­‐raising as a replacement for calling out • Analyze data with S to interpret progress, and have S identify a goal and show the distance between current and future performance Peer Response to Chapter 12 -­‐ Screencast notes • Behavior contract: not a form of reinforcement in sense that there’s a consequence after behavior; it states IF this, THEN that • Mystery walker/motivator: great tool for reinforcement because S don’t know WHEN they will get reinforcement o VI-­‐variable interval-­‐ schedule o similar to gambling behaviors o not knowing acts as huge motivator o also called randomized behaviors § can be used in good behavior game as group contingency § S not knowing what they will get as reward o Can also be used with levels of on-­‐task behaviors; variance in terms of percentage they must be on-­‐task § T monitors behavior and then pulls percentage out of hat when observation is over, and determine if S gets reward § Make sure to set up S for success; weight it for success based on their typical on-­‐task behavior

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Suppose that you know that a golfer plays the first hole