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What is Probability?

Diversity of Learners Adaptation

Original lesson plan retrieved from the Ohio Department of Education website: http://ims.ode.state.oh.us/ODE/IMS/Lessons/Content/What_Is_the_Probability.doc,

adaptation by Debra L. Clark, PhD

One of the primary pieces of knowledge to utilize when ensuring that a lesson addresses a diversity of learners is Howard Gardner's Theory of Multiple Intelligences.  Below are web sites that can be utilized to refresh one's memory or to learn for the first time about Gardner's theory:

http://www.ldpride.net/learningstyles.MI.htm

http://www.newhorizons.org/strategies/mi/front_mi.htm

http://www.multi-intell.com/MI_chart.html

http://www.education-world.com/a_curr/curr054.shtml

Many scholars argue that females learn better in collaborative settings (see http://www.icme-organisers.dk/tsg26/3MaryBarnes.rtf for a discussion of this belief); others argue that some ethnicities, such as African-Americans and Native Americans also learn better in a collaborative setting (see http://www.evergreen.edu/washcenter/spring1993_15-17.pdf for a discussion of this belief).  Thus by addressing the interpersonal intelligence as defined by Gardner one should be engaging in the first step of attending to  a diversity of learners as it may relate to gender and ethnicities.  By addressing all of the intelligences one is also more likely to attend to language differences as well as learning disabilities.  Below is a list of ways to incorporate Gardner's theory and to also address a diversity of learners.

Though students will be drawn to those activities that are in line with their individual intelligences, it is advised that all students at least attempt a try all of the activities.  In doing so, they might discover an unknown talent or intelligence.

Application of Gardner's theory:

For the application of Gardner's Theory of Multiple Intelligences, one activity will be used to address all of the intelligences.  Have the students organize and design a Probability Carnival and if possible, run a Probability Carnival for other students and/or parents.   One group of activities at the carnival will be board games that utilize probability.  The first step in organizing a Probability Carnival is determining activities for different booths.  Below are a few ideas, but brainstorm additional booth activities with the class.

1.  An activity involving the game of Scrabble should appeal to students with verbal/linguistic intelligence.  The points on the scrabble letters are tied to the probability that they can be used in creating words.  This could be demonstrated in a carnival booth by giving participants a handful of scrabble letters and having them create as many words as possible with the letters and then count the number of times a letter is used and the probability of using that letter.

2.  Yatzee is a game of probability that should appeal to students with logical/mathematical intelligence.  A booth similar to the Scrabble booth could be created use the game of Yatzee

3. The students with visual/spatial intelligence could design probability toys, such as a multicolored, spinning top that can fall on only one color.  The students could demonstrate the top at the carnival.

4.  Twister is another game involving probability and one that would be attractive for students with visual/spatial intelligence.  Much in the same way that Scrabble and Yatzee are use to create a carnival booth activity, Twister could also be utilized.

5.  No carnival is complete without musical entertainment.  Have the class write and perform a probability rap.  This portion of the carnival should be particularly appealing to those students with musical/rhythmical intelligence.         

6.  If watching the news is a common event in the lives of students, they have repeatedly watched probability reports.  Weather reports are probability reports.  Have students study the process of making predictions regarding the weather and include a weather forecast booth in the carnival.  This booth should be one that appeals to the student with naturalist intelligence.  The following are websites that can help students and teachers understand weather forecasting and probability:

http://www.bbc.co.uk/weather/features/az/alphabet48.shtml

http://www3.roanoke.com/weather%5C5251.html

http://www.nws.noaa.gov/

http://www.weather.com/

http://tropical.atmos.colostate.edu/forecasts/

http://www.msnbc.msn.com/id/8797726/

Final Thoughts on Gardner's Theory of Multiple Intelligences

All of the above intelligences are content specific.  The intelligences of interpersonal and intrapersonal are different in that they are more tied to another theory Myers Briggs theory of personality development, specifically the introvert/extrovert dimension.  A commonly held belief is that introverts are shy and non-verbal, whereas extroverts are outgoing and very verbal.  This is only part of the story of this dimension.  Yes, introverts tend to be less verbal and extroverts tend to be more verbal.  However, the reason behind these tendencies is what is important for teachers to understand.  The reasons behind these tendencies are directly tied to the intelligences of interpersonal and intrapersonal.

Introverts and individuals with intrapersonal intelligence are very able to speak, but must be given the opportunity to do so.  Introverts and individuals with intrapersonal intelligence have an internal energy base.  In other words, these individuals become energized when able to spend time alone.  This internal energy base is also why individuals who are introverts and have intrapersonal intelligence need quiet time to think and process information.  Once these students are given the time to process information internally, they are very willing and able to share their thoughts.  A classroom activity that should occur everyday is time to think.  An easy way for teachers to ensure this occurs is to put into the daily schedule time for journaling. Extroverts and individuals with interpersonal intelligence process information and gain energy in an opposite process.  Extroverts gain energy through interactions with others; extroverts need to talk to think.  Thus, whereas introverts and individuals with intrapersonal intelligence need quiet time to think, extroverts need others to speak to in order to think.  To meet the needs of these students, small and large group activities are most beneficial.    

Working with students with visual impairments

When working with a disabled student it is important for the teacher to understand how the student experiences the world.  The following links will assist a teacher in better understanding the life of a student with a visual impairment:

http://www.as.wvu.edu/~scidis/text/vision_impair.html

http://www.cnib.ca/e3a/team4/tieachblind-visualimpared.htm

http://www.blind.net/bg340001.htm

http://www.lifesci.sussex.ac.uk/reginald-phillips/beginnersPaper.htm (materials to assist visually impaired students)

If you would like to learn more about Braille materials and other teaching tools for students who are blind, the American Foundation for the Blind web site provides numerous resources for classroom teachers:  http://www.afb.org.

For the above tasks, students with visual impairments would be best off to work in the booths in which tactile knowledge can be used in place of visual knowledge.  The Yatzee and Scrabble booths best meet this requirement due to indents on the letters and die.  Also students with a visual impairment should be paired with students with interpersonal intelligence who would be more likely to share decision making responsibilities.

Working with students with Auditory impairments

the following web sites will assist teachers in better understanding the life of a student with a auditory impairment:

http://www.ohlone.edu/org/dsps/dspsfacultyhandbook/classroomtips.html         

http://snow.utoronto.ca/best/accommodate/deaf.html

http://www.und.edu/dept/dss/Questions%20Commonly%20Asked%20About%20Teaching%20Deaf%20Adult%20Students.htm

http://deafness.about.com/cs/schooling/a/backtoschool.htm

None of the above tasks should be problematic for the student with an auditory impairment.  Even the rap can be performed if the student is made aware of the lyrics and timing of the rap.

Working with students with behavioral problems

The following web sites will assist teachers in better understanding the life of a student with a behavioral impairment: 

http://www.as.wvu.edu/~scidis/behavior.html

http://www.kidsource.com/kidsource/content2/behavior_disorders.html

http://www.nichcy.org/pubs/research/rb1txt.htm

Students with behavioral problems respond well to structure and systematic rewards.  Thus two types of classroom situations can become problematic.  When students are required to sit quietly for an extended period of time, this presents a unique challenge for the child with a behavioral impairment.  In contrast, new activities that give students much freedom to make decisions can also be problematic for the child with a behavioral impairment.  Nonetheless, students with behavioral problems need to adapt to these situations.  Thus, when these diametrically opposed situations occur, the teacher needs to be cognizant of the challenges a student with behavior problems might be experiencing and provide positive reinforcement in these situation.  For the above tasks, the independence given to students is necessary, but could be problematic for a student with a behavioral problem.  Thus, an adult assisting in the management of a booth that includes a student with behavioral problems would be advantageous.  Perhaps a parent volunteer will be available for this assistance. 

Working with students with autism

The following web sites will assist teachers in better understanding the life of a student with autism.

http://ericec.org/digests/e582.html

http://www.bced.gov.bc.ca/specialed/docs/autism.pdf

http://members.aol.com/Room5/strat.html

http://www.ddc.ohio.gov/Pub/ASDGuide.PDF

Students with autism are much like students with behavioral problems in that structure and positive reinforcements are very important.  Another important aspect of the classroom environment is repetition.   All of the above activities should be repeatedly tied back to the original lesson plan about probabilities.  This will assist the learning of all students, but especially the student with autism.