Exploring Middle School Mathematics with ® NCTM Hartford, CT 2012

Christina Gawlik, Ph.D [email protected] Saint Xavier University

Description: Engaging students in meaningful and fun mathematics can be accomplished using the Nintendo Wii™ through interdisciplinary units and differentiated instruction for grades 6-8. Come participate in lessons using the Wii™, discussion of managing all class sizes, diverse learners, teachable moments, and preparing students for high stakes tests.

Lesson 1 – The Baseball Investigation One student at a time will practice hitting 10 consecutive baseballs. Awaiting students will cheer on their classmates and record data such as distance, speed, and type of ball hit. Analysis of data will include determining the percentage of each type of ball hit (foul balls, base hits, home runs, strikes), and create a circle graph representing the class data. Moreover, students will determine the average speed of balls hit per person and as a class.

Lesson 2 – The Power Throw Bowling Investigation Students will bowl 10 rounds within the Power Throw training session, where the number of pins increases each round. Students will describe and create an expression for the pattern of increasing pins, as well as predict outcomes and calculate the maximum possible score. Data will later be transferred into scatter plots and line plots.

Lesson 3 – The Ball Return Tennis Investigation Students will record the total number of balls returned during the training session called Returning Balls. Class data will be analyzed to determine central tendencies, and five-number summary to create a box-and-whisker and line plots.

Additional Lesson Titles Lesson 4 – The Tennis Tournament Investigation Lesson 5 – The Golf Game Investigation Lesson 6 – The Scientific Experiment Investigation

The lessons presented are available in the book called, Investigating Middle School Mathematics: Classroom Lessons Using ® by Christina Gawlik. Information about this resource can be found at any of these locations:

1) Amazon.com: Search for Christina Gawlik or Investigating Middle School Mathematics 2) CreateSpace: https://www.createspace.com/3695735 For $2.50 off your purchase use code: UATMHTSD 3) facebook: Search for Investigating Middle School Mathematics page 4) primetwu.wordpress.com – abbreviated sample lessons

Other Titles of Interest Fancy Fractions: Mastering Fraction Concepts & Computations for Grades K-8 by Christina Gawlik, found on Amazon.com or direct webpage https://www.createspace.com/3823695 For $5 off your purchase use code: 9YQY7MM9

1 Exploring Middle School Mathematics with Nintendo Wii® NCTM Hartford, CT 2012 Samples can be found at: primetwu.wordpress.com

Lesson 1 – The Baseball Investigation

Lesson 2 – Power Throw Investigation

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Lesson 3 – The Ball Return Tennis Investigation

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NCTM Regional Conference Hartford, CT October 24th – 26th, 2012 Exploring Middle School Mathematics with Nintendo Wii™

Christina Gawlik, Ph.D Saint Xavier University [email protected]

Educational Video Gaming ! Provides intrinsic motivation in the learning environment ! Learning context is meaningful to students ! Games and the act of play, have positive effect on student motivation and retention of knowledge

(NCTM, 2000; Ma and Kishor, 1997; Sedig, 2008)

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What will we explore today? 1. Activities that require application of math to solve problems in familiar contexts a) Identifying and describing patterns, relationships, and algebraic thinking b) Process of data collection and analysis c) Apply concepts of probability and statistics 2. Student Created Experiments a) Allow students to use statistical procedures to collect and describe data, make predictions, and communicate mathematical ideas 3. Observe connections supporting NCTM Standards 4. Easily utilize differentiated instruction – Supporting all students

What will we explore today? 1. Activities that require application of math to solve problems in familiar contexts a) Identifying and describing patterns, relationships, and algebraic thinking b) Process of data collection and analysis c) Apply concepts of probability and statistics 2. Student Created Experiments a) Allow students to use statistical procedures to collect and describe data, make predictions, and communicate mathematical ideas 3. Observe connections supporting NCTM Standards 4. Easily utilize differentiated instruction – Supporting all students

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Getting Started: Using Wii Sports What are potential types of data to be collected when playing…?

! Baseball ! Tennis ! Bowling ! Golf

Home Run Derby Baseball Investigation ! Volunteers!!

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Example with Baseball: Home Run Derby Ball$ Round$1$ Round$2$ Round$3$ 1$ 0" 472" 0" 2$ 0" 0" 0" 3$ 0" 0" 0" 4$ 0" 0" 0" 5$ 0" 485" 515" 6$ 0" 547" 501" 7$ 518" 449" 0" 8$ 518" 0" 583" 9$ 0" 528" 534" 10$ 0" 521" 501" Total$Distance$ 1036" 3002" 2634" #$of$Homeruns$ 2" 6" 5"

Find the mean total distance. What is the probability that in Round 2 you will NOT hit a homerun? Create a scatterplot of the data collected from three rounds. Does a relationship exist between distance hit per ball? Explain.

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Homerun Derby 600

500

400

300 Round 1 Round 2

200 Round 3 Distance Hit in Feet

100

0 0 1 2 3 4 5 6 7 8 9 10 Ball

Home Run Derby

Round 1 Round 2 Round 3 Probability of hitting a What does each probability homerun 2/10 6/10 5/10 represent? Simplify if How can you make sure you possible 1/5 3/5 1/2 simplified correctly? On average, how many Write as a homeruns will you hit? percent 20% 60% 50% Explain.

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Power Throw Bowling Investigation ! Volunteers!!

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Ball Return Tennis Investigation ! Volunteers!!

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NCTM – Supporting Student Learning

! Process Standards that are addressed in each lesson ! Problem Solving ! Reasoning & Proof ! Communication ! Connections ! Representations

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Student Created Experiments

Where do we begin?

Have students determine variables to compare. ! Gender ! Number of wins/losses ! Dominant/Non-dominant ! Game averages handedness ! High/low scores ! Time of day ! Students who regularly play ! Height of student Wii, and those who don’t ! Eyes open/close

So, what can we do with this information?

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Student Created Experiments ! Ask a Question ! Do Background Research ! Construct a Hypothesis ! Design an Experiment ! Test your Hypothesis by Doing the Experiment ! Analyze your Data and Draw a Conclusion ! Communicate your Results ! Discuss Future Extensions

Student Created Experiments

1. Ask a Question 1. Who has higher bowling scores, boys or girls? 2. Construct a 2. 3rd grade students in Mrs. Byrd’s class will have Hypothesis higher bowling scores than 3. Conduct Background Mrs. Woodlock’s 5th grade class. Research 3. Research professional bowling teams 4. Design an Experiment to Test 4. Boys and girls will take turns bowling 3 games your Hypothesis each, and determining personal averages. 5. Carry Out Averages of boys scores and girls scores will be Experiment & compared. Collect Data 5. Create a schedule to collect data 6. Analyze your Data 6. Compute personal averages, the average score and Draw a Conclusion for boys, and girls. Determine a conclusion. 7. Communicate your 7. Create a presentation of results that discuss Results & Discuss findings and explain further extensions of Future Extensions experiment

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How can this project support Differentiated Instruction?

! Changing Expectations ! no need for a rules-based approach to mathematics ! Problem based learning ! Getting to know your students – contextual factors ! Transforming tasks to meet the needs of all learners ! Bloom’s Taxonomy

How to use Differentiate Instruction Independent Students Students who Dependent Students ! Allow students to need Probing • Supply students create their own ! Provide suggestions with more experiment for hypothesis direction: ! Self directed ! Use guiding hypothesis &discussion of ! Minimal teacher questions to what data to facilitation encourage background collect research, data • Facilitate collection strategies background and analysis research & analysis

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Background Research ! Compare data from their favorite professional or local sports team with the data collected from their experiment ! United States Bowling Congress www.bowl.com ! KC Royals http://kansascity.royals.mlb.com/index.jsp?c_id=kc ! Consider drawing similarities and differences between virtual play and actual play ! Take a fieldtrip to the bowling alley ! Analyze data on http://www.bowlingstats.net/ for FREE!

Example Hypotheses ! Students will bowl higher scores using their dominant hand ! Boys will throw more strikes ! Students who don’t play video games will have a lower game average than those who do ! Students who play sports will have higher scores than those who don’t

17 Exploring Middle School Mathematics with Nintendo Wii® NCTM Hartford, CT 2012 Carryout Experiment & Collect Data ! What is your class plan for collecting ? ! How many experiments do you want running at once? ! What type of data do you want your students to collect?

Analyze Data & Make Conclusions ! Calculate statistical analyses ! Averages ! Ranges ! Maximums ! Minimums ! Quartiles ! Regressions ! Make Concluding Statements

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Communicate Your Results & Address Ideas for Experiment Extensions ! Write a report ! Create a presentation ! Present to class/other classes/Principal/Parents ! Collect all studies and create a class book ! Student portfolios

Bloom’s Taxonomy

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Questioning Key Words: High to Low ! Conclude, criticize, defend, describe, evaluate, explain, justify, relate, support ! Categorize, compile, compose, modify, organize, summarize, devise, explain ! Analyze, compare, contrast, deconstruct, differentiate, distinguish ! Predicts, produce, solve, demonstrate, apply ! Convert, estimate, generalize, give examples, interprets ! Define, describe, identify, label, match, name, select

A Suggested Timeline Week 1 & 2 ! Creating ’s and becoming familiar with the equipment ! Introduction & Initial Experimental Design ! Creating a hypothesis, a plan to carry out experiment, & create data recording apparatus (table, poster, excel) ! Data Collection & Background Research ! Students begin collecting data ! Before/after school, lunch, recess, or create centers to engage all students during class, use afterschool programs ! Others are conducting background research ! Practice problems ! Example data from websites, texts, and/or newspapers ! Calculate central tendencies, probabilities, and representations of data ! Write about results

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Suggested Timeline

Week 3 & 4 ! Continue Data Collection with Wii ! Collect “Real” Data by Mimicking Student Experiments ! Fieldtrip to a bowling alley ! Play softball or tennis on school grounds

Suggested Timeline Week 5 & 6 ! Analyze Data ! Draw Conclusions about Video & Real Data ! Calculate central tendencies, probabilities, and representations of data ! Explore relationships among variables, if any exist and explain why. ! Discuss similarities and differences from virtual vs. non-virtual experiences

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Suggested Timeline Week 7 & 8 ! Conclude Analysis & Write up Results ! Create Presentation & Communicate Experimental Design & Results ! Posters, PowerPoint, Website ! Create a class book of student group experiments

Suggested Timeline Week 9 ! Presentations ! Present to class, other classes, administration, parents ! Parent/Teacher Conferences ! Parent Math Night ! Community Events

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Additional Project Ideas ! Class challenges among ! Economics – SimCity Creater same grade levels or across Game grade levels ! Music – Wii Music ! Challenge adults (parents, ! MSNBC Article http://www.msnbc.msn.com/id/29127548/ teacher, other staff) vs. students ! ! Ability to store and graph data over ! Discuss geometric time probabilities when playing ! Set personal goals Tennis Target Training ! Record other activities and the amount of time

Other Fun Wii Games ! Wii Fit ! Set personal goals and get fit simultaneously ! Sim City ! Develop a functioning city and track the economics ! Wii Music ! Learn to read music and become a musician ! ! Start a rock band with up to 4 players ! Hero: Aerosmith ! **Wi-Fi: play against your friends from another location

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How could YOU implement the Wii into your classroom?

Christina Gawlik, Ph.D Saint Xavier University [email protected]

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