2012 Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule

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2012 CAT Symposium Schedule

Transcript of 2012 Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule

Third Annual Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule

September 15, 2012 Ohio University, Athens Morton Hall

9:30 Symposium Registration Foyer

10:00 Welcome 235 Ralph Martin, Noyce and WWTF Co-Director

10:15 Opening Remarks 235 Aimee Howley, Associate Dean of the Patton College

10:30 Introduction of Speaker 235 Gregory D. Foley, CAT Program Director

10:35 Keynote Address 235 Tom Reardon, Mathematics Teacher and Consultant

What I Have Learned While Teaching Math for 30+ Years

11:20 Break

11:30 Concurrent Sessions 219 Mark Lucas, Physics, Ohio University, 30 min

Science Outreach in Southeastern Ohio

222 Pam Beam, Teacher Education, Ohio University, 30 min

Classroom Strategies for the First Year Teacher

223 Lisa Gillespie1, Ohio Virtual Academy, 30 min

Being an Educator with Ohio Virtual Academy

227 Julio Camacho2, University of Rio Grande, 30 min

UDL and Scientific Creationism4

226 Sam Carpenter2, Ohio University, 15 min

Motivating the Modern Math Student

11:45 226 Justin Malone2, Shawnee State University, 15 min

Utilizing Classroom Seating Arrangement for Management

Purposes in the Secondary Science Classroom

12:00 Lunch and Conversations 226 CAT Scholar Meeting

in rooms 219–235 227 Noyce Scholar Meeting

12:50 Concurrent Sessions 219 Michael Smith3 and Kay Casto, Mathematics Education

and Mathematics, Ohio University and Vinton County

High School, 30 min

Statistical Literacy in the High School Mathematics and

Science Classroom

222 Donna Shepherd, Chemistry and Physics, Adams County

Ohio Valley High School, 30 min

Bringing STEM to K–12 Students: Locating and

Researching Sinkholes

223 Jeff Taylor3, Ohio University, 30 min

Algebra for All in Grade 8: What's Different about the

1 Noyce scholar 2 Choose Appalachian Teaching (CAT) scholar 3 OU PhD student 4 Julio Camacho did not present.

Third Annual Appalachian Ohio Mathematics and Science Teaching Research Symposium Schedule

September 15, 2012 Ohio University, Athens Morton Hall

Common Core?

12:50 Concurrent Sessions 227 Aaron Sickel, Teacher Education, Ohio University, 30 min

Struggles and Successes: What Beginning Mathematics and

Science Teachers Should Know About the First Three Years

226 Nick Conroy1, Ohio University, 15 min

The Wow Factor: Demonstrations in the Science Classroom

1:05 226 Calee Reeves1, Ohio University, 15 min

Science Teacher Methods Opinions

1:20 Break

1:25 Concurrent Sessions 219 Gregory D. Foley, Teacher Education, Ohio University,

30 min

Advanced Quantitative Reasoning: Ohio Core Mathematics

for High School Seniors

222 Donald Storer, Chemistry, Southern State Community

College, 30 min

How a Chemical Education Research Project Led to a

“Flipped" Classroom

223 Nina Sudnick, Elementary School Mathematics and

Science, Athens City Schools, 30 min

"I LOVE Math! This is my BEST year ever!!" 4th grader,

West Elementary 3

226 Al Coté and Mark Lucas, SEOCEMS and Physics, Ohio

University, 30 min

Bring STEM to the Classroom: Integrating Science and

Math through Real World Investigations

227 Art Trese, Environmental Biology, Ohio University, 30 min

Garden Spaces as Educational Tools

2:00 Panel Discussion 235 Voices from the Field, 30 min

Starr Adkins2, Mathematics, Collins Career Center

Micah Freeman2, Mathematics, Grove City Christian High

School

Zachary Graves1, Mathematics, Wellston High School

Dan Oliver2, Mathematics, Ripley-Union-Lewis-Huntington

High School

Mallory Spengler1–2, Science, Jackson High School

2:30 Closing Remarks 235 Gregory D. Foley, CAT Program Director

Jeff Connor, Noyce and WWTF Co-Director

1 Choose Appalachian Teaching (CAT) scholar 2 Noyce scholar 3 Nina Sudnick was unable to attend and present.

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Advanced Quantitative Reasoning Ohio Core Mathematics for

High School Seniors

Gregory D. Foley Morton Professor of Mathematics Education

Ohio University

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Advanced Quantitative Reasoning (AQR) is a course in mathematics, statistics, and modeling for students who have completed Algebra I, Geometry, and Algebra II—or Integrated Mathematics I–III.���

In Ohio, students graduating in 2014 and beyond will be required to complete 4 years of high school mathematics. AQR is a 4th-year course designed for the average student.���

The AQR project is developing and testing student materials and teacher resources (75% done) for such a course. AQR has pilot-tested textbook materials for the past three school years and now is field-testing them at 10 high schools in 2012–2013.

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Our society thrives on numbers, yet many high school graduates are ill-equipped to make informed judgments using quantitative information. ���

Many graduates are not ready for the mathematical and statistical demands of college, with 35.1% of U.S. college mathematics enrollments in remedial courses: 1.4 million out of 3.9 million in fall 2010.

(R. Blair, 7 April 2012)

Perhaps the worst thing that can happen to a student at the end of his or her secondary mathematics preparation is to enter college not having studied mathematics after a lapse of a year or more.

(Seeley, 2004, p. 24)

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NCTM Math Takes Time position statement (2006): •  Every student should study mathematics every year through high school,

progressing to a more advanced level each year.

•  All students need to be engaged in learning challenging mathematics.

•  At every grade level, students must have time to become engaged in mathematics that promotes reasoning and fosters communication.

•  Evidence supports the enrollment of high school students in a mathematics course every year, continuing beyond the equivalent of a second year of algebra and a year of geometry.

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The aims of the AQR springboard course are"•  to reinforce, build on, and solidify the student’s working

knowledge of middle grades mathematics through Algebra I, Geometry, and Algebra II

•  to develop the student’s quantitative literacy for effective citizenship, for everyday decision making, for workplace readiness, and for postsecondary education

•  to develop the student’s ability to investigate and solve substantial problems and to communicate with precision

•  to prepare the student for postsecondary course work in STEM and non-STEM fields—and

•  for students who complete the course in the 11th grade—to prepare them to study AP Statistics, AP Computer Sciences, or Precalculus in their senior year of high school.

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Common Core conceptual categories for high school mathematics"

•  Number & Quantity •  Algebra •  Functions •  Modeling •  Geometry •  Statistics & Probability

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Common Core standards for mathematical practice!

1. Make sense of problems and persevere in solving them. 2. Reason abstractly and quantitatively. 3. Construct viable arguments and critique the reasoning of

others. [mathematical communication] 4. Model with mathematics. 5. Use appropriate tools strategically. 6. Attend to precision. 7. Look for and make use of structure. 8. Look for and express regularity in repeated reasoning. 

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Advanced Quantitative Reasoning course outline!

Core. Quick questions, explorations, investigations, examples, exercises, and increasingly involved projects and presentations.

•  Numerical reasoning •  Statistical reasoning •  Modeling using discrete and continuous functions •  Geometric modeling and spatial reasoning

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Some AQR numerical reasoning topics"

•  Problem solving strategies •  Fractions, decimals, percent •  Proportional reasoning •  Quarterback ratings •  Reading indices •  ID numbers and check digits •  Richter scale analysis •  Transition matrices •  Applications of Pascal’s triangle •  Probability

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Probability task"Drug testing. Suppose a recent national study

indicates that about 3% of high school athletes use steroids and related performance-enhancing drugs. Suppose further that the accuracy of the standard test used is roughly 97%. That means that 3% of the time, the test returns an incorrect result (either a false positive or a false negative).

What is the probability that a randomly selected student athlete who tests “positive” is actually a user of performance-enhancing drugs?

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How to design an investigation"Is a DoubleStuf Oreo cookie really double stuffed?

What concepts and relationships are involved?"

Ancient Alligators. Alligators, crocodiles, and their relatives and ancestors are known as crocodilians. On Earth for 250 million years, they have survived mass extinctions that killed other animals. The modern American alligator thrives in the coastlands of the Southern states from Texas to the Carolinas. A typical adult male is about 12 ft long and weighs 800 lb.

Suppose that a scientific team excavates an ancient crocodilian with the same proportions (same shape) but twice as long (24 ft) as an adult male American alligator. How much would you expect this ancient beast to have weighed?

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What is the relationship between the area and the side length of an equilateral triangle?

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Modeling activity: Zipfʼs law"

“In a given country . . . , the largest city is always about twice as big as the second largest, and three times as big as the third largest, and so on” (Strogatz, 2009).

How accurate is this model for city population in the United States?

2010 U.S. Census Bureau Data (in millions of persons)"

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1 New York 8.175 2 Los Angeles 3.793 3 Chicago 2.696 4 Houston 2.099 5 Philadelphia 1.526 6 Phoenix 1.446 7 San Antonio 1.327 8 San Diego 1.307 9 Dallas 1.198 10 San Jose 0.946

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Modeling activity: Zipfʼs law"

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Modeling activity: Zipfʼs law"

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Modeling longitude and latitude with fruit"

(a) Identify two antipodal points as the north and south poles. Mark and label the two points as N and S.

(b) Draw an arc from the north pole to the south pole. Label it as 0° longitude. This is the prime meridian.

(c) Locate and mark the midpoint of the prime meridian. Mark the midpoints for 4 or 5 other meridians (lines of longitude). Draw in the great circle that represents the equator.

(d) With the aid of a globe, an atlas, or the Internet—locate, mark, and label points for London, England; Quito, Ecuador; and your home city or county on the orange.

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Geometric modeling: Spherical geometry"If you are traveling along a great-circle shortest

path from Athens, Texas to Athens, Greece will you pass closer to Athens, Georgia, USA or Athens, Ohio?

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Advanced Teacher Capacity: An associated professional development program"

•  Two-week summer institutes (60 contact hours). !•  Two daylong follow-up workshops plus online support

•  TPACK: technology, pedagogy, & content knowledge

•  Technology: TI-nspire (additional tools for Modspar)

•  Pedagogy: Tasks, tools, and talk

•  QUANT: Statistics and probability

•  Modspar: Modeling and spatial reasoning

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QUANT: Quantifying uncertainty and analyzing numerical trends"•  Words of statistics; measurement and data collection "•  Formulating statistical questions and designing of

statistical studies

•  Data analysis and descriptive statistics

•  Combinatorics, random processes, and probability, including conditional probability

•  Using data, probability, and distributions to justify conclusions and to make decisions

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Modspar: Modeling and spatial reasoning"•  What is modeling? !•  Discrete dynamical systems: Finite differences,

difference equations, web plots

•  Recursively and explicitly defined functions

•  General proportional model and reexpressing data

•  Modeling with polar and parametric equations

•  Three-dimensional geometry and modeling

•  Spherical geometry and modeling

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Acknowledgement and appreciation"•  Thomas R. Butts, Stephen W. Phelps, Daniel A. Showalter,

Joseph T. Champine, Carmen Wilson, Allen Bradley, Tarasa Sheffield, Mary Harmison, Andy Lovejoy, Sara Vance, Wei Lin, George A. Johanson, Jeffery Connor, Laura J. Moss, Jeremy F. Strayer, Michael Todd Edwards, Sigrid Wagner, Pascal D. Forgione, Jr., Cathy L. Seeley, Michelle Reed, Jerry L. Moreno, Ralph Martin, S. Nihan Er, Michael A. Smith, Heba Bakr Khoshaim, Maha Alsaeed, David A. Young, Ruth M. Casey, Rebekah Boyd, Douglas Roberts, Michael Houston, John Ashurst, Michael Lafreniere.

•  Advanced Teacher Capacity QUANT and Modspar scholars •  A host of other colleagues, graduate students, and support staff •  Our wives and families

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Acknowledgement and appreciation"AQR and ATC have been supported by grants from •  the Improving Teacher Quality Program of the Ohio

Board of Regents, •  the Mathematics Professional Development Program

of the Ohio Department of Education, •  the U.S. Department of Education, •  the South East Ohio Center for Excellence in

Mathematics and Science, and •  Texas Instruments, Inc.

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Advanced Quantitative Reasoning Ohio Core Mathematics for

High School Seniors

Greg Foley foleyg@ohio.edu

Science

Teacher

Methods

Opinions Calee Reeves

Ohio University CAT Scholar

Background for Survey

Science teachers grades 7-12

Appalachian Ohio counties

813 emails

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14

13 16

24

8

Grade

Seventh

Eighth

Ninth

Tenth

Eleventh

Twelfth

5

18

16

8 5

17

5

0 14

Class Taught

A & P

Biology

Chemistry

Earth

Life

Physical

Physics

Space

Other

0

3

2

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38

14 2

Class Size

0-5

6-10

11-15

16-20

21-25

26-30

30+

Methods and Modes Surveyed Direct Instruction v. Lecture

Labs v. Demonstrations

Bookwork, Seatwork, Homework

Availability of Blackboard, Whiteboard, SmartBoard

Participants were asked to rate how frequently a

method is used and then offer an amount of

agreement or disagreement with various

statements about the method.

Frequency of Use

Direct Instruction:

daily

Lecture: 2

times/week

Labs: 1 time/week

Demonstrations: 1

time/week

Bookwork:

rarely/never

Seatwork: 2

times/week

Homework: 2

times/week

Delivery Modes

Available

Blackboard: 25

Whiteboard: 61

SmartBoard: 45

Use

Blackboard: 19

Whiteboard: 59

SmartBoard: 45

Direct Instruction

Helps students learn

Is not a difficult teaching method

Is beneficial

Lecture

Benefits students

Easy teaching method

Students do not prefer lecture over other

methods

Labs

Helpful to student learning

Not easy to plan

Students benefit from hands-on

Best performed in pairs

Students enjoy

Demonstrations

Cost effective

Easy to set up and perform

Preferable during lessons

Effective teaching method

Students prefer labs over demonstrations

Bookwork

Good use of time

Students don’t resist bookwork

Effective

Seatwork

Effective

Helpful for reinforcement

Not meant to be busy work

Students don’t resist seatwork

Homework

Meant to be graded

Useful reinforcement tool

Not better than bookwork or seatwork

Standout Quotes “I present students with the questions I will ask in

advance and then spend class time listening to

their responses a[nd] correcting errors and honing

their answers to be sure they have understanding.”

“No one method fills a whole class period.”

“A good mix of several methods/styles in any given

class period will reach all types of learners. I believe

each method has an impact and is effective when

not overused.”

Standout Quotes Continued

“Students benefit only if they understand

what they are supposed to be learning in

lab.”

“ I think that demonstrations are

beneficial as a precursor to a hands-on

lab experience.”

Ideal Modes of Delivery

SmartBoard* with Smart Slates

Promethean Board

Laptops or iPads for each student

Document camera and Smart Pad

Edmodo (online community for teachers,

students, schools, and districts to

communicate)

Elmo

Modes Most Enjoyed by

Students

SmartBoard*

Promethean Board

Laptops or iPads

“All of them! Students love technology!”

Modes Most Beneficial for

Students

SmartBoard*

Promethean Board

“I think all modes have some benefit to

the students, depending on how they are

used.”

“All of them.”

Simplest Modes to

Learn/Manipulate

White board

Blackboard

Smart Board

Overhead

“THEY ARE ALL EASY!”

Struggles and Successes: What Beginning Mathematics and Science Teachers Should Know About the First Three Years

Aaron J. Sickel

Department of Teacher Education

Ohio University

Question

• Why do you / did you want to become a teacher?

• #1 Reason: Desire to work with young people and help them succeed

• Other Reasons

• Drawn to subject / grade level (enjoys math, high schoolers)

• Drawn to teaching-learning process (“light bulb” moment)

• Drawn to teaching lifestyle (e.g. conducive for family)

• (www.teachersnetwork.com; www.scholastic.com)

Question

• What are the goals of teacher preparation programs?

• Introduce preservice teachers to the teaching profession

• Prepare preservice teachers in both content and pedagogy

• Learn to teach in reform-based ways

Teach in Reform-Based Ways?

• What does “reform” mean in teacher education?

• Education is a constantly evolving field – we are constantly learning about how to facilitate meaningful learning for students

• Mathematics and Science Education Reforms

• Elicit students’ mathematical thinking; ideas about the natural world

• Manage and facilitate discourse in the classroom

• Support students’ abilities in doing the things that mathematicians and scientists do – problem-solving; engaging in scientific inquiry

(Bennett, 2010; Kelly, 2007; National Research Council, 1996; Sleep & Boerst, 2012)

Problem

• Good News

• Preservice teachers are excited to join the profession

• The teacher education community has developed research-based teaching strategies to teach mathematics and science in reform-based ways

• Problem?

• Beginning teachers are not likely to teach in reform-based ways

• Beginning teachers are likely to leave the profession within the first 3-5 years

Beginning Teachers’ Practices

• 1999 – Simmons et al. interviewed and observed 69 beginning teachers

• What percentage of beginning teachers consistently engaged in student-centered practices?

• 5-10%

Beginning Teacher Practices

(Luft et al., 2011)

Beginning Teacher Practices

(Ingersoll et al., 2012)

Why, Why, Why?

• Why do these difficulties persist?

Teachers Must Learn To:

• Interact with the next generation

Teachers Must Learn To:

• Develop classroom management strategies

Teachers Must Learn To:

• Teach students who lack motivation

Teachers Must Learn To:

• Give up some control of the learning process to students

Teachers Must Learn To:

• Work in professional learning teams

• Prepare students for state assessments

• Learn the scope and sequence of the curriculum

• Learn to assess students in equitable ways

• Learn to teach in culturally relevant ways

• Learn to incorporate technology in the classroom

• Develop practical knowledge and skills for teaching in reform-based ways

Why Teachers Leave…

• Lack of support mechanisms (Ingersoll et al., 2012)

• Administrative support

• Support in discipline (mathematics; science)

• Inability to reconcile images of ideal teaching with the realities of the classroom (Friedrichsen et al., 2007) • Classroom management

• Perceived students’ abilities

Stay or Leave?

Ideal Images of Teaching

Realities of Classroom

Teacher Preparation

1st Three Years

Stay in Profession

Leave Profession

Coping strategies – find support

No coping strategies – little support

Sources of Support

• Friedrichsen et al. (2007)

Internal (Local Teacher Preparation Program)

External (Outside Local Program)

People Assigned Mentor District PD Teacher Down the Hall University staff / faculty Feedback from students

Other Math/Science Teachers Family, Friends

Programs Local Induction Program Professional organizations Conferences Graduate programs

What is the Point?

• Important to find mentors! – Effect of Online Paired Mentoring

Pedagogical Content Knowledge

Content • Cells • Genetics • Evolution • Ecology

Pedagogy • Students’

difficulties • Teaching

Strategies

PCK • Students

misunderstand Punnett Squares – Teach rules of probability

Managing Tensions

• Classroom Management

• Being understanding vs. being consistent

• Curriculum

• Giving students ownership vs. covering the curriculum

• Student Frustration

• Letting students struggle vs. providing support

• Assessing

• Providing opportunities for formative vs. summative assessment

• Personal Life

• Committing yourself to teaching vs. spending time with family / friends

Conclusions

• Struggles

• Classroom management

• Adjusting to school culture

• Perceived student abilities

• Practical knowledge and resources

• Support

• Mentors – especially discipline-specific mentors

• Induction programs

• Finding strategies to balance tensions

• Seeking out opportunities to become a part of the larger math and science education community

S

Statistical Literacy in the

High School Mathematics

and Science Classroom Michael Smith, Ohio University

Kay Casto, Vinton County High School

Goals for the project

S Our goals are both to integrate mathematics and science

learning into one lesson

S To make mathematics more relevant to their own lives

S To cause the students to question findings and investigate

statistical conclusions, instead of accepting verbatim

S To allow the students to make informed decisions based on

data

Motivation for the lesson

S “Statistics are like diamonds. Like diamonds, statistics are

not found naturally without context; they are socially

constructed by people who make decisions about how they

will be cut” -Lawrence M. Lesser

The BooKS2 project

S Students collected data from the

Ohio River on key water quality

measurements

S The students then submitted their

findings to ORSANCO for

inclusion on the multi-state water

quality testing

S Next we learned how water

quality indices are calculated

Statistics are Everywhere

S Slugging percentage (baseball)

S Quarterback rating (football)

S GPA (school)

S Index of Social Progress (sociology)

Global Warming as Example

S This is from Forbes Magazine, in

which the author uses the

argument that global warming

has stopped to talk about people

“cherry-picking” data to fit their

agenda. The author used the

NOAA climate data to argue that

there is definite global warming

if you look at long term analysis.

Global Warming rebuttal

S On Fox News, they post an article saying that global

warming isn’t as strong a trend as previously reported

because the weather monitoring stations aren’t positioned so

that they avoid people.

S These two articles are looking at the same data and drawing

completely different conclusions. What’s a student

supposed to believe?

Our lesson

S Our lesson takes the raw data that students collected from

the river, and gives them the task of using both the

weighting factors given by ORSANCO as well as creating

weighting factors of their own to tell the exact opposite

story. They then were to find out who created the

ORSANCO factors, and whether or not the students felt

these people were credible.

Integrating math and science

S Our students collected the water quality markers on their

own.

S They measured the Ph, Phosphate Levels, Dissolved

Oxygen, Fecal coliform bacteria, Nitrate Levels, and

Turbidity of the water

S The students took this data and calculated the water quality

index

Weighted grades as an

introduction

S Before we introduced the water quality index, we wanted

the students to understand the idea of weighting

S To make the idea more relevant, the students first were given

their own list of grades

S They were then introduced to the idea of weights, and asked

to create a weighting system that would be the most useful

for their grades, as well as the worst possible weighting

system

Water quality index

Student participation

S The students both collected their own data and calculated

the water quality index

S They created the new indices as a class, as well as creating

their own

S There was rich discussion between students as well as whole

class discussion on the idea of credibility

Student comments

S It was interesting to see how we rely on others to interpret

our data

S It was great to see hands on applications of math

Did we meet our goals?

S Students saw the interplay between mathematics and

science, and actively participated in the discussion

S The relevance of the mathematics was noted in students

comments

S Discussion about credibility showed that the students were

now questioning instead of accepting

S The students did choose the ORSANCO model after more

information

Conclusions

S This project was useful for mathematics classes by allowing

the students to develop some actual relevance in their

mathematics class, as well as develop higher levels of

statistical literacy

S In a science classroom, this would also be useful for having

the students to create their own conjectures based on data

they have collected, as well as creating more informed

science consumers of information.

Citations

S http://www.foxnews.com/scitech/2012/07/30/weather-

station-temp-claims-are-overheated-report-claims/

S http://www.forbes.com/sites/petergleick/2012/02/05/glob

al-warming-has-stopped-how-to-fool-people-using-cherry-

picked-climate-data/2/

S Lesser, Lawrence M. “Sizing up class size: A deeper

classroom investigation of central tendency”, Mathematics

teacher Vol 103 No 5, December 2009

Thank You

S Mike Smith, Ohio University

ms114409@ohio.edu

S Kay Casto, Vinton County High School

kay.casto@vinton.k12.oh.us

S http://www.seocems.org/books2/lessons/lesson5.html

BY: Nick Conroy

“I remember how exciting it was when the teacher had “stuff” on the front desk: unfamiliar objects and other things out of place in the traditional classroom”

-Richard Black

Demonstrations don’t have to be in your face activities or even teacher centered.

Have things set out so they can spark discussion.

Toys are great because it is what students are most familiar with.

Research

Great for getting instructions.

Google is your Best friend:

See Resources Section for good Online Resources.

Great for putting a purpose to the Demonstration

Keep it Simple, Stupid!

Keep it simple sir

Keep it Stupidly Simple

Keep it Straightforward and Simple

The KISS principle states that most things work best if they are kept simple rather than made complex, therefore simplicity should be a key goal in designing a demonstration and unnecessary complexity should be avoided.

When there is more going on there is more room for error

Be Prepared and Practice

Have Fun!!

Water Rocket ◦ Air Pressure moves High to low

◦ Newton’s 3rd Law

Note: Title of projects are

Hyperlinks to Instructions

Ping Pong Cannon ◦ Air Pressure moves High to Low

◦ Air Resistance

Rueben's Tube : Another version Here ◦ Sound Wave Anatomy

Note: the Larger

Diameter of the

Pipe the easier

It is to see the

Waves.

http://littleshop.physics.colostate.edu/index.html

http://phun.physics.virginia.edu/demos/

http://www.mip.berkeley.edu/physics/physics.html

http://sprott.physics.wisc.edu/demobook/intro.htm

http://scienceclub.org/kidproj1.html

http://www.sciencetoymaker.org/

Physics Demonstrations: A sourcebook for teachers of physics ◦ By: Julien Clinton Sprott

http://www.artistsupplysource.com/home.php?cat=9010&path=alt

http://www.sciplus.com/index.cfm

My family ◦ Mom, Dad and My 3 Brothers

Sara Beyoglides

Cody Price

Dr. Lucas

Dr. Foley

FedEx

Algebra for All? The Common Core & Doctor Hacker

Jeff Taylor

Mathematics Education

Ohio University

www.wivalley.net

To our nation’s shame, one in four ninth graders fail to finish high school. In South Carolina, 34 percent fell away in 2008-9, according to national data released last year; for Nevada, it was 45 percent. Most of the educators I’ve talked with cite algebra as the major academic reason.

Another dropout statistic should cause equal chagrin. Of all who embark on higher education, only 58 percent end up with bachelor’s degrees. The main impediment to graduation: freshman math.

-Andrew Hacker (2012) “Is Algebra Necessary?”

Algebra in U.S. Schools

1742: at Yale, “Specious Arithmetic”

1840s: Required for college admission

1894: Committee of Ten “Algebra for All” (10% of 14-18 year olds in HS)

1910: 57% of HS students in Algebra, now “a major source of failure”

1950: Less than 25% of HS students take Algebra

2.5 Rationales for “Algebra for All”

Global competitiveness

Learning to Reason

Social Equity

Global competitiveness?

The “STEM elite”—BA+ in Math/Sci/Engineering —make up 5% of the U.S. workforce

The greatest projected growth in STEM is for those with HS diploma or Associate degree

Health care professionals and Management/finance careers have higher projected lifetime earnings

“virtualism”: a vision of the future in which we somehow take leave of material reality and glide about in a pure information economy.

-Matt Crawford, Shop Class as Soul Craft

Learning to Reason

The “Mental Muscle” theory of learning went out with faculty psychology around 1900.

Learning transfer is not straightforward or common.

Social Equity

Algebra as “Gatekeeper” of our economic system.

- Robert P. Moses, Radical Equations

“I believe that the absence of math literacy in urban and rural communities throughout this country is an issue as urgent as the lack of registered Black voters in Mississippi was in 1961.”

The great tragedy is we create this school structure, at least in the old days of tracking, where kids were either vocational education kids or college prep kids. The result is that vocational types view mathematics, say, with suspicion, and think that studying mathematics is, well, bullshit. And the college prep kids develop a terribly narrow sense of intelligence.

-Mike Rose, interview on The Mind at Work

Transcript studies indicate that 83 percent of students who take geometry in ninth grade, most of whom completed algebra in eighth grade, complete calculus or another advanced math course during high school. Research also suggests that students who take algebra earlier rather than later subsequently have higher math skills.

These findings, however, are clouded by selection effects.

-Loveless, T. (2008) The Misplaced Math Student

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260 265 270 275 280 285 290 295 300

Alg

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NAEP

NAEP

Linear (NAEP)

-Loveless, T. (2008) The Misplaced Math Student

-Loveless, T. (2008) The Misplaced Math Student

-National Center for Educational Statistics

(2010). Eighth-Grade Algebra: Findings

From the Eighth- Grade Round of the

Early Childhood Longitudinal Study,

Kindergarten Class of 1998–99 (ECLS-K).

-National Center for

Educational Statistics (2010).

Eighth-Grade Algebra:

Findings From the Eighth-

Grade Round of the Early

Childhood Longitudinal Study,

Kindergarten Class of 1998–99

(ECLS-K).

-National Center for Educational Statistics (2010). Eighth-Grade Algebra:

Findings From the Eighth- Grade Round of the Early Childhood

Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K).

Algebra enrollment is related to fifth grade mathematics ability Only 3/5 of the top 40% in Mathematics ability in fifth grade, are in Algebra in grade eight 19% of eighth grade algebra students were in the lowest 40% in fifth grade mathematics achievement Algebra enrollment is associated with slightly higher eighth grade mathematics scores Average mathematics score for students in high algebra enrollment schools was lower than scores for students in low enrollment schools, but there was no difference in scores for students who had been in the top 20% in fifth grade.

The TIMSS Data

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

s.d.=100

-Schmidt, W. H. (2009). Exploring the Relationship of Content Coverage

and Achievement: Unpacking the Meaning of Tracking in Eighth

Grade Mathematics.

More-qualified and prepared teachers were in fact more likely to enroll in content-focused workshops.

teachers [in the neediest schools] do not more often take mathematics professional development, do not select into the most mathematically intensive of these opportunities, and do not overpopulate the one opportunity found to be associated with 2006 scores: math methods coursework.

-Hill, H (2011) “The Nature and Effects of Middle

School Mathematics Teacher Learning

Experiences”

Professional Development programs remain brief, disconnected and incoherent

Individual and school level incentives for professional development remain perverse.

Mathematization

“Mathematics as a human activity”

Re-invention

vs “Didactic Inversion”

Quine insisted that elementary arithmetic, elementary logic, and elementary set theory get started by what he called “the regimentation of ordinary discourse, mathematization in situ.” To which we now add elementary algebra. Scientists, Quine said, put a straitjacket on language.

- Robert P. Moses, Radical Equations

Algebraic

Formula

Table Graph

Concrete or pictorial

representation

Verbal description

Multiple Representations

The goal is not the apex…

…but moving fluidly between all five vertices!

Carlos took a trip on I-70, at a constant 60 miles per hour. a. How far had he gone in 3.5 hours?

b. How long did it take him to go 440 miles?

Carlos took a trip on I-70 at a constant rate of speed. After some time, he noticed he had been speeding, so he reduced to a lower constant speed. When he arrived at his destination, he noticed that he had driven 510 miles in 8 hours. a. Sketch a time-distance graph showing one way this

might have occurred.

b. Suppose Carlos slowed down to the speed limit, 50 miles per hour. Give one possible speed he could have started at, and show how many miles he would have travelled at each speed.

The Professional Development Dilemma

15 to 20 sessions over a school year 20 teachers per course 150,000 HS math teachers + 28,000 Elem math teachers + 1,100,000 elem classroom teacher = 1,278,000 teachers Dividing by 20 gives 639,000 workshops Dividing by 1,200 colleges granting education BA/BE/BS gives a mean of 53 workshops per college Assume 1 fulltime professor can do 5 workshops a year…

Then every teachers college would need to commit 11 full time professors for a full year to meet the need!

With 1 full-time professor, a year each, it would take 11 years….

Summary

1. Here comes everybody!

2. Focus on students’ mathematizing skills

3. Focus on Algebraicizing tasks

4. Teaching growth comes from talking about teaching tasks, both the making and the enacting of them

In Tanzania, where I lived for a time in the 1970s, the Swahili word fundi refers to a concept of passing on knowledge through direct contact with people who are fundis—skilled craftsmen and instructors

- Robert P. Moses, Radical Equations