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Science and Mathematics for a New Generation
NWO Symposium
Daniel J. BrahierBowling Green State University
St. Rose School, PerrysburgSaturday, November 21, 2015
8:30 – 9:45 a.m., 101 Olscamp Hall, BGSU
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Boston Globe Article
Did you see this Opinion piece in the Boston Globe from February 12, 2015?
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Best Jobs (CareerCast, 2014)
1. Mathematician
2. Tenured University Professor
3. Statistician
4. Actuary
5. Audiologist
6. Dental Hygenist
7. Software Engineer
8. Computer Systems Analyst
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Best Jobs (CareerCast, 2014)
1. Mathematician
2. Tenured University Professor
3. Statistician
4. Actuary
5. Audiologist
6. Dental Hygenist
7. Software Engineer
8. Computer Systems Analyst
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7
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Some History
1989 – NCTM Curriculum Standards
1991 – Ohio Model (8 Strands)
2000 – NCTM Principles and Standards
2002 – Ohio Academic Content Standards
2010 – Common Core State Standards
2011 – Ohio Model Curriculum
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Principles to Actions:Ensuring Mathematical Success for All
9
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Principles to Actions: Ensuring Mathematical Success for All
Now, twenty-five years later, the widespread adoption of college- and career-readiness standards, including adoption in the United States of the Common Core State Standards for Mathematics (CCSSM) by forty-five of the fifty states, provides an opportunity to reenergize and focus our commitment to significant improvement in mathematics education.
10
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The “End Product”?
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Batting Averages
Batting Average = ratio of “hits” to “times at bat” (e.g., 3 hits for 10 at bats is a 0.300 Average)
0.132
Hits a Single!
0.154
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How many hits does the player have, and how many times has he been “at bat” so far this season?
Can you think of at least two different ways to come up with a solution?
0.132 0.154
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Simultaneous Equations
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Graph/Table
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Premise/Assumption
Technology is an inescapable fact of life in the world in which we live and should be embraced as a powerful tool for doing mathematics. Use of technology can assist students in visualizing and understanding important mathematical concepts and support students’ mathematical reasoning and problem solving.
-Principles to Actions, page 83
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Methods Student - Technology
“Since the students were unable to download the Puffin Application to their iPads, the technology specialist gave the class a laptop cart to use. This is where we hit another problem. The laptops they used had to be logged into with a password. Luckily, one of the students discovered that the password was “pchs”. Once logged on, it was discovered that the students did not have internet access. As a class, we went through some different strategies and successfully got the internet to work. After that, students went to an internet browser where it said that the latest Adobe Flash Player had to be installed. So, each student downloaded the latest version and then proceeded to the website that had the virtual manipulatives. When we finally got to the website, the lesson officially began.”
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Investigation
Let’s examine some data to see if we can predict when Old Faithful Geyser will erupt.
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Data Table
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Process
• Each table randomly chooses 2 days.
• Each person asks, “What do I notice? What do I wonder about?”
• Each person creates some kind of display of the data by hand.
• Team compares displays, chooses favorite, and predicts wait time.
• Each team presents solution.
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Graphs – Day 1
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Problem
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Samantha
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Samantha
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Samantha
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Samantha
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Eric
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Discussion Questions
• Would you want Samantha or Eric to present her/his solution first to the class? Why?
• Is it necessary or even important for both of them to present their solutions?
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Common Ground in Mathematics and Science
• Mathematical/Scientific Practices
• Modeling
• Use of Variables (Algebra)
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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.
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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Practices for Science and Engineering
1. Asking questions and defining problems
2. Developing and using models
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations and designing solutions
7. Engage in argument from evidence
8. Obtaining, evaluation, and communicating information
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Practices for Science and Engineering
1. Asking questions and defining problems
2. Developing and using models
3. Planning and carrying out investigations
4. Analyzing and interpreting data
5. Using mathematics and computational thinking
6. Constructing explanations and designing solutions
7. Engage in argument from evidence
8. Obtaining, evaluation, and communicating information
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Action Research
Two high school teachers asked Precalculus students to complete the phrase,
“I like math most when …”
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I can
lear
n it
mys
elf
I am
giv
en st
eps to
follo
w
I can
hav
e m
any
prac
tice
prob
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I can
pur
sue
my
own
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tions
I can
colla
bora
te w
ith m
y pe
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I can
use
pro
blem
sol
ving
I can
mem
orize
how
to d
o it
Other
0
5
10
15
20
25
30
35
10
32
19
3
14
10
14
4
I like math best when...
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Discussion
How do you explain the results of this survey?
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Modeling
1. Identifying the key variables in the problem
2. Creating models (algebraic, geometric, etc.) using the variables
3. Analyzing the relationships and performing operations to draw conclusions
4. Interpreting the results
5. Validating the conclusions, with the possibility of modifying the model
Common Core State Standards for Mathematics, 2010
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Uses of Variables
#1• Represent a number in a generalized
pattern
• Example: a + b = b + a
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Uses of Variables
#2• Represent a fixed but unknown number
• Example: The letter “x” in the equation 2x – 3 = 7
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Uses of Variables
#3• Represent a quantity that varies, especially
in relation to another quantity
• Example: The letters “x” and “y” in 3y = x
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Uses of Variables
#4• Represent a parameter (i.e., a quantity
whose value determines the characteristics of another variable)
• Example: The letter “m” in y = mx or in E = mc2
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Application of Formulas
Consider F = ma
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Uses of Variables
#5• Represent an arbitrary or abstract place
holder in an algebraic process
• Example: The letter “t” in the statement, “Factor the trinomial: t2 + 3t - 10
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Myth About “Being Bad” at Math
Consider this article published in September 2015
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Mindset – Dr. Carol Dweck
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Thought
Advice to teachers:
Avoid saying, “You’re so smart” and, instead, acknowledge the work they did to accomplish something (e.g., “I can only imagine how long you spent studying for this test”).
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A “Gift”?
“It’s hard to watch, and it’s even harder to not jump in when we see our kids frustrated or upset … [but] learning that comes with challenge is stored more effectively and more durably in the brain than learning that comes easily … errors are an integral part of learning” (2015, pp. 39-41)
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Lessons Learned in Singapore
• “Just because our students were #1 in the world last year doesn’t mean they will be next year.”
• “If our students aren’t scoring 100%, then we can do better – we can always improve.”
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Final Thought
Instead of saying “I can’t do this because” …
say
“I can do this until” …
Steve Meiring, Retired, Ohio Department of Education
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Joel Barker, Futurist
“Those who say it cannot be done should get out of the way of the people who are already doing it!”
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Science and Mathematics for a New Generation
NWO Symposium
Daniel J. BrahierBowling Green State University
St. Rose School, PerrysburgSaturday, November 21, 2015
8:30 – 9:45 a.m., 101 Olscamp Hall, BGSU