Transcript Developments in Developmental Mathematics

Developments in Developmental
Mathematics
Kirsty J. Eisenhart
Western Michigan University
Conversations Among Colleagues
Dearborn, MI
March 21, 2009
WMU’s Develpmental
Mathematics Program
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Math 1090: Basic Computational Skills
Prerequisite for Algebra I
MATH 1100: Algebra I
Prerequisite for either Algebra II or a
non-calculus gen ed
MATH 1110: Algebra II
Prerequisite for calculus or chemistry
Spring 2008 Curriculum
Committee Survey
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What are the most important mathematical skills,
concepts &/or techniques that your students need
in order to be successful in this course?
What errors &/or more general misconceptions do
your students have that make their success in your
course problematic? What do you do to remedy
this situation?
What connections do your students fail to make?
What Do Students’ Need
To Be Successful
 Number Sense
 Algebra Sense
 Reasoning Skills
 Making Connections
 Student Skills/Responsibilities
(shift from HS to College)
Class Work Skills
 Calculator Skills
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Reasoning Skills
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Mathematics as a logical process
Does my answer make sense?
Don’t consider reasonableness of solution (even
numeric ones)
Is this step mathematically legal? Is it helpful?
What is the big picture?
Step back and ask why am I doing this? Did I
answer the question?
There is more than one way to solve a problem
Making Connections
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Between mathematical ideas/strategies and
real-world applications
Between algebraic and graphical
representations
between hypotheses and conclusions
between different problems for which the
same strategy works
among strategies/techniques
Prealgbra
When the temperature increases from 2F to 6F,
we find the change in temperature by performing a
subtraction: 6 – 2 = 4. If the temperature increases
from -2F to 6F, we find the change in
temperature by eventually performing an addition:
6 – (-2) = 6 + 2 = 8. Use number lines (or
thermometers) to illustrate why it makes sense that
in the first situation we subtract and in the second
situation we eventually add. Be sure to explain
your illustrations.
Prealgbra
Kelly and her study group want to know if 527 is a prime or
composite number. She explained to her group that neither 2, 3, 4,
nor 5 were factors of 527 by using divisibility rules. She then
suggested that the group divide 6 into 527 and see if it is a factor or
if there is a remainder. Mary, a member of the group, claimed that
they did not have to check 6 since they all ready knew 3 was not a
factor, but Kelly disagreed. Kelly claimed that it was possible for 6
to be a factor of a number even if 3 was not a factor.
a. Is Kelly’s claim correct? Explain.
b. Google divisibility rules and write down the rules you
understand. Be sure to rewrite the rules in your own words and
provide examples to demonstrate how to use each of the rules.
Prealgebra
Completing the following will show that 2
is the only even prime number.
a. Explain why 2 is a prime number
b.Explain why any other even number cannot be
prime.
Algebra I
We have discussed in class that if you have multiple percent
discounts and/or percent increases then regardless of the
order you apply these increases and/or decreases you will
end up with the same result due to the commutative property
of multiplication. What if you have a $10 off coupon and a
20% off coupon that you were allowed to apply together?
Should you apply the coupons in a specific order to
maximize your savings or will you pay the same amount
regardless of the order you apply the coupons? Explain
your answer. Be sure your explanation has numerical
examples to clarify your thoughts.
Algebra I
Consider the equation
4x 
3
5
a. Solve this equation by dividing both sides by 4.
1
b. Solve this equation by multiplying both sides by 4 .
c. Which method did you prefer and why?
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Algebra I
Without solving the following equation, explain
3(2x  4)
why
 2 cannot have a solution.
(6x 12)
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Algebra I
In Activity 2.13 there is a typo on page 246. The typo
appears at 35F and 45 mph. What are possible values for
this chart entry? Explain your reasoning.
Productive Sources
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Observed student errors or inefficiencies
Common misconceptions
Connections between sections
Extend concepts
Compare different strategies
Thank you for coming.
Let’s keep the conversations flowing.
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