Developments in Developmental Mathematics Kirsty J. Eisenhart Western Michigan University Conversations Among Colleagues Dearborn, MI March 21, 2009

WMU’s Develpmental Mathematics Program 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 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

Reasoning Skills 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 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) = = 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 a. Solve this equation by dividing both sides by 4. b. Solve this equation by multiplying both sides by. c. Which method did you prefer and why?

Algebra I Without solving the following equation, explain why cannot have a solution.

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 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.