1 las teaching academy problems (and solutions) with problem solving don decoste...
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LAS Teaching Academy
Problems (and Solutions) with Problem Solving
Don DeCoste ([email protected])University of Illinois at Urbana-ChampaignGeneral ChemistryMarch 6, 2015
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Same words, different meaning
“…novel approaches to problem-solving…”
“..approaches to solving novel problems…”
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What Students Have Taught Me
Students define “understand” and “problem-solving” differently from the way I do.
Students have different ideas about the roles of teacher and learner than I do.
I need to be as explicit with students about definitions and concepts of teaching and learning as I am with those of chemistry.
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The least significant numerical predictor of success in UIUC chemistry is the
a) number of years of high school chemistry.
b) score on the national American Chemical Society standardized chemistry exam.
c) score on the University of Illinois Chemistry Placement Exam.
d) score on the Math ACT.
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The most significant numerical predictor of success in UIUC chemistry is the
a) number of years of high school chemistry.
b) score on the national American Chemical Society standardized chemistry exam.
c) score on the University of Illinois Chemistry Placement Exam.
d) score on the Math ACT.
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UIUC Chemistry majors rank in the _______ percentile on the math ACT.
a) 70th
b) 80th
c) 90th
d) 95th
e) 98th
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Teaching Chemistry Must Be Easy!
Chemistry 202 Students (Accelerated Chem I)Average Math ACT
33.04 (98th percentile)
Average composite ACT30.74 (97th percentile)
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How Do They Solve Problems?
Consider two samples of pure water at different temperatures. Answer the following.
The pH values of the two samples of water are (the same/different).
Is one of the samples more acidic than another? (yes or no)
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Four Possible Answers
The pH values are different.
The pH values are the same.
One sample is more acidic than the other.
The samples are both neutral.
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Incoming Chemistry Graduate Students
The pH values are different.
(36%)
The pH values are the same.
(64%)
One sample is more acidic than the other. (31%)
25% 6%
The samples are both neutral.
(69%)11% 58%
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Incoming Chemistry Graduate Students
The pH values are different.
(36%)
The pH values are the same.
(64%)
One sample is more acidic than the other. (31%)
25% 6%
The samples are both neutral.
(69%) 11% 58%
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What Do We Do Now?
• What did the students do “right”?
• What did the students do “wrong”?
• What could we do to help?
What information do we have about our students?
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Student Quotes While Discussing...
• We're just remembering it being more acidic but it really has something else in it, I really do remember it being, I was like whoa, how could water not be water, you know, seven?
• That totally contradicts stuff.
• We should have a certain amount of questions we have to answer.
What information do we have about our students?
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Who Are These People?
“I like just plugging the formulas in the equations.”
“Understanding a problem conceptually is alright, but I just want to solve the problems.”
“I like those problems where we just have to plug in numbers.”
“I can solve problems once they are set up.”
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Where Did They Come From?
Student 1: “It would be a lot easier if the questions were set up for us.”
Student 2: “That's what we've been taught our whole lives.”
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Where Did They Come From?
“Chemistry in high school was all plug and chug.”
“We didn't have to understand everything. We just had to do the problems.”
“Chemistry in high school was all math, hardly any concepts. This is a huge change for me.”
“Like people would ask him 'How do you do this question?' He'd do it on the board, we'd copy it down.”
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WHAT DO WE DO NOW?
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What Students Have Taught Me
Students define “understand” and “problem-solving” differently from the way I do.
Students have different ideas about the roles of teacher and learner than I do.
I need to be as explicit with students about definitions and concepts of teaching and learning as I am with those of chemistry.
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Be Explicit about Chemistry!
Chemistry should make sense (for the most part) and it should be consistent.
Models are not the same as reality but they are still very useful.
There is a difference between “law” and “theory”. Both are important.
Chemistry is difficult.
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Be Explicit About Teaching and Learning!
I cannot learn for the student.
Knowing and understanding are both important, but we can “know” something without “understanding” it.
To evaluate our ideas it is good to verbalize them.
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Be Explicit About Teaching and Learning!
We usually try to avoid pain. Growth is painful. We learn a lot from our mistakes. Don’t be
afraid to make them.
It takes time to solve complex problems. It takes time to confront misconceptions and
overcome confusion. Don’t neglect to start a problem because you
don’t see the entire solution at once.
So What Can We Do?
Getting the students involved during class time is good, but at least provide a “big picture”.
Take time to think through a problem. Provide a window into how you solve
problems. Show the inherent messiness involved.
Explicitly teach students to be aware of their habits and their thinking.
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Types of Questions Matter!
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2
3
1+ = ?
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Types of Questions Matter!
Explicitly ask:
Why must we have a common denominator when adding fractions?
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Types of Questions Matter!
Even deeper:
Why don’t we use common denominators in baseball?
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Types of Questions Matter!
4
2
3
1+ = ?
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Types of Questions Matter!
4
2
3
1
7
3+ =
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Discussion Questions
Students work together during class.
The problems should require the students to explain or justify their answer.
The problems should not be solved with an easily applied algorithm.
Students need to be able to make mistakes and reach a workable level of frustration.
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“Typical” Chemistry Question
Calculate the number of atoms in a 50.0 g sample of aluminum.
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A Discussion Question
Estimate the number of atoms in an average human.
Support your answer.
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What If…?
Students must think of the significance of rules, laws, or definitions.
Sometimes “change the rules” to make the questions more engaging.
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What If…?
What if… the first law of thermodynamics was true, but the second law was not?
What if … all atoms had the same electronegativity values?
What if … all gases always behaved perfectly ideally?
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Problem Solving Approach What are we trying to solve? That is, “where are
we going?” Define terms carefully.
What do we know? That is, “where have we been?” If appropriate, draw a picture of the situation.
What procedures do we know? That is, “how do we get there?” Is it OK to ass-u-me?
Requires knowledge and understanding!
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But wait…
Irony of a “critical thinking algorithm”? Not so regimented, but a guideline.
Shouldn’t the students know this already? That is, isn’t this obvious? We also thought if students could solve a
math-based chemistry problem they understood the concepts.
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Some Closing Thoughts
Be explicit with your goals and expectations for the students.
Be explicit with your definitions of teaching and learning.
Be explicit with how to think about the problems.
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LAS Teaching Academy
Problems (and Solutions) with Problem Solving
Don DeCoste ([email protected])University of Illinois at Urbana-ChampaignGeneral ChemistryMarch 6, 2015