The problem
My students don't yet understand <y>, deeply, because they don't <do x> first.
-Anonymous Faculty
My students don't yet deeply understand what a solution is because don't verify their answers to see if they are solutions.
– Anurag
Head
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Tail
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Reorder content and Delivery
Productively Probing Products
Anurag Katyal
Professor I, Mathematics
Palm Beach State College, FL
Heat
Oxygen
Team Based Inquiry Learning
A (Potential) Solution
The Serendipitous Fire Triangle of Math™
(circa Summer 2023)
Active Learning Studios
Doenet
Fuel
Question 1
What number would you add to 1 to get 4?
Question 2
What number would you add to 1 to not get 4?
Question 3
How do you know the first number is 3?
Question 4
How do you know the second number is 4?
x+1=4\\3+1=4\\4=4~~(\checkmark)
x+1=4\\4+1=4\\5=4~~(\chi)
Week 1, Day 2
Look here!
Week 15, Day 1
1
Students don't check to see if their answers are solutions.
2
Students don't deeply understand what a solution is.
3
Students favor memorizing different algorithms for seemingly different types of problems.
5
Bad things happen on quizzes.
4
Students miss the modularity of the solution pathways.
6
Very bad things happen on tests/in following courses.
The Problem(s)
Team BAsed Inquiry Learning
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Permanent teams selected by the instructor
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Students held accountable through Readiness Assurance Process
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Students receive frequent and immediate feedback
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Teams work collaboratively on activities.
TBIL=TBL+IBL
Students Collaborate
(while i listen)
Hands must remain in pockets (As much as possible)
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Free and open-source interactive activities
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Immediate feedback in class
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Open-ended response
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Try different approaches
Collaborative Research: Empowering faculty to run online learning experiments
- (Tail)Verify solutions
- (Body and Tail) Solve equations and verify solutions
- (Head, Body and Tail) Translate English to Math, solve equations, and verify solutions
Experimental
- (Head) Translate English to Math
- (Body) Solve equations
- (Tail) Verify Solutions
- (The Problem) At the start of the course, all answers are solutions.
Standard
Head
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Reorder content and Delivery
'What is a Solution?' Activity
The 'product'
- Fall 2023 and Spring 2024 - 8 Intermediate Algebra sections (76 and 80 students)
- Week 1 - "What do you think it means for a number to be a solution to an equation?"
- 11% of students answered correctly.
- Week 15 - Solve \(\color{blue}\sqrt{2 x+2}=3+\sqrt{2 x-1}\) for \(x\).
- 66% of students answered correctly (they also checked to see if their answers were solutions).
- Historically, a maximum of 25% in semesters with at least 65 students and an average of ~19%.
- Overall passing rates went up by 20%.
〞
I personally liked Doenet activities because it helped me get hands on learning as a group. The way the course was set up allowed me to open up in ways I haven’t before and also hear my peers talk. It also broke down steps that helped answer complex questions later in the semester.
– Intermediate Algebra student
〞
I hate this man so much. He could have just taught the normal way.
– Intermediate and College Algebra student
I'll see him in College Algebra.
He tricked me into liking math.
An Example from Chemistry
A chemical reaction is said to be balanced when the total number of atoms present in the reactant and the product side are equal.
Balance the following chemical equation:
\mathrm{NaOH}+\mathrm{H}_2 \mathrm{SO}_4 \rightarrow \mathrm{Na}_2 \mathrm{SO}_4+\mathrm{H}_2 \mathrm{O}
- Why aren't all letters capitalized? Let's Balance An Equation (BAE).
- What's an atom? What's a molecule? What's a compound? Let's BAE.
- What's an acid? What's a base? Let's BAE.
- What are the different states of matter? Let's BAE.
- What is a reactant? What is a product? Let's BAE.
- How do they interact to initiate a chemical reaction? Let's BAE.
The procedural skill of balancing a chemical equation was used to motivate the entire Chemistry 101 course.
Head
Head
Body
Tail
Body
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Tail
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Reorder content and Delivery
What can you DO
to reorder content and delivery in your domain to stop saying, "My students don't yet deeply understand <y> because they don't <do x> first" ?
So students
stop saying, "My professor doesn't yet deeply understand why I struggle because they don't listen to Taylor Swift, first" ?
Acknowledgements
- Doenet (NSF Award # 1915363)
- PI - Duane Nykamp, Uni. of Minnesota
- Doenet Learning Experiment Mini-Grant
- www.doenet.org
- Team Based Inquiry Learning (NSF Award # 2011807)
- PI - Steven Clontz, Uni. of South Alabama
- www.tbil.org
Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
Sabbatical from Aug 2024 to May 2025.
Please reach out if you have ideas or suggestions!
\pi \cdot \pi
IFALC Talk
By Anurag Katyal
