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Building Student Success: Engaging in STEM
Lesson Study at the Tertiary Level
Juliet Langman, Jorge Solís, Harry Millwater, John
Joseph, Lina Martin-Corredor, and Nguyen Dao
The University of Texas at San Antonio
Project Overview
5 year-study project funded by National Science
Foundation
Goal: To improve undergraduate student persistence
from lower-division to upper-division courses, a team of
UTSA faculty members from science, engineering, and
education and human development will implement six
strategies, building on the Language, Literacy and STEM
(LA-STEM) Framework.
https://www.utsa.edu/today/2018/09/story/STEMgrant.html
LA-STEM Framework
Lesson Study Approach
Faculty collaboratively plan, teach, &
observe target lessons, with the goal of
improving student learning (Wood &
Cajkler, 2017).
LA-STEM Framework
Rooted in belief that literacy skills support
success across all academic disciplines and
are a necessity for students learning STEM
concepts.
Academic Literacy
The language of schooling required to
develop and display expertise in particular
disciplines
UTSA Context – Hispanic Serving Institution
UTSA designated Hispanic-Serving Institution aiming to
become a Hispanic-Thriving Institution. Over 50% of
students Hispanic. Challenge: Passing rates STEM
students in gateway courses low overall with Hispanic
students lagging behind non-Hispanic peers.Engineering Science/Math
Hispanic & Low-income 56.9% 55.9%
Non-Hispanic 61.1% 61.9%
Difference -4.2% -6.0%
Aim of this paper
● Examine individual and institutional affordances and
constraints that affect the lesson study cycle
● Reflect on LA-STEM Framework
Research Questions
1) How are organizational routines for lesson study
accomplished in university STEM contexts?
2) To what extent can lesson study activity establish a
routine focus on academic literacy, pedagogical practice
and students learning?
3) How can we determine students’ perceptions of their
learning and connection to pedagogical activities in large
lecture contexts?
Students’ Self-identified Ethnicity. (n=499)
Language Background of Student. ( n=501)
(N=501) Language and Education Survey
33.9%
•I was born outside of the U.S.
•I attended one or more years of K-12 school outside of the U.S.
41% •I speak a language other than English
39.4%
•When I grew up, I spoke Spanish the home
•When I grew up, I spoke another language in the home
Data: Lesson Study
Data Source Year 1
Engineering Physics
Lesson study faculty and classes 2 1
Lesson Study cycles 2 2
Lesson Study Meetings 10
(roughly weekly)
4
(every 2-3 weeks)
Lesson Study Lesson 1 Translating word problems Interpreting visual
representations
Lesson Study Lesson 2 Unit step function Outlining steps in problem
solving: Elastic & inelastic
collisions
Faculty Reflections 4 4
LS Participants – Year 1
Engineering Physics
Students 199 94
Student Interviews 22 21
Student Group Activity
Samples
69
46
N/A
Comparison groups 2 /172 students 3 /286 students
Student Surveys Pre-survey
(n=501/749)
Post-survey
(n=387/749)
Initial Findings
Q1: How are organizational routines for LS
accomplished in university setting?
Multiple levels of organization require a high level of coordination
Faculty LS
EGR PHY
Engineering LS Physics LS
Team members of roughly equal status Team members of differential status (faculty
and TA)
Team members met regularly outside LS
planned meetings
Team members often missed regular meetings
Team members completed two full rounds of
LS and incorporated pedagogical practices in
additional activities
Team member completed 1 partial round of LS
with TA engaging in delivery of
Team members engaged in full –scale
redesign of syllabus and integration of lecture
with recitation.
Department leadership transition resulted in no
support for LS
College level engagement led to design of TA
training in LS and appointment of lead TA for
TA sections
Year 2 LS will continue with overlap of
participants and common
Year 2 LS to begin with no overlap of
participants.
Engineering trajectory
Constraints
● Shifting faculty
assignments
○ multiple
departments
● Late appointment of TA
● Sustaining attention
over time
Redesigned
Syllabus & tight
connection
between Lecture
and Recitation
Planned
semester long
TA training –
assignment of
lead TA
1 new faculty + 1
continuing faculty
participating in LS
Physics Trajectory
● Lessons learned
○ Work with at least two faculty
● New Beginnings
○ New Dean
○ New Department Chair
○ 2 new LS faculty participants
Initial Findings
Q2:To what extent can lesson study activity
establish a routine focus on academic
literacy, pedagogical practice and student
learning?
Academic Literacy
Lesson Planning and Linguistic Features
Linguistic features (N=27), including text structures
(N=15) and vocabulary (N=12) were most highly
emphasized in the lesson planning stage in
comparison to the other LS stages.
Academic
Literacy
Linguistic
Features
Visual
Representations
Derivations
Notations
Vocabulary
Example:
JL: Yeah. Would you like me to insert the word “differential” appear? Because.. at one level, this is true
for all equations.
HM: Yeah, what we're talking about doesn't have to be differential. It is because the word "rate" is in
there, but if maybe there's plenty of other ones that aren't… (2019SpringEGRMeeting01_24)
Plan a Lesson
Academic
Literacy
Linguistic
Features
Visual
Representations
Derivations
Notations
Vocabulary
Plan a Lesson
Academic Literacy shared focus
Equitable participation and knowledge production related to
academic literacy
❏ Lens on what counts as academic literacy varied by discipline, but
not the understanding of the importance of conceptual and
academic literacy connections.
Idea Initiator/Authoring Connect to New Practices
- Authoring
Academic
Literacy
EDU EGR EDU EGR
12 12 12 9
Total= 24 Total= 21
Academic Literacy and Framing the lesson
Example 1:
❏ EDU1: Yeah. So you might even have something like an intro slide for each lesson
that says, you know, “today we're covering differential equations”, you know, it's
connected to test one, learning goals, you know, yeah, one and two.
(2019SpringEGRMeeting01_17)
Example 2:
❏ EDU1: So one of the things that I was going to propose is, you know, coming up
with a time to sit down and sort of talk through not so much the content, but the
framing of the syllabus, in terms of readability. And- and, you know, based on my
experience, trying to read the syllabus as a person from outside
(2019SpringEGRMeeting05_09)
Academic Literacy
Planning Materials, Modeling and
Scaffolding Academic Literacy
occurred often (N=28) during the
stage of lesson planning.
Academic
Literacy
Teaching
Practices:
Related to
AL
Modeling &
ScaffoldingMaterials
Example:
JL: Exactly. You could even add a little bit more context. As an engineer, imagine
that you're working on a water level? Because this example is about I mean, I
don't know if water level is the right way to put it but..
JJ: Yeah, “physical reality of a water level” or something. Yeah, I can work on that.
I could change it to “fluid level” and make it more this kind of civil engineering
fluid, maybe more mechanical, broaden it up a little (but make it specific)
(2019SpringEGRMeeting01_17)
Academic Literacy – Outlining problems
Example 3:
❏ EGR1: Yeah, and the best way around is, well, it's kinda like the word problems. In the section
2.7 here, they're all just have time, so they don't even think about that ODE's. Some just put
the formula down, because they already know what it looks like, and they don't even write
down the ODE and go to solve it ,so for us, I think the way to emphasize that ODE writing, that
writing the ODE is important is to have problems where that's the only thing you do, these
problems, you just write the ODE.
EDU2: Yeah. (2019SpringEGRMeeting01_17)
Example 4:
❏ EGR1: I think you're right. But that's why I'm saying if we make and put in numbers for the argument, to make
it crystallized "Oh, it's minus two" then use =
❏ EGR2: = Yeah that's what I did on that worksheet, not just integers, but also like negative three powered by
two, 1.6 times and negative 14 all that (2019SpringEGRMeeting05_09).
Initial Findings
Q3: How can we determine students’
perceptions of their learning and connection
to pedagogical activities in large lecture
contexts?
Interview Data: Can you tell me what the key concept(s) in this class were?
Example:
“How the graph is affected by the function, how can you plot them.”
Course A Course B Both Courses
• Graphing unit step functions (N=3)
• Learning T-Shifts (N=2)
• Graphing
• Purpose of U function and how to
plot them
• Inverses
•Graphing unit step functions (N=3)
•Cosine functions
•T-transform
•Graphing (N=2)
• Graphing unit step
functions (N=6)
• T-
shifts/transformations
(N=2)
• Graphing (N=3)
Can you give an example of what the concept is good for?
Course A Course B Both Courses
•Businesses
•Income and outcome
•Performance rate for cars
•Changing differential
equations
•Electronics/Circuits
•Turning something on/off
•Circuits (N=2)
•Heating/cooling systems
•Fluid tanks
•I don't know
Circuits (N=3)
Examples:
“Get a ordinary differential equation into a form that is easier to manipulate”
“Usually when you have different variables, you try to accommodate into
one graph. It helps to show how affects it and so you can see how another
thing affects the system.”
“Useful in representing heating/cooling systems, fluid tanks and describing
the amount of power they take up and on/off switches”
Can you compare your level of understanding typically, with your level of
understanding during this lesson?
Course A Course B Both Courses
•Graph helps visualization
•Not typically go over every
question
•Better understanding during this
lesson (N=3)
•Same
•Better understanding during this
lesson (N=3)
•Changes in teaching style
•Graphs and examples were helpful
•Both are good
More understanding in the target
lesson (N=6)
Same/Both are good (N=2)
Changes in teaching style
Graphs/examples are helpful (N=2)
Not typically go over every question
“Typically a 6 (level of understanding) modified lesson plan was an 8.”
“I think at the end of the semester it was better because our professor was teaching more
calmly like step-by-step... he always tries to make us learn..”
“I think the group work is good. It's slower and it kinda simplified the problems. But sometimes
since you're like going at a slower pace you seem like you may not be able to learn as much.
It's hard to say. I think they're both useful. I think this is good coz you definitely do what you
learn coz you have to be engaged during the groupwork. You can't just like zone out or
whatever, sometimes it happens when you take notes.
Lesson Study : Emerging Theme 1: Syllabus and Learning Goals
Discussions initially began with the planning and teaching of the target
lessons with regard to a specific focus, i.e., “translating word problems into
equations” for Cycle I and “Unit Step function” for Cycle II,
At the end of Cycle II (6/19/2019) shifted back to the initial discussions at the
beginning of Cycle I (1/17/2019), which centered on the overall redesign of
materials
(I) the course syllabus
(II) the reorganization of the learning goals.
Those were later incorporated along with
(I) the birth of the recitation syllabus,
(II) the integration of TA training (with a new position of a TA coordinator)
starting from Fall 2019.
Examples
JJ: Yeah, there's a thing with listing learning goals, they’re kind of, it gets really
messy ... they come back and like, there's some overlap so you end up, then
the student sees more and more like, what they would call clutter. I don't
know. There's solving initial value problems were that’s covered earlier in the
course. But it's related, it contributes to this I don't know, I would have to think
about that one. (John Joseph, LS meeting on 1/17/2019)
VM: Well we basically just made it more visually appealing. Well, we've turned
it into kind of table format. We renamed the goals to be like test one goal one,
test one goal two.. I would have organized them chronologically just to show
which goals they should be learning first, and we added a “builds upon
column” that shows ‘Hey, you need to know this before you start working on
this other goal’.
(Victor Mendes, TA coordinator, LS meeting on 6/19/2019)
Example
HM: Changing the whole culture of the TAs could affect everyone
JL: So if we're going to do that, then we probably need a couple of pre
meetings to figure out you know, we can figure out the pedagogical stuff that
we need…. for this Engineering class, the thing where we're going to have, in a
sense, the biggest bang for the buck is if we do a really good job of thinking
through what happens in the recitation.
....
HM: You know, that's a great comment to me, because that would have a
large impact if, if we're able to re-constitute the recitation and what happens
in here and make it consistent.
(Harry Millwater and Juliet Langman, LS meeting on 5/9/2019)
Lesson Study Emerging Theme 2: Pedagogical Practice Internalization
The second finding suggests that although the potential challenges (i.e.,
translating word problems and unit step functions) may not be incorporated
into the next LS cycles (Cycle III and IV for the academic year 2019-2020),
- the Lesson Study process has enabled the STEM Faculty to get
accustomed to and internalize critical pedagogical practices, i.e., lesson
planning, connecting classroom activities with learning goals, using
academic literacy as a resource, incorporating group work to
facilitate problem solving and explaining
(e.g., Debates frequently occurred between STEM faculty members over
proper vocabulary choice and text structures when creating the materials
for the target lessons).
Example
JL: and so the words you’re pinpointing are ‘rate’, ‘proportional’
JJ & HM: proportional
HM: and ‘radius’
JL: ‘radius’ and ‘area’, so those are the only key words right?=
JJ: = but it's true that ‘rate of change’ and ‘proportional’ are almost universal?..
they are all-throughout all the translations you have a rate of change cuz you
want the differential equations, then the ‘rate of change’, then there's the
‘proportionality’..
(Juliet Langman, Harry Millwater, and John Joseph, LS meeting on 1/10/2019)
Questions
Thank you

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WALS 2019 presentation

  • 1. Building Student Success: Engaging in STEM Lesson Study at the Tertiary Level Juliet Langman, Jorge Solís, Harry Millwater, John Joseph, Lina Martin-Corredor, and Nguyen Dao The University of Texas at San Antonio
  • 2. Project Overview 5 year-study project funded by National Science Foundation Goal: To improve undergraduate student persistence from lower-division to upper-division courses, a team of UTSA faculty members from science, engineering, and education and human development will implement six strategies, building on the Language, Literacy and STEM (LA-STEM) Framework. https://www.utsa.edu/today/2018/09/story/STEMgrant.html
  • 3. LA-STEM Framework Lesson Study Approach Faculty collaboratively plan, teach, & observe target lessons, with the goal of improving student learning (Wood & Cajkler, 2017). LA-STEM Framework Rooted in belief that literacy skills support success across all academic disciplines and are a necessity for students learning STEM concepts. Academic Literacy The language of schooling required to develop and display expertise in particular disciplines
  • 4. UTSA Context – Hispanic Serving Institution UTSA designated Hispanic-Serving Institution aiming to become a Hispanic-Thriving Institution. Over 50% of students Hispanic. Challenge: Passing rates STEM students in gateway courses low overall with Hispanic students lagging behind non-Hispanic peers.Engineering Science/Math Hispanic & Low-income 56.9% 55.9% Non-Hispanic 61.1% 61.9% Difference -4.2% -6.0%
  • 5. Aim of this paper ● Examine individual and institutional affordances and constraints that affect the lesson study cycle ● Reflect on LA-STEM Framework
  • 6. Research Questions 1) How are organizational routines for lesson study accomplished in university STEM contexts? 2) To what extent can lesson study activity establish a routine focus on academic literacy, pedagogical practice and students learning? 3) How can we determine students’ perceptions of their learning and connection to pedagogical activities in large lecture contexts?
  • 8. Language Background of Student. ( n=501) (N=501) Language and Education Survey 33.9% •I was born outside of the U.S. •I attended one or more years of K-12 school outside of the U.S. 41% •I speak a language other than English 39.4% •When I grew up, I spoke Spanish the home •When I grew up, I spoke another language in the home
  • 9. Data: Lesson Study Data Source Year 1 Engineering Physics Lesson study faculty and classes 2 1 Lesson Study cycles 2 2 Lesson Study Meetings 10 (roughly weekly) 4 (every 2-3 weeks) Lesson Study Lesson 1 Translating word problems Interpreting visual representations Lesson Study Lesson 2 Unit step function Outlining steps in problem solving: Elastic & inelastic collisions Faculty Reflections 4 4
  • 10. LS Participants – Year 1 Engineering Physics Students 199 94 Student Interviews 22 21 Student Group Activity Samples 69 46 N/A Comparison groups 2 /172 students 3 /286 students Student Surveys Pre-survey (n=501/749) Post-survey (n=387/749)
  • 11. Initial Findings Q1: How are organizational routines for LS accomplished in university setting?
  • 12. Multiple levels of organization require a high level of coordination Faculty LS EGR PHY
  • 13. Engineering LS Physics LS Team members of roughly equal status Team members of differential status (faculty and TA) Team members met regularly outside LS planned meetings Team members often missed regular meetings Team members completed two full rounds of LS and incorporated pedagogical practices in additional activities Team member completed 1 partial round of LS with TA engaging in delivery of Team members engaged in full –scale redesign of syllabus and integration of lecture with recitation. Department leadership transition resulted in no support for LS College level engagement led to design of TA training in LS and appointment of lead TA for TA sections Year 2 LS will continue with overlap of participants and common Year 2 LS to begin with no overlap of participants.
  • 14. Engineering trajectory Constraints ● Shifting faculty assignments ○ multiple departments ● Late appointment of TA ● Sustaining attention over time Redesigned Syllabus & tight connection between Lecture and Recitation Planned semester long TA training – assignment of lead TA 1 new faculty + 1 continuing faculty participating in LS
  • 15. Physics Trajectory ● Lessons learned ○ Work with at least two faculty ● New Beginnings ○ New Dean ○ New Department Chair ○ 2 new LS faculty participants
  • 16. Initial Findings Q2:To what extent can lesson study activity establish a routine focus on academic literacy, pedagogical practice and student learning?
  • 17. Academic Literacy Lesson Planning and Linguistic Features Linguistic features (N=27), including text structures (N=15) and vocabulary (N=12) were most highly emphasized in the lesson planning stage in comparison to the other LS stages. Academic Literacy Linguistic Features Visual Representations Derivations Notations Vocabulary Example: JL: Yeah. Would you like me to insert the word “differential” appear? Because.. at one level, this is true for all equations. HM: Yeah, what we're talking about doesn't have to be differential. It is because the word "rate" is in there, but if maybe there's plenty of other ones that aren't… (2019SpringEGRMeeting01_24) Plan a Lesson
  • 19. Academic Literacy shared focus Equitable participation and knowledge production related to academic literacy ❏ Lens on what counts as academic literacy varied by discipline, but not the understanding of the importance of conceptual and academic literacy connections. Idea Initiator/Authoring Connect to New Practices - Authoring Academic Literacy EDU EGR EDU EGR 12 12 12 9 Total= 24 Total= 21
  • 20. Academic Literacy and Framing the lesson Example 1: ❏ EDU1: Yeah. So you might even have something like an intro slide for each lesson that says, you know, “today we're covering differential equations”, you know, it's connected to test one, learning goals, you know, yeah, one and two. (2019SpringEGRMeeting01_17) Example 2: ❏ EDU1: So one of the things that I was going to propose is, you know, coming up with a time to sit down and sort of talk through not so much the content, but the framing of the syllabus, in terms of readability. And- and, you know, based on my experience, trying to read the syllabus as a person from outside (2019SpringEGRMeeting05_09)
  • 21. Academic Literacy Planning Materials, Modeling and Scaffolding Academic Literacy occurred often (N=28) during the stage of lesson planning. Academic Literacy Teaching Practices: Related to AL Modeling & ScaffoldingMaterials Example: JL: Exactly. You could even add a little bit more context. As an engineer, imagine that you're working on a water level? Because this example is about I mean, I don't know if water level is the right way to put it but.. JJ: Yeah, “physical reality of a water level” or something. Yeah, I can work on that. I could change it to “fluid level” and make it more this kind of civil engineering fluid, maybe more mechanical, broaden it up a little (but make it specific) (2019SpringEGRMeeting01_17)
  • 22. Academic Literacy – Outlining problems Example 3: ❏ EGR1: Yeah, and the best way around is, well, it's kinda like the word problems. In the section 2.7 here, they're all just have time, so they don't even think about that ODE's. Some just put the formula down, because they already know what it looks like, and they don't even write down the ODE and go to solve it ,so for us, I think the way to emphasize that ODE writing, that writing the ODE is important is to have problems where that's the only thing you do, these problems, you just write the ODE. EDU2: Yeah. (2019SpringEGRMeeting01_17) Example 4: ❏ EGR1: I think you're right. But that's why I'm saying if we make and put in numbers for the argument, to make it crystallized "Oh, it's minus two" then use = ❏ EGR2: = Yeah that's what I did on that worksheet, not just integers, but also like negative three powered by two, 1.6 times and negative 14 all that (2019SpringEGRMeeting05_09).
  • 23. Initial Findings Q3: How can we determine students’ perceptions of their learning and connection to pedagogical activities in large lecture contexts?
  • 24. Interview Data: Can you tell me what the key concept(s) in this class were? Example: “How the graph is affected by the function, how can you plot them.” Course A Course B Both Courses • Graphing unit step functions (N=3) • Learning T-Shifts (N=2) • Graphing • Purpose of U function and how to plot them • Inverses •Graphing unit step functions (N=3) •Cosine functions •T-transform •Graphing (N=2) • Graphing unit step functions (N=6) • T- shifts/transformations (N=2) • Graphing (N=3)
  • 25. Can you give an example of what the concept is good for? Course A Course B Both Courses •Businesses •Income and outcome •Performance rate for cars •Changing differential equations •Electronics/Circuits •Turning something on/off •Circuits (N=2) •Heating/cooling systems •Fluid tanks •I don't know Circuits (N=3) Examples: “Get a ordinary differential equation into a form that is easier to manipulate” “Usually when you have different variables, you try to accommodate into one graph. It helps to show how affects it and so you can see how another thing affects the system.” “Useful in representing heating/cooling systems, fluid tanks and describing the amount of power they take up and on/off switches”
  • 26. Can you compare your level of understanding typically, with your level of understanding during this lesson? Course A Course B Both Courses •Graph helps visualization •Not typically go over every question •Better understanding during this lesson (N=3) •Same •Better understanding during this lesson (N=3) •Changes in teaching style •Graphs and examples were helpful •Both are good More understanding in the target lesson (N=6) Same/Both are good (N=2) Changes in teaching style Graphs/examples are helpful (N=2) Not typically go over every question “Typically a 6 (level of understanding) modified lesson plan was an 8.” “I think at the end of the semester it was better because our professor was teaching more calmly like step-by-step... he always tries to make us learn..” “I think the group work is good. It's slower and it kinda simplified the problems. But sometimes since you're like going at a slower pace you seem like you may not be able to learn as much. It's hard to say. I think they're both useful. I think this is good coz you definitely do what you learn coz you have to be engaged during the groupwork. You can't just like zone out or whatever, sometimes it happens when you take notes.
  • 27. Lesson Study : Emerging Theme 1: Syllabus and Learning Goals Discussions initially began with the planning and teaching of the target lessons with regard to a specific focus, i.e., “translating word problems into equations” for Cycle I and “Unit Step function” for Cycle II, At the end of Cycle II (6/19/2019) shifted back to the initial discussions at the beginning of Cycle I (1/17/2019), which centered on the overall redesign of materials (I) the course syllabus (II) the reorganization of the learning goals. Those were later incorporated along with (I) the birth of the recitation syllabus, (II) the integration of TA training (with a new position of a TA coordinator) starting from Fall 2019.
  • 28. Examples JJ: Yeah, there's a thing with listing learning goals, they’re kind of, it gets really messy ... they come back and like, there's some overlap so you end up, then the student sees more and more like, what they would call clutter. I don't know. There's solving initial value problems were that’s covered earlier in the course. But it's related, it contributes to this I don't know, I would have to think about that one. (John Joseph, LS meeting on 1/17/2019) VM: Well we basically just made it more visually appealing. Well, we've turned it into kind of table format. We renamed the goals to be like test one goal one, test one goal two.. I would have organized them chronologically just to show which goals they should be learning first, and we added a “builds upon column” that shows ‘Hey, you need to know this before you start working on this other goal’. (Victor Mendes, TA coordinator, LS meeting on 6/19/2019)
  • 29. Example HM: Changing the whole culture of the TAs could affect everyone JL: So if we're going to do that, then we probably need a couple of pre meetings to figure out you know, we can figure out the pedagogical stuff that we need…. for this Engineering class, the thing where we're going to have, in a sense, the biggest bang for the buck is if we do a really good job of thinking through what happens in the recitation. .... HM: You know, that's a great comment to me, because that would have a large impact if, if we're able to re-constitute the recitation and what happens in here and make it consistent. (Harry Millwater and Juliet Langman, LS meeting on 5/9/2019)
  • 30. Lesson Study Emerging Theme 2: Pedagogical Practice Internalization The second finding suggests that although the potential challenges (i.e., translating word problems and unit step functions) may not be incorporated into the next LS cycles (Cycle III and IV for the academic year 2019-2020), - the Lesson Study process has enabled the STEM Faculty to get accustomed to and internalize critical pedagogical practices, i.e., lesson planning, connecting classroom activities with learning goals, using academic literacy as a resource, incorporating group work to facilitate problem solving and explaining (e.g., Debates frequently occurred between STEM faculty members over proper vocabulary choice and text structures when creating the materials for the target lessons).
  • 31. Example JL: and so the words you’re pinpointing are ‘rate’, ‘proportional’ JJ & HM: proportional HM: and ‘radius’ JL: ‘radius’ and ‘area’, so those are the only key words right?= JJ: = but it's true that ‘rate of change’ and ‘proportional’ are almost universal?.. they are all-throughout all the translations you have a rate of change cuz you want the differential equations, then the ‘rate of change’, then there's the ‘proportionality’.. (Juliet Langman, Harry Millwater, and John Joseph, LS meeting on 1/10/2019)